diff -Nru gsl-doc-1.16/aclocal.m4 gsl-doc-2.3/aclocal.m4
--- gsl-doc-1.16/aclocal.m4	2013-07-19 15:14:50.000000000 +0000
+++ gsl-doc-2.3/aclocal.m4	2016-12-09 00:04:18.000000000 +0000
@@ -1,4 +1,4 @@
-# generated automatically by aclocal 1.13.2 -*- Autoconf -*-
+# generated automatically by aclocal 1.13.4 -*- Autoconf -*-
 
 # Copyright (C) 1996-2013 Free Software Foundation, Inc.
 
@@ -2683,10 +2683,14 @@
   # before this can be enabled.
   hardcode_into_libs=yes
 
+  # Add ABI-specific directories to the system library path.
+  sys_lib_dlsearch_path_spec="/lib64 /usr/lib64 /lib /usr/lib"
+
   # Append ld.so.conf contents to the search path
   if test -f /etc/ld.so.conf; then
     lt_ld_extra=`awk '/^include / { system(sprintf("cd /etc; cat %s 2>/dev/null", \[$]2)); skip = 1; } { if (!skip) print \[$]0; skip = 0; }' < /etc/ld.so.conf | $SED -e 's/#.*//;/^[	 ]*hwcap[	 ]/d;s/[:,	]/ /g;s/=[^=]*$//;s/=[^= ]* / /g;s/"//g;/^$/d' | tr '\n' ' '`
-    sys_lib_dlsearch_path_spec="/lib /usr/lib $lt_ld_extra"
+    sys_lib_dlsearch_path_spec="$sys_lib_dlsearch_path_spec $lt_ld_extra"
+
   fi
 
   # We used to test for /lib/ld.so.1 and disable shared libraries on
@@ -8622,7 +8626,7 @@
 [am__api_version='1.13'
 dnl Some users find AM_AUTOMAKE_VERSION and mistake it for a way to
 dnl require some minimum version.  Point them to the right macro.
-m4_if([$1], [1.13.2], [],
+m4_if([$1], [1.13.4], [],
       [AC_FATAL([Do not call $0, use AM_INIT_AUTOMAKE([$1]).])])dnl
 ])
 
@@ -8638,7 +8642,7 @@
 # Call AM_AUTOMAKE_VERSION and AM_AUTOMAKE_VERSION so they can be traced.
 # This function is AC_REQUIREd by AM_INIT_AUTOMAKE.
 AC_DEFUN([AM_SET_CURRENT_AUTOMAKE_VERSION],
-[AM_AUTOMAKE_VERSION([1.13.2])dnl
+[AM_AUTOMAKE_VERSION([1.13.4])dnl
 m4_ifndef([AC_AUTOCONF_VERSION],
   [m4_copy([m4_PACKAGE_VERSION], [AC_AUTOCONF_VERSION])])dnl
 _AM_AUTOCONF_VERSION(m4_defn([AC_AUTOCONF_VERSION]))])
diff -Nru gsl-doc-1.16/AUTHORS gsl-doc-2.3/AUTHORS
--- gsl-doc-1.16/AUTHORS	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/AUTHORS	2015-11-09 06:17:18.000000000 +0000
@@ -25,7 +25,8 @@
 Ivo Alxneit (ivo.alxneit@psi.ch) - multidimensional minimization, wavelet 
   transforms
 Jason H. Stover (jason@sakla.net) - cumulative distribution functions
-Patrick Alken <patrick.alken@colorado.edu> - nonsymmetric and generalized eigensystems, B-splines
+Patrick Alken <patrick.alken@colorado.edu> - nonsymmetric and generalized
+  eigensystems, B-splines, sparse matrices, linear and nonlinear least squares
 Rhys Ulerich (rhys.ulerich@gmail.com) - multisets
 Pavel Holoborodko <pavel@holoborodko.com> - fixed order Gauss-Legendre quadrature
 Pedro Gonnet <gonnet@maths.ox.ac.uk> - CQUAD integration routines.
diff -Nru gsl-doc-1.16/autogen.sh gsl-doc-2.3/autogen.sh
--- gsl-doc-1.16/autogen.sh	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/autogen.sh	2015-11-03 16:21:55.000000000 +0000
@@ -1,15 +1,11 @@
 #! /bin/sh
 
-echo "If you use a recent version of autotools, this script is obsolete"
-echo "Just run autoreconf -i -f -v"
-echo "followed by ./configure --enable-maintainer-mode"
-echo 
-
 # Run this to generate all the auto-generated files needed by the GNU
 # configure program
-libtoolize --automake
-aclocal
-autoheader
-automake --add-missing --gnu --force-missing
-autoconf
+#libtoolize --automake
+#aclocal
+#autoheader
+#automake --add-missing --gnu --force-missing
+#autoconf
+autoreconf -i -f -v
 echo "Now use ./configure --enable-maintainer-mode"
diff -Nru gsl-doc-1.16/blas/Makefile.am gsl-doc-2.3/blas/Makefile.am
--- gsl-doc-1.16/blas/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/blas/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_blas.h gsl_blas_types.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslblas_la_SOURCES = blas.c 
 
diff -Nru gsl-doc-1.16/blas/Makefile.in gsl-doc-2.3/blas/Makefile.in
--- gsl-doc-1.16/blas/Makefile.in	2013-07-19 15:14:52.000000000 +0000
+++ gsl-doc-2.3/blas/Makefile.in	2016-12-09 00:04:20.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -193,6 +193,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -215,7 +216,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -331,7 +335,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslblas.la
 pkginclude_HEADERS = gsl_blas.h gsl_blas_types.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslblas_la_SOURCES = blas.c 
 all: all-am
 
diff -Nru gsl-doc-1.16/block/fprintf_source.c gsl-doc-2.3/block/fprintf_source.c
--- gsl-doc-1.16/block/fprintf_source.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/block/fprintf_source.c	2015-11-03 16:21:55.000000000 +0000
@@ -161,7 +161,9 @@
           data [MULTIPLICITY * i * stride + k] = tmp;
 
           if (status != 1)
-            GSL_ERROR ("fscanf failed", GSL_EFAILED);
+            {
+              GSL_ERROR ("fscanf failed", GSL_EFAILED);
+            }
         }
     }
 
diff -Nru gsl-doc-1.16/block/init.c gsl-doc-2.3/block/init.c
--- gsl-doc-1.16/block/init.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/block/init.c	2015-11-03 16:21:55.000000000 +0000
@@ -1,5 +1,6 @@
 #include <config.h>
 #include <stdlib.h>
+#include <string.h>
 #include <gsl/gsl_block.h>
 
 #define BASE_GSL_COMPLEX_LONG
diff -Nru gsl-doc-1.16/block/init_source.c gsl-doc-2.3/block/init_source.c
--- gsl-doc-1.16/block/init_source.c	2013-07-17 20:20:40.000000000 +0000
+++ gsl-doc-2.3/block/init_source.c	2015-11-03 16:21:55.000000000 +0000
@@ -36,7 +36,7 @@
                         GSL_ENOMEM, 0);
     }
 
-  b->data = (ATOMIC *) calloc (1, MULTIPLICITY * n * sizeof (ATOMIC));
+  b->data = (ATOMIC *) malloc (MULTIPLICITY * n * sizeof (ATOMIC));
 
   if (b->data == 0)
     {
@@ -61,7 +61,8 @@
   if (b == 0)
     return 0;
 
-  /* initialize block to zero */
+  /* initialize block to zero; the memset call takes care of padding bytes */
+  memset(b->data, 0, MULTIPLICITY * n * sizeof(ATOMIC));
 
   for (i = 0; i < MULTIPLICITY * n; i++)
     {
diff -Nru gsl-doc-1.16/block/Makefile.am gsl-doc-2.3/block/Makefile.am
--- gsl-doc-1.16/block/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/block/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -4,7 +4,7 @@
 
 pkginclude_HEADERS = gsl_block.h gsl_block_char.h gsl_block_complex_double.h gsl_block_complex_float.h gsl_block_complex_long_double.h gsl_block_double.h gsl_block_float.h gsl_block_int.h gsl_block_long.h gsl_block_long_double.h gsl_block_short.h gsl_block_uchar.h gsl_block_uint.h gsl_block_ulong.h gsl_block_ushort.h gsl_check_range.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 TESTS = $(check_PROGRAMS)
 
diff -Nru gsl-doc-1.16/block/Makefile.in gsl-doc-2.3/block/Makefile.in
--- gsl-doc-1.16/block/Makefile.in	2013-07-19 15:14:52.000000000 +0000
+++ gsl-doc-2.3/block/Makefile.in	2016-12-09 00:04:20.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -377,6 +377,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -399,7 +400,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -515,7 +519,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslblock.la 
 pkginclude_HEADERS = gsl_block.h gsl_block_char.h gsl_block_complex_double.h gsl_block_complex_float.h gsl_block_complex_long_double.h gsl_block_double.h gsl_block_float.h gsl_block_int.h gsl_block_long.h gsl_block_long_double.h gsl_block_short.h gsl_block_uchar.h gsl_block_uint.h gsl_block_ulong.h gsl_block_ushort.h gsl_check_range.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 TESTS = $(check_PROGRAMS)
 test_LDADD = libgslblock.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
 test_SOURCES = test.c
diff -Nru gsl-doc-1.16/bspline/bspline.c gsl-doc-2.3/bspline/bspline.c
--- gsl-doc-1.16/bspline/bspline.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/bspline/bspline.c	2015-11-03 16:21:55.000000000 +0000
@@ -64,13 +64,13 @@
     {
       gsl_bspline_workspace *w;
 
-      w = (gsl_bspline_workspace *) malloc (sizeof (gsl_bspline_workspace));
+      w = calloc (1, sizeof (gsl_bspline_workspace));
 
       if (w == 0)
-	{
-	  GSL_ERROR_NULL ("failed to allocate space for workspace",
-			  GSL_ENOMEM);
-	}
+        {
+          GSL_ERROR_NULL ("failed to allocate space for workspace",
+            GSL_ENOMEM);
+        }
 
       w->k = k;
       w->km1 = k - 1;
@@ -80,47 +80,96 @@
 
       w->knots = gsl_vector_alloc (w->n + k);
       if (w->knots == 0)
-	{
-	  free (w);
-	  GSL_ERROR_NULL ("failed to allocate space for knots vector",
-			  GSL_ENOMEM);
-	}
+        {
+          gsl_bspline_free (w);
+          GSL_ERROR_NULL ("failed to allocate space for knots vector",
+            GSL_ENOMEM);
+        }
 
       w->deltal = gsl_vector_alloc (k);
       if (w->deltal == 0)
-	{
-	  gsl_vector_free (w->knots);
-	  free (w);
-	  GSL_ERROR_NULL ("failed to allocate space for deltal vector",
-			  GSL_ENOMEM);
-	}
+        {
+          gsl_bspline_free (w);
+          GSL_ERROR_NULL ("failed to allocate space for deltal vector",
+            GSL_ENOMEM);
+        }
 
       w->deltar = gsl_vector_alloc (k);
       if (w->deltar == 0)
-	{
-	  gsl_vector_free (w->deltal);
-	  gsl_vector_free (w->knots);
-	  free (w);
-	  GSL_ERROR_NULL ("failed to allocate space for deltar vector",
-			  GSL_ENOMEM);
-	}
-
+        {
+          gsl_bspline_free (w);
+          GSL_ERROR_NULL ("failed to allocate space for deltar vector",
+            GSL_ENOMEM);
+        }
 
       w->B = gsl_vector_alloc (k);
       if (w->B == 0)
-	{
-	  gsl_vector_free (w->deltar);;
-	  gsl_vector_free (w->deltal);
-	  gsl_vector_free (w->knots);
-	  free (w);
-	  GSL_ERROR_NULL
-	    ("failed to allocate space for temporary spline vector",
-	     GSL_ENOMEM);
-	}
+        {
+          gsl_bspline_free (w);
+          GSL_ERROR_NULL
+            ("failed to allocate space for temporary spline vector",
+             GSL_ENOMEM);
+        }
+
+      w->A = gsl_matrix_alloc (k, k);
+      if (w->A == 0)
+        {
+          gsl_bspline_free (w);
+          GSL_ERROR_NULL
+            ("failed to allocate space for derivative work matrix",
+             GSL_ENOMEM);
+        }
+
+      w->dB = gsl_matrix_alloc (k, k + 1);
+      if (w->dB == 0)
+        {
+          gsl_bspline_free (w);
+          GSL_ERROR_NULL
+            ("failed to allocate space for temporary derivative matrix",
+             GSL_ENOMEM);
+        }
 
       return w;
     }
-}				/* gsl_bspline_alloc() */
+} /* gsl_bspline_alloc() */
+
+/*
+gsl_bspline_free()
+  Free a gsl_bspline_workspace.
+
+Inputs: w - workspace to free
+
+Return: none
+*/
+
+void
+gsl_bspline_free (gsl_bspline_workspace * w)
+{
+  RETURN_IF_NULL (w);
+
+  if (w->knots)
+    gsl_vector_free (w->knots);
+
+  if (w->deltal)
+    gsl_vector_free (w->deltal);
+
+  if (w->deltar)
+    gsl_vector_free (w->deltar);
+
+  if (w->B)
+    gsl_vector_free (w->B);
+
+  if (w->A)
+    gsl_matrix_free(w->A);
+
+  if (w->dB)
+    gsl_matrix_free(w->dB);
+
+  free (w);
+} /* gsl_bspline_free() */
+
+
+#ifndef GSL_DISABLE_DEPRECATED
 
 /*
 gsl_bspline_deriv_alloc()
@@ -178,6 +227,26 @@
     }
 }				/* gsl_bspline_deriv_alloc() */
 
+/*
+gsl_bspline_deriv_free()
+  Free a gsl_bspline_deriv_workspace.
+
+Inputs: dw - workspace to free
+
+Return: none
+*/
+
+void
+gsl_bspline_deriv_free (gsl_bspline_deriv_workspace * dw)
+{
+  RETURN_IF_NULL (dw);
+  gsl_matrix_free (dw->A);
+  gsl_matrix_free (dw->dB);
+  free (dw);
+}				/* gsl_bspline_deriv_free() */
+
+#endif /* !GSL_DISABLE_DEPRECATED */
+
 /* Return number of coefficients */
 size_t
 gsl_bspline_ncoeffs (gsl_bspline_workspace * w)
@@ -208,44 +277,6 @@
 }
 
 /*
-gsl_bspline_free()
-  Free a gsl_bspline_workspace.
-
-Inputs: w - workspace to free
-
-Return: none
-*/
-
-void
-gsl_bspline_free (gsl_bspline_workspace * w)
-{
-  RETURN_IF_NULL (w);
-  gsl_vector_free (w->knots);
-  gsl_vector_free (w->deltal);
-  gsl_vector_free (w->deltar);
-  gsl_vector_free (w->B);
-  free (w);
-}				/* gsl_bspline_free() */
-
-/*
-gsl_bspline_deriv_free()
-  Free a gsl_bspline_deriv_workspace.
-
-Inputs: dw - workspace to free
-
-Return: none
-*/
-
-void
-gsl_bspline_deriv_free (gsl_bspline_deriv_workspace * dw)
-{
-  RETURN_IF_NULL (dw);
-  gsl_matrix_free (dw->A);
-  gsl_matrix_free (dw->dB);
-  free (dw);
-}				/* gsl_bspline_deriv_free() */
-
-/*
 gsl_bspline_knots()
   Compute the knots from the given breakpoints:
 
@@ -276,23 +307,23 @@
     }
   else
     {
-      size_t i;			/* looping */
+      size_t i; /* looping */
 
       for (i = 0; i < w->k; i++)
-	gsl_vector_set (w->knots, i, gsl_vector_get (breakpts, 0));
+        gsl_vector_set (w->knots, i, gsl_vector_get (breakpts, 0));
 
       for (i = 1; i < w->l; i++)
-	{
-	  gsl_vector_set (w->knots, w->k - 1 + i,
-			  gsl_vector_get (breakpts, i));
-	}
+        {
+          gsl_vector_set (w->knots, w->k - 1 + i,
+          gsl_vector_get (breakpts, i));
+        }
 
       for (i = w->n; i < w->n + w->k; i++)
-	gsl_vector_set (w->knots, i, gsl_vector_get (breakpts, w->l));
+        gsl_vector_set (w->knots, i, gsl_vector_get (breakpts, w->l));
 
       return GSL_SUCCESS;
     }
-}				/* gsl_bspline_knots() */
+} /* gsl_bspline_knots() */
 
 /*
 gsl_bspline_knots_uniform()
@@ -319,10 +350,10 @@
 
 int
 gsl_bspline_knots_uniform (const double a, const double b,
-			   gsl_bspline_workspace * w)
+                           gsl_bspline_workspace * w)
 {
-  size_t i;			/* looping */
-  double delta;			/* interval spacing */
+  size_t i;     /* looping */
+  double delta; /* interval spacing */
   double x;
 
   delta = (b - a) / (double) w->l;
@@ -341,7 +372,7 @@
     gsl_vector_set (w->knots, i, b);
 
   return GSL_SUCCESS;
-}				/* gsl_bspline_knots_uniform() */
+} /* gsl_bspline_knots_uniform() */
 
 /*
 gsl_bspline_eval()
@@ -378,23 +409,21 @@
       /* find all non-zero B_i(x) values */
       error = gsl_bspline_eval_nonzero (x, w->B, &istart, &iend, w);
       if (error)
-	{
-	  return error;
-	}
+        return error;
 
       /* store values in appropriate part of given vector */
       for (i = 0; i < istart; i++)
-	gsl_vector_set (B, i, 0.0);
+        gsl_vector_set (B, i, 0.0);
 
       for (i = istart; i <= iend; i++)
-	gsl_vector_set (B, i, gsl_vector_get (w->B, i - istart));
+        gsl_vector_set (B, i, gsl_vector_get (w->B, i - istart));
 
       for (i = iend + 1; i < w->n; i++)
-	gsl_vector_set (B, i, 0.0);
+        gsl_vector_set (B, i, 0.0);
 
       return GSL_SUCCESS;
     }
-}				/* gsl_bspline_eval() */
+} /* gsl_bspline_eval() */
 
 /*
 gsl_bspline_eval_nonzero()
@@ -426,7 +455,7 @@
 
 int
 gsl_bspline_eval_nonzero (const double x, gsl_vector * Bk, size_t * istart,
-			  size_t * iend, gsl_bspline_workspace * w)
+                          size_t * iend, gsl_bspline_workspace * w)
 {
   if (Bk->size != w->k)
     {
@@ -442,19 +471,17 @@
       i = bspline_find_interval (x, &flag, w);
       error = bspline_process_interval_for_eval (x, &i, flag, w);
       if (error)
-	{
-	  return error;
-	}
+        return error;
 
       *istart = i - w->k + 1;
       *iend = i;
 
       bspline_pppack_bsplvb (w->knots, w->k, 1, x, *iend, &j, w->deltal,
-			     w->deltar, Bk);
+                             w->deltar, Bk);
 
       return GSL_SUCCESS;
     }
-}				/* gsl_bspline_eval_nonzero() */
+} /* gsl_bspline_eval_nonzero() */
 
 /*
 gsl_bspline_deriv_eval()
@@ -479,9 +506,8 @@
 */
 
 int
-gsl_bspline_deriv_eval (const double x, const size_t nderiv, gsl_matrix * dB,
-			gsl_bspline_workspace * w,
-			gsl_bspline_deriv_workspace * dw)
+gsl_bspline_deriv_eval (const double x, const size_t nderiv,
+                        gsl_matrix * dB, gsl_bspline_workspace * w)
 {
   if (dB->size1 != w->n)
     {
@@ -490,12 +516,8 @@
   else if (dB->size2 < nderiv + 1)
     {
       GSL_ERROR
-	("dB matrix second dimension must be at least length nderiv+1",
-	 GSL_EBADLEN);
-    }
-  else if (dw->k < w->k) 
-    {
-      GSL_ERROR ("derivative workspace is too small", GSL_EBADLEN);
+        ("dB matrix second dimension must be at least length nderiv+1",
+         GSL_EBADLEN);
     }
   else
     {
@@ -507,29 +529,26 @@
 
       /* find all non-zero d^j/dx^j B_i(x) values */
       error =
-	gsl_bspline_deriv_eval_nonzero (x, nderiv, dw->dB, &istart, &iend, w,
-					dw);
+        gsl_bspline_deriv_eval_nonzero (x, nderiv, w->dB, &istart, &iend, w);
       if (error)
-	{
-	  return error;
-	}
+        return error;
 
       /* store values in appropriate part of given matrix */
       for (j = 0; j <= nderiv; j++)
-	{
-	  for (i = 0; i < istart; i++)
-	    gsl_matrix_set (dB, i, j, 0.0);
-
-	  for (i = istart; i <= iend; i++)
-	    gsl_matrix_set (dB, i, j, gsl_matrix_get (dw->dB, i - istart, j));
-
-	  for (i = iend + 1; i < w->n; i++)
-	    gsl_matrix_set (dB, i, j, 0.0);
-	}
+        {
+          for (i = 0; i < istart; i++)
+          gsl_matrix_set (dB, i, j, 0.0);
+
+          for (i = istart; i <= iend; i++)
+            gsl_matrix_set (dB, i, j, gsl_matrix_get (w->dB, i - istart, j));
+
+          for (i = iend + 1; i < w->n; i++)
+            gsl_matrix_set (dB, i, j, 0.0);
+        }
 
       return GSL_SUCCESS;
     }
-}				/* gsl_bspline_deriv_eval() */
+} /* gsl_bspline_deriv_eval() */
 
 /*
 gsl_bspline_deriv_eval_nonzero()
@@ -573,9 +592,8 @@
 
 int
 gsl_bspline_deriv_eval_nonzero (const double x, const size_t nderiv,
-				gsl_matrix * dB, size_t * istart,
-				size_t * iend, gsl_bspline_workspace * w,
-				gsl_bspline_deriv_workspace * dw)
+                                gsl_matrix * dB, size_t * istart,
+                                size_t * iend, gsl_bspline_workspace * w)
 {
   if (dB->size1 != w->k)
     {
@@ -584,12 +602,8 @@
   else if (dB->size2 < nderiv + 1)
     {
       GSL_ERROR
-	("dB matrix second dimension must be at least length nderiv+1",
-	 GSL_EBADLEN);
-    }
-  else if (dw->k < w->k) 
-    {
-      GSL_ERROR ("derivative workspace is too small", GSL_EBADLEN);
+        ("dB matrix second dimension must be at least length nderiv+1",
+         GSL_EBADLEN);
     }
   else
     {
@@ -602,30 +616,26 @@
       i = bspline_find_interval (x, &flag, w);
       error = bspline_process_interval_for_eval (x, &i, flag, w);
       if (error)
-	{
-	  return error;
-	}
+        return error;
 
       *istart = i - w->k + 1;
       *iend = i;
 
       bspline_pppack_bsplvd (w->knots, w->k, x, *iend,
-			     w->deltal, w->deltar, dw->A, dB, nderiv);
+                             w->deltal, w->deltar, w->A, dB, nderiv);
 
       /* An order k b-spline has at most k-1 nonzero derivatives
          so we need to zero all requested higher order derivatives */
       min_nderivk = GSL_MIN_INT (nderiv, w->k - 1);
       for (j = min_nderivk + 1; j <= nderiv; j++)
-	{
-	  for (i = 0; i < w->k; i++)
-	    {
-	      gsl_matrix_set (dB, i, j, 0.0);
-	    }
-	}
+        {
+          for (i = 0; i < w->k; i++)
+            gsl_matrix_set (dB, i, j, 0.0);
+        }
 
       return GSL_SUCCESS;
     }
-}				/* gsl_bspline_deriv_eval_nonzero() */
+} /* gsl_bspline_deriv_eval_nonzero() */
 
 /****************************************
  *          INTERNAL ROUTINES           *
diff -Nru gsl-doc-1.16/bspline/gsl_bspline.h gsl-doc-2.3/bspline/gsl_bspline.h
--- gsl-doc-1.16/bspline/gsl_bspline.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/bspline/gsl_bspline.h	2015-11-03 16:21:55.000000000 +0000
@@ -40,18 +40,24 @@
 
 typedef struct
 {
-    size_t k; /* spline order */
-    size_t km1; /* k - 1 (polynomial order) */
-    size_t l; /* number of polynomial pieces on interval */
+    size_t k;      /* spline order */
+    size_t km1;    /* k - 1 (polynomial order) */
+    size_t l;      /* number of polynomial pieces on interval */
     size_t nbreak; /* number of breakpoints (l + 1) */
-    size_t n; /* number of bspline basis functions (l + k - 1) */
+    size_t n;      /* number of bspline basis functions (l + k - 1) */
 
-    gsl_vector *knots; /* knots vector */
+    gsl_vector *knots;  /* knots vector */
     gsl_vector *deltal; /* left delta */
     gsl_vector *deltar; /* right delta */
-    gsl_vector *B; /* temporary spline results */
+    gsl_vector *B;      /* temporary spline results */
+
+    /* bspline derivative parameters */
+    gsl_matrix *A;      /* work matrix */
+    gsl_matrix *dB;     /* temporary derivative results */
 } gsl_bspline_workspace;
 
+#ifndef GSL_DISABLE_DEPRECATED
+
 typedef struct
 {
     size_t k; /* spline order */
@@ -59,6 +65,11 @@
     gsl_matrix *dB; /* temporary derivative results */
 } gsl_bspline_deriv_workspace;
 
+gsl_bspline_deriv_workspace *gsl_bspline_deriv_alloc(const size_t k);
+void gsl_bspline_deriv_free(gsl_bspline_deriv_workspace *w);
+
+#endif /* !GSL_DISABLE_DEPRECATED */
+
 gsl_bspline_workspace *
 gsl_bspline_alloc(const size_t k, const size_t nbreak);
 
@@ -92,18 +103,11 @@
                          size_t *iend,
                          gsl_bspline_workspace *w);
 
-gsl_bspline_deriv_workspace *
-gsl_bspline_deriv_alloc(const size_t k);
-
-void
-gsl_bspline_deriv_free(gsl_bspline_deriv_workspace *w);
-
 int
 gsl_bspline_deriv_eval(const double x,
                        const size_t nderiv,
                        gsl_matrix *dB,
-                       gsl_bspline_workspace *w,
-                       gsl_bspline_deriv_workspace *dw);
+                       gsl_bspline_workspace *w);
 
 int
 gsl_bspline_deriv_eval_nonzero(const double x,
@@ -111,8 +115,7 @@
                                gsl_matrix *dB,
                                size_t *istart,
                                size_t *iend,
-                               gsl_bspline_workspace *w,
-                               gsl_bspline_deriv_workspace *dw);
+                               gsl_bspline_workspace *w);
 
 __END_DECLS
 
diff -Nru gsl-doc-1.16/bspline/Makefile.am gsl-doc-2.3/bspline/Makefile.am
--- gsl-doc-1.16/bspline/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/bspline/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_bspline.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslbspline_la_SOURCES = bspline.c greville.c
 
diff -Nru gsl-doc-1.16/bspline/Makefile.in gsl-doc-2.3/bspline/Makefile.in
--- gsl-doc-1.16/bspline/Makefile.in	2013-07-19 15:14:52.000000000 +0000
+++ gsl-doc-2.3/bspline/Makefile.in	2016-12-09 00:04:20.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -381,6 +381,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -403,7 +404,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -519,7 +523,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslbspline.la 
 pkginclude_HEADERS = gsl_bspline.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslbspline_la_SOURCES = bspline.c greville.c
 noinst_HEADERS = bspline.h
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/bspline/test.c gsl-doc-2.3/bspline/test.c
--- gsl-doc-1.16/bspline/test.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/bspline/test.c	2015-11-03 16:21:55.000000000 +0000
@@ -26,7 +26,7 @@
 #include <gsl/gsl_nan.h>
 
 void
-test_bspline(gsl_bspline_workspace * bw, gsl_bspline_deriv_workspace * dbw)
+test_bspline(gsl_bspline_workspace * bw)
 {
   gsl_vector *B;
   gsl_matrix *dB;
@@ -68,7 +68,7 @@
     {
       double xi = a + (b - a) * (i / (n - 1.0));
       gsl_bspline_eval(xi, B, bw);
-      gsl_bspline_deriv_eval(xi, 0, dB, bw, dbw);
+      gsl_bspline_deriv_eval(xi, 0, dB, bw);
 
       for (j = 0; j < ncoeffs; j++)
         {
@@ -100,10 +100,8 @@
         {
           double a = -1.23 * order, b = 45.6 * order;
           gsl_bspline_workspace *bw = gsl_bspline_alloc(order, breakpoints);
-          gsl_bspline_deriv_workspace *dbw = gsl_bspline_deriv_alloc(order);
           gsl_bspline_knots_uniform(a, b, bw);
-          test_bspline(bw, dbw);
-          gsl_bspline_deriv_free(dbw);
+          test_bspline(bw);
           gsl_bspline_free(bw);
         }
     }
@@ -115,7 +113,6 @@
         {
           double a = -1.23 * order, b = 45.6 * order;
           gsl_bspline_workspace *bw = gsl_bspline_alloc(order, breakpoints);
-          gsl_bspline_deriv_workspace *dbw = gsl_bspline_deriv_alloc(order);
           gsl_vector *k = gsl_vector_alloc(breakpoints);
           for (i = 0; i < breakpoints; i++)
             {
@@ -125,9 +122,8 @@
               gsl_vector_set(k, i, x);
             };
           gsl_bspline_knots(k, bw);
-          test_bspline(bw, dbw);
+          test_bspline(bw);
           gsl_vector_free(k);
-          gsl_bspline_deriv_free(dbw);
           gsl_bspline_free(bw);
         }
     }
@@ -147,7 +143,6 @@
     };
 
     gsl_bspline_workspace *bw = gsl_bspline_alloc(2, 3);
-    gsl_bspline_deriv_workspace *dbw = gsl_bspline_deriv_alloc(2);
     gsl_matrix *dB = gsl_matrix_alloc(gsl_bspline_ncoeffs(bw),
                                       gsl_bspline_order(bw) + 1);
 
@@ -163,7 +158,7 @@
         /* Initialize dB with poison to ensure we overwrite it */
         gsl_matrix_set_all(dB, GSL_NAN);
 
-        gsl_bspline_deriv_eval(xloc[i], gsl_bspline_order(bw), dB, bw, dbw);
+        gsl_bspline_deriv_eval(xloc[i], gsl_bspline_order(bw), dB, bw);
         for (j = 0; j < gsl_bspline_ncoeffs(bw) ; ++j)
           {
             /* check basis function 1st deriv */
@@ -183,7 +178,6 @@
       }
 
     gsl_matrix_free(dB);
-    gsl_bspline_deriv_free(dbw);
     gsl_bspline_free(bw);
     gsl_vector_free(breakpts);
   }
@@ -219,7 +213,6 @@
     };
 
     gsl_bspline_workspace *bw = gsl_bspline_alloc(3, 5);
-    gsl_bspline_deriv_workspace *dbw = gsl_bspline_deriv_alloc(3);
 
     gsl_matrix *dB = gsl_matrix_alloc(gsl_bspline_ncoeffs(bw),
                                       gsl_bspline_order(bw) + 1);
@@ -236,7 +229,7 @@
       {
         /* Initialize dB with poison to ensure we overwrite it */
         gsl_matrix_set_all(dB, GSL_NAN);
-        gsl_bspline_deriv_eval(xloc[i], gsl_bspline_order(bw), dB, bw, dbw);
+        gsl_bspline_deriv_eval(xloc[i], gsl_bspline_order(bw), dB, bw);
 
         /* check basis function evaluation */
         for (j = 0; j < gsl_bspline_ncoeffs(bw); ++j)
@@ -262,7 +255,6 @@
       }
 
     gsl_matrix_free(dB);
-    gsl_bspline_deriv_free(dbw);
     gsl_bspline_free(bw);
     gsl_vector_free(breakpts);
   }
diff -Nru gsl-doc-1.16/BUGS gsl-doc-2.3/BUGS
--- gsl-doc-1.16/BUGS	2013-07-18 16:23:38.000000000 +0000
+++ gsl-doc-2.3/BUGS	2015-11-03 16:21:55.000000000 +0000
@@ -1,136 +0,0 @@
-The GSL Bugs Database is at http://savannah.gnu.org/bugs/?group=gsl
-
-This file was generated from it at Thu Jul 18 10:23:38 2013
-
-------------------------------------------------------------------------
-BUG-ID:   28267   
-STATUS:   Open/Postponed  
-CATEGORY: Accuracy problem
-SUMMARY:  poor convergence region for gsl_sf_hyperg_1F1
-
-The magnitude of the error is greater than the value itself for
-a<<0, b>0, x>>0 
-
-gsl_sf_hyperg1F1(-3.78e+01, 2, 1.035e+02) =>  -7.00055e+18 +/- 3.77654e+19
-
------------------------------------------------
-From: Weibin Li <weibinli@mpipks-dresden.mpg.de>
-To: bug-gsl@gnu.org
-Subject: [Bug-gsl] gsl_sf_hyperg_1F1
-Date: Mon, 30 Nov 2009 15:26:11 +0100
-
-Hi, guys
-
-I experienced bugs with gsl_sf_hyperg_1F1. The version  is gsl_1.12, but
-the testing is also done with gsl_1.13, using a  mac with version 10.5.8
-and hp-workstation with gnome_2.24.1.
-
-#include<stdlib.h>
-#include<stdio.h>
-#include<math.h>
-#include "gsl/gsl_sf_hyperg.h"
-
-int main(int argc, char **argv)
-{
- int ii;
- double Ri;
- double v0;
-
- gsl_sf_result r;
- for(ii = 10; ii< 140;ii++)
-{
-     Ri = 2013;
-     v0 =38.86871 +ii*2.5e-10;
-
-    gsl_sf_hyperg_1F1_e(1.0-v0,2,2.0*Ri/v0,&r);
-    printf("%lg\t%14.13g\t%14.13g\n",v0,r.val,r.err);
-
- }
-return 0;
-}
-
-The output of above code shows an extremely large error. by increasing
-Ri, the relative error decreases. Is there any idea to fix this?
-
-Thank you very much.
-
-Best
-
-Weibin
-
--It's inherently difficult to compute the value in this region either way as there is massive cancellation in both the series and the Kummer transformed series.I cannot find any algorithm which handles this case.Confirmed
-
-------------------------------------------------------------------------
-BUG-ID:   21828   
-STATUS:   Open/Confirmed  
-CATEGORY: Performance
-SUMMARY:  suboptimal performance of gsl_fdfsolver_lmsder
-
-From: "Alexander Usov" <a.s.usov@gmail.com>
-To: help-gsl@gnu.org
-Subject: [Help-gsl] Strange performance of gsl_fdfsolver_lmsder
-Date: Wed, 24 Oct 2007 20:45:01 +0200
-
-Hi all,
-
-I am currently working on the problem involving source extraction from
-astronomical images, which essentially boils down to fitting a number of
-2d gaussians to the image.
-
-One of the traditionally used fitters in this field is a Levenberg-Marquardt,
-which gsl_fdfsolver_lmsder is and implementation of.
-
-At some moment I have notices that for the bigger images (about 550
-pixels, 20-30 parameters) gsl's lmsder algorithm spends a large fraction
-of the run-time (about 50%) doing household transform.
-
-While looking around for are different minimization algorithms I have made
-a surprising finding that original netlib/minpack/lmder is almost twice faster
-that that of gsl.
-
-Could anyone explain such a big difference in performace?
-
--- 
-Best regards,
-  Alexander.
-
-_______________________________________________
-Help-gsl mailing list
-Help-gsl@gnu.org
-http://lists.gnu.org/mailman/listinfo/help-gsl
-
-Reply-To: help-gsl@gnu.org
-From: Brian Gough <bjg@network-theory.co.uk>
-To: "Alexander Usov" <a.s.usov@gmail.com>
-Cc: help-gsl@gnu.org
-Subject: Re: [Help-gsl] Strange performance of gsl_fdfsolver_lmsder
-Date: Thu, 25 Oct 2007 21:57:08 +0100
-
-At Wed, 24 Oct 2007 20:45:01 +0200,
-Alexander Usov wrote:
-> At some moment I have notices that for the bigger images (about 550
-> pixels, 20-30 parameters) gsl's lmsder algorithm spends a large fraction
-> of the run-time (about 50%) doing household transform.
-> 
-> While looking around for are different minimization algorithms I have made
-> a surprising finding that original netlib/minpack/lmder is almost twice faster
-> that that of gsl.
-> 
-> Could anyone explain such a big difference in performace?
-
-I have a vague memory that there was some quantity (Jacobian?) that
-MINPACK only computes fully at the end, but in GSL it is accessible to
-the user at each step so I felt I had to update it on each iteration
-in the absence of some alternate scheme.  Sorry this is not a great
-answer but I am not able to look at it in detail now.
-
--- 
-Brian Gough
-
-_______________________________________________
-Help-gsl mailing list
-Help-gsl@gnu.org
-http://lists.gnu.org/mailman/listinfo/help-gsl
-
-1824
-
diff -Nru gsl-doc-1.16/cblas/Makefile.am gsl-doc-2.3/cblas/Makefile.am
--- gsl-doc-1.16/cblas/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/cblas/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -1,14 +1,9 @@
 lib_LTLIBRARIES = libgslcblas.la
-libgslcblas_la_LDFLAGS = -version-info $(GSL_LT_CBLAS_VERSION)
-
-MINGW32_HOST = @MINGW32_HOST@
-if MINGW32_HOST
-libgslcblas_la_LDFLAGS += -no-undefined
-endif
+libgslcblas_la_LDFLAGS = $(GSLCBLAS_LDFLAGS) -version-info $(GSL_LT_CBLAS_VERSION)
 
 pkginclude_HEADERS = gsl_cblas.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslcblas_la_SOURCES = sasum.c saxpy.c scasum.c scnrm2.c scopy.c sdot.c sdsdot.c sgbmv.c sgemm.c sgemv.c sger.c snrm2.c srot.c srotg.c srotm.c srotmg.c ssbmv.c sscal.c sspmv.c sspr.c sspr2.c sswap.c ssymm.c ssymv.c ssyr.c ssyr2.c ssyr2k.c ssyrk.c stbmv.c stbsv.c stpmv.c stpsv.c strmm.c strmv.c strsm.c strsv.c dasum.c daxpy.c dcopy.c ddot.c dgbmv.c dgemm.c dgemv.c dger.c dnrm2.c drot.c drotg.c drotm.c drotmg.c dsbmv.c dscal.c dsdot.c dspmv.c dspr.c dspr2.c dswap.c dsymm.c dsymv.c dsyr.c dsyr2.c dsyr2k.c dsyrk.c dtbmv.c dtbsv.c dtpmv.c dtpsv.c dtrmm.c dtrmv.c dtrsm.c dtrsv.c dzasum.c dznrm2.c caxpy.c ccopy.c cdotc_sub.c cdotu_sub.c cgbmv.c cgemm.c cgemv.c cgerc.c cgeru.c chbmv.c chemm.c chemv.c cher.c cher2.c cher2k.c cherk.c chpmv.c chpr.c chpr2.c cscal.c csscal.c cswap.c csymm.c csyr2k.c csyrk.c ctbmv.c ctbsv.c ctpmv.c ctpsv.c ctrmm.c ctrmv.c ctrsm.c ctrsv.c zaxpy.c zcopy.c zdotc_sub.c zdotu_sub.c zdscal.c zgbmv.c zgemm.c zgemv.c zgerc.c zgeru.c zhbmv.c zhemm.c zhemv.c zher.c zher2.c zher2k.c zherk.c zhpmv.c zhpr.c zhpr2.c zscal.c zswap.c zsymm.c zsyr2k.c zsyrk.c ztbmv.c ztbsv.c ztpmv.c ztpsv.c ztrmm.c ztrmv.c ztrsm.c ztrsv.c icamax.c idamax.c isamax.c izamax.c xerbla.c
 
diff -Nru gsl-doc-1.16/cblas/Makefile.in gsl-doc-2.3/cblas/Makefile.in
--- gsl-doc-1.16/cblas/Makefile.in	2013-07-19 15:14:52.000000000 +0000
+++ gsl-doc-2.3/cblas/Makefile.in	2016-12-09 00:04:20.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -79,7 +79,6 @@
 POST_UNINSTALL = :
 build_triplet = @build@
 host_triplet = @host@
-@MINGW32_HOST_TRUE@am__append_1 = -no-undefined
 check_PROGRAMS = test$(EXEEXT)
 subdir = cblas
 DIST_COMMON = $(srcdir)/Makefile.in $(srcdir)/Makefile.am \
@@ -417,6 +416,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -439,7 +439,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -554,11 +557,9 @@
 top_builddir = @top_builddir@
 top_srcdir = @top_srcdir@
 lib_LTLIBRARIES = libgslcblas.la
-libgslcblas_la_LDFLAGS = -version-info $(GSL_LT_CBLAS_VERSION) \
-	$(am__append_1)
-MINGW32_HOST = @MINGW32_HOST@
+libgslcblas_la_LDFLAGS = $(GSLCBLAS_LDFLAGS) -version-info $(GSL_LT_CBLAS_VERSION)
 pkginclude_HEADERS = gsl_cblas.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslcblas_la_SOURCES = sasum.c saxpy.c scasum.c scnrm2.c scopy.c \
 	sdot.c sdsdot.c sgbmv.c sgemm.c sgemv.c sger.c snrm2.c srot.c \
 	srotg.c srotm.c srotmg.c ssbmv.c sscal.c sspmv.c sspr.c \
diff -Nru gsl-doc-1.16/cdf/Makefile.am gsl-doc-2.3/cdf/Makefile.am
--- gsl-doc-1.16/cdf/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/cdf/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -3,7 +3,7 @@
 
 pkginclude_HEADERS= gsl_cdf.h 
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslcdf_la_SOURCES = beta.c betainv.c cauchy.c cauchyinv.c chisq.c chisqinv.c exponential.c exponentialinv.c exppow.c fdist.c fdistinv.c flat.c flatinv.c gamma.c gammainv.c gauss.c gaussinv.c gumbel1.c gumbel1inv.c gumbel2.c gumbel2inv.c laplace.c laplaceinv.c logistic.c logisticinv.c lognormal.c lognormalinv.c pareto.c paretoinv.c rayleigh.c rayleighinv.c tdist.c tdistinv.c weibull.c weibullinv.c binomial.c poisson.c geometric.c nbinomial.c pascal.c hypergeometric.c
 
diff -Nru gsl-doc-1.16/cdf/Makefile.in gsl-doc-2.3/cdf/Makefile.in
--- gsl-doc-1.16/cdf/Makefile.in	2013-07-19 15:14:52.000000000 +0000
+++ gsl-doc-2.3/cdf/Makefile.in	2016-12-09 00:04:20.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -387,6 +387,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -409,7 +410,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -525,7 +529,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslcdf.la
 pkginclude_HEADERS = gsl_cdf.h 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslcdf_la_SOURCES = beta.c betainv.c cauchy.c cauchyinv.c chisq.c chisqinv.c exponential.c exponentialinv.c exppow.c fdist.c fdistinv.c flat.c flatinv.c gamma.c gammainv.c gauss.c gaussinv.c gumbel1.c gumbel1inv.c gumbel2.c gumbel2inv.c laplace.c laplaceinv.c logistic.c logisticinv.c lognormal.c lognormalinv.c pareto.c paretoinv.c rayleigh.c rayleighinv.c tdist.c tdistinv.c weibull.c weibullinv.c binomial.c poisson.c geometric.c nbinomial.c pascal.c hypergeometric.c
 noinst_HEADERS = beta_inc.c rat_eval.h test_auto.c error.h
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/cheb/Makefile.am gsl-doc-2.3/cheb/Makefile.am
--- gsl-doc-1.16/cheb/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/cheb/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_chebyshev.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslcheb_la_SOURCES =  deriv.c eval.c init.c integ.c
 
diff -Nru gsl-doc-1.16/cheb/Makefile.in gsl-doc-2.3/cheb/Makefile.in
--- gsl-doc-1.16/cheb/Makefile.in	2013-07-19 15:14:52.000000000 +0000
+++ gsl-doc-2.3/cheb/Makefile.in	2016-12-09 00:04:20.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -376,6 +376,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -398,7 +399,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -514,7 +518,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslcheb.la 
 pkginclude_HEADERS = gsl_chebyshev.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslcheb_la_SOURCES = deriv.c eval.c init.c integ.c
 TESTS = $(check_PROGRAMS)
 test_LDADD = libgslcheb.la ../ieee-utils/libgslieeeutils.la ../test/libgsltest.la ../sys/libgslsys.la ../err/libgslerr.la ../utils/libutils.la
diff -Nru gsl-doc-1.16/combination/Makefile.am gsl-doc-2.3/combination/Makefile.am
--- gsl-doc-1.16/combination/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/combination/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_combination.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslcombination_la_SOURCES = init.c file.c combination.c inline.c
 
diff -Nru gsl-doc-1.16/combination/Makefile.in gsl-doc-2.3/combination/Makefile.in
--- gsl-doc-1.16/combination/Makefile.in	2013-07-19 15:14:52.000000000 +0000
+++ gsl-doc-2.3/combination/Makefile.in	2016-12-09 00:04:20.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -379,6 +379,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -401,7 +402,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -517,7 +521,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslcombination.la 
 pkginclude_HEADERS = gsl_combination.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslcombination_la_SOURCES = init.c file.c combination.c inline.c
 noinst_HEADERS = 
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/complex/Makefile.am gsl-doc-2.3/complex/Makefile.am
--- gsl-doc-1.16/complex/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/complex/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_complex.h gsl_complex_math.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslcomplex_la_SOURCES = math.c inline.c
 
diff -Nru gsl-doc-1.16/complex/Makefile.in gsl-doc-2.3/complex/Makefile.in
--- gsl-doc-1.16/complex/Makefile.in	2013-07-19 15:14:52.000000000 +0000
+++ gsl-doc-2.3/complex/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -376,6 +376,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -398,7 +399,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -514,7 +518,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslcomplex.la 
 pkginclude_HEADERS = gsl_complex.h gsl_complex_math.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslcomplex_la_SOURCES = math.c inline.c
 TESTS = $(check_PROGRAMS)
 test_SOURCES = test.c results.h results1.h results2.h results_real.h results_zreal.h
diff -Nru gsl-doc-1.16/complex/math.c gsl-doc-2.3/complex/math.c
--- gsl-doc-1.16/complex/math.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/complex/math.c	2016-09-15 17:11:00.000000000 +0000
@@ -1,6 +1,6 @@
 /* complex/math.c
  * 
- * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Jorma Olavi Tähtinen, Brian Gough
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Jorma Olavi T�htinen, Brian Gough
  * 
  * This program is free software; you can redistribute it and/or modify
  * it under the terms of the GNU General Public License as published by
@@ -19,7 +19,7 @@
 
 /* Basic complex arithmetic functions
 
- * Original version by Jorma Olavi Tähtinen <jotahtin@cc.hut.fi>
+ * Original version by Jorma Olavi T�htinen <jotahtin@cc.hut.fi>
  *
  * Modified for GSL by Brian Gough, 3/2000
  */
@@ -489,14 +489,10 @@
     }
   else
     {
-      double u = exp (-I);
-      double C = 2 * u / (1 - pow (u, 2.0));
-      double D = 1 + pow (cos (R), 2.0) * pow (C, 2.0);
-
-      double S = pow (C, 2.0);
-      double T = 1.0 / tanh (I);
+      double D = pow (cos (R), 2.0) + pow (sinh (I), 2.0);
+      double F = 1 + pow(cos (R)/sinh (I), 2.0);
 
-      GSL_SET_COMPLEX (&z, 0.5 * sin (2 * R) * S / D, T / D);
+      GSL_SET_COMPLEX (&z, 0.5 * sin (2 * R) / D, 1 / (tanh (I) * F));
     }
 
   return z;
diff -Nru gsl-doc-1.16/complex/results2.h gsl-doc-2.3/complex/results2.h
--- gsl-doc-1.16/complex/results2.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/complex/results2.h	2016-09-15 17:31:49.000000000 +0000
@@ -40,3 +40,4 @@
   {FN (pow), ARG(5.0e-01,-1.00000000000000005551e-01), ARG(0.0e+00,-1.0e+00), RES(6.4160554864378080418e-1, 5.1201864456768275590e-1)},
   {FN (pow), ARG(5.0e-01,-1.00000000000000005551e-01), ARG(5.0e-01,1.00000000000000005551e-01), RES(7.1829191470060938876e-1, -1.2038189555821612762e-1)},
   {FN (pow), ARG(5.0e-01,-1.00000000000000005551e-01), ARG(5.0e-01,-1.00000000000000005551e-01), RES(6.9977300530987816719e-1, -2.1940939105372143160e-2)},
+  {FN (pow), ARG(0.0e+00,9.0e+00), ARG(2.0e+00,0.0e+00), RES(-8.1e+01, 0.0e+00)},
diff -Nru gsl-doc-1.16/complex/results.h gsl-doc-2.3/complex/results.h
--- gsl-doc-1.16/complex/results.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/complex/results.h	2016-09-15 17:11:00.000000000 +0000
@@ -1351,6 +1351,11 @@
   {FN (tan), ARG(9.42512322775237976202e+00,-2.0e+00), RES(2.439339541035071690e-5, -9.6402758819508310550e-1)},
   {FN (tan), ARG(-9.42512322775237976202e+00,2.0e+00), RES(-2.439339541035071690e-5, 9.6402758819508310550e-1)},
   {FN (tan), ARG(-9.42512322775237976202e+00,-2.0e+00), RES(-2.439339541035071690e-5, -9.6402758819508310550e-1)},
+  {FN (tan), ARG(0.0e+00,1.0e+03), RES(0.0, 1.0)},
+  {FN (tan), ARG(0.0e+00,-1.0e+03), RES(0.0, -1.0)},
+  {FN (tan), ARG(0.0e+00,-1.23456e+05), RES(0.0, -1.0)},
+  {FN (tan), ARG(1.0e+03,0.0e+00), RES(1.470324155702718e+00, 0.0)},
+  {FN (tan), ARG(-1.0e+03,0.0e+00), RES(-1.470324155702718e+00, 0.0)},
   {FN (arcsin), ARG(0.0e+00,0.0e+00), RES(0e0, 0.0)},
   {FN (arcsin), ARG(0.0e+00,1.19209289550781250e-07), RES(0, 1.1920928955078096766e-7)},
   {FN (arcsin), ARG(0.0e+00,-1.19209289550781250e-07), RES(0, -1.1920928955078096766e-7)},
diff -Nru gsl-doc-1.16/complex/test.c gsl-doc-2.3/complex/test.c
--- gsl-doc-1.16/complex/test.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/complex/test.c	2016-09-15 17:11:00.000000000 +0000
@@ -113,7 +113,7 @@
 struct fzreal listzreal[] =
 {
 #include "results_zreal.h"
-  {"", 0, 0, 0, 0}
+  {"", 0, 0, 0, 0, 0, 0}
 };
 
 
diff -Nru gsl-doc-1.16/config.guess gsl-doc-2.3/config.guess
--- gsl-doc-1.16/config.guess	2013-07-18 16:30:00.000000000 +0000
+++ gsl-doc-2.3/config.guess	2015-12-03 18:34:33.000000000 +0000
@@ -2,7 +2,7 @@
 # Attempt to guess a canonical system name.
 #   Copyright 1992-2013 Free Software Foundation, Inc.
 
-timestamp='2013-04-24'
+timestamp='2013-06-10'
 
 # This file is free software; you can redistribute it and/or modify it
 # under the terms of the GNU General Public License as published by
@@ -132,6 +132,27 @@
 UNAME_SYSTEM=`(uname -s) 2>/dev/null`  || UNAME_SYSTEM=unknown
 UNAME_VERSION=`(uname -v) 2>/dev/null` || UNAME_VERSION=unknown
 
+case "${UNAME_SYSTEM}" in
+Linux|GNU|GNU/*)
+	# If the system lacks a compiler, then just pick glibc.
+	# We could probably try harder.
+	LIBC=gnu
+
+	eval $set_cc_for_build
+	cat <<-EOF > $dummy.c
+	#include <features.h>
+	#if defined(__UCLIBC__)
+	LIBC=uclibc
+	#elif defined(__dietlibc__)
+	LIBC=dietlibc
+	#else
+	LIBC=gnu
+	#endif
+	EOF
+	eval `$CC_FOR_BUILD -E $dummy.c 2>/dev/null | grep '^LIBC'`
+	;;
+esac
+
 # Note: order is significant - the case branches are not exclusive.
 
 case "${UNAME_MACHINE}:${UNAME_SYSTEM}:${UNAME_RELEASE}:${UNAME_VERSION}" in
@@ -853,21 +874,21 @@
 	exit ;;
     *:GNU:*:*)
 	# the GNU system
-	echo `echo ${UNAME_MACHINE}|sed -e 's,[-/].*$,,'`-unknown-gnu`echo ${UNAME_RELEASE}|sed -e 's,/.*$,,'`
+	echo `echo ${UNAME_MACHINE}|sed -e 's,[-/].*$,,'`-unknown-${LIBC}`echo ${UNAME_RELEASE}|sed -e 's,/.*$,,'`
 	exit ;;
     *:GNU/*:*:*)
 	# other systems with GNU libc and userland
-	echo ${UNAME_MACHINE}-unknown-`echo ${UNAME_SYSTEM} | sed 's,^[^/]*/,,' | tr '[A-Z]' '[a-z]'``echo ${UNAME_RELEASE}|sed -e 's/[-(].*//'`-gnu
+	echo ${UNAME_MACHINE}-unknown-`echo ${UNAME_SYSTEM} | sed 's,^[^/]*/,,' | tr '[A-Z]' '[a-z]'``echo ${UNAME_RELEASE}|sed -e 's/[-(].*//'`-${LIBC}
 	exit ;;
     i*86:Minix:*:*)
 	echo ${UNAME_MACHINE}-pc-minix
 	exit ;;
     aarch64:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     aarch64_be:Linux:*:*)
 	UNAME_MACHINE=aarch64_be
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     alpha:Linux:*:*)
 	case `sed -n '/^cpu model/s/^.*: \(.*\)/\1/p' < /proc/cpuinfo` in
@@ -880,67 +901,54 @@
 	  EV68*) UNAME_MACHINE=alphaev68 ;;
 	esac
 	objdump --private-headers /bin/sh | grep -q ld.so.1
-	if test "$?" = 0 ; then LIBC="libc1" ; else LIBC="" ; fi
-	echo ${UNAME_MACHINE}-unknown-linux-gnu${LIBC}
+	if test "$?" = 0 ; then LIBC="gnulibc1" ; fi
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     arc:Linux:*:* | arceb:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     arm*:Linux:*:*)
 	eval $set_cc_for_build
 	if echo __ARM_EABI__ | $CC_FOR_BUILD -E - 2>/dev/null \
 	    | grep -q __ARM_EABI__
 	then
-	    echo ${UNAME_MACHINE}-unknown-linux-gnu
+	    echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	else
 	    if echo __ARM_PCS_VFP | $CC_FOR_BUILD -E - 2>/dev/null \
 		| grep -q __ARM_PCS_VFP
 	    then
-		echo ${UNAME_MACHINE}-unknown-linux-gnueabi
+		echo ${UNAME_MACHINE}-unknown-linux-${LIBC}eabi
 	    else
-		echo ${UNAME_MACHINE}-unknown-linux-gnueabihf
+		echo ${UNAME_MACHINE}-unknown-linux-${LIBC}eabihf
 	    fi
 	fi
 	exit ;;
     avr32*:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     cris:Linux:*:*)
-	echo ${UNAME_MACHINE}-axis-linux-gnu
+	echo ${UNAME_MACHINE}-axis-linux-${LIBC}
 	exit ;;
     crisv32:Linux:*:*)
-	echo ${UNAME_MACHINE}-axis-linux-gnu
+	echo ${UNAME_MACHINE}-axis-linux-${LIBC}
 	exit ;;
     frv:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     hexagon:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     i*86:Linux:*:*)
-	LIBC=gnu
-	eval $set_cc_for_build
-	sed 's/^	//' << EOF >$dummy.c
-	#ifdef __dietlibc__
-	LIBC=dietlibc
-	#endif
-	#else
-	#include <features.h>
-	#ifdef __UCLIBC__
-	LIBC=uclibc
-	#endif
-EOF
-	eval `$CC_FOR_BUILD -E $dummy.c 2>/dev/null | grep '^LIBC'`
-	echo "${UNAME_MACHINE}-pc-linux-${LIBC}"
+	echo ${UNAME_MACHINE}-pc-linux-${LIBC}
 	exit ;;
     ia64:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     m32r*:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     m68*:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     mips:Linux:*:* | mips64:Linux:*:*)
 	eval $set_cc_for_build
@@ -959,59 +967,63 @@
 	#endif
 EOF
 	eval `$CC_FOR_BUILD -E $dummy.c 2>/dev/null | grep '^CPU'`
-	test x"${CPU}" != x && { echo "${CPU}-unknown-linux-gnu"; exit; }
+	test x"${CPU}" != x && { echo "${CPU}-unknown-linux-${LIBC}"; exit; }
 	;;
     or1k:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     or32:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     padre:Linux:*:*)
-	echo sparc-unknown-linux-gnu
+	echo sparc-unknown-linux-${LIBC}
 	exit ;;
     parisc64:Linux:*:* | hppa64:Linux:*:*)
-	echo hppa64-unknown-linux-gnu
+	echo hppa64-unknown-linux-${LIBC}
 	exit ;;
     parisc:Linux:*:* | hppa:Linux:*:*)
 	# Look for CPU level
 	case `grep '^cpu[^a-z]*:' /proc/cpuinfo 2>/dev/null | cut -d' ' -f2` in
-	  PA7*) echo hppa1.1-unknown-linux-gnu ;;
-	  PA8*) echo hppa2.0-unknown-linux-gnu ;;
-	  *)    echo hppa-unknown-linux-gnu ;;
+	  PA7*) echo hppa1.1-unknown-linux-${LIBC} ;;
+	  PA8*) echo hppa2.0-unknown-linux-${LIBC} ;;
+	  *)    echo hppa-unknown-linux-${LIBC} ;;
 	esac
 	exit ;;
     ppc64:Linux:*:*)
-	echo powerpc64-unknown-linux-gnu
+	echo powerpc64-unknown-linux-${LIBC}
 	exit ;;
     ppc:Linux:*:*)
-	echo powerpc-unknown-linux-gnu
+	echo powerpc-unknown-linux-${LIBC}
+	exit ;;
+    ppc64le:Linux:*:*)
+	echo powerpc64le-unknown-linux-${LIBC}
+	exit ;;
+    ppcle:Linux:*:*)
+	echo powerpcle-unknown-linux-${LIBC}
 	exit ;;
     s390:Linux:*:* | s390x:Linux:*:*)
-	echo ${UNAME_MACHINE}-ibm-linux
+	echo ${UNAME_MACHINE}-ibm-linux-${LIBC}
 	exit ;;
     sh64*:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     sh*:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     sparc:Linux:*:* | sparc64:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     tile*:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     vax:Linux:*:*)
-	echo ${UNAME_MACHINE}-dec-linux-gnu
+	echo ${UNAME_MACHINE}-dec-linux-${LIBC}
 	exit ;;
     x86_64:Linux:*:*)
-	LIBC=gnu
-	test -r /lib/libc.so && od -An -S13 /lib/libc.so | grep -q __uClibc_main && LIBC=uclibc
 	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     xtensa*:Linux:*:*)
-	echo ${UNAME_MACHINE}-unknown-linux-gnu
+	echo ${UNAME_MACHINE}-unknown-linux-${LIBC}
 	exit ;;
     i*86:DYNIX/ptx:4*:*)
 	# ptx 4.0 does uname -s correctly, with DYNIX/ptx in there.
@@ -1244,19 +1256,21 @@
 	exit ;;
     *:Darwin:*:*)
 	UNAME_PROCESSOR=`uname -p` || UNAME_PROCESSOR=unknown
-	case $UNAME_PROCESSOR in
-	    i386)
-		eval $set_cc_for_build
-		if [ "$CC_FOR_BUILD" != 'no_compiler_found' ]; then
-		  if (echo '#ifdef __LP64__'; echo IS_64BIT_ARCH; echo '#endif') | \
-		      (CCOPTS= $CC_FOR_BUILD -E - 2>/dev/null) | \
-		      grep IS_64BIT_ARCH >/dev/null
-		  then
-		      UNAME_PROCESSOR="x86_64"
-		  fi
-		fi ;;
-	    unknown) UNAME_PROCESSOR=powerpc ;;
-	esac
+	eval $set_cc_for_build
+	if test "$UNAME_PROCESSOR" = unknown ; then
+	    UNAME_PROCESSOR=powerpc
+	fi
+	if [ "$CC_FOR_BUILD" != 'no_compiler_found' ]; then
+	    if (echo '#ifdef __LP64__'; echo IS_64BIT_ARCH; echo '#endif') | \
+		(CCOPTS= $CC_FOR_BUILD -E - 2>/dev/null) | \
+		grep IS_64BIT_ARCH >/dev/null
+	    then
+		case $UNAME_PROCESSOR in
+		    i386) UNAME_PROCESSOR=x86_64 ;;
+		    powerpc) UNAME_PROCESSOR=powerpc64 ;;
+		esac
+	    fi
+	fi
 	echo ${UNAME_PROCESSOR}-apple-darwin${UNAME_RELEASE}
 	exit ;;
     *:procnto*:*:* | *:QNX:[0123456789]*:*)
diff -Nru gsl-doc-1.16/config.sub gsl-doc-2.3/config.sub
--- gsl-doc-1.16/config.sub	2013-07-18 16:30:00.000000000 +0000
+++ gsl-doc-2.3/config.sub	2015-12-03 18:34:33.000000000 +0000
@@ -1006,7 +1006,7 @@
 		;;
 	ppc64)	basic_machine=powerpc64-unknown
 		;;
-	ppc64-*) basic_machine=powerpc64-`echo $basic_machine | sed 's/^[^-]*-//'`
+	ppc64-* | ppc64p7-*) basic_machine=powerpc64-`echo $basic_machine | sed 's/^[^-]*-//'`
 		;;
 	ppc64le | powerpc64little | ppc64-le | powerpc64-little)
 		basic_machine=powerpc64le-unknown
diff -Nru gsl-doc-1.16/configure gsl-doc-2.3/configure
--- gsl-doc-1.16/configure	2013-07-19 15:14:51.000000000 +0000
+++ gsl-doc-2.3/configure	2016-12-09 00:04:19.000000000 +0000
@@ -1,6 +1,6 @@
 #! /bin/sh
 # Guess values for system-dependent variables and create Makefiles.
-# Generated by GNU Autoconf 2.69 for gsl 1.16.
+# Generated by GNU Autoconf 2.69 for gsl 2.3.
 #
 #
 # Copyright (C) 1992-1996, 1998-2012 Free Software Foundation, Inc.
@@ -587,8 +587,8 @@
 # Identity of this package.
 PACKAGE_NAME='gsl'
 PACKAGE_TARNAME='gsl'
-PACKAGE_VERSION='1.16'
-PACKAGE_STRING='gsl 1.16'
+PACKAGE_VERSION='2.3'
+PACKAGE_STRING='gsl 2.3'
 PACKAGE_BUGREPORT=''
 PACKAGE_URL=''
 
@@ -650,8 +650,9 @@
 HAVE_GNUM68K_IEEE_INTERFACE
 HAVE_GNUSPARC_IEEE_INTERFACE
 LIBOBJS
-MINGW32_HOST_FALSE
-MINGW32_HOST_TRUE
+GSL_LIBADD
+GSL_LDFLAGS
+GSLCBLAS_LDFLAGS
 GSL_LIBM
 GSL_LIBS
 GSL_CFLAGS
@@ -665,8 +666,6 @@
 RANLIB
 ac_ct_AR
 AR
-DLLTOOL
-OBJDUMP
 NM
 ac_ct_DUMPBIN
 DUMPBIN
@@ -675,6 +674,9 @@
 EGREP
 GREP
 LIBTOOL
+OBJDUMP
+DLLTOOL
+AS
 LN_S
 CPP
 am__fastdepCC_FALSE
@@ -1338,7 +1340,7 @@
   # Omit some internal or obsolete options to make the list less imposing.
   # This message is too long to be a string in the A/UX 3.1 sh.
   cat <<_ACEOF
-\`configure' configures gsl 1.16 to adapt to many kinds of systems.
+\`configure' configures gsl 2.3 to adapt to many kinds of systems.
 
 Usage: $0 [OPTION]... [VAR=VALUE]...
 
@@ -1408,7 +1410,7 @@
 
 if test -n "$ac_init_help"; then
   case $ac_init_help in
-     short | recursive ) echo "Configuration of gsl 1.16:";;
+     short | recursive ) echo "Configuration of gsl 2.3:";;
    esac
   cat <<\_ACEOF
 
@@ -1516,7 +1518,7 @@
 test -n "$ac_init_help" && exit $ac_status
 if $ac_init_version; then
   cat <<\_ACEOF
-gsl configure 1.16
+gsl configure 2.3
 generated by GNU Autoconf 2.69
 
 Copyright (C) 2012 Free Software Foundation, Inc.
@@ -1981,7 +1983,7 @@
 This file contains any messages produced by compilers while
 running configure, to aid debugging if configure makes a mistake.
 
-It was created by gsl $as_me 1.16, which was
+It was created by gsl $as_me 2.3, which was
 generated by GNU Autoconf 2.69.  Invocation command line was
 
   $ $0 $@
@@ -2846,7 +2848,7 @@
 
 # Define the identity of the package.
  PACKAGE='gsl'
- VERSION='1.16'
+ VERSION='2.3'
 
 
 cat >>confdefs.h <<_ACEOF
@@ -2924,9 +2926,9 @@
 
 
 
-GSL_CURRENT=17
+GSL_CURRENT=22
 GSL_REVISION=0
-GSL_AGE=17
+GSL_AGE=3
 CBLAS_CURRENT=0
 CBLAS_REVISION=0
 CBLAS_AGE=0
@@ -5380,9 +5382,6 @@
 
 
 
-
-
-
 { $as_echo "$as_me:${as_lineno-$LINENO}: checking how to recognize dependent libraries" >&5
 $as_echo_n "checking how to recognize dependent libraries... " >&6; }
 if ${lt_cv_deplibs_check_method+:} false; then :
@@ -5727,9 +5726,6 @@
 
 
 
-
-
-
 { $as_echo "$as_me:${as_lineno-$LINENO}: checking how to associate runtime and link libraries" >&5
 $as_echo_n "checking how to associate runtime and link libraries... " >&6; }
 if ${lt_cv_sharedlib_from_linklib_cmd+:} false; then :
@@ -7620,13 +7616,311 @@
 
 
 # Set options
+enable_win32_dll=yes
 
+case $host in
+*-*-cygwin* | *-*-mingw* | *-*-pw32* | *-*-cegcc*)
+  if test -n "$ac_tool_prefix"; then
+  # Extract the first word of "${ac_tool_prefix}as", so it can be a program name with args.
+set dummy ${ac_tool_prefix}as; ac_word=$2
+{ $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5
+$as_echo_n "checking for $ac_word... " >&6; }
+if ${ac_cv_prog_AS+:} false; then :
+  $as_echo_n "(cached) " >&6
+else
+  if test -n "$AS"; then
+  ac_cv_prog_AS="$AS" # Let the user override the test.
+else
+as_save_IFS=$IFS; IFS=$PATH_SEPARATOR
+for as_dir in $PATH
+do
+  IFS=$as_save_IFS
+  test -z "$as_dir" && as_dir=.
+    for ac_exec_ext in '' $ac_executable_extensions; do
+  if as_fn_executable_p "$as_dir/$ac_word$ac_exec_ext"; then
+    ac_cv_prog_AS="${ac_tool_prefix}as"
+    $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5
+    break 2
+  fi
+done
+  done
+IFS=$as_save_IFS
 
+fi
+fi
+AS=$ac_cv_prog_AS
+if test -n "$AS"; then
+  { $as_echo "$as_me:${as_lineno-$LINENO}: result: $AS" >&5
+$as_echo "$AS" >&6; }
+else
+  { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5
+$as_echo "no" >&6; }
+fi
 
-        enable_dlopen=no
+
+fi
+if test -z "$ac_cv_prog_AS"; then
+  ac_ct_AS=$AS
+  # Extract the first word of "as", so it can be a program name with args.
+set dummy as; ac_word=$2
+{ $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5
+$as_echo_n "checking for $ac_word... " >&6; }
+if ${ac_cv_prog_ac_ct_AS+:} false; then :
+  $as_echo_n "(cached) " >&6
+else
+  if test -n "$ac_ct_AS"; then
+  ac_cv_prog_ac_ct_AS="$ac_ct_AS" # Let the user override the test.
+else
+as_save_IFS=$IFS; IFS=$PATH_SEPARATOR
+for as_dir in $PATH
+do
+  IFS=$as_save_IFS
+  test -z "$as_dir" && as_dir=.
+    for ac_exec_ext in '' $ac_executable_extensions; do
+  if as_fn_executable_p "$as_dir/$ac_word$ac_exec_ext"; then
+    ac_cv_prog_ac_ct_AS="as"
+    $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5
+    break 2
+  fi
+done
+  done
+IFS=$as_save_IFS
+
+fi
+fi
+ac_ct_AS=$ac_cv_prog_ac_ct_AS
+if test -n "$ac_ct_AS"; then
+  { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_ct_AS" >&5
+$as_echo "$ac_ct_AS" >&6; }
+else
+  { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5
+$as_echo "no" >&6; }
+fi
+
+  if test "x$ac_ct_AS" = x; then
+    AS="false"
+  else
+    case $cross_compiling:$ac_tool_warned in
+yes:)
+{ $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: using cross tools not prefixed with host triplet" >&5
+$as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;}
+ac_tool_warned=yes ;;
+esac
+    AS=$ac_ct_AS
+  fi
+else
+  AS="$ac_cv_prog_AS"
+fi
+
+  if test -n "$ac_tool_prefix"; then
+  # Extract the first word of "${ac_tool_prefix}dlltool", so it can be a program name with args.
+set dummy ${ac_tool_prefix}dlltool; ac_word=$2
+{ $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5
+$as_echo_n "checking for $ac_word... " >&6; }
+if ${ac_cv_prog_DLLTOOL+:} false; then :
+  $as_echo_n "(cached) " >&6
+else
+  if test -n "$DLLTOOL"; then
+  ac_cv_prog_DLLTOOL="$DLLTOOL" # Let the user override the test.
+else
+as_save_IFS=$IFS; IFS=$PATH_SEPARATOR
+for as_dir in $PATH
+do
+  IFS=$as_save_IFS
+  test -z "$as_dir" && as_dir=.
+    for ac_exec_ext in '' $ac_executable_extensions; do
+  if as_fn_executable_p "$as_dir/$ac_word$ac_exec_ext"; then
+    ac_cv_prog_DLLTOOL="${ac_tool_prefix}dlltool"
+    $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5
+    break 2
+  fi
+done
+  done
+IFS=$as_save_IFS
+
+fi
+fi
+DLLTOOL=$ac_cv_prog_DLLTOOL
+if test -n "$DLLTOOL"; then
+  { $as_echo "$as_me:${as_lineno-$LINENO}: result: $DLLTOOL" >&5
+$as_echo "$DLLTOOL" >&6; }
+else
+  { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5
+$as_echo "no" >&6; }
+fi
+
+
+fi
+if test -z "$ac_cv_prog_DLLTOOL"; then
+  ac_ct_DLLTOOL=$DLLTOOL
+  # Extract the first word of "dlltool", so it can be a program name with args.
+set dummy dlltool; ac_word=$2
+{ $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5
+$as_echo_n "checking for $ac_word... " >&6; }
+if ${ac_cv_prog_ac_ct_DLLTOOL+:} false; then :
+  $as_echo_n "(cached) " >&6
+else
+  if test -n "$ac_ct_DLLTOOL"; then
+  ac_cv_prog_ac_ct_DLLTOOL="$ac_ct_DLLTOOL" # Let the user override the test.
+else
+as_save_IFS=$IFS; IFS=$PATH_SEPARATOR
+for as_dir in $PATH
+do
+  IFS=$as_save_IFS
+  test -z "$as_dir" && as_dir=.
+    for ac_exec_ext in '' $ac_executable_extensions; do
+  if as_fn_executable_p "$as_dir/$ac_word$ac_exec_ext"; then
+    ac_cv_prog_ac_ct_DLLTOOL="dlltool"
+    $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5
+    break 2
+  fi
+done
+  done
+IFS=$as_save_IFS
+
+fi
+fi
+ac_ct_DLLTOOL=$ac_cv_prog_ac_ct_DLLTOOL
+if test -n "$ac_ct_DLLTOOL"; then
+  { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_ct_DLLTOOL" >&5
+$as_echo "$ac_ct_DLLTOOL" >&6; }
+else
+  { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5
+$as_echo "no" >&6; }
+fi
+
+  if test "x$ac_ct_DLLTOOL" = x; then
+    DLLTOOL="false"
+  else
+    case $cross_compiling:$ac_tool_warned in
+yes:)
+{ $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: using cross tools not prefixed with host triplet" >&5
+$as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;}
+ac_tool_warned=yes ;;
+esac
+    DLLTOOL=$ac_ct_DLLTOOL
+  fi
+else
+  DLLTOOL="$ac_cv_prog_DLLTOOL"
+fi
+
+  if test -n "$ac_tool_prefix"; then
+  # Extract the first word of "${ac_tool_prefix}objdump", so it can be a program name with args.
+set dummy ${ac_tool_prefix}objdump; ac_word=$2
+{ $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5
+$as_echo_n "checking for $ac_word... " >&6; }
+if ${ac_cv_prog_OBJDUMP+:} false; then :
+  $as_echo_n "(cached) " >&6
+else
+  if test -n "$OBJDUMP"; then
+  ac_cv_prog_OBJDUMP="$OBJDUMP" # Let the user override the test.
+else
+as_save_IFS=$IFS; IFS=$PATH_SEPARATOR
+for as_dir in $PATH
+do
+  IFS=$as_save_IFS
+  test -z "$as_dir" && as_dir=.
+    for ac_exec_ext in '' $ac_executable_extensions; do
+  if as_fn_executable_p "$as_dir/$ac_word$ac_exec_ext"; then
+    ac_cv_prog_OBJDUMP="${ac_tool_prefix}objdump"
+    $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5
+    break 2
+  fi
+done
+  done
+IFS=$as_save_IFS
+
+fi
+fi
+OBJDUMP=$ac_cv_prog_OBJDUMP
+if test -n "$OBJDUMP"; then
+  { $as_echo "$as_me:${as_lineno-$LINENO}: result: $OBJDUMP" >&5
+$as_echo "$OBJDUMP" >&6; }
+else
+  { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5
+$as_echo "no" >&6; }
+fi
+
+
+fi
+if test -z "$ac_cv_prog_OBJDUMP"; then
+  ac_ct_OBJDUMP=$OBJDUMP
+  # Extract the first word of "objdump", so it can be a program name with args.
+set dummy objdump; ac_word=$2
+{ $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5
+$as_echo_n "checking for $ac_word... " >&6; }
+if ${ac_cv_prog_ac_ct_OBJDUMP+:} false; then :
+  $as_echo_n "(cached) " >&6
+else
+  if test -n "$ac_ct_OBJDUMP"; then
+  ac_cv_prog_ac_ct_OBJDUMP="$ac_ct_OBJDUMP" # Let the user override the test.
+else
+as_save_IFS=$IFS; IFS=$PATH_SEPARATOR
+for as_dir in $PATH
+do
+  IFS=$as_save_IFS
+  test -z "$as_dir" && as_dir=.
+    for ac_exec_ext in '' $ac_executable_extensions; do
+  if as_fn_executable_p "$as_dir/$ac_word$ac_exec_ext"; then
+    ac_cv_prog_ac_ct_OBJDUMP="objdump"
+    $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5
+    break 2
+  fi
+done
+  done
+IFS=$as_save_IFS
+
+fi
+fi
+ac_ct_OBJDUMP=$ac_cv_prog_ac_ct_OBJDUMP
+if test -n "$ac_ct_OBJDUMP"; then
+  { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_ct_OBJDUMP" >&5
+$as_echo "$ac_ct_OBJDUMP" >&6; }
+else
+  { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5
+$as_echo "no" >&6; }
+fi
+
+  if test "x$ac_ct_OBJDUMP" = x; then
+    OBJDUMP="false"
+  else
+    case $cross_compiling:$ac_tool_warned in
+yes:)
+{ $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: using cross tools not prefixed with host triplet" >&5
+$as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;}
+ac_tool_warned=yes ;;
+esac
+    OBJDUMP=$ac_ct_OBJDUMP
+  fi
+else
+  OBJDUMP="$ac_cv_prog_OBJDUMP"
+fi
+
+  ;;
+esac
+
+test -z "$AS" && AS=as
+
+
+
+
+
+test -z "$DLLTOOL" && DLLTOOL=dlltool
 
 
-  enable_win32_dll=no
+
+
+
+test -z "$OBJDUMP" && OBJDUMP=objdump
+
+
+
+
+
+
+
+        enable_dlopen=no
+
 
 
             # Check whether --enable-shared was given.
@@ -10634,10 +10928,14 @@
   # before this can be enabled.
   hardcode_into_libs=yes
 
+  # Add ABI-specific directories to the system library path.
+  sys_lib_dlsearch_path_spec="/lib64 /usr/lib64 /lib /usr/lib"
+
   # Append ld.so.conf contents to the search path
   if test -f /etc/ld.so.conf; then
     lt_ld_extra=`awk '/^include / { system(sprintf("cd /etc; cat %s 2>/dev/null", \$2)); skip = 1; } { if (!skip) print \$0; skip = 0; }' < /etc/ld.so.conf | $SED -e 's/#.*//;/^[	 ]*hwcap[	 ]/d;s/[:,	]/ /g;s/=[^=]*$//;s/=[^= ]* / /g;s/"//g;/^$/d' | tr '\n' ' '`
-    sys_lib_dlsearch_path_spec="/lib /usr/lib $lt_ld_extra"
+    sys_lib_dlsearch_path_spec="$sys_lib_dlsearch_path_spec $lt_ld_extra"
+
   fi
 
   # We used to test for /lib/ld.so.1 and disable shared libraries on
@@ -11984,19 +12282,18 @@
 
 
 
-case "$host_os" in
-     *mingw*)
-	MINGW=true
-	;;
+case $host in
+  *-*-cygwin* | *-*-mingw* )
+  if test "$enable_shared" = yes; then
+    GSLCBLAS_LDFLAGS="$GSLCBLAS_LDFLAGS -no-undefined"
+    GSL_LDFLAGS="$GSL_LDFLAGS -no-undefined"
+    GSL_LIBADD="cblas/libgslcblas.la"
+  fi
+  ;;
 esac
 
- if test "$MINGW" = "true"; then
-  MINGW32_HOST_TRUE=
-  MINGW32_HOST_FALSE='#'
-else
-  MINGW32_HOST_TRUE='#'
-  MINGW32_HOST_FALSE=
-fi
+
+
 
 
 
@@ -12788,7 +13085,8 @@
 
 
 
-ac_config_files="$ac_config_files gsl_version.h gsl.spec gsl/Makefile test/Makefile err/Makefile sys/Makefile utils/Makefile const/Makefile min/Makefile multimin/Makefile ieee-utils/Makefile fft/Makefile specfunc/Makefile dht/Makefile fit/Makefile multifit/Makefile bspline/Makefile statistics/Makefile sum/Makefile roots/Makefile multiroots/Makefile ntuple/Makefile poly/Makefile qrng/Makefile rng/Makefile randist/Makefile siman/Makefile integration/Makefile interpolation/Makefile doc/Makefile block/Makefile vector/Makefile matrix/Makefile histogram/Makefile monte/Makefile ode-initval/Makefile ode-initval2/Makefile cblas/Makefile blas/Makefile linalg/Makefile eigen/Makefile permutation/Makefile combination/Makefile multiset/Makefile sort/Makefile complex/Makefile diff/Makefile deriv/Makefile cheb/Makefile cdf/Makefile wavelet/Makefile Makefile"
+ac_config_files="$ac_config_files Makefile gsl_version.h gsl.spec blas/Makefile block/Makefile bspline/Makefile cblas/Makefile cdf/Makefile cheb/Makefile combination/Makefile complex/Makefile const/Makefile deriv/Makefile dht/Makefile diff/Makefile doc/Makefile doc/examples/Makefile eigen/Makefile err/Makefile fit/Makefile fft/Makefile gsl/Makefile histogram/Makefile ieee-utils/Makefile integration/Makefile interpolation/Makefile linalg/Makefile matrix/Makefile min/Makefile monte/Makefile multifit/Makefile multifit_nlinear/Makefile multilarge/Makefile multilarge_nlinear/Makefile multimin/Makefile multiroots/Makefile multiset/Makefile ntuple/Makefile ode-initval/Makefile ode-initval2/Makefile permutation/Makefile poly/Makefile qrng/Makefile randist/Makefile rng/Makefile roots/Makefile rstat/Makefile siman/Makefile sort/Makefile spblas/Makefile splinalg/Makefile spmatrix/Makefile specfunc/Makefile statistics/Makefile sum/Makefile sys/Makefile test/Makefile utils/Makefile vector/Makefile wavelet/Makefile"
+
 
 cat >confcache <<\_ACEOF
 # This file is a shell script that caches the results of configure
@@ -12927,10 +13225,6 @@
   as_fn_error $? "conditional \"am__fastdepCC\" was never defined.
 Usually this means the macro was only invoked conditionally." "$LINENO" 5
 fi
-if test -z "${MINGW32_HOST_TRUE}" && test -z "${MINGW32_HOST_FALSE}"; then
-  as_fn_error $? "conditional \"MINGW32_HOST\" was never defined.
-Usually this means the macro was only invoked conditionally." "$LINENO" 5
-fi
 
 : "${CONFIG_STATUS=./config.status}"
 ac_write_fail=0
@@ -13328,7 +13622,7 @@
 # report actual input values of CONFIG_FILES etc. instead of their
 # values after options handling.
 ac_log="
-This file was extended by gsl $as_me 1.16, which was
+This file was extended by gsl $as_me 2.3, which was
 generated by GNU Autoconf 2.69.  Invocation command line was
 
   CONFIG_FILES    = $CONFIG_FILES
@@ -13394,7 +13688,7 @@
 cat >>$CONFIG_STATUS <<_ACEOF || ac_write_fail=1
 ac_cs_config="`$as_echo "$ac_configure_args" | sed 's/^ //; s/[\\""\`\$]/\\\\&/g'`"
 ac_cs_version="\\
-gsl config.status 1.16
+gsl config.status 2.3
 configured by $0, generated by GNU Autoconf 2.69,
   with options \\"\$ac_cs_config\\"
 
@@ -13525,6 +13819,9 @@
 delay_variable_subst='$delay_variable_subst'
 macro_version='`$ECHO "$macro_version" | $SED "$delay_single_quote_subst"`'
 macro_revision='`$ECHO "$macro_revision" | $SED "$delay_single_quote_subst"`'
+AS='`$ECHO "$AS" | $SED "$delay_single_quote_subst"`'
+DLLTOOL='`$ECHO "$DLLTOOL" | $SED "$delay_single_quote_subst"`'
+OBJDUMP='`$ECHO "$OBJDUMP" | $SED "$delay_single_quote_subst"`'
 enable_shared='`$ECHO "$enable_shared" | $SED "$delay_single_quote_subst"`'
 enable_static='`$ECHO "$enable_static" | $SED "$delay_single_quote_subst"`'
 pic_mode='`$ECHO "$pic_mode" | $SED "$delay_single_quote_subst"`'
@@ -13556,12 +13853,10 @@
 lt_cv_to_tool_file_cmd='`$ECHO "$lt_cv_to_tool_file_cmd" | $SED "$delay_single_quote_subst"`'
 reload_flag='`$ECHO "$reload_flag" | $SED "$delay_single_quote_subst"`'
 reload_cmds='`$ECHO "$reload_cmds" | $SED "$delay_single_quote_subst"`'
-OBJDUMP='`$ECHO "$OBJDUMP" | $SED "$delay_single_quote_subst"`'
 deplibs_check_method='`$ECHO "$deplibs_check_method" | $SED "$delay_single_quote_subst"`'
 file_magic_cmd='`$ECHO "$file_magic_cmd" | $SED "$delay_single_quote_subst"`'
 file_magic_glob='`$ECHO "$file_magic_glob" | $SED "$delay_single_quote_subst"`'
 want_nocaseglob='`$ECHO "$want_nocaseglob" | $SED "$delay_single_quote_subst"`'
-DLLTOOL='`$ECHO "$DLLTOOL" | $SED "$delay_single_quote_subst"`'
 sharedlib_from_linklib_cmd='`$ECHO "$sharedlib_from_linklib_cmd" | $SED "$delay_single_quote_subst"`'
 AR='`$ECHO "$AR" | $SED "$delay_single_quote_subst"`'
 AR_FLAGS='`$ECHO "$AR_FLAGS" | $SED "$delay_single_quote_subst"`'
@@ -13667,7 +13962,10 @@
 }
 
 # Quote evaled strings.
-for var in SHELL \
+for var in AS \
+DLLTOOL \
+OBJDUMP \
+SHELL \
 ECHO \
 PATH_SEPARATOR \
 SED \
@@ -13680,12 +13978,10 @@
 lt_SP2NL \
 lt_NL2SP \
 reload_flag \
-OBJDUMP \
 deplibs_check_method \
 file_magic_cmd \
 file_magic_glob \
 want_nocaseglob \
-DLLTOOL \
 sharedlib_from_linklib_cmd \
 AR \
 AR_FLAGS \
@@ -13803,58 +14099,66 @@
     "config.h") CONFIG_HEADERS="$CONFIG_HEADERS config.h" ;;
     "depfiles") CONFIG_COMMANDS="$CONFIG_COMMANDS depfiles" ;;
     "libtool") CONFIG_COMMANDS="$CONFIG_COMMANDS libtool" ;;
+    "Makefile") CONFIG_FILES="$CONFIG_FILES Makefile" ;;
     "gsl_version.h") CONFIG_FILES="$CONFIG_FILES gsl_version.h" ;;
     "gsl.spec") CONFIG_FILES="$CONFIG_FILES gsl.spec" ;;
-    "gsl/Makefile") CONFIG_FILES="$CONFIG_FILES gsl/Makefile" ;;
-    "test/Makefile") CONFIG_FILES="$CONFIG_FILES test/Makefile" ;;
-    "err/Makefile") CONFIG_FILES="$CONFIG_FILES err/Makefile" ;;
-    "sys/Makefile") CONFIG_FILES="$CONFIG_FILES sys/Makefile" ;;
-    "utils/Makefile") CONFIG_FILES="$CONFIG_FILES utils/Makefile" ;;
+    "blas/Makefile") CONFIG_FILES="$CONFIG_FILES blas/Makefile" ;;
+    "block/Makefile") CONFIG_FILES="$CONFIG_FILES block/Makefile" ;;
+    "bspline/Makefile") CONFIG_FILES="$CONFIG_FILES bspline/Makefile" ;;
+    "cblas/Makefile") CONFIG_FILES="$CONFIG_FILES cblas/Makefile" ;;
+    "cdf/Makefile") CONFIG_FILES="$CONFIG_FILES cdf/Makefile" ;;
+    "cheb/Makefile") CONFIG_FILES="$CONFIG_FILES cheb/Makefile" ;;
+    "combination/Makefile") CONFIG_FILES="$CONFIG_FILES combination/Makefile" ;;
+    "complex/Makefile") CONFIG_FILES="$CONFIG_FILES complex/Makefile" ;;
     "const/Makefile") CONFIG_FILES="$CONFIG_FILES const/Makefile" ;;
-    "min/Makefile") CONFIG_FILES="$CONFIG_FILES min/Makefile" ;;
-    "multimin/Makefile") CONFIG_FILES="$CONFIG_FILES multimin/Makefile" ;;
-    "ieee-utils/Makefile") CONFIG_FILES="$CONFIG_FILES ieee-utils/Makefile" ;;
-    "fft/Makefile") CONFIG_FILES="$CONFIG_FILES fft/Makefile" ;;
-    "specfunc/Makefile") CONFIG_FILES="$CONFIG_FILES specfunc/Makefile" ;;
+    "deriv/Makefile") CONFIG_FILES="$CONFIG_FILES deriv/Makefile" ;;
     "dht/Makefile") CONFIG_FILES="$CONFIG_FILES dht/Makefile" ;;
+    "diff/Makefile") CONFIG_FILES="$CONFIG_FILES diff/Makefile" ;;
+    "doc/Makefile") CONFIG_FILES="$CONFIG_FILES doc/Makefile" ;;
+    "doc/examples/Makefile") CONFIG_FILES="$CONFIG_FILES doc/examples/Makefile" ;;
+    "eigen/Makefile") CONFIG_FILES="$CONFIG_FILES eigen/Makefile" ;;
+    "err/Makefile") CONFIG_FILES="$CONFIG_FILES err/Makefile" ;;
     "fit/Makefile") CONFIG_FILES="$CONFIG_FILES fit/Makefile" ;;
-    "multifit/Makefile") CONFIG_FILES="$CONFIG_FILES multifit/Makefile" ;;
-    "bspline/Makefile") CONFIG_FILES="$CONFIG_FILES bspline/Makefile" ;;
-    "statistics/Makefile") CONFIG_FILES="$CONFIG_FILES statistics/Makefile" ;;
-    "sum/Makefile") CONFIG_FILES="$CONFIG_FILES sum/Makefile" ;;
-    "roots/Makefile") CONFIG_FILES="$CONFIG_FILES roots/Makefile" ;;
-    "multiroots/Makefile") CONFIG_FILES="$CONFIG_FILES multiroots/Makefile" ;;
-    "ntuple/Makefile") CONFIG_FILES="$CONFIG_FILES ntuple/Makefile" ;;
-    "poly/Makefile") CONFIG_FILES="$CONFIG_FILES poly/Makefile" ;;
-    "qrng/Makefile") CONFIG_FILES="$CONFIG_FILES qrng/Makefile" ;;
-    "rng/Makefile") CONFIG_FILES="$CONFIG_FILES rng/Makefile" ;;
-    "randist/Makefile") CONFIG_FILES="$CONFIG_FILES randist/Makefile" ;;
-    "siman/Makefile") CONFIG_FILES="$CONFIG_FILES siman/Makefile" ;;
+    "fft/Makefile") CONFIG_FILES="$CONFIG_FILES fft/Makefile" ;;
+    "gsl/Makefile") CONFIG_FILES="$CONFIG_FILES gsl/Makefile" ;;
+    "histogram/Makefile") CONFIG_FILES="$CONFIG_FILES histogram/Makefile" ;;
+    "ieee-utils/Makefile") CONFIG_FILES="$CONFIG_FILES ieee-utils/Makefile" ;;
     "integration/Makefile") CONFIG_FILES="$CONFIG_FILES integration/Makefile" ;;
     "interpolation/Makefile") CONFIG_FILES="$CONFIG_FILES interpolation/Makefile" ;;
-    "doc/Makefile") CONFIG_FILES="$CONFIG_FILES doc/Makefile" ;;
-    "block/Makefile") CONFIG_FILES="$CONFIG_FILES block/Makefile" ;;
-    "vector/Makefile") CONFIG_FILES="$CONFIG_FILES vector/Makefile" ;;
+    "linalg/Makefile") CONFIG_FILES="$CONFIG_FILES linalg/Makefile" ;;
     "matrix/Makefile") CONFIG_FILES="$CONFIG_FILES matrix/Makefile" ;;
-    "histogram/Makefile") CONFIG_FILES="$CONFIG_FILES histogram/Makefile" ;;
+    "min/Makefile") CONFIG_FILES="$CONFIG_FILES min/Makefile" ;;
     "monte/Makefile") CONFIG_FILES="$CONFIG_FILES monte/Makefile" ;;
+    "multifit/Makefile") CONFIG_FILES="$CONFIG_FILES multifit/Makefile" ;;
+    "multifit_nlinear/Makefile") CONFIG_FILES="$CONFIG_FILES multifit_nlinear/Makefile" ;;
+    "multilarge/Makefile") CONFIG_FILES="$CONFIG_FILES multilarge/Makefile" ;;
+    "multilarge_nlinear/Makefile") CONFIG_FILES="$CONFIG_FILES multilarge_nlinear/Makefile" ;;
+    "multimin/Makefile") CONFIG_FILES="$CONFIG_FILES multimin/Makefile" ;;
+    "multiroots/Makefile") CONFIG_FILES="$CONFIG_FILES multiroots/Makefile" ;;
+    "multiset/Makefile") CONFIG_FILES="$CONFIG_FILES multiset/Makefile" ;;
+    "ntuple/Makefile") CONFIG_FILES="$CONFIG_FILES ntuple/Makefile" ;;
     "ode-initval/Makefile") CONFIG_FILES="$CONFIG_FILES ode-initval/Makefile" ;;
     "ode-initval2/Makefile") CONFIG_FILES="$CONFIG_FILES ode-initval2/Makefile" ;;
-    "cblas/Makefile") CONFIG_FILES="$CONFIG_FILES cblas/Makefile" ;;
-    "blas/Makefile") CONFIG_FILES="$CONFIG_FILES blas/Makefile" ;;
-    "linalg/Makefile") CONFIG_FILES="$CONFIG_FILES linalg/Makefile" ;;
-    "eigen/Makefile") CONFIG_FILES="$CONFIG_FILES eigen/Makefile" ;;
     "permutation/Makefile") CONFIG_FILES="$CONFIG_FILES permutation/Makefile" ;;
-    "combination/Makefile") CONFIG_FILES="$CONFIG_FILES combination/Makefile" ;;
-    "multiset/Makefile") CONFIG_FILES="$CONFIG_FILES multiset/Makefile" ;;
+    "poly/Makefile") CONFIG_FILES="$CONFIG_FILES poly/Makefile" ;;
+    "qrng/Makefile") CONFIG_FILES="$CONFIG_FILES qrng/Makefile" ;;
+    "randist/Makefile") CONFIG_FILES="$CONFIG_FILES randist/Makefile" ;;
+    "rng/Makefile") CONFIG_FILES="$CONFIG_FILES rng/Makefile" ;;
+    "roots/Makefile") CONFIG_FILES="$CONFIG_FILES roots/Makefile" ;;
+    "rstat/Makefile") CONFIG_FILES="$CONFIG_FILES rstat/Makefile" ;;
+    "siman/Makefile") CONFIG_FILES="$CONFIG_FILES siman/Makefile" ;;
     "sort/Makefile") CONFIG_FILES="$CONFIG_FILES sort/Makefile" ;;
-    "complex/Makefile") CONFIG_FILES="$CONFIG_FILES complex/Makefile" ;;
-    "diff/Makefile") CONFIG_FILES="$CONFIG_FILES diff/Makefile" ;;
-    "deriv/Makefile") CONFIG_FILES="$CONFIG_FILES deriv/Makefile" ;;
-    "cheb/Makefile") CONFIG_FILES="$CONFIG_FILES cheb/Makefile" ;;
-    "cdf/Makefile") CONFIG_FILES="$CONFIG_FILES cdf/Makefile" ;;
+    "spblas/Makefile") CONFIG_FILES="$CONFIG_FILES spblas/Makefile" ;;
+    "splinalg/Makefile") CONFIG_FILES="$CONFIG_FILES splinalg/Makefile" ;;
+    "spmatrix/Makefile") CONFIG_FILES="$CONFIG_FILES spmatrix/Makefile" ;;
+    "specfunc/Makefile") CONFIG_FILES="$CONFIG_FILES specfunc/Makefile" ;;
+    "statistics/Makefile") CONFIG_FILES="$CONFIG_FILES statistics/Makefile" ;;
+    "sum/Makefile") CONFIG_FILES="$CONFIG_FILES sum/Makefile" ;;
+    "sys/Makefile") CONFIG_FILES="$CONFIG_FILES sys/Makefile" ;;
+    "test/Makefile") CONFIG_FILES="$CONFIG_FILES test/Makefile" ;;
+    "utils/Makefile") CONFIG_FILES="$CONFIG_FILES utils/Makefile" ;;
+    "vector/Makefile") CONFIG_FILES="$CONFIG_FILES vector/Makefile" ;;
     "wavelet/Makefile") CONFIG_FILES="$CONFIG_FILES wavelet/Makefile" ;;
-    "Makefile") CONFIG_FILES="$CONFIG_FILES Makefile" ;;
 
   *) as_fn_error $? "invalid argument: \`$ac_config_target'" "$LINENO" 5;;
   esac
@@ -14601,6 +14905,15 @@
 macro_version=$macro_version
 macro_revision=$macro_revision
 
+# Assembler program.
+AS=$lt_AS
+
+# DLL creation program.
+DLLTOOL=$lt_DLLTOOL
+
+# Object dumper program.
+OBJDUMP=$lt_OBJDUMP
+
 # Whether or not to build shared libraries.
 build_libtool_libs=$enable_shared
 
@@ -14677,9 +14990,6 @@
 # convert \$build files to toolchain format.
 to_tool_file_cmd=$lt_cv_to_tool_file_cmd
 
-# An object symbol dumper.
-OBJDUMP=$lt_OBJDUMP
-
 # Method to check whether dependent libraries are shared objects.
 deplibs_check_method=$lt_deplibs_check_method
 
@@ -14692,9 +15002,6 @@
 # Find potential files using nocaseglob when deplibs_check_method = "file_magic".
 want_nocaseglob=$lt_want_nocaseglob
 
-# DLL creation program.
-DLLTOOL=$lt_DLLTOOL
-
 # Command to associate shared and link libraries.
 sharedlib_from_linklib_cmd=$lt_sharedlib_from_linklib_cmd
 
diff -Nru gsl-doc-1.16/configure.ac gsl-doc-2.3/configure.ac
--- gsl-doc-1.16/configure.ac	2013-07-19 15:14:45.000000000 +0000
+++ gsl-doc-2.3/configure.ac	2016-12-09 00:04:13.000000000 +0000
@@ -1,6 +1,6 @@
 dnl Process this file with autoconf to produce a configure script.
 
-AC_INIT([gsl],[1.16])
+AC_INIT([gsl],[2.3])
 AC_CONFIG_SRCDIR(gsl_math.h)
 
 AM_INIT_AUTOMAKE([gnu])
@@ -28,6 +28,11 @@
 dnl gsl-1.14   libgsl 15:0:15  libgslcblas 0:0:0 
 dnl gsl-1.15   libgsl 16:0:16  libgslcblas 0:0:0 
 dnl gsl-1.16   libgsl 17:0:17  libgslcblas 0:0:0 
+dnl gsl-2.0    libgsl 18:0:18  (**) libgslcblas 0:0:0 
+dnl gsl-2.1    libgsl 19:0:0   libgslcblas 0:0:0 
+dnl gsl-2.2    libgsl 20:0:1   libgslcblas 0:0:0 
+dnl gsl-2.2.1  libgsl 21:0:2   libgslcblas 0:0:0 
+dnl gsl-2.3    libgsl 22:0:3   libgslcblas 0:0:0 
 dnl 
 dnl (*) There was an error on this release.  Firstly, the versioning
 dnl numbers were not updated.  Secondly, 2 functions were removed, but
@@ -35,6 +40,9 @@
 dnl functions were not documented and are regarded as internal, so we
 dnl will assume 11:0:11.
 dnl
+dnl (**) There was an error on this release. Age should have been
+dnl reset to 18:0:0
+dnl
 dnl How to update library version number
 dnl ====================================
 dnl 
@@ -46,11 +54,14 @@
 dnl A: increment if any interfaces have been added; set to 0 if any
 dnl interfaces have been removed. removal has precedence over adding,
 dnl so set to 0 if both happened.
+dnl
+dnl See https://www.gnu.org/software/libtool/manual/html_node/Updating-version-info.html
+dnl for more detailed info
 
 dnl
-GSL_CURRENT=17
+GSL_CURRENT=22
 GSL_REVISION=0
-GSL_AGE=17
+GSL_AGE=3
 dnl
 CBLAS_CURRENT=0
 CBLAS_REVISION=0
@@ -92,7 +103,7 @@
 AC_PROG_CPP
 AC_PROG_INSTALL
 AC_PROG_LN_S
-AC_PROG_LIBTOOL
+LT_INIT([win32-dll])
 
 dnl Check compiler features
 AC_TYPE_SIZE_T
@@ -104,7 +115,7 @@
 GSL_CFLAGS="-I$includedir"
 GSL_LIBS="-L$libdir -lgsl"
 dnl macro from libtool - can be replaced with LT_LIB_M when we require libtool 2
-AC_CHECK_LIBM
+LT_LIB_M
 GSL_LIBM=$LIBM
 
 AC_SUBST(GSL_CFLAGS)
@@ -148,13 +159,19 @@
 
 dnl Checks for typedefs, structures, and compiler characteristics.
 
-case "$host_os" in
-     *mingw*)
-	MINGW=true
-	;;
+case $host in
+  *-*-cygwin* | *-*-mingw* )
+  if test "$enable_shared" = yes; then
+    GSLCBLAS_LDFLAGS="$GSLCBLAS_LDFLAGS -no-undefined"
+    GSL_LDFLAGS="$GSL_LDFLAGS -no-undefined"
+    GSL_LIBADD="cblas/libgslcblas.la"
+  fi
+  ;;
 esac
 
-AM_CONDITIONAL(MINGW32_HOST, test "$MINGW" = "true")
+AC_SUBST(GSLCBLAS_LDFLAGS)
+AC_SUBST(GSL_LDFLAGS)
+AC_SUBST(GSL_LIBADD)
 
 dnl Checks for library functions.
 
@@ -564,5 +581,67 @@
 #define GSL_DISABLE_DEPRECATED 1])
 
 dnl
-AC_CONFIG_FILES([gsl_version.h gsl.spec gsl/Makefile test/Makefile err/Makefile sys/Makefile utils/Makefile const/Makefile min/Makefile multimin/Makefile ieee-utils/Makefile fft/Makefile specfunc/Makefile dht/Makefile fit/Makefile multifit/Makefile bspline/Makefile statistics/Makefile sum/Makefile roots/Makefile multiroots/Makefile ntuple/Makefile poly/Makefile qrng/Makefile rng/Makefile randist/Makefile siman/Makefile integration/Makefile interpolation/Makefile doc/Makefile block/Makefile vector/Makefile matrix/Makefile histogram/Makefile monte/Makefile ode-initval/Makefile ode-initval2/Makefile cblas/Makefile blas/Makefile linalg/Makefile eigen/Makefile permutation/Makefile combination/Makefile multiset/Makefile sort/Makefile complex/Makefile diff/Makefile deriv/Makefile cheb/Makefile cdf/Makefile wavelet/Makefile Makefile])
+AC_CONFIG_FILES([            \
+Makefile                     \
+gsl_version.h                \
+gsl.spec                     \
+blas/Makefile                \
+block/Makefile               \
+bspline/Makefile             \
+cblas/Makefile               \
+cdf/Makefile                 \
+cheb/Makefile                \
+combination/Makefile         \
+complex/Makefile             \
+const/Makefile               \
+deriv/Makefile               \
+dht/Makefile                 \
+diff/Makefile                \
+doc/Makefile                 \
+doc/examples/Makefile        \
+eigen/Makefile               \
+err/Makefile                 \
+fit/Makefile                 \
+fft/Makefile                 \
+gsl/Makefile                 \
+histogram/Makefile           \
+ieee-utils/Makefile          \
+integration/Makefile         \
+interpolation/Makefile       \
+linalg/Makefile              \
+matrix/Makefile              \
+min/Makefile                 \
+monte/Makefile               \
+multifit/Makefile            \
+multifit_nlinear/Makefile    \
+multilarge/Makefile          \
+multilarge_nlinear/Makefile  \
+multimin/Makefile            \
+multiroots/Makefile          \
+multiset/Makefile            \
+ntuple/Makefile              \
+ode-initval/Makefile         \
+ode-initval2/Makefile        \
+permutation/Makefile         \
+poly/Makefile                \
+qrng/Makefile                \
+randist/Makefile             \
+rng/Makefile                 \
+roots/Makefile               \
+rstat/Makefile               \
+siman/Makefile               \
+sort/Makefile                \
+spblas/Makefile              \
+splinalg/Makefile            \
+spmatrix/Makefile            \
+specfunc/Makefile            \
+statistics/Makefile          \
+sum/Makefile                 \
+sys/Makefile                 \
+test/Makefile                \
+utils/Makefile               \
+vector/Makefile              \
+wavelet/Makefile             \
+])
+
 AC_OUTPUT
diff -Nru gsl-doc-1.16/const/Makefile.am gsl-doc-2.3/const/Makefile.am
--- gsl-doc-1.16/const/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/const/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -1,6 +1,6 @@
 pkginclude_HEADERS = gsl_const.h gsl_const_cgs.h gsl_const_mks.h gsl_const_cgsm.h gsl_const_mksa.h gsl_const_num.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 TESTS = $(check_PROGRAMS)
 
diff -Nru gsl-doc-1.16/const/Makefile.in gsl-doc-2.3/const/Makefile.in
--- gsl-doc-1.16/const/Makefile.in	2013-07-19 15:14:52.000000000 +0000
+++ gsl-doc-2.3/const/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -371,6 +371,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -393,7 +394,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -508,7 +512,7 @@
 top_builddir = @top_builddir@
 top_srcdir = @top_srcdir@
 pkginclude_HEADERS = gsl_const.h gsl_const_cgs.h gsl_const_mks.h gsl_const_cgsm.h gsl_const_mksa.h gsl_const_num.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 TESTS = $(check_PROGRAMS)
 test_SOURCES = test.c
 test_LDADD = ../ieee-utils/libgslieeeutils.la  ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
diff -Nru gsl-doc-1.16/debian/changelog gsl-doc-2.3/debian/changelog
--- gsl-doc-1.16/debian/changelog	2017-03-02 01:15:34.000000000 +0000
+++ gsl-doc-2.3/debian/changelog	2017-03-02 01:15:35.000000000 +0000
@@ -1,3 +1,15 @@
+gsl-doc (2.3-1) unstable; urgency=medium
+
+  * New upstream release
+
+  * debian/control: Set Standards-Version: to current version 
+
+  * debian/compat: Increased to 9
+
+  * debian/control: Update Suggests: to libgsl2
+
+ -- Dirk Eddelbuettel <edd@debian.org>  Wed, 01 Mar 2017 06:16:49 -0600
+
 gsl-doc (1.16-1) unstable; urgency=low
 
   * New upstream release of what is considered 'non-free' GSL documentation
diff -Nru gsl-doc-1.16/debian/compat gsl-doc-2.3/debian/compat
--- gsl-doc-1.16/debian/compat	2017-03-02 01:15:34.000000000 +0000
+++ gsl-doc-2.3/debian/compat	2017-03-02 01:15:35.000000000 +0000
@@ -1 +1 @@
-5
+9
diff -Nru gsl-doc-1.16/debian/control gsl-doc-2.3/debian/control
--- gsl-doc-1.16/debian/control	2017-03-02 01:15:34.000000000 +0000
+++ gsl-doc-2.3/debian/control	2017-03-02 01:15:35.000000000 +0000
@@ -2,7 +2,7 @@
 Section: non-free/math
 Priority: optional
 Maintainer: Dirk Eddelbuettel <edd@debian.org>
-Standards-Version: 3.9.4
+Standards-Version: 3.9.8
 Build-Depends: debhelper (>= 7.2.17), autotools-dev
 Build-Depends-Indep: texlive-base, texlive-latex-base, texlive-generic-recommended, texlive-font-utils, texinfo, ghostscript, ps2eps
 Homepage: http://www.gnu.org/software/gsl
@@ -11,7 +11,7 @@
 Section: non-free/doc
 Architecture: all
 Depends: ${misc:Depends}
-Suggests: libgsl0ldbl, gv | pdf-viewer 
+Suggests: libgsl2, gv | pdf-viewer 
 Description: GNU Scientific Library (GSL) Reference Manual in pdf
  This package provides a pdf file with the reference manual for the
  GNU Scientific Library (GSL), a collection of routines for numerical 
diff -Nru gsl-doc-1.16/debian/rules gsl-doc-2.3/debian/rules
--- gsl-doc-1.16/debian/rules	2017-03-02 01:15:34.000000000 +0000
+++ gsl-doc-2.3/debian/rules	2017-03-02 01:15:35.000000000 +0000
@@ -90,7 +90,7 @@
 install-work:
 	dh_testdir
 	dh_testroot
-	dh_clean -k
+	dh_prep
 	dh_installdirs
         #$(MAKE) prefix=$(debtmp)/usr                    \
         #        libdir=$(debtmp)/usr/lib                \
diff -Nru gsl-doc-1.16/depcomp gsl-doc-2.3/depcomp
--- gsl-doc-1.16/depcomp	2013-07-18 16:30:04.000000000 +0000
+++ gsl-doc-2.3/depcomp	2015-12-03 18:34:36.000000000 +0000
@@ -1,7 +1,7 @@
 #! /bin/sh
 # depcomp - compile a program generating dependencies as side-effects
 
-scriptversion=2012-10-18.11; # UTC
+scriptversion=2013-05-30.07; # UTC
 
 # Copyright (C) 1999-2013 Free Software Foundation, Inc.
 
@@ -552,6 +552,7 @@
   G
   p
 }' >> "$depfile"
+  echo >> "$depfile" # make sure the fragment doesn't end with a backslash
   rm -f "$tmpdepfile"
   ;;
 
diff -Nru gsl-doc-1.16/deriv/Makefile.am gsl-doc-2.3/deriv/Makefile.am
--- gsl-doc-1.16/deriv/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/deriv/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -1,6 +1,6 @@
 noinst_LTLIBRARIES = libgslderiv.la
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslderiv_la_SOURCES = deriv.c
 
diff -Nru gsl-doc-1.16/deriv/Makefile.in gsl-doc-2.3/deriv/Makefile.in
--- gsl-doc-1.16/deriv/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/deriv/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -376,6 +376,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -398,7 +399,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -513,7 +517,7 @@
 top_builddir = @top_builddir@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslderiv.la
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslderiv_la_SOURCES = deriv.c
 pkginclude_HEADERS = gsl_deriv.h
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/dht/Makefile.am gsl-doc-2.3/dht/Makefile.am
--- gsl-doc-1.16/dht/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/dht/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_dht.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 TESTS = $(check_PROGRAMS)
 
diff -Nru gsl-doc-1.16/dht/Makefile.in gsl-doc-2.3/dht/Makefile.in
--- gsl-doc-1.16/dht/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/dht/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -377,6 +377,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -399,7 +400,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -515,7 +519,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgsldht.la 
 pkginclude_HEADERS = gsl_dht.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 TESTS = $(check_PROGRAMS)
 test_LDADD = libgsldht.la ../specfunc/libgslspecfunc.la ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
 test_SOURCES = test.c
diff -Nru gsl-doc-1.16/diff/Makefile.am gsl-doc-2.3/diff/Makefile.am
--- gsl-doc-1.16/diff/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/diff/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -1,6 +1,6 @@
 noinst_LTLIBRARIES = libgsldiff.la
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgsldiff_la_SOURCES = diff.c
 
diff -Nru gsl-doc-1.16/diff/Makefile.in gsl-doc-2.3/diff/Makefile.in
--- gsl-doc-1.16/diff/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/diff/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -376,6 +376,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -398,7 +399,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -513,7 +517,7 @@
 top_builddir = @top_builddir@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgsldiff.la
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgsldiff_la_SOURCES = diff.c
 pkginclude_HEADERS = gsl_diff.h
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/doc/blas.texi gsl-doc-2.3/doc/blas.texi
--- gsl-doc-1.16/doc/blas.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/blas.texi	2015-11-09 05:23:40.000000000 +0000
@@ -652,7 +652,7 @@
 
 @example
 $ ./a.out
-@verbatiminclude examples/blas.out
+@verbatiminclude examples/blas.txt
 @end example
 
 @node BLAS References and Further Reading
diff -Nru gsl-doc-1.16/doc/bspline.texi gsl-doc-2.3/doc/bspline.texi
--- gsl-doc-1.16/doc/bspline.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/bspline.texi	2015-11-10 20:59:47.000000000 +0000
@@ -18,7 +18,7 @@
 * Evaluation of B-spline basis function derivatives::
 * Working with the Greville abscissae::
 * Example programs for B-splines::
-* References and Further Reading::
+* B-Spline References and Further Reading::
 @end menu
 
 @node Overview of B-splines
@@ -88,35 +88,21 @@
 @cindex basis splines, initializing
 
 The computation of B-spline functions requires a preallocated
-workspace of type @code{gsl_bspline_workspace}. If B-spline
-derivatives are also required, an additional
-@code{gsl_bspline_deriv_workspace} is needed.
+workspace of type @code{gsl_bspline_workspace}.
 
 @deftypefun {gsl_bspline_workspace *} gsl_bspline_alloc (const size_t @var{k}, const size_t @var{nbreak})
-@tpindex gsl_bspline_workspace
+@tindex gsl_bspline_workspace
 This function allocates a workspace for computing B-splines of order
 @var{k}. The number of breakpoints is given by @var{nbreak}. This
 leads to @math{n = nbreak + k - 2} basis functions. Cubic B-splines
 are specified by @math{k = 4}. The size of the workspace is
-@math{O(5k + nbreak)}.
+@math{O(2k^2 + 5k + nbreak)}.
 @end deftypefun
 
 @deftypefun void gsl_bspline_free (gsl_bspline_workspace * @var{w})
 This function frees the memory associated with the workspace @var{w}.
 @end deftypefun
 
-@deftypefun {gsl_bspline_deriv_workspace *} gsl_bspline_deriv_alloc (const size_t @var{k})
-@tpindex gsl_bspline_deriv_workspace
-This function allocates a workspace for computing the derivatives of a
-B-spline basis function of order @var{k}.  The size of the workspace
-is @math{O(2k^2)}.
-@end deftypefun
-
-@deftypefun void gsl_bspline_deriv_free (gsl_bspline_deriv_workspace * @var{w})
-This function frees the memory associated with the derivative
-workspace @var{w}.
-@end deftypefun
-
 @node Constructing the knots vector
 @section Constructing the knots vector
 @cindex knots, basis splines
@@ -172,7 +158,7 @@
 @section Evaluation of B-spline derivatives
 @cindex basis splines, derivatives
 
-@deftypefun int gsl_bspline_deriv_eval (const double @var{x}, const size_t @var{nderiv}, gsl_matrix * @var{dB}, gsl_bspline_workspace * @var{w}, gsl_bspline_deriv_workspace * @var{dw})
+@deftypefun int gsl_bspline_deriv_eval (const double @var{x}, const size_t @var{nderiv}, gsl_matrix * @var{dB}, gsl_bspline_workspace * @var{w})
 This function evaluates all B-spline basis function derivatives of orders
 @math{0} through @math{nderiv} (inclusive) at the position @var{x}
 and stores them in the matrix @var{dB}.  The @math{(i,j)}-th element of @var{dB}
@@ -186,7 +172,7 @@
 recurrence relation.
 @end deftypefun
 
-@deftypefun int gsl_bspline_deriv_eval_nonzero (const double @var{x}, const size_t @var{nderiv}, gsl_matrix * @var{dB}, size_t * @var{istart}, size_t * @var{iend}, gsl_bspline_workspace * @var{w}, gsl_bspline_deriv_workspace * @var{dw})
+@deftypefun int gsl_bspline_deriv_eval_nonzero (const double @var{x}, const size_t @var{nderiv}, gsl_matrix * @var{dB}, size_t * @var{istart}, size_t * @var{iend}, gsl_bspline_workspace * @var{w})
 This function evaluates all potentially nonzero B-spline basis function
 derivatives of orders @math{0} through @math{nderiv} (inclusive) at
 the position @var{x} and stores them in the matrix @var{dB}.  The
@@ -253,9 +239,9 @@
 The output can be plotted with @sc{gnu} @code{graph}.
 
 @example
-$ ./a.out > bspline.dat
+$ ./a.out > bspline.txt
 chisq/dof = 1.118217e+00, Rsq = 0.989771
-$ graph -T ps -X x -Y y -x 0 15 -y -1 1.3 < bspline.dat > bspline.ps
+$ graph -T ps -X x -Y y -x 0 15 -y -1 1.3 < bspline.txt > bspline.ps
 @end example
 
 @iftex
@@ -263,8 +249,8 @@
 @center @image{bspline,3.4in}
 @end iftex
 
-@node References and Further Reading
-@section References and Further Reading
+@node B-Spline References and Further Reading
+@section B-Spline References and Further Reading
 
 Further information on the algorithms described in this section can be
 found in the following book,
diff -Nru gsl-doc-1.16/doc/cblas.texi gsl-doc-2.3/doc/cblas.texi
--- gsl-doc-1.16/doc/cblas.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/cblas.texi	2015-11-09 05:23:40.000000000 +0000
@@ -510,5 +510,5 @@
 
 @example
 $ ./a.out
-@verbatiminclude examples/cblas.out
+@verbatiminclude examples/cblas.txt
 @end example
diff -Nru gsl-doc-1.16/doc/cheb.texi gsl-doc-2.3/doc/cheb.texi
--- gsl-doc-1.16/doc/cheb.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/cheb.texi	2015-11-03 16:21:55.000000000 +0000
@@ -27,7 +27,7 @@
 
 @node Chebyshev Definitions
 @section Definitions
-@tpindex gsl_cheb_series
+@tindex gsl_cheb_series
 A Chebyshev series  is stored using the following structure,
 
 @example
diff -Nru gsl-doc-1.16/doc/combination.texi gsl-doc-2.3/doc/combination.texi
--- gsl-doc-1.16/doc/combination.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/combination.texi	2015-11-09 05:23:40.000000000 +0000
@@ -24,7 +24,7 @@
 
 @node The Combination struct
 @section The Combination struct
-@tpindex gsl_combination
+@tindex gsl_combination
 A combination is defined by a structure containing three components, the
 values of @math{n} and @math{k}, and a pointer to the combination array.
 The elements of the combination array are all of type @code{size_t}, and
@@ -197,7 +197,7 @@
 
 @example
 $ ./a.out 
-@verbatiminclude examples/combination.out
+@verbatiminclude examples/combination.txt
 @end example
 
 @noindent
diff -Nru gsl-doc-1.16/doc/const.texi gsl-doc-2.3/doc/const.texi
--- gsl-doc-1.16/doc/const.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/const.texi	2015-11-09 05:23:40.000000000 +0000
@@ -555,7 +555,7 @@
 Here is the output from the program,
 
 @example
-@verbatiminclude examples/const.out
+@verbatiminclude examples/const.txt
 @end example
 
 @node Physical Constant References and Further Reading
diff -Nru gsl-doc-1.16/doc/dht.texi gsl-doc-2.3/doc/dht.texi
--- gsl-doc-1.16/doc/dht.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/dht.texi	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 @cindex Hankel transforms, discrete
 @cindex transforms, Hankel
 This chapter describes functions for performing Discrete Hankel
-Transforms (DHTs).  The functions are declared in the header file
+Transforms (DHTs). The functions are declared in the header file
 @file{gsl_dht.h}.
 
 @menu
@@ -16,78 +16,115 @@
 
 The discrete Hankel transform acts on a vector of sampled data, where
 the samples are assumed to have been taken at points related to the
-zeroes of a Bessel function of fixed order; compare this to the case of
+zeros of a Bessel function of fixed order; compare this to the case of
 the discrete Fourier transform, where samples are taken at points
 related to the zeroes of the sine or cosine function.
 
-Specifically, let @math{f(t)} be a function on the unit interval and 
-@c{$j_{\nu,m}$}
-@math{j_(\nu,m)} the @math{m}-th zero of the Bessel function
-@math{J_\nu(x)}.  Then the finite @math{\nu}-Hankel transform of
-@math{f(t)} is defined to be the set of numbers @math{g_m} given by,
+Starting with its definition, the Hankel transform (or Bessel transform) of
+order @math{\nu} of a function @math{f} with @math{\nu > -1/2} is defined as
+(see Johnson, 1987 and Lemoine, 1994)
 @tex
 \beforedisplay
 $$
-g_m = \int_0^1 t dt\, J_\nu(j_{\nu,m}t) f(t),
+F_\nu(u) = \int_0^\infty f(t) J_\nu(u t) t dt
 $$
 \afterdisplay
 @end tex
 @ifinfo
 @example
-g_m = \int_0^1 t dt J_\nu(j_(\nu,m)t) f(t),
+F_\nu(u) = \int_0^\infty f(t) J_\nu(u t) t dt
 @end example
-
 @end ifinfo
+
 @noindent
-so that,
+If the integral exists, @math{F_\nu} is called the Hankel transformation
+of @math{f}. The reverse transform is given by
 @tex
 \beforedisplay
 $$
-f(t) = \sum_{m=1}^\infty {{2 J_\nu(j_{\nu,m}t)}\over{J_{\nu+1}(j_{\nu,m})^2}} g_m.
+f(t) = \int_0^\infty F_\nu(u) J_\nu(u t) u du ,
 $$
 \afterdisplay
 @end tex
 @ifinfo
 @example
-f(t) = \sum_@{m=1@}^\infty (2 J_\nu(j_(\nu,m)t) / J_(\nu+1)(j_(\nu,m))^2) g_m.
+f(t) = \int_0^\infty F_\nu(u) J_\nu(u t) u du ,
 @end example
-
 @end ifinfo
+
 @noindent
-Suppose that @math{f} is band-limited in the sense that
-@math{g_m=0} for @math{m > M}. Then we have the following
-fundamental sampling theorem.
+where @math{\int_0^\infty f(t) t^{1/2} dt} must exist and be
+absolutely convergent, and where @math{f(t)} satisfies Dirichlet's
+conditions (of limited total fluctuations) in the interval
+@math{[0,\infty]}.
+
+Now the discrete Hankel transform works on a discrete function
+@math{f}, which is sampled on points @math{n=1...M} located at
+positions @math{t_n=(j_{\nu,n}/j_{\nu,M}) X} in real space and
+at @math{u_n=j_{\nu,n}/X} in reciprocal space. Here,
+@math{j_{\nu,m}} are the m-th zeros of the Bessel function
+@math{J_\nu(x)} arranged in ascending order. Moreover, the
+discrete functions are assumed to be band limited, so
+@math{f(t_n)=0} and @math{F(u_n)=0} for @math{n>M}. Accordingly,
+the function @math{f} is defined on the interval @math{[0,X]}.
+
+Following the work of Johnson, 1987 and
+Lemoine, 1994, the discrete Hankel transform is given by
 @tex
 \beforedisplay
 $$
-g_m = {{2}\over{j_{\nu,M}^2}}
-      \sum_{k=1}^{M-1} f\left({{j_{\nu,k}}\over{j_{\nu,M}}}\right)
+F_\nu(u_m) = {{2 X^2}\over{j_{\nu,M}^2}}
+      \sum_{k=1}^{M-1} f\left({{j_{\nu,k} X}\over{j_{\nu,M}}}\right)
           {{J_\nu(j_{\nu,m} j_{\nu,k} / j_{\nu,M})}\over{J_{\nu+1}(j_{\nu,k})^2}}.
 $$
 \afterdisplay
 @end tex
 @ifinfo
 @example
-g_m = (2 / j_(\nu,M)^2)
-      \sum_@{k=1@}^@{M-1@} f(j_(\nu,k)/j_(\nu,M))
+F_\nu(u_m) = (2 X^2 / j_(\nu,M)^2)
+      \sum_@{k=1@}^@{M-1@} f(j_(\nu,k) X/j_(\nu,M))
           (J_\nu(j_(\nu,m) j_(\nu,k) / j_(\nu,M)) / J_(\nu+1)(j_(\nu,k))^2).
 @end example
 
 @end ifinfo
 @noindent
 It is this discrete expression which defines the discrete Hankel
-transform. The kernel in the summation above defines the matrix of the
-@math{\nu}-Hankel transform of size @math{M-1}.  The coefficients of
+transform calculated by GSL. In GSL, forward and backward transforms
+are defined equally and calculate @math{F_\nu(u_m)}.
+Following Johnson, the backward transform reads
+@tex
+\beforedisplay
+$$
+f(t_k) = {{2}\over{X^2}}
+      \sum_{m=1}^{M-1} F\left({{j_{\nu,m}}\over{X}}\right)
+          {{J_\nu(j_{\nu,m} j_{\nu,k} / j_{\nu,M})}\over{J_{\nu+1}(j_{\nu,m})^2}}.
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+f(t_k) = (2 / X^2)
+      \sum_@{m=1@}^@{M-1@} F(j_(\nu,m)/X)
+          (J_\nu(j_(\nu,m) j_(\nu,k) / j_(\nu,M)) / J_(\nu+1)(j_(\nu,m))^2).
+@end example
+
+@end ifinfo
+@noindent
+Obviously, using the forward transform instead of the backward transform gives an
+additional factor @math{X^4/j_{\nu,M}^2=t_m^2/u_m^2}.
+
+The kernel in the summation above defines the matrix of the
+@math{\nu}-Hankel transform of size @math{M-1}. The coefficients of
 this matrix, being dependent on @math{\nu} and @math{M}, must be
 precomputed and stored; the @code{gsl_dht} object encapsulates this
-data.  The allocation function @code{gsl_dht_alloc} returns a
+data. The allocation function @code{gsl_dht_alloc} returns a
 @code{gsl_dht} object which must be properly initialized with
 @code{gsl_dht_init} before it can be used to perform transforms on data
 sample vectors, for fixed @math{\nu} and @math{M}, using the
-@code{gsl_dht_apply} function. The implementation allows a scaling of
-the fundamental interval, for convenience, so that one can assume the
-function is defined on the interval @math{[0,X]}, rather than the unit
-interval.
+@code{gsl_dht_apply} function. The implementation allows to define the
+length @math{X} of the fundamental interval, for convenience, while
+discrete Hankel transforms are often defined on the unit interval
+instead of @math{[0,X]}.
 
 Notice that by assumption @math{f(t)} vanishes at the endpoints
 of the interval, consistent with the inversion formula
@@ -95,12 +132,11 @@
 corresponds to an orthogonal expansion in eigenfunctions
 of the Dirichlet problem for the Bessel differential equation.
 
-
 @node Discrete Hankel Transform Functions
 @section Functions
 
 @deftypefun {gsl_dht *} gsl_dht_alloc (size_t @var{size})
-@tpindex gsl_dht
+@tindex gsl_dht
 This function allocates a Discrete Hankel transform object of size
 @var{size}.
 @end deftypefun
@@ -126,7 +162,7 @@
 in the array @var{f_out} which must be of the same length.   
 
 Applying this function to its output gives the original data
-multiplied by @c{$(1/j_{\nu,M})^2$}
+multiplied by @c{$(X^2/j_{\nu,M})^2$}
 @math{(1/j_(\nu,M))^2}, up to numerical errors.
 @end deftypefun
 
diff -Nru gsl-doc-1.16/doc/diff.texi gsl-doc-2.3/doc/diff.texi
--- gsl-doc-1.16/doc/diff.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/diff.texi	2015-11-09 05:23:40.000000000 +0000
@@ -86,7 +86,7 @@
 
 @example
 $ ./a.out
-@verbatiminclude examples/diff.out
+@verbatiminclude examples/diff.txt
 @end example
 
 @node Numerical Differentiation References
diff -Nru gsl-doc-1.16/doc/dwt.texi gsl-doc-2.3/doc/dwt.texi
--- gsl-doc-1.16/doc/dwt.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/dwt.texi	2015-11-10 18:06:56.000000000 +0000
@@ -114,13 +114,13 @@
 @node DWT Initialization
 @section Initialization
 @cindex DWT initialization
-@tpindex gsl_wavelet_type
+@tindex gsl_wavelet_type
 
 The @code{gsl_wavelet} structure contains the filter coefficients
 defining the wavelet and any associated offset parameters.
 
 @deftypefun {gsl_wavelet *} gsl_wavelet_alloc (const gsl_wavelet_type * @var{T}, size_t @var{k})
-@tpindex gsl_wavelet
+@tindex gsl_wavelet
 This function allocates and initializes a wavelet object of type
 @var{T}.  The parameter @var{k} selects the specific member of the
 wavelet family.  A null pointer is returned if insufficient memory is
@@ -179,7 +179,7 @@
 during the transform.
 
 @deftypefun {gsl_wavelet_workspace *} gsl_wavelet_workspace_alloc (size_t @var{n})
-@tpindex gsl_wavelet_workspace
+@tindex gsl_wavelet_workspace
 This function allocates a workspace for the discrete wavelet transform.
 To perform a one-dimensional transform on @var{n} elements, a workspace
 of size @var{n} must be provided.  For two-dimensional transforms of
@@ -347,8 +347,8 @@
 The output can be used with the @sc{gnu} plotutils @code{graph} program,
 
 @example
-$ ./a.out ecg.dat > dwt.dat
-$ graph -T ps -x 0 256 32 -h 0.3 -a dwt.dat > dwt.ps
+$ ./a.out ecg.dat > dwt.txt
+$ graph -T ps -x 0 256 32 -h 0.3 -a dwt.txt > dwt.ps
 @end example
 
 @iftex
diff -Nru gsl-doc-1.16/doc/eigen.texi gsl-doc-2.3/doc/eigen.texi
--- gsl-doc-1.16/doc/eigen.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/eigen.texi	2015-11-03 16:21:55.000000000 +0000
@@ -36,7 +36,7 @@
 the machine precision.
 
 @deftypefun {gsl_eigen_symm_workspace *} gsl_eigen_symm_alloc (const size_t @var{n})
-@tpindex gsl_eigen_symm_workspace
+@tindex gsl_eigen_symm_workspace
 This function allocates a workspace for computing eigenvalues of
 @var{n}-by-@var{n} real symmetric matrices.  The size of the workspace
 is @math{O(2n)}.
@@ -56,7 +56,7 @@
 @end deftypefun
 
 @deftypefun {gsl_eigen_symmv_workspace *} gsl_eigen_symmv_alloc (const size_t @var{n})
-@tpindex gsl_eigen_symmv_workspace
+@tindex gsl_eigen_symmv_workspace
 This function allocates a workspace for computing eigenvalues and
 eigenvectors of @var{n}-by-@var{n} real symmetric matrices.  The size of
 the workspace is @math{O(4n)}.
@@ -88,7 +88,7 @@
 @cindex hermitian matrix, complex, eigensystem
 @cindex complex hermitian matrix, eigensystem
 @deftypefun {gsl_eigen_herm_workspace *} gsl_eigen_herm_alloc (const size_t @var{n})
-@tpindex gsl_eigen_herm_workspace
+@tindex gsl_eigen_herm_workspace
 This function allocates a workspace for computing eigenvalues of
 @var{n}-by-@var{n} complex hermitian matrices.  The size of the workspace
 is @math{O(3n)}.
@@ -109,7 +109,7 @@
 @end deftypefun
 
 @deftypefun {gsl_eigen_hermv_workspace *} gsl_eigen_hermv_alloc (const size_t @var{n})
-@tpindex gsl_eigen_hermv_workspace
+@tindex gsl_eigen_hermv_workspace
 This function allocates a workspace for computing eigenvalues and
 eigenvectors of @var{n}-by-@var{n} complex hermitian matrices.  The size of
 the workspace is @math{O(5n)}.
@@ -162,7 +162,7 @@
 Francis method.
 
 @deftypefun {gsl_eigen_nonsymm_workspace *} gsl_eigen_nonsymm_alloc (const size_t @var{n})
-@tpindex gsl_eigen_nonsymm_workspace
+@tindex gsl_eigen_nonsymm_workspace
 This function allocates a workspace for computing eigenvalues of
 @var{n}-by-@var{n} real nonsymmetric matrices. The size of the workspace
 is @math{O(2n)}.
@@ -248,7 +248,7 @@
 @end deftypefun
 
 @deftypefun {gsl_eigen_nonsymmv_workspace *} gsl_eigen_nonsymmv_alloc (const size_t @var{n})
-@tpindex gsl_eigen_nonsymmv_workspace
+@tindex gsl_eigen_nonsymmv_workspace
 This function allocates a workspace for computing eigenvalues and
 eigenvectors of @var{n}-by-@var{n} real nonsymmetric matrices. The
 size of the workspace is @math{O(5n)}.
@@ -334,7 +334,7 @@
 of the generalized symmetric-definite eigenproblem are always real.
 
 @deftypefun {gsl_eigen_gensymm_workspace *} gsl_eigen_gensymm_alloc (const size_t @var{n})
-@tpindex gsl_eigen_gensymm_workspace
+@tindex gsl_eigen_gensymm_workspace
 This function allocates a workspace for computing eigenvalues of
 @var{n}-by-@var{n} real generalized symmetric-definite eigensystems. The
 size of the workspace is @math{O(2n)}.
@@ -352,7 +352,7 @@
 @end deftypefun
 
 @deftypefun {gsl_eigen_gensymmv_workspace *} gsl_eigen_gensymmv_alloc (const size_t @var{n})
-@tpindex gsl_eigen_gensymmv_workspace
+@tindex gsl_eigen_gensymmv_workspace
 This function allocates a workspace for computing eigenvalues and
 eigenvectors of @var{n}-by-@var{n} real generalized symmetric-definite
 eigensystems. The size of the workspace is @math{O(4n)}.
@@ -402,7 +402,7 @@
 of the generalized hermitian-definite eigenproblem are always real.
 
 @deftypefun {gsl_eigen_genherm_workspace *} gsl_eigen_genherm_alloc (const size_t @var{n})
-@tpindex gsl_eigen_genherm_workspace
+@tindex gsl_eigen_genherm_workspace
 This function allocates a workspace for computing eigenvalues of
 @var{n}-by-@var{n} complex generalized hermitian-definite eigensystems. The
 size of the workspace is @math{O(3n)}.
@@ -420,7 +420,7 @@
 @end deftypefun
 
 @deftypefun {gsl_eigen_genhermv_workspace *} gsl_eigen_genhermv_alloc (const size_t @var{n})
-@tpindex gsl_eigen_genhermv_workspace
+@tindex gsl_eigen_genhermv_workspace
 This function allocates a workspace for computing eigenvalues and
 eigenvectors of @var{n}-by-@var{n} complex generalized hermitian-definite
 eigensystems. The size of the workspace is @math{O(5n)}.
@@ -526,7 +526,7 @@
 (see references).
 
 @deftypefun {gsl_eigen_gen_workspace *} gsl_eigen_gen_alloc (const size_t @var{n})
-@tpindex gsl_eigen_gen_workspace
+@tindex gsl_eigen_gen_workspace
 This function allocates a workspace for computing eigenvalues of
 @var{n}-by-@var{n} real generalized nonsymmetric eigensystems. The
 size of the workspace is @math{O(n)}.
@@ -584,7 +584,7 @@
 @end deftypefun
 
 @deftypefun {gsl_eigen_genv_workspace *} gsl_eigen_genv_alloc (const size_t @var{n})
-@tpindex gsl_eigen_genv_workspace
+@tindex gsl_eigen_genv_workspace
 This function allocates a workspace for computing eigenvalues and
 eigenvectors of @var{n}-by-@var{n} real generalized nonsymmetric
 eigensystems. The size of the workspace is @math{O(7n)}.
diff -Nru gsl-doc-1.16/doc/examples/blas.out gsl-doc-2.3/doc/examples/blas.out
--- gsl-doc-1.16/doc/examples/blas.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/blas.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,2 +0,0 @@
-[ 367.76, 368.12
-  674.06, 674.72 ]
\ No newline at end of file
diff -Nru gsl-doc-1.16/doc/examples/blas.txt gsl-doc-2.3/doc/examples/blas.txt
--- gsl-doc-1.16/doc/examples/blas.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/blas.txt	2015-11-10 17:45:14.000000000 +0000
@@ -0,0 +1,2 @@
+[ 367.76, 368.12
+  674.06, 674.72 ]
diff -Nru gsl-doc-1.16/doc/examples/block.c gsl-doc-2.3/doc/examples/block.c
--- gsl-doc-1.16/doc/examples/block.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/block.c	2015-11-09 19:06:11.000000000 +0000
@@ -6,8 +6,8 @@
 {
   gsl_block * b = gsl_block_alloc (100);
   
-  printf ("length of block = %u\n", b->size);
-  printf ("block data address = %#x\n", b->data);
+  printf ("length of block = %zu\n", b->size);
+  printf ("block data address = %p\n", b->data);
 
   gsl_block_free (b);
   return 0;
diff -Nru gsl-doc-1.16/doc/examples/block.out gsl-doc-2.3/doc/examples/block.out
--- gsl-doc-1.16/doc/examples/block.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/block.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,2 +0,0 @@
-length of block = 100
-block data address = 0x804b0d8
diff -Nru gsl-doc-1.16/doc/examples/block.txt gsl-doc-2.3/doc/examples/block.txt
--- gsl-doc-1.16/doc/examples/block.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/block.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,2 @@
+length of block = 100
+block data address = 0x804b0d8
diff -Nru gsl-doc-1.16/doc/examples/bspline.txt gsl-doc-2.3/doc/examples/bspline.txt
--- gsl-doc-1.16/doc/examples/bspline.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/bspline.txt	2015-11-10 18:19:30.000000000 +0000
@@ -0,0 +1,353 @@
+#m=0,S=0
+0.000000 1.013392
+0.075377 0.980953
+0.150754 1.136930
+0.226131 1.022649
+0.301508 1.018952
+0.376884 0.781034
+0.452261 0.653645
+0.527638 0.763919
+0.603015 0.772400
+0.678392 0.792524
+0.753769 0.674983
+0.829146 0.541142
+0.904523 0.526895
+0.979899 0.514283
+1.055276 0.480481
+1.130653 0.359657
+1.206030 0.296027
+1.281407 0.251224
+1.356784 0.173015
+1.432161 0.109840
+1.507538 0.057700
+1.582915 -0.009964
+1.658291 -0.071887
+1.733668 -0.123842
+1.809045 -0.185449
+1.884422 -0.257174
+1.959799 -0.313225
+2.035176 -0.337965
+2.110553 -0.410140
+2.185930 -0.532190
+2.261307 -0.497535
+2.336683 -0.534430
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+2.487437 -0.461417
+2.562814 -0.685286
+2.638191 -0.670396
+2.713568 -0.677885
+2.788945 -0.760828
+2.864322 -0.836176
+2.939698 -0.701519
+3.015075 -0.820581
+3.090452 -0.864657
+3.165829 -0.675148
+3.241206 -0.674258
+3.316583 -0.853122
+3.391960 -0.627814
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+3.844221 -0.505355
+3.919598 -0.479103
+3.994975 -0.476144
+4.070352 -0.420115
+4.145729 -0.357678
+4.221106 -0.351235
+4.296482 -0.263275
+4.371859 -0.231913
+4.447236 -0.141524
+4.522613 -0.117161
+4.597990 -0.074501
+4.673367 -0.024253
+4.748744 0.021384
+4.824121 0.059326
+4.899497 0.133528
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+5.050251 0.230545
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+5.276382 0.356921
+5.351759 0.320297
+5.427136 0.410395
+5.502513 0.376859
+5.577889 0.432169
+5.653266 0.527822
+5.728643 0.498471
+5.804020 0.662444
+5.879397 0.602791
+5.954774 0.613485
+6.030151 0.565095
+6.105528 0.478371
+6.180905 0.553815
+6.256281 0.559066
+6.331658 0.405827
+6.407035 0.490786
+6.482412 0.401802
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+6.633166 0.461542
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+6.783920 0.453343
+6.859296 0.405652
+6.934673 0.331105
+7.010050 0.335669
+7.085427 0.342361
+7.160804 0.348337
+7.236181 0.333673
+7.311558 0.251268
+7.386935 0.219000
+7.462312 0.204136
+7.537688 0.154734
+7.613065 0.106188
+7.688442 0.079925
+7.763819 0.049781
+7.839196 0.008202
+7.914573 -0.026424
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+9.195980 -0.404115
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+10.552764 -0.191308
+10.628141 -0.115893
+10.703518 -0.092357
+10.778894 -0.086082
+10.854271 -0.054768
+10.929648 -0.022839
+11.005025 0.003120
+11.080402 0.027484
+11.155779 0.039650
+11.231156 0.068622
+11.306533 0.098587
+11.381910 0.120223
+11.457286 0.139761
+11.532663 0.163363
+11.608040 0.192581
+11.683417 0.184073
+11.758794 0.212051
+11.834171 0.224144
+11.909548 0.241003
+11.984925 0.286442
+12.060302 0.226233
+12.135678 0.296165
+12.211055 0.247044
+12.286432 0.298468
+12.361809 0.293579
+12.437186 0.294012
+12.512563 0.306141
+12.587940 0.277510
+12.663317 0.285759
+12.738693 0.302944
+12.814070 0.257310
+12.889447 0.243150
+12.964824 0.218764
+13.040201 0.264436
+13.115578 0.221957
+13.190955 0.196140
+13.266332 0.228542
+13.341709 0.156622
+13.417085 0.192438
+13.492462 0.156691
+13.567839 0.144335
+13.643216 0.148104
+13.718593 0.117823
+13.793970 0.082832
+13.869347 0.062686
+13.944724 0.040703
+14.020101 0.026491
+14.095477 0.010098
+14.170854 -0.007478
+14.246231 -0.029452
+14.321608 -0.042866
+14.396985 -0.057775
+14.472362 -0.071364
+14.547739 -0.098028
+14.623116 -0.130422
+14.698492 -0.133196
+14.773869 -0.131368
+14.849246 -0.152986
+14.924623 -0.156311
+15.000000 -0.163284
+#m=1,S=0
+0.000000 1.020318
+0.100000 1.001004
+0.200000 0.971769
+0.300000 0.933425
+0.400000 0.886787
+0.500000 0.832667
+0.600000 0.771879
+0.700000 0.705235
+0.800000 0.633550
+0.900000 0.557635
+1.000000 0.478304
+1.100000 0.396370
+1.200000 0.312647
+1.300000 0.227948
+1.400000 0.143085
+1.500000 0.058872
+1.600000 -0.023878
+1.700000 -0.104354
+1.800000 -0.181913
+1.900000 -0.256170
+2.000000 -0.326761
+2.100000 -0.393322
+2.200000 -0.455491
+2.300000 -0.512905
+2.400000 -0.565199
+2.500000 -0.612011
+2.600000 -0.652978
+2.700000 -0.687736
+2.800000 -0.715922
+2.900000 -0.737172
+3.000000 -0.751124
+3.100000 -0.757414
+3.200000 -0.755680
+3.300000 -0.745556
+3.400000 -0.726738
+3.500000 -0.699577
+3.600000 -0.664851
+3.700000 -0.623345
+3.800000 -0.575842
+3.900000 -0.523128
+4.000000 -0.465986
+4.100000 -0.405202
+4.200000 -0.341560
+4.300000 -0.275845
+4.400000 -0.208840
+4.500000 -0.141331
+4.600000 -0.074102
+4.700000 -0.007938
+4.800000 0.056378
+4.900000 0.118059
+5.000000 0.176323
+5.100000 0.230505
+5.200000 0.280423
+5.300000 0.326019
+5.400000 0.367230
+5.500000 0.403998
+5.600000 0.436261
+5.700000 0.463960
+5.800000 0.487034
+5.900000 0.505422
+6.000000 0.519064
+6.100000 0.527901
+6.200000 0.531871
+6.300000 0.530914
+6.400000 0.524970
+6.500000 0.513979
+6.600000 0.497880
+6.700000 0.476616
+6.800000 0.450349
+6.900000 0.419577
+7.000000 0.384827
+7.100000 0.346626
+7.200000 0.305503
+7.300000 0.261983
+7.400000 0.216596
+7.500000 0.169867
+7.600000 0.122325
+7.700000 0.074497
+7.800000 0.026910
+7.900000 -0.019908
+8.000000 -0.065431
+8.100000 -0.109130
+8.200000 -0.150478
+8.300000 -0.188949
+8.400000 -0.224041
+8.500000 -0.255567
+8.600000 -0.283542
+8.700000 -0.307985
+8.800000 -0.328913
+8.900000 -0.346344
+9.000000 -0.360298
+9.100000 -0.370791
+9.200000 -0.377843
+9.300000 -0.381471
+9.400000 -0.381694
+9.500000 -0.378529
+9.600000 -0.371996
+9.700000 -0.362111
+9.800000 -0.348894
+9.900000 -0.332363
+10.000000 -0.312535
+10.100000 -0.289491
+10.200000 -0.263558
+10.300000 -0.235124
+10.400000 -0.204580
+10.500000 -0.172313
+10.600000 -0.138713
+10.700000 -0.104170
+10.800000 -0.069070
+10.900000 -0.033805
+11.000000 0.001238
+11.100000 0.035668
+11.200000 0.069098
+11.300000 0.101139
+11.400000 0.131400
+11.500000 0.159494
+11.600000 0.185031
+11.700000 0.207625
+11.800000 0.227067
+11.900000 0.243418
+12.000000 0.256764
+12.100000 0.267192
+12.200000 0.274787
+12.300000 0.279636
+12.400000 0.281823
+12.500000 0.281436
+12.600000 0.278560
+12.700000 0.273281
+12.800000 0.265685
+12.900000 0.255858
+13.000000 0.243886
+13.100000 0.229854
+13.200000 0.213850
+13.300000 0.195957
+13.400000 0.176273
+13.500000 0.155000
+13.600000 0.132411
+13.700000 0.108780
+13.800000 0.084383
+13.900000 0.059492
+14.000000 0.034382
+14.100000 0.009328
+14.200000 -0.015397
+14.300000 -0.039517
+14.400000 -0.062760
+14.500000 -0.084850
+14.600000 -0.105514
+14.700000 -0.124477
+14.800000 -0.141465
+14.900000 -0.156204
+15.000000 -0.168419
diff -Nru gsl-doc-1.16/doc/examples/cblas.out gsl-doc-2.3/doc/examples/cblas.out
--- gsl-doc-1.16/doc/examples/cblas.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/cblas.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,2 +0,0 @@
-[ 367.76, 368.12
-  674.06, 674.72 ]
diff -Nru gsl-doc-1.16/doc/examples/cblas.txt gsl-doc-2.3/doc/examples/cblas.txt
--- gsl-doc-1.16/doc/examples/cblas.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/cblas.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,2 @@
+[ 367.76, 368.12
+  674.06, 674.72 ]
diff -Nru gsl-doc-1.16/doc/examples/cdf.out gsl-doc-2.3/doc/examples/cdf.out
--- gsl-doc-1.16/doc/examples/cdf.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/cdf.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,4 +0,0 @@
-prob(x < 2.000000) = 0.977250
-prob(x > 2.000000) = 0.022750
-Pinv(0.977250) = 2.000000
-Qinv(0.022750) = 2.000000
diff -Nru gsl-doc-1.16/doc/examples/cdf.txt gsl-doc-2.3/doc/examples/cdf.txt
--- gsl-doc-1.16/doc/examples/cdf.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/cdf.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,4 @@
+prob(x < 2.000000) = 0.977250
+prob(x > 2.000000) = 0.022750
+Pinv(0.977250) = 2.000000
+Qinv(0.022750) = 2.000000
diff -Nru gsl-doc-1.16/doc/examples/cheb.c gsl-doc-2.3/doc/examples/cheb.c
--- gsl-doc-1.16/doc/examples/cheb.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/cheb.c	2015-11-09 19:08:25.000000000 +0000
@@ -5,6 +5,8 @@
 double
 f (double x, void *p)
 {
+  (void)(p); /* avoid unused parameter warning */
+
   if (x < 0.5)
     return 0.25;
   else
diff -Nru gsl-doc-1.16/doc/examples/cheb.txt gsl-doc-2.3/doc/examples/cheb.txt
--- gsl-doc-1.16/doc/examples/cheb.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/cheb.txt	2015-11-10 17:57:34.000000000 +0000
@@ -0,0 +1,10000 @@
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+0.9996 0.75 0.758259 0.749594
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diff -Nru gsl-doc-1.16/doc/examples/combination.out gsl-doc-2.3/doc/examples/combination.out
--- gsl-doc-1.16/doc/examples/combination.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/combination.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,17 +0,0 @@
-All subsets of {0,1,2,3} by size:
-{ }
-{ 0 }
-{ 1 }
-{ 2 }
-{ 3 }
-{ 0 1 }
-{ 0 2 }
-{ 0 3 }
-{ 1 2 }
-{ 1 3 }
-{ 2 3 }
-{ 0 1 2 }
-{ 0 1 3 }
-{ 0 2 3 }
-{ 1 2 3 }
-{ 0 1 2 3 }
diff -Nru gsl-doc-1.16/doc/examples/combination.txt gsl-doc-2.3/doc/examples/combination.txt
--- gsl-doc-1.16/doc/examples/combination.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/combination.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,17 @@
+All subsets of {0,1,2,3} by size:
+{ }
+{ 0 }
+{ 1 }
+{ 2 }
+{ 3 }
+{ 0 1 }
+{ 0 2 }
+{ 0 3 }
+{ 1 2 }
+{ 1 3 }
+{ 2 3 }
+{ 0 1 2 }
+{ 0 1 3 }
+{ 0 2 3 }
+{ 1 2 3 }
+{ 0 1 2 3 }
diff -Nru gsl-doc-1.16/doc/examples/const.out gsl-doc-2.3/doc/examples/const.out
--- gsl-doc-1.16/doc/examples/const.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/const.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,3 +0,0 @@
-light travel time from Earth to Mars:
-minimum = 4.3 minutes
-maximum = 21.0 minutes
diff -Nru gsl-doc-1.16/doc/examples/const.txt gsl-doc-2.3/doc/examples/const.txt
--- gsl-doc-1.16/doc/examples/const.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/const.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,3 @@
+light travel time from Earth to Mars:
+minimum = 4.3 minutes
+maximum = 21.0 minutes
diff -Nru gsl-doc-1.16/doc/examples/demo_fn.c gsl-doc-2.3/doc/examples/demo_fn.c
--- gsl-doc-1.16/doc/examples/demo_fn.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/demo_fn.c	2015-11-09 19:15:37.000000000 +0000
@@ -19,7 +19,6 @@
 
   double a = p->a;
   double b = p->b;
-  double c = p->c;
 
   return 2.0 * a * x + b;
 }
diff -Nru gsl-doc-1.16/doc/examples/diff.c gsl-doc-2.3/doc/examples/diff.c
--- gsl-doc-1.16/doc/examples/diff.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/diff.c	2015-11-09 19:08:59.000000000 +0000
@@ -4,6 +4,7 @@
 
 double f (double x, void * params)
 {
+  (void)(params); /* avoid unused parameter warning */
   return pow (x, 1.5);
 }
 
diff -Nru gsl-doc-1.16/doc/examples/diff.out gsl-doc-2.3/doc/examples/diff.out
--- gsl-doc-1.16/doc/examples/diff.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/diff.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,8 +0,0 @@
-f(x) = x^(3/2)
-x = 2.0
-f'(x) = 2.1213203120 +/- 0.0000004064
-exact = 2.1213203436
-
-x = 0.0
-f'(x) = 0.0000000160 +/- 0.0000000339
-exact = 0.0000000000
diff -Nru gsl-doc-1.16/doc/examples/diff.txt gsl-doc-2.3/doc/examples/diff.txt
--- gsl-doc-1.16/doc/examples/diff.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/diff.txt	2015-11-10 18:02:10.000000000 +0000
@@ -0,0 +1,8 @@
+f(x) = x^(3/2)
+x = 2.0
+f'(x) = 2.1213203120 +/- 0.0000005006
+exact = 2.1213203436
+
+x = 0.0
+f'(x) = 0.0000000160 +/- 0.0000000339
+exact = 0.0000000000
diff -Nru gsl-doc-1.16/doc/examples/dwt.c gsl-doc-2.3/doc/examples/dwt.c
--- gsl-doc-1.16/doc/examples/dwt.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/dwt.c	2015-11-09 19:17:56.000000000 +0000
@@ -6,6 +6,7 @@
 int
 main (int argc, char **argv)
 {
+  (void)(argc); /* avoid unused parameter warning */
   int i, n = 256, nc = 20;
   double *data = malloc (n * sizeof (double));
   double *abscoeff = malloc (n * sizeof (double));
diff -Nru gsl-doc-1.16/doc/examples/dwt.dat gsl-doc-2.3/doc/examples/dwt.dat
--- gsl-doc-1.16/doc/examples/dwt.dat	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/dwt.dat	1970-01-01 00:00:00.000000000 +0000
@@ -1,256 +0,0 @@
-0.0167729
-0.031888
-0.0412921
-0.0522264
-0.0574496
-0.0642031
-0.0724869
-0.0803607
-0.0825233
-0.0862162
-0.0914394
-0.0962525
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-0.108529
-0.114053
-0.119686
-0.104007
-0.094039
-0.0897813
-0.0839935
-0.0839162
-0.0823088
-0.0791713
-0.0764437
-0.0509741
-0.0315983
-0.0183161
-0.00340114
--0.00542012
--0.0158742
--0.0279611
--0.0396104
--0.0160286
--0.00188697
-0.00281451
-0.0100455
-0.00783627
-0.00815656
-0.0110063
-0.0131783
-0.00591016
-0.00117148
--0.00103772
--0.00392469
--0.00428218
--0.00531744
--0.00703047
--0.0085619
--0.014332
--0.0189663
--0.0224649
--0.0262678
--0.0289349
--0.0319064
--0.0351822
--0.0383765
--0.0801973
--0.111668
--0.132789
--0.156683
--0.162696
--0.1735
--0.189095
--0.203407
--0.00510083
-0.136235
-0.341101
-0.528945
-0.801527
-1.0514
-1.15485
-1.29754
-1.16912
-1.11335
-0.760921
-0.487984
-0.24772
--0.00129903
--0.0610099
--0.171446
--0.102442
--0.081519
--0.108677
--0.122951
--0.0931296
--0.0751235
--0.0689329
--0.0595764
--0.0723311
--0.0791611
--0.0800665
--0.0825593
--0.0791275
--0.0772832
--0.0770263
--0.0763442
--0.078946
--0.080668
--0.0815099
--0.0825877
--0.0827855
--0.083219
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--0.0844945
--0.0842208
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--0.0870057
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--0.0874562
--0.08769
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--0.0881405
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--0.0885764
--0.0887984
--0.0890196
--0.0890797
--0.0891829
--0.0893293
--0.0894642
--0.0896423
--0.0898087
--0.0899636
--0.0901216
--0.0903228
--0.0905125
--0.0906905
--0.0908717
--0.0910413
--0.0912139
--0.0913897
--0.0915647
--0.0917828
--0.0919894
--0.0921844
--0.0923825
--0.092569
--0.0927586
--0.0929514
--0.0931433
--0.0933236
--0.093507
--0.0936935
--0.0938792
--0.094068
--0.094256
--0.0944431
--0.0946305
--0.103627
--0.110264
--0.11454
--0.119448
--0.121996
--0.125177
--0.12899
--0.132633
--0.133916
--0.135831
--0.138379
--0.140758
--0.143768
--0.14661
--0.149282
--0.151999
--0.121242
--0.0994544
--0.0866362
--0.0714146
--0.0651625
--0.056507
--0.0454482
--0.0350333
--0.033588
--0.0297392
--0.0234871
--0.017879
--0.00986753
--0.00250002
-0.00422351
-0.0111196
--0.00226639
--0.0102178
--0.0127347
--0.0167077
--0.0152462
--0.0152409
--0.0166917
--0.0177524
--0.0133785
--0.0104608
--0.00899926
--0.00714755
--0.00675204
--0.00596633
--0.00479045
--0.00371911
-0.00278678
-0.00783649
-0.01143
-0.0154137
-0.0179412
-0.0208589
-0.0241668
-0.0273702
-0.0291173
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-0.0337822
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-0.0347545
-0.0265225
-0.0222671
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-0.0156016
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-0.00971622
-0.00652626
-0.00731282
-0.00703387
-0.00568942
-0.00463047
-0.00250601
-0.000667052
--0.000886403
--0.00251636
--0.000169788
-0.00111128
-0.00132683
-0.00182789
-0.00126344
-0.000984496
-0.000991051
-0.000921107
--0.000214344
--0.00106429
--0.00162874
--0.00226969
--0.00262514
--0.00305708
--0.00356553
--0.00405348
diff -Nru gsl-doc-1.16/doc/examples/dwt.txt gsl-doc-2.3/doc/examples/dwt.txt
--- gsl-doc-1.16/doc/examples/dwt.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/dwt.txt	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,256 @@
+0.0167729
+0.031888
+0.0412921
+0.0522264
+0.0574496
+0.0642031
+0.0724869
+0.0803607
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+0.104007
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+0.0839935
+0.0839162
+0.0823088
+0.0791713
+0.0764437
+0.0509741
+0.0315983
+0.0183161
+0.00340114
+-0.00542012
+-0.0158742
+-0.0279611
+-0.0396104
+-0.0160286
+-0.00188697
+0.00281451
+0.0100455
+0.00783627
+0.00815656
+0.0110063
+0.0131783
+0.00591016
+0.00117148
+-0.00103772
+-0.00392469
+-0.00428218
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+-0.00226969
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+-0.00356553
+-0.00405348
diff -Nru gsl-doc-1.16/doc/examples/ecg.dat gsl-doc-2.3/doc/examples/ecg.dat
--- gsl-doc-1.16/doc/examples/ecg.dat	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/ecg.dat	1970-01-01 00:00:00.000000000 +0000
@@ -1,256 +0,0 @@
- 0.0462458471760794
- 0.0462458471760794
- 0.0512458471760794
- 0.0712458471760795
- 0.0712458471760795
- 0.0662458471760795
- 0.0962458471760795
- 0.101245847176079
- 0.116245847176079
- 0.121245847176079
- 0.116245847176079
- 0.106245847176079
- 0.0912458471760794
- 0.101245847176079
- 0.0962458471760795
- 0.0962458471760795
- 0.0962458471760795
- 0.0912458471760794
- 0.0862458471760795
- 0.0812458471760795
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- 0.101245847176079
- 0.111245847176079
- 0.116245847176079
- 0.0762458471760795
- 0.0362458471760795
- 0.0362458471760795
- 0.0212458471760795
- 0.0112458471760795
- -0.00875415282392056
- -0.00875415282392056
- -0.00375415282392055
- 0.00624584717607946
- 0.00124584717607945
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- 0.306245847176079
- 0.556245847176079
- 0.81124584717608
- 1.04124584717608
- 1.19624584717608
- 1.26124584717608
- 1.22624584717608
- 1.07624584717608
- 0.81124584717608
- 0.486245847176079
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- -0.00375415282392055
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- 0.0262458471760795
- 0.0312458471760795
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- 0.0112458471760795
- 0.00124584717607945
- 0.00624584717607946
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- 0.00624584717607946
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- -0.00375415282392055
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- -0.0187541528239206
- -0.0137541528239206
- -0.0137541528239206
- -0.00875415282392056
- -0.00375415282392055
- -0.0237541528239205
- -0.0287541528239205
- -0.0237541528239205
- -0.0137541528239206
- -0.00875415282392056
- -0.00875415282392056
- -0.0237541528239205
- -0.0237541528239205
- -0.0237541528239205
- 0.00124584717607945
- -0.00875415282392056
- -0.0137541528239206
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- -0.0337541528239205
- -0.0137541528239206
- -0.00875415282392056
- -0.00875415282392056
diff -Nru gsl-doc-1.16/doc/examples/eigen_nonsymm.txt gsl-doc-2.3/doc/examples/eigen_nonsymm.txt
--- gsl-doc-1.16/doc/examples/eigen_nonsymm.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/eigen_nonsymm.txt	2015-11-10 18:10:38.000000000 +0000
@@ -0,0 +1,24 @@
+eigenvalue = -6.41391 + 0i
+eigenvector = 
+0.0998822 + 0i
+0.111251 + 0i
+-0.292501 + 0i
+-0.944505 + 0i
+eigenvalue = 5.54555 + 3.08545i
+eigenvector = 
+0.0430757 + 0.00968662i
+-0.0709124 + 0.138917i
+0.516595 + -0.0160059i
+0.839574 + 0.0413888i
+eigenvalue = 5.54555 + -3.08545i
+eigenvector = 
+0.0430757 + -0.00968662i
+-0.0709124 + -0.138917i
+0.516595 + 0.0160059i
+0.839574 + -0.0413888i
+eigenvalue = 2.3228 + 0i
+eigenvector = 
+-0.144933 + 0i
+0.356601 + 0i
+0.919369 + 0i
+0.0811836 + 0i
diff -Nru gsl-doc-1.16/doc/examples/eigen.txt gsl-doc-2.3/doc/examples/eigen.txt
--- gsl-doc-1.16/doc/examples/eigen.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/eigen.txt	2015-11-10 18:09:48.000000000 +0000
@@ -0,0 +1,24 @@
+eigenvalue = 9.67023e-05
+eigenvector = 
+-0.0291933
+0.328712
+-0.791411
+0.514553
+eigenvalue = 0.00673827
+eigenvector = 
+-0.179186
+0.741918
+-0.100228
+-0.638283
+eigenvalue = 0.169141
+eigenvector = 
+0.582076
+-0.370502
+-0.509579
+-0.514048
+eigenvalue = 1.50021
+eigenvector = 
+0.792608
+0.451923
+0.322416
+0.252161
diff -Nru gsl-doc-1.16/doc/examples/expfit.c gsl-doc-2.3/doc/examples/expfit.c
--- gsl-doc-1.16/doc/examples/expfit.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/expfit.c	1970-01-01 00:00:00.000000000 +0000
@@ -1,70 +0,0 @@
-/* expfit.c -- model functions for exponential + background */
-
-struct data {
-  size_t n;
-  double * y;
-  double * sigma;
-};
-
-int
-expb_f (const gsl_vector * x, void *data, 
-        gsl_vector * f)
-{
-  size_t n = ((struct data *)data)->n;
-  double *y = ((struct data *)data)->y;
-  double *sigma = ((struct data *) data)->sigma;
-
-  double A = gsl_vector_get (x, 0);
-  double lambda = gsl_vector_get (x, 1);
-  double b = gsl_vector_get (x, 2);
-
-  size_t i;
-
-  for (i = 0; i < n; i++)
-    {
-      /* Model Yi = A * exp(-lambda * i) + b */
-      double t = i;
-      double Yi = A * exp (-lambda * t) + b;
-      gsl_vector_set (f, i, (Yi - y[i])/sigma[i]);
-    }
-
-  return GSL_SUCCESS;
-}
-
-int
-expb_df (const gsl_vector * x, void *data, 
-         gsl_matrix * J)
-{
-  size_t n = ((struct data *)data)->n;
-  double *sigma = ((struct data *) data)->sigma;
-
-  double A = gsl_vector_get (x, 0);
-  double lambda = gsl_vector_get (x, 1);
-
-  size_t i;
-
-  for (i = 0; i < n; i++)
-    {
-      /* Jacobian matrix J(i,j) = dfi / dxj, */
-      /* where fi = (Yi - yi)/sigma[i],      */
-      /*       Yi = A * exp(-lambda * i) + b  */
-      /* and the xj are the parameters (A,lambda,b) */
-      double t = i;
-      double s = sigma[i];
-      double e = exp(-lambda * t);
-      gsl_matrix_set (J, i, 0, e/s); 
-      gsl_matrix_set (J, i, 1, -t * A * e/s);
-      gsl_matrix_set (J, i, 2, 1/s);
-    }
-  return GSL_SUCCESS;
-}
-
-int
-expb_fdf (const gsl_vector * x, void *data,
-          gsl_vector * f, gsl_matrix * J)
-{
-  expb_f (x, data, f);
-  expb_df (x, data, J);
-
-  return GSL_SUCCESS;
-}
diff -Nru gsl-doc-1.16/doc/examples/fftmr.c gsl-doc-2.3/doc/examples/fftmr.c
--- gsl-doc-1.16/doc/examples/fftmr.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/fftmr.c	2015-11-09 19:10:38.000000000 +0000
@@ -39,9 +39,9 @@
   wavetable = gsl_fft_complex_wavetable_alloc (n);
   workspace = gsl_fft_complex_workspace_alloc (n);
 
-  for (i = 0; i < wavetable->nf; i++)
+  for (i = 0; i < (int) wavetable->nf; i++)
     {
-       printf ("# factor %d: %d\n", i, 
+       printf ("# factor %d: %zu\n", i, 
                wavetable->factor[i]);
     }
 
diff -Nru gsl-doc-1.16/doc/examples/fftmr.txt gsl-doc-2.3/doc/examples/fftmr.txt
--- gsl-doc-1.16/doc/examples/fftmr.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/fftmr.txt	2015-11-10 18:14:15.000000000 +0000
@@ -0,0 +1,1265 @@
+0: 1.000000e+00 0.000000e+00
+1: 1.000000e+00 0.000000e+00
+2: 1.000000e+00 0.000000e+00
+3: 1.000000e+00 0.000000e+00
+4: 1.000000e+00 0.000000e+00
+5: 1.000000e+00 0.000000e+00
+6: 1.000000e+00 0.000000e+00
+7: 1.000000e+00 0.000000e+00
+8: 1.000000e+00 0.000000e+00
+9: 1.000000e+00 0.000000e+00
+10: 1.000000e+00 0.000000e+00
+11: 0.000000e+00 0.000000e+00
+12: 0.000000e+00 0.000000e+00
+13: 0.000000e+00 0.000000e+00
+14: 0.000000e+00 0.000000e+00
+15: 0.000000e+00 0.000000e+00
+16: 0.000000e+00 0.000000e+00
+17: 0.000000e+00 0.000000e+00
+18: 0.000000e+00 0.000000e+00
+19: 0.000000e+00 0.000000e+00
+20: 0.000000e+00 0.000000e+00
+21: 0.000000e+00 0.000000e+00
+22: 0.000000e+00 0.000000e+00
+23: 0.000000e+00 0.000000e+00
+24: 0.000000e+00 0.000000e+00
+25: 0.000000e+00 0.000000e+00
+26: 0.000000e+00 0.000000e+00
+27: 0.000000e+00 0.000000e+00
+28: 0.000000e+00 0.000000e+00
+29: 0.000000e+00 0.000000e+00
+30: 0.000000e+00 0.000000e+00
+31: 0.000000e+00 0.000000e+00
+32: 0.000000e+00 0.000000e+00
+33: 0.000000e+00 0.000000e+00
+34: 0.000000e+00 0.000000e+00
+35: 0.000000e+00 0.000000e+00
+36: 0.000000e+00 0.000000e+00
+37: 0.000000e+00 0.000000e+00
+38: 0.000000e+00 0.000000e+00
+39: 0.000000e+00 0.000000e+00
+40: 0.000000e+00 0.000000e+00
+41: 0.000000e+00 0.000000e+00
+42: 0.000000e+00 0.000000e+00
+43: 0.000000e+00 0.000000e+00
+44: 0.000000e+00 0.000000e+00
+45: 0.000000e+00 0.000000e+00
+46: 0.000000e+00 0.000000e+00
+47: 0.000000e+00 0.000000e+00
+48: 0.000000e+00 0.000000e+00
+49: 0.000000e+00 0.000000e+00
+50: 0.000000e+00 0.000000e+00
+51: 0.000000e+00 0.000000e+00
+52: 0.000000e+00 0.000000e+00
+53: 0.000000e+00 0.000000e+00
+54: 0.000000e+00 0.000000e+00
+55: 0.000000e+00 0.000000e+00
+56: 0.000000e+00 0.000000e+00
+57: 0.000000e+00 0.000000e+00
+58: 0.000000e+00 0.000000e+00
+59: 0.000000e+00 0.000000e+00
+60: 0.000000e+00 0.000000e+00
+61: 0.000000e+00 0.000000e+00
+62: 0.000000e+00 0.000000e+00
+63: 0.000000e+00 0.000000e+00
+64: 0.000000e+00 0.000000e+00
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diff -Nru gsl-doc-1.16/doc/examples/fftreal.txt gsl-doc-2.3/doc/examples/fftreal.txt
--- gsl-doc-1.16/doc/examples/fftreal.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/fftreal.txt	2015-11-10 18:14:51.000000000 +0000
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diff -Nru gsl-doc-1.16/doc/examples/fft.txt gsl-doc-2.3/doc/examples/fft.txt
--- gsl-doc-1.16/doc/examples/fft.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/fft.txt	2015-11-10 18:12:54.000000000 +0000
@@ -0,0 +1,257 @@
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diff -Nru gsl-doc-1.16/doc/examples/fitreg2.c gsl-doc-2.3/doc/examples/fitreg2.c
--- gsl-doc-1.16/doc/examples/fitreg2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/fitreg2.c	2016-10-27 11:23:41.000000000 +0000
@@ -0,0 +1,142 @@
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_multifit.h>
+#include <gsl/gsl_blas.h>
+
+static int
+hilbert_matrix(gsl_matrix * m)
+{
+  const size_t N = m->size1;
+  const size_t M = m->size2;
+  size_t i, j;
+
+  for (i = 0; i < N; i++)
+    {
+      for (j = 0; j < M; j++)
+        {
+          gsl_matrix_set(m, i, j, 1.0/(i+j+1.0));
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+int
+main()
+{
+  const size_t n = 10; /* number of observations */
+  const size_t p = 8;  /* number of model parameters */
+  size_t i;
+  gsl_matrix *X = gsl_matrix_alloc(n, p);
+  gsl_vector *y = gsl_vector_alloc(n);
+
+  /* construct Hilbert matrix and rhs vector */
+  hilbert_matrix(X);
+
+  {
+    double val = 1.0;
+    for (i = 0; i < n; ++i)
+      {
+        gsl_vector_set(y, i, val);
+        val *= -1.0;
+      }
+  }
+
+  {
+    const size_t npoints = 200;                   /* number of points on L-curve and GCV curve */
+    gsl_multifit_linear_workspace *w =
+      gsl_multifit_linear_alloc(n, p);
+    gsl_vector *c = gsl_vector_alloc(p);          /* OLS solution */
+    gsl_vector *c_lcurve = gsl_vector_alloc(p);   /* regularized solution (L-curve) */
+    gsl_vector *c_gcv = gsl_vector_alloc(p);      /* regularized solution (GCV) */
+    gsl_vector *reg_param = gsl_vector_alloc(npoints);
+    gsl_vector *rho = gsl_vector_alloc(npoints);  /* residual norms */
+    gsl_vector *eta = gsl_vector_alloc(npoints);  /* solution norms */
+    gsl_vector *G = gsl_vector_alloc(npoints);    /* GCV function values */
+    double lambda_l;                              /* optimal regularization parameter (L-curve) */
+    double lambda_gcv;                            /* optimal regularization parameter (GCV) */
+    double G_gcv;                                 /* G(lambda_gcv) */
+    size_t reg_idx;                               /* index of optimal lambda */
+    double rcond;                                 /* reciprocal condition number of X */
+    double chisq, rnorm, snorm;
+
+    /* compute SVD of X */
+    gsl_multifit_linear_svd(X, w);
+
+    rcond = gsl_multifit_linear_rcond(w);
+    fprintf(stderr, "matrix condition number = %e\n", 1.0 / rcond);
+
+    /* unregularized (standard) least squares fit, lambda = 0 */
+    gsl_multifit_linear_solve(0.0, X, y, c, &rnorm, &snorm, w);
+    chisq = pow(rnorm, 2.0);
+
+    fprintf(stderr, "=== Unregularized fit ===\n");
+    fprintf(stderr, "residual norm = %g\n", rnorm);
+    fprintf(stderr, "solution norm = %g\n", snorm);
+    fprintf(stderr, "chisq/dof = %g\n", chisq / (n - p));
+
+    /* calculate L-curve and find its corner */
+    gsl_multifit_linear_lcurve(y, reg_param, rho, eta, w);
+    gsl_multifit_linear_lcorner(rho, eta, &reg_idx);
+
+    /* store optimal regularization parameter */
+    lambda_l = gsl_vector_get(reg_param, reg_idx);
+
+    /* regularize with lambda_l */
+    gsl_multifit_linear_solve(lambda_l, X, y, c_lcurve, &rnorm, &snorm, w);
+    chisq = pow(rnorm, 2.0) + pow(lambda_l * snorm, 2.0);
+
+    fprintf(stderr, "=== Regularized fit (L-curve) ===\n");
+    fprintf(stderr, "optimal lambda: %g\n", lambda_l);
+    fprintf(stderr, "residual norm = %g\n", rnorm);
+    fprintf(stderr, "solution norm = %g\n", snorm);
+    fprintf(stderr, "chisq/dof = %g\n", chisq / (n - p));
+
+    /* calculate GCV curve and find its minimum */
+    gsl_multifit_linear_gcv(y, reg_param, G, &lambda_gcv, &G_gcv, w);
+
+    /* regularize with lambda_gcv */
+    gsl_multifit_linear_solve(lambda_gcv, X, y, c_gcv, &rnorm, &snorm, w);
+    chisq = pow(rnorm, 2.0) + pow(lambda_gcv * snorm, 2.0);
+
+    fprintf(stderr, "=== Regularized fit (GCV) ===\n");
+    fprintf(stderr, "optimal lambda: %g\n", lambda_gcv);
+    fprintf(stderr, "residual norm = %g\n", rnorm);
+    fprintf(stderr, "solution norm = %g\n", snorm);
+    fprintf(stderr, "chisq/dof = %g\n", chisq / (n - p));
+
+    /* output L-curve and GCV curve */
+    for (i = 0; i < npoints; ++i)
+      {
+        printf("%e %e %e %e\n",
+               gsl_vector_get(reg_param, i),
+               gsl_vector_get(rho, i),
+               gsl_vector_get(eta, i),
+               gsl_vector_get(G, i));
+      }
+
+    /* output L-curve corner point */
+    printf("\n\n%f %f\n",
+           gsl_vector_get(rho, reg_idx),
+           gsl_vector_get(eta, reg_idx));
+
+    /* output GCV curve corner minimum */
+    printf("\n\n%e %e\n",
+           lambda_gcv,
+           G_gcv);
+
+    gsl_multifit_linear_free(w);
+    gsl_vector_free(c);
+    gsl_vector_free(c_lcurve);
+    gsl_vector_free(reg_param);
+    gsl_vector_free(rho);
+    gsl_vector_free(eta);
+    gsl_vector_free(G);
+  }
+
+  gsl_matrix_free(X);
+  gsl_vector_free(y);
+
+  return 0;
+}
diff -Nru gsl-doc-1.16/doc/examples/fitreg2.txt gsl-doc-2.3/doc/examples/fitreg2.txt
--- gsl-doc-1.16/doc/examples/fitreg2.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/fitreg2.txt	2016-10-27 11:23:47.000000000 +0000
@@ -0,0 +1,206 @@
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diff -Nru gsl-doc-1.16/doc/examples/fitreg.c gsl-doc-2.3/doc/examples/fitreg.c
--- gsl-doc-1.16/doc/examples/fitreg.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/fitreg.c	2016-10-27 11:20:46.000000000 +0000
@@ -0,0 +1,140 @@
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_randist.h>
+#include <gsl/gsl_multifit.h>
+
+int
+main()
+{
+  const size_t n = 1000; /* number of observations */
+  const size_t p = 2;    /* number of model parameters */
+  size_t i;
+  gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+  gsl_matrix *X = gsl_matrix_alloc(n, p);
+  gsl_vector *y = gsl_vector_alloc(n);
+
+  for (i = 0; i < n; ++i)
+    {
+      /* generate first random variable u */
+      double ui = 5.0 * gsl_ran_gaussian(r, 1.0);
+
+      /* set v = u + noise */
+      double vi = ui + gsl_ran_gaussian(r, 0.001);
+
+      /* set y = u + v + noise */
+      double yi = ui + vi + gsl_ran_gaussian(r, 1.0);
+
+      /* since u =~ v, the matrix X is ill-conditioned */
+      gsl_matrix_set(X, i, 0, ui);
+      gsl_matrix_set(X, i, 1, vi);
+
+      /* rhs vector */
+      gsl_vector_set(y, i, yi);
+    }
+
+  {
+    const size_t npoints = 200;                   /* number of points on L-curve and GCV curve */
+    gsl_multifit_linear_workspace *w =
+      gsl_multifit_linear_alloc(n, p);
+    gsl_vector *c = gsl_vector_alloc(p);          /* OLS solution */
+    gsl_vector *c_lcurve = gsl_vector_alloc(p);   /* regularized solution (L-curve) */
+    gsl_vector *c_gcv = gsl_vector_alloc(p);      /* regularized solution (GCV) */
+    gsl_vector *reg_param = gsl_vector_alloc(npoints);
+    gsl_vector *rho = gsl_vector_alloc(npoints);  /* residual norms */
+    gsl_vector *eta = gsl_vector_alloc(npoints);  /* solution norms */
+    gsl_vector *G = gsl_vector_alloc(npoints);    /* GCV function values */
+    double lambda_l;                              /* optimal regularization parameter (L-curve) */
+    double lambda_gcv;                            /* optimal regularization parameter (GCV) */
+    double G_gcv;                                 /* G(lambda_gcv) */
+    size_t reg_idx;                               /* index of optimal lambda */
+    double rcond;                                 /* reciprocal condition number of X */
+    double chisq, rnorm, snorm;
+
+    /* compute SVD of X */
+    gsl_multifit_linear_svd(X, w);
+
+    rcond = gsl_multifit_linear_rcond(w);
+    fprintf(stderr, "matrix condition number = %e\n", 1.0 / rcond);
+
+    /* unregularized (standard) least squares fit, lambda = 0 */
+    gsl_multifit_linear_solve(0.0, X, y, c, &rnorm, &snorm, w);
+    chisq = pow(rnorm, 2.0);
+
+    fprintf(stderr, "=== Unregularized fit ===\n");
+    fprintf(stderr, "best fit: y = %g u + %g v\n",
+      gsl_vector_get(c, 0), gsl_vector_get(c, 1));
+    fprintf(stderr, "residual norm = %g\n", rnorm);
+    fprintf(stderr, "solution norm = %g\n", snorm);
+    fprintf(stderr, "chisq/dof = %g\n", chisq / (n - p));
+
+    /* calculate L-curve and find its corner */
+    gsl_multifit_linear_lcurve(y, reg_param, rho, eta, w);
+    gsl_multifit_linear_lcorner(rho, eta, &reg_idx);
+
+    /* store optimal regularization parameter */
+    lambda_l = gsl_vector_get(reg_param, reg_idx);
+
+    /* regularize with lambda_l */
+    gsl_multifit_linear_solve(lambda_l, X, y, c_lcurve, &rnorm, &snorm, w);
+    chisq = pow(rnorm, 2.0) + pow(lambda_l * snorm, 2.0);
+
+    fprintf(stderr, "=== Regularized fit (L-curve) ===\n");
+    fprintf(stderr, "optimal lambda: %g\n", lambda_l);
+    fprintf(stderr, "best fit: y = %g u + %g v\n",
+            gsl_vector_get(c_lcurve, 0), gsl_vector_get(c_lcurve, 1));
+    fprintf(stderr, "residual norm = %g\n", rnorm);
+    fprintf(stderr, "solution norm = %g\n", snorm);
+    fprintf(stderr, "chisq/dof = %g\n", chisq / (n - p));
+
+    /* calculate GCV curve and find its minimum */
+    gsl_multifit_linear_gcv(y, reg_param, G, &lambda_gcv, &G_gcv, w);
+
+    /* regularize with lambda_gcv */
+    gsl_multifit_linear_solve(lambda_gcv, X, y, c_gcv, &rnorm, &snorm, w);
+    chisq = pow(rnorm, 2.0) + pow(lambda_gcv * snorm, 2.0);
+
+    fprintf(stderr, "=== Regularized fit (GCV) ===\n");
+    fprintf(stderr, "optimal lambda: %g\n", lambda_gcv);
+    fprintf(stderr, "best fit: y = %g u + %g v\n",
+            gsl_vector_get(c_gcv, 0), gsl_vector_get(c_gcv, 1));
+    fprintf(stderr, "residual norm = %g\n", rnorm);
+    fprintf(stderr, "solution norm = %g\n", snorm);
+    fprintf(stderr, "chisq/dof = %g\n", chisq / (n - p));
+
+    /* output L-curve and GCV curve */
+    for (i = 0; i < npoints; ++i)
+      {
+        printf("%e %e %e %e\n",
+               gsl_vector_get(reg_param, i),
+               gsl_vector_get(rho, i),
+               gsl_vector_get(eta, i),
+               gsl_vector_get(G, i));
+      }
+
+    /* output L-curve corner point */
+    printf("\n\n%f %f\n",
+           gsl_vector_get(rho, reg_idx),
+           gsl_vector_get(eta, reg_idx));
+
+    /* output GCV curve corner minimum */
+    printf("\n\n%e %e\n",
+           lambda_gcv,
+           G_gcv);
+
+    gsl_multifit_linear_free(w);
+    gsl_vector_free(c);
+    gsl_vector_free(c_lcurve);
+    gsl_vector_free(reg_param);
+    gsl_vector_free(rho);
+    gsl_vector_free(eta);
+    gsl_vector_free(G);
+  }
+
+  gsl_rng_free(r);
+  gsl_matrix_free(X);
+  gsl_vector_free(y);
+
+  return 0;
+}
diff -Nru gsl-doc-1.16/doc/examples/fitreg.txt gsl-doc-2.3/doc/examples/fitreg.txt
--- gsl-doc-1.16/doc/examples/fitreg.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/fitreg.txt	2016-10-27 11:20:46.000000000 +0000
@@ -0,0 +1,206 @@
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+
+
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+
+
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diff -Nru gsl-doc-1.16/doc/examples/fitting2.txt gsl-doc-2.3/doc/examples/fitting2.txt
--- gsl-doc-1.16/doc/examples/fitting2.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/fitting2.txt	2015-11-10 18:40:34.000000000 +0000
@@ -0,0 +1,25 @@
+0.1 0.97935 +/- 0.110517
+0.2 1.3359 +/- 0.12214
+0.3 1.52573 +/- 0.134986
+0.4 1.60318 +/- 0.149182
+0.5 1.81731 +/- 0.164872
+0.6 1.92475 +/- 0.182212
+0.7 1.93249 +/- 0.201375
+0.8 2.5107 +/- 0.222554
+0.9 2.45078 +/- 0.24596
+1 2.24949 +/- 0.271828
+1.1 3.08955 +/- 0.300417
+1.2 3.82315 +/- 0.332012
+1.3 4.26766 +/- 0.36693
+1.4 3.2597 +/- 0.40552
+1.5 4.98914 +/- 0.448169
+1.6 4.14527 +/- 0.495303
+1.7 5.22382 +/- 0.547395
+1.8 6.3838 +/- 0.604965
+1.9 6.00277 +/- 0.668589
+# best fit: Y = 1.02318 + 0.956201 X + 0.876796 X^2
+# covariance matrix:
+[ +1.25612e-02, -3.64387e-02, +1.94389e-02  
+  -3.64387e-02, +1.42339e-01, -8.48761e-02  
+  +1.94389e-02, -8.48761e-02, +5.60243e-02 ]
+# chisq = 23.0987
diff -Nru gsl-doc-1.16/doc/examples/fitting.txt gsl-doc-2.3/doc/examples/fitting.txt
--- gsl-doc-1.16/doc/examples/fitting.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/fitting.txt	2015-11-10 18:29:34.000000000 +0000
@@ -0,0 +1,490 @@
+# best fit: Y = -106.6 + 0.06 X
+# covariance matrix:
+# [ 39602, -19.9
+#   -19.9, 0.01]
+# chisq = 0.8
+data: 1970 12 3.16228
+data: 1980 11 2.23607
+data: 1990 14 1.82574
+data: 2000 13 1.58114
+
+fit: 1961 11.06
+hi : 1961 14.1276
+lo : 1961 7.99243
+fit: 1961.3 11.078
+hi : 1961.3 14.1172
+lo : 1961.3 8.03877
+fit: 1961.6 11.096
+hi : 1961.6 14.1069
+lo : 1961.6 8.08509
+fit: 1961.9 11.114
+hi : 1961.9 14.0966
+lo : 1961.9 8.13137
+fit: 1962.2 11.132
+hi : 1962.2 14.0864
+lo : 1962.2 8.17761
+fit: 1962.5 11.15
+hi : 1962.5 14.0762
+lo : 1962.5 8.22383
+fit: 1962.8 11.168
+hi : 1962.8 14.066
+lo : 1962.8 8.27
+fit: 1963.1 11.186
+hi : 1963.1 14.0559
+lo : 1963.1 8.31614
+fit: 1963.4 11.204
+hi : 1963.4 14.0458
+lo : 1963.4 8.36224
+fit: 1963.7 11.222
+hi : 1963.7 14.0357
+lo : 1963.7 8.4083
+fit: 1964 11.24
+hi : 1964 14.0257
+lo : 1964 8.45432
+fit: 1964.3 11.258
+hi : 1964.3 14.0157
+lo : 1964.3 8.5003
+fit: 1964.6 11.276
+hi : 1964.6 14.0058
+lo : 1964.6 8.54624
+fit: 1964.9 11.294
+hi : 1964.9 13.9959
+lo : 1964.9 8.59213
+fit: 1965.2 11.312
+hi : 1965.2 13.986
+lo : 1965.2 8.63798
+fit: 1965.5 11.33
+hi : 1965.5 13.9762
+lo : 1965.5 8.68378
+fit: 1965.8 11.348
+hi : 1965.8 13.9665
+lo : 1965.8 8.72953
+fit: 1966.1 11.366
+hi : 1966.1 13.9568
+lo : 1966.1 8.77523
+fit: 1966.4 11.384
+hi : 1966.4 13.9471
+lo : 1966.4 8.82088
+fit: 1966.7 11.402
+hi : 1966.7 13.9375
+lo : 1966.7 8.86647
+fit: 1967 11.42
+hi : 1967 13.928
+lo : 1967 8.91201
+fit: 1967.3 11.438
+hi : 1967.3 13.9185
+lo : 1967.3 8.9575
+fit: 1967.6 11.456
+hi : 1967.6 13.9091
+lo : 1967.6 9.00292
+fit: 1967.9 11.474
+hi : 1967.9 13.8997
+lo : 1967.9 9.04828
+fit: 1968.2 11.492
+hi : 1968.2 13.8904
+lo : 1968.2 9.09358
+fit: 1968.5 11.51
+hi : 1968.5 13.8812
+lo : 1968.5 9.13882
+fit: 1968.8 11.528
+hi : 1968.8 13.872
+lo : 1968.8 9.18399
+fit: 1969.1 11.546
+hi : 1969.1 13.8629
+lo : 1969.1 9.22908
+fit: 1969.4 11.564
+hi : 1969.4 13.8539
+lo : 1969.4 9.27411
+fit: 1969.7 11.582
+hi : 1969.7 13.8449
+lo : 1969.7 9.31906
+fit: 1970 11.6
+hi : 1970 13.8361
+lo : 1970 9.36393
+fit: 1970.3 11.618
+hi : 1970.3 13.8273
+lo : 1970.3 9.40872
+fit: 1970.6 11.636
+hi : 1970.6 13.8186
+lo : 1970.6 9.45343
+fit: 1970.9 11.654
+hi : 1970.9 13.8099
+lo : 1970.9 9.49805
+fit: 1971.2 11.672
+hi : 1971.2 13.8014
+lo : 1971.2 9.54259
+fit: 1971.5 11.69
+hi : 1971.5 13.793
+lo : 1971.5 9.58703
+fit: 1971.8 11.708
+hi : 1971.8 13.7846
+lo : 1971.8 9.63137
+fit: 1972.1 11.726
+hi : 1972.1 13.7764
+lo : 1972.1 9.67561
+fit: 1972.4 11.744
+hi : 1972.4 13.7683
+lo : 1972.4 9.71975
+fit: 1972.7 11.762
+hi : 1972.7 13.7602
+lo : 1972.7 9.76378
+fit: 1973 11.78
+hi : 1973 13.7523
+lo : 1973 9.80769
+fit: 1973.3 11.798
+hi : 1973.3 13.7445
+lo : 1973.3 9.85149
+fit: 1973.6 11.816
+hi : 1973.6 13.7368
+lo : 1973.6 9.89517
+fit: 1973.9 11.834
+hi : 1973.9 13.7293
+lo : 1973.9 9.93872
+fit: 1974.2 11.852
+hi : 1974.2 13.7219
+lo : 1974.2 9.98213
+fit: 1974.5 11.87
+hi : 1974.5 13.7146
+lo : 1974.5 10.0254
+fit: 1974.8 11.888
+hi : 1974.8 13.7075
+lo : 1974.8 10.0685
+fit: 1975.1 11.906
+hi : 1975.1 13.7005
+lo : 1975.1 10.1115
+fit: 1975.4 11.924
+hi : 1975.4 13.6936
+lo : 1975.4 10.1544
+fit: 1975.7 11.942
+hi : 1975.7 13.687
+lo : 1975.7 10.197
+fit: 1976 11.96
+hi : 1976 13.6805
+lo : 1976 10.2395
+fit: 1976.3 11.978
+hi : 1976.3 13.6741
+lo : 1976.3 10.2819
+fit: 1976.6 11.996
+hi : 1976.6 13.668
+lo : 1976.6 10.324
+fit: 1976.9 12.014
+hi : 1976.9 13.6621
+lo : 1976.9 10.3659
+fit: 1977.2 12.032
+hi : 1977.2 13.6563
+lo : 1977.2 10.4077
+fit: 1977.5 12.05
+hi : 1977.5 13.6508
+lo : 1977.5 10.4492
+fit: 1977.8 12.068
+hi : 1977.8 13.6455
+lo : 1977.8 10.4905
+fit: 1978.1 12.086
+hi : 1978.1 13.6404
+lo : 1978.1 10.5316
+fit: 1978.4 12.104
+hi : 1978.4 13.6355
+lo : 1978.4 10.5725
+fit: 1978.7 12.122
+hi : 1978.7 13.6309
+lo : 1978.7 10.6131
+fit: 1979 12.14
+hi : 1979 13.6266
+lo : 1979 10.6534
+fit: 1979.3 12.158
+hi : 1979.3 13.6225
+lo : 1979.3 10.6935
+fit: 1979.6 12.176
+hi : 1979.6 13.6188
+lo : 1979.6 10.7332
+fit: 1979.9 12.194
+hi : 1979.9 13.6153
+lo : 1979.9 10.7727
+fit: 1980.2 12.212
+hi : 1980.2 13.6121
+lo : 1980.2 10.8119
+fit: 1980.5 12.23
+hi : 1980.5 13.6093
+lo : 1980.5 10.8507
+fit: 1980.8 12.248
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+lo : 1980.8 10.8892
+fit: 1981.1 12.266
+hi : 1981.1 13.6047
+lo : 1981.1 10.9273
+fit: 1981.4 12.284
+hi : 1981.4 13.6029
+lo : 1981.4 10.9651
+fit: 1981.7 12.302
+hi : 1981.7 13.6016
+lo : 1981.7 11.0024
+fit: 1982 12.32
+hi : 1982 13.6006
+lo : 1982 11.0394
+fit: 1982.3 12.338
+hi : 1982.3 13.6001
+lo : 1982.3 11.0759
+fit: 1982.6 12.356
+hi : 1982.6 13.6
+lo : 1982.6 11.112
+fit: 1982.9 12.374
+hi : 1982.9 13.6004
+lo : 1982.9 11.1476
+fit: 1983.2 12.392
+hi : 1983.2 13.6013
+lo : 1983.2 11.1827
+fit: 1983.5 12.41
+hi : 1983.5 13.6027
+lo : 1983.5 11.2173
+fit: 1983.8 12.428
+hi : 1983.8 13.6046
+lo : 1983.8 11.2514
+fit: 1984.1 12.446
+hi : 1984.1 13.6071
+lo : 1984.1 11.2849
+fit: 1984.4 12.464
+hi : 1984.4 13.6101
+lo : 1984.4 11.3179
+fit: 1984.7 12.482
+hi : 1984.7 13.6138
+lo : 1984.7 11.3502
+fit: 1985 12.5
+hi : 1985 13.618
+lo : 1985 11.382
+fit: 1985.3 12.518
+hi : 1985.3 13.6229
+lo : 1985.3 11.4131
+fit: 1985.6 12.536
+hi : 1985.6 13.6285
+lo : 1985.6 11.4435
+fit: 1985.9 12.554
+hi : 1985.9 13.6348
+lo : 1985.9 11.4732
+fit: 1986.2 12.572
+hi : 1986.2 13.6418
+lo : 1986.2 11.5022
+fit: 1986.5 12.59
+hi : 1986.5 13.6495
+lo : 1986.5 11.5305
+fit: 1986.8 12.608
+hi : 1986.8 13.658
+lo : 1986.8 11.558
+fit: 1987.1 12.626
+hi : 1987.1 13.6672
+lo : 1987.1 11.5848
+fit: 1987.4 12.644
+hi : 1987.4 13.6772
+lo : 1987.4 11.6108
+fit: 1987.7 12.662
+hi : 1987.7 13.6881
+lo : 1987.7 11.6359
+fit: 1988 12.68
+hi : 1988 13.6998
+lo : 1988 11.6602
+fit: 1988.3 12.698
+hi : 1988.3 13.7123
+lo : 1988.3 11.6837
+fit: 1988.6 12.716
+hi : 1988.6 13.7258
+lo : 1988.6 11.7062
+fit: 1988.9 12.734
+hi : 1988.9 13.74
+lo : 1988.9 11.728
+fit: 1989.2 12.752
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+lo : 1989.5 11.7688
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+lo : 1989.8 11.7878
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+hi : 1990.4 13.8248
+lo : 1990.4 11.8232
+fit: 1990.7 12.842
+hi : 1990.7 13.8444
+lo : 1990.7 11.8396
+fit: 1991 12.86
+hi : 1991 13.865
+lo : 1991 11.855
+fit: 1991.3 12.878
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+lo : 1991.3 11.8696
+fit: 1991.6 12.896
+hi : 1991.6 13.9087
+lo : 1991.6 11.8833
+fit: 1991.9 12.914
+hi : 1991.9 13.9319
+lo : 1991.9 11.8961
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+lo : 1992.2 11.9081
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+lo : 1992.5 11.9192
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+lo : 1993.4 11.9478
+fit: 1993.7 13.022
+hi : 1993.7 14.0883
+lo : 1993.7 11.9557
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+hi : 1994 14.117
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+hi : 1996.7 14.4057
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+hi : 1997.3 14.4761
+lo : 1997.3 11.9999
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diff -Nru gsl-doc-1.16/doc/examples/histogram2d.txt gsl-doc-2.3/doc/examples/histogram2d.txt
--- gsl-doc-1.16/doc/examples/histogram2d.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/histogram2d.txt	2015-11-10 18:41:47.000000000 +0000
@@ -0,0 +1,1000 @@
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diff -Nru gsl-doc-1.16/doc/examples/ieeeround.txt gsl-doc-2.3/doc/examples/ieeeround.txt
--- gsl-doc-1.16/doc/examples/ieeeround.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/ieeeround.txt	2015-11-10 18:43:43.000000000 +0000
@@ -0,0 +1,19 @@
+i= 1 sum=1.000000000000000000 error=-1.71828
+i= 2 sum=2.000000000000000000 error=-0.718282
+i= 3 sum=2.500000000000000000 error=-0.218282
+i= 4 sum=2.666666666666666519 error=-0.0516152
+i= 5 sum=2.708333333333333037 error=-0.0099485
+i= 6 sum=2.716666666666666341 error=-0.00161516
+i= 7 sum=2.718055555555555447 error=-0.000226273
+i= 8 sum=2.718253968253968367 error=-2.78602e-05
+i= 9 sum=2.718278769841270037 error=-3.05862e-06
+i=10 sum=2.718281525573192248 error=-3.02886e-07
+i=11 sum=2.718281801146384513 error=-2.73127e-08
+i=12 sum=2.718281826198492901 error=-2.26055e-09
+i=13 sum=2.718281828286168711 error=-1.72876e-10
+i=14 sum=2.718281828446759363 error=-1.22857e-11
+i=15 sum=2.718281828458230187 error=-8.14904e-13
+i=16 sum=2.718281828458994909 error=-5.01821e-14
+i=17 sum=2.718281828459042870 error=-2.22045e-15
+i=18 sum=2.718281828459045535 error=4.44089e-16
+i=19 sum=2.718281828459045535 error=4.44089e-16
diff -Nru gsl-doc-1.16/doc/examples/ieee.txt gsl-doc-2.3/doc/examples/ieee.txt
--- gsl-doc-1.16/doc/examples/ieee.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/ieee.txt	2015-11-10 18:42:56.000000000 +0000
@@ -0,0 +1,3 @@
+ f= 1.01010101010101010101011*2^-2
+fd= 1.0101010101010101010101100000000000000000000000000000*2^-2
+ d= 1.0101010101010101010101010101010101010101010101010101*2^-2
diff -Nru gsl-doc-1.16/doc/examples/integration.c gsl-doc-2.3/doc/examples/integration.c
--- gsl-doc-1.16/doc/examples/integration.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/integration.c	2015-11-09 19:11:09.000000000 +0000
@@ -29,7 +29,7 @@
   printf ("exact result    = % .18f\n", expected);
   printf ("estimated error = % .18f\n", error);
   printf ("actual error    = % .18f\n", result - expected);
-  printf ("intervals =  %d\n", w->size);
+  printf ("intervals       = %zu\n", w->size);
 
   gsl_integration_workspace_free (w);
 
diff -Nru gsl-doc-1.16/doc/examples/integration.out gsl-doc-2.3/doc/examples/integration.out
--- gsl-doc-1.16/doc/examples/integration.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/integration.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,5 +0,0 @@
-result          = -3.999999999999973799
-exact result    = -4.000000000000000000
-estimated error =  0.000000000000246025
-actual error    =  0.000000000000026201
-intervals =  8
diff -Nru gsl-doc-1.16/doc/examples/integration.txt gsl-doc-2.3/doc/examples/integration.txt
--- gsl-doc-1.16/doc/examples/integration.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/integration.txt	2015-11-10 18:44:36.000000000 +0000
@@ -0,0 +1,5 @@
+result          = -4.000000000000085265
+exact result    = -4.000000000000000000
+estimated error =  0.000000000000135447
+actual error    = -0.000000000000085265
+intervals       = 8
diff -Nru gsl-doc-1.16/doc/examples/interp2d.c gsl-doc-2.3/doc/examples/interp2d.c
--- gsl-doc-1.16/doc/examples/interp2d.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/interp2d.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,53 @@
+#include <stdio.h>
+#include <stdlib.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_interp2d.h>
+#include <gsl/gsl_spline2d.h>
+
+int
+main()
+{
+  const gsl_interp2d_type *T = gsl_interp2d_bilinear;
+  const size_t N = 100;             /* number of points to interpolate */
+  const double xa[] = { 0.0, 1.0 }; /* define unit square */
+  const double ya[] = { 0.0, 1.0 };
+  const size_t nx = sizeof(xa) / sizeof(double); /* x grid points */
+  const size_t ny = sizeof(ya) / sizeof(double); /* y grid points */
+  double *za = malloc(nx * ny * sizeof(double));
+  gsl_spline2d *spline = gsl_spline2d_alloc(T, nx, ny);
+  gsl_interp_accel *xacc = gsl_interp_accel_alloc();
+  gsl_interp_accel *yacc = gsl_interp_accel_alloc();
+  size_t i, j;
+
+  /* set z grid values */
+  gsl_spline2d_set(spline, za, 0, 0, 0.0);
+  gsl_spline2d_set(spline, za, 0, 1, 1.0);
+  gsl_spline2d_set(spline, za, 1, 1, 0.5);
+  gsl_spline2d_set(spline, za, 1, 0, 1.0);
+
+  /* initialize interpolation */
+  gsl_spline2d_init(spline, xa, ya, za, nx, ny);
+
+  /* interpolate N values in x and y and print out grid for plotting */
+  for (i = 0; i < N; ++i)
+    {
+      double xi = i / (N - 1.0);
+
+      for (j = 0; j < N; ++j)
+        {
+          double yj = j / (N - 1.0);
+          double zij = gsl_spline2d_eval(spline, xi, yj, xacc, yacc);
+
+          printf("%f %f %f\n", xi, yj, zij);
+        }
+      printf("\n");
+    }
+
+  gsl_spline2d_free(spline);
+  gsl_interp_accel_free(xacc);
+  gsl_interp_accel_free(yacc);
+  free(za);
+
+  return 0;
+}
diff -Nru gsl-doc-1.16/doc/examples/interp2d.txt gsl-doc-2.3/doc/examples/interp2d.txt
--- gsl-doc-1.16/doc/examples/interp2d.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/interp2d.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,10100 @@
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+1.000000 0.787879 0.606061
+1.000000 0.797980 0.601010
+1.000000 0.808081 0.595960
+1.000000 0.818182 0.590909
+1.000000 0.828283 0.585859
+1.000000 0.838384 0.580808
+1.000000 0.848485 0.575758
+1.000000 0.858586 0.570707
+1.000000 0.868687 0.565657
+1.000000 0.878788 0.560606
+1.000000 0.888889 0.555556
+1.000000 0.898990 0.550505
+1.000000 0.909091 0.545455
+1.000000 0.919192 0.540404
+1.000000 0.929293 0.535354
+1.000000 0.939394 0.530303
+1.000000 0.949495 0.525253
+1.000000 0.959596 0.520202
+1.000000 0.969697 0.515152
+1.000000 0.979798 0.510101
+1.000000 0.989899 0.505051
+1.000000 1.000000 0.500000
+
diff -Nru gsl-doc-1.16/doc/examples/interp_compare.c gsl-doc-2.3/doc/examples/interp_compare.c
--- gsl-doc-1.16/doc/examples/interp_compare.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/interp_compare.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,53 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_spline.h>
+
+int
+main(void)
+{
+  size_t i;
+  const size_t N = 9;
+
+  /* this dataset is taken from
+   * J. M. Hyman, Accurate Monotonicity preserving cubic interpolation,
+   * SIAM J. Sci. Stat. Comput. 4, 4, 1983. */
+  const double x[] = { 7.99, 8.09, 8.19, 8.7, 9.2,
+                       10.0, 12.0, 15.0, 20.0 };
+  const double y[] = { 0.0, 2.76429e-5, 4.37498e-2,
+                       0.169183, 0.469428, 0.943740,
+                       0.998636, 0.999919, 0.999994 };
+
+  gsl_interp_accel *acc = gsl_interp_accel_alloc();
+  gsl_spline *spline_cubic = gsl_spline_alloc(gsl_interp_cspline, N);
+  gsl_spline *spline_akima = gsl_spline_alloc(gsl_interp_akima, N);
+  gsl_spline *spline_steffen = gsl_spline_alloc(gsl_interp_steffen, N);
+
+  gsl_spline_init(spline_cubic, x, y, N);
+  gsl_spline_init(spline_akima, x, y, N);
+  gsl_spline_init(spline_steffen, x, y, N);
+
+  for (i = 0; i < N; ++i)
+    printf("%g %g\n", x[i], y[i]);
+
+  printf("\n\n");
+
+  for (i = 0; i <= 100; ++i)
+    {
+      double xi = (1 - i / 100.0) * x[0] + (i / 100.0) * x[N-1];
+      double yi_cubic = gsl_spline_eval(spline_cubic, xi, acc);
+      double yi_akima = gsl_spline_eval(spline_akima, xi, acc);
+      double yi_steffen = gsl_spline_eval(spline_steffen, xi, acc);
+
+      printf("%g %g %g %g\n", xi, yi_cubic, yi_akima, yi_steffen);
+    }
+
+  gsl_spline_free(spline_cubic);
+  gsl_spline_free(spline_akima);
+  gsl_spline_free(spline_steffen);
+  gsl_interp_accel_free(acc);
+
+  return 0;
+}
diff -Nru gsl-doc-1.16/doc/examples/interp_compare.txt gsl-doc-2.3/doc/examples/interp_compare.txt
--- gsl-doc-1.16/doc/examples/interp_compare.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/interp_compare.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,112 @@
+7.99 0
+8.09 2.76429e-05
+8.19 0.0437498
+8.7 0.169183
+9.2 0.469428
+10 0.94374
+12 0.998636
+15 0.999919
+20 0.999994
+
+
+7.99 0 0 0
+8.1101 0.00610446 0.00744955 0.00331374
+8.2302 0.0614194 0.0555643 0.0585695
+8.3503 0.0977872 0.077852 0.0890428
+8.4704 0.119747 0.0939162 0.109376
+8.5905 0.140403 0.120807 0.133115
+8.7106 0.172856 0.175411 0.173766
+8.8307 0.226073 0.246775 0.235226
+8.9508 0.296298 0.319125 0.309035
+9.0709 0.377336 0.391778 0.387772
+9.191 0.462995 0.464047 0.464021
+9.3111 0.54776 0.537332 0.542831
+9.4312 0.629514 0.612947 0.632609
+9.5513 0.707207 0.688966 0.724776
+9.6714 0.779786 0.76345 0.810671
+9.7915 0.846198 0.834458 0.881632
+9.9116 0.905394 0.900051 0.928998
+10.0317 0.956324 0.958173 0.945466
+10.1518 0.998494 1.0054 0.951748
+10.2719 1.03243 1.04165 0.957624
+10.392 1.05878 1.06799 0.963098
+10.5121 1.07819 1.08551 0.96817
+10.6322 1.0913 1.09528 0.972843
+10.7523 1.09875 1.09837 0.97712
+10.8724 1.10119 1.09586 0.981003
+10.9925 1.09925 1.08883 0.984493
+11.1126 1.09359 1.07836 0.987594
+11.2327 1.08484 1.06552 0.990307
+11.3528 1.07366 1.05138 0.992634
+11.4729 1.06067 1.03704 0.994578
+11.593 1.04654 1.02355 0.996142
+11.7131 1.03189 1.012 0.997326
+11.8332 1.01737 1.00347 0.998134
+11.9533 1.00363 0.999027 0.998568
+12.0734 0.991283 0.998669 0.998698
+12.1935 0.980549 0.998727 0.998796
+12.3136 0.971356 0.998787 0.998889
+12.4337 0.963625 0.99885 0.998979
+12.5538 0.957277 0.998914 0.999063
+12.6739 0.952232 0.99898 0.999144
+12.794 0.94841 0.999047 0.999221
+12.9141 0.945733 0.999114 0.999293
+13.0342 0.944121 0.999182 0.999361
+13.1543 0.943493 0.999249 0.999425
+13.2744 0.943772 0.999316 0.999485
+13.3945 0.944877 0.999381 0.999541
+13.5146 0.946729 0.999445 0.999593
+13.6347 0.949248 0.999507 0.999641
+13.7548 0.952355 0.999566 0.999685
+13.8749 0.955971 0.999622 0.999725
+13.995 0.960016 0.999674 0.999762
+14.1151 0.964411 0.999723 0.999794
+14.2352 0.969075 0.999767 0.999823
+14.3553 0.973931 0.999807 0.999848
+14.4754 0.978897 0.999841 0.999869
+14.5955 0.983896 0.99987 0.999887
+14.7156 0.988847 0.999893 0.9999
+14.8357 0.99367 0.999909 0.999911
+14.9558 0.998288 0.999918 0.999917
+15.0759 1.00262 0.999921 0.999921
+15.196 1.00665 0.999925 0.999925
+15.3161 1.01037 0.999929 0.999928
+15.4362 1.0138 0.999935 0.999931
+15.5563 1.01694 0.999941 0.999934
+15.6764 1.01979 0.999949 0.999937
+15.7965 1.02238 0.999956 0.999939
+15.9166 1.0247 0.999965 0.999942
+16.0367 1.02677 0.999974 0.999944
+16.1568 1.02858 0.999983 0.999947
+16.2769 1.03015 0.999993 0.999949
+16.397 1.03149 1 0.999951
+16.5171 1.0326 1.00001 0.999953
+16.6372 1.03349 1.00002 0.999955
+16.7573 1.03417 1.00003 0.999956
+16.8774 1.03464 1.00004 0.999958
+16.9975 1.03492 1.00005 0.99996
+17.1176 1.035 1.00006 0.999961
+17.2377 1.03491 1.00007 0.999963
+17.3578 1.03464 1.00008 0.999964
+17.4779 1.03421 1.00009 0.999966
+17.598 1.03361 1.0001 0.999967
+17.7181 1.03287 1.0001 0.999968
+17.8382 1.03198 1.00011 0.99997
+17.9583 1.03095 1.00011 0.999971
+18.0784 1.0298 1.00012 0.999972
+18.1985 1.02852 1.00012 0.999973
+18.3186 1.02713 1.00012 0.999974
+18.4387 1.02563 1.00013 0.999976
+18.5588 1.02404 1.00012 0.999977
+18.6789 1.02236 1.00012 0.999978
+18.799 1.02059 1.00012 0.999979
+18.9191 1.01875 1.00012 0.999981
+19.0392 1.01683 1.00011 0.999982
+19.1593 1.01486 1.0001 0.999983
+19.2794 1.01284 1.00009 0.999985
+19.3995 1.01076 1.00008 0.999986
+19.5196 1.00866 1.00007 0.999987
+19.6397 1.00652 1.00005 0.999989
+19.7598 1.00436 1.00004 0.999991
+19.8799 1.00218 1.00002 0.999992
+20 0.999994 0.999994 0.999994
diff -Nru gsl-doc-1.16/doc/examples/interpp.txt gsl-doc-2.3/doc/examples/interpp.txt
--- gsl-doc-1.16/doc/examples/interpp.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/interpp.txt	2015-11-10 18:47:31.000000000 +0000
@@ -0,0 +1,107 @@
+#m=0,S=5
+0 0.15
+0.1 0.7
+0.27 -0.1
+0.3 0.15
+#m=1,S=0
+0 0.15
+0.003 0.178463
+0.006 0.206683
+0.009 0.234613
+0.012 0.262204
+0.015 0.28941
+0.018 0.316182
+0.021 0.342474
+0.024 0.368236
+0.027 0.393423
+0.03 0.417986
+0.033 0.441878
+0.036 0.465051
+0.039 0.487458
+0.042 0.50905
+0.045 0.529781
+0.048 0.549603
+0.051 0.568468
+0.054 0.586329
+0.057 0.603138
+0.06 0.618847
+0.063 0.633409
+0.066 0.646777
+0.069 0.658902
+0.072 0.669737
+0.075 0.679235
+0.078 0.687348
+0.081 0.694029
+0.084 0.699229
+0.087 0.702901
+0.09 0.704998
+0.093 0.705472
+0.096 0.704276
+0.099 0.701362
+0.102 0.696687
+0.105 0.690283
+0.108 0.682225
+0.111 0.672587
+0.114 0.661448
+0.117 0.648882
+0.12 0.634965
+0.123 0.619775
+0.126 0.603387
+0.129 0.585877
+0.132 0.567321
+0.135 0.547796
+0.138 0.527377
+0.141 0.506141
+0.144 0.484164
+0.147 0.461522
+0.15 0.43829
+0.153 0.414546
+0.156 0.390366
+0.159 0.365824
+0.162 0.340999
+0.165 0.315964
+0.168 0.290798
+0.171 0.265576
+0.174 0.240373
+0.177 0.215267
+0.18 0.190333
+0.183 0.165648
+0.186 0.141287
+0.189 0.117326
+0.192 0.0938429
+0.195 0.0709122
+0.198 0.0486106
+0.201 0.0270141
+0.204 0.00619895
+0.207 -0.0137588
+0.21 -0.0327831
+0.213 -0.0507978
+0.216 -0.0677266
+0.219 -0.0834936
+0.222 -0.0980226
+0.225 -0.111237
+0.228 -0.123062
+0.231 -0.13342
+0.234 -0.142236
+0.237 -0.149433
+0.24 -0.154935
+0.243 -0.158667
+0.246 -0.160551
+0.249 -0.160512
+0.252 -0.158475
+0.255 -0.154361
+0.258 -0.148096
+0.261 -0.139604
+0.264 -0.128808
+0.267 -0.115632
+0.27 -0.1
+0.273 -0.0818941
+0.276 -0.0615288
+0.279 -0.0391769
+0.282 -0.0151111
+0.285 0.0103957
+0.288 0.0370709
+0.291 0.0646417
+0.294 0.0928353
+0.297 0.121379
+0.3 0.15
diff -Nru gsl-doc-1.16/doc/examples/interp.txt gsl-doc-2.3/doc/examples/interp.txt
--- gsl-doc-1.16/doc/examples/interp.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/interp.txt	2015-11-10 18:44:58.000000000 +0000
@@ -0,0 +1,933 @@
+#m=0,S=2
+0 1
+1.42074 1.5403
+2.45465 1.34636
+3.07056 2.08887
+3.6216 3.04234
+4.52054 5.9912
+5.86029 5.87204
+7.32849 7.30059
+8.49468 8.39186
+9.20606 9.77669
+#m=1,S=0
+0 1
+0.01 1.00699
+0.02 1.01397
+0.03 1.02096
+0.04 1.02794
+0.05 1.03492
+0.06 1.04189
+0.07 1.04886
+0.08 1.05582
+0.09 1.06278
+0.1 1.06972
+0.11 1.07666
+0.12 1.08358
+0.13 1.0905
+0.14 1.0974
+0.15 1.10429
+0.16 1.11116
+0.17 1.11802
+0.18 1.12487
+0.19 1.13169
+0.2 1.1385
+0.21 1.14529
+0.22 1.15206
+0.23 1.15881
+0.24 1.16553
+0.25 1.17224
+0.26 1.17892
+0.27 1.18557
+0.28 1.1922
+0.29 1.19881
+0.3 1.20538
+0.31 1.21193
+0.32 1.21845
+0.33 1.22494
+0.34 1.23139
+0.35 1.23782
+0.36 1.24421
+0.37 1.25057
+0.38 1.25689
+0.39 1.26317
+0.4 1.26942
+0.41 1.27564
+0.42 1.28181
+0.43 1.28794
+0.44 1.29403
+0.45 1.30008
+0.46 1.30609
+0.47 1.31206
+0.48 1.31798
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+0.53 1.34688
+0.54 1.35251
+0.55 1.35809
+0.56 1.36362
+0.57 1.3691
+0.58 1.37452
+0.59 1.37989
+0.6 1.3852
+0.61 1.39046
+0.62 1.39565
+0.63 1.40079
+0.64 1.40587
+0.65 1.41089
+0.66 1.41585
+0.67 1.42074
+0.68 1.42557
+0.69 1.43034
+0.7 1.43504
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+0.73 1.44874
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+0.75 1.45754
+0.76 1.46182
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+0.78 1.47019
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+0.8 1.47825
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+0.9 1.51389
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+0.92 1.52003
+0.93 1.52297
+0.94 1.52582
+0.95 1.52858
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+0.97 1.53383
+0.98 1.53631
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+1 1.54101
+1.01 1.54322
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+1.04 1.54926
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+1.09 1.55735
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+1.14 1.56286
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diff -Nru gsl-doc-1.16/doc/examples/intro.out gsl-doc-2.3/doc/examples/intro.out
--- gsl-doc-1.16/doc/examples/intro.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/intro.out	1970-01-01 00:00:00.000000000 +0000
@@ -1 +0,0 @@
-J0(5) = -1.775967713143382920e-01
diff -Nru gsl-doc-1.16/doc/examples/intro.txt gsl-doc-2.3/doc/examples/intro.txt
--- gsl-doc-1.16/doc/examples/intro.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/intro.txt	2015-11-10 18:48:30.000000000 +0000
@@ -0,0 +1 @@
+J0(5) = -1.775967713143382642e-01
diff -Nru gsl-doc-1.16/doc/examples/largefit2.txt gsl-doc-2.3/doc/examples/largefit2.txt
--- gsl-doc-1.16/doc/examples/largefit2.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/largefit2.txt	2016-08-12 17:51:55.000000000 +0000
@@ -0,0 +1,1006 @@
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diff -Nru gsl-doc-1.16/doc/examples/largefit.c gsl-doc-2.3/doc/examples/largefit.c
--- gsl-doc-1.16/doc/examples/largefit.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/largefit.c	2016-08-12 17:52:51.000000000 +0000
@@ -0,0 +1,173 @@
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_randist.h>
+#include <gsl/gsl_multifit.h>
+#include <gsl/gsl_multilarge.h>
+#include <gsl/gsl_blas.h>
+
+/* function to be fitted */
+double
+func(const double t)
+{
+  double x = sin(10.0 * t);
+  return exp(x*x*x);
+}
+
+/* construct a row of the least squares matrix */
+int
+build_row(const double t, gsl_vector *row)
+{
+  const size_t p = row->size;
+  double Xj = 1.0;
+  size_t j;
+
+  for (j = 0; j < p; ++j)
+    {
+      gsl_vector_set(row, j, Xj);
+      Xj *= t;
+    }
+
+  return 0;
+}
+
+int
+solve_system(const int print_data, const gsl_multilarge_linear_type * T,
+             const double lambda, const size_t n, const size_t p,
+             gsl_vector * c)
+{
+  const size_t nblock = 5;         /* number of blocks to accumulate */
+  const size_t nrows = n / nblock; /* number of rows per block */
+  gsl_multilarge_linear_workspace * w =
+    gsl_multilarge_linear_alloc(T, p);
+  gsl_matrix *X = gsl_matrix_alloc(nrows, p);
+  gsl_vector *y = gsl_vector_alloc(nrows);
+  gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+  const size_t nlcurve = 200;
+  gsl_vector *reg_param = gsl_vector_alloc(nlcurve);
+  gsl_vector *rho = gsl_vector_alloc(nlcurve);
+  gsl_vector *eta = gsl_vector_alloc(nlcurve);
+  size_t rowidx = 0;
+  double rnorm, snorm, rcond;
+  double t = 0.0;
+  double dt = 1.0 / (n - 1.0);
+
+  while (rowidx < n)
+    {
+      size_t nleft = n - rowidx;         /* number of rows left to accumulate */
+      size_t nr = GSL_MIN(nrows, nleft); /* number of rows in this block */
+      gsl_matrix_view Xv = gsl_matrix_submatrix(X, 0, 0, nr, p);
+      gsl_vector_view yv = gsl_vector_subvector(y, 0, nr);
+      size_t i;
+
+      /* build (X,y) block with 'nr' rows */
+      for (i = 0; i < nr; ++i)
+        {
+          gsl_vector_view row = gsl_matrix_row(&Xv.matrix, i);
+          double fi = func(t);
+          double ei = gsl_ran_gaussian (r, 0.1 * fi); /* noise */
+          double yi = fi + ei;
+
+          /* construct this row of LS matrix */
+          build_row(t, &row.vector);
+
+          /* set right hand side value with added noise */
+          gsl_vector_set(&yv.vector, i, yi);
+
+          if (print_data && (i % 100 == 0))
+            printf("%f %f\n", t, yi);
+
+          t += dt;
+        }
+
+      /* accumulate (X,y) block into LS system */
+      gsl_multilarge_linear_accumulate(&Xv.matrix, &yv.vector, w);
+
+      rowidx += nr;
+    }
+
+  if (print_data)
+    printf("\n\n");
+
+  /* compute L-curve */
+  gsl_multilarge_linear_lcurve(reg_param, rho, eta, w);
+
+  /* solve large LS system and store solution in c */
+  gsl_multilarge_linear_solve(lambda, c, &rnorm, &snorm, w);
+
+  /* compute reciprocal condition number */
+  gsl_multilarge_linear_rcond(&rcond, w);
+
+  fprintf(stderr, "=== Method %s ===\n", gsl_multilarge_linear_name(w));
+  fprintf(stderr, "condition number = %e\n", 1.0 / rcond);
+  fprintf(stderr, "residual norm    = %e\n", rnorm);
+  fprintf(stderr, "solution norm    = %e\n", snorm);
+
+  /* output L-curve */
+  {
+    size_t i;
+    for (i = 0; i < nlcurve; ++i)
+      {
+        printf("%.12e %.12e %.12e\n",
+               gsl_vector_get(reg_param, i),
+               gsl_vector_get(rho, i),
+               gsl_vector_get(eta, i));
+      }
+    printf("\n\n");
+  }
+
+  gsl_matrix_free(X);
+  gsl_vector_free(y);
+  gsl_multilarge_linear_free(w);
+  gsl_rng_free(r);
+  gsl_vector_free(reg_param);
+  gsl_vector_free(rho);
+  gsl_vector_free(eta);
+
+  return 0;
+}
+
+int
+main(int argc, char *argv[])
+{
+  const size_t n = 50000;   /* number of observations */
+  const size_t p = 16;      /* polynomial order + 1 */
+  double lambda = 0.0;      /* regularization parameter */
+  gsl_vector *c_tsqr = gsl_vector_alloc(p);
+  gsl_vector *c_normal = gsl_vector_alloc(p);
+
+  if (argc > 1)
+    lambda = atof(argv[1]);
+
+  /* solve system with TSQR method */
+  solve_system(1, gsl_multilarge_linear_tsqr, lambda, n, p, c_tsqr);
+
+  /* solve system with Normal equations method */
+  solve_system(0, gsl_multilarge_linear_normal, lambda, n, p, c_normal);
+
+  /* output solutions */
+  {
+    gsl_vector *v = gsl_vector_alloc(p);
+    double t;
+
+    for (t = 0.0; t <= 1.0; t += 0.01)
+      {
+        double f_exact = func(t);
+        double f_tsqr, f_normal;
+
+        build_row(t, v);
+        gsl_blas_ddot(v, c_tsqr, &f_tsqr);
+        gsl_blas_ddot(v, c_normal, &f_normal);
+
+        printf("%f %e %e %e\n", t, f_exact, f_tsqr, f_normal);
+      }
+
+    gsl_vector_free(v);
+  }
+
+  gsl_vector_free(c_tsqr);
+  gsl_vector_free(c_normal);
+
+  return 0;
+}
diff -Nru gsl-doc-1.16/doc/examples/largefit.txt gsl-doc-2.3/doc/examples/largefit.txt
--- gsl-doc-1.16/doc/examples/largefit.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/largefit.txt	2016-08-12 17:51:38.000000000 +0000
@@ -0,0 +1,1006 @@
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diff -Nru gsl-doc-1.16/doc/examples/linalglu.out gsl-doc-2.3/doc/examples/linalglu.out
--- gsl-doc-1.16/doc/examples/linalglu.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/linalglu.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,4 +0,0 @@
-x = -4.05205
--12.6056
-1.66091
-8.69377
diff -Nru gsl-doc-1.16/doc/examples/linalglu.txt gsl-doc-2.3/doc/examples/linalglu.txt
--- gsl-doc-1.16/doc/examples/linalglu.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/linalglu.txt	2015-11-10 18:54:46.000000000 +0000
@@ -0,0 +1,5 @@
+x = 
+-4.05205
+-12.6056
+1.66091
+8.69377
diff -Nru gsl-doc-1.16/doc/examples/Makefile.am gsl-doc-2.3/doc/examples/Makefile.am
--- gsl-doc-1.16/doc/examples/Makefile.am	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/Makefile.am	2016-10-27 11:20:46.000000000 +0000
@@ -0,0 +1,12 @@
+## Process this file with automake to produce Makefile.in
+
+check_PROGRAMS = blas block cblas cdf cheb combination multiset const diff eigen fft fftmr fftreal fitting fitting2 fitting3 fitreg fitreg2 histogram histogram2d ieee ieeeround integration interp interp2d intro linalglu largefit matrix matrixw min monte ntupler ntuplew ode-initval permseq permshuffle polyroots qrng randpoisson randwalk rng rngunif robfit rootnewt roots siman sortsmall specfun specfun_e rstat rquantile stat statsort sum vector vectorr vectorview vectorw dwt nlfit nlfit2 nlfit3 nlfit4 interpp eigen_nonsymm bspline poisson interp_compare spmatrix
+
+examples_src = blas.c block.c cblas.c cdf.c cheb.c combination.c multiset.c const.c demo_fn.c diff.c eigen.c fft.c fftmr.c fftreal.c fitting.c fitting2.c fitting3.c fitreg.c fitreg2.c histogram.c histogram2d.c ieee.c ieeeround.c integration.c interp.c interp2d.c intro.c linalglu.c largefit.c matrix.c matrixw.c min.c monte.c ntupler.c ntuplew.c ode-initval.c odefixed.c permseq.c permshuffle.c polyroots.c qrng.c randpoisson.c randwalk.c rng.c rngunif.c robfit.c rootnewt.c roots.c siman.c sortsmall.c specfun.c specfun_e.c rstat.c rquantile.c stat.c statsort.c sum.c vector.c vectorr.c vectorview.c vectorw.c demo_fn.h dwt.c nlfit.c nlfit2.c nlfit3.c interpp.c eigen_nonsymm.c bspline.c multimin.c multiminfn.c nmsimplex.c ode-initval-low-level.c poisson.c interp_compare.c spmatrix.c
+
+examples_txt = blas.txt block.txt bspline.txt cblas.txt cdf.txt cheb.txt combination.txt const.txt diff.txt dwt.txt eigen_nonsymm.txt eigen.txt fftmr.txt fftreal.txt fft.txt fitreg.txt fitreg2.txt fitting2.txt fitting.txt histogram2d.txt ieeeround.txt ieee.txt integration.txt interp2d.txt interp_compare.txt interpp.txt interp.txt intro.txt largefit.txt largefit2.txt linalglu.txt matrix.txt matrixw.txt min.txt monte.txt multimin.txt multiset.txt nlfit.txt nlfit2.txt nlfit3.txt nmsimplex.txt ntuple.txt ode-initval.txt permseq.txt permshuffle.txt poisson.txt polyroots.txt qrng.txt randpoisson2.txt randpoisson.txt randwalk.txt rng.txt rngunif.txt rngunif2.txt robfit.txt rootnewt.txt roots.txt rquantile.txt rstat.txt siman.txt sortsmall.txt specfun.txt specfun_e.txt spmatrix.txt statsort.txt stat.txt sum.txt vectorr.txt vectorview.txt
+
+dist_noinst_DATA = $(examples_src) $(examples_txt)
+
+LDADD = ../../libgsl.la ../../cblas/libgslcblas.la
+AM_DEFAULT_SOURCE_EXT = .c
diff -Nru gsl-doc-1.16/doc/examples/Makefile.in gsl-doc-2.3/doc/examples/Makefile.in
--- gsl-doc-1.16/doc/examples/Makefile.in	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -0,0 +1,1269 @@
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
+# @configure_input@
+
+# Copyright (C) 1994-2013 Free Software Foundation, Inc.
+
+# This Makefile.in is free software; the Free Software Foundation
+# gives unlimited permission to copy and/or distribute it,
+# with or without modifications, as long as this notice is preserved.
+
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY, to the extent permitted by law; without
+# even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+# PARTICULAR PURPOSE.
+
+@SET_MAKE@
+
+VPATH = @srcdir@
+am__is_gnu_make = test -n '$(MAKEFILE_LIST)' && test -n '$(MAKELEVEL)'
+am__make_running_with_option = \
+  case $${target_option-} in \
+      ?) ;; \
+      *) echo "am__make_running_with_option: internal error: invalid" \
+              "target option '$${target_option-}' specified" >&2; \
+         exit 1;; \
+  esac; \
+  has_opt=no; \
+  sane_makeflags=$$MAKEFLAGS; \
+  if $(am__is_gnu_make); then \
+    sane_makeflags=$$MFLAGS; \
+  else \
+    case $$MAKEFLAGS in \
+      *\\[\ \	]*) \
+        bs=\\; \
+        sane_makeflags=`printf '%s\n' "$$MAKEFLAGS" \
+          | sed "s/$$bs$$bs[$$bs $$bs	]*//g"`;; \
+    esac; \
+  fi; \
+  skip_next=no; \
+  strip_trailopt () \
+  { \
+    flg=`printf '%s\n' "$$flg" | sed "s/$$1.*$$//"`; \
+  }; \
+  for flg in $$sane_makeflags; do \
+    test $$skip_next = yes && { skip_next=no; continue; }; \
+    case $$flg in \
+      *=*|--*) continue;; \
+        -*I) strip_trailopt 'I'; skip_next=yes;; \
+      -*I?*) strip_trailopt 'I';; \
+        -*O) strip_trailopt 'O'; skip_next=yes;; \
+      -*O?*) strip_trailopt 'O';; \
+        -*l) strip_trailopt 'l'; skip_next=yes;; \
+      -*l?*) strip_trailopt 'l';; \
+      -[dEDm]) skip_next=yes;; \
+      -[JT]) skip_next=yes;; \
+    esac; \
+    case $$flg in \
+      *$$target_option*) has_opt=yes; break;; \
+    esac; \
+  done; \
+  test $$has_opt = yes
+am__make_dryrun = (target_option=n; $(am__make_running_with_option))
+am__make_keepgoing = (target_option=k; $(am__make_running_with_option))
+pkgdatadir = $(datadir)/@PACKAGE@
+pkgincludedir = $(includedir)/@PACKAGE@
+pkglibdir = $(libdir)/@PACKAGE@
+pkglibexecdir = $(libexecdir)/@PACKAGE@
+am__cd = CDPATH="$${ZSH_VERSION+.}$(PATH_SEPARATOR)" && cd
+install_sh_DATA = $(install_sh) -c -m 644
+install_sh_PROGRAM = $(install_sh) -c
+install_sh_SCRIPT = $(install_sh) -c
+INSTALL_HEADER = $(INSTALL_DATA)
+transform = $(program_transform_name)
+NORMAL_INSTALL = :
+PRE_INSTALL = :
+POST_INSTALL = :
+NORMAL_UNINSTALL = :
+PRE_UNINSTALL = :
+POST_UNINSTALL = :
+build_triplet = @build@
+host_triplet = @host@
+check_PROGRAMS = blas$(EXEEXT) block$(EXEEXT) cblas$(EXEEXT) \
+	cdf$(EXEEXT) cheb$(EXEEXT) combination$(EXEEXT) \
+	multiset$(EXEEXT) const$(EXEEXT) diff$(EXEEXT) eigen$(EXEEXT) \
+	fft$(EXEEXT) fftmr$(EXEEXT) fftreal$(EXEEXT) fitting$(EXEEXT) \
+	fitting2$(EXEEXT) fitting3$(EXEEXT) fitreg$(EXEEXT) \
+	fitreg2$(EXEEXT) histogram$(EXEEXT) histogram2d$(EXEEXT) \
+	ieee$(EXEEXT) ieeeround$(EXEEXT) integration$(EXEEXT) \
+	interp$(EXEEXT) interp2d$(EXEEXT) intro$(EXEEXT) \
+	linalglu$(EXEEXT) largefit$(EXEEXT) matrix$(EXEEXT) \
+	matrixw$(EXEEXT) min$(EXEEXT) monte$(EXEEXT) ntupler$(EXEEXT) \
+	ntuplew$(EXEEXT) ode-initval$(EXEEXT) permseq$(EXEEXT) \
+	permshuffle$(EXEEXT) polyroots$(EXEEXT) qrng$(EXEEXT) \
+	randpoisson$(EXEEXT) randwalk$(EXEEXT) rng$(EXEEXT) \
+	rngunif$(EXEEXT) robfit$(EXEEXT) rootnewt$(EXEEXT) \
+	roots$(EXEEXT) siman$(EXEEXT) sortsmall$(EXEEXT) \
+	specfun$(EXEEXT) specfun_e$(EXEEXT) rstat$(EXEEXT) \
+	rquantile$(EXEEXT) stat$(EXEEXT) statsort$(EXEEXT) \
+	sum$(EXEEXT) vector$(EXEEXT) vectorr$(EXEEXT) \
+	vectorview$(EXEEXT) vectorw$(EXEEXT) dwt$(EXEEXT) \
+	nlfit$(EXEEXT) nlfit2$(EXEEXT) nlfit3$(EXEEXT) nlfit4$(EXEEXT) \
+	interpp$(EXEEXT) eigen_nonsymm$(EXEEXT) bspline$(EXEEXT) \
+	poisson$(EXEEXT) interp_compare$(EXEEXT) spmatrix$(EXEEXT)
+subdir = doc/examples
+DIST_COMMON = $(srcdir)/Makefile.in $(srcdir)/Makefile.am \
+	$(top_srcdir)/mkinstalldirs $(top_srcdir)/depcomp \
+	$(dist_noinst_DATA)
+ACLOCAL_M4 = $(top_srcdir)/aclocal.m4
+am__aclocal_m4_deps = $(top_srcdir)/configure.ac
+am__configure_deps = $(am__aclocal_m4_deps) $(CONFIGURE_DEPENDENCIES) \
+	$(ACLOCAL_M4)
+mkinstalldirs = $(SHELL) $(top_srcdir)/mkinstalldirs
+CONFIG_HEADER = $(top_builddir)/config.h
+CONFIG_CLEAN_FILES =
+CONFIG_CLEAN_VPATH_FILES =
+blas_SOURCES = blas.c
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+examples_src = blas.c block.c cblas.c cdf.c cheb.c combination.c multiset.c const.c demo_fn.c diff.c eigen.c fft.c fftmr.c fftreal.c fitting.c fitting2.c fitting3.c fitreg.c fitreg2.c histogram.c histogram2d.c ieee.c ieeeround.c integration.c interp.c interp2d.c intro.c linalglu.c largefit.c matrix.c matrixw.c min.c monte.c ntupler.c ntuplew.c ode-initval.c odefixed.c permseq.c permshuffle.c polyroots.c qrng.c randpoisson.c randwalk.c rng.c rngunif.c robfit.c rootnewt.c roots.c siman.c sortsmall.c specfun.c specfun_e.c rstat.c rquantile.c stat.c statsort.c sum.c vector.c vectorr.c vectorview.c vectorw.c demo_fn.h dwt.c nlfit.c nlfit2.c nlfit3.c interpp.c eigen_nonsymm.c bspline.c multimin.c multiminfn.c nmsimplex.c ode-initval-low-level.c poisson.c interp_compare.c spmatrix.c
+examples_txt = blas.txt block.txt bspline.txt cblas.txt cdf.txt cheb.txt combination.txt const.txt diff.txt dwt.txt eigen_nonsymm.txt eigen.txt fftmr.txt fftreal.txt fft.txt fitreg.txt fitreg2.txt fitting2.txt fitting.txt histogram2d.txt ieeeround.txt ieee.txt integration.txt interp2d.txt interp_compare.txt interpp.txt interp.txt intro.txt largefit.txt largefit2.txt linalglu.txt matrix.txt matrixw.txt min.txt monte.txt multimin.txt multiset.txt nlfit.txt nlfit2.txt nlfit3.txt nmsimplex.txt ntuple.txt ode-initval.txt permseq.txt permshuffle.txt poisson.txt polyroots.txt qrng.txt randpoisson2.txt randpoisson.txt randwalk.txt rng.txt rngunif.txt rngunif2.txt robfit.txt rootnewt.txt roots.txt rquantile.txt rstat.txt siman.txt sortsmall.txt specfun.txt specfun_e.txt spmatrix.txt statsort.txt stat.txt sum.txt vectorr.txt vectorview.txt
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diff -Nru gsl-doc-1.16/doc/examples/matrix.txt gsl-doc-2.3/doc/examples/matrix.txt
--- gsl-doc-1.16/doc/examples/matrix.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/matrix.txt	2015-11-10 18:57:49.000000000 +0000
@@ -0,0 +1,30 @@
+m(0,0) = 0.23
+m(0,1) = 1.23
+m(0,2) = 2.23
+m(1,0) = 100.23
+m(1,1) = 101.23
+m(1,2) = 102.23
+m(2,0) = 200.23
+m(2,1) = 201.23
+m(2,2) = 202.23
+m(3,0) = 300.23
+m(3,1) = 301.23
+m(3,2) = 302.23
+m(4,0) = 400.23
+m(4,1) = 401.23
+m(4,2) = 402.23
+m(5,0) = 500.23
+m(5,1) = 501.23
+m(5,2) = 502.23
+m(6,0) = 600.23
+m(6,1) = 601.23
+m(6,2) = 602.23
+m(7,0) = 700.23
+m(7,1) = 701.23
+m(7,2) = 702.23
+m(8,0) = 800.23
+m(8,1) = 801.23
+m(8,2) = 802.23
+m(9,0) = 900.23
+m(9,1) = 901.23
+m(9,2) = 902.23
diff -Nru gsl-doc-1.16/doc/examples/matrixw.txt gsl-doc-2.3/doc/examples/matrixw.txt
--- gsl-doc-1.16/doc/examples/matrixw.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/matrixw.txt	2015-11-10 18:59:04.000000000 +0000
@@ -0,0 +1 @@
+differences = 0 (should be zero)
diff -Nru gsl-doc-1.16/doc/examples/min.c gsl-doc-2.3/doc/examples/min.c
--- gsl-doc-1.16/doc/examples/min.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/min.c	2015-11-09 19:11:38.000000000 +0000
@@ -5,6 +5,7 @@
 
 double fn1 (double x, void * params)
 {
+  (void)(params); /* avoid unused parameter warning */
   return cos(x) + 1.0;
 }
 
diff -Nru gsl-doc-1.16/doc/examples/min.out gsl-doc-2.3/doc/examples/min.out
--- gsl-doc-1.16/doc/examples/min.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/min.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,13 +0,0 @@
-    0 [0.0000000, 6.0000000] 2.0000000 -1.1415927 6.0000000
-    1 [2.0000000, 6.0000000] 3.2758640 +0.1342713 4.0000000
-    2 [2.0000000, 3.2831929] 3.2758640 +0.1342713 1.2831929
-    3 [2.8689068, 3.2831929] 3.2758640 +0.1342713 0.4142862
-    4 [2.8689068, 3.2831929] 3.2758640 +0.1342713 0.4142862
-    5 [2.8689068, 3.2758640] 3.1460585 +0.0044658 0.4069572
-    6 [3.1346075, 3.2758640] 3.1460585 +0.0044658 0.1412565
-    7 [3.1346075, 3.1874620] 3.1460585 +0.0044658 0.0528545
-    8 [3.1346075, 3.1460585] 3.1460585 +0.0044658 0.0114510
-    9 [3.1346075, 3.1460585] 3.1424060 +0.0008133 0.0114510
-   10 [3.1346075, 3.1424060] 3.1415885 -0.0000041 0.0077985
-Converged:                            
-   11 [3.1415885, 3.1424060] 3.1415927 -0.0000000 0.0008175
diff -Nru gsl-doc-1.16/doc/examples/min.txt gsl-doc-2.3/doc/examples/min.txt
--- gsl-doc-1.16/doc/examples/min.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/min.txt	2015-11-10 19:01:40.000000000 +0000
@@ -0,0 +1,10 @@
+using brent method
+ iter [    lower,     upper]       min        err  err(est)
+    0 [0.0000000, 6.0000000] 2.0000000 -1.1415927 6.0000000
+    1 [2.0000000, 6.0000000] 3.5278640 +0.3862713 4.0000000
+    2 [2.0000000, 3.5278640] 3.1748217 +0.0332290 1.5278640
+    3 [2.0000000, 3.1748217] 3.1264576 -0.0151351 1.1748217
+    4 [3.1264576, 3.1748217] 3.1414743 -0.0001183 0.0483641
+    5 [3.1414743, 3.1748217] 3.1415930 +0.0000004 0.0333474
+Converged:
+    6 [3.1414743, 3.1415930] 3.1415927 +0.0000000 0.0001187
diff -Nru gsl-doc-1.16/doc/examples/monte.c gsl-doc-2.3/doc/examples/monte.c
--- gsl-doc-1.16/doc/examples/monte.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/monte.c	2015-11-09 19:12:29.000000000 +0000
@@ -24,6 +24,8 @@
 double
 g (double *k, size_t dim, void *params)
 {
+  (void)(dim); /* avoid unused parameter warnings */
+  (void)(params);
   double A = 1.0 / (M_PI * M_PI * M_PI);
   return A / (1.0 - cos (k[0]) * cos (k[1]) * cos (k[2]));
 }
diff -Nru gsl-doc-1.16/doc/examples/monte.txt gsl-doc-2.3/doc/examples/monte.txt
--- gsl-doc-1.16/doc/examples/monte.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/monte.txt	2015-11-10 19:02:56.000000000 +0000
@@ -0,0 +1,22 @@
+plain ==================
+result =  1.412209
+sigma  =  0.013436
+exact  =  1.393204
+error  =  0.019005 = 1.4 sigma
+miser ==================
+result =  1.391322
+sigma  =  0.003461
+exact  =  1.393204
+error  = -0.001882 = 0.54 sigma
+vegas warm-up ==================
+result =  1.392673
+sigma  =  0.003410
+exact  =  1.393204
+error  = -0.000531 = 0.16 sigma
+converging...
+result =  1.393281 sigma =  0.000362 chisq/dof = 1.5
+vegas final ==================
+result =  1.393281
+sigma  =  0.000362
+exact  =  1.393204
+error  =  0.000077 = 0.21 sigma
diff -Nru gsl-doc-1.16/doc/examples/multimin.out gsl-doc-2.3/doc/examples/multimin.out
--- gsl-doc-1.16/doc/examples/multimin.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/multimin.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,15 +0,0 @@
-         x       y         f
-    1 4.99629 6.99072  687.84780
-    2 4.98886 6.97215  683.55456
-    3 4.97400 6.93501  675.01278
-    4 4.94429 6.86073  658.10798
-    5 4.88487 6.71217  625.01340
-    6 4.76602 6.41506  561.68440
-    7 4.52833 5.82083  446.46694
-    8 4.05295 4.63238  261.79422
-    9 3.10219 2.25548   75.49762
-   10 2.85185 1.62963   67.03704
-   11 2.19088 1.76182   45.31640
-   12 0.86892 2.02622   30.18555
-Minimum found at:
-   13 1.00000 2.00000   30.00000
diff -Nru gsl-doc-1.16/doc/examples/multimin.txt gsl-doc-2.3/doc/examples/multimin.txt
--- gsl-doc-1.16/doc/examples/multimin.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/multimin.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,15 @@
+         x       y         f
+    1 4.99629 6.99072  687.84780
+    2 4.98886 6.97215  683.55456
+    3 4.97400 6.93501  675.01278
+    4 4.94429 6.86073  658.10798
+    5 4.88487 6.71217  625.01340
+    6 4.76602 6.41506  561.68440
+    7 4.52833 5.82083  446.46694
+    8 4.05295 4.63238  261.79422
+    9 3.10219 2.25548   75.49762
+   10 2.85185 1.62963   67.03704
+   11 2.19088 1.76182   45.31640
+   12 0.86892 2.02622   30.18555
+Minimum found at:
+   13 1.00000 2.00000   30.00000
diff -Nru gsl-doc-1.16/doc/examples/multiset.out gsl-doc-2.3/doc/examples/multiset.out
--- gsl-doc-1.16/doc/examples/multiset.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/multiset.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,71 +0,0 @@
-all multisets of {0,1,2,3} by size:
-{ }
-{ 0 }
-{ 1 }
-{ 2 }
-{ 3 }
-{ 0 0 }
-{ 0 1 }
-{ 0 2 }
-{ 0 3 }
-{ 1 1 }
-{ 1 2 }
-{ 1 3 }
-{ 2 2 }
-{ 2 3 }
-{ 3 3 }
-{ 0 0 0 }
-{ 0 0 1 }
-{ 0 0 2 }
-{ 0 0 3 }
-{ 0 1 1 }
-{ 0 1 2 }
-{ 0 1 3 }
-{ 0 2 2 }
-{ 0 2 3 }
-{ 0 3 3 }
-{ 1 1 1 }
-{ 1 1 2 }
-{ 1 1 3 }
-{ 1 2 2 }
-{ 1 2 3 }
-{ 1 3 3 }
-{ 2 2 2 }
-{ 2 2 3 }
-{ 2 3 3 }
-{ 3 3 3 }
-{ 0 0 0 0 }
-{ 0 0 0 1 }
-{ 0 0 0 2 }
-{ 0 0 0 3 }
-{ 0 0 1 1 }
-{ 0 0 1 2 }
-{ 0 0 1 3 }
-{ 0 0 2 2 }
-{ 0 0 2 3 }
-{ 0 0 3 3 }
-{ 0 1 1 1 }
-{ 0 1 1 2 }
-{ 0 1 1 3 }
-{ 0 1 2 2 }
-{ 0 1 2 3 }
-{ 0 1 3 3 }
-{ 0 2 2 2 }
-{ 0 2 2 3 }
-{ 0 2 3 3 }
-{ 0 3 3 3 }
-{ 1 1 1 1 }
-{ 1 1 1 2 }
-{ 1 1 1 3 }
-{ 1 1 2 2 }
-{ 1 1 2 3 }
-{ 1 1 3 3 }
-{ 1 2 2 2 }
-{ 1 2 2 3 }
-{ 1 2 3 3 }
-{ 1 3 3 3 }
-{ 2 2 2 2 }
-{ 2 2 2 3 }
-{ 2 2 3 3 }
-{ 2 3 3 3 }
-{ 3 3 3 3 }
diff -Nru gsl-doc-1.16/doc/examples/multiset.txt gsl-doc-2.3/doc/examples/multiset.txt
--- gsl-doc-1.16/doc/examples/multiset.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/multiset.txt	2015-11-10 19:04:56.000000000 +0000
@@ -0,0 +1,71 @@
+All multisets of {0,1,2,3} by size:
+{ }
+{ 0 }
+{ 1 }
+{ 2 }
+{ 3 }
+{ 0 0 }
+{ 0 1 }
+{ 0 2 }
+{ 0 3 }
+{ 1 1 }
+{ 1 2 }
+{ 1 3 }
+{ 2 2 }
+{ 2 3 }
+{ 3 3 }
+{ 0 0 0 }
+{ 0 0 1 }
+{ 0 0 2 }
+{ 0 0 3 }
+{ 0 1 1 }
+{ 0 1 2 }
+{ 0 1 3 }
+{ 0 2 2 }
+{ 0 2 3 }
+{ 0 3 3 }
+{ 1 1 1 }
+{ 1 1 2 }
+{ 1 1 3 }
+{ 1 2 2 }
+{ 1 2 3 }
+{ 1 3 3 }
+{ 2 2 2 }
+{ 2 2 3 }
+{ 2 3 3 }
+{ 3 3 3 }
+{ 0 0 0 0 }
+{ 0 0 0 1 }
+{ 0 0 0 2 }
+{ 0 0 0 3 }
+{ 0 0 1 1 }
+{ 0 0 1 2 }
+{ 0 0 1 3 }
+{ 0 0 2 2 }
+{ 0 0 2 3 }
+{ 0 0 3 3 }
+{ 0 1 1 1 }
+{ 0 1 1 2 }
+{ 0 1 1 3 }
+{ 0 1 2 2 }
+{ 0 1 2 3 }
+{ 0 1 3 3 }
+{ 0 2 2 2 }
+{ 0 2 2 3 }
+{ 0 2 3 3 }
+{ 0 3 3 3 }
+{ 1 1 1 1 }
+{ 1 1 1 2 }
+{ 1 1 1 3 }
+{ 1 1 2 2 }
+{ 1 1 2 3 }
+{ 1 1 3 3 }
+{ 1 2 2 2 }
+{ 1 2 2 3 }
+{ 1 2 3 3 }
+{ 1 3 3 3 }
+{ 2 2 2 2 }
+{ 2 2 2 3 }
+{ 2 2 3 3 }
+{ 2 3 3 3 }
+{ 3 3 3 3 }
diff -Nru gsl-doc-1.16/doc/examples/nlfit2.c gsl-doc-2.3/doc/examples/nlfit2.c
--- gsl-doc-1.16/doc/examples/nlfit2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/nlfit2.c	2016-07-07 20:36:10.000000000 +0000
@@ -0,0 +1,165 @@
+#include <stdlib.h>
+#include <stdio.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_multifit_nlinear.h>
+
+int
+func_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, 100.0 * (x2 - x1*x1));
+  gsl_vector_set(f, 1, 1.0 - x1);
+
+  return GSL_SUCCESS;
+}
+
+int
+func_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+
+  gsl_matrix_set(J, 0, 0, -200.0*x1);
+  gsl_matrix_set(J, 0, 1, 100.0);
+  gsl_matrix_set(J, 1, 0, -1.0);
+  gsl_matrix_set(J, 1, 1, 0.0);
+
+  return GSL_SUCCESS;
+}
+
+int
+func_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  double v1 = gsl_vector_get(v, 0);
+
+  gsl_vector_set(fvv, 0, -200.0 * v1 * v1);
+  gsl_vector_set(fvv, 1, 0.0);
+
+  return GSL_SUCCESS;
+}
+
+void
+callback(const size_t iter, void *params,
+         const gsl_multifit_nlinear_workspace *w)
+{
+  gsl_vector * x = gsl_multifit_nlinear_position(w);
+
+  /* print out current location */
+  printf("%f %f\n",
+         gsl_vector_get(x, 0),
+         gsl_vector_get(x, 1));
+}
+
+void
+solve_system(gsl_vector *x0, gsl_multifit_nlinear_fdf *fdf,
+             gsl_multifit_nlinear_parameters *params)
+{
+  const gsl_multifit_nlinear_type *T = gsl_multifit_nlinear_trust;
+  const size_t max_iter = 200;
+  const double xtol = 1.0e-8;
+  const double gtol = 1.0e-8;
+  const double ftol = 1.0e-8;
+  const size_t n = fdf->n;
+  const size_t p = fdf->p;
+  gsl_multifit_nlinear_workspace *work =
+    gsl_multifit_nlinear_alloc(T, params, n, p);
+  gsl_vector * f = gsl_multifit_nlinear_residual(work);
+  gsl_vector * x = gsl_multifit_nlinear_position(work);
+  int info;
+  double chisq0, chisq, rcond;
+
+  /* initialize solver */
+  gsl_multifit_nlinear_init(x0, fdf, work);
+
+  /* store initial cost */
+  gsl_blas_ddot(f, f, &chisq0);
+
+  /* iterate until convergence */
+  gsl_multifit_nlinear_driver(max_iter, xtol, gtol, ftol,
+                              callback, NULL, &info, work);
+
+  /* store final cost */
+  gsl_blas_ddot(f, f, &chisq);
+
+  /* store cond(J(x)) */
+  gsl_multifit_nlinear_rcond(&rcond, work);
+
+  /* print summary */
+
+  fprintf(stderr, "NITER         = %zu\n", gsl_multifit_nlinear_niter(work));
+  fprintf(stderr, "NFEV          = %zu\n", fdf->nevalf);
+  fprintf(stderr, "NJEV          = %zu\n", fdf->nevaldf);
+  fprintf(stderr, "NAEV          = %zu\n", fdf->nevalfvv);
+  fprintf(stderr, "initial cost  = %.12e\n", chisq0);
+  fprintf(stderr, "final cost    = %.12e\n", chisq);
+  fprintf(stderr, "final x       = (%.12e, %.12e)\n",
+          gsl_vector_get(x, 0), gsl_vector_get(x, 1));
+  fprintf(stderr, "final cond(J) = %.12e\n", 1.0 / rcond);
+
+  printf("\n\n");
+
+  gsl_multifit_nlinear_free(work);
+}
+
+int
+main (void)
+{
+  const size_t n = 2;
+  const size_t p = 2;
+  gsl_vector *f = gsl_vector_alloc(n);
+  gsl_vector *x = gsl_vector_alloc(p);
+  gsl_multifit_nlinear_fdf fdf;
+  gsl_multifit_nlinear_parameters fdf_params =
+    gsl_multifit_nlinear_default_parameters();
+
+  /* print map of Phi(x1, x2) */
+  {
+    double x1, x2, chisq;
+    double *f1 = gsl_vector_ptr(f, 0);
+    double *f2 = gsl_vector_ptr(f, 1);
+
+    for (x1 = -1.2; x1 < 1.3; x1 += 0.1)
+      {
+        for (x2 = -0.5; x2 < 2.1; x2 += 0.1)
+          {
+            gsl_vector_set(x, 0, x1);
+            gsl_vector_set(x, 1, x2);
+            func_f(x, NULL, f);
+
+            chisq = (*f1) * (*f1) + (*f2) * (*f2);
+            printf("%f %f %f\n", x1, x2, chisq);
+          }
+        printf("\n");
+      }
+    printf("\n\n");
+  }
+
+  /* define function to be minimized */
+  fdf.f = func_f;
+  fdf.df = func_df;
+  fdf.fvv = func_fvv;
+  fdf.n = n;
+  fdf.p = p;
+  fdf.params = NULL;
+
+  /* starting point */
+  gsl_vector_set(x, 0, -0.5);
+  gsl_vector_set(x, 1, 1.75);
+
+  fprintf(stderr, "=== Solving system without acceleration ===\n");
+  fdf_params.trs = gsl_multifit_nlinear_trs_lm;
+  solve_system(x, &fdf, &fdf_params);
+
+  fprintf(stderr, "=== Solving system with acceleration ===\n");
+  fdf_params.trs = gsl_multifit_nlinear_trs_lmaccel;
+  solve_system(x, &fdf, &fdf_params);
+
+  gsl_vector_free(f);
+  gsl_vector_free(x);
+
+  return 0;
+}
diff -Nru gsl-doc-1.16/doc/examples/nlfit2.txt gsl-doc-2.3/doc/examples/nlfit2.txt
--- gsl-doc-1.16/doc/examples/nlfit2.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/nlfit2.txt	2016-07-07 20:36:10.000000000 +0000
@@ -0,0 +1,751 @@
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+
diff -Nru gsl-doc-1.16/doc/examples/nlfit3.c gsl-doc-2.3/doc/examples/nlfit3.c
--- gsl-doc-1.16/doc/examples/nlfit3.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/nlfit3.c	2016-08-22 19:33:19.000000000 +0000
@@ -0,0 +1,209 @@
+#include <stdlib.h>
+#include <stdio.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_multifit_nlinear.h>
+
+/* parameters to model */
+struct model_params
+{
+  double a1;
+  double a2;
+  double a3;
+  double a4;
+  double a5;
+};
+
+/* Branin function */
+int
+func_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  struct model_params *par = (struct model_params *) params;
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double f1 = x2 + par->a1 * x1 * x1 + par->a2 * x1 + par->a3;
+  double f2 = sqrt(par->a4) * sqrt(1.0 + (1.0 - par->a5) * cos(x1));
+
+  gsl_vector_set(f, 0, f1);
+  gsl_vector_set(f, 1, f2);
+
+  return GSL_SUCCESS;
+}
+
+int
+func_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  struct model_params *par = (struct model_params *) params;
+  double x1 = gsl_vector_get(x, 0);
+  double f2 = sqrt(par->a4) * sqrt(1.0 + (1.0 - par->a5) * cos(x1));
+
+  gsl_matrix_set(J, 0, 0, 2.0 * par->a1 * x1 + par->a2);
+  gsl_matrix_set(J, 0, 1, 1.0);
+
+  gsl_matrix_set(J, 1, 0, -0.5 * par->a4 / f2 * (1.0 - par->a5) * sin(x1));
+  gsl_matrix_set(J, 1, 1, 0.0);
+
+  return GSL_SUCCESS;
+}
+
+int
+func_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  struct model_params *par = (struct model_params *) params;
+  double x1 = gsl_vector_get(x, 0);
+  double v1 = gsl_vector_get(v, 0);
+  double c = cos(x1);
+  double s = sin(x1);
+  double f2 = sqrt(par->a4) * sqrt(1.0 + (1.0 - par->a5) * c);
+  double t = 0.5 * par->a4 * (1.0 - par->a5) / f2;
+
+  gsl_vector_set(fvv, 0, 2.0 * par->a1 * v1 * v1);
+  gsl_vector_set(fvv, 1, -t * (c + s*s/f2) * v1 * v1);
+
+  return GSL_SUCCESS;
+}
+
+void
+callback(const size_t iter, void *params,
+         const gsl_multifit_nlinear_workspace *w)
+{
+  gsl_vector * x = gsl_multifit_nlinear_position(w);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  /* print out current location */
+  printf("%f %f\n", x1, x2);
+}
+
+void
+solve_system(gsl_vector *x0, gsl_multifit_nlinear_fdf *fdf,
+             gsl_multifit_nlinear_parameters *params)
+{
+  const gsl_multifit_nlinear_type *T = gsl_multifit_nlinear_trust;
+  const size_t max_iter = 200;
+  const double xtol = 1.0e-8;
+  const double gtol = 1.0e-8;
+  const double ftol = 1.0e-8;
+  const size_t n = fdf->n;
+  const size_t p = fdf->p;
+  gsl_multifit_nlinear_workspace *work =
+    gsl_multifit_nlinear_alloc(T, params, n, p);
+  gsl_vector * f = gsl_multifit_nlinear_residual(work);
+  gsl_vector * x = gsl_multifit_nlinear_position(work);
+  int info;
+  double chisq0, chisq, rcond;
+
+  printf("# %s/%s\n",
+         gsl_multifit_nlinear_name(work),
+         gsl_multifit_nlinear_trs_name(work));
+
+  /* initialize solver */
+  gsl_multifit_nlinear_init(x0, fdf, work);
+
+  /* store initial cost */
+  gsl_blas_ddot(f, f, &chisq0);
+
+  /* iterate until convergence */
+  gsl_multifit_nlinear_driver(max_iter, xtol, gtol, ftol,
+                              callback, NULL, &info, work);
+
+  /* store final cost */
+  gsl_blas_ddot(f, f, &chisq);
+
+  /* store cond(J(x)) */
+  gsl_multifit_nlinear_rcond(&rcond, work);
+
+  /* print summary */
+  fprintf(stderr, "%-25s %-6zu %-5zu %-5zu %-13.4e %-12.4e %-13.4e (%.2e, %.2e)\n",
+          gsl_multifit_nlinear_trs_name(work),
+          gsl_multifit_nlinear_niter(work),
+          fdf->nevalf,
+          fdf->nevaldf,
+          chisq0,
+          chisq,
+          1.0 / rcond,
+          gsl_vector_get(x, 0),
+          gsl_vector_get(x, 1));
+
+  printf("\n\n");
+
+  gsl_multifit_nlinear_free(work);
+}
+
+int
+main (void)
+{
+  const size_t n = 2;
+  const size_t p = 2;
+  gsl_vector *f = gsl_vector_alloc(n);
+  gsl_vector *x = gsl_vector_alloc(p);
+  gsl_multifit_nlinear_fdf fdf;
+  gsl_multifit_nlinear_parameters fdf_params =
+    gsl_multifit_nlinear_default_parameters();
+  struct model_params params;
+
+  params.a1 = -5.1 / (4.0 * M_PI * M_PI);
+  params.a2 = 5.0 / M_PI;
+  params.a3 = -6.0;
+  params.a4 = 10.0;
+  params.a5 = 1.0 / (8.0 * M_PI);
+
+  /* print map of Phi(x1, x2) */
+  {
+    double x1, x2, chisq;
+
+    for (x1 = -5.0; x1 < 15.0; x1 += 0.1)
+      {
+        for (x2 = -5.0; x2 < 15.0; x2 += 0.1)
+          {
+            gsl_vector_set(x, 0, x1);
+            gsl_vector_set(x, 1, x2);
+            func_f(x, &params, f);
+
+            gsl_blas_ddot(f, f, &chisq);
+
+            printf("%f %f %f\n", x1, x2, chisq);
+          }
+        printf("\n");
+      }
+    printf("\n\n");
+  }
+
+  /* define function to be minimized */
+  fdf.f = func_f;
+  fdf.df = func_df;
+  fdf.fvv = func_fvv;
+  fdf.n = n;
+  fdf.p = p;
+  fdf.params = &params;
+
+  /* starting point */
+  gsl_vector_set(x, 0, 6.0);
+  gsl_vector_set(x, 1, 14.5);
+
+  fprintf(stderr, "%-25s %-6s %-5s %-5s %-13s %-12s %-13s %-15s\n",
+          "Method", "NITER", "NFEV", "NJEV", "Initial Cost",
+          "Final cost", "Final cond(J)", "Final x");
+  
+  fdf_params.trs = gsl_multifit_nlinear_trs_lm;
+  solve_system(x, &fdf, &fdf_params);
+
+  fdf_params.trs = gsl_multifit_nlinear_trs_lmaccel;
+  solve_system(x, &fdf, &fdf_params);
+
+  fdf_params.trs = gsl_multifit_nlinear_trs_dogleg;
+  solve_system(x, &fdf, &fdf_params);
+
+  fdf_params.trs = gsl_multifit_nlinear_trs_ddogleg;
+  solve_system(x, &fdf, &fdf_params);
+
+  fdf_params.trs = gsl_multifit_nlinear_trs_subspace2D;
+  solve_system(x, &fdf, &fdf_params);
+
+  gsl_vector_free(f);
+  gsl_vector_free(x);
+
+  return 0;
+}
diff -Nru gsl-doc-1.16/doc/examples/nlfit3.txt gsl-doc-2.3/doc/examples/nlfit3.txt
--- gsl-doc-1.16/doc/examples/nlfit3.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/nlfit3.txt	2016-09-08 18:00:12.000000000 +0000
@@ -0,0 +1,40741 @@
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+15.000000 8.900000 7.964493
+15.000000 9.000000 7.515838
+15.000000 9.100000 7.087183
+15.000000 9.200000 6.678529
+15.000000 9.300000 6.289874
+15.000000 9.400000 5.921219
+15.000000 9.500000 5.572565
+15.000000 9.600000 5.243910
+15.000000 9.700000 4.935256
+15.000000 9.800000 4.646601
+15.000000 9.900000 4.377946
+15.000000 10.000000 4.129292
+15.000000 10.100000 3.900637
+15.000000 10.200000 3.691983
+15.000000 10.300000 3.503328
+15.000000 10.400000 3.334673
+15.000000 10.500000 3.186019
+15.000000 10.600000 3.057364
+15.000000 10.700000 2.948709
+15.000000 10.800000 2.860055
+15.000000 10.900000 2.791400
+15.000000 11.000000 2.742746
+15.000000 11.100000 2.714091
+15.000000 11.200000 2.705436
+15.000000 11.300000 2.716782
+15.000000 11.400000 2.748127
+15.000000 11.500000 2.799472
+15.000000 11.600000 2.870818
+15.000000 11.700000 2.962163
+15.000000 11.800000 3.073509
+15.000000 11.900000 3.204854
+15.000000 12.000000 3.356199
+15.000000 12.100000 3.527545
+15.000000 12.200000 3.718890
+15.000000 12.300000 3.930236
+15.000000 12.400000 4.161581
+15.000000 12.500000 4.412926
+15.000000 12.600000 4.684272
+15.000000 12.700000 4.975617
+15.000000 12.800000 5.286962
+15.000000 12.900000 5.618308
+15.000000 13.000000 5.969653
+15.000000 13.100000 6.340999
+15.000000 13.200000 6.732344
+15.000000 13.300000 7.143689
+15.000000 13.400000 7.575035
+15.000000 13.500000 8.026380
+15.000000 13.600000 8.497725
+15.000000 13.700000 8.989071
+15.000000 13.800000 9.500416
+15.000000 13.900000 10.031762
+15.000000 14.000000 10.583107
+15.000000 14.100000 11.154452
+15.000000 14.200000 11.745798
+15.000000 14.300000 12.357143
+15.000000 14.400000 12.988489
+15.000000 14.500000 13.639834
+15.000000 14.600000 14.311179
+15.000000 14.700000 15.002525
+15.000000 14.800000 15.713870
+15.000000 14.900000 16.445215
+15.000000 15.000000 17.196561
+
+
+
+# trust-region/levenberg-marquardt
+6.000000 14.500000
+-2.440721 8.052493
+-2.649759 10.338367
+-3.079780 11.922784
+-3.207953 12.376764
+-3.113030 12.240580
+-3.156168 12.295063
+-3.135422 12.267922
+-3.144145 12.278083
+-3.140628 12.273947
+-3.141954 12.275411
+-3.141465 12.274866
+-3.141638 12.275049
+-3.141577 12.274984
+-3.141598 12.275006
+-3.141591 12.274998
+-3.141593 12.275001
+-3.141592 12.275000
+-3.141593 12.275000
+-3.141593 12.275000
+-3.141593 12.275000
+
+
+# trust-region/levenberg-marquardt+accel
+6.000000 14.500000
+5.434266 14.105210
+4.860709 13.032737
+4.081924 10.582719
+3.243692 6.790283
+2.058201 4.197091
+2.873516 2.930922
+3.372929 2.246210
+3.036675 2.318015
+3.239950 2.237589
+3.128135 2.263146
+3.145861 2.267710
+3.141215 2.271767
+3.141969 2.273339
+3.141552 2.274340
+3.141685 2.274699
+3.141514 2.274945
+3.141678 2.274938
+3.141578 2.274977
+3.141598 2.274987
+3.141593 2.274994
+3.141593 2.274997
+3.141592 2.275000
+3.141593 2.275000
+3.141592 2.275000
+3.141593 2.275000
+3.141593 2.275000
+3.141593 2.275000
+
+
+# trust-region/dogleg
+6.000000 14.500000
+0.084715 10.513103
+4.386135 -0.771406
+2.863958 2.202150
+3.445763 2.006013
+2.862516 2.458756
+3.367235 2.256024
+3.115028 2.153453
+3.159338 2.237666
+3.131967 2.268437
+3.146763 2.280079
+3.139564 2.273509
+3.143245 2.276490
+3.141432 2.274895
+3.141664 2.275075
+3.141552 2.274970
+3.141610 2.275017
+3.141581 2.274991
+3.141596 2.275003
+3.141592 2.275000
+3.141593 2.275000
+3.141593 2.275000
+3.141593 2.275000
+3.141593 2.275000
+
+
+# trust-region/double-dogleg
+6.000000 14.500000
+0.084715 10.513103
+4.525217 -0.637424
+2.784094 2.178685
+3.382281 2.048555
+3.138220 2.084792
+3.163691 2.189933
+3.107123 2.326539
+3.150882 2.300348
+3.133654 2.271698
+3.144331 2.279648
+3.139620 2.273460
+3.142196 2.275844
+3.140984 2.274394
+3.141615 2.275040
+3.141578 2.274991
+3.141599 2.275008
+3.141589 2.274997
+3.141594 2.275002
+3.141592 2.274999
+3.141593 2.275000
+3.141593 2.275000
+3.141593 2.275000
+3.141593 2.275000
+3.141593 2.275000
+
+
+# trust-region/2D-subspace
+6.000000 14.500000
+0.443880 10.464140
+4.859341 -0.766174
+2.457734 2.123629
+3.300727 2.062365
+3.096528 2.222788
+3.149836 2.246128
+3.139418 2.264724
+3.145814 2.269650
+3.139332 2.274037
+3.142734 2.274079
+3.141074 2.274870
+3.141924 2.274792
+3.141505 2.274946
+3.141610 2.274967
+3.141586 2.274990
+3.141599 2.274993
+3.141593 2.274996
+3.141592 2.275000
+3.141593 2.275000
+3.141593 2.275000
+3.141593 2.275000
+3.141593 2.275000
+3.141593 2.275000
+
+
diff -Nru gsl-doc-1.16/doc/examples/nlfit4.c gsl-doc-2.3/doc/examples/nlfit4.c
--- gsl-doc-1.16/doc/examples/nlfit4.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/nlfit4.c	2016-09-16 22:52:48.000000000 +0000
@@ -0,0 +1,219 @@
+#include <stdlib.h>
+#include <stdio.h>
+#include <sys/time.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_multilarge_nlinear.h>
+#include <gsl/gsl_spblas.h>
+#include <gsl/gsl_spmatrix.h>
+
+/* parameters for functions */
+struct model_params
+{
+  double alpha;
+  gsl_spmatrix *J;
+};
+
+/* penalty function */
+int
+penalty_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  struct model_params *par = (struct model_params *) params;
+  const double sqrt_alpha = sqrt(par->alpha);
+  const size_t p = x->size;
+  size_t i;
+  double sum = 0.0;
+
+  for (i = 0; i < p; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+
+      gsl_vector_set(f, i, sqrt_alpha*(xi - 1.0));
+
+      sum += xi * xi;
+    }
+
+  gsl_vector_set(f, p, sum - 0.25);
+
+  return GSL_SUCCESS;
+}
+
+int
+penalty_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+            const gsl_vector * u, void * params, gsl_vector * v,
+            gsl_matrix * JTJ)
+{
+  struct model_params *par = (struct model_params *) params;
+  const size_t p = x->size;
+  size_t j;
+
+  /* store 2*x in last row of J */
+  for (j = 0; j < p; ++j)
+    {
+      double xj = gsl_vector_get(x, j);
+      gsl_spmatrix_set(par->J, p, j, 2.0 * xj);
+    }
+
+  /* compute v = op(J) u */
+  if (v)
+    gsl_spblas_dgemv(TransJ, 1.0, par->J, u, 0.0, v);
+
+  if (JTJ)
+    {
+      gsl_vector_view diag = gsl_matrix_diagonal(JTJ);
+
+      /* compute J^T J = [ alpha*I_p + 4 x x^T ] */
+      gsl_matrix_set_zero(JTJ);
+
+      /* store 4 x x^T in lower half of JTJ */
+      gsl_blas_dsyr(CblasLower, 4.0, x, JTJ);
+
+      /* add alpha to diag(JTJ) */
+      gsl_vector_add_constant(&diag.vector, par->alpha);
+    }
+
+  return GSL_SUCCESS;
+}
+
+int
+penalty_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  const size_t p = x->size;
+  double normv = gsl_blas_dnrm2(v);
+
+  gsl_vector_set_zero(fvv);
+  gsl_vector_set(fvv, p, 2.0 * normv * normv);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+void
+solve_system(const gsl_vector *x0, gsl_multilarge_nlinear_fdf *fdf,
+             gsl_multilarge_nlinear_parameters *params)
+{
+  const gsl_multilarge_nlinear_type *T = gsl_multilarge_nlinear_trust;
+  const size_t max_iter = 200;
+  const double xtol = 1.0e-8;
+  const double gtol = 1.0e-8;
+  const double ftol = 1.0e-8;
+  const size_t n = fdf->n;
+  const size_t p = fdf->p;
+  gsl_multilarge_nlinear_workspace *work =
+    gsl_multilarge_nlinear_alloc(T, params, n, p);
+  gsl_vector * f = gsl_multilarge_nlinear_residual(work);
+  gsl_vector * x = gsl_multilarge_nlinear_position(work);
+  int info;
+  double chisq0, chisq, rcond, xsq;
+  struct timeval tv0, tv1;
+
+  gettimeofday(&tv0, NULL);
+
+  /* initialize solver */
+  gsl_multilarge_nlinear_init(x0, fdf, work);
+
+  /* store initial cost */
+  gsl_blas_ddot(f, f, &chisq0);
+
+  /* iterate until convergence */
+  gsl_multilarge_nlinear_driver(max_iter, xtol, gtol, ftol,
+                                NULL, NULL, &info, work);
+
+  gettimeofday(&tv1, NULL);
+
+  /* store final cost */
+  gsl_blas_ddot(f, f, &chisq);
+
+  /* compute final ||x||^2 */
+  gsl_blas_ddot(x, x, &xsq);
+
+  /* store cond(J(x)) */
+  gsl_multilarge_nlinear_rcond(&rcond, work);
+
+  /* print summary */
+  fprintf(stderr, "%-25s %-5zu %-4zu %-5zu %-6zu %-4zu %-10.4e %-10.4e %-7.2f %-11.4e %.2f\n",
+          gsl_multilarge_nlinear_trs_name(work),
+          gsl_multilarge_nlinear_niter(work),
+          fdf->nevalf,
+          fdf->nevaldfu,
+          fdf->nevaldf2,
+          fdf->nevalfvv,
+          chisq0,
+          chisq,
+          1.0 / rcond,
+          xsq,
+          (tv1.tv_sec - tv0.tv_sec) + 1.0e-6 * (tv1.tv_usec - tv0.tv_usec));
+
+  gsl_multilarge_nlinear_free(work);
+}
+
+int
+main (void)
+{
+  const size_t p = 2000;
+  const size_t n = p + 1;
+  gsl_vector *f = gsl_vector_alloc(n);
+  gsl_vector *x = gsl_vector_alloc(p);
+
+  /* allocate sparse Jacobian matrix with 2*p non-zero elements in triplet format */
+  gsl_spmatrix *J = gsl_spmatrix_alloc_nzmax(n, p, 2 * p, GSL_SPMATRIX_TRIPLET);
+
+  gsl_multilarge_nlinear_fdf fdf;
+  gsl_multilarge_nlinear_parameters fdf_params =
+    gsl_multilarge_nlinear_default_parameters();
+  struct model_params params;
+  size_t i;
+
+  params.alpha = 1.0e-5;
+  params.J = J;
+
+  /* define function to be minimized */
+  fdf.f = penalty_f;
+  fdf.df = penalty_df;
+  fdf.fvv = penalty_fvv;
+  fdf.n = n;
+  fdf.p = p;
+  fdf.params = &params;
+
+  for (i = 0; i < p; ++i)
+    {
+      /* starting point */
+      gsl_vector_set(x, i, i + 1.0);
+
+      /* store sqrt(alpha)*I_p in upper p-by-p block of J */
+      gsl_spmatrix_set(J, i, i, sqrt(params.alpha));
+    }
+
+  fprintf(stderr, "%-25s %-4s %-4s %-5s %-6s %-4s %-10s %-10s %-7s %-11s %-10s\n",
+          "Method", "NITER", "NFEV", "NJUEV", "NJTJEV", "NAEV", "Init Cost",
+          "Final cost", "cond(J)", "Final |x|^2", "Time (s)");
+  
+  fdf_params.scale = gsl_multilarge_nlinear_scale_levenberg;
+
+  fdf_params.trs = gsl_multilarge_nlinear_trs_lm;
+  solve_system(x, &fdf, &fdf_params);
+
+  fdf_params.trs = gsl_multilarge_nlinear_trs_lmaccel;
+  solve_system(x, &fdf, &fdf_params);
+
+  fdf_params.trs = gsl_multilarge_nlinear_trs_dogleg;
+  solve_system(x, &fdf, &fdf_params);
+
+  fdf_params.trs = gsl_multilarge_nlinear_trs_ddogleg;
+  solve_system(x, &fdf, &fdf_params);
+
+  fdf_params.trs = gsl_multilarge_nlinear_trs_subspace2D;
+  solve_system(x, &fdf, &fdf_params);
+
+  fdf_params.trs = gsl_multilarge_nlinear_trs_cgst;
+  solve_system(x, &fdf, &fdf_params);
+
+  gsl_vector_free(f);
+  gsl_vector_free(x);
+  gsl_spmatrix_free(J);
+
+  return 0;
+}
diff -Nru gsl-doc-1.16/doc/examples/nlfit.c gsl-doc-2.3/doc/examples/nlfit.c
--- gsl-doc-1.16/doc/examples/nlfit.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/nlfit.c	2016-09-24 10:58:59.000000000 +0000
@@ -2,114 +2,193 @@
 #include <stdio.h>
 #include <gsl/gsl_rng.h>
 #include <gsl/gsl_randist.h>
+#include <gsl/gsl_matrix.h>
 #include <gsl/gsl_vector.h>
 #include <gsl/gsl_blas.h>
-#include <gsl/gsl_multifit_nlin.h>
-
-#include "expfit.c"
+#include <gsl/gsl_multifit_nlinear.h>
 
+/* number of data points to fit */
 #define N 40
 
-void print_state (size_t iter, gsl_multifit_fdfsolver * s);
+struct data {
+  size_t n;
+  double * y;
+};
+
+int
+expb_f (const gsl_vector * x, void *data, 
+        gsl_vector * f)
+{
+  size_t n = ((struct data *)data)->n;
+  double *y = ((struct data *)data)->y;
+
+  double A = gsl_vector_get (x, 0);
+  double lambda = gsl_vector_get (x, 1);
+  double b = gsl_vector_get (x, 2);
+
+  size_t i;
+
+  for (i = 0; i < n; i++)
+    {
+      /* Model Yi = A * exp(-lambda * i) + b */
+      double t = i;
+      double Yi = A * exp (-lambda * t) + b;
+      gsl_vector_set (f, i, Yi - y[i]);
+    }
+
+  return GSL_SUCCESS;
+}
+
+int
+expb_df (const gsl_vector * x, void *data, 
+         gsl_matrix * J)
+{
+  size_t n = ((struct data *)data)->n;
+
+  double A = gsl_vector_get (x, 0);
+  double lambda = gsl_vector_get (x, 1);
+
+  size_t i;
+
+  for (i = 0; i < n; i++)
+    {
+      /* Jacobian matrix J(i,j) = dfi / dxj, */
+      /* where fi = (Yi - yi)/sigma[i],      */
+      /*       Yi = A * exp(-lambda * i) + b  */
+      /* and the xj are the parameters (A,lambda,b) */
+      double t = i;
+      double e = exp(-lambda * t);
+      gsl_matrix_set (J, i, 0, e); 
+      gsl_matrix_set (J, i, 1, -t * A * e);
+      gsl_matrix_set (J, i, 2, 1.0);
+    }
+  return GSL_SUCCESS;
+}
+
+void
+callback(const size_t iter, void *params,
+         const gsl_multifit_nlinear_workspace *w)
+{
+  gsl_vector *f = gsl_multifit_nlinear_residual(w);
+  gsl_vector *x = gsl_multifit_nlinear_position(w);
+  double rcond;
+
+  /* compute reciprocal condition number of J(x) */
+  gsl_multifit_nlinear_rcond(&rcond, w);
+
+  fprintf(stderr, "iter %2zu: A = %.4f, lambda = %.4f, b = %.4f, cond(J) = %8.4f, |f(x)| = %.4f\n",
+          iter,
+          gsl_vector_get(x, 0),
+          gsl_vector_get(x, 1),
+          gsl_vector_get(x, 2),
+          1.0 / rcond,
+          gsl_blas_dnrm2(f));
+}
 
 int
 main (void)
 {
-  const gsl_multifit_fdfsolver_type *T;
-  gsl_multifit_fdfsolver *s;
-  int status;
-  unsigned int i, iter = 0;
+  const gsl_multifit_nlinear_type *T = gsl_multifit_nlinear_trust;
+  gsl_multifit_nlinear_workspace *w;
+  gsl_multifit_nlinear_fdf fdf;
+  gsl_multifit_nlinear_parameters fdf_params =
+    gsl_multifit_nlinear_default_parameters();
   const size_t n = N;
   const size_t p = 3;
 
+  gsl_vector *f;
+  gsl_matrix *J;
   gsl_matrix *covar = gsl_matrix_alloc (p, p);
-  double y[N], sigma[N];
-  struct data d = { n, y, sigma};
-  gsl_multifit_function_fdf f;
-  double x_init[3] = { 1.0, 0.0, 0.0 };
+  double y[N], weights[N];
+  struct data d = { n, y };
+  double x_init[3] = { 1.0, 1.0, 0.0 }; /* starting values */
   gsl_vector_view x = gsl_vector_view_array (x_init, p);
-  const gsl_rng_type * type;
+  gsl_vector_view wts = gsl_vector_view_array(weights, n);
   gsl_rng * r;
+  double chisq, chisq0;
+  int status, info;
+  size_t i;
+
+  const double xtol = 1e-8;
+  const double gtol = 1e-8;
+  const double ftol = 0.0;
 
   gsl_rng_env_setup();
+  r = gsl_rng_alloc(gsl_rng_default);
 
-  type = gsl_rng_default;
-  r = gsl_rng_alloc (type);
-
-  f.f = &expb_f;
-  f.df = &expb_df;
-  f.fdf = &expb_fdf;
-  f.n = n;
-  f.p = p;
-  f.params = &d;
-
-  /* This is the data to be fitted */
+  /* define the function to be minimized */
+  fdf.f = expb_f;
+  fdf.df = expb_df;   /* set to NULL for finite-difference Jacobian */
+  fdf.fvv = NULL;     /* not using geodesic acceleration */
+  fdf.n = n;
+  fdf.p = p;
+  fdf.params = &d;
 
+  /* this is the data to be fitted */
   for (i = 0; i < n; i++)
     {
       double t = i;
-      y[i] = 1.0 + 5 * exp (-0.1 * t) 
-                 + gsl_ran_gaussian (r, 0.1);
-      sigma[i] = 0.1;
-      printf ("data: %u %g %g\n", i, y[i], sigma[i]);
+      double yi = 1.0 + 5 * exp (-0.1 * t);
+      double si = 0.1 * yi;
+      double dy = gsl_ran_gaussian(r, si);
+
+      weights[i] = 1.0 / (si * si);
+      y[i] = yi + dy;
+      printf ("data: %zu %g %g\n", i, y[i], si);
     };
 
-  T = gsl_multifit_fdfsolver_lmsder;
-  s = gsl_multifit_fdfsolver_alloc (T, n, p);
-  gsl_multifit_fdfsolver_set (s, &f, &x.vector);
+  /* allocate workspace with default parameters */
+  w = gsl_multifit_nlinear_alloc (T, &fdf_params, n, p);
 
-  print_state (iter, s);
+  /* initialize solver with starting point and weights */
+  gsl_multifit_nlinear_winit (&x.vector, &wts.vector, &fdf, w);
 
-  do
-    {
-      iter++;
-      status = gsl_multifit_fdfsolver_iterate (s);
-
-      printf ("status = %s\n", gsl_strerror (status));
-
-      print_state (iter, s);
+  /* compute initial cost function */
+  f = gsl_multifit_nlinear_residual(w);
+  gsl_blas_ddot(f, f, &chisq0);
 
-      if (status)
-        break;
+  /* solve the system with a maximum of 20 iterations */
+  status = gsl_multifit_nlinear_driver(20, xtol, gtol, ftol,
+                                       callback, NULL, &info, w);
 
-      status = gsl_multifit_test_delta (s->dx, s->x,
-                                        1e-4, 1e-4);
-    }
-  while (status == GSL_CONTINUE && iter < 500);
+  /* compute covariance of best fit parameters */
+  J = gsl_multifit_nlinear_jac(w);
+  gsl_multifit_nlinear_covar (J, 0.0, covar);
 
-  gsl_multifit_covar (s->J, 0.0, covar);
+  /* compute final cost */
+  gsl_blas_ddot(f, f, &chisq);
 
-#define FIT(i) gsl_vector_get(s->x, i)
+#define FIT(i) gsl_vector_get(w->x, i)
 #define ERR(i) sqrt(gsl_matrix_get(covar,i,i))
 
+  fprintf(stderr, "summary from method '%s/%s'\n",
+          gsl_multifit_nlinear_name(w),
+          gsl_multifit_nlinear_trs_name(w));
+  fprintf(stderr, "number of iterations: %zu\n",
+          gsl_multifit_nlinear_niter(w));
+  fprintf(stderr, "function evaluations: %zu\n", fdf.nevalf);
+  fprintf(stderr, "Jacobian evaluations: %zu\n", fdf.nevaldf);
+  fprintf(stderr, "reason for stopping: %s\n",
+          (info == 1) ? "small step size" : "small gradient");
+  fprintf(stderr, "initial |f(x)| = %f\n", sqrt(chisq0));
+  fprintf(stderr, "final   |f(x)| = %f\n", sqrt(chisq));
+
   { 
-    double chi = gsl_blas_dnrm2(s->f);
     double dof = n - p;
-    double c = GSL_MAX_DBL(1, chi / sqrt(dof)); 
+    double c = GSL_MAX_DBL(1, sqrt(chisq / dof));
 
-    printf("chisq/dof = %g\n",  pow(chi, 2.0) / dof);
+    fprintf(stderr, "chisq/dof = %g\n", chisq / dof);
 
-    printf ("A      = %.5f +/- %.5f\n", FIT(0), c*ERR(0));
-    printf ("lambda = %.5f +/- %.5f\n", FIT(1), c*ERR(1));
-    printf ("b      = %.5f +/- %.5f\n", FIT(2), c*ERR(2));
+    fprintf (stderr, "A      = %.5f +/- %.5f\n", FIT(0), c*ERR(0));
+    fprintf (stderr, "lambda = %.5f +/- %.5f\n", FIT(1), c*ERR(1));
+    fprintf (stderr, "b      = %.5f +/- %.5f\n", FIT(2), c*ERR(2));
   }
 
-  printf ("status = %s\n", gsl_strerror (status));
+  fprintf (stderr, "status = %s\n", gsl_strerror (status));
 
-  gsl_multifit_fdfsolver_free (s);
+  gsl_multifit_nlinear_free (w);
   gsl_matrix_free (covar);
   gsl_rng_free (r);
-  return 0;
-}
 
-void
-print_state (size_t iter, gsl_multifit_fdfsolver * s)
-{
-  printf ("iter: %3u x = % 15.8f % 15.8f % 15.8f "
-          "|f(x)| = %g\n",
-          iter,
-          gsl_vector_get (s->x, 0), 
-          gsl_vector_get (s->x, 1),
-          gsl_vector_get (s->x, 2), 
-          gsl_blas_dnrm2 (s->f));
+  return 0;
 }
diff -Nru gsl-doc-1.16/doc/examples/nlfit.txt gsl-doc-2.3/doc/examples/nlfit.txt
--- gsl-doc-1.16/doc/examples/nlfit.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/nlfit.txt	2015-11-10 19:05:33.000000000 +0000
@@ -0,0 +1,40 @@
+data: 0 6.08035 0.6
+data: 1 5.47552 0.552419
+data: 2 5.94654 0.509365
+data: 3 5.0492 0.470409
+data: 4 4.78568 0.43516
+data: 5 3.51748 0.403265
+data: 6 2.84671 0.374406
+data: 7 3.24634 0.348293
+data: 8 3.23395 0.324664
+data: 9 3.30385 0.303285
+data: 10 2.83439 0.28394
+data: 11 2.31891 0.266436
+data: 12 2.33858 0.250597
+data: 13 2.40559 0.236266
+data: 14 2.41856 0.223298
+data: 15 1.99966 0.211565
+data: 16 1.88127 0.200948
+data: 17 1.91477 0.191342
+data: 18 1.70415 0.182649
+data: 19 1.60316 0.174784
+data: 20 1.77937 0.167668
+data: 21 1.55302 0.161228
+data: 22 1.50903 0.155402
+data: 23 1.36364 0.150129
+data: 24 1.36873 0.145359
+data: 25 1.41954 0.141042
+data: 26 1.37778 0.137137
+data: 27 1.23573 0.133603
+data: 28 1.28524 0.130405
+data: 29 1.46327 0.127512
+data: 30 1.22315 0.124894
+data: 31 1.1933 0.122525
+data: 32 1.18717 0.120381
+data: 33 0.883172 0.118442
+data: 34 1.23424 0.116687
+data: 35 1.14683 0.115099
+data: 36 1.11091 0.113662
+data: 37 1.20396 0.112362
+data: 38 1.28722 0.111185
+data: 39 1.05801 0.110121
diff -Nru gsl-doc-1.16/doc/examples/nmsimplex.out gsl-doc-2.3/doc/examples/nmsimplex.out
--- gsl-doc-1.16/doc/examples/nmsimplex.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/nmsimplex.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,25 +0,0 @@
-    1  6.500e+00  5.000e+00 f() = 512.500 size = 1.130
-    2  5.250e+00  4.000e+00 f() = 290.625 size = 1.409
-    3  5.250e+00  4.000e+00 f() = 290.625 size = 1.409
-    4  5.500e+00  1.000e+00 f() = 252.500 size = 1.409
-    5  2.625e+00  3.500e+00 f() = 101.406 size = 1.847
-    6  2.625e+00  3.500e+00 f() = 101.406 size = 1.847
-    7  0.000e+00  3.000e+00 f() =  60.000 size = 1.847
-    8  2.094e+00  1.875e+00 f() =  42.275 size = 1.321
-    9  2.578e-01  1.906e+00 f() =  35.684 size = 1.069
-   10  5.879e-01  2.445e+00 f() =  35.664 size = 0.841
-   11  1.258e+00  2.025e+00 f() =  30.680 size = 0.476
-   12  1.258e+00  2.025e+00 f() =  30.680 size = 0.367
-   13  1.093e+00  1.849e+00 f() =  30.539 size = 0.300
-   14  8.830e-01  2.004e+00 f() =  30.137 size = 0.172
-   15  8.830e-01  2.004e+00 f() =  30.137 size = 0.126
-   16  9.582e-01  2.060e+00 f() =  30.090 size = 0.106
-   17  1.022e+00  2.004e+00 f() =  30.005 size = 0.063
-   18  1.022e+00  2.004e+00 f() =  30.005 size = 0.043
-   19  1.022e+00  2.004e+00 f() =  30.005 size = 0.043
-   20  1.022e+00  2.004e+00 f() =  30.005 size = 0.027
-   21  1.022e+00  2.004e+00 f() =  30.005 size = 0.022
-   22  9.920e-01  1.997e+00 f() =  30.001 size = 0.016
-   23  9.920e-01  1.997e+00 f() =  30.001 size = 0.013
-converged to minimum at
-   24  9.920e-01  1.997e+00 f() =  30.001 size = 0.008
diff -Nru gsl-doc-1.16/doc/examples/nmsimplex.txt gsl-doc-2.3/doc/examples/nmsimplex.txt
--- gsl-doc-1.16/doc/examples/nmsimplex.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/nmsimplex.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,25 @@
+    1  6.500e+00  5.000e+00 f() = 512.500 size = 1.130
+    2  5.250e+00  4.000e+00 f() = 290.625 size = 1.409
+    3  5.250e+00  4.000e+00 f() = 290.625 size = 1.409
+    4  5.500e+00  1.000e+00 f() = 252.500 size = 1.409
+    5  2.625e+00  3.500e+00 f() = 101.406 size = 1.847
+    6  2.625e+00  3.500e+00 f() = 101.406 size = 1.847
+    7  0.000e+00  3.000e+00 f() =  60.000 size = 1.847
+    8  2.094e+00  1.875e+00 f() =  42.275 size = 1.321
+    9  2.578e-01  1.906e+00 f() =  35.684 size = 1.069
+   10  5.879e-01  2.445e+00 f() =  35.664 size = 0.841
+   11  1.258e+00  2.025e+00 f() =  30.680 size = 0.476
+   12  1.258e+00  2.025e+00 f() =  30.680 size = 0.367
+   13  1.093e+00  1.849e+00 f() =  30.539 size = 0.300
+   14  8.830e-01  2.004e+00 f() =  30.137 size = 0.172
+   15  8.830e-01  2.004e+00 f() =  30.137 size = 0.126
+   16  9.582e-01  2.060e+00 f() =  30.090 size = 0.106
+   17  1.022e+00  2.004e+00 f() =  30.005 size = 0.063
+   18  1.022e+00  2.004e+00 f() =  30.005 size = 0.043
+   19  1.022e+00  2.004e+00 f() =  30.005 size = 0.043
+   20  1.022e+00  2.004e+00 f() =  30.005 size = 0.027
+   21  1.022e+00  2.004e+00 f() =  30.005 size = 0.022
+   22  9.920e-01  1.997e+00 f() =  30.001 size = 0.016
+   23  9.920e-01  1.997e+00 f() =  30.001 size = 0.013
+converged to minimum at
+   24  9.920e-01  1.997e+00 f() =  30.001 size = 0.008
diff -Nru gsl-doc-1.16/doc/examples/ntupler.c gsl-doc-2.3/doc/examples/ntupler.c
--- gsl-doc-1.16/doc/examples/ntupler.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/ntupler.c	2015-11-10 19:45:36.000000000 +0000
@@ -61,6 +61,7 @@
 double
 val_func (void *ntuple_data, void *params)
 {
+  (void)(params); /* avoid unused parameter warning */
   struct data * data = (struct data *) ntuple_data;  
   double x, y, z;
 
diff -Nru gsl-doc-1.16/doc/examples/ntuple.txt gsl-doc-2.3/doc/examples/ntuple.txt
--- gsl-doc-1.16/doc/examples/ntuple.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/ntuple.txt	2015-11-10 19:11:14.000000000 +0000
@@ -0,0 +1,100 @@
+0.000000 0.100000 0.000000
+0.100000 0.200000 0.000000
+0.200000 0.300000 0.000000
+0.300000 0.400000 0.000000
+0.400000 0.500000 0.000000
+0.500000 0.600000 0.000000
+0.600000 0.700000 0.000000
+0.700000 0.800000 0.000000
+0.800000 0.900000 0.000000
+0.900000 1.000000 0.000000
+1.000000 1.100000 0.000000
+1.100000 1.200000 0.000000
+1.200000 1.300000 0.000000
+1.300000 1.400000 0.000000
+1.400000 1.500000 0.000000
+1.500000 1.600000 210.000000
+1.600000 1.700000 221.000000
+1.700000 1.800000 237.000000
+1.800000 1.900000 207.000000
+1.900000 2.000000 208.000000
+2.000000 2.100000 212.000000
+2.100000 2.200000 214.000000
+2.200000 2.300000 177.000000
+2.300000 2.400000 204.000000
+2.400000 2.500000 172.000000
+2.500000 2.600000 194.000000
+2.600000 2.700000 167.000000
+2.700000 2.800000 166.000000
+2.800000 2.900000 174.000000
+2.900000 3.000000 157.000000
+3.000000 3.100000 159.000000
+3.100000 3.200000 126.000000
+3.200000 3.300000 146.000000
+3.300000 3.400000 135.000000
+3.400000 3.500000 129.000000
+3.500000 3.600000 124.000000
+3.600000 3.700000 110.000000
+3.700000 3.800000 109.000000
+3.800000 3.900000 120.000000
+3.900000 4.000000 103.000000
+4.000000 4.100000 104.000000
+4.100000 4.200000 107.000000
+4.200000 4.300000 104.000000
+4.300000 4.400000 94.000000
+4.400000 4.500000 88.000000
+4.500000 4.600000 97.000000
+4.600000 4.700000 82.000000
+4.700000 4.800000 81.000000
+4.800000 4.900000 69.000000
+4.900000 5.000000 74.000000
+5.000000 5.100000 67.000000
+5.100000 5.200000 77.000000
+5.200000 5.300000 66.000000
+5.300000 5.400000 61.000000
+5.400000 5.500000 66.000000
+5.500000 5.600000 57.000000
+5.600000 5.700000 62.000000
+5.700000 5.800000 54.000000
+5.800000 5.900000 52.000000
+5.900000 6.000000 44.000000
+6.000000 6.100000 43.000000
+6.100000 6.200000 44.000000
+6.200000 6.300000 46.000000
+6.300000 6.400000 35.000000
+6.400000 6.500000 37.000000
+6.500000 6.600000 32.000000
+6.600000 6.700000 37.000000
+6.700000 6.800000 27.000000
+6.800000 6.900000 38.000000
+6.900000 7.000000 37.000000
+7.000000 7.100000 38.000000
+7.100000 7.200000 24.000000
+7.200000 7.300000 33.000000
+7.300000 7.400000 24.000000
+7.400000 7.500000 25.000000
+7.500000 7.600000 24.000000
+7.600000 7.700000 20.000000
+7.700000 7.800000 23.000000
+7.800000 7.900000 19.000000
+7.900000 8.000000 26.000000
+8.000000 8.100000 18.000000
+8.100000 8.200000 22.000000
+8.200000 8.300000 22.000000
+8.300000 8.400000 15.000000
+8.400000 8.500000 14.000000
+8.500000 8.600000 20.000000
+8.600000 8.700000 17.000000
+8.700000 8.800000 15.000000
+8.800000 8.900000 9.000000
+8.900000 9.000000 8.000000
+9.000000 9.100000 12.000000
+9.100000 9.200000 7.000000
+9.200000 9.300000 10.000000
+9.300000 9.400000 12.000000
+9.400000 9.500000 9.000000
+9.500000 9.600000 13.000000
+9.600000 9.700000 12.000000
+9.700000 9.800000 11.000000
+9.800000 9.900000 13.000000
+9.900000 10.000000 8.000000
diff -Nru gsl-doc-1.16/doc/examples/ode-initval.c gsl-doc-2.3/doc/examples/ode-initval.c
--- gsl-doc-1.16/doc/examples/ode-initval.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/ode-initval.c	2015-11-09 19:13:41.000000000 +0000
@@ -7,6 +7,7 @@
 func (double t, const double y[], double f[],
       void *params)
 {
+  (void)(t); /* avoid unused parameter warning */
   double mu = *(double *)params;
   f[0] = y[1];
   f[1] = -y[0] - mu*y[1]*(y[0]*y[0] - 1);
@@ -17,6 +18,7 @@
 jac (double t, const double y[], double *dfdy, 
      double dfdt[], void *params)
 {
+  (void)(t); /* avoid unused parameter warning */
   double mu = *(double *)params;
   gsl_matrix_view dfdy_mat 
     = gsl_matrix_view_array (dfdy, 2, 2);
diff -Nru gsl-doc-1.16/doc/examples/ode-initval.txt gsl-doc-2.3/doc/examples/ode-initval.txt
--- gsl-doc-1.16/doc/examples/ode-initval.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/ode-initval.txt	2015-11-10 19:12:04.000000000 +0000
@@ -0,0 +1,100 @@
+1.00000e+00 -1.45686e+00 -1.15474e+01
+2.00000e+00 -1.95608e+00 6.90647e-02
+3.00000e+00 -1.88481e+00 7.36425e-02
+4.00000e+00 -1.80842e+00 7.93679e-02
+5.00000e+00 -1.72550e+00 8.68268e-02
+6.00000e+00 -1.63383e+00 9.71295e-02
+7.00000e+00 -1.52952e+00 1.12715e-01
+8.00000e+00 -1.40454e+00 1.40376e-01
+9.00000e+00 -1.23605e+00 2.10149e-01
+1.00000e+01 -8.53916e-01 9.01984e-01
+1.10000e+01 1.99274e+00 -6.69455e-02
+1.20000e+01 1.92381e+00 -7.10572e-02
+1.30000e+01 1.85032e+00 -7.61105e-02
+1.40000e+01 1.77113e+00 -8.25398e-02
+1.50000e+01 1.68453e+00 -9.11205e-02
+1.60000e+01 1.58767e+00 -1.03413e-01
+1.70000e+01 1.47528e+00 -1.23181e-01
+1.80000e+01 1.33506e+00 -1.62840e-01
+1.90000e+01 1.12079e+00 -3.05570e-01
+2.00000e+01 -1.59837e+00 -9.82301e+00
+2.10000e+01 -1.96148e+00 6.87433e-02
+2.20000e+01 -1.89057e+00 7.32476e-02
+2.30000e+01 -1.81462e+00 7.88663e-02
+2.40000e+01 -1.73228e+00 8.61590e-02
+2.50000e+01 -1.64141e+00 9.61768e-02
+2.60000e+01 -1.53829e+00 1.11197e-01
+2.70000e+01 -1.41542e+00 1.37412e-01
+2.80000e+01 -1.25215e+00 2.00819e-01
+2.90000e+01 -9.15979e-01 6.98133e-01
+3.00000e+01 1.99798e+00 -6.66422e-02
+3.10000e+01 1.92936e+00 -7.07053e-02
+3.20000e+01 1.85626e+00 -7.56719e-02
+3.30000e+01 1.77758e+00 -8.19715e-02
+3.40000e+01 1.69164e+00 -9.03420e-02
+3.50000e+01 1.59573e+00 -1.02252e-01
+3.60000e+01 1.48485e+00 -1.21185e-01
+3.70000e+01 1.34764e+00 -1.58256e-01
+3.80000e+01 1.14377e+00 -2.81644e-01
+3.90000e+01 -5.76613e-01 -1.26648e+01
+4.00000e+01 -1.96686e+00 6.84268e-02
+4.10000e+01 -1.89629e+00 7.28598e-02
+4.20000e+01 -1.82078e+00 7.83750e-02
+4.30000e+01 -1.73901e+00 8.55074e-02
+4.40000e+01 -1.64891e+00 9.52534e-02
+4.50000e+01 -1.54695e+00 1.09742e-01
+4.60000e+01 -1.42608e+00 1.34632e-01
+4.70000e+01 -1.26756e+00 1.92566e-01
+4.80000e+01 -9.65230e-01 5.67682e-01
+4.90000e+01 2.00319e+00 -6.62229e-02
+5.00000e+01 1.93489e+00 -7.03588e-02
+5.10000e+01 1.86218e+00 -7.52414e-02
+5.20000e+01 1.78398e+00 -8.14156e-02
+5.30000e+01 1.69869e+00 -8.95845e-02
+5.40000e+01 1.60370e+00 -1.01133e-01
+5.50000e+01 1.49428e+00 -1.19287e-01
+5.60000e+01 1.35987e+00 -1.54035e-01
+5.70000e+01 1.16505e+00 -2.61951e-01
+5.80000e+01 1.42891e-01 -6.13207e+00
+5.90000e+01 -1.97221e+00 6.81150e-02
+6.00000e+01 -1.90199e+00 7.24784e-02
+6.10000e+01 -1.82690e+00 7.78933e-02
+6.20000e+01 -1.74568e+00 8.48713e-02
+6.30000e+01 -1.65634e+00 9.43576e-02
+6.40000e+01 -1.55550e+00 1.08345e-01
+6.50000e+01 -1.43653e+00 1.32018e-01
+6.60000e+01 -1.28235e+00 1.85208e-01
+6.70000e+01 -1.00603e+00 4.78809e-01
+6.80000e+01 2.00833e+00 -6.45142e-02
+6.90000e+01 1.94039e+00 -7.00179e-02
+7.00000e+01 1.86806e+00 -7.48186e-02
+7.10000e+01 1.79034e+00 -8.08716e-02
+7.20000e+01 1.70568e+00 -8.88470e-02
+7.30000e+01 1.61158e+00 -1.00051e-01
+7.40000e+01 1.50355e+00 -1.17479e-01
+7.50000e+01 1.37179e+00 -1.50135e-01
+7.60000e+01 1.18491e+00 -2.45468e-01
+7.70000e+01 4.84591e-01 -3.05853e+00
+7.80000e+01 -1.97754e+00 6.78077e-02
+7.90000e+01 -1.90765e+00 7.21034e-02
+8.00000e+01 -1.83299e+00 7.74210e-02
+8.10000e+01 -1.75231e+00 8.42502e-02
+8.20000e+01 -1.66370e+00 9.34883e-02
+8.30000e+01 -1.56393e+00 1.07003e-01
+8.40000e+01 -1.44678e+00 1.29554e-01
+8.50000e+01 -1.29661e+00 1.78603e-01
+8.60000e+01 -1.04093e+00 4.15185e-01
+8.70000e+01 2.01299e+00 -4.86619e-02
+8.80000e+01 1.94586e+00 -6.96821e-02
+8.90000e+01 1.87390e+00 -7.44034e-02
+9.00000e+01 1.79665e+00 -8.03392e-02
+9.10000e+01 1.71261e+00 -8.81285e-02
+9.20000e+01 1.61938e+00 -9.90050e-02
+9.30000e+01 1.51269e+00 -1.15754e-01
+9.40000e+01 1.38341e+00 -1.46518e-01
+9.50000e+01 1.20359e+00 -2.31470e-01
+9.60000e+01 6.68012e-01 -1.79285e+00
+9.70000e+01 -1.98284e+00 6.75047e-02
+9.80000e+01 -1.91329e+00 7.17346e-02
+9.90000e+01 -1.83904e+00 7.69577e-02
+1.00000e+02 -1.75889e+00 8.36435e-02
diff -Nru gsl-doc-1.16/doc/examples/permseq.txt gsl-doc-2.3/doc/examples/permseq.txt
--- gsl-doc-1.16/doc/examples/permseq.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/permseq.txt	2015-11-10 19:13:08.000000000 +0000
@@ -0,0 +1,6 @@
+ 0 1 2
+ 0 2 1
+ 1 0 2
+ 1 2 0
+ 2 0 1
+ 2 1 0
diff -Nru gsl-doc-1.16/doc/examples/permshuffle.txt gsl-doc-2.3/doc/examples/permshuffle.txt
--- gsl-doc-1.16/doc/examples/permshuffle.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/permshuffle.txt	2015-11-10 19:14:14.000000000 +0000
@@ -0,0 +1,3 @@
+initial permutation: 0 1 2 3 4 5 6 7 8 9
+ random permutation: 0 5 4 3 7 8 6 2 1 9
+inverse permutation: 0 8 7 3 2 1 6 4 5 9
diff -Nru gsl-doc-1.16/doc/examples/poisson.c gsl-doc-2.3/doc/examples/poisson.c
--- gsl-doc-1.16/doc/examples/poisson.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/poisson.c	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,101 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_spmatrix.h>
+#include <gsl/gsl_splinalg.h>
+
+int
+main()
+{
+  const size_t N = 100;                       /* number of grid points */
+  const size_t n = N - 2;                     /* subtract 2 to exclude boundaries */
+  const double h = 1.0 / (N - 1.0);           /* grid spacing */
+  gsl_spmatrix *A = gsl_spmatrix_alloc(n ,n); /* triplet format */
+  gsl_spmatrix *C;                            /* compressed format */
+  gsl_vector *f = gsl_vector_alloc(n);        /* right hand side vector */
+  gsl_vector *u = gsl_vector_alloc(n);        /* solution vector */
+  size_t i;
+
+  /* construct the sparse matrix for the finite difference equation */
+
+  /* construct first row */
+  gsl_spmatrix_set(A, 0, 0, -2.0);
+  gsl_spmatrix_set(A, 0, 1, 1.0);
+
+  /* construct rows [1:n-2] */
+  for (i = 1; i < n - 1; ++i)
+    {
+      gsl_spmatrix_set(A, i, i + 1, 1.0);
+      gsl_spmatrix_set(A, i, i, -2.0);
+      gsl_spmatrix_set(A, i, i - 1, 1.0);
+    }
+
+  /* construct last row */
+  gsl_spmatrix_set(A, n - 1, n - 1, -2.0);
+  gsl_spmatrix_set(A, n - 1, n - 2, 1.0);
+
+  /* scale by h^2 */
+  gsl_spmatrix_scale(A, 1.0 / (h * h));
+
+  /* construct right hand side vector */
+  for (i = 0; i < n; ++i)
+    {
+      double xi = (i + 1) * h;
+      double fi = -M_PI * M_PI * sin(M_PI * xi);
+      gsl_vector_set(f, i, fi);
+    }
+
+  /* convert to compressed column format */
+  C = gsl_spmatrix_ccs(A);
+
+  /* now solve the system with the GMRES iterative solver */
+  {
+    const double tol = 1.0e-6;  /* solution relative tolerance */
+    const size_t max_iter = 10; /* maximum iterations */
+    const gsl_splinalg_itersolve_type *T = gsl_splinalg_itersolve_gmres;
+    gsl_splinalg_itersolve *work =
+      gsl_splinalg_itersolve_alloc(T, n, 0);
+    size_t iter = 0;
+    double residual;
+    int status;
+
+    /* initial guess u = 0 */
+    gsl_vector_set_zero(u);
+
+    /* solve the system A u = f */
+    do
+      {
+        status = gsl_splinalg_itersolve_iterate(C, f, tol, u, work);
+
+        /* print out residual norm ||A*u - f|| */
+        residual = gsl_splinalg_itersolve_normr(work);
+        fprintf(stderr, "iter %zu residual = %.12e\n", iter, residual);
+
+        if (status == GSL_SUCCESS)
+          fprintf(stderr, "Converged\n");
+      }
+    while (status == GSL_CONTINUE && ++iter < max_iter);
+
+    /* output solution */
+    for (i = 0; i < n; ++i)
+      {
+        double xi = (i + 1) * h;
+        double u_exact = sin(M_PI * xi);
+        double u_gsl = gsl_vector_get(u, i);
+
+        printf("%f %.12e %.12e\n", xi, u_gsl, u_exact);
+      }
+
+    gsl_splinalg_itersolve_free(work);
+  }
+
+  gsl_spmatrix_free(A);
+  gsl_spmatrix_free(C);
+  gsl_vector_free(f);
+  gsl_vector_free(u);
+
+  return 0;
+} /* main() */
diff -Nru gsl-doc-1.16/doc/examples/poisson.txt gsl-doc-2.3/doc/examples/poisson.txt
--- gsl-doc-1.16/doc/examples/poisson.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/poisson.txt	2015-11-10 19:15:21.000000000 +0000
@@ -0,0 +1,98 @@
+0.010101 3.173059613385e-02 3.172793349807e-02
+0.020202 6.342924224708e-02 6.342391965656e-02
+0.030303 9.506402049003e-02 9.505604330418e-02
+0.040404 1.266030773226e-01 1.265924535737e-01
+0.050505 1.580146555880e-01 1.580013959733e-01
+0.060606 1.892671264895e-01 1.892512443604e-01
+0.070707 2.203290214381e-01 2.203105327865e-01
+0.080808 2.511690637386e-01 2.511479871811e-01
+0.090909 2.817562000827e-01 2.817325568414e-01
+0.101010 3.120596318167e-01 3.120334456985e-01
+0.111111 3.420488459536e-01 3.420201433257e-01
+0.121212 3.716936458969e-01 3.716624556603e-01
+0.131313 4.009641818459e-01 4.009305354066e-01
+0.141414 4.298309808521e-01 4.297949120892e-01
+0.151515 4.582649764957e-01 4.582265217274e-01
+0.161616 4.862375381535e-01 4.861967361005e-01
+0.171717 5.137204998270e-01 5.136773915734e-01
+0.181818 5.406861885033e-01 5.406408174556e-01
+0.191919 5.671074520199e-01 5.670598638628e-01
+0.202020 5.929576864038e-01 5.929079290546e-01
+0.212121 6.182108626605e-01 6.181589862206e-01
+0.222222 6.428415529819e-01 6.427876096865e-01
+0.232323 6.668249563509e-01 6.667690005163e-01
+0.242424 6.901369235131e-01 6.900790114821e-01
+0.252525 7.127539812937e-01 7.126941713789e-01
+0.262626 7.346533562328e-01 7.345917086575e-01
+0.272727 7.558129975160e-01 7.557495743543e-01
+0.282828 7.762115991782e-01 7.761464642918e-01
+0.292929 7.958286215568e-01 7.957618405308e-01
+0.303030 8.146443119729e-01 8.145759520503e-01
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+0.323232 8.497967396468e-01 8.497254299495e-01
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+0.767677 6.668249563509e-01 6.667690005163e-01
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+0.787879 6.182108626605e-01 6.181589862206e-01
+0.797980 5.929576864038e-01 5.929079290546e-01
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+0.818182 5.406861885033e-01 5.406408174556e-01
+0.828283 5.137204998270e-01 5.136773915734e-01
+0.838384 4.862375381535e-01 4.861967361005e-01
+0.848485 4.582649764957e-01 4.582265217274e-01
+0.858586 4.298309808521e-01 4.297949120892e-01
+0.868687 4.009641818459e-01 4.009305354066e-01
+0.878788 3.716936458969e-01 3.716624556603e-01
+0.888889 3.420488459536e-01 3.420201433257e-01
+0.898990 3.120596318167e-01 3.120334456985e-01
+0.909091 2.817562000827e-01 2.817325568414e-01
+0.919192 2.511690637386e-01 2.511479871811e-01
+0.929293 2.203290214381e-01 2.203105327865e-01
+0.939394 1.892671264895e-01 1.892512443604e-01
+0.949495 1.580146555880e-01 1.580013959733e-01
+0.959596 1.266030773226e-01 1.265924535737e-01
+0.969697 9.506402049003e-02 9.505604330418e-02
+0.979798 6.342924224708e-02 6.342391965656e-02
+0.989899 3.173059613385e-02 3.172793349807e-02
diff -Nru gsl-doc-1.16/doc/examples/polyroots.out gsl-doc-2.3/doc/examples/polyroots.out
--- gsl-doc-1.16/doc/examples/polyroots.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/polyroots.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,5 +0,0 @@
-z0 = -0.809016994374947451 +0.587785252292473137
-z1 = -0.809016994374947451 -0.587785252292473137
-z2 = +0.309016994374947451 +0.951056516295153642
-z3 = +0.309016994374947451 -0.951056516295153642
-z4 = +1.000000000000000000 +0.000000000000000000
diff -Nru gsl-doc-1.16/doc/examples/polyroots.txt gsl-doc-2.3/doc/examples/polyroots.txt
--- gsl-doc-1.16/doc/examples/polyroots.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/polyroots.txt	2015-11-10 19:16:44.000000000 +0000
@@ -0,0 +1,5 @@
+z0 = -0.809016994374947673 +0.587785252292473359
+z1 = -0.809016994374947673 -0.587785252292473359
+z2 = +0.309016994374947507 +0.951056516295152976
+z3 = +0.309016994374947507 -0.951056516295152976
+z4 = +0.999999999999999889 +0.000000000000000000
diff -Nru gsl-doc-1.16/doc/examples/qrng.txt gsl-doc-2.3/doc/examples/qrng.txt
--- gsl-doc-1.16/doc/examples/qrng.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/qrng.txt	2015-11-10 19:17:00.000000000 +0000
@@ -0,0 +1,1024 @@
+0.50000 0.50000
+0.75000 0.25000
+0.25000 0.75000
+0.37500 0.37500
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+0.42285 0.89355
+0.29785 0.26855
+0.79785 0.76855
+0.54785 0.01855
+0.04785 0.51855
+0.03223 0.28418
+0.53223 0.78418
+0.78223 0.03418
+0.28223 0.53418
+0.40723 0.15918
+0.90723 0.65918
+0.65723 0.40918
+0.15723 0.90918
+0.21973 0.09668
+0.71973 0.59668
+0.96973 0.34668
+0.46973 0.84668
+0.34473 0.47168
+0.84473 0.97168
+0.59473 0.22168
+0.09473 0.72168
+0.06348 0.19043
+0.56348 0.69043
+0.81348 0.44043
+0.31348 0.94043
+0.43848 0.31543
+0.93848 0.81543
+0.68848 0.06543
+0.18848 0.56543
+0.12598 0.37793
+0.62598 0.87793
+0.87598 0.12793
+0.37598 0.62793
+0.25098 0.00293
+0.75098 0.50293
+0.50098 0.25293
+0.00098 0.75293
+0.00146 0.37646
diff -Nru gsl-doc-1.16/doc/examples/randpoisson.2.out gsl-doc-2.3/doc/examples/randpoisson.2.out
--- gsl-doc-1.16/doc/examples/randpoisson.2.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/randpoisson.2.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,2 +0,0 @@
-GSL_RNG_SEED=123
- 4 5 6 3 3 1 4 2 5 5
diff -Nru gsl-doc-1.16/doc/examples/randpoisson2.txt gsl-doc-2.3/doc/examples/randpoisson2.txt
--- gsl-doc-1.16/doc/examples/randpoisson2.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/randpoisson2.txt	2015-11-10 19:21:27.000000000 +0000
@@ -0,0 +1 @@
+ 4 5 6 3 3 1 4 2 5 5
diff -Nru gsl-doc-1.16/doc/examples/randpoisson.out gsl-doc-2.3/doc/examples/randpoisson.out
--- gsl-doc-1.16/doc/examples/randpoisson.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/randpoisson.out	1970-01-01 00:00:00.000000000 +0000
@@ -1 +0,0 @@
- 2 5 5 2 1 0 3 4 1 1
diff -Nru gsl-doc-1.16/doc/examples/randpoisson.txt gsl-doc-2.3/doc/examples/randpoisson.txt
--- gsl-doc-1.16/doc/examples/randpoisson.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/randpoisson.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1 @@
+ 2 5 5 2 1 0 3 4 1 1
diff -Nru gsl-doc-1.16/doc/examples/randwalk.txt gsl-doc-2.3/doc/examples/randwalk.txt
--- gsl-doc-1.16/doc/examples/randwalk.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/randwalk.txt	2015-11-10 19:24:35.000000000 +0000
@@ -0,0 +1,11 @@
+0 0
+-0.617746 -0.786378
+0.376003 -0.674734
+-0.569808 -0.350015
+-0.112542 0.539315
+-0.575798 -0.34691
+-1.56878 -0.465204
+-2.47057 -0.0330451
+-2.50057 0.966505
+-1.72376 1.59625
+-2.64634 1.98207
diff -Nru gsl-doc-1.16/doc/examples/rng.out gsl-doc-2.3/doc/examples/rng.out
--- gsl-doc-1.16/doc/examples/rng.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/rng.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,3 +0,0 @@
-generator type: mt19937
-seed = 0
-first value = 4293858116
diff -Nru gsl-doc-1.16/doc/examples/rng.txt gsl-doc-2.3/doc/examples/rng.txt
--- gsl-doc-1.16/doc/examples/rng.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/rng.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,3 @@
+generator type: mt19937
+seed = 0
+first value = 4293858116
diff -Nru gsl-doc-1.16/doc/examples/rngunif.2.out gsl-doc-2.3/doc/examples/rngunif.2.out
--- gsl-doc-1.16/doc/examples/rngunif.2.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/rngunif.2.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,12 +0,0 @@
-GSL_RNG_TYPE=mrg
-GSL_RNG_SEED=123
-0.33050
-0.86631
-0.32982
-0.67620
-0.53391
-0.06457
-0.16847
-0.70229
-0.04371
-0.86374
diff -Nru gsl-doc-1.16/doc/examples/rngunif2.txt gsl-doc-2.3/doc/examples/rngunif2.txt
--- gsl-doc-1.16/doc/examples/rngunif2.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/rngunif2.txt	2015-11-10 19:28:02.000000000 +0000
@@ -0,0 +1,10 @@
+0.33050
+0.86631
+0.32982
+0.67620
+0.53391
+0.06457
+0.16847
+0.70229
+0.04371
+0.86374
diff -Nru gsl-doc-1.16/doc/examples/rngunif.out gsl-doc-2.3/doc/examples/rngunif.out
--- gsl-doc-1.16/doc/examples/rngunif.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/rngunif.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,10 +0,0 @@
-0.99974
-0.16291
-0.28262
-0.94720
-0.23166
-0.48497
-0.95748
-0.74431
-0.54004
-0.73995
diff -Nru gsl-doc-1.16/doc/examples/rngunif.txt gsl-doc-2.3/doc/examples/rngunif.txt
--- gsl-doc-1.16/doc/examples/rngunif.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/rngunif.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,10 @@
+0.99974
+0.16291
+0.28262
+0.94720
+0.23166
+0.48497
+0.95748
+0.74431
+0.54004
+0.73995
diff -Nru gsl-doc-1.16/doc/examples/robfit.c gsl-doc-2.3/doc/examples/robfit.c
--- gsl-doc-1.16/doc/examples/robfit.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/robfit.c	2015-11-09 19:14:42.000000000 +0000
@@ -20,7 +20,7 @@
 int
 main (int argc, char **argv)
 {
-  int i;
+  size_t i;
   size_t n;
   const size_t p = 2; /* linear fit */
   gsl_matrix *X, *cov;
diff -Nru gsl-doc-1.16/doc/examples/robfit.txt gsl-doc-2.3/doc/examples/robfit.txt
--- gsl-doc-1.16/doc/examples/robfit.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/robfit.txt	2015-11-10 19:30:24.000000000 +0000
@@ -0,0 +1,104 @@
+-5 -2.37026 -2.87902 -2.10098
+-4.89899 -3.06063 -2.73364 -1.98182
+-4.79798 -2.79445 -2.58825 -1.86266
+-4.69697 -1.9834 -2.44287 -1.7435
+-4.59596 -2.55248 -2.29749 -1.62435
+-4.49495 -2.1527 -2.1521 -1.50519
+-4.39394 -1.53374 -2.00672 -1.38603
+-4.29293 -1.60044 -1.86134 -1.26687
+-4.19192 -1.65824 -1.71596 -1.14772
+-4.09091 -1.31187 -1.57057 -1.02856
+-3.9899 -1.14541 -1.42519 -0.909399
+-3.88889 -1.10025 -1.27981 -0.790242
+-3.78788 -1.29679 -1.13443 -0.671084
+-3.68687 -0.661557 -0.989042 -0.551926
+-3.58586 -0.799823 -0.843659 -0.432768
+-3.48485 -1.00446 -0.698277 -0.31361
+-3.38384 -0.551036 -0.552894 -0.194452
+-3.28283 -0.487787 -0.407511 -0.0752942
+-3.18182 -0.511969 -0.262128 0.0438637
+-3.08081 -0.373981 -0.116746 0.163022
+-2.9798 -0.410372 0.0286373 0.282179
+-2.87879 0.0392968 0.17402 0.401337
+-2.77778 0.0463711 0.319403 0.520495
+-2.67677 0.942404 0.464786 0.639653
+-2.57576 0.725083 0.610168 0.758811
+-2.47475 1.18992 0.755551 0.877969
+-2.37374 1.10364 0.900934 0.997127
+-2.27273 1.08316 1.04632 1.11628
+-2.17172 1.29164 1.1917 1.23544
+-2.07071 1.05976 1.33708 1.3546
+-1.9697 1.32046 1.48247 1.47376
+-1.86869 1.28781 1.62785 1.59292
+-1.76768 1.37979 1.77323 1.71207
+-1.66667 2.11146 1.91861 1.83123
+-1.56566 2.33522 2.064 1.95039
+-1.46465 2.39339 2.20938 2.06955
+-1.36364 2.61661 2.35476 2.18871
+-1.26263 2.14877 2.50014 2.30786
+-1.16162 2.89492 2.64553 2.42702
+-1.06061 2.44993 2.79091 2.54618
+-0.959596 2.61783 2.93629 2.66534
+-0.858586 3.13745 3.08168 2.7845
+-0.757576 2.9893 3.22706 2.90365
+-0.656566 3.21689 3.37244 3.02281
+-0.555556 3.15762 3.51782 3.14197
+-0.454545 3.34903 3.66321 3.26113
+-0.353535 3.91475 3.80859 3.38028
+-0.252525 3.59616 3.95397 3.49944
+-0.151515 3.95244 4.09936 3.6186
+-0.0505051 4.69839 4.24474 3.73776
+0.0505051 4.18035 4.39012 3.85692
+0.151515 4.53154 4.5355 3.97607
+0.252525 4.38689 4.68089 4.09523
+0.353535 4.79302 4.82627 4.21439
+0.454545 5.22604 4.97165 4.33355
+0.555556 4.85623 5.11704 4.45271
+0.656566 5.27284 5.26242 4.57186
+0.757576 5.02382 5.4078 4.69102
+0.858586 5.43625 5.55318 4.81018
+0.959596 5.7776 5.69857 4.92934
+1.06061 5.60029 5.84395 5.0485
+1.16162 6.07538 5.98933 5.16765
+1.26263 6.4516 6.13471 5.28681
+1.36364 6.22326 6.2801 5.40597
+1.46465 6.16455 6.42548 5.52513
+1.56566 6.61031 6.57086 5.64428
+1.66667 6.9245 6.71625 5.76344
+1.76768 7.12074 6.86163 5.8826
+1.86869 7.28779 7.00701 6.00176
+1.9697 7.2146 7.15239 6.12092
+2.07071 6.97263 7.29778 6.24007
+2.17172 7.36772 7.44316 6.35923
+2.27273 7.27067 7.58854 6.47839
+2.37374 7.75846 7.73393 6.59755
+2.47475 7.94306 7.87931 6.71671
+2.57576 8.03409 8.02469 6.83586
+2.67677 8.53885 8.17007 6.95502
+2.77778 8.53239 8.31546 7.07418
+2.87879 9.03468 8.46084 7.19334
+2.9798 8.57114 8.60622 7.31249
+3.08081 9.17798 8.7516 7.43165
+3.18182 8.63444 8.89699 7.55081
+3.28283 9.38419 9.04237 7.66997
+3.38384 9.61631 9.18775 7.78913
+3.48485 9.32413 9.33314 7.90828
+3.58586 9.70145 9.47852 8.02744
+3.68687 9.57266 9.6239 8.1466
+3.78788 9.41859 9.76928 8.26576
+3.88889 10.132 9.91467 8.38492
+3.9899 10.2327 10.0601 8.50407
+4.09091 10.3107 10.2054 8.62323
+4.19192 10.6821 10.3508 8.74239
+4.29293 10.2493 10.4962 8.86155
+4.39394 10.2935 10.6416 8.98071
+4.49495 10.7085 10.787 9.09986
+4.59596 10.6658 10.9323 9.21902
+4.69697 10.9327 11.0777 9.33818
+4.7 -8.3 11.0821 9.34175
+3.5 -6.7 9.35494 7.92616
+4.1 -6 10.2185 8.63396
+# best fit: Y = 4.31743 + 1.43929 X
+# covariance matrix:
+# [ +4.01177e-03, +1.15955e-05
+#   +1.15955e-05, +4.83755e-04
diff -Nru gsl-doc-1.16/doc/examples/rootnewt.txt gsl-doc-2.3/doc/examples/rootnewt.txt
--- gsl-doc-1.16/doc/examples/rootnewt.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/rootnewt.txt	2015-11-10 19:31:24.000000000 +0000
@@ -0,0 +1,7 @@
+using newton method
+iter        root        err   err(est)
+    1  3.0000000 +0.7639320 -2.0000000
+    2  2.3333333 +0.0972654 -0.6666667
+    3  2.2380952 +0.0020273 -0.0952381
+Converged:
+    4  2.2360689 +0.0000009 -0.0020263
diff -Nru gsl-doc-1.16/doc/examples/roots.txt gsl-doc-2.3/doc/examples/roots.txt
--- gsl-doc-1.16/doc/examples/roots.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/roots.txt	2015-11-10 19:32:06.000000000 +0000
@@ -0,0 +1,9 @@
+using brent method
+ iter [    lower,     upper]      root        err  err(est)
+    1 [1.0000000, 5.0000000] 1.0000000 -1.2360680 4.0000000
+    2 [1.0000000, 3.0000000] 3.0000000 +0.7639320 2.0000000
+    3 [2.0000000, 3.0000000] 2.0000000 -0.2360680 1.0000000
+    4 [2.2000000, 3.0000000] 2.2000000 -0.0360680 0.8000000
+    5 [2.2000000, 2.2366300] 2.2366300 +0.0005621 0.0366300
+Converged:
+    6 [2.2360634, 2.2366300] 2.2360634 -0.0000046 0.0005666
diff -Nru gsl-doc-1.16/doc/examples/rquantile.c gsl-doc-2.3/doc/examples/rquantile.c
--- gsl-doc-1.16/doc/examples/rquantile.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/rquantile.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,60 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <gsl/gsl_rstat.h>
+#include <gsl/gsl_statistics.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_randist.h>
+#include <gsl/gsl_sort.h>
+
+int
+main(void)
+{
+  const size_t N = 10000;
+  double *data = malloc(N * sizeof(double));
+  gsl_rstat_quantile_workspace *work_25 = gsl_rstat_quantile_alloc(0.25);
+  gsl_rstat_quantile_workspace *work_50 = gsl_rstat_quantile_alloc(0.5);
+  gsl_rstat_quantile_workspace *work_75 = gsl_rstat_quantile_alloc(0.75);
+  gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+  double exact_p25, exact_p50, exact_p75;
+  double val_p25, val_p50, val_p75;
+  size_t i;
+
+  /* add data to quantile accumulators; also store data for exact
+   * comparisons */
+  for (i = 0; i < N; ++i)
+    {
+      data[i] = gsl_ran_rayleigh(r, 1.0);
+      gsl_rstat_quantile_add(data[i], work_25);
+      gsl_rstat_quantile_add(data[i], work_50);
+      gsl_rstat_quantile_add(data[i], work_75);
+    }
+
+  /* exact values */
+  gsl_sort(data, 1, N);
+  exact_p25 = gsl_stats_quantile_from_sorted_data(data, 1, N, 0.25);
+  exact_p50 = gsl_stats_quantile_from_sorted_data(data, 1, N, 0.5);
+  exact_p75 = gsl_stats_quantile_from_sorted_data(data, 1, N, 0.75);
+
+  /* estimated values */
+  val_p25 = gsl_rstat_quantile_get(work_25);
+  val_p50 = gsl_rstat_quantile_get(work_50);
+  val_p75 = gsl_rstat_quantile_get(work_75);
+
+  printf ("The dataset is %g, %g, %g, %g, %g, ...\n",
+         data[0], data[1], data[2], data[3], data[4]);
+
+  printf ("0.25 quartile: exact = %.5f, estimated = %.5f, error = %.6e\n",
+          exact_p25, val_p25, (val_p25 - exact_p25) / exact_p25);
+  printf ("0.50 quartile: exact = %.5f, estimated = %.5f, error = %.6e\n",
+          exact_p50, val_p50, (val_p50 - exact_p50) / exact_p50);
+  printf ("0.75 quartile: exact = %.5f, estimated = %.5f, error = %.6e\n",
+          exact_p75, val_p75, (val_p75 - exact_p75) / exact_p75);
+
+  gsl_rstat_quantile_free(work_25);
+  gsl_rstat_quantile_free(work_50);
+  gsl_rstat_quantile_free(work_75);
+  gsl_rng_free(r);
+  free(data);
+
+  return 0;
+}
diff -Nru gsl-doc-1.16/doc/examples/rquantile.txt gsl-doc-2.3/doc/examples/rquantile.txt
--- gsl-doc-1.16/doc/examples/rquantile.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/rquantile.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,4 @@
+The dataset is 0.00645272, 0.0074002, 0.0120706, 0.0207256, 0.0227282, ...
+0.25 quartile: exact = 0.75766, estimated = 0.75580, error = -2.450209e-03
+0.50 quartile: exact = 1.17508, estimated = 1.17438, error = -5.995912e-04
+0.75 quartile: exact = 1.65347, estimated = 1.65696, error = 2.110571e-03
diff -Nru gsl-doc-1.16/doc/examples/rstat.c gsl-doc-2.3/doc/examples/rstat.c
--- gsl-doc-1.16/doc/examples/rstat.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/rstat.c	2016-10-03 09:08:46.000000000 +0000
@@ -0,0 +1,51 @@
+#include <stdio.h>
+#include <gsl/gsl_rstat.h>
+
+int
+main(void)
+{
+  double data[5] = {17.2, 18.1, 16.5, 18.3, 12.6};
+  double mean, variance, largest, smallest, sd,
+         rms, sd_mean, median, skew, kurtosis;
+  gsl_rstat_workspace *rstat_p = gsl_rstat_alloc();
+  size_t i, n;
+
+  /* add data to rstat accumulator */
+  for (i = 0; i < 5; ++i)
+    gsl_rstat_add(data[i], rstat_p);
+
+  mean     = gsl_rstat_mean(rstat_p);
+  variance = gsl_rstat_variance(rstat_p);
+  largest  = gsl_rstat_max(rstat_p);
+  smallest = gsl_rstat_min(rstat_p);
+  median   = gsl_rstat_median(rstat_p);
+  sd       = gsl_rstat_sd(rstat_p);
+  sd_mean  = gsl_rstat_sd_mean(rstat_p);
+  skew     = gsl_rstat_skew(rstat_p);
+  rms      = gsl_rstat_rms(rstat_p);
+  kurtosis = gsl_rstat_kurtosis(rstat_p);
+  n        = gsl_rstat_n(rstat_p);
+
+  printf ("The dataset is %g, %g, %g, %g, %g\n",
+         data[0], data[1], data[2], data[3], data[4]);
+
+  printf ("The sample mean is %g\n", mean);
+  printf ("The estimated variance is %g\n", variance);
+  printf ("The largest value is %g\n", largest);
+  printf ("The smallest value is %g\n", smallest);
+  printf( "The median is %g\n", median);
+  printf( "The standard deviation is %g\n", sd);
+  printf( "The root mean square is %g\n", rms);
+  printf( "The standard devation of the mean is %g\n", sd_mean);
+  printf( "The skew is %g\n", skew);
+  printf( "The kurtosis %g\n", kurtosis);
+  printf( "There are %zu items in the accumulator\n", n);
+
+  gsl_rstat_reset(rstat_p);
+  n = gsl_rstat_n(rstat_p);
+  printf( "There are %zu items in the accumulator\n", n);
+
+  gsl_rstat_free(rstat_p);
+
+  return 0;
+}
diff -Nru gsl-doc-1.16/doc/examples/rstat.txt gsl-doc-2.3/doc/examples/rstat.txt
--- gsl-doc-1.16/doc/examples/rstat.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/rstat.txt	2016-10-03 09:08:46.000000000 +0000
@@ -0,0 +1,13 @@
+The dataset is 17.2, 18.1, 16.5, 18.3, 12.6
+The sample mean is 16.54
+The estimated variance is 5.373
+The largest value is 18.3
+The smallest value is 12.6
+The median is 16.5
+The standard deviation is 2.31797
+The root mean square is 16.6694
+The standard devation of the mean is 1.03663
+The skew is -0.829058
+The kurtosis -1.2217
+There are 5 items in the accumulator
+There are 0 items in the accumulator
diff -Nru gsl-doc-1.16/doc/examples/siman.c gsl-doc-2.3/doc/examples/siman.c
--- gsl-doc-1.16/doc/examples/siman.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/siman.c	2015-11-09 19:16:21.000000000 +0000
@@ -61,7 +61,7 @@
 }
 
 int
-main(int argc, char *argv[])
+main(void)
 {
   const gsl_rng_type * T;
   gsl_rng * r;
diff -Nru gsl-doc-1.16/doc/examples/siman.txt gsl-doc-2.3/doc/examples/siman.txt
--- gsl-doc-1.16/doc/examples/siman.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/siman.txt	2015-11-10 19:37:13.000000000 +0000
@@ -0,0 +1,2770 @@
+#-iter  #-evals   temperature     position   energy
+    0      1001         0.008      1.3507     -0.868361     -0.872837
+    1      2001    0.00797607     1.37079     -0.871175      -0.87287
+    2      3001    0.00795222     1.38039     -0.864303      -0.87287
+    3      4001    0.00792843     1.36375      -0.87286     -0.872871
+    4      5001    0.00790472     0.61174     -0.845934     -0.872871
+    5      6001    0.00788107     1.40147     -0.831327     -0.872871
+    6      7001     0.0078575     1.35283     -0.869778     -0.872871
+    7      8001      0.007834      1.3638     -0.872858     -0.872871
+    8      9001    0.00781057     1.36943     -0.871721     -0.872871
+    9     10001     0.0077872     1.38445     -0.859842     -0.872871
+   10     11001    0.00776391     1.34438     -0.862599     -0.872871
+   11     12001    0.00774069    0.601995     -0.848928     -0.872871
+   12     13001    0.00771754     1.37681      -0.86748     -0.872871
+   13     14001    0.00769445      1.3528     -0.869761     -0.872871
+   14     15001    0.00767144     1.34345     -0.861549     -0.872871
+   15     16001     0.0076485     1.34485      -0.86311     -0.872871
+   16     17001    0.00762562     1.35505     -0.870971     -0.872871
+   17     18001    0.00760281      1.3606     -0.872685     -0.872871
+   18     19001    0.00758007    0.603733      -0.84879     -0.872871
+   19     20001     0.0075574     1.37855     -0.866026     -0.872871
+   20     21001    0.00753479     1.36968     -0.871629     -0.872871
+   21     22001    0.00751226     1.36059     -0.872684     -0.872871
+   22     23001    0.00748979     1.34605     -0.864345     -0.872871
+   23     24001    0.00746738     1.36367     -0.872863     -0.872871
+   24     25001    0.00744505     1.36304     -0.872871     -0.872871
+   25     26001    0.00742278    0.613129     -0.845066     -0.872871
+   26     27001    0.00740058     1.36855     -0.872021     -0.872871
+   27     28001    0.00737844     1.37322      -0.86993     -0.872871
+   28     29001    0.00735638     1.36499     -0.872771     -0.872871
+   29     30001    0.00733437     1.35743     -0.871925     -0.872871
+   30     31001    0.00731243     1.35513     -0.871008     -0.872871
+   31     32001    0.00729056     1.37978     -0.864895     -0.872871
+   32     33001    0.00726876     1.35101     -0.868582     -0.872871
+   33     34001    0.00724702     1.34567     -0.863959     -0.872871
+   34     35001    0.00722534     1.37749     -0.866933     -0.872871
+   35     36001    0.00720373     1.36842     -0.872061     -0.872871
+   36     37001    0.00718218      1.3651     -0.872759     -0.872871
+   37     38001     0.0071607     1.34729     -0.865547     -0.872871
+   38     39001    0.00713928     1.36695     -0.872448     -0.872871
+   39     40001    0.00711793     1.36643     -0.872556     -0.872871
+   40     41001    0.00709664     1.35418     -0.870539     -0.872871
+   41     42001    0.00707541    0.594794     -0.847683     -0.872871
+   42     43001    0.00705425     1.35379      -0.87033     -0.872871
+   43     44001    0.00703315     1.36793     -0.872204     -0.872871
+   44     45001    0.00701211     1.36258     -0.872863     -0.872871
+   45     46001    0.00699114     1.36767     -0.872274     -0.872871
+   46     47001    0.00697023     1.39137      -0.85014     -0.872871
+   47     48001    0.00694938     1.38381     -0.860609     -0.872871
+   48     49001     0.0069286     1.37191     -0.870645     -0.872871
+   49     50001    0.00690787     1.36438     -0.872826     -0.872871
+   50     51001    0.00688721     1.36643     -0.872556     -0.872871
+   51     52001    0.00686661     1.34557     -0.863864     -0.872871
+   52     53001    0.00684607     1.35271     -0.869704     -0.872871
+   53     54001     0.0068256     1.35461     -0.870755     -0.872871
+   54     55001    0.00680518     1.34705     -0.865317     -0.872871
+   55     56001    0.00678483     1.34555     -0.863844     -0.872871
+   56     57001    0.00676453      1.3544     -0.870651     -0.872871
+   57     58001     0.0067443     1.37319     -0.869947     -0.872871
+   58     59001    0.00672413     1.37289      -0.87012     -0.872871
+   59     60001    0.00670401     1.36561     -0.872692     -0.872871
+   60     61001    0.00668396     1.36889     -0.871909     -0.872871
+   61     62001    0.00666397      1.3717     -0.870748     -0.872871
+   62     63001    0.00664404     1.38076      -0.86394     -0.872871
+   63     64001    0.00662417     1.33705     -0.852963     -0.872871
+   64     65001    0.00660435     1.37052     -0.871291     -0.872871
+   65     66001     0.0065846     1.38734     -0.856103     -0.872871
+   66     67001     0.0065649      1.3718     -0.870701     -0.872871
+   67     68001    0.00654527     1.34896     -0.867008     -0.872871
+   68     69001    0.00652569     1.35488     -0.870887     -0.872871
+   69     70001    0.00650617     1.37107     -0.871048     -0.872871
+   70     71001    0.00648671     1.36726     -0.872376     -0.872871
+   71     72001    0.00646731     1.36707     -0.872421     -0.872871
+   72     73001    0.00644797     1.34789      -0.86609     -0.872871
+   73     74001    0.00642868      1.3705       -0.8713     -0.872871
+   74     75001    0.00640945     1.37711     -0.867239     -0.872871
+   75     76001    0.00639028     1.35185     -0.869158     -0.872871
+   76     77001    0.00637117    0.616273     -0.842692     -0.872871
+   77     78001    0.00635211     1.35411     -0.870502     -0.872871
+   78     79001    0.00633311     1.36347     -0.872868     -0.872871
+   79     80001    0.00631417     1.36476     -0.872794     -0.872871
+   80     81001    0.00629528      1.3997     -0.835005     -0.872871
+   81     82001    0.00627645     1.38277     -0.861803     -0.872871
+   82     83001    0.00625768     1.37485     -0.868909     -0.872871
+   83     84001    0.00623896     1.35295     -0.869852     -0.872871
+   84     85001     0.0062203     1.35708     -0.871806     -0.872871
+   85     86001     0.0062017      1.3662     -0.872597     -0.872871
+   86     87001    0.00618315     1.37209     -0.870549     -0.872871
+   87     88001    0.00616466     1.35771     -0.872016     -0.872871
+   88     89001    0.00614622     1.35419      -0.87054     -0.872871
+   89     90001    0.00612783     1.35902     -0.872379     -0.872871
+   90     91001     0.0061095     1.37822     -0.866319     -0.872871
+   91     92001    0.00609123     1.37957     -0.865102     -0.872871
+   92     93001    0.00607301     1.35634      -0.87153     -0.872871
+   93     94001    0.00605485     1.37988       -0.8648     -0.872871
+   94     95001    0.00603674     1.37147     -0.870862     -0.872871
+   95     96001    0.00601868     1.34329     -0.861361     -0.872871
+   96     97001    0.00600068     1.37891     -0.865705     -0.872871
+   97     98001    0.00598273     1.36987     -0.871556     -0.872871
+   98     99001    0.00596484     1.38152     -0.863159     -0.872871
+   99    100001      0.005947     1.37272     -0.870212     -0.872871
+  100    101001    0.00592921     1.38517     -0.858957     -0.872871
+  101    102001    0.00591147     1.36958     -0.871666     -0.872871
+  102    103001    0.00589379     1.35112     -0.868666     -0.872871
+  103    104001    0.00587616     1.35983     -0.872554     -0.872871
+  104    105001    0.00585859     1.34827     -0.866422     -0.872871
+  105    106001    0.00584106     1.36394     -0.872852     -0.872871
+  106    107001    0.00582359     1.35721      -0.87185     -0.872871
+  107    108001    0.00580618     1.37301     -0.870054     -0.872871
+  108    109001    0.00578881     1.35705     -0.871794     -0.872871
+  109    110001    0.00577149     1.36788     -0.872218     -0.872871
+  110    111001    0.00575423     1.35034       -0.8681     -0.872871
+  111    112001    0.00573702     1.38082      -0.86388     -0.872871
+  112    113001    0.00571986      1.3645     -0.872817     -0.872871
+  113    114001    0.00570275     1.36162     -0.872805     -0.872871
+  114    115001     0.0056857     1.37579     -0.868252     -0.872871
+  115    116001    0.00566869     1.37627     -0.867897     -0.872871
+  116    117001    0.00565173     1.37343     -0.869809     -0.872871
+  117    118001    0.00563483     1.36924     -0.871792     -0.872871
+  118    119001    0.00561798     1.36836      -0.87208     -0.872871
+  119    120001    0.00560117     1.37157      -0.87081     -0.872871
+  120    121001    0.00558442     1.35632     -0.871522     -0.872871
+  121    122001    0.00556772     1.35976     -0.872541     -0.872871
+  122    123001    0.00555106     1.38023     -0.864462     -0.872871
+  123    124001    0.00553446     1.38095     -0.863748     -0.872871
+  124    125001    0.00551791     1.36894     -0.871894     -0.872871
+  125    126001     0.0055014      1.3784     -0.866157     -0.872871
+  126    127001    0.00548495     1.37446     -0.869164     -0.872871
+  127    128001    0.00546854     1.33953     -0.856572     -0.872871
+  128    129001    0.00545218     1.36883     -0.871932     -0.872871
+  129    130001    0.00543588     1.35546     -0.871156     -0.872871
+  130    131001    0.00541962     1.35448     -0.870693     -0.872871
+  131    132001    0.00540341     1.38166     -0.863013     -0.872871
+  132    133001    0.00538725     1.36231     -0.872852     -0.872871
+  133    134001    0.00537113     1.35093     -0.868532     -0.872871
+  134    135001    0.00535507     1.36347     -0.872868     -0.872871
+  135    136001    0.00533905     1.36546     -0.872714     -0.872871
+  136    137001    0.00532308      1.3565     -0.871593     -0.872871
+  137    138001    0.00530716     1.36342     -0.872869     -0.872871
+  138    139001    0.00529129     1.37767     -0.866785     -0.872871
+  139    140001    0.00527546     1.35735       -0.8719     -0.872871
+  140    141001    0.00525968     1.35466     -0.870779     -0.872871
+  141    142001    0.00524395     1.36762     -0.872288     -0.872871
+  142    143001    0.00522826     1.34728     -0.865538     -0.872871
+  143    144001    0.00521263     1.36686     -0.872469     -0.872871
+  144    145001    0.00519703      1.3457     -0.863996     -0.872871
+  145    146001    0.00518149     1.36457     -0.872811     -0.872871
+  146    147001    0.00516599     1.36191     -0.872828     -0.872871
+  147    148001    0.00515054     1.35299     -0.869874     -0.872871
+  148    149001    0.00513514     1.37083     -0.871156     -0.872871
+  149    150001    0.00511978     1.36041     -0.872656     -0.872871
+  150    151001    0.00510446     1.36889      -0.87191     -0.872871
+  151    152001     0.0050892     1.35861     -0.872278     -0.872871
+  152    153001    0.00507397     1.37867     -0.865921     -0.872871
+  153    154001     0.0050588     1.35613     -0.871444     -0.872871
+  154    155001    0.00504367     1.36702     -0.872434     -0.872871
+  155    156001    0.00502858     1.36367     -0.872863     -0.872871
+  156    157001    0.00501354     1.33862     -0.855295     -0.872871
+  157    158001    0.00499854     1.36721     -0.872388     -0.872871
+  158    159001    0.00498359     1.37434     -0.869244     -0.872871
+  159    160001    0.00496869      1.3711     -0.871035     -0.872871
+  160    161001    0.00495383     1.37796     -0.866542     -0.872871
+  161    162001    0.00493901     1.35155     -0.868962     -0.872871
+  162    163001    0.00492424     1.36935     -0.871751     -0.872871
+  163    164001    0.00490951     1.37406     -0.869424     -0.872871
+  164    165001    0.00489482        1.37     -0.871508     -0.872871
+  165    166001    0.00488018     1.36735     -0.872355     -0.872871
+  166    167001    0.00486559     1.37326     -0.869909     -0.872871
+  167    168001    0.00485103     1.33658     -0.852239     -0.872871
+  168    169001    0.00483652     1.36361     -0.872864     -0.872871
+  169    170001    0.00482206     1.37817     -0.866362     -0.872871
+  170    171001    0.00480763     1.36476     -0.872794     -0.872871
+  171    172001    0.00479325      1.3458     -0.864091     -0.872871
+  172    173001    0.00477892     1.36734     -0.872358     -0.872871
+  173    174001    0.00476462     1.34898     -0.867027     -0.872871
+  174    175001    0.00475037     1.35619     -0.871468     -0.872871
+  175    176001    0.00473616     1.38367     -0.860772     -0.872871
+  176    177001      0.004722     1.36996     -0.871522     -0.872871
+  177    178001    0.00470787     1.34626     -0.864555     -0.872871
+  178    179001    0.00469379     1.34821     -0.866372     -0.872871
+  179    180001    0.00467975     1.38758     -0.855774     -0.872871
+  180    181001    0.00466576     1.34724     -0.865497     -0.872871
+  181    182001     0.0046518     1.35349     -0.870165     -0.872871
+  182    183001    0.00463789     1.36837     -0.872075     -0.872871
+  183    184001    0.00462402     1.37752     -0.866909     -0.872871
+  184    185001    0.00461018     1.35046     -0.868189     -0.872871
+  185    186001     0.0045964     1.36951     -0.871694     -0.872871
+  186    187001    0.00458265     1.35783     -0.872054     -0.872871
+  187    188001    0.00456894     1.37784     -0.866644     -0.872871
+  188    189001    0.00455527     1.34244     -0.860352     -0.872871
+  189    190001    0.00454165      1.3553     -0.871086     -0.872871
+  190    191001    0.00452807     1.37205      -0.87057     -0.872871
+  191    192001    0.00451452     1.35714     -0.871827     -0.872871
+  192    193001    0.00450102     1.36194      -0.87283     -0.872871
+  193    194001    0.00448756     1.36681     -0.872478     -0.872871
+  194    195001    0.00447413     1.35001     -0.867852     -0.872871
+  195    196001    0.00446075     1.36337      -0.87287     -0.872871
+  196    197001    0.00444741     1.36626     -0.872587     -0.872871
+  197    198001    0.00443411     1.36089     -0.872725     -0.872871
+  198    199001    0.00442084     1.36872     -0.871966     -0.872871
+  199    200001    0.00440762     1.36137     -0.872781     -0.872871
+  200    201001    0.00439444     1.37496     -0.868831     -0.872871
+  201    202001    0.00438129     1.37225     -0.870468     -0.872871
+  202    203001    0.00436819     1.35427     -0.870583     -0.872871
+  203    204001    0.00435512     1.36808      -0.87216     -0.872871
+  204    205001     0.0043421     1.35467     -0.870788     -0.872871
+  205    206001    0.00432911     1.37245     -0.870362     -0.872871
+  206    207001    0.00431616     1.37061     -0.871253     -0.872871
+  207    208001    0.00430325     1.35811     -0.872138     -0.872871
+  208    209001    0.00429038     1.35285     -0.869791     -0.872871
+  209    210001    0.00427755     1.35997     -0.872582     -0.872871
+  210    211001    0.00426475     1.36263     -0.872864     -0.872871
+  211    212001      0.004252      1.3777     -0.866761     -0.872871
+  212    213001    0.00423928     1.36066     -0.872695     -0.872871
+  213    214001     0.0042266     1.36446      -0.87282     -0.872871
+  214    215001    0.00421396     1.36274     -0.872867     -0.872871
+  215    216001    0.00420136     1.36139     -0.872783     -0.872871
+  216    217001    0.00418879    0.600455     -0.848907     -0.872871
+  217    218001    0.00417626      1.3655     -0.872708     -0.872871
+  218    219001    0.00416377     1.35761     -0.871983     -0.872871
+  219    220001    0.00415131     1.35207     -0.869303     -0.872871
+  220    221001     0.0041389     1.37308     -0.870012     -0.872871
+  221    222001    0.00412652    0.604398     -0.848692     -0.872871
+  222    223001    0.00411418     1.35878     -0.872322     -0.872871
+  223    224001    0.00410187     1.35973     -0.872536     -0.872871
+  224    225001     0.0040896     1.34116     -0.858756     -0.872871
+  225    226001    0.00407737     1.36912     -0.871832     -0.872871
+  226    227001    0.00406517     1.36083     -0.872718     -0.872871
+  227    228001    0.00405301     1.35755     -0.871965     -0.872871
+  228    229001    0.00404089     1.36452     -0.872816     -0.872871
+  229    230001    0.00402881     1.34913     -0.867153     -0.872871
+  230    231001    0.00401676     1.37163     -0.870783     -0.872871
+  231    232001    0.00400474     1.36975     -0.871601     -0.872871
+  232    233001    0.00399276     1.36343     -0.872869     -0.872871
+  233    234001    0.00398082     1.38015     -0.864542     -0.872871
+  234    235001    0.00396891     1.36349     -0.872867     -0.872871
+  235    236001    0.00395704     1.37645      -0.86776     -0.872871
+  236    237001    0.00394521     1.36781     -0.872236     -0.872871
+  237    238001    0.00393341     1.36205     -0.872837     -0.872871
+  238    239001    0.00392164     1.35652     -0.871598     -0.872871
+  239    240001    0.00390991      1.3626     -0.872863     -0.872871
+  240    241001    0.00389822     1.36858     -0.872011     -0.872871
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+ 2597   2598001   3.34632e-06     1.36282     -0.872868     -0.872871
+ 2598   2599001   3.33631e-06     1.36282     -0.872868     -0.872871
+ 2599   2600001   3.32633e-06     1.36282     -0.872868     -0.872871
+ 2600   2601001   3.31638e-06     1.36337     -0.872869     -0.872871
+ 2601   2602001   3.30646e-06     1.36337     -0.872869     -0.872871
+ 2602   2603001   3.29657e-06     1.36337     -0.872869     -0.872871
+ 2603   2604001   3.28671e-06     1.36337     -0.872869     -0.872871
+ 2604   2605001   3.27688e-06     1.36337     -0.872869     -0.872871
+ 2605   2606001   3.26708e-06     1.36337     -0.872869     -0.872871
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+ 2691   2692001    2.5251e-06     1.36317     -0.872871     -0.872871
+ 2692   2693001   2.51755e-06     1.36317     -0.872871     -0.872871
+ 2693   2694001   2.51002e-06     1.36317     -0.872871     -0.872871
+ 2694   2695001   2.50251e-06     1.36317     -0.872871     -0.872871
+ 2695   2696001   2.49503e-06     1.36317     -0.872871     -0.872871
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+ 2717   2718001    2.3359e-06     1.36291      -0.87287     -0.872871
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+ 2736   2737001   2.20667e-06     1.36323     -0.872871     -0.872871
+ 2737   2738001   2.20007e-06     1.36323     -0.872871     -0.872871
+ 2738   2739001   2.19349e-06     1.36323     -0.872871     -0.872871
+ 2739   2740001   2.18693e-06     1.36294      -0.87287     -0.872871
+ 2740   2741001   2.18039e-06     1.36294      -0.87287     -0.872871
+ 2741   2742001   2.17387e-06     1.36294      -0.87287     -0.872871
+ 2742   2743001   2.16736e-06     1.36294      -0.87287     -0.872871
+ 2743   2744001   2.16088e-06      1.3629      -0.87287     -0.872871
+ 2744   2745001   2.15442e-06     1.36279     -0.872868     -0.872871
+ 2745   2746001   2.14797e-06     1.36279     -0.872868     -0.872871
+ 2746   2747001   2.14155e-06     1.36281     -0.872868     -0.872871
+ 2747   2748001   2.13514e-06     1.36281     -0.872868     -0.872871
+ 2748   2749001   2.12876e-06     1.36281     -0.872868     -0.872871
+ 2749   2750001   2.12239e-06     1.36281     -0.872868     -0.872871
+ 2750   2751001   2.11604e-06     1.36281     -0.872868     -0.872871
+ 2751   2752001   2.10971e-06     1.36281     -0.872868     -0.872871
+ 2752   2753001    2.1034e-06     1.36286     -0.872869     -0.872871
+ 2753   2754001   2.09711e-06     1.36286     -0.872869     -0.872871
+ 2754   2755001   2.09084e-06     1.36286     -0.872869     -0.872871
+ 2755   2756001   2.08458e-06     1.36309     -0.872871     -0.872871
+ 2756   2757001   2.07835e-06     1.36309     -0.872871     -0.872871
+ 2757   2758001   2.07213e-06     1.36338     -0.872869     -0.872871
+ 2758   2759001   2.06594e-06     1.36344     -0.872868     -0.872871
+ 2759   2760001   2.05976e-06     1.36317     -0.872871     -0.872871
+ 2760   2761001    2.0536e-06     1.36317     -0.872871     -0.872871
+ 2761   2762001   2.04745e-06     1.36326     -0.872871     -0.872871
+ 2762   2763001   2.04133e-06     1.36326     -0.872871     -0.872871
+ 2763   2764001   2.03522e-06     1.36317     -0.872871     -0.872871
+ 2764   2765001   2.02914e-06     1.36317     -0.872871     -0.872871
+ 2765   2766001   2.02307e-06     1.36317     -0.872871     -0.872871
+ 2766   2767001   2.01702e-06     1.36328     -0.872871     -0.872871
+ 2767   2768001   2.01098e-06     1.36323     -0.872871     -0.872871
+ 2768   2769001   2.00497e-06     1.36323     -0.872871     -0.872871
diff -Nru gsl-doc-1.16/doc/examples/sortsmall.c gsl-doc-2.3/doc/examples/sortsmall.c
--- gsl-doc-1.16/doc/examples/sortsmall.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/sortsmall.c	2015-11-09 19:16:49.000000000 +0000
@@ -24,11 +24,11 @@
 
   gsl_sort_smallest (small, k, x, 1, N);
 
-  printf ("%d smallest values from %d\n", k, N);
+  printf ("%zu smallest values from %zu\n", k, N);
 
   for (i = 0; i < k; i++)
     {
-      printf ("%d: %.18f\n", i, small[i]);
+      printf ("%zu: %.18f\n", i, small[i]);
     }
 
   free (x);
diff -Nru gsl-doc-1.16/doc/examples/sortsmall.out gsl-doc-2.3/doc/examples/sortsmall.out
--- gsl-doc-1.16/doc/examples/sortsmall.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/sortsmall.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,6 +0,0 @@
-5 smallest values from 100000
-0: 0.000003489200025797
-1: 0.000008199829608202
-2: 0.000008953968062997
-3: 0.000010712770745158
-4: 0.000033531803637743
diff -Nru gsl-doc-1.16/doc/examples/sortsmall.txt gsl-doc-2.3/doc/examples/sortsmall.txt
--- gsl-doc-1.16/doc/examples/sortsmall.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/sortsmall.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,6 @@
+5 smallest values from 100000
+0: 0.000003489200025797
+1: 0.000008199829608202
+2: 0.000008953968062997
+3: 0.000010712770745158
+4: 0.000033531803637743
diff -Nru gsl-doc-1.16/doc/examples/specfun_e.out gsl-doc-2.3/doc/examples/specfun_e.out
--- gsl-doc-1.16/doc/examples/specfun_e.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/specfun_e.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,4 +0,0 @@
-status  = success
-J0(5.0) = -0.177596771314338292 
-      +/-  0.000000000000000193
-exact   = -0.177596771314338292
diff -Nru gsl-doc-1.16/doc/examples/specfun_e.txt gsl-doc-2.3/doc/examples/specfun_e.txt
--- gsl-doc-1.16/doc/examples/specfun_e.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/specfun_e.txt	2015-11-10 19:39:13.000000000 +0000
@@ -0,0 +1,4 @@
+status  = success
+J0(5.0) = -0.177596771314338264
+      +/-  0.000000000000000193
+exact   = -0.177596771314338292
diff -Nru gsl-doc-1.16/doc/examples/specfun.out gsl-doc-2.3/doc/examples/specfun.out
--- gsl-doc-1.16/doc/examples/specfun.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/specfun.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,2 +0,0 @@
-J0(5.0) = -0.177596771314338292
-exact   = -0.177596771314338292
diff -Nru gsl-doc-1.16/doc/examples/specfun.txt gsl-doc-2.3/doc/examples/specfun.txt
--- gsl-doc-1.16/doc/examples/specfun.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/specfun.txt	2015-11-10 19:38:39.000000000 +0000
@@ -0,0 +1,2 @@
+J0(5.0) = -0.177596771314338264
+exact   = -0.177596771314338292
diff -Nru gsl-doc-1.16/doc/examples/spmatrix.c gsl-doc-2.3/doc/examples/spmatrix.c
--- gsl-doc-1.16/doc/examples/spmatrix.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/spmatrix.c	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,76 @@
+#include <stdio.h>
+#include <stdlib.h>
+
+#include <gsl/gsl_spmatrix.h>
+
+int
+main()
+{
+  gsl_spmatrix *A = gsl_spmatrix_alloc(5, 4); /* triplet format */
+  gsl_spmatrix *B, *C;
+  size_t i, j;
+
+  /* build the sparse matrix */
+  gsl_spmatrix_set(A, 0, 2, 3.1);
+  gsl_spmatrix_set(A, 0, 3, 4.6);
+  gsl_spmatrix_set(A, 1, 0, 1.0);
+  gsl_spmatrix_set(A, 1, 2, 7.2);
+  gsl_spmatrix_set(A, 3, 0, 2.1);
+  gsl_spmatrix_set(A, 3, 1, 2.9);
+  gsl_spmatrix_set(A, 3, 3, 8.5);
+  gsl_spmatrix_set(A, 4, 0, 4.1);
+
+  printf("printing all matrix elements:\n");
+  for (i = 0; i < 5; ++i)
+    for (j = 0; j < 4; ++j)
+      printf("A(%zu,%zu) = %g\n", i, j,
+             gsl_spmatrix_get(A, i, j));
+
+  /* print out elements in triplet format */
+  printf("matrix in triplet format (i,j,Aij):\n");
+  gsl_spmatrix_fprintf(stdout, A, "%.1f");
+
+  /* convert to compressed column format */
+  B = gsl_spmatrix_ccs(A);
+
+  printf("matrix in compressed column format:\n");
+  printf("i = [ ");
+  for (i = 0; i < B->nz; ++i)
+    printf("%zu, ", B->i[i]);
+  printf("]\n");
+
+  printf("p = [ ");
+  for (i = 0; i < B->size2 + 1; ++i)
+    printf("%zu, ", B->p[i]);
+  printf("]\n");
+
+  printf("d = [ ");
+  for (i = 0; i < B->nz; ++i)
+    printf("%g, ", B->data[i]);
+  printf("]\n");
+
+  /* convert to compressed row format */
+  C = gsl_spmatrix_crs(A);
+
+  printf("matrix in compressed row format:\n");
+  printf("i = [ ");
+  for (i = 0; i < C->nz; ++i)
+    printf("%zu, ", C->i[i]);
+  printf("]\n");
+
+  printf("p = [ ");
+  for (i = 0; i < C->size1 + 1; ++i)
+    printf("%zu, ", C->p[i]);
+  printf("]\n");
+
+  printf("d = [ ");
+  for (i = 0; i < C->nz; ++i)
+    printf("%g, ", C->data[i]);
+  printf("]\n");
+
+  gsl_spmatrix_free(A);
+  gsl_spmatrix_free(B);
+  gsl_spmatrix_free(C);
+
+  return 0;
+}
diff -Nru gsl-doc-1.16/doc/examples/spmatrix.txt gsl-doc-2.3/doc/examples/spmatrix.txt
--- gsl-doc-1.16/doc/examples/spmatrix.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/spmatrix.txt	2016-07-07 20:36:10.000000000 +0000
@@ -0,0 +1,40 @@
+printing all matrix elements:
+A(0,0) = 0
+A(0,1) = 0
+A(0,2) = 3.1
+A(0,3) = 4.6
+A(1,0) = 1
+A(1,1) = 0
+A(1,2) = 7.2
+A(1,3) = 0
+A(2,0) = 0
+A(2,1) = 0
+A(2,2) = 0
+A(2,3) = 0
+A(3,0) = 2.1
+A(3,1) = 2.9
+A(3,2) = 0
+A(3,3) = 8.5
+A(4,0) = 4.1
+A(4,1) = 0
+A(4,2) = 0
+A(4,3) = 0
+matrix in triplet format (i,j,Aij):
+%%MatrixMarket matrix coordinate real general
+5	4	8
+1	3	3.1
+1	4	4.6
+2	1	1.0
+2	3	7.2
+4	1	2.1
+4	2	2.9
+4	4	8.5
+5	1	4.1
+matrix in compressed column format:
+i = [ 1, 3, 4, 3, 0, 1, 0, 3, ]
+p = [ 0, 3, 4, 6, 8, ]
+d = [ 1, 2.1, 4.1, 2.9, 3.1, 7.2, 4.6, 8.5, ]
+matrix in compressed row format:
+i = [ 2, 3, 0, 2, 0, 1, 3, 0, ]
+p = [ 0, 2, 4, 4, 7, 8, ]
+d = [ 3.1, 4.6, 1, 7.2, 2.1, 2.9, 8.5, 4.1, ]
diff -Nru gsl-doc-1.16/doc/examples/stat.out gsl-doc-2.3/doc/examples/stat.out
--- gsl-doc-1.16/doc/examples/stat.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/stat.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,5 +0,0 @@
-The dataset is 17.2, 18.1, 16.5, 18.3, 12.6
-The sample mean is 16.54
-The estimated variance is 5.373
-The largest value is 18.3
-The smallest value is 12.6
diff -Nru gsl-doc-1.16/doc/examples/statsort.out gsl-doc-2.3/doc/examples/statsort.out
--- gsl-doc-1.16/doc/examples/statsort.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/statsort.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,5 +0,0 @@
-Original dataset: 17.2, 18.1, 16.5, 18.3, 12.6
-Sorted dataset: 12.6, 16.5, 17.2, 18.1, 18.3
-The median is 17.2
-The upper quartile is 18.1
-The lower quartile is 16.5
diff -Nru gsl-doc-1.16/doc/examples/statsort.txt gsl-doc-2.3/doc/examples/statsort.txt
--- gsl-doc-1.16/doc/examples/statsort.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/statsort.txt	2015-11-10 19:41:17.000000000 +0000
@@ -0,0 +1,5 @@
+Original dataset:  17.2, 18.1, 16.5, 18.3, 12.6
+Sorted dataset: 12.6, 16.5, 17.2, 18.1, 18.3
+The median is 17.2
+The upper quartile is 18.1
+The lower quartile is 16.5
diff -Nru gsl-doc-1.16/doc/examples/stat.txt gsl-doc-2.3/doc/examples/stat.txt
--- gsl-doc-1.16/doc/examples/stat.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/stat.txt	2015-11-10 19:33:29.000000000 +0000
@@ -0,0 +1,5 @@
+The dataset is 17.2, 18.1, 16.5, 18.3, 12.6
+The sample mean is 16.54
+The estimated variance is 5.373
+The largest value is 18.3
+The smallest value is 12.6
diff -Nru gsl-doc-1.16/doc/examples/sum.c gsl-doc-2.3/doc/examples/sum.c
--- gsl-doc-1.16/doc/examples/sum.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/sum.c	2015-11-09 19:17:18.000000000 +0000
@@ -31,11 +31,11 @@
   printf ("term-by-term sum = % .16f using %d terms\n", 
           sum, N);
 
-  printf ("term-by-term sum = % .16f using %d terms\n", 
+  printf ("term-by-term sum = % .16f using %zu terms\n", 
           w->sum_plain, w->terms_used);
 
   printf ("exact value      = % .16f\n", zeta_2);
-  printf ("accelerated sum  = % .16f using %d terms\n", 
+  printf ("accelerated sum  = % .16f using %zu terms\n", 
           sum_accel, w->terms_used);
 
   printf ("estimated error  = % .16f\n", err);
diff -Nru gsl-doc-1.16/doc/examples/sum.out gsl-doc-2.3/doc/examples/sum.out
--- gsl-doc-1.16/doc/examples/sum.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/sum.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,6 +0,0 @@
-term-by-term sum =  1.5961632439130233 using 20 terms
-term-by-term sum =  1.5759958390005426 using 13 terms
-exact value      =  1.6449340668482264
-accelerated sum  =  1.6449340668166479 using 13 terms
-estimated error  =  0.0000000000508580
-actual error     = -0.0000000000315785
diff -Nru gsl-doc-1.16/doc/examples/sum.txt gsl-doc-2.3/doc/examples/sum.txt
--- gsl-doc-1.16/doc/examples/sum.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/sum.txt	2015-11-10 19:42:12.000000000 +0000
@@ -0,0 +1,6 @@
+term-by-term sum =  1.5961632439130233 using 20 terms
+term-by-term sum =  1.5759958390005426 using 13 terms
+exact value      =  1.6449340668482264
+accelerated sum  =  1.6449340669228176 using 13 terms
+estimated error  =  0.0000000000888360
+actual error     =  0.0000000000745912
diff -Nru gsl-doc-1.16/doc/examples/vectorr.txt gsl-doc-2.3/doc/examples/vectorr.txt
--- gsl-doc-1.16/doc/examples/vectorr.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/vectorr.txt	2015-11-10 19:44:10.000000000 +0000
@@ -0,0 +1,10 @@
+1.23
+2.23
+3.23
+4.23
+5.23
+6.23
+7.23
+8.23
+9.23
+10.23
diff -Nru gsl-doc-1.16/doc/examples/vectorview.c gsl-doc-2.3/doc/examples/vectorview.c
--- gsl-doc-1.16/doc/examples/vectorview.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/vectorview.c	2015-11-09 19:17:28.000000000 +0000
@@ -21,7 +21,7 @@
 
       d = gsl_blas_dnrm2 (&column.vector);
 
-      printf ("matrix column %d, norm = %g\n", j, d);
+      printf ("matrix column %zu, norm = %g\n", j, d);
     }
 
   gsl_matrix_free (m);
diff -Nru gsl-doc-1.16/doc/examples/vectorview.out gsl-doc-2.3/doc/examples/vectorview.out
--- gsl-doc-1.16/doc/examples/vectorview.out	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/examples/vectorview.out	1970-01-01 00:00:00.000000000 +0000
@@ -1,10 +0,0 @@
-matrix column 0, norm = 4.31461
-matrix column 1, norm = 3.1205
-matrix column 2, norm = 2.19316
-matrix column 3, norm = 3.26114
-matrix column 4, norm = 2.53416
-matrix column 5, norm = 2.57281
-matrix column 6, norm = 4.20469
-matrix column 7, norm = 3.65202
-matrix column 8, norm = 2.08524
-matrix column 9, norm = 3.07313
diff -Nru gsl-doc-1.16/doc/examples/vectorview.txt gsl-doc-2.3/doc/examples/vectorview.txt
--- gsl-doc-1.16/doc/examples/vectorview.txt	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/examples/vectorview.txt	2015-11-09 05:23:40.000000000 +0000
@@ -0,0 +1,10 @@
+matrix column 0, norm = 4.31461
+matrix column 1, norm = 3.1205
+matrix column 2, norm = 2.19316
+matrix column 3, norm = 3.26114
+matrix column 4, norm = 2.53416
+matrix column 5, norm = 2.57281
+matrix column 6, norm = 4.20469
+matrix column 7, norm = 3.65202
+matrix column 8, norm = 2.08524
+matrix column 9, norm = 3.07313
diff -Nru gsl-doc-1.16/doc/fft.texi gsl-doc-2.3/doc/fft.texi
--- gsl-doc-1.16/doc/fft.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/fft.texi	2015-11-03 16:21:55.000000000 +0000
@@ -436,7 +436,7 @@
 the intermediate steps of the transform.
 
 @deftypefun {gsl_fft_complex_workspace *} gsl_fft_complex_workspace_alloc (size_t @var{n})
-@tpindex gsl_fft_complex_workspace
+@tindex gsl_fft_complex_workspace
 This function allocates a workspace for a complex transform of length
 @var{n}.
 @end deftypefun
@@ -778,8 +778,8 @@
 
 @deftypefun {gsl_fft_real_wavetable *} gsl_fft_real_wavetable_alloc (size_t @var{n})
 @deftypefunx {gsl_fft_halfcomplex_wavetable *} gsl_fft_halfcomplex_wavetable_alloc (size_t @var{n})
-@tpindex gsl_fft_real_wavetable
-@tpindex gsl_fft_halfcomplex_wavetable
+@tindex gsl_fft_real_wavetable
+@tindex gsl_fft_halfcomplex_wavetable
 These functions prepare trigonometric lookup tables for an FFT of size
 @math{n} real elements.  The functions return a pointer to the newly
 allocated struct if no errors were detected, and a null pointer in the
@@ -810,7 +810,7 @@
 the intermediate steps of the transform,
 
 @deftypefun {gsl_fft_real_workspace *} gsl_fft_real_workspace_alloc (size_t @var{n})
-@tpindex gsl_fft_real_workspace
+@tindex gsl_fft_real_workspace
 This function allocates a workspace for a real transform of length
 @var{n}.  The same workspace can be used for both forward real and inverse
 halfcomplex transforms.
diff -Nru gsl-doc-1.16/doc/fit-exp.eps gsl-doc-2.3/doc/fit-exp.eps
--- gsl-doc-1.16/doc/fit-exp.eps	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/fit-exp.eps	2015-11-03 16:21:55.000000000 +0000
@@ -1,764 +1,1101 @@
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diff -Nru gsl-doc-1.16/doc/fitting.texi gsl-doc-2.3/doc/fitting.texi
--- gsl-doc-1.16/doc/fitting.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/fitting.texi	2016-11-18 19:29:40.000000000 +0000
@@ -12,17 +12,17 @@
 variance-covariance matrix.
 
 The functions are divided into separate versions for simple one- or
-two-parameter regression and multiple-parameter fits.  The functions
-are declared in the header file @file{gsl_fit.h}.
+two-parameter regression and multiple-parameter fits.
 
 @menu
 * Fitting Overview::            
 * Linear regression::           
-* Linear fitting without a constant term::
-* Multi-parameter fitting::
+* Multi-parameter regression::
+* Regularized regression::
 * Robust linear regression::
+* Large Dense Linear Systems::
 * Troubleshooting::
-* Fitting Examples::            
+* Fitting Examples::
 * Fitting References and Further Reading::  
 @end menu
 
@@ -139,6 +139,17 @@
 @section Linear regression
 @cindex linear regression
 
+The functions in this section are used to fit simple one or two
+parameter linear regression models. The functions are declared in
+the header file @file{gsl_fit.h}.
+
+@menu
+* Linear regression with a constant term::
+* Linear regression without a constant term::
+@end menu
+
+@node Linear regression with a constant term
+@subsection Linear regression with a constant term
 The functions described in this section can be used to perform
 least-squares fits to a straight line model, @math{Y(c,x) = c_0 + c_1 x}.
 
@@ -179,8 +190,8 @@
 c_0 + c_1 X} at the point @var{x}.
 @end deftypefun
 
-@node Linear fitting without a constant term
-@section Linear fitting without a constant term
+@node Linear regression without a constant term
+@subsection Linear regression without a constant term
 
 The functions described in this section can be used to perform
 least-squares fits to a straight line model without a constant term,
@@ -218,15 +229,30 @@
 c_1 X} at the point @var{x}.
 @end deftypefun
 
-@node Multi-parameter fitting
-@section Multi-parameter fitting
+@node Multi-parameter regression
+@section Multi-parameter regression
 @cindex multi-parameter regression
 @cindex fits, multi-parameter linear
-The functions described in this section perform least-squares fits to a
-general linear model, @math{y = X c} where @math{y} is a vector of
-@math{n} observations, @math{X} is an @math{n} by @math{p} matrix of
-predictor variables, and the elements of the vector @math{c} are the @math{p} unknown best-fit parameters which are to be estimated.  The chi-squared value is given by @c{$\chi^2 = \sum_i w_i (y_i - \sum_j X_{ij} c_j)^2$}
-@math{\chi^2 = \sum_i w_i (y_i - \sum_j X_@{ij@} c_j)^2}.
+This section describes routines which perform least squares fits
+to a linear model by minimizing the cost function
+@tex
+\beforedisplay
+$$
+\chi^2 = \sum_i w_i (y_i - \sum_j X_{ij} c_j)^2 = || y - Xc ||_W^2
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+\chi^2 = \sum_i w_i (y_i - \sum_j X_ij c_j)^2 = || y - Xc ||_W^2
+@end example
+@end ifinfo
+where @math{y} is a vector of @math{n} observations, @math{X} is an
+@math{n}-by-@math{p} matrix of predictor variables, @math{c}
+is a vector of the @math{p} unknown best-fit parameters to be estimated,
+and @math{||r||_W^2 = r^T W r}.
+The matrix @math{W = } diag@math{(w_1,w_2,...,w_n)}
+defines the weights or uncertainties of the observation vector.
 
 This formulation can be used for fits to any number of functions and/or
 variables by preparing the @math{n}-by-@math{p} matrix @math{X}
@@ -287,23 +313,36 @@
 where @math{x_j(i)} is the @math{i}-th value of the predictor variable
 @math{x_j}.
 
-The functions described in this section are declared in the header file
-@file{gsl_multifit.h}.
-
 The solution of the general linear least-squares system requires an
 additional working space for intermediate results, such as the singular
 value decomposition of the matrix @math{X}.
 
-@deftypefun {gsl_multifit_linear_workspace *} gsl_multifit_linear_alloc (size_t @var{n}, size_t @var{p})
-@tpindex gsl_multifit_linear_workspace
-This function allocates a workspace for fitting a model to @var{n}
-observations using @var{p} parameters.
+These functions are declared in the header file @file{gsl_multifit.h}.
+
+@deftypefun {gsl_multifit_linear_workspace *} gsl_multifit_linear_alloc (const size_t @var{n}, const size_t @var{p})
+@tindex gsl_multifit_linear_workspace
+This function allocates a workspace for fitting a model to a maximum of @var{n}
+observations using a maximum of @var{p} parameters. The user may later supply
+a smaller least squares system if desired. The size of the workspace is
+@math{O(np + p^2)}.
 @end deftypefun
 
 @deftypefun void gsl_multifit_linear_free (gsl_multifit_linear_workspace * @var{work})
 This function frees the memory associated with the workspace @var{w}.
 @end deftypefun
 
+@deftypefun int gsl_multifit_linear_svd (const gsl_matrix * @var{X}, gsl_multifit_linear_workspace * @var{work})
+This function performs a singular value decomposition of the
+matrix @var{X} and stores the SVD factors internally in @var{work}.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_bsvd (const gsl_matrix * @var{X}, gsl_multifit_linear_workspace * @var{work})
+This function performs a singular value decomposition of the
+matrix @var{X} and stores the SVD factors internally in @var{work}.
+The matrix @var{X} is first balanced by applying column scaling
+factors to improve the accuracy of the singular values.
+@end deftypefun
+
 @deftypefun int gsl_multifit_linear (const gsl_matrix * @var{X}, const gsl_vector * @var{y}, gsl_vector * @var{c}, gsl_matrix * @var{cov}, double * @var{chisq}, gsl_multifit_linear_workspace * @var{work})
 This function computes the best-fit parameters @var{c} of the model
 @math{y = X c} for the observations @var{y} and the matrix of
@@ -324,6 +363,24 @@
 from the fit.
 @end deftypefun
 
+@deftypefun int gsl_multifit_linear_tsvd (const gsl_matrix * @var{X}, const gsl_vector * @var{y}, const double @var{tol}, gsl_vector * @var{c}, gsl_matrix * @var{cov}, double * @var{chisq}, size_t * @var{rank}, gsl_multifit_linear_workspace * @var{work})
+This function computes the best-fit parameters @var{c} of the model
+@math{y = X c} for the observations @var{y} and the matrix of
+predictor variables @var{X}, using a truncated SVD expansion.
+Singular values which satisfy @math{s_i \le tol \times s_0}
+are discarded from the fit, where @math{s_0} is the largest singular value.
+The @math{p}-by-@math{p} variance-covariance matrix of the model parameters
+@var{cov} is set to @math{\sigma^2 (X^T X)^{-1}}, where @math{\sigma} is
+the standard deviation of the fit residuals.
+The sum of squares of the residuals from the best-fit,
+@math{\chi^2}, is returned in @var{chisq}. The effective rank
+(number of singular values used in solution) is returned in @var{rank}.
+If the coefficient of
+determination is desired, it can be computed from the expression
+@math{R^2 = 1 - \chi^2 / TSS}, where the total sum of squares (TSS) of
+the observations @var{y} may be computed from @code{gsl_stats_tss}.
+@end deftypefun
+
 @deftypefun int gsl_multifit_wlinear (const gsl_matrix * @var{X}, const gsl_vector * @var{w}, const gsl_vector * @var{y}, gsl_vector * @var{c}, gsl_matrix * @var{cov}, double * @var{chisq}, gsl_multifit_linear_workspace * @var{work})
 This function computes the best-fit parameters @var{c} of the weighted
 model @math{y = X c} for the observations @var{y} with weights @var{w}
@@ -337,16 +394,21 @@
 observations @var{y} may be computed from @code{gsl_stats_wtss}.
 @end deftypefun
 
-@deftypefun int gsl_multifit_linear_svd (const gsl_matrix * @var{X}, const gsl_vector * @var{y}, double @var{tol}, size_t * @var{rank}, gsl_vector * @var{c}, gsl_matrix * @var{cov}, double * @var{chisq}, gsl_multifit_linear_workspace * @var{work})
-@deftypefunx int gsl_multifit_wlinear_svd (const gsl_matrix * @var{X}, const gsl_vector * @var{w}, const gsl_vector * @var{y}, double @var{tol}, size_t * @var{rank}, gsl_vector * @var{c}, gsl_matrix * @var{cov}, double * @var{chisq}, gsl_multifit_linear_workspace * @var{work})
-In these functions components of the fit are discarded if the ratio of
-singular values @math{s_i/s_0} falls below the user-specified
-tolerance @var{tol}, and the effective rank is returned in @var{rank}.
-@end deftypefun
-
-@deftypefun int gsl_multifit_linear_usvd (const gsl_matrix * @var{X}, const gsl_vector * @var{y}, double @var{tol}, size_t * @var{rank}, gsl_vector * @var{c}, gsl_matrix * @var{cov}, double * @var{chisq}, gsl_multifit_linear_workspace * @var{work})
-@deftypefunx int gsl_multifit_wlinear_usvd (const gsl_matrix * @var{X}, const gsl_vector * @var{w}, const gsl_vector * @var{y}, double @var{tol}, size_t * @var{rank}, gsl_vector * @var{c}, gsl_matrix * @var{cov}, double * @var{chisq}, gsl_multifit_linear_workspace * @var{work})
-These functions compute the fit using an SVD without column scaling.
+@deftypefun int gsl_multifit_wlinear_tsvd (const gsl_matrix * @var{X}, const gsl_vector * @var{w}, const gsl_vector * @var{y}, const double @var{tol}, gsl_vector * @var{c}, gsl_matrix * @var{cov}, double * @var{chisq}, size_t * @var{rank}, gsl_multifit_linear_workspace * @var{work})
+This function computes the best-fit parameters @var{c} of the weighted
+model @math{y = X c} for the observations @var{y} with weights @var{w}
+and the matrix of predictor variables @var{X}, using a truncated SVD expansion.
+Singular values which satisfy @math{s_i \le tol \times s_0}
+are discarded from the fit, where @math{s_0} is the largest singular value.
+The @math{p}-by-@math{p} covariance matrix of the model
+parameters @var{cov} is computed as @math{(X^T W X)^{-1}}. The weighted
+sum of squares of the residuals from the best-fit, @math{\chi^2}, is
+returned in @var{chisq}. The effective rank of the system (number of
+singular values used in the solution) is returned in @var{rank}.
+If the coefficient of determination is
+desired, it can be computed from the expression @math{R^2 = 1 - \chi^2
+/ WTSS}, where the weighted total sum of squares (WTSS) of the
+observations @var{y} may be computed from @code{gsl_stats_wtss}.
 @end deftypefun
 
 @deftypefun int gsl_multifit_linear_est (const gsl_vector * @var{x}, const gsl_vector * @var{c}, const gsl_matrix * @var{cov}, double * @var{y}, double * @var{y_err})
@@ -363,9 +425,411 @@
 variables @var{X}.
 @end deftypefun
 
+@deftypefun size_t gsl_multifit_linear_rank (const double @var{tol}, const gsl_multifit_linear_workspace * @var{work})
+This function returns the rank of the matrix @math{X} which must first have its
+singular value decomposition computed. The rank is computed by counting the number
+of singular values @math{\sigma_j} which satisfy @math{\sigma_j > tol \times \sigma_0},
+where @math{\sigma_0} is the largest singular value.
+@end deftypefun
+
+@node Regularized regression
+@section Regularized regression
+@cindex ridge regression
+@cindex Tikhonov regression
+@cindex regression, ridge
+@cindex regression, Tikhonov
+@cindex least squares, regularized
+
+Ordinary weighted least squares models seek a solution vector @math{c}
+which minimizes the residual
+@tex
+\beforedisplay
+$$
+\chi^2 = || y - Xc ||_W^2
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+\chi^2 = || y - Xc ||_W^2
+@end example
+@end ifinfo
+where @math{y} is the @math{n}-by-@math{1} observation vector,
+@math{X} is the @math{n}-by-@math{p} design matrix, @math{c} is
+the @math{p}-by-@math{1} solution vector,
+@math{W =} diag@math{(w_1,...,w_n)} is the data weighting matrix,
+and @math{||r||_W^2 = r^T W r}.
+In cases where the least squares matrix @math{X} is ill-conditioned,
+small perturbations (ie: noise) in the observation vector could lead to
+widely different solution vectors @math{c}.
+One way of dealing with ill-conditioned matrices is to use a ``truncated SVD''
+in which small singular values, below some given tolerance, are discarded
+from the solution. The truncated SVD method is available using the functions
+@code{gsl_multifit_linear_tsvd} and @code{gsl_multifit_wlinear_tsvd}. Another way
+to help solve ill-posed problems is to include a regularization term in the least squares
+minimization
+@tex
+\beforedisplay
+$$
+\chi^2 = || y - Xc ||_W^2 + \lambda^2 || L c ||^2
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+\chi^2 = || y - Xc ||_W^2 + \lambda^2 || L c ||^2
+@end example
+@end ifinfo
+for a suitably chosen regularization parameter @math{\lambda} and
+matrix @math{L}. This type of regularization is known as Tikhonov, or ridge,
+regression. In some applications, @math{L} is chosen as the identity matrix, giving
+preference to solution vectors @math{c} with smaller norms.
+Including this regularization term leads to the explicit ``normal equations'' solution
+@tex
+\beforedisplay
+$$
+c = \left( X^T W X + \lambda^2 L^T L \right)^{-1} X^T W y
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+c = ( X^T W X + \lambda^2 L^T L )^-1 X^T W y
+@end example
+@end ifinfo
+which reduces to the ordinary least squares solution when @math{L = 0}.
+In practice, it is often advantageous to transform a regularized least
+squares system into the form
+@tex
+\beforedisplay
+$$
+\chi^2 = || \tilde{y} - \tilde{X} \tilde{c} ||^2 + \lambda^2 || \tilde{c} ||^2
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+\chi^2 = || y~ - X~ c~ ||^2 + \lambda^2 || c~ ||^2
+@end example
+@end ifinfo
+This is known as the Tikhonov ``standard form'' and has the normal equations solution
+@math{\tilde{c} = \left( \tilde{X}^T \tilde{X} + \lambda^2 I \right)^{-1} \tilde{X}^T \tilde{y}}.
+For an @math{m}-by-@math{p} matrix @math{L} which is full rank and has @math{m >= p} (ie: @math{L} is
+square or has more rows than columns), we can calculate the ``thin'' QR decomposition of @math{L}, and
+note that @math{||L c||} = @math{||R c||} since the @math{Q} factor will not change the norm. Since
+@math{R} is @math{p}-by-@math{p}, we can then use the transformation
+@tex
+\beforedisplay
+$$
+\eqalign{
+\tilde{X} &= W^{1 \over 2} X R^{-1} \cr
+\tilde{y} &= W^{1 \over 2} y \cr
+\tilde{c} &= R c
+}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+X~ = sqrt(W) X R^-1
+y~ = sqrt(W) y
+c~ = R c
+@end example
+@end ifinfo
+to achieve the standard form. For a rectangular matrix @math{L} with @math{m < p},
+a more sophisticated approach is needed (see Hansen 1998, chapter 2.3).
+In practice, the normal equations solution above is not desirable due to
+numerical instabilities, and so the system is solved using the
+singular value decomposition of the matrix @math{\tilde{X}}.
+The matrix @math{L} is often chosen as the identity matrix, or as a first
+or second finite difference operator, to ensure a smoothly varying
+coefficient vector @math{c}, or as a diagonal matrix to selectively damp
+each model parameter differently. If @math{L \ne I}, the user must first
+convert the least squares problem to standard form using
+@code{gsl_multifit_linear_stdform1} or @code{gsl_multifit_linear_stdform2},
+solve the system, and then backtransform the solution vector to recover
+the solution of the original problem (see
+@code{gsl_multifit_linear_genform1} and @code{gsl_multifit_linear_genform2}).
+
+In many regularization problems, care must be taken when choosing
+the regularization parameter @math{\lambda}. Since both the
+residual norm @math{||y - X c||} and solution norm @math{||L c||}
+are being minimized, the parameter @math{\lambda} represents
+a tradeoff between minimizing either the residuals or the
+solution vector. A common tool for visualizing the comprimise between
+the minimization of these two quantities is known as the L-curve.
+The L-curve is a log-log plot of the residual norm @math{||y - X c||}
+on the horizontal axis and the solution norm @math{||L c||} on the
+vertical axis. This curve nearly always as an @math{L} shaped
+appearance, with a distinct corner separating the horizontal
+and vertical sections of the curve. The regularization parameter
+corresponding to this corner is often chosen as the optimal
+value. GSL provides routines to calculate the L-curve for all
+relevant regularization parameters as well as locating the corner.
+
+Another method of choosing the regularization parameter is known
+as Generalized Cross Validation (GCV). This method is based on
+the idea that if an arbitrary element @math{y_i} is left out of the
+right hand side, the resulting regularized solution should predict this element
+accurately. This leads to choosing the parameter @math{\lambda}
+which minimizes the GCV function
+@tex
+\beforedisplay
+$$
+G(\lambda) = {||y - X c_{\lambda}||^2 \over \textrm{Tr}(I_n - X X_{\lambda}^I)^2}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+G(\lambda) = (||y - X c_@{\lambda@}||^2) / Tr(I_n - X X^I)^2
+@end example
+
+@end ifinfo
+where @math{X_{\lambda}^I} is the matrix which relates the solution @math{c_{\lambda}}
+to the right hand side @math{y}, ie: @math{c_{\lambda} = X_{\lambda}^I y}. GSL
+provides routines to compute the GCV curve and its minimum.
+
+@noindent
+For most applications, the steps required to solve a regularized least
+squares problem are as follows:
+
+@enumerate
+
+@item Construct the least squares system (@math{X}, @math{y}, @math{W}, @math{L})
+
+@item Transform the system to standard form (@math{\tilde{X}},@math{\tilde{y}}). This
+step can be skipped if @math{L = I_p} and @math{W = I_n}.
+
+@item Calculate the SVD of @math{\tilde{X}}.
+
+@item Determine an appropriate regularization parameter @math{\lambda} (using for example
+L-curve or GCV analysis).
+
+@item Solve the standard form system using the chosen @math{\lambda} and the SVD of @math{\tilde{X}}.
+
+@item Backtransform the standard form solution @math{\tilde{c}} to recover the
+original solution vector @math{c}.
+
+@end enumerate
+
+@deftypefun int gsl_multifit_linear_stdform1 (const gsl_vector * @var{L}, const gsl_matrix * @var{X}, const gsl_vector * @var{y}, gsl_matrix * @var{Xs}, gsl_vector * @var{ys}, gsl_multifit_linear_workspace * @var{work})
+@deftypefunx int gsl_multifit_linear_wstdform1 (const gsl_vector * @var{L}, const gsl_matrix * @var{X}, const gsl_vector * @var{w}, const gsl_vector * @var{y}, gsl_matrix * @var{Xs}, gsl_vector * @var{ys}, gsl_multifit_linear_workspace * @var{work})
+These functions define a regularization matrix
+@math{L =} diag@math{(l_0,l_1,...,l_{p-1})}.
+The diagonal matrix element @math{l_i} is provided by the
+@math{i}th element of the input vector @var{L}.
+The @math{n}-by-@math{p} least squares matrix @var{X} and
+vector @var{y} of length @math{n} are then
+converted to standard form as described above and the parameters
+(@math{\tilde{X}},@math{\tilde{y}}) are stored in @var{Xs} and @var{ys}
+on output.  @var{Xs} and @var{ys} have the same dimensions as
+@var{X} and @var{y}. Optional data weights may be supplied in the
+vector @var{w} of length @math{n}. In order to apply this transformation,
+@math{L^{-1}} must exist and so none of the @math{l_i}
+may be zero. After the standard form system has been solved,
+use @code{gsl_multifit_linear_genform1} to recover the original solution vector.
+It is allowed to have @var{X} = @var{Xs} and @var{y} = @var{ys} for an in-place transform.
+In order to perform a weighted regularized fit with @math{L = I}, the user may
+call @code{gsl_multifit_linear_applyW} to convert to standard form.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_L_decomp (gsl_matrix * @var{L}, gsl_vector * @var{tau})
+This function factors the @math{m}-by-@math{p} regularization matrix
+@var{L} into a form needed for the later transformation to standard form. @var{L}
+may have any number of rows @math{m}. If @math{m \ge p} the QR decomposition of
+@var{L} is computed and stored in @var{L} on output. If @math{m < p}, the QR decomposition
+of @math{L^T} is computed and stored in @var{L} on output. On output,
+the Householder scalars are stored in the vector @var{tau} of size @math{MIN(m,p)}.
+These outputs will be used by @code{gsl_multifit_linear_wstdform2} to complete the
+transformation to standard form.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_stdform2 (const gsl_matrix * @var{LQR}, const gsl_vector * @var{Ltau}, const gsl_matrix * @var{X}, const gsl_vector * @var{y}, gsl_matrix * @var{Xs}, gsl_vector * @var{ys}, gsl_matrix * @var{M}, gsl_multifit_linear_workspace * @var{work})
+@deftypefunx int gsl_multifit_linear_wstdform2 (const gsl_matrix * @var{LQR}, const gsl_vector * @var{Ltau}, const gsl_matrix * @var{X}, const gsl_vector * @var{w}, const gsl_vector * @var{y}, gsl_matrix * @var{Xs}, gsl_vector * @var{ys}, gsl_matrix * @var{M}, gsl_multifit_linear_workspace * @var{work})
+These functions convert the least squares system (@var{X},@var{y},@var{W},@math{L}) to standard
+form (@math{\tilde{X}},@math{\tilde{y}}) which are stored in @var{Xs} and @var{ys}
+respectively. The @math{m}-by-@math{p} regularization matrix @var{L} is specified by the inputs
+@var{LQR} and @var{Ltau}, which are outputs from @code{gsl_multifit_linear_L_decomp}.
+The dimensions of the standard form parameters (@math{\tilde{X}},@math{\tilde{y}})
+depend on whether @math{m} is larger or less than @math{p}. For @math{m \ge p},
+@var{Xs} is @math{n}-by-@math{p}, @var{ys} is @math{n}-by-1, and @var{M} is
+not used. For @math{m < p}, @var{Xs} is @math{(n - p + m)}-by-@math{m},
+@var{ys} is @math{(n - p + m)}-by-1, and @var{M} is additional @math{n}-by-@math{p} workspace,
+which is required to recover the original solution vector after the system has been
+solved (see @code{gsl_multifit_linear_genform2}). Optional data weights may be supplied in the
+vector @var{w} of length @math{n}, where @math{W =} diag(w).
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_solve (const double @var{lambda}, const gsl_matrix * @var{Xs}, const gsl_vector * @var{ys}, gsl_vector * @var{cs}, double * @var{rnorm}, double * @var{snorm}, gsl_multifit_linear_workspace * @var{work})
+This function computes the regularized best-fit parameters @math{\tilde{c}}
+which minimize the cost function
+@math{\chi^2 = || \tilde{y} - \tilde{X} \tilde{c} ||^2 + \lambda^2 || \tilde{c} ||^2} which is
+in standard form. The least squares system must therefore be converted
+to standard form prior to calling this function.
+The observation vector @math{\tilde{y}} is provided in @var{ys} and the matrix of
+predictor variables @math{\tilde{X}} in @var{Xs}. The solution vector @math{\tilde{c}} is
+returned in @var{cs}, which has length min(@math{m,p}). The SVD of @var{Xs} must be computed prior
+to calling this function, using @code{gsl_multifit_linear_svd}.
+The regularization parameter @math{\lambda} is provided in @var{lambda}.
+The residual norm @math{|| \tilde{y} - \tilde{X} \tilde{c} || = ||y - X c||_W} is returned in @var{rnorm}.
+The solution norm @math{|| \tilde{c} || = ||L c||} is returned in
+@var{snorm}.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_genform1 (const gsl_vector * @var{L}, const gsl_vector * @var{cs}, gsl_vector * @var{c}, gsl_multifit_linear_workspace * @var{work})
+After a regularized system has been solved with
+@math{L =} diag@math{(\l_0,\l_1,...,\l_{p-1})},
+this function backtransforms the standard form solution vector @var{cs}
+to recover the solution vector of the original problem @var{c}. The
+diagonal matrix elements @math{l_i} are provided in
+the vector @var{L}. It is allowed to have @var{c} = @var{cs} for an
+in-place transform.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_genform2 (const gsl_matrix * @var{LQR}, const gsl_vector * @var{Ltau}, const gsl_matrix * @var{X}, const gsl_vector * @var{y}, const gsl_vector * @var{cs}, const gsl_matrix * @var{M}, gsl_vector * @var{c}, gsl_multifit_linear_workspace * @var{work})
+@deftypefunx int gsl_multifit_linear_wgenform2 (const gsl_matrix * @var{LQR}, const gsl_vector * @var{Ltau}, const gsl_matrix * @var{X}, const gsl_vector * @var{w}, const gsl_vector * @var{y}, const gsl_vector * @var{cs}, const gsl_matrix * @var{M}, gsl_vector * @var{c}, gsl_multifit_linear_workspace * @var{work})
+After a regularized system has been solved with a general rectangular matrix @math{L},
+specified by (@var{LQR},@var{Ltau}), this function backtransforms the standard form solution @var{cs}
+to recover the solution vector of the original problem, which is stored in @var{c},
+of length @math{p}. The original least squares matrix and observation vector are provided in
+@var{X} and @var{y} respectively. @var{M} is the matrix computed by
+@code{gsl_multifit_linear_stdform2}. For weighted fits, the weight vector
+@var{w} must also be supplied.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_applyW (const gsl_matrix * @var{X}, const gsl_vector * @var{w}, const gsl_vector * @var{y}, gsl_matrix * @var{WX}, gsl_vector * @var{Wy})
+For weighted least squares systems with @math{L = I}, this function may be used to
+convert the system to standard form by applying the weight matrix @math{W =} diag(@var{w})
+to the least squares matrix @var{X} and observation vector @var{y}. On output, @var{WX}
+is equal to @math{W^{1/2} X} and @var{Wy} is equal to @math{W^{1/2} y}. It is allowed
+for @var{WX} = @var{X} and @var{Wy} = @var{y} for an in-place transform.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_lcurve (const gsl_vector * @var{y}, gsl_vector * @var{reg_param}, gsl_vector * @var{rho}, gsl_vector * @var{eta}, gsl_multifit_linear_workspace * @var{work})
+This function computes the L-curve for a least squares system
+using the right hand side vector @var{y} and the SVD decomposition
+of the least squares matrix @var{X}, which must be provided
+to @code{gsl_multifit_linear_svd} prior to
+calling this function. The output vectors @var{reg_param},
+@var{rho}, and @var{eta} must all be the same size, and will
+contain the regularization parameters @math{\lambda_i}, residual norms
+@math{||y - X c_i||}, and solution norms @math{|| L c_i ||}
+which compose the L-curve, where @math{c_i} is the regularized
+solution vector corresponding to @math{\lambda_i}.
+The user may determine the number of points on the L-curve by
+adjusting the size of these input arrays. The regularization
+parameters @math{\lambda_i} are estimated from the singular values
+of @var{X}, and chosen to represent the most relevant portion of
+the L-curve.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_lcorner (const gsl_vector * @var{rho}, const gsl_vector * @var{eta}, size_t * @var{idx})
+This function attempts to locate the corner of the L-curve
+@math{(||y - X c||, ||L c||)} defined by the @var{rho} and @var{eta}
+input arrays respectively. The corner is defined as the point of maximum
+curvature of the L-curve in log-log scale. The @var{rho} and @var{eta}
+arrays can be outputs of @code{gsl_multifit_linear_lcurve}. The
+algorithm used simply fits a circle to 3 consecutive points on the L-curve
+and uses the circle's radius to determine the curvature at
+the middle point. Therefore, the input array sizes must be
+@math{\ge 3}. With more points provided for the L-curve, a better
+estimate of the curvature can be obtained. The array index
+corresponding to maximum curvature (ie: the corner) is returned
+in @var{idx}. If the input arrays contain colinear points,
+this function could fail and return @code{GSL_EINVAL}.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_lcorner2 (const gsl_vector * @var{reg_param}, const gsl_vector * @var{eta}, size_t * @var{idx})
+This function attempts to locate the corner of an alternate L-curve
+@math{(\lambda^2, ||L c||^2)} studied by Rezghi and Hosseini, 2009.
+This alternate L-curve can provide better estimates of the
+regularization parameter for smooth solution vectors. The regularization
+parameters @math{\lambda} and solution norms @math{||L c||} are provided
+in the @var{reg_param} and @var{eta} input arrays respectively. The
+corner is defined as the point of maximum curvature of this
+alternate L-curve in linear scale. The @var{reg_param} and @var{eta}
+arrays can be outputs of @code{gsl_multifit_linear_lcurve}. The
+algorithm used simply fits a circle to 3 consecutive points on the L-curve
+and uses the circle's radius to determine the curvature at
+the middle point. Therefore, the input array sizes must be
+@math{\ge 3}. With more points provided for the L-curve, a better
+estimate of the curvature can be obtained. The array index
+corresponding to maximum curvature (ie: the corner) is returned
+in @var{idx}. If the input arrays contain colinear points,
+this function could fail and return @code{GSL_EINVAL}.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_gcv_init(const gsl_vector * @var{y}, gsl_vector * @var{reg_param}, gsl_vector * @var{UTy}, double * @var{delta0}, gsl_multifit_linear_workspace * @var{work})
+This function performs some initialization in preparation for computing
+the GCV curve and its minimum. The right hand side vector is provided
+in @var{y}. On output, @var{reg_param} is set to a vector of regularization
+parameters in decreasing order and may be of any size. The vector
+@var{UTy} of size @math{p} is set to @math{U^T y}. The parameter
+@var{delta0} is needed for subsequent steps of the GCV calculation.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_gcv_curve(const gsl_vector * @var{reg_param}, const gsl_vector * @var{UTy}, const double @var{delta0}, gsl_vector * @var{G}, gsl_multifit_linear_workspace * @var{work})
+This funtion calculates the GCV curve @math{G(\lambda)} and stores it in
+@var{G} on output, which must be the same size as @var{reg_param}. The
+inputs @var{reg_param}, @var{UTy} and @var{delta0} are computed in
+@code{gsl_multifit_linear_gcv_init}.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_gcv_min(const gsl_vector * @var{reg_param}, const gsl_vector * @var{UTy}, const gsl_vector * @var{G}, const double @var{delta0}, double * @var{lambda}, gsl_multifit_linear_workspace * @var{work})
+This function computes the value of the regularization parameter
+which minimizes the GCV curve @math{G(\lambda)} and stores it in
+@var{lambda}. The input @var{G} is calculated by
+@code{gsl_multifit_linear_gcv_curve} and the inputs
+@var{reg_param}, @var{UTy} and @var{delta0} are computed by
+@code{gsl_multifit_linear_gcv_init}.
+@end deftypefun
+
+@deftypefun double gsl_multifit_linear_gcv_calc(const double @var{lambda}, const gsl_vector * @var{UTy}, const double @var{delta0}, gsl_multifit_linear_workspace * @var{work})
+This function returns the value of the GCV curve @math{G(\lambda)} corresponding
+to the input @var{lambda}.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_gcv(const gsl_vector * @var{y}, gsl_vector * @var{reg_param}, gsl_vector * @var{G}, double * @var{lambda}, double * @var{G_lambda}, gsl_multifit_linear_workspace * @var{work})
+This function combines the steps @code{gcv_init}, @code{gcv_curve},
+and @code{gcv_min} defined above into a single function. The input
+@var{y} is the right hand side vector. On output, @var{reg_param} and
+@var{G}, which must be the same size, are set to vectors of
+@math{\lambda} and @math{G(\lambda)} values respectively. The
+output @var{lambda} is set to the optimal value of @math{\lambda}
+which minimizes the GCV curve. The minimum value of the GCV curve is
+returned in @var{G_lambda}.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_Lk (const size_t @var{p}, const size_t @var{k}, gsl_matrix * @var{L})
+This function computes the discrete approximation to the derivative operator @math{L_k} of
+order @var{k} on a regular grid of @var{p} points and stores it in @var{L}. The dimensions of @var{L} are
+@math{(p-k)}-by-@math{p}.
+@end deftypefun
+
+@deftypefun int gsl_multifit_linear_Lsobolev (const size_t @var{p}, const size_t @var{kmax}, const gsl_vector * @var{alpha}, gsl_matrix * @var{L}, gsl_multifit_linear_workspace * @var{work})
+This function computes the regularization matrix @var{L} corresponding to the weighted Sobolov norm
+@math{||L c||^2 = \sum_k \alpha_k^2 ||L_k c||^2} where @math{L_k} approximates the derivative
+operator of order @math{k}. This regularization norm can be useful in applications where
+it is necessary to smooth several derivatives of the solution. @var{p} is the number of
+model parameters, @var{kmax} is the highest derivative to include in the summation above, and
+@var{alpha} is the vector of weights of size @var{kmax} + 1, where @var{alpha}[k] = @math{\alpha_k}
+is the weight assigned to the derivative of order @math{k}.  The output matrix @var{L} is size
+@var{p}-by-@var{p} and upper triangular.
+@end deftypefun
+
+@deftypefun double gsl_multifit_linear_rcond (const gsl_multifit_linear_workspace * @var{work})
+This function returns the reciprocal condition number of the least squares matrix @math{X},
+defined as the ratio of the smallest and largest singular values, rcond = @math{\sigma_{min}/\sigma_{max}}.
+The routine @code{gsl_multifit_linear_svd} must first be called to compute the SVD of @math{X}.
+@end deftypefun
+
 @node Robust linear regression
 @section Robust linear regression
 @cindex robust regression
+@cindex regression, robust
+@cindex least squares, robust
 
 Ordinary least squares (OLS) models are often heavily influenced by the presence of outliers.
 Outliers are data points which do not follow the general trend of the other observations,
@@ -475,9 +939,10 @@
 having very little or no effect on the fitted model.
 
 @deftypefun {gsl_multifit_robust_workspace *} gsl_multifit_robust_alloc (const gsl_multifit_robust_type * @var{T}, const size_t @var{n}, const size_t @var{p})
-@tpindex gsl_multifit_robust_workspace
+@tindex gsl_multifit_robust_workspace
 This function allocates a workspace for fitting a model to @var{n}
-observations using @var{p} parameters. The type @var{T} specifies the
+observations using @var{p} parameters. The size of the workspace
+is @math{O(np + p^2)}. The type @var{T} specifies the
 function @math{\psi} and can be selected from the following choices.
 @deffn {Robust type} gsl_multifit_robust_default
 This specifies the @code{gsl_multifit_robust_bisquare} type (see below) and is a good
@@ -627,6 +1092,22 @@
 the tuning constant decreases the downweight assigned to large residuals.
 @end deftypefun
 
+@deftypefun int gsl_multifit_robust_maxiter (const size_t @var{maxiter}, gsl_multifit_robust_workspace * @var{w})
+This function sets the maximum number of iterations in the iteratively
+reweighted least squares algorithm to @var{maxiter}. By default,
+this value is set to 100 by @code{gsl_multifit_robust_alloc}.
+@end deftypefun
+
+@deftypefun int gsl_multifit_robust_weights (const gsl_vector * @var{r}, gsl_vector * @var{wts}, gsl_multifit_robust_workspace * @var{w})
+This function assigns weights to the vector @var{wts} using the residual vector @var{r} and
+previously specified weighting function. The output weights are given by @math{wts_i = w(r_i / (t \sigma))},
+where the weighting functions @math{w} are detailed in @code{gsl_multifit_robust_alloc}. @math{\sigma}
+is an estimate of the residual standard deviation based on the Median-Absolute-Deviation and @math{t}
+is the tuning constant. This
+function is useful if the user wishes to implement their own robust regression rather than using
+the supplied @code{gsl_multifit_robust} routine below.
+@end deftypefun
+
 @deftypefun int gsl_multifit_robust (const gsl_matrix * @var{X}, const gsl_vector * @var{y}, gsl_vector * @var{c}, gsl_matrix * @var{cov}, gsl_multifit_robust_workspace * @var{w})
 This function computes the best-fit parameters @var{c} of the model
 @math{y = X c} for the observations @var{y} and the matrix of
@@ -639,6 +1120,12 @@
 other statistics such as @math{R^2}, and so these
 are computed internally and are available by calling the function
 @code{gsl_multifit_robust_statistics}.
+
+If the coefficients do not converge within the maximum iteration
+limit, the function returns @code{GSL_EMAXITER}. In this case,
+the current estimates of the coefficients and covariance matrix
+are returned in @var{c} and @var{cov} and the internal fit statistics
+are computed with these estimates.
 @end deftypefun
 
 @deftypefun int gsl_multifit_robust_est (const gsl_vector * @var{x}, const gsl_vector * @var{c}, const gsl_matrix * @var{cov}, double * @var{y}, double * @var{y_err})
@@ -649,6 +1136,15 @@
 at the point @var{x}.
 @end deftypefun
 
+@deftypefun int gsl_multifit_robust_residuals (const gsl_matrix * @var{X}, const gsl_vector * @var{y}, const gsl_vector * @var{c}, gsl_vector * @var{r}, gsl_multifit_robust_workspace * @var{w})
+This function computes the vector of studentized residuals
+@math{r_i = {y_i - (X c)_i \over \sigma \sqrt{1 - h_i}}} for
+the observations @var{y}, coefficients @var{c} and matrix of predictor
+variables @var{X}. The routine @code{gsl_multifit_robust} must
+first be called to compute the statisical leverages @math{h_i} of
+the matrix @var{X} and residual standard deviation estimate @math{\sigma}.
+@end deftypefun
+
 @deftypefun gsl_multifit_robust_stats gsl_multifit_robust_statistics (const gsl_multifit_robust_workspace * @var{w})
 This function returns a structure containing relevant statistics from a robust regression. The function
 @code{gsl_multifit_robust} must be called first to perform the regression and calculate these statistics.
@@ -681,6 +1177,437 @@
 @end itemize
 @end deftypefun
 
+@node Large Dense Linear Systems
+@section Large dense linear systems
+@cindex large dense linear least squares
+@cindex linear least squares, large
+
+This module is concerned with solving large dense least squares systems
+@math{X c = y} where the @math{n}-by-@math{p} matrix
+@math{X} has @math{n >> p} (ie: many more rows than columns).
+This type of matrix is called a ``tall skinny'' matrix, and for
+some applications, it may not be possible to fit the
+entire matrix in memory at once to use the standard SVD approach.
+Therefore, the algorithms in this module are designed to allow
+the user to construct smaller blocks of the matrix @math{X} and
+accumulate those blocks into the larger system one at a time. The
+algorithms in this module never need to store the entire matrix
+@math{X} in memory. The large linear least squares routines
+support data weights and Tikhonov regularization, and are
+designed to minimize the residual
+@tex
+\beforedisplay
+$$
+\chi^2 = || y - Xc ||_W^2 + \lambda^2 || L c ||^2
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+\chi^2 = || y - Xc ||_W^2 + \lambda^2 || L c ||^2
+@end example
+@end ifinfo
+where @math{y} is the @math{n}-by-@math{1} observation vector,
+@math{X} is the @math{n}-by-@math{p} design matrix, @math{c} is
+the @math{p}-by-@math{1} solution vector,
+@math{W =} diag@math{(w_1,...,w_n)} is the data weighting matrix,
+@math{L} is an @math{m}-by-@math{p} regularization matrix,
+@math{\lambda} is a regularization parameter,
+and @math{||r||_W^2 = r^T W r}. In the discussion which follows,
+we will assume that the system has been converted into Tikhonov
+standard form,
+@tex
+\beforedisplay
+$$
+\chi^2 = || \tilde{y} - \tilde{X} \tilde{c} ||^2 + \lambda^2 || \tilde{c} ||^2
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+\chi^2 = || y~ - X~ c~ ||^2 + \lambda^2 || c~ ||^2
+@end example
+@end ifinfo
+and we will drop the tilde characters from the various parameters.
+For a discussion of the transformation to standard form
+@pxref{Regularized regression}.
+
+The basic idea is to partition the matrix @math{X} and observation
+vector @math{y} as
+@tex
+\beforedisplay
+$$
+\left(
+\matrix{
+X_1 \cr
+X_2 \cr
+X_3 \cr
+\vdots \cr
+X_k \cr
+}
+\right)
+c =
+\left(
+\matrix{
+y_1 \cr
+y_2 \cr
+y_3 \cr
+\vdots \cr
+y_k \cr
+}
+\right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+[ X_1 ] c = [ y_1 ]
+[ X_2 ]     [ y_2 ]
+[ X_3 ]     [ y_3 ]
+[ ... ]     [ ... ]
+[ X_k ]     [ y_k ]
+@end example
+@end ifinfo
+into @math{k} blocks, where each block (@math{X_i,y_i}) may have
+any number of rows, but each @math{X_i} has @math{p} columns.
+The sections below describe the methods available for solving
+this partitioned system. The functions are declared in
+the header file @file{gsl_multilarge.h}.
+
+@menu
+* Large Dense Linear Systems Normal Equations::
+* Large Dense Linear Systems TSQR::
+* Large Dense Linear Systems Solution Steps::
+* Large Dense Linear Systems Routines::
+@end menu
+
+@node Large Dense Linear Systems Normal Equations
+@subsection Normal Equations Approach
+@cindex large linear least squares, normal equations
+
+The normal equations approach to the large linear least squares
+problem described above is popular due to its speed and simplicity.
+Since the normal equations solution to the problem is given by
+@tex
+\beforedisplay
+$$
+c = \left( X^T X + \lambda^2 I \right)^{-1} X^T y
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+c = ( X^T X + \lambda^2 I )^-1 X^T y
+@end example
+@end ifinfo
+only the @math{p}-by-@math{p} matrix @math{X^T X} and
+@math{p}-by-1 vector @math{X^T y} need to be stored. Using
+the partition scheme described above, these are given by
+@tex
+\beforedisplay
+$$
+\eqalign{
+X^T X &= \sum_i X_i^T X_i \cr
+X^T y &= \sum_i X_i^T y_i
+}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+X^T X = \sum_i X_i^T X_i
+X^T y = \sum_i X_i^T y_i
+@end example
+@end ifinfo
+Since the matrix @math{X^T X} is symmetric, only half of it
+needs to be calculated. Once all of the blocks (@math{X_i,y_i})
+have been accumulated into the final @math{X^T X} and @math{X^T y},
+the system can be solved with a Cholesky factorization of the
+@math{X^T X} matrix. If the Cholesky factorization fails (occasionally
+due to numerical rounding errors), a QR decomposition is then used.
+In both cases, the @math{X^T X} matrix is first transformed via
+a diagonal scaling transformation to attempt to reduce its condition
+number as much as possible to recover a more accurate solution vector.
+The normal equations approach is the fastest method for solving the
+large least squares problem, and is accurate for well-conditioned
+matrices @math{X}. However, for ill-conditioned matrices, as is often
+the case for large systems, this method can suffer from numerical
+instabilities (see Trefethen and Bau, 1997).  The number of operations
+for this method is @math{O(np^2 + {1 \over 3}p^3)}.
+
+@node Large Dense Linear Systems TSQR
+@subsection Tall Skinny QR (TSQR) Approach
+@cindex large linear least squares, TSQR
+
+An algorithm which has better numerical stability for ill-conditioned
+problems is known as the Tall Skinny QR (TSQR) method. This method
+is based on computing the thin QR decomposition of the least squares
+matrix @math{X = Q R}, where @math{Q} is an @math{n}-by-@math{p} matrix
+with orthogonal columns, and @math{R} is a @math{p}-by-@math{p}
+upper triangular matrix. Once these factors are calculated, the
+residual becomes
+@tex
+\beforedisplay
+$$
+\chi^2 = || Q^T y - R c ||^2 + \lambda^2 || c ||^2
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+\chi^2 = || Q^T y - R c ||^2 + \lambda^2 || c ||^2
+@end example
+@end ifinfo
+which can be written as the matrix equation
+@tex
+\beforedisplay
+$$
+\left(
+\matrix{
+R \cr
+\lambda I
+} \right) c =
+\left(
+\matrix{
+Q^T y \cr
+0
+} \right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+[ R ; \lambda I ] c = [ Q^T b ; 0 ]
+@end example
+@end ifinfo
+The matrix on the left hand side is now a much
+smaller @math{2p}-by-@math{p} matrix which can
+be solved with a standard SVD approach. The
+@math{Q} matrix is just as large as the original
+matrix @math{X}, however it does not need to be
+explicitly constructed. The TSQR algorithm
+computes only the @math{p}-by-@math{p} matrix
+@math{R} and the @math{p}-by-1 vector @math{Q^T y},
+and updates these quantities as new blocks
+are added to the system. Each time a new block of rows
+(@math{X_i,y_i}) is added, the algorithm performs a QR decomposition
+of the matrix
+@tex
+\beforedisplay
+$$
+\left(
+\matrix{
+R_{i-1} \cr
+X_i
+} \right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+[ R_(i-1) ; X_i ]
+@end example
+@end ifinfo
+where @math{R_{i-1}} is the upper triangular
+@math{R} factor for the matrix
+@tex
+\beforedisplay
+$$
+\left(
+\matrix{
+X_1 \cr
+\vdots \cr
+X_{i-1}
+} \right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+[ X_1 ; ... ; X_(i-1) ]
+@end example
+@end ifinfo
+This QR decomposition is done efficiently taking into account
+the sparse structure of @math{R_{i-1}}. See Demmel et al, 2008 for
+more details on how this is accomplished. The number
+of operations for this method is @math{O(2np^2 - {2 \over 3}p^3)}.
+
+@node Large Dense Linear Systems Solution Steps
+@subsection Large Dense Linear Systems Solution Steps
+@cindex large linear least squares, steps
+The typical steps required to solve large regularized linear least
+squares problems are as follows:
+
+@enumerate
+
+@item Choose the regularization matrix @math{L}.
+
+@item Construct a block of rows of the least squares matrix, right
+hand side vector, and weight vector (@math{X_i}, @math{y_i}, @math{w_i}).
+
+@item Transform the block to standard form (@math{\tilde{X_i}},@math{\tilde{y_i}}). This
+step can be skipped if @math{L = I} and @math{W = I}.
+
+@item Accumulate the standard form block (@math{\tilde{X_i}},@math{\tilde{y_i}}) into
+the system.
+
+@item Repeat steps 2-4 until the entire matrix and right hand side vector have
+been accumulated.
+
+@item Determine an appropriate regularization parameter @math{\lambda} (using for example
+L-curve analysis).
+
+@item Solve the standard form system using the chosen @math{\lambda}.
+
+@item Backtransform the standard form solution @math{\tilde{c}} to recover the
+original solution vector @math{c}.
+
+@end enumerate
+
+@node Large Dense Linear Systems Routines
+@subsection Large Dense Linear Least Squares Routines
+@cindex large linear least squares, routines
+
+@deftypefun {gsl_multilarge_linear_workspace *} gsl_multilarge_linear_alloc (const gsl_multilarge_linear_type * @var{T}, const size_t @var{p})
+This function allocates a workspace for solving large linear least squares
+systems. The least squares matrix @math{X} has @var{p} columns,
+but may have any number of rows. The parameter @var{T} specifies
+the method to be used for solving the large least squares system
+and may be selected from the following choices
+
+@deffn {Multilarge type} gsl_multilarge_linear_normal
+This specifies the normal equations approach for
+solving the least squares system. This method is suitable
+in cases where performance is critical and it is known that the
+least squares matrix @math{X} is well conditioned. The size
+of this workspace is @math{O(p^2)}.
+@end deffn
+
+@deffn {Multilarge type} gsl_multilarge_linear_tsqr
+This specifies the sequential Tall Skinny QR (TSQR) approach for
+solving the least squares system. This method is a good
+general purpose choice for large systems, but requires about
+twice as many operations as the normal equations method for
+@math{n >> p}. The size of this workspace is @math{O(p^2)}.
+@end deffn
+@end deftypefun
+
+@deftypefun void gsl_multilarge_linear_free (gsl_multilarge_linear_workspace * @var{w})
+This function frees the memory associated with the
+workspace @var{w}.
+@end deftypefun
+
+@deftypefun {const char *} gsl_multilarge_linear_name (gsl_multilarge_linear_workspace * @var{w})
+This function returns a string pointer to the name
+of the multilarge solver.
+@end deftypefun
+
+@deftypefun int gsl_multilarge_linear_reset (gsl_multilarge_linear_workspace * @var{w})
+This function resets the workspace @var{w} so
+it can begin to accumulate a new least squares
+system.
+@end deftypefun
+
+@deftypefun int gsl_multilarge_linear_stdform1 (const gsl_vector * @var{L}, const gsl_matrix * @var{X}, const gsl_vector * @var{y}, gsl_matrix * @var{Xs}, gsl_vector * @var{ys}, gsl_multilarge_linear_workspace * @var{work})
+@deftypefunx int gsl_multilarge_linear_wstdform1 (const gsl_vector * @var{L}, const gsl_matrix * @var{X}, const gsl_vector * @var{w}, const gsl_vector * @var{y}, gsl_matrix * @var{Xs}, gsl_vector * @var{ys}, gsl_multilarge_linear_workspace * @var{work})
+These functions define a regularization matrix
+@math{L =} diag@math{(l_0,l_1,...,l_{p-1})}.
+The diagonal matrix element @math{l_i} is provided by the
+@math{i}th element of the input vector @var{L}.
+The block (@var{X},@var{y}) is converted to standard form and
+the parameters (@math{\tilde{X}},@math{\tilde{y}}) are stored in @var{Xs}
+and @var{ys} on output.  @var{Xs} and @var{ys} have the same dimensions as
+@var{X} and @var{y}. Optional data weights may be supplied in the
+vector @var{w}. In order to apply this transformation,
+@math{L^{-1}} must exist and so none of the @math{l_i}
+may be zero. After the standard form system has been solved,
+use @code{gsl_multilarge_linear_genform1} to recover the original solution vector.
+It is allowed to have @var{X} = @var{Xs} and @var{y} = @var{ys} for an in-place transform.
+@end deftypefun
+
+@deftypefun int gsl_multilarge_linear_L_decomp (gsl_matrix * @var{L}, gsl_vector * @var{tau})
+This function calculates the QR decomposition of the @math{m}-by-@math{p} regularization matrix
+@var{L}. @var{L} must have @math{m \ge p}.  On output,
+the Householder scalars are stored in the vector @var{tau} of size @math{p}.
+These outputs will be used by @code{gsl_multilarge_linear_wstdform2} to complete the
+transformation to standard form.
+@end deftypefun
+
+@deftypefun int gsl_multilarge_linear_stdform2 (const gsl_matrix * @var{LQR}, const gsl_vector * @var{Ltau}, const gsl_matrix * @var{X}, const gsl_vector * @var{y}, gsl_matrix * @var{Xs}, gsl_vector * @var{ys}, gsl_multilarge_linear_workspace * @var{work})
+@deftypefunx int gsl_multilarge_linear_wstdform2 (const gsl_matrix * @var{LQR}, const gsl_vector * @var{Ltau}, const gsl_matrix * @var{X}, const gsl_vector * @var{w}, const gsl_vector * @var{y}, gsl_matrix * @var{Xs}, gsl_vector * @var{ys}, gsl_multilarge_linear_workspace * @var{work})
+These functions convert a block of rows (@var{X},@var{y},@var{w}) to standard
+form (@math{\tilde{X}},@math{\tilde{y}}) which are stored in @var{Xs} and @var{ys}
+respectively. @var{X}, @var{y}, and @var{w} must all have the same number of rows.
+The @math{m}-by-@math{p} regularization matrix @var{L} is specified by the inputs
+@var{LQR} and @var{Ltau}, which are outputs from @code{gsl_multilarge_linear_L_decomp}.
+@var{Xs} and @var{ys} have the same dimensions as @var{X} and @var{y}. After the
+standard form system has been solved, use @code{gsl_multilarge_linear_genform2} to
+recover the original solution vector. Optional data weights may be supplied in the
+vector @var{w}, where @math{W =} diag(w).
+@end deftypefun
+
+@deftypefun int gsl_multilarge_linear_accumulate (gsl_matrix * @var{X}, gsl_vector * @var{y}, gsl_multilarge_linear_workspace * @var{w})
+This function accumulates the standard form block (@math{X,y}) into the
+current least squares system. @var{X} and @var{y} have the same number
+of rows, which can be arbitrary.  @var{X} must have @math{p} columns.
+For the TSQR method, @var{X} and @var{y} are destroyed on output.
+For the normal equations method, they are both unchanged.
+@end deftypefun
+
+@deftypefun int gsl_multilarge_linear_solve (const double @var{lambda}, gsl_vector * @var{c}, double * @var{rnorm}, double * @var{snorm}, gsl_multilarge_linear_workspace * @var{w})
+After all blocks (@math{X_i,y_i}) have been accumulated into
+the large least squares system, this function will compute
+the solution vector which is stored in @var{c} on output.
+The regularization parameter @math{\lambda} is provided in
+@var{lambda}. On output, @var{rnorm} contains the residual norm
+@math{||y - X c||_W} and @var{snorm} contains the solution
+norm @math{||L c||}.
+@end deftypefun
+
+@deftypefun int gsl_multilarge_linear_genform1 (const gsl_vector * @var{L}, const gsl_vector * @var{cs}, gsl_vector * @var{c}, gsl_multilarge_linear_workspace * @var{work})
+After a regularized system has been solved with
+@math{L =} diag@math{(\l_0,\l_1,...,\l_{p-1})},
+this function backtransforms the standard form solution vector @var{cs}
+to recover the solution vector of the original problem @var{c}. The
+diagonal matrix elements @math{l_i} are provided in
+the vector @var{L}. It is allowed to have @var{c} = @var{cs} for an
+in-place transform.
+@end deftypefun
+
+@deftypefun int gsl_multilarge_linear_genform2 (const gsl_matrix * @var{LQR}, const gsl_vector * @var{Ltau}, const gsl_vector * @var{cs}, gsl_vector * @var{c}, gsl_multilarge_linear_workspace * @var{work})
+After a regularized system has been solved with a regularization matrix @math{L},
+specified by (@var{LQR},@var{Ltau}), this function backtransforms the standard form solution @var{cs}
+to recover the solution vector of the original problem, which is stored in @var{c},
+of length @math{p}.
+@end deftypefun
+
+@deftypefun int gsl_multilarge_linear_lcurve (gsl_vector * @var{reg_param}, gsl_vector * @var{rho}, gsl_vector * @var{eta}, gsl_multilarge_linear_workspace * @var{work})
+This function computes the L-curve for a large least squares system
+after it has been fully accumulated into the workspace @var{work}.
+The output vectors @var{reg_param}, @var{rho}, and @var{eta} must all
+be the same size, and will contain the regularization parameters
+@math{\lambda_i}, residual norms @math{||y - X c_i||}, and solution
+norms @math{|| L c_i ||} which compose the L-curve, where @math{c_i}
+is the regularized solution vector corresponding to @math{\lambda_i}.
+The user may determine the number of points on the L-curve by
+adjusting the size of these input arrays. For the TSQR method,
+the regularization parameters @math{\lambda_i} are estimated from the
+singular values of the triangular @math{R} factor. For the normal
+equations method, they are estimated from the eigenvalues of the
+@math{X^T X} matrix.
+@end deftypefun
+
+@deftypefun int gsl_multilarge_linear_rcond (double * @var{rcond}, gsl_multilarge_linear_workspace * @var{work})
+This function computes the reciprocal condition number, stored in
+@var{rcond}, of the least squares matrix after it has been accumulated
+into the workspace @var{work}. For the TSQR algorithm, this is
+accomplished by calculating the SVD of the @math{R} factor, which
+has the same singular values as the matrix @math{X}. For the normal
+equations method, this is done by computing the eigenvalues of
+@math{X^T X}, which could be inaccurate for ill-conditioned matrices
+@math{X}.
+@end deftypefun
+
 @node Troubleshooting
 @section Troubleshooting
 @cindex least squares troubleshooting
@@ -709,6 +1636,20 @@
 @node Fitting Examples
 @section Examples
 
+The example programs in this section demonstrate the various linear regression methods.
+
+@menu
+* Fitting linear regression example::
+* Fitting multi-parameter linear regression example::
+* Fitting regularized linear regression example 1::
+* Fitting regularized linear regression example 2::
+* Fitting robust linear regression example::
+* Fitting large linear systems example::
+@end menu
+
+@node Fitting linear regression example
+@subsection Simple Linear Regression Example
+
 The following program computes a least squares straight-line fit to a
 simple dataset, and outputs the best-fit line and its
 associated one standard-deviation error bars.
@@ -743,7 +1684,10 @@
 @center @image{fit-wlinear,3.0in}
 @end iftex
 
-The next program performs a quadratic fit @math{y = c_0 + c_1 x + c_2
+@node Fitting multi-parameter linear regression example
+@subsection Multi-parameter Linear Regression Example
+
+The following program performs a quadratic fit @math{y = c_0 + c_1 x + c_2
 x^2} to a weighted dataset using the generalised linear fitting function
 @code{gsl_multifit_wlinear}.  The model matrix @math{X} for a quadratic
 fit is given by,
@@ -835,6 +1779,149 @@
 @center @image{fit-wlinear2,3.0in}
 @end iftex
 
+@node Fitting regularized linear regression example 1
+@subsection Regularized Linear Regression Example 1
+
+The next program demonstrates the difference between ordinary and
+regularized least squares when the design matrix is near-singular.
+In this program, we generate two random normally distributed variables
+@math{u} and @math{v}, with @math{v = u + noise} so that @math{u}
+and @math{v} are nearly colinear. We then set a third dependent
+variable @math{y = u + v + noise} and solve for the coefficients
+@math{c_1,c_2} of the model @math{Y(c_1,c_2) = c_1 u + c_2 v}.
+Since @math{u \approx v}, the design matrix @math{X} is nearly
+singular, leading to unstable ordinary least squares solutions.
+
+@noindent
+Here is the program output:
+@example
+matrix condition number = 1.025113e+04
+=== Unregularized fit ===
+best fit: y = -43.6588 u + 45.6636 v
+residual norm = 31.6248
+solution norm = 63.1764
+chisq/dof = 1.00213
+=== Regularized fit (L-curve) ===
+optimal lambda: 4.51103
+best fit: y = 1.00113 u + 1.0032 v
+residual norm = 31.6547
+solution norm = 1.41728
+chisq/dof = 1.04499
+=== Regularized fit (GCV) ===
+optimal lambda: 0.0232029
+best fit: y = -19.8367 u + 21.8417 v
+residual norm = 31.6332
+solution norm = 29.5051
+chisq/dof = 1.00314
+@end example
+
+@noindent
+We see that the ordinary least squares solution is completely wrong,
+while the L-curve regularized method with the optimal
+@math{\lambda = 4.51103} finds the correct solution
+@math{c_1 \approx c_2 \approx 1}. The GCV regularized method finds
+a regularization parameter @math{\lambda = 0.0232029} which is too
+small to give an accurate solution, although it performs better than OLS.
+The L-curve and its computed corner, as well as the GCV curve and its
+minimum are plotted below.
+
+@iftex
+@sp 1
+@center @image{regularized,5.0in}
+@end iftex
+
+@noindent The program is given below.
+@example
+@verbatiminclude examples/fitreg.c
+@end example
+
+@node Fitting regularized linear regression example 2
+@subsection Regularized Linear Regression Example 2
+
+The following example program minimizes the cost function
+@tex
+\beforedisplay
+$$
+||y - X c||^2 + \lambda^2 ||x||^2
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+||y - X c||^2 + \lambda^2 ||x||^2
+@end example
+
+@end ifinfo
+@noindent
+where @math{X} is the @math{10}-by-@math{8} Hilbert matrix whose
+entries are given by
+@tex
+\beforedisplay
+$$
+X_{ij} = {1 \over i + j - 1}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+X_@{ij@} = 1 / (i + j - 1)
+@end example
+
+@end ifinfo
+@noindent
+and the right hand side vector is given by
+@math{y = [1,-1,1,-1,1,-1,1,-1,1,-1]^T}. Solutions
+are computed for @math{\lambda = 0} (unregularized) as
+well as for optimal parameters @math{\lambda} chosen by
+analyzing the L-curve and GCV curve.
+
+@noindent
+Here is the program output:
+@example
+matrix condition number = 3.565872e+09
+=== Unregularized fit ===
+residual norm = 2.15376
+solution norm = 2.92217e+09
+chisq/dof = 2.31934
+=== Regularized fit (L-curve) ===
+optimal lambda: 7.11407e-07
+residual norm = 2.60386
+solution norm = 424507
+chisq/dof = 3.43565
+=== Regularized fit (GCV) ===
+optimal lambda: 1.72278
+residual norm = 3.1375
+solution norm = 0.139357
+chisq/dof = 4.95076
+@end example
+
+@noindent
+Here we see the unregularized solution results in a large solution
+norm due to the ill-conditioned matrix. The L-curve solution finds
+a small value of @math{\lambda = 7.11e-7} which still results in
+a badly conditioned system and a large solution norm. The GCV method
+finds a parameter @math{\lambda = 1.72} which results in a well-conditioned
+system and small solution norm.
+
+@noindent
+The L-curve and its computed corner, as well as the GCV curve and its
+minimum are plotted below.
+
+@iftex
+@sp 1
+@center @image{regularized2,5.0in}
+@end iftex
+
+@noindent The program is given below.
+@example
+@verbatiminclude examples/fitreg2.c
+@end example
+
+@node Fitting robust linear regression example
+@subsection Robust Linear Regression Example
+
 The next program demonstrates the advantage of robust least squares on
 a dataset with outliers. The program generates linear @math{(x,y)}
 data pairs on the line @math{y = 1.45 x + 3.88}, adds some random
@@ -853,6 +1940,49 @@
 @center @image{robust,3.0in}
 @end iftex
 
+@node Fitting large linear systems example
+@subsection Large Dense Linear Regression Example
+
+The following program demostrates the large dense linear least squares
+solvers. This example is adapted from Trefethen and Bau,
+and fits the function @math{f(t) = \exp{(\sin^3{(10t)}})} on
+the interval @math{[0,1]} with a degree 15 polynomial. The
+program generates @math{n = 50000} equally spaced points
+@math{t_i} on this interval, calculates the function value
+and adds random noise to determine the observation value
+@math{y_i}. The entries of the least squares matrix are
+@math{X_{ij} = t_i^j}, representing a polynomial fit. The
+matrix is highly ill-conditioned, with a condition number
+of about @math{1.4 \cdot 10^{11}}. The program accumulates the
+matrix into the least squares system in 5 blocks, each with
+10000 rows. This way the full matrix @math{X} is never
+stored in memory. We solve the system with both the
+normal equations and TSQR methods. The results are shown
+in the plot below. In the top left plot, we see the unregularized
+normal equations solution has larger error than TSQR due to
+the ill-conditioning of the matrix. In the bottom left plot,
+we show the L-curve, which exhibits multiple corners.
+In the top right panel, we plot a regularized solution using
+@math{\lambda = 10^{-6}}. The TSQR and normal solutions now agree,
+however they are unable to provide a good fit due to the damping.
+This indicates that for some ill-conditioned
+problems, regularizing the normal equations does not improve the
+solution. This is further illustrated in the bottom right panel,
+where we plot the L-curve calculated from the normal equations.
+The curve agrees with the TSQR curve for larger damping parameters,
+but for small @math{\lambda}, the normal equations approach cannot
+provide accurate solution vectors leading to numerical
+inaccuracies in the left portion of the curve.
+
+@iftex
+@sp 1
+@center @image{multilarge,6.0in}
+@end iftex
+
+@example
+@verbatiminclude examples/largefit.c
+@end example
+
 @node Fitting References and Further Reading
 @section References and Further Reading
 
@@ -880,6 +2010,19 @@
 @center @uref{http://www.nist.gov/itl/div898/strd/index.html}.
 
 @noindent
+More information on Tikhonov regularization can be found in
+
+@itemize @w{}
+@item Hansen, P. C. (1998), Rank-Deficient and Discrete Ill-Posed Problems:
+Numerical Aspects of Linear Inversion. SIAM Monogr. on Mathematical
+Modeling and Computation, Society for Industrial and Applied Mathematics
+
+@item M. Rezghi and S. M. Hosseini (2009), A new variant of L-curve for
+Tikhonov regularization, Journal of Computational and Applied Mathematics,
+Volume 231, Issue 2, pages 914-924.
+@end itemize
+
+@noindent
 The GSL implementation of robust linear regression closely follows the publications
 
 @itemize @w{}
@@ -893,3 +2036,15 @@
 reweighted least squares," The American Statistician, v. 42, 
 pp. 152-154.
 @end itemize
+
+@noindent
+More information about the normal equations and TSQR approach for solving
+large linear least squares systems can be found in the publications
+
+@itemize @w{}
+@item Trefethen, L. N. and Bau, D. (1997), "Numerical Linear Algebra", SIAM.
+
+@item Demmel, J., Grigori, L., Hoemmen, M. F., and Langou, J.
+"Communication-optimal parallel and sequential QR and LU factorizations",
+UCB Technical Report No. UCB/EECS-2008-89, 2008.
+@end itemize
diff -Nru gsl-doc-1.16/doc/gsl-ref.info gsl-doc-2.3/doc/gsl-ref.info
--- gsl-doc-1.16/doc/gsl-ref.info	2013-07-19 15:17:48.000000000 +0000
+++ gsl-doc-2.3/doc/gsl-ref.info	2016-12-09 00:08:10.000000000 +0000
@@ -2,13 +2,20 @@
 gsl-ref.texi.
 
 Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,
-2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 The GSL Team.
+2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016
+The GSL Team.
 
    Permission is granted to copy, distribute and/or modify this document
 under the terms of the GNU Free Documentation License, Version 1.3 or
-any later version published by the Free Software Foundation; with no
-Invariant Sections and no cover texts.  A copy of the license is
-included in the section entitled "GNU Free Documentation License".
+any later version published by the Free Software Foundation; with the
+Invariant Sections being "GNU General Public License" and "Free Software
+Needs Free Documentation", the Front-Cover text being "A GNU Manual",
+and with the Back-Cover Text being (a) (see below).  A copy of the
+license is included in the section entitled "GNU Free Documentation
+License".
+
+   (a) The Back-Cover Text is: "You have the freedom to copy and modify
+this GNU Manual."
 INFO-DIR-SECTION Software libraries
 START-INFO-DIR-ENTRY
 * gsl-ref: (gsl-ref).                   GNU Scientific Library - Reference
@@ -16,610 +23,680 @@
 
 
 Indirect:
-gsl-ref.info-1: 707
-gsl-ref.info-2: 301602
-gsl-ref.info-3: 601000
-gsl-ref.info-4: 902430
-gsl-ref.info-5: 1443412
+gsl-ref.info-1: 973
+gsl-ref.info-2: 302546
+gsl-ref.info-3: 601121
+gsl-ref.info-4: 902718
+gsl-ref.info-5: 1201856
+gsl-ref.info-6: 1705030
 
 Tag Table:
 (Indirect)
-Node: Top707
-Node: Introduction3656
-Node: Routines available in GSL4376
-Node: GSL is Free Software5989
-Node: Obtaining GSL8381
-Node: No Warranty9409
-Node: Reporting Bugs9915
-Ref: Reporting Bugs-Footnote-110867
-Node: Further Information10917
-Node: Conventions used in this manual11931
-Node: Using the library12695
-Node: An Example Program13418
-Ref: An Example Program-Footnote-114161
-Node: Compiling and Linking14268
-Node: Linking programs with the library15341
-Ref: Linking programs with the library-Footnote-116744
-Ref: Linking programs with the library-Footnote-216781
-Node: Linking with an alternative BLAS library16834
-Node: Shared Libraries17917
-Ref: Shared Libraries-Footnote-119392
-Node: ANSI C Compliance19440
-Node: Inline functions20533
-Node: Long double22071
-Node: Portability functions23659
-Node: Alternative optimized functions25057
-Node: Support for different numeric types26515
-Node: Compatibility with C++29579
-Node: Aliasing of arrays30151
-Node: Thread-safety30902
-Node: Deprecated Functions31990
-Node: Code Reuse32615
-Node: Error Handling33260
-Node: Error Reporting34060
-Node: Error Codes35952
-Node: Error Handlers37809
-Node: Using GSL error reporting in your own functions41449
-Node: Error Reporting Examples43409
-Node: Mathematical Functions44621
-Node: Mathematical Constants45414
-Node: Infinities and Not-a-number46544
-Ref: Infinities and Not-a-number-Footnote-147654
-Node: Elementary Functions48064
-Node: Small integer powers50521
-Node: Testing the Sign of Numbers52170
-Node: Testing for Odd and Even Numbers52603
-Node: Maximum and Minimum functions53162
-Node: Approximate Comparison of Floating Point Numbers55443
-Node: Complex Numbers56803
-Ref: Complex Numbers-Footnote-158148
-Node: Representation of complex numbers58212
-Node: Properties of complex numbers60152
-Node: Complex arithmetic operators61158
-Node: Elementary Complex Functions63904
-Node: Complex Trigonometric Functions65728
-Node: Inverse Complex Trigonometric Functions66949
-Node: Complex Hyperbolic Functions69562
-Node: Inverse Complex Hyperbolic Functions70858
-Node: Complex Number References and Further Reading72846
-Node: Polynomials74242
-Node: Polynomial Evaluation75046
-Node: Divided Difference Representation of Polynomials76457
-Node: Quadratic Equations80319
-Node: Cubic Equations82256
-Node: General Polynomial Equations83839
-Node: Roots of Polynomials Examples86196
-Node: Roots of Polynomials References and Further Reading87585
-Node: Special Functions88631
-Node: Special Function Usage90879
-Node: The gsl_sf_result struct92063
-Node: Special Function Modes93327
-Node: Airy Functions and Derivatives94261
-Node: Airy Functions94986
-Node: Derivatives of Airy Functions96346
-Node: Zeros of Airy Functions97858
-Node: Zeros of Derivatives of Airy Functions98577
-Node: Bessel Functions99336
-Node: Regular Cylindrical Bessel Functions100554
-Node: Irregular Cylindrical Bessel Functions101878
-Node: Regular Modified Cylindrical Bessel Functions103336
-Node: Irregular Modified Cylindrical Bessel Functions106164
-Node: Regular Spherical Bessel Functions109137
-Node: Irregular Spherical Bessel Functions111350
-Node: Regular Modified Spherical Bessel Functions113036
-Node: Irregular Modified Spherical Bessel Functions115037
-Node: Regular Bessel Function - Fractional Order117100
-Node: Irregular Bessel Functions - Fractional Order118098
-Node: Regular Modified Bessel Functions - Fractional Order118680
-Node: Irregular Modified Bessel Functions - Fractional Order119605
-Node: Zeros of Regular Bessel Functions120841
-Node: Clausen Functions121944
-Node: Coulomb Functions122548
-Node: Normalized Hydrogenic Bound States123007
-Node: Coulomb Wave Functions124120
-Node: Coulomb Wave Function Normalization Constant127532
-Node: Coupling Coefficients128285
-Node: 3-j Symbols129059
-Node: 6-j Symbols129663
-Node: 9-j Symbols130287
-Node: Dawson Function130993
-Node: Debye Functions131560
-Node: Dilogarithm133334
-Node: Real Argument133656
-Node: Complex Argument134350
-Node: Elementary Operations134820
-Node: Elliptic Integrals135644
-Node: Definition of Legendre Forms136239
-Node: Definition of Carlson Forms137059
-Node: Legendre Form of Complete Elliptic Integrals137756
-Node: Legendre Form of Incomplete Elliptic Integrals139309
-Node: Carlson Forms141496
-Node: Elliptic Functions (Jacobi)143043
-Node: Error Functions143624
-Node: Error Function144100
-Node: Complementary Error Function144473
-Node: Log Complementary Error Function144933
-Node: Probability functions145385
-Node: Exponential Functions146638
-Node: Exponential Function147033
-Node: Relative Exponential Functions148255
-Node: Exponentiation With Error Estimate149927
-Node: Exponential Integrals151136
-Node: Exponential Integral151692
-Node: Ei(x)152613
-Node: Hyperbolic Integrals153061
-Node: Ei_3(x)153716
-Node: Trigonometric Integrals154108
-Node: Arctangent Integral154707
-Node: Fermi-Dirac Function155107
-Node: Complete Fermi-Dirac Integrals155481
-Node: Incomplete Fermi-Dirac Integrals158046
-Node: Gamma and Beta Functions158689
-Node: Gamma Functions159324
-Node: Factorials162432
-Node: Pochhammer Symbol164985
-Node: Incomplete Gamma Functions166486
-Node: Beta Functions167735
-Node: Incomplete Beta Function168487
-Node: Gegenbauer Functions169197
-Node: Hypergeometric Functions170847
-Node: Laguerre Functions175111
-Node: Lambert W Functions176674
-Node: Legendre Functions and Spherical Harmonics177714
-Node: Legendre Polynomials178326
-Node: Associated Legendre Polynomials and Spherical Harmonics180382
-Node: Conical Functions183211
-Node: Radial Functions for Hyperbolic Space185334
-Node: Logarithm and Related Functions187511
-Node: Mathieu Functions189135
-Node: Mathieu Function Workspace190495
-Node: Mathieu Function Characteristic Values191308
-Node: Angular Mathieu Functions192380
-Node: Radial Mathieu Functions193416
-Node: Power Function194653
-Node: Psi (Digamma) Function195581
-Node: Digamma Function196134
-Node: Trigamma Function196964
-Node: Polygamma Function197541
-Node: Synchrotron Functions197925
-Node: Transport Functions198688
-Node: Trigonometric Functions199835
-Node: Circular Trigonometric Functions200481
-Node: Trigonometric Functions for Complex Arguments201490
-Node: Hyperbolic Trigonometric Functions202526
-Node: Conversion Functions203129
-Node: Restriction Functions203912
-Node: Trigonometric Functions With Error Estimates204843
-Node: Zeta Functions205753
-Node: Riemann Zeta Function206211
-Node: Riemann Zeta Function Minus One206890
-Node: Hurwitz Zeta Function207661
-Node: Eta Function208166
-Node: Special Functions Examples208725
-Node: Special Functions References and Further Reading210420
-Node: Vectors and Matrices211688
-Node: Data types212531
-Node: Blocks213734
-Node: Block allocation214667
-Node: Reading and writing blocks216071
-Node: Example programs for blocks218135
-Node: Vectors218762
-Node: Vector allocation220730
-Node: Accessing vector elements222267
-Ref: Accessing vector elements-Footnote-1225408
-Node: Initializing vector elements225647
-Node: Reading and writing vectors226341
-Node: Vector views228431
-Node: Copying vectors235897
-Node: Exchanging elements236757
-Node: Vector operations237315
-Node: Finding maximum and minimum elements of vectors239088
-Node: Vector properties240675
-Node: Example programs for vectors241649
-Node: Matrices243938
-Node: Matrix allocation246878
-Node: Accessing matrix elements248464
-Node: Initializing matrix elements250413
-Node: Reading and writing matrices251210
-Node: Matrix views253313
-Node: Creating row and column views260449
-Node: Copying matrices264926
-Node: Copying rows and columns265522
-Node: Exchanging rows and columns267199
-Node: Matrix operations268677
-Node: Finding maximum and minimum elements of matrices270647
-Node: Matrix properties272547
-Node: Example programs for matrices273650
-Node: Vector and Matrix References and Further Reading277721
-Node: Permutations278207
-Node: The Permutation struct279544
-Node: Permutation allocation280047
-Node: Accessing permutation elements281483
-Node: Permutation properties282326
-Node: Permutation functions283031
-Node: Applying Permutations284288
-Node: Reading and writing permutations286215
-Ref: Reading and writing permutations-Footnote-1288431
-Node: Permutations in cyclic form288543
-Node: Permutation Examples291970
-Node: Permutation References and Further Reading294513
-Node: Combinations295187
-Node: The Combination struct296072
-Node: Combination allocation296623
-Node: Accessing combination elements298410
-Node: Combination properties299069
-Node: Combination functions299955
-Node: Reading and writing combinations301602
-Ref: Reading and writing combinations-Footnote-1303835
-Node: Combination Examples303947
-Node: Combination References and Further Reading305255
-Node: Multisets305658
-Node: The Multiset struct306584
-Node: Multiset allocation307105
-Node: Accessing multiset elements308800
-Node: Multiset properties309429
-Node: Multiset functions310242
-Node: Reading and writing multisets311152
-Ref: Reading and writing multisets-Footnote-1313303
-Node: Multiset Examples313415
-Node: Sorting315523
-Node: Sorting objects316522
-Node: Sorting vectors319435
-Node: Selecting the k smallest or largest elements322596
-Node: Computing the rank325937
-Node: Sorting Examples327138
-Node: Sorting References and Further Reading328782
-Node: BLAS Support329328
-Ref: BLAS Support-Footnote-1332714
-Node: GSL BLAS Interface332883
-Node: Level 1 GSL BLAS Interface333376
-Node: Level 2 GSL BLAS Interface340116
-Node: Level 3 GSL BLAS Interface349406
-Node: BLAS Examples360504
-Node: BLAS References and Further Reading361925
-Node: Linear Algebra363267
-Node: LU Decomposition364461
-Node: QR Decomposition369697
-Node: QR Decomposition with Column Pivoting376006
-Node: Singular Value Decomposition380470
-Node: Cholesky Decomposition384890
-Node: Tridiagonal Decomposition of Real Symmetric Matrices388132
-Node: Tridiagonal Decomposition of Hermitian Matrices389980
-Node: Hessenberg Decomposition of Real Matrices391932
-Node: Hessenberg-Triangular Decomposition of Real Matrices394344
-Node: Bidiagonalization395467
-Node: Householder Transformations397892
-Node: Householder solver for linear systems400244
-Node: Tridiagonal Systems401151
-Node: Balancing404024
-Node: Linear Algebra Examples404827
-Node: Linear Algebra References and Further Reading406816
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-Node: Real Symmetric Matrices409692
-Node: Complex Hermitian Matrices412206
-Node: Real Nonsymmetric Matrices414835
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-Node: Complex Generalized Hermitian-Definite Eigensystems423449
-Node: Real Generalized Nonsymmetric Eigensystems426163
-Node: Sorting Eigenvalues and Eigenvectors432770
-Node: Eigenvalue and Eigenvector Examples436048
-Node: Eigenvalue and Eigenvector References441439
-Node: Fast Fourier Transforms442466
-Node: Mathematical Definitions443692
-Node: Overview of complex data FFTs446097
-Node: Radix-2 FFT routines for complex data449042
-Node: Mixed-radix FFT routines for complex data453261
-Node: Overview of real data FFTs462594
-Node: Radix-2 FFT routines for real data465029
-Node: Mixed-radix FFT routines for real data469453
-Node: FFT References and Further Reading480138
-Node: Numerical Integration483008
-Node: Numerical Integration Introduction484806
-Node: Integrands without weight functions487081
-Node: Integrands with weight functions487911
-Node: Integrands with singular weight functions488622
-Node: QNG non-adaptive Gauss-Kronrod integration489540
-Node: QAG adaptive integration490822
-Node: QAGS adaptive integration with singularities493611
-Node: QAGP adaptive integration with known singular points495411
-Node: QAGI adaptive integration on infinite intervals496725
-Node: QAWC adaptive integration for Cauchy principal values499005
-Node: QAWS adaptive integration for singular functions500175
-Node: QAWO adaptive integration for oscillatory functions503401
-Node: QAWF adaptive integration for Fourier integrals507189
-Node: CQUAD doubly-adaptive integration509813
-Node: Fixed order Gauss-Legendre integration513071
-Node: Numerical integration error codes515059
-Node: Numerical integration examples515815
-Node: Numerical integration References and Further Reading517861
-Node: Random Number Generation518852
-Node: General comments on random numbers520386
-Node: The Random Number Generator Interface522338
-Node: Random number generator initialization523696
-Node: Sampling from a random number generator526067
-Node: Auxiliary random number generator functions529311
-Node: Random number environment variables531631
-Node: Copying random number generator state534156
-Node: Reading and writing random number generator state535130
-Node: Random number generator algorithms536524
-Node: Unix random number generators546466
-Node: Other random number generators550180
-Node: Random Number Generator Performance558831
-Node: Random Number Generator Examples559952
-Node: Random Number References and Further Reading561508
-Node: Random Number Acknowledgements562803
-Node: Quasi-Random Sequences563289
-Node: Quasi-random number generator initialization564409
-Node: Sampling from a quasi-random number generator565424
-Node: Auxiliary quasi-random number generator functions566121
-Node: Saving and resorting quasi-random number generator state567067
-Node: Quasi-random number generator algorithms567875
-Node: Quasi-random number generator examples569013
-Node: Quasi-random number references569998
-Node: Random Number Distributions570524
-Node: Random Number Distribution Introduction573855
-Node: The Gaussian Distribution575650
-Node: The Gaussian Tail Distribution578310
-Node: The Bivariate Gaussian Distribution579974
-Node: The Exponential Distribution581288
-Node: The Laplace Distribution582427
-Node: The Exponential Power Distribution583519
-Node: The Cauchy Distribution584787
-Node: The Rayleigh Distribution586036
-Node: The Rayleigh Tail Distribution587208
-Node: The Landau Distribution588081
-Node: The Levy alpha-Stable Distributions589036
-Node: The Levy skew alpha-Stable Distribution590094
-Node: The Gamma Distribution591706
-Node: The Flat (Uniform) Distribution593361
-Node: The Lognormal Distribution594509
-Node: The Chi-squared Distribution595857
-Node: The F-distribution597262
-Node: The t-distribution598899
-Node: The Beta Distribution601000
-Node: The Logistic Distribution602159
-Node: The Pareto Distribution603288
-Node: Spherical Vector Distributions604458
-Node: The Weibull Distribution607294
-Node: The Type-1 Gumbel Distribution608488
-Node: The Type-2 Gumbel Distribution609724
-Node: The Dirichlet Distribution610955
-Node: General Discrete Distributions612623
-Node: The Poisson Distribution616491
-Node: The Bernoulli Distribution617498
-Node: The Binomial Distribution618249
-Node: The Multinomial Distribution619452
-Node: The Negative Binomial Distribution621226
-Node: The Pascal Distribution622591
-Node: The Geometric Distribution623749
-Node: The Hypergeometric Distribution624997
-Node: The Logarithmic Distribution626650
-Node: Shuffling and Sampling627442
-Node: Random Number Distribution Examples630254
-Node: Random Number Distribution References and Further Reading633450
-Node: Statistics635594
-Node: Mean and standard deviation and variance637080
-Node: Absolute deviation640588
-Node: Higher moments (skewness and kurtosis)641880
-Node: Autocorrelation644013
-Node: Covariance644826
-Node: Correlation645792
-Node: Weighted Samples647161
-Node: Maximum and Minimum values653011
-Node: Median and Percentiles655750
-Node: Example statistical programs658165
-Node: Statistics References and Further Reading660825
-Node: Histograms662033
-Node: The histogram struct663886
-Node: Histogram allocation665690
-Node: Copying Histograms668647
-Node: Updating and accessing histogram elements669323
-Node: Searching histogram ranges672592
-Node: Histogram Statistics673592
-Node: Histogram Operations675458
-Node: Reading and writing histograms677533
-Node: Resampling from histograms680575
-Node: The histogram probability distribution struct681374
-Node: Example programs for histograms684408
-Node: Two dimensional histograms686471
-Node: The 2D histogram struct687192
-Node: 2D Histogram allocation689002
-Node: Copying 2D Histograms691076
-Node: Updating and accessing 2D histogram elements691781
-Node: Searching 2D histogram ranges695438
-Node: 2D Histogram Statistics696452
-Node: 2D Histogram Operations699317
-Node: Reading and writing 2D histograms701495
-Node: Resampling from 2D histograms705124
-Node: Example programs for 2D histograms708145
-Node: N-tuples709972
-Node: The ntuple struct711295
-Node: Creating ntuples711774
-Node: Opening an existing ntuple file712441
-Node: Writing ntuples713070
-Node: Reading ntuples713531
-Node: Closing an ntuple file713862
-Node: Histogramming ntuple values714202
-Node: Example ntuple programs716212
-Node: Ntuple References and Further Reading719541
-Node: Monte Carlo Integration719862
-Node: Monte Carlo Interface721173
-Node: PLAIN Monte Carlo723800
-Node: MISER726255
-Ref: MISER-Footnote-1732935
-Node: VEGAS733060
-Node: Monte Carlo Examples742621
-Node: Monte Carlo Integration References and Further Reading748608
-Node: Simulated Annealing749390
-Node: Simulated Annealing algorithm750606
-Node: Simulated Annealing functions751758
-Node: Examples with Simulated Annealing756288
-Node: Trivial example756857
-Node: Traveling Salesman Problem759508
-Node: Simulated Annealing References and Further Reading762821
-Node: Ordinary Differential Equations763232
-Node: Defining the ODE System764472
-Node: Stepping Functions767300
-Node: Adaptive Step-size Control774270
-Node: Evolution780347
-Node: Driver784476
-Node: ODE Example programs788710
-Node: ODE References and Further Reading793756
-Node: Interpolation795520
-Node: Introduction to Interpolation796721
-Node: Interpolation Functions797162
-Node: Interpolation Types798369
-Node: Index Look-up and Acceleration801091
-Node: Evaluation of Interpolating Functions803143
-Node: Higher-level Interface805639
-Node: Interpolation Example programs807679
-Node: Interpolation References and Further Reading810899
-Node: Numerical Differentiation811471
-Node: Numerical Differentiation functions812066
-Node: Numerical Differentiation Examples814923
-Node: Numerical Differentiation References816336
-Node: Chebyshev Approximations816887
-Node: Chebyshev Definitions817968
-Node: Creation and Calculation of Chebyshev Series818757
-Node: Auxiliary Functions for Chebyshev Series819742
-Node: Chebyshev Series Evaluation820482
-Node: Derivatives and Integrals821862
-Node: Chebyshev Approximation Examples823100
-Node: Chebyshev Approximation References and Further Reading824596
-Node: Series Acceleration825046
-Node: Acceleration functions825823
-Node: Acceleration functions without error estimation828150
-Node: Example of accelerating a series830774
-Node: Series Acceleration References833120
-Node: Wavelet Transforms834008
-Node: DWT Definitions834607
-Node: DWT Initialization835559
-Node: DWT Transform Functions838207
-Node: DWT in one dimension838758
-Node: DWT in two dimension840779
-Node: DWT Examples845358
-Node: DWT References847175
-Node: Discrete Hankel Transforms849339
-Node: Discrete Hankel Transform Definition849813
-Node: Discrete Hankel Transform Functions852016
-Node: Discrete Hankel Transform References853681
-Node: One dimensional Root-Finding854085
-Node: Root Finding Overview855391
-Node: Root Finding Caveats857247
-Node: Initializing the Solver859016
-Node: Providing the function to solve861649
-Node: Search Bounds and Guesses865203
-Node: Root Finding Iteration866066
-Node: Search Stopping Parameters867917
-Node: Root Bracketing Algorithms870428
-Node: Root Finding Algorithms using Derivatives873726
-Ref: Root Finding Algorithms using Derivatives-Footnote-1877269
-Node: Root Finding Examples877425
-Node: Root Finding References and Further Reading884713
-Node: One dimensional Minimization885352
-Node: Minimization Overview886695
-Node: Minimization Caveats888402
-Node: Initializing the Minimizer889740
-Node: Providing the function to minimize891981
-Node: Minimization Iteration892459
-Node: Minimization Stopping Parameters894597
-Node: Minimization Algorithms896202
-Node: Minimization Examples898796
-Node: Minimization References and Further Reading902430
-Node: Multidimensional Root-Finding902886
-Node: Overview of Multidimensional Root Finding904394
-Node: Initializing the Multidimensional Solver906581
-Node: Providing the multidimensional system of equations to solve909811
-Node: Iteration of the multidimensional solver914723
-Node: Search Stopping Parameters for the multidimensional solver917004
-Node: Algorithms using Derivatives918742
-Node: Algorithms without Derivatives923567
-Node: Example programs for Multidimensional Root finding926657
-Node: References and Further Reading for Multidimensional Root Finding935281
-Node: Multidimensional Minimization936520
-Node: Multimin Overview937930
-Node: Multimin Caveats940010
-Node: Initializing the Multidimensional Minimizer940759
-Node: Providing a function to minimize943993
-Node: Multimin Iteration948054
-Node: Multimin Stopping Criteria950248
-Node: Multimin Algorithms with Derivatives951819
-Node: Multimin Algorithms without Derivatives955350
-Node: Multimin Examples958352
-Node: Multimin References and Further Reading964922
-Node: Least-Squares Fitting965786
-Node: Fitting Overview966872
-Node: Linear regression969205
-Node: Linear fitting without a constant term971807
-Node: Multi-parameter fitting974001
-Node: Robust linear regression979860
-Node: Troubleshooting990108
-Node: Fitting Examples990731
-Node: Fitting References and Further Reading1001255
-Node: Nonlinear Least-Squares Fitting1002627
-Node: Overview of Nonlinear Least-Squares Fitting1004151
-Node: Initializing the Nonlinear Least-Squares Solver1005618
-Node: Providing the Function to be Minimized1008483
-Node: Finite Difference Jacobian1011946
-Node: Iteration of the Minimization Algorithm1013817
-Node: Search Stopping Parameters for Minimization Algorithms1015657
-Node: High Level Driver1017730
-Node: Minimization Algorithms using Derivatives1018636
-Ref: Minimization Algorithms using Derivatives-Footnote-11022084
-Node: Minimization Algorithms without Derivatives1022173
-Node: Computing the covariance matrix of best fit parameters1022565
-Node: Example programs for Nonlinear Least-Squares Fitting1024602
-Node: References and Further Reading for Nonlinear Least-Squares Fitting1032335
-Node: Basis Splines1033071
-Node: Overview of B-splines1033950
-Node: Initializing the B-splines solver1035266
-Node: Constructing the knots vector1036647
-Node: Evaluation of B-spline basis functions1037435
-Node: Evaluation of B-spline basis function derivatives1039083
-Node: Working with the Greville abscissae1041053
-Node: Example programs for B-splines1042047
-Node: References and Further Reading1046042
-Node: Physical Constants1046848
-Node: Fundamental Constants1048427
-Node: Astronomy and Astrophysics1049567
-Node: Atomic and Nuclear Physics1050232
-Node: Measurement of Time1051883
-Node: Imperial Units1052313
-Node: Speed and Nautical Units1052755
-Node: Printers Units1053259
-Node: Volume Area and Length1053582
-Node: Mass and Weight1054268
-Node: Thermal Energy and Power1055087
-Node: Pressure1055510
-Node: Viscosity1056123
-Node: Light and Illumination1056399
-Node: Radioactivity1056991
-Node: Force and Energy1057326
-Node: Prefixes1057730
-Node: Physical Constant Examples1058473
-Node: Physical Constant References and Further Reading1060262
-Node: IEEE floating-point arithmetic1060992
-Node: Representation of floating point numbers1061584
-Node: Setting up your IEEE environment1066070
-Node: IEEE References and Further Reading1073043
-Node: Debugging Numerical Programs1074203
-Node: Using gdb1074720
-Node: Examining floating point registers1078063
-Node: Handling floating point exceptions1079348
-Node: GCC warning options for numerical programs1080760
-Node: Debugging References1084708
-Node: Contributors to GSL1085420
-Node: Autoconf Macros1089914
-Node: GSL CBLAS Library1093946
-Node: Level 1 CBLAS Functions1094486
-Node: Level 2 CBLAS Functions1099788
-Node: Level 3 CBLAS Functions1116418
-Node: GSL CBLAS Examples1126080
-Node: GNU General Public License1127643
-Node: GNU Free Documentation License1165217
-Node: Function Index1190366
-Node: Variable Index1443412
-Node: Type Index1446715
-Node: Concept Index1461784
+Node: Top973
+Node: Introduction4283
+Node: Routines available in GSL5003
+Node: GSL is Free Software6616
+Node: Obtaining GSL9008
+Node: No Warranty10036
+Node: Reporting Bugs10542
+Ref: Reporting Bugs-Footnote-111494
+Node: Further Information11544
+Node: Conventions used in this manual12558
+Node: Using the library13322
+Node: An Example Program14045
+Ref: An Example Program-Footnote-114788
+Node: Compiling and Linking14895
+Node: Linking programs with the library15968
+Ref: Linking programs with the library-Footnote-117371
+Ref: Linking programs with the library-Footnote-217408
+Node: Linking with an alternative BLAS library17461
+Node: Shared Libraries18544
+Ref: Shared Libraries-Footnote-120019
+Node: ANSI C Compliance20067
+Node: Inline functions21160
+Node: Long double22698
+Node: Portability functions24286
+Node: Alternative optimized functions25684
+Node: Support for different numeric types27142
+Node: Compatibility with C++30206
+Node: Aliasing of arrays30778
+Node: Thread-safety31529
+Node: Deprecated Functions32617
+Node: Code Reuse33242
+Node: Error Handling33887
+Node: Error Reporting34687
+Node: Error Codes36579
+Node: Error Handlers38436
+Node: Using GSL error reporting in your own functions42076
+Node: Error Reporting Examples44036
+Node: Mathematical Functions45248
+Node: Mathematical Constants46041
+Node: Infinities and Not-a-number47171
+Ref: Infinities and Not-a-number-Footnote-148281
+Node: Elementary Functions48691
+Node: Small integer powers51148
+Node: Testing the Sign of Numbers52797
+Node: Testing for Odd and Even Numbers53230
+Node: Maximum and Minimum functions53789
+Node: Approximate Comparison of Floating Point Numbers56070
+Node: Complex Numbers57430
+Ref: Complex Numbers-Footnote-158775
+Node: Representation of complex numbers58839
+Node: Properties of complex numbers60779
+Node: Complex arithmetic operators61785
+Node: Elementary Complex Functions64531
+Node: Complex Trigonometric Functions66355
+Node: Inverse Complex Trigonometric Functions67576
+Node: Complex Hyperbolic Functions70189
+Node: Inverse Complex Hyperbolic Functions71485
+Node: Complex Number References and Further Reading73473
+Node: Polynomials74869
+Node: Polynomial Evaluation75673
+Node: Divided Difference Representation of Polynomials77084
+Node: Quadratic Equations80946
+Node: Cubic Equations82883
+Node: General Polynomial Equations84466
+Node: Roots of Polynomials Examples86823
+Node: Roots of Polynomials References and Further Reading88212
+Node: Special Functions89258
+Node: Special Function Usage91506
+Node: The gsl_sf_result struct92690
+Node: Special Function Modes93954
+Node: Airy Functions and Derivatives94888
+Node: Airy Functions95613
+Node: Derivatives of Airy Functions96973
+Node: Zeros of Airy Functions98485
+Node: Zeros of Derivatives of Airy Functions99204
+Node: Bessel Functions99963
+Node: Regular Cylindrical Bessel Functions101181
+Node: Irregular Cylindrical Bessel Functions102505
+Node: Regular Modified Cylindrical Bessel Functions103963
+Node: Irregular Modified Cylindrical Bessel Functions106791
+Node: Regular Spherical Bessel Functions109764
+Node: Irregular Spherical Bessel Functions111977
+Node: Regular Modified Spherical Bessel Functions113663
+Node: Irregular Modified Spherical Bessel Functions115662
+Node: Regular Bessel Function - Fractional Order117725
+Node: Irregular Bessel Functions - Fractional Order118723
+Node: Regular Modified Bessel Functions - Fractional Order119305
+Node: Irregular Modified Bessel Functions - Fractional Order120230
+Node: Zeros of Regular Bessel Functions121466
+Node: Clausen Functions122569
+Node: Coulomb Functions123173
+Node: Normalized Hydrogenic Bound States123632
+Node: Coulomb Wave Functions124745
+Node: Coulomb Wave Function Normalization Constant128157
+Node: Coupling Coefficients128910
+Node: 3-j Symbols129684
+Node: 6-j Symbols130288
+Node: 9-j Symbols130912
+Node: Dawson Function131618
+Node: Debye Functions132185
+Node: Dilogarithm133959
+Node: Real Argument134281
+Node: Complex Argument134975
+Node: Elementary Operations135445
+Node: Elliptic Integrals136269
+Node: Definition of Legendre Forms136864
+Node: Definition of Carlson Forms137684
+Node: Legendre Form of Complete Elliptic Integrals138381
+Node: Legendre Form of Incomplete Elliptic Integrals139934
+Node: Carlson Forms142026
+Node: Elliptic Functions (Jacobi)143573
+Node: Error Functions144154
+Node: Error Function144630
+Node: Complementary Error Function145003
+Node: Log Complementary Error Function145463
+Node: Probability functions145915
+Node: Exponential Functions147168
+Node: Exponential Function147563
+Node: Relative Exponential Functions148785
+Node: Exponentiation With Error Estimate150457
+Node: Exponential Integrals151666
+Node: Exponential Integral152222
+Node: Ei(x)153143
+Node: Hyperbolic Integrals153591
+Node: Ei_3(x)154246
+Node: Trigonometric Integrals154638
+Node: Arctangent Integral155237
+Node: Fermi-Dirac Function155637
+Node: Complete Fermi-Dirac Integrals156011
+Node: Incomplete Fermi-Dirac Integrals158576
+Node: Gamma and Beta Functions159219
+Node: Gamma Functions159854
+Node: Factorials162962
+Node: Pochhammer Symbol165515
+Node: Incomplete Gamma Functions167016
+Node: Beta Functions168265
+Node: Incomplete Beta Function169017
+Node: Gegenbauer Functions169727
+Node: Hypergeometric Functions171377
+Node: Laguerre Functions175641
+Node: Lambert W Functions177204
+Node: Legendre Functions and Spherical Harmonics178244
+Node: Legendre Polynomials178856
+Node: Associated Legendre Polynomials and Spherical Harmonics180912
+Node: Conical Functions191665
+Node: Radial Functions for Hyperbolic Space193788
+Node: Logarithm and Related Functions195965
+Node: Mathieu Functions197589
+Node: Mathieu Function Workspace198949
+Node: Mathieu Function Characteristic Values199762
+Node: Angular Mathieu Functions200944
+Node: Radial Mathieu Functions202112
+Node: Power Function203495
+Node: Psi (Digamma) Function204423
+Node: Digamma Function204976
+Node: Trigamma Function205806
+Node: Polygamma Function206383
+Node: Synchrotron Functions206767
+Node: Transport Functions207530
+Node: Trigonometric Functions208677
+Node: Circular Trigonometric Functions209323
+Node: Trigonometric Functions for Complex Arguments210332
+Node: Hyperbolic Trigonometric Functions211368
+Node: Conversion Functions211971
+Node: Restriction Functions212754
+Node: Trigonometric Functions With Error Estimates213685
+Node: Zeta Functions214595
+Node: Riemann Zeta Function215053
+Node: Riemann Zeta Function Minus One215732
+Node: Hurwitz Zeta Function216503
+Node: Eta Function217008
+Node: Special Functions Examples217567
+Node: Special Functions References and Further Reading219262
+Node: Vectors and Matrices220779
+Node: Data types221622
+Node: Blocks222825
+Node: Block allocation223758
+Node: Reading and writing blocks225162
+Node: Example programs for blocks227226
+Node: Vectors227853
+Node: Vector allocation229821
+Node: Accessing vector elements231358
+Ref: Accessing vector elements-Footnote-1234531
+Node: Initializing vector elements234770
+Node: Reading and writing vectors235464
+Node: Vector views237554
+Node: Copying vectors245020
+Node: Exchanging elements245880
+Node: Vector operations246438
+Node: Finding maximum and minimum elements of vectors248211
+Node: Vector properties249798
+Node: Example programs for vectors250772
+Node: Matrices253061
+Node: Matrix allocation256001
+Node: Accessing matrix elements257587
+Node: Initializing matrix elements259560
+Node: Reading and writing matrices260357
+Node: Matrix views262460
+Node: Creating row and column views269596
+Node: Copying matrices274073
+Node: Copying rows and columns274669
+Node: Exchanging rows and columns276346
+Node: Matrix operations277824
+Node: Finding maximum and minimum elements of matrices279794
+Node: Matrix properties281694
+Node: Example programs for matrices282797
+Node: Vector and Matrix References and Further Reading286869
+Node: Permutations287355
+Node: The Permutation struct288692
+Node: Permutation allocation289195
+Node: Accessing permutation elements290631
+Node: Permutation properties291474
+Node: Permutation functions292179
+Node: Applying Permutations293436
+Node: Reading and writing permutations295818
+Ref: Reading and writing permutations-Footnote-1298034
+Node: Permutations in cyclic form298146
+Node: Permutation Examples302546
+Node: Permutation References and Further Reading305089
+Node: Combinations305763
+Node: The Combination struct306648
+Node: Combination allocation307199
+Node: Accessing combination elements308986
+Node: Combination properties309645
+Node: Combination functions310531
+Node: Reading and writing combinations311471
+Ref: Reading and writing combinations-Footnote-1313704
+Node: Combination Examples313816
+Node: Combination References and Further Reading315124
+Node: Multisets315527
+Node: The Multiset struct316453
+Node: Multiset allocation316974
+Node: Accessing multiset elements318669
+Node: Multiset properties319298
+Node: Multiset functions320111
+Node: Reading and writing multisets321021
+Ref: Reading and writing multisets-Footnote-1323172
+Node: Multiset Examples323284
+Node: Sorting325392
+Node: Sorting objects326391
+Node: Sorting vectors329304
+Node: Selecting the k smallest or largest elements332465
+Node: Computing the rank335806
+Node: Sorting Examples337007
+Node: Sorting References and Further Reading338654
+Node: BLAS Support339200
+Ref: BLAS Support-Footnote-1342586
+Node: GSL BLAS Interface342755
+Node: Level 1 GSL BLAS Interface343248
+Node: Level 2 GSL BLAS Interface349988
+Node: Level 3 GSL BLAS Interface359278
+Node: BLAS Examples370376
+Node: BLAS References and Further Reading371797
+Node: Linear Algebra373139
+Node: LU Decomposition374489
+Node: QR Decomposition379714
+Node: QR Decomposition with Column Pivoting386023
+Node: Complete Orthogonal Decomposition393522
+Node: Singular Value Decomposition397149
+Node: Cholesky Decomposition401565
+Node: Pivoted Cholesky Decomposition408281
+Node: Modified Cholesky Decomposition413578
+Node: Tridiagonal Decomposition of Real Symmetric Matrices417083
+Node: Tridiagonal Decomposition of Hermitian Matrices418940
+Node: Hessenberg Decomposition of Real Matrices420894
+Node: Hessenberg-Triangular Decomposition of Real Matrices423308
+Node: Bidiagonalization424433
+Node: Givens Rotations426847
+Node: Householder Transformations428178
+Node: Householder solver for linear systems430799
+Node: Tridiagonal Systems431706
+Node: Triangular Systems434588
+Node: Balancing436002
+Node: Linear Algebra Examples436804
+Node: Linear Algebra References and Further Reading438798
+Node: Eigensystems440762
+Node: Real Symmetric Matrices441991
+Node: Complex Hermitian Matrices444505
+Node: Real Nonsymmetric Matrices447134
+Node: Real Generalized Symmetric-Definite Eigensystems452869
+Node: Complex Generalized Hermitian-Definite Eigensystems455748
+Node: Real Generalized Nonsymmetric Eigensystems458462
+Node: Sorting Eigenvalues and Eigenvectors465069
+Node: Eigenvalue and Eigenvector Examples468347
+Node: Eigenvalue and Eigenvector References473738
+Node: Fast Fourier Transforms474765
+Node: Mathematical Definitions475991
+Node: Overview of complex data FFTs478396
+Node: Radix-2 FFT routines for complex data481341
+Node: Mixed-radix FFT routines for complex data485560
+Node: Overview of real data FFTs494900
+Node: Radix-2 FFT routines for real data497335
+Node: Mixed-radix FFT routines for real data501759
+Node: FFT References and Further Reading512444
+Node: Numerical Integration515314
+Node: Numerical Integration Introduction517112
+Node: Integrands without weight functions519387
+Node: Integrands with weight functions520217
+Node: Integrands with singular weight functions520928
+Node: QNG non-adaptive Gauss-Kronrod integration521846
+Node: QAG adaptive integration523128
+Node: QAGS adaptive integration with singularities525917
+Node: QAGP adaptive integration with known singular points527717
+Node: QAGI adaptive integration on infinite intervals529031
+Node: QAWC adaptive integration for Cauchy principal values531311
+Node: QAWS adaptive integration for singular functions532481
+Node: QAWO adaptive integration for oscillatory functions535707
+Node: QAWF adaptive integration for Fourier integrals539495
+Node: CQUAD doubly-adaptive integration542119
+Node: Fixed order Gauss-Legendre integration545377
+Node: Numerical integration error codes547365
+Node: Numerical integration examples548121
+Node: Numerical integration References and Further Reading550178
+Node: Random Number Generation551169
+Node: General comments on random numbers552703
+Node: The Random Number Generator Interface554655
+Node: Random number generator initialization556013
+Node: Sampling from a random number generator558384
+Node: Auxiliary random number generator functions561628
+Node: Random number environment variables563948
+Node: Copying random number generator state566473
+Node: Reading and writing random number generator state567447
+Node: Random number generator algorithms568841
+Node: Unix random number generators578783
+Node: Other random number generators582497
+Node: Random Number Generator Performance591148
+Node: Random Number Generator Examples592269
+Node: Random Number References and Further Reading593781
+Node: Random Number Acknowledgements595076
+Node: Quasi-Random Sequences595562
+Node: Quasi-random number generator initialization596682
+Node: Sampling from a quasi-random number generator597697
+Node: Auxiliary quasi-random number generator functions598394
+Node: Saving and restoring quasi-random number generator state599340
+Node: Quasi-random number generator algorithms601121
+Node: Quasi-random number generator examples602259
+Node: Quasi-random number references603244
+Node: Random Number Distributions603770
+Node: Random Number Distribution Introduction607146
+Node: The Gaussian Distribution608941
+Node: The Gaussian Tail Distribution611601
+Node: The Bivariate Gaussian Distribution613265
+Node: The Multivariate Gaussian Distribution614589
+Node: The Exponential Distribution617437
+Node: The Laplace Distribution618579
+Node: The Exponential Power Distribution619671
+Node: The Cauchy Distribution620939
+Node: The Rayleigh Distribution622188
+Node: The Rayleigh Tail Distribution623362
+Node: The Landau Distribution624235
+Node: The Levy alpha-Stable Distributions625190
+Node: The Levy skew alpha-Stable Distribution626248
+Node: The Gamma Distribution627860
+Node: The Flat (Uniform) Distribution629515
+Node: The Lognormal Distribution630663
+Node: The Chi-squared Distribution632011
+Node: The F-distribution633416
+Node: The t-distribution635053
+Node: The Beta Distribution636447
+Node: The Logistic Distribution637606
+Node: The Pareto Distribution638735
+Node: Spherical Vector Distributions639905
+Node: The Weibull Distribution642741
+Node: The Type-1 Gumbel Distribution643935
+Node: The Type-2 Gumbel Distribution645171
+Node: The Dirichlet Distribution646402
+Node: General Discrete Distributions648070
+Node: The Poisson Distribution651938
+Node: The Bernoulli Distribution652945
+Node: The Binomial Distribution653696
+Node: The Multinomial Distribution654899
+Node: The Negative Binomial Distribution656673
+Node: The Pascal Distribution658038
+Node: The Geometric Distribution659196
+Node: The Hypergeometric Distribution660444
+Node: The Logarithmic Distribution662097
+Node: Shuffling and Sampling662889
+Node: Random Number Distribution Examples665701
+Node: Random Number Distribution References and Further Reading668875
+Node: Statistics671019
+Node: Mean and standard deviation and variance672513
+Node: Absolute deviation676021
+Node: Higher moments (skewness and kurtosis)677313
+Node: Autocorrelation679446
+Node: Covariance680259
+Node: Correlation681225
+Node: Weighted Samples682594
+Node: Maximum and Minimum values688444
+Node: Median and Percentiles691183
+Node: Example statistical programs693598
+Node: Statistics References and Further Reading696259
+Node: Running Statistics697467
+Node: Running Statistics Initializing the Accumulator698769
+Node: Running Statistics Adding Data to the Accumulator699481
+Node: Running Statistics Current Statistics700170
+Node: Running Statistics Quantiles702301
+Node: Running Statistics Example programs703901
+Node: Running Statistics References and Further Reading709451
+Node: Histograms709984
+Node: The histogram struct711845
+Node: Histogram allocation713649
+Node: Copying Histograms716606
+Node: Updating and accessing histogram elements717282
+Node: Searching histogram ranges720551
+Node: Histogram Statistics721551
+Node: Histogram Operations723417
+Node: Reading and writing histograms725492
+Node: Resampling from histograms728534
+Node: The histogram probability distribution struct729333
+Node: Example programs for histograms732367
+Node: Two dimensional histograms734430
+Node: The 2D histogram struct735151
+Node: 2D Histogram allocation736961
+Node: Copying 2D Histograms739035
+Node: Updating and accessing 2D histogram elements739740
+Node: Searching 2D histogram ranges743397
+Node: 2D Histogram Statistics744411
+Node: 2D Histogram Operations747276
+Node: Reading and writing 2D histograms749454
+Node: Resampling from 2D histograms753083
+Node: Example programs for 2D histograms756104
+Node: N-tuples757931
+Node: The ntuple struct759254
+Node: Creating ntuples759733
+Node: Opening an existing ntuple file760400
+Node: Writing ntuples761029
+Node: Reading ntuples761490
+Node: Closing an ntuple file761821
+Node: Histogramming ntuple values762161
+Node: Example ntuple programs764171
+Node: Ntuple References and Further Reading767560
+Node: Monte Carlo Integration767881
+Node: Monte Carlo Interface769192
+Node: PLAIN Monte Carlo771819
+Node: MISER774274
+Ref: MISER-Footnote-1780954
+Node: VEGAS781079
+Node: Monte Carlo Examples790640
+Node: Monte Carlo Integration References and Further Reading796708
+Node: Simulated Annealing797490
+Node: Simulated Annealing algorithm798706
+Node: Simulated Annealing functions799858
+Node: Examples with Simulated Annealing804388
+Node: Trivial example804957
+Node: Traveling Salesman Problem807590
+Node: Simulated Annealing References and Further Reading810903
+Node: Ordinary Differential Equations811314
+Node: Defining the ODE System812554
+Node: Stepping Functions815566
+Node: Adaptive Step-size Control822536
+Node: Evolution828613
+Node: Driver832742
+Node: ODE Example programs836976
+Node: ODE References and Further Reading842132
+Node: Interpolation843896
+Node: 1D Introduction to Interpolation845470
+Node: 1D Interpolation Functions845957
+Node: 1D Interpolation Types847179
+Node: 1D Index Look-up and Acceleration850438
+Node: 1D Evaluation of Interpolating Functions852505
+Node: 1D Higher-level Interface855016
+Node: 1D Interpolation Example programs857071
+Node: 1D Interpolation References and Further Reading862627
+Node: 2D Introduction to Interpolation863382
+Node: 2D Interpolation Functions863930
+Node: 2D Interpolation Grids865461
+Node: 2D Interpolation Types866680
+Node: 2D Evaluation of Interpolating Functions867945
+Node: 2D Higher-level Interface874052
+Node: 2D Interpolation Example programs877796
+Node: Numerical Differentiation879978
+Node: Numerical Differentiation functions880573
+Node: Numerical Differentiation Examples883430
+Node: Numerical Differentiation References884903
+Node: Chebyshev Approximations885454
+Node: Chebyshev Definitions886535
+Node: Creation and Calculation of Chebyshev Series887324
+Node: Auxiliary Functions for Chebyshev Series888309
+Node: Chebyshev Series Evaluation889049
+Node: Derivatives and Integrals890429
+Node: Chebyshev Approximation Examples891667
+Node: Chebyshev Approximation References and Further Reading893219
+Node: Series Acceleration893669
+Node: Acceleration functions894446
+Node: Acceleration functions without error estimation896773
+Node: Example of accelerating a series899397
+Node: Series Acceleration References902718
+Node: Wavelet Transforms903606
+Node: DWT Definitions904205
+Node: DWT Initialization905157
+Node: DWT Transform Functions907805
+Node: DWT in one dimension908356
+Node: DWT in two dimension910377
+Node: DWT Examples914956
+Node: DWT References916831
+Node: Discrete Hankel Transforms918995
+Node: Discrete Hankel Transform Definition919469
+Node: Discrete Hankel Transform Functions922780
+Node: Discrete Hankel Transform References924445
+Node: One dimensional Root-Finding924849
+Node: Root Finding Overview926155
+Node: Root Finding Caveats928011
+Node: Initializing the Solver929780
+Node: Providing the function to solve932413
+Node: Search Bounds and Guesses935967
+Node: Root Finding Iteration936830
+Node: Search Stopping Parameters938681
+Node: Root Bracketing Algorithms941192
+Node: Root Finding Algorithms using Derivatives944490
+Ref: Root Finding Algorithms using Derivatives-Footnote-1948033
+Node: Root Finding Examples948189
+Node: Root Finding References and Further Reading955453
+Node: One dimensional Minimization956092
+Node: Minimization Overview957435
+Node: Minimization Caveats959142
+Node: Initializing the Minimizer960480
+Node: Providing the function to minimize962721
+Node: Minimization Iteration963199
+Node: Minimization Stopping Parameters965337
+Node: Minimization Algorithms966942
+Node: Minimization Examples969536
+Node: Minimization References and Further Reading972287
+Node: Multidimensional Root-Finding972743
+Node: Overview of Multidimensional Root Finding974251
+Node: Initializing the Multidimensional Solver976438
+Node: Providing the multidimensional system of equations to solve979668
+Node: Iteration of the multidimensional solver984580
+Node: Search Stopping Parameters for the multidimensional solver986861
+Node: Algorithms using Derivatives988599
+Node: Algorithms without Derivatives993424
+Node: Example programs for Multidimensional Root finding996514
+Node: References and Further Reading for Multidimensional Root Finding1005138
+Node: Multidimensional Minimization1006377
+Node: Multimin Overview1007787
+Node: Multimin Caveats1009867
+Node: Initializing the Multidimensional Minimizer1010616
+Node: Providing a function to minimize1013850
+Node: Multimin Iteration1017911
+Node: Multimin Stopping Criteria1020255
+Node: Multimin Algorithms with Derivatives1021826
+Node: Multimin Algorithms without Derivatives1025357
+Node: Multimin Examples1028359
+Node: Multimin References and Further Reading1034929
+Node: Least-Squares Fitting1035793
+Node: Fitting Overview1036825
+Node: Linear regression1039158
+Node: Linear regression with a constant term1039601
+Node: Linear regression without a constant term1042244
+Node: Multi-parameter regression1044436
+Node: Regularized regression1052576
+Node: Robust linear regression1071950
+Node: Large Dense Linear Systems1084161
+Node: Large Dense Linear Systems Normal Equations1086384
+Node: Large Dense Linear Systems TSQR1087977
+Node: Large Dense Linear Systems Solution Steps1089622
+Node: Large Dense Linear Systems Routines1090764
+Node: Troubleshooting1099087
+Node: Fitting Examples1099712
+Node: Fitting linear regression example1100268
+Node: Fitting multi-parameter linear regression example1102470
+Node: Fitting regularized linear regression example 11107464
+Node: Fitting regularized linear regression example 21115049
+Node: Fitting robust linear regression example1121969
+Node: Fitting large linear systems example1125926
+Node: Fitting References and Further Reading1133145
+Node: Nonlinear Least-Squares Fitting1135426
+Node: Nonlinear Least-Squares Overview1137383
+Node: Nonlinear Least-Squares TRS Overview1141784
+Node: Nonlinear Least-Squares TRS Levenberg-Marquardt1143918
+Node: Nonlinear Least-Squares TRS Levenberg-Marquardt with Geodesic Acceleration1145525
+Node: Nonlinear Least-Squares TRS Dogleg1147279
+Node: Nonlinear Least-Squares TRS Double Dogleg1148749
+Node: Nonlinear Least-Squares TRS 2D Subspace1149547
+Node: Nonlinear Least-Squares TRS Steihaug-Toint Conjugate Gradient1150519
+Node: Nonlinear Least-Squares Weighted Overview1151263
+Node: Nonlinear Least-Squares Tunable Parameters1152481
+Node: Nonlinear Least-Squares Initialization1164018
+Node: Nonlinear Least-Squares Function Definition1168948
+Node: Nonlinear Least-Squares Iteration1176030
+Node: Nonlinear Least-Squares Testing for Convergence1180568
+Node: Nonlinear Least-Squares High Level Driver1183464
+Node: Nonlinear Least-Squares Covariance Matrix1185684
+Node: Nonlinear Least-Squares Troubleshooting1187892
+Node: Nonlinear Least-Squares Examples1189916
+Node: Nonlinear Least-Squares Exponential Fit Example1190462
+Node: Nonlinear Least-Squares Geodesic Acceleration Example1201856
+Node: Nonlinear Least-Squares Comparison Example1209181
+Node: Nonlinear Least-Squares Large Example1217943
+Node: Nonlinear Least-Squares References and Further Reading1226889
+Node: Basis Splines1228483
+Node: Overview of B-splines1229368
+Node: Initializing the B-splines solver1230684
+Node: Constructing the knots vector1231549
+Node: Evaluation of B-spline basis functions1232337
+Node: Evaluation of B-spline basis function derivatives1233985
+Node: Working with the Greville abscissae1235867
+Node: Example programs for B-splines1236861
+Node: B-Spline References and Further Reading1240865
+Node: Sparse Matrices1241698
+Node: Sparse Matrices Overview1243024
+Node: Sparse Matrices Allocation1246235
+Node: Sparse Matrices Accessing Elements1249246
+Node: Sparse Matrices Initializing Elements1250209
+Node: Sparse Matrices Reading and Writing1250844
+Node: Sparse Matrices Copying1253066
+Node: Sparse Matrices Exchanging Rows and Columns1253548
+Node: Sparse Matrices Operations1254943
+Node: Sparse Matrices Properties1255623
+Node: Sparse Matrices Finding Maximum and Minimum Elements1256275
+Node: Sparse Matrices Compressed Format1256818
+Node: Sparse Matrices Conversion Between Sparse and Dense1257897
+Node: Sparse Matrices Examples1258719
+Node: Sparse Matrices References and Further Reading1262365
+Node: Sparse BLAS Support1262813
+Node: Sparse BLAS operations1263444
+Node: Sparse BLAS References and Further Reading1264398
+Node: Sparse Linear Algebra1264842
+Node: Overview of Sparse Linear Algebra1265469
+Node: Sparse Iterative Solvers1266221
+Node: Sparse Iterative Solver Overview1266567
+Node: Sparse Iterative Solvers Types1267417
+Node: Iterating the Sparse Linear System1269521
+Node: Sparse Linear Algebra Examples1271991
+Node: Sparse Linear Algebra References and Further Reading1276456
+Node: Physical Constants1276989
+Node: Fundamental Constants1278576
+Node: Astronomy and Astrophysics1279716
+Node: Atomic and Nuclear Physics1280381
+Node: Measurement of Time1282032
+Node: Imperial Units1282462
+Node: Speed and Nautical Units1282904
+Node: Printers Units1283408
+Node: Volume Area and Length1283731
+Node: Mass and Weight1284417
+Node: Thermal Energy and Power1285236
+Node: Pressure1285659
+Node: Viscosity1286272
+Node: Light and Illumination1286548
+Node: Radioactivity1287140
+Node: Force and Energy1287475
+Node: Prefixes1287879
+Node: Physical Constant Examples1288622
+Node: Physical Constant References and Further Reading1290411
+Node: IEEE floating-point arithmetic1291141
+Node: Representation of floating point numbers1291733
+Node: Setting up your IEEE environment1296219
+Node: IEEE References and Further Reading1303192
+Node: Debugging Numerical Programs1304352
+Node: Using gdb1304869
+Node: Examining floating point registers1308212
+Node: Handling floating point exceptions1309497
+Node: GCC warning options for numerical programs1310909
+Node: Debugging References1314857
+Node: Contributors to GSL1315569
+Node: Autoconf Macros1320080
+Node: GSL CBLAS Library1324112
+Node: Level 1 CBLAS Functions1324652
+Node: Level 2 CBLAS Functions1329954
+Node: Level 3 CBLAS Functions1346584
+Node: GSL CBLAS Examples1356246
+Node: GNU General Public License1357809
+Node: GNU Free Documentation License1395383
+Node: Function Index1420532
+Node: Variable Index1705030
+Node: Type Index1713866
+Node: Concept Index1729090
 
 End Tag Table
diff -Nru gsl-doc-1.16/doc/gsl-ref.info-1 gsl-doc-2.3/doc/gsl-ref.info-1
--- gsl-doc-1.16/doc/gsl-ref.info-1	2013-07-19 15:17:32.000000000 +0000
+++ gsl-doc-2.3/doc/gsl-ref.info-1	2016-12-09 00:08:00.000000000 +0000
@@ -2,13 +2,20 @@
 gsl-ref.texi.
 
 Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,
-2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 The GSL Team.
+2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016
+The GSL Team.
 
    Permission is granted to copy, distribute and/or modify this document
 under the terms of the GNU Free Documentation License, Version 1.3 or
-any later version published by the Free Software Foundation; with no
-Invariant Sections and no cover texts.  A copy of the license is
-included in the section entitled "GNU Free Documentation License".
+any later version published by the Free Software Foundation; with the
+Invariant Sections being "GNU General Public License" and "Free Software
+Needs Free Documentation", the Front-Cover text being "A GNU Manual",
+and with the Back-Cover Text being (a) (see below).  A copy of the
+license is included in the section entitled "GNU Free Documentation
+License".
+
+   (a) The Back-Cover Text is: "You have the freedom to copy and modify
+this GNU Manual."
 INFO-DIR-SECTION Software libraries
 START-INFO-DIR-ENTRY
 * gsl-ref: (gsl-ref).                   GNU Scientific Library - Reference
@@ -22,7 +29,7 @@
 
 This file documents the GNU Scientific Library (GSL), a collection of
 numerical routines for scientific computing.  It corresponds to release
-1.16 of the library.  Please report any errors in this manual to
+2.3 of the library.  Please report any errors in this manual to
 <bug-gsl@gnu.org>.
 
    More information about GSL can be found at the project homepage,
@@ -36,13 +43,20 @@
 project homepage thanks to Daisuke Tominaga.
 
    Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,
-2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 The GSL Team.
+2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016
+The GSL Team.
 
    Permission is granted to copy, distribute and/or modify this document
 under the terms of the GNU Free Documentation License, Version 1.3 or
-any later version published by the Free Software Foundation; with no
-Invariant Sections and no cover texts.  A copy of the license is
-included in the section entitled "GNU Free Documentation License".
+any later version published by the Free Software Foundation; with the
+Invariant Sections being "GNU General Public License" and "Free Software
+Needs Free Documentation", the Front-Cover text being "A GNU Manual",
+and with the Back-Cover Text being (a) (see below).  A copy of the
+license is included in the section entitled "GNU Free Documentation
+License".
+
+   (a) The Back-Cover Text is: "You have the freedom to copy and modify
+this GNU Manual."
 
 * Menu:
 
@@ -67,6 +81,7 @@
 * Quasi-Random Sequences::      
 * Random Number Distributions::  
 * Statistics::                  
+* Running Statistics::                  
 * Histograms::                  
 * N-tuples::                    
 * Monte Carlo Integration::     
@@ -84,7 +99,10 @@
 * Multidimensional Minimization::  
 * Least-Squares Fitting::       
 * Nonlinear Least-Squares Fitting::  
-* Basis Splines::               
+* Basis Splines::
+* Sparse Matrices::
+* Sparse BLAS Support::
+* Sparse Linear Algebra::
 * Physical Constants::          
 * IEEE floating-point arithmetic::  
 * Debugging Numerical Programs::  
@@ -375,7 +393,7 @@
 The output is shown below, and should be correct to double-precision
 accuracy,(1)
 
-     J0(5) = -1.775967713143382920e-01
+     J0(5) = -1.775967713143382642e-01
 
 The steps needed to compile this program are described in the following
 sections.
@@ -2150,11 +2168,11 @@
 The output of the program is,
 
      $ ./a.out
-     z0 = -0.809016994374947451 +0.587785252292473137
-     z1 = -0.809016994374947451 -0.587785252292473137
-     z2 = +0.309016994374947451 +0.951056516295153642
-     z3 = +0.309016994374947451 -0.951056516295153642
-     z4 = +1.000000000000000000 +0.000000000000000000
+     z0 = -0.809016994374947673 +0.587785252292473359
+     z1 = -0.809016994374947673 -0.587785252292473359
+     z2 = +0.309016994374947507 +0.951056516295152976
+     z3 = +0.309016994374947507 -0.951056516295152976
+     z4 = +0.999999999999999889 +0.000000000000000000
 
 which agrees with the analytic result, z_n = \exp(2 \pi n i/5).
 
@@ -2783,7 +2801,7 @@
  -- Function: int gsl_sf_bessel_il_scaled_array (int LMAX, double X,
           double RESULT_ARRAY[])
      This routine computes the values of the scaled regular modified
-     cylindrical Bessel functions \exp(-|x|) i_l(x) for l from 0 to LMAX
+     spherical Bessel functions \exp(-|x|) i_l(x) for l from 0 to LMAX
      inclusive for lmax >= 0, storing the results in the array
      RESULT_ARRAY.  The values are computed using recurrence relations
      for efficiency, and therefore may differ slightly from the exact
@@ -3401,16 +3419,15 @@
      parameters m = k^2 and \sin^2(\alpha) = k^2, with the change of
      sign n \to -n.
 
- -- Function: double gsl_sf_ellint_D (double PHI, double K, double N,
-          gsl_mode_t MODE)
- -- Function: int gsl_sf_ellint_D_e (double PHI, double K, double N,
-          gsl_mode_t MODE, gsl_sf_result * RESULT)
+ -- Function: double gsl_sf_ellint_D (double PHI, double K, gsl_mode_t
+          MODE)
+ -- Function: int gsl_sf_ellint_D_e (double PHI, double K, gsl_mode_t
+          MODE, gsl_sf_result * RESULT)
      These functions compute the incomplete elliptic integral D(\phi,k)
      which is defined through the Carlson form RD(x,y,z) by the
      following relation,
 
-          D(\phi,k,n) = (1/3)(\sin(\phi))^3 RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1).
-     The argument N is not used and will be removed in a future release.
+          D(\phi,k) = (1/3)(\sin(\phi))^3 RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1).
 
 
 File: gsl-ref.info,  Node: Carlson Forms,  Prev: Legendre Form of Incomplete Elliptic Integrals,  Up: Elliptic Integrals
@@ -4356,16 +4373,168 @@
 7.24.2 Associated Legendre Polynomials and Spherical Harmonics
 --------------------------------------------------------------
 
-The following functions compute the associated Legendre Polynomials
-P_l^m(x).  Note that this function grows combinatorially with l and can
-overflow for l larger than about 150.  There is no trouble for small m,
-but overflow occurs when m and l are both large.  Rather than allow
-overflows, these functions refuse to calculate P_l^m(x) and return
-'GSL_EOVRFLW' when they can sense that l and m are too big.
-
-   If you want to calculate a spherical harmonic, then _do not_ use
-these functions.  Instead use 'gsl_sf_legendre_sphPlm' below, which uses
-a similar recursion, but with the normalized functions.
+The following functions compute the associated Legendre polynomials
+P_l^m(x) which are solutions of the differential equation
+
+     (1 - x^2) d^2 P_l^m(x) / dx^2 P_l^m(x) - 2x d/dx P_l^m(x) +
+     ( l(l+1) - m^2 / (1 - x^2) ) P_l^m(x) = 0
+
+   where the degree l and order m satisfy 0 \le l and 0 \le m \le l.
+The functions P_l^m(x) grow combinatorially with l and can overflow for
+l larger than about 150.  Alternatively, one may calculate normalized
+associated Legendre polynomials.  There are a number of different
+normalization conventions, and these functions can be stably computed up
+to degree and order 2700.  The following normalizations are provided:
+'Schmidt semi-normalization'
+     Schmidt semi-normalized associated Legendre polynomials are often
+     used in the magnetics community and are defined as
+          S_l^0(x) = P_l^0(x)
+          S_l^m(x) = (-1)^m \sqrt((2(l-m)! / (l+m)!)) P_l^m(x), m > 0
+     The factor of (-1)^m is called the Condon-Shortley phase factor and
+     can be excluded if desired by setting the parameter 'csphase = 1'
+     in the functions below.
+
+'Spherical Harmonic Normalization'
+     The associated Legendre polynomials suitable for calculating
+     spherical harmonics are defined as
+          Y_l^m(x) = (-1)^m \sqrt((2l + 1) * (l-m)! / (4 \pi) / (l+m)!) P_l^m(x)
+     where again the phase factor (-1)^m can be included or excluded if
+     desired.
+
+'Full Normalization'
+     The fully normalized associated Legendre polynomials are defined as
+          N_l^m(x) = (-1)^m \sqrt((l + 1/2) * (l-m)! / (l+m)!) P_l^m(x)
+     and have the property
+          \int_(-1)^1 ( N_l^m(x) )^2 dx = 1
+
+   The normalized associated Legendre routines below use a recurrence
+relation which is stable up to a degree and order of about 2700.  Beyond
+this, the computed functions could suffer from underflow leading to
+incorrect results.  Routines are provided to compute first and second
+derivatives dP_l^m(x)/dx and d^2 P_l^m(x)/dx^2 as well as their
+alternate versions d P_l^m(\cos{\theta})/d\theta and d^2
+P_l^m(\cos{\theta})/d\theta^2.  While there is a simple scaling
+relationship between the two forms, the derivatives involving \theta are
+heavily used in spherical harmonic expansions and so these routines are
+also provided.
+
+   In the functions below, a parameter of type 'gsl_sf_legendre_t'
+specifies the type of normalization to use.  The possible values are
+'GSL_SF_LEGENDRE_NONE'
+     This specifies the computation of the unnormalized associated
+     Legendre polynomials P_l^m(x).
+
+'GSL_SF_LEGENDRE_SCHMIDT'
+     This specifies the computation of the Schmidt semi-normalized
+     associated Legendre polynomials S_l^m(x).
+
+'GSL_SF_LEGENDRE_SPHARM'
+     This specifies the computation of the spherical harmonic associated
+     Legendre polynomials Y_l^m(x).
+
+'GSL_SF_LEGENDRE_FULL'
+     This specifies the computation of the fully normalized associated
+     Legendre polynomials N_l^m(x).
+
+ -- Function: int gsl_sf_legendre_array (const gsl_sf_legendre_t NORM,
+          const size_t LMAX, const double X, double RESULT_ARRAY[])
+ -- Function: int gsl_sf_legendre_array_e (const gsl_sf_legendre_t NORM,
+          const size_t LMAX, const double X, const double CSPHASE,
+          double RESULT_ARRAY[])
+     These functions calculate all normalized associated Legendre
+     polynomials for 0 \le l \le lmax and 0 \le m \le l for |x| <= 1.
+     The NORM parameter specifies which normalization is used.  The
+     normalized P_l^m(x) values are stored in RESULT_ARRAY, whose
+     minimum size can be obtained from calling
+     'gsl_sf_legendre_array_n'.  The array index of P_l^m(x) is obtained
+     from calling 'gsl_sf_legendre_array_index(l, m)'.  To include or
+     exclude the Condon-Shortley phase factor of (-1)^m, set the
+     parameter CSPHASE to either -1 or 1 respectively in the '_e'
+     function.  This factor is included by default.
+
+ -- Function: int gsl_sf_legendre_deriv_array (const gsl_sf_legendre_t
+          NORM, const size_t LMAX, const double X, double
+          RESULT_ARRAY[], double RESULT_DERIV_ARRAY[])
+ -- Function: int gsl_sf_legendre_deriv_array_e (const gsl_sf_legendre_t
+          NORM, const size_t LMAX, const double X, const double CSPHASE,
+          double RESULT_ARRAY[], double RESULT_DERIV_ARRAY[])
+     These functions calculate all normalized associated Legendre
+     functions and their first derivatives up to degree LMAX for |x| <
+     1.  The parameter NORM specifies the normalization used.  The
+     normalized P_l^m(x) values and their derivatives dP_l^m(x)/dx are
+     stored in RESULT_ARRAY and RESULT_DERIV_ARRAY respectively.  To
+     include or exclude the Condon-Shortley phase factor of (-1)^m, set
+     the parameter CSPHASE to either -1 or 1 respectively in the '_e'
+     function.  This factor is included by default.
+
+ -- Function: int gsl_sf_legendre_deriv_alt_array (const
+          gsl_sf_legendre_t NORM, const size_t LMAX, const double X,
+          double RESULT_ARRAY[], double RESULT_DERIV_ARRAY[])
+ -- Function: int gsl_sf_legendre_deriv_alt_array_e (const
+          gsl_sf_legendre_t NORM, const size_t LMAX, const double X,
+          const double CSPHASE, double RESULT_ARRAY[], double
+          RESULT_DERIV_ARRAY[])
+     These functions calculate all normalized associated Legendre
+     functions and their (alternate) first derivatives up to degree LMAX
+     for |x| < 1.  The normalized P_l^m(x) values and their derivatives
+     dP_l^m(\cos{\theta})/d\theta are stored in RESULT_ARRAY and
+     RESULT_DERIV_ARRAY respectively.  To include or exclude the
+     Condon-Shortley phase factor of (-1)^m, set the parameter CSPHASE
+     to either -1 or 1 respectively in the '_e' function.  This factor
+     is included by default.
+
+ -- Function: int gsl_sf_legendre_deriv2_array (const gsl_sf_legendre_t
+          NORM, const size_t LMAX, const double X, double
+          RESULT_ARRAY[], double RESULT_DERIV_ARRAY[], double
+          RESULT_DERIV2_ARRAY[])
+ -- Function: int gsl_sf_legendre_deriv2_array_e (const
+          gsl_sf_legendre_t NORM, const size_t LMAX, const double X,
+          const double CSPHASE, double RESULT_ARRAY[], double
+          RESULT_DERIV_ARRAY[], double RESULT_DERIV2_ARRAY[])
+     These functions calculate all normalized associated Legendre
+     functions and their first and second derivatives up to degree LMAX
+     for |x| < 1.  The parameter NORM specifies the normalization used.
+     The normalized P_l^m(x), their first derivatives dP_l^m(x)/dx, and
+     their second derivatives d^2 P_l^m(x)/dx^2 are stored in
+     RESULT_ARRAY, RESULT_DERIV_ARRAY, and RESULT_DERIV2_ARRAY
+     respectively.  To include or exclude the Condon-Shortley phase
+     factor of (-1)^m, set the parameter CSPHASE to either -1 or 1
+     respectively in the '_e' function.  This factor is included by
+     default.
+
+ -- Function: int gsl_sf_legendre_deriv2_alt_array (const
+          gsl_sf_legendre_t NORM, const size_t LMAX, const double X,
+          double RESULT_ARRAY[], double RESULT_DERIV_ARRAY[], double
+          RESULT_DERIV2_ARRAY[])
+ -- Function: int gsl_sf_legendre_deriv2_alt_array_e (const
+          gsl_sf_legendre_t NORM, const size_t LMAX, const double X,
+          const double CSPHASE, double RESULT_ARRAY[], double
+          RESULT_DERIV_ARRAY[], double RESULT_DERIV2_ARRAY[])
+     These functions calculate all normalized associated Legendre
+     functions and their (alternate) first and second derivatives up to
+     degree LMAX for |x| < 1.  The parameter NORM specifies the
+     normalization used.  The normalized P_l^m(x), their first
+     derivatives dP_l^m(\cos{\theta})/d\theta, and their second
+     derivatives d^2 P_l^m(\cos{\theta})/d\theta^2 are stored in
+     RESULT_ARRAY, RESULT_DERIV_ARRAY, and RESULT_DERIV2_ARRAY
+     respectively.  To include or exclude the Condon-Shortley phase
+     factor of (-1)^m, set the parameter CSPHASE to either -1 or 1
+     respectively in the '_e' function.  This factor is included by
+     default.
+
+ -- Function: size_t gsl_sf_legendre_array_n (const size_t LMAX)
+     This function returns the minimum array size for maximum degree
+     LMAX needed for the array versions of the associated Legendre
+     functions.  Size is calculated as the total number of P_l^m(x)
+     functions, plus extra space for precomputing multiplicative factors
+     used in the recurrence relations.
+
+ -- Function: size_t gsl_sf_legendre_array_index (const size_t L, const
+          size_t M)
+     This function returns the index into RESULT_ARRAY,
+     RESULT_DERIV_ARRAY, or RESULT_DERIV2_ARRAY corresponding to
+     P_l^m(x), P_l^{'m}(x), or P_l^{''m}(x).  The index is given by
+     l(l+1)/2 + m.
 
  -- Function: double gsl_sf_legendre_Plm (int L, int M, double X)
  -- Function: int gsl_sf_legendre_Plm_e (int L, int M, double X,
@@ -4373,13 +4542,6 @@
      These routines compute the associated Legendre polynomial P_l^m(x)
      for m >= 0, l >= m, |x| <= 1.
 
- -- Function: int gsl_sf_legendre_Plm_array (int LMAX, int M, double X,
-          double RESULT_ARRAY[])
- -- Function: int gsl_sf_legendre_Plm_deriv_array (int LMAX, int M,
-          double X, double RESULT_ARRAY[], double RESULT_DERIV_ARRAY[])
-     These functions compute arrays of Legendre polynomials P_l^m(x) and
-     derivatives dP_l^m(x)/dx, for m >= 0, l = |m|, ..., lmax, |x| <= 1.
-
  -- Function: double gsl_sf_legendre_sphPlm (int L, int M, double X)
  -- Function: int gsl_sf_legendre_sphPlm_e (int L, int M, double X,
           gsl_sf_result * RESULT)
@@ -4389,19 +4551,26 @@
      satisfy m >= 0, l >= m, |x| <= 1.  Theses routines avoid the
      overflows that occur for the standard normalization of P_l^m(x).
 
+ -- Function: int gsl_sf_legendre_Plm_array (int LMAX, int M, double X,
+          double RESULT_ARRAY[])
+ -- Function: int gsl_sf_legendre_Plm_deriv_array (int LMAX, int M,
+          double X, double RESULT_ARRAY[], double RESULT_DERIV_ARRAY[])
+     These functions are now deprecated and will be removed in a future
+     release; see 'gsl_sf_legendre_array' and
+     'gsl_sf_legendre_deriv_array'.
+
  -- Function: int gsl_sf_legendre_sphPlm_array (int LMAX, int M, double
           X, double RESULT_ARRAY[])
  -- Function: int gsl_sf_legendre_sphPlm_deriv_array (int LMAX, int M,
           double X, double RESULT_ARRAY[], double RESULT_DERIV_ARRAY[])
-     These functions compute arrays of normalized associated Legendre
-     functions \sqrt{(2l+1)/(4\pi)} \sqrt{(l-m)!/(l+m)!} P_l^m(x), and
-     derivatives, for m >= 0, l = |m|, ..., lmax, |x| <= 1.0
+     These functions are now deprecated and will be removed in a future
+     release; see 'gsl_sf_legendre_array' and
+     'gsl_sf_legendre_deriv_array'.
 
  -- Function: int gsl_sf_legendre_array_size (const int LMAX, const int
           M)
-     This function returns the size of RESULT_ARRAY[] needed for the
-     array versions of P_l^m(x), LMAX - M + 1.  An inline version of
-     this function is used when 'HAVE_INLINE' is defined.
+     This function is now deprecated and will be removed in a future
+     release.
 
 
 File: gsl-ref.info,  Node: Conical Functions,  Next: Radial Functions for Hyperbolic Space,  Prev: Associated Legendre Polynomials and Spherical Harmonics,  Up: Legendre Functions and Spherical Harmonics
@@ -4592,9 +4761,11 @@
 7.26.2 Mathieu Function Characteristic Values
 ---------------------------------------------
 
- -- Function: int gsl_sf_mathieu_a (int N, double Q, gsl_sf_result *
+ -- Function: int gsl_sf_mathieu_a (int N, double Q)
+ -- Function: int gsl_sf_mathieu_a_e (int N, double Q, gsl_sf_result *
           RESULT)
- -- Function: int gsl_sf_mathieu_b (int N, double Q, gsl_sf_result *
+ -- Function: int gsl_sf_mathieu_b (int N, double Q)
+ -- Function: int gsl_sf_mathieu_b_e (int N, double Q, gsl_sf_result *
           RESULT)
      These routines compute the characteristic values a_n(q), b_n(q) of
      the Mathieu functions ce_n(q,x) and se_n(q,x), respectively.
@@ -4615,9 +4786,11 @@
 7.26.3 Angular Mathieu Functions
 --------------------------------
 
- -- Function: int gsl_sf_mathieu_ce (int N, double Q, double X,
+ -- Function: int gsl_sf_mathieu_ce (int N, double Q, double X)
+ -- Function: int gsl_sf_mathieu_ce_e (int N, double Q, double X,
           gsl_sf_result * RESULT)
- -- Function: int gsl_sf_mathieu_se (int N, double Q, double X,
+ -- Function: int gsl_sf_mathieu_se (int N, double Q, double X)
+ -- Function: int gsl_sf_mathieu_se_e (int N, double Q, double X,
           gsl_sf_result * RESULT)
      These routines compute the angular Mathieu functions ce_n(q,x) and
      se_n(q,x), respectively.
@@ -4638,9 +4811,11 @@
 7.26.4 Radial Mathieu Functions
 -------------------------------
 
- -- Function: int gsl_sf_mathieu_Mc (int J, int N, double Q, double X,
+ -- Function: int gsl_sf_mathieu_Mc (int J, int N, double Q, double X)
+ -- Function: int gsl_sf_mathieu_Mc_e (int J, int N, double Q, double X,
           gsl_sf_result * RESULT)
- -- Function: int gsl_sf_mathieu_Ms (int J, int N, double Q, double X,
+ -- Function: int gsl_sf_mathieu_Ms (int J, int N, double Q, double X)
+ -- Function: int gsl_sf_mathieu_Ms_e (int J, int N, double Q, double X,
           gsl_sf_result * RESULT)
      These routines compute the radial J-th kind Mathieu functions
      Mc_n^{(j)}(q,x) and Ms_n^{(j)}(q,x) of order N.
@@ -5062,7 +5237,7 @@
 
      $ ./a.out
      status  = success
-     J0(5.0) = -0.177596771314338292
+     J0(5.0) = -0.177596771314338264
            +/-  0.000000000000000193
      exact   = -0.177596771314338292
 
@@ -5089,7 +5264,7 @@
 The results of the function are the same,
 
      $ ./a.out
-     J0(5.0) = -0.177596771314338292
+     J0(5.0) = -0.177596771314338264
      exact   = -0.177596771314338292
 
 
@@ -5125,6 +5300,11 @@
      Y.Y. Luke, Algorithms for the Computation of Mathematical
      Functions, Academic Press, New York (1977).
 
+     S. A. Holmes and W. E. Featherstone, A unified approach to the
+     Clenshaw summation and the recursive computation of very high
+     degree and order normalised associated Legendre functions, Journal
+     of Geodesy, 76, pg.  279-299, 2002.
+
 
 File: gsl-ref.info,  Node: Vectors and Matrices,  Next: Permutations,  Prev: Special Functions,  Up: Top
 
@@ -5296,8 +5476,8 @@
      {
        gsl_block * b = gsl_block_alloc (100);
 
-       printf ("length of block = %u\n", b->size);
-       printf ("block data address = %#x\n", b->data);
+       printf ("length of block = %zu\n", b->size);
+       printf ("block data address = %p\n", b->data);
 
        gsl_block_free (b);
        return 0;
@@ -5433,13 +5613,15 @@
 'gsl_check_range' to zero.  Due to function-call overhead, there is less
 benefit in disabling range checking here than for inline functions.
 
- -- Function: double gsl_vector_get (const gsl_vector * V, size_t I)
+ -- Function: double gsl_vector_get (const gsl_vector * V, const size_t
+          I)
      This function returns the I-th element of a vector V.  If I lies
      outside the allowed range of 0 to N-1 then the error handler is
      invoked and 0 is returned.  An inline version of this function is
      used when 'HAVE_INLINE' is defined.
 
- -- Function: void gsl_vector_set (gsl_vector * V, size_t I, double X)
+ -- Function: void gsl_vector_set (gsl_vector * V, const size_t I,
+          double X)
      This function sets the value of the I-th element of a vector V to
      X.  If I lies outside the allowed range of 0 to N-1 then the error
      handler is invoked.  An inline version of this function is used
@@ -6042,15 +6224,15 @@
 
 where TDA is the physical row-length of the matrix.
 
- -- Function: double gsl_matrix_get (const gsl_matrix * M, size_t I,
-          size_t J)
+ -- Function: double gsl_matrix_get (const gsl_matrix * M, const size_t
+          I, const size_t J)
      This function returns the (i,j)-th element of a matrix M.  If I or
      J lie outside the allowed range of 0 to N1-1 and 0 to N2-1 then the
      error handler is invoked and 0 is returned.  An inline version of
      this function is used when 'HAVE_INLINE' is defined.
 
- -- Function: void gsl_matrix_set (gsl_matrix * M, size_t I, size_t J,
-          double X)
+ -- Function: void gsl_matrix_set (gsl_matrix * M, const size_t I, const
+          size_t J, double X)
      This function sets the value of the (i,j)-th element of a matrix M
      to X.  If I or J lies outside the allowed range of 0 to N1-1 and 0
      to N2-1 then the error handler is invoked.  An inline version of
@@ -6694,7 +6876,7 @@
 
            d = gsl_blas_dnrm2 (&column.vector);
 
-           printf ("matrix column %d, norm = %g\n", j, d);
+           printf ("matrix column %zu, norm = %g\n", j, d);
          }
 
        gsl_matrix_free (m);
@@ -6925,6 +7107,15 @@
      column of the identity matrix.  The permutation P and the vector V
      must have the same length.
 
+ -- Function: int gsl_permute_matrix (const gsl_permutation * P,
+          gsl_matrix * A)
+     This function applies the permutation P to the matrix A from the
+     right, A' = A P.  The j-th column of the permutation matrix P is
+     given by the P_j-th column of the identity matrix.  This
+     effectively permutes the columns of A according to the permutation
+     P, and so the number of columns of A must equal the size of the
+     permutation P.
+
  -- Function: int gsl_permutation_mul (gsl_permutation * P, const
           gsl_permutation * PA, const gsl_permutation * PB)
      This function combines the two permutations PA and PB into a single
@@ -7052,262 +7243,3 @@
      This function counts the number of cycles in the permutation Q,
      given in canonical form.
 
-
-File: gsl-ref.info,  Node: Permutation Examples,  Next: Permutation References and Further Reading,  Prev: Permutations in cyclic form,  Up: Permutations
-
-9.9 Examples
-============
-
-The example program below creates a random permutation (by shuffling the
-elements of the identity) and finds its inverse.
-
-     #include <stdio.h>
-     #include <gsl/gsl_rng.h>
-     #include <gsl/gsl_randist.h>
-     #include <gsl/gsl_permutation.h>
-
-     int
-     main (void)
-     {
-       const size_t N = 10;
-       const gsl_rng_type * T;
-       gsl_rng * r;
-
-       gsl_permutation * p = gsl_permutation_alloc (N);
-       gsl_permutation * q = gsl_permutation_alloc (N);
-
-       gsl_rng_env_setup();
-       T = gsl_rng_default;
-       r = gsl_rng_alloc (T);
-
-       printf ("initial permutation:");
-       gsl_permutation_init (p);
-       gsl_permutation_fprintf (stdout, p, " %u");
-       printf ("\n");
-
-       printf (" random permutation:");
-       gsl_ran_shuffle (r, p->data, N, sizeof(size_t));
-       gsl_permutation_fprintf (stdout, p, " %u");
-       printf ("\n");
-
-       printf ("inverse permutation:");
-       gsl_permutation_inverse (q, p);
-       gsl_permutation_fprintf (stdout, q, " %u");
-       printf ("\n");
-
-       gsl_permutation_free (p);
-       gsl_permutation_free (q);
-       gsl_rng_free (r);
-
-       return 0;
-     }
-
-Here is the output from the program,
-
-     $ ./a.out
-     initial permutation: 0 1 2 3 4 5 6 7 8 9
-      random permutation: 1 3 5 2 7 6 0 4 9 8
-     inverse permutation: 6 0 3 1 7 2 5 4 9 8
-
-The random permutation 'p[i]' and its inverse 'q[i]' are related through
-the identity 'p[q[i]] = i', which can be verified from the output.
-
-   The next example program steps forwards through all possible third
-order permutations, starting from the identity,
-
-     #include <stdio.h>
-     #include <gsl/gsl_permutation.h>
-
-     int
-     main (void)
-     {
-       gsl_permutation * p = gsl_permutation_alloc (3);
-
-       gsl_permutation_init (p);
-
-       do
-        {
-           gsl_permutation_fprintf (stdout, p, " %u");
-           printf ("\n");
-        }
-       while (gsl_permutation_next(p) == GSL_SUCCESS);
-
-       gsl_permutation_free (p);
-
-       return 0;
-     }
-
-Here is the output from the program,
-
-     $ ./a.out
-      0 1 2
-      0 2 1
-      1 0 2
-      1 2 0
-      2 0 1
-      2 1 0
-
-The permutations are generated in lexicographic order.  To reverse the
-sequence, begin with the final permutation (which is the reverse of the
-identity) and replace 'gsl_permutation_next' with
-'gsl_permutation_prev'.
-
-
-File: gsl-ref.info,  Node: Permutation References and Further Reading,  Prev: Permutation Examples,  Up: Permutations
-
-9.10 References and Further Reading
-===================================
-
-The subject of permutations is covered extensively in Knuth's 'Sorting
-and Searching',
-
-     Donald E. Knuth, 'The Art of Computer Programming: Sorting and
-     Searching' (Vol 3, 3rd Ed, 1997), Addison-Wesley, ISBN 0201896850.
-
-For the definition of the "canonical form" see,
-
-     Donald E. Knuth, 'The Art of Computer Programming: Fundamental
-     Algorithms' (Vol 1, 3rd Ed, 1997), Addison-Wesley, ISBN 0201896850.
-     Section 1.3.3, 'An Unusual Correspondence', p.178-179.
-
-
-File: gsl-ref.info,  Node: Combinations,  Next: Multisets,  Prev: Permutations,  Up: Top
-
-10 Combinations
-***************
-
-This chapter describes functions for creating and manipulating
-combinations.  A combination c is represented by an array of k integers
-in the range 0 to n-1, where each value c_i occurs at most once.  The
-combination c corresponds to indices of k elements chosen from an n
-element vector.  Combinations are useful for iterating over all
-k-element subsets of a set.
-
-   The functions described in this chapter are defined in the header
-file 'gsl_combination.h'.
-
-* Menu:
-
-* The Combination struct::      
-* Combination allocation::      
-* Accessing combination elements::  
-* Combination properties::      
-* Combination functions::       
-* Reading and writing combinations::  
-* Combination Examples::        
-* Combination References and Further Reading::
-
-
-File: gsl-ref.info,  Node: The Combination struct,  Next: Combination allocation,  Up: Combinations
-
-10.1 The Combination struct
-===========================
-
-A combination is defined by a structure containing three components, the
-values of n and k, and a pointer to the combination array.  The elements
-of the combination array are all of type 'size_t', and are stored in
-increasing order.  The 'gsl_combination' structure looks like this,
-
-     typedef struct
-     {
-       size_t n;
-       size_t k;
-       size_t *data;
-     } gsl_combination;
-
-
-File: gsl-ref.info,  Node: Combination allocation,  Next: Accessing combination elements,  Prev: The Combination struct,  Up: Combinations
-
-10.2 Combination allocation
-===========================
-
- -- Function: gsl_combination * gsl_combination_alloc (size_t N, size_t
-          K)
-     This function allocates memory for a new combination with
-     parameters N, K.  The combination is not initialized and its
-     elements are undefined.  Use the function 'gsl_combination_calloc'
-     if you want to create a combination which is initialized to the
-     lexicographically first combination.  A null pointer is returned if
-     insufficient memory is available to create the combination.
-
- -- Function: gsl_combination * gsl_combination_calloc (size_t N, size_t
-          K)
-     This function allocates memory for a new combination with
-     parameters N, K and initializes it to the lexicographically first
-     combination.  A null pointer is returned if insufficient memory is
-     available to create the combination.
-
- -- Function: void gsl_combination_init_first (gsl_combination * C)
-     This function initializes the combination C to the
-     lexicographically first combination, i.e.  (0,1,2,...,k-1).
-
- -- Function: void gsl_combination_init_last (gsl_combination * C)
-     This function initializes the combination C to the
-     lexicographically last combination, i.e.  (n-k,n-k+1,...,n-1).
-
- -- Function: void gsl_combination_free (gsl_combination * C)
-     This function frees all the memory used by the combination C.
-
- -- Function: int gsl_combination_memcpy (gsl_combination * DEST, const
-          gsl_combination * SRC)
-     This function copies the elements of the combination SRC into the
-     combination DEST.  The two combinations must have the same size.
-
-
-File: gsl-ref.info,  Node: Accessing combination elements,  Next: Combination properties,  Prev: Combination allocation,  Up: Combinations
-
-10.3 Accessing combination elements
-===================================
-
-The following function can be used to access the elements of a
-combination.
-
- -- Function: size_t gsl_combination_get (const gsl_combination * C,
-          const size_t I)
-     This function returns the value of the I-th element of the
-     combination C.  If I lies outside the allowed range of 0 to K-1
-     then the error handler is invoked and 0 is returned.  An inline
-     version of this function is used when 'HAVE_INLINE' is defined.
-
-
-File: gsl-ref.info,  Node: Combination properties,  Next: Combination functions,  Prev: Accessing combination elements,  Up: Combinations
-
-10.4 Combination properties
-===========================
-
- -- Function: size_t gsl_combination_n (const gsl_combination * C)
-     This function returns the range (n) of the combination C.
-
- -- Function: size_t gsl_combination_k (const gsl_combination * C)
-     This function returns the number of elements (k) in the combination
-     C.
-
- -- Function: size_t * gsl_combination_data (const gsl_combination * C)
-     This function returns a pointer to the array of elements in the
-     combination C.
-
- -- Function: int gsl_combination_valid (gsl_combination * C)
-     This function checks that the combination C is valid.  The K
-     elements should lie in the range 0 to N-1, with each value
-     occurring once at most and in increasing order.
-
-
-File: gsl-ref.info,  Node: Combination functions,  Next: Reading and writing combinations,  Prev: Combination properties,  Up: Combinations
-
-10.5 Combination functions
-==========================
-
- -- Function: int gsl_combination_next (gsl_combination * C)
-     This function advances the combination C to the next combination in
-     lexicographic order and returns 'GSL_SUCCESS'.  If no further
-     combinations are available it returns 'GSL_FAILURE' and leaves C
-     unmodified.  Starting with the first combination and repeatedly
-     applying this function will iterate through all possible
-     combinations of a given order.
-
- -- Function: int gsl_combination_prev (gsl_combination * C)
-     This function steps backwards from the combination C to the
-     previous combination in lexicographic order, returning
-     'GSL_SUCCESS'.  If no previous combination is available it returns
-     'GSL_FAILURE' and leaves C unmodified.
-
diff -Nru gsl-doc-1.16/doc/gsl-ref.info-2 gsl-doc-2.3/doc/gsl-ref.info-2
--- gsl-doc-1.16/doc/gsl-ref.info-2	2013-07-19 15:17:39.000000000 +0000
+++ gsl-doc-2.3/doc/gsl-ref.info-2	2016-12-09 00:08:03.000000000 +0000
@@ -2,19 +2,285 @@
 gsl-ref.texi.
 
 Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,
-2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 The GSL Team.
+2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016
+The GSL Team.
 
    Permission is granted to copy, distribute and/or modify this document
 under the terms of the GNU Free Documentation License, Version 1.3 or
-any later version published by the Free Software Foundation; with no
-Invariant Sections and no cover texts.  A copy of the license is
-included in the section entitled "GNU Free Documentation License".
+any later version published by the Free Software Foundation; with the
+Invariant Sections being "GNU General Public License" and "Free Software
+Needs Free Documentation", the Front-Cover text being "A GNU Manual",
+and with the Back-Cover Text being (a) (see below).  A copy of the
+license is included in the section entitled "GNU Free Documentation
+License".
+
+   (a) The Back-Cover Text is: "You have the freedom to copy and modify
+this GNU Manual."
 INFO-DIR-SECTION Software libraries
 START-INFO-DIR-ENTRY
 * gsl-ref: (gsl-ref).                   GNU Scientific Library - Reference
 END-INFO-DIR-ENTRY
 
 
+File: gsl-ref.info,  Node: Permutation Examples,  Next: Permutation References and Further Reading,  Prev: Permutations in cyclic form,  Up: Permutations
+
+9.9 Examples
+============
+
+The example program below creates a random permutation (by shuffling the
+elements of the identity) and finds its inverse.
+
+     #include <stdio.h>
+     #include <gsl/gsl_rng.h>
+     #include <gsl/gsl_randist.h>
+     #include <gsl/gsl_permutation.h>
+
+     int
+     main (void)
+     {
+       const size_t N = 10;
+       const gsl_rng_type * T;
+       gsl_rng * r;
+
+       gsl_permutation * p = gsl_permutation_alloc (N);
+       gsl_permutation * q = gsl_permutation_alloc (N);
+
+       gsl_rng_env_setup();
+       T = gsl_rng_default;
+       r = gsl_rng_alloc (T);
+
+       printf ("initial permutation:");
+       gsl_permutation_init (p);
+       gsl_permutation_fprintf (stdout, p, " %u");
+       printf ("\n");
+
+       printf (" random permutation:");
+       gsl_ran_shuffle (r, p->data, N, sizeof(size_t));
+       gsl_permutation_fprintf (stdout, p, " %u");
+       printf ("\n");
+
+       printf ("inverse permutation:");
+       gsl_permutation_inverse (q, p);
+       gsl_permutation_fprintf (stdout, q, " %u");
+       printf ("\n");
+
+       gsl_permutation_free (p);
+       gsl_permutation_free (q);
+       gsl_rng_free (r);
+
+       return 0;
+     }
+
+Here is the output from the program,
+
+     $ ./a.out
+     initial permutation: 0 1 2 3 4 5 6 7 8 9
+      random permutation: 1 3 5 2 7 6 0 4 9 8
+     inverse permutation: 6 0 3 1 7 2 5 4 9 8
+
+The random permutation 'p[i]' and its inverse 'q[i]' are related through
+the identity 'p[q[i]] = i', which can be verified from the output.
+
+   The next example program steps forwards through all possible third
+order permutations, starting from the identity,
+
+     #include <stdio.h>
+     #include <gsl/gsl_permutation.h>
+
+     int
+     main (void)
+     {
+       gsl_permutation * p = gsl_permutation_alloc (3);
+
+       gsl_permutation_init (p);
+
+       do
+        {
+           gsl_permutation_fprintf (stdout, p, " %u");
+           printf ("\n");
+        }
+       while (gsl_permutation_next(p) == GSL_SUCCESS);
+
+       gsl_permutation_free (p);
+
+       return 0;
+     }
+
+Here is the output from the program,
+
+     $ ./a.out
+      0 1 2
+      0 2 1
+      1 0 2
+      1 2 0
+      2 0 1
+      2 1 0
+
+The permutations are generated in lexicographic order.  To reverse the
+sequence, begin with the final permutation (which is the reverse of the
+identity) and replace 'gsl_permutation_next' with
+'gsl_permutation_prev'.
+
+
+File: gsl-ref.info,  Node: Permutation References and Further Reading,  Prev: Permutation Examples,  Up: Permutations
+
+9.10 References and Further Reading
+===================================
+
+The subject of permutations is covered extensively in Knuth's 'Sorting
+and Searching',
+
+     Donald E. Knuth, 'The Art of Computer Programming: Sorting and
+     Searching' (Vol 3, 3rd Ed, 1997), Addison-Wesley, ISBN 0201896850.
+
+For the definition of the "canonical form" see,
+
+     Donald E. Knuth, 'The Art of Computer Programming: Fundamental
+     Algorithms' (Vol 1, 3rd Ed, 1997), Addison-Wesley, ISBN 0201896850.
+     Section 1.3.3, 'An Unusual Correspondence', p.178-179.
+
+
+File: gsl-ref.info,  Node: Combinations,  Next: Multisets,  Prev: Permutations,  Up: Top
+
+10 Combinations
+***************
+
+This chapter describes functions for creating and manipulating
+combinations.  A combination c is represented by an array of k integers
+in the range 0 to n-1, where each value c_i occurs at most once.  The
+combination c corresponds to indices of k elements chosen from an n
+element vector.  Combinations are useful for iterating over all
+k-element subsets of a set.
+
+   The functions described in this chapter are defined in the header
+file 'gsl_combination.h'.
+
+* Menu:
+
+* The Combination struct::      
+* Combination allocation::      
+* Accessing combination elements::  
+* Combination properties::      
+* Combination functions::       
+* Reading and writing combinations::  
+* Combination Examples::        
+* Combination References and Further Reading::
+
+
+File: gsl-ref.info,  Node: The Combination struct,  Next: Combination allocation,  Up: Combinations
+
+10.1 The Combination struct
+===========================
+
+A combination is defined by a structure containing three components, the
+values of n and k, and a pointer to the combination array.  The elements
+of the combination array are all of type 'size_t', and are stored in
+increasing order.  The 'gsl_combination' structure looks like this,
+
+     typedef struct
+     {
+       size_t n;
+       size_t k;
+       size_t *data;
+     } gsl_combination;
+
+
+File: gsl-ref.info,  Node: Combination allocation,  Next: Accessing combination elements,  Prev: The Combination struct,  Up: Combinations
+
+10.2 Combination allocation
+===========================
+
+ -- Function: gsl_combination * gsl_combination_alloc (size_t N, size_t
+          K)
+     This function allocates memory for a new combination with
+     parameters N, K.  The combination is not initialized and its
+     elements are undefined.  Use the function 'gsl_combination_calloc'
+     if you want to create a combination which is initialized to the
+     lexicographically first combination.  A null pointer is returned if
+     insufficient memory is available to create the combination.
+
+ -- Function: gsl_combination * gsl_combination_calloc (size_t N, size_t
+          K)
+     This function allocates memory for a new combination with
+     parameters N, K and initializes it to the lexicographically first
+     combination.  A null pointer is returned if insufficient memory is
+     available to create the combination.
+
+ -- Function: void gsl_combination_init_first (gsl_combination * C)
+     This function initializes the combination C to the
+     lexicographically first combination, i.e.  (0,1,2,...,k-1).
+
+ -- Function: void gsl_combination_init_last (gsl_combination * C)
+     This function initializes the combination C to the
+     lexicographically last combination, i.e.  (n-k,n-k+1,...,n-1).
+
+ -- Function: void gsl_combination_free (gsl_combination * C)
+     This function frees all the memory used by the combination C.
+
+ -- Function: int gsl_combination_memcpy (gsl_combination * DEST, const
+          gsl_combination * SRC)
+     This function copies the elements of the combination SRC into the
+     combination DEST.  The two combinations must have the same size.
+
+
+File: gsl-ref.info,  Node: Accessing combination elements,  Next: Combination properties,  Prev: Combination allocation,  Up: Combinations
+
+10.3 Accessing combination elements
+===================================
+
+The following function can be used to access the elements of a
+combination.
+
+ -- Function: size_t gsl_combination_get (const gsl_combination * C,
+          const size_t I)
+     This function returns the value of the I-th element of the
+     combination C.  If I lies outside the allowed range of 0 to K-1
+     then the error handler is invoked and 0 is returned.  An inline
+     version of this function is used when 'HAVE_INLINE' is defined.
+
+
+File: gsl-ref.info,  Node: Combination properties,  Next: Combination functions,  Prev: Accessing combination elements,  Up: Combinations
+
+10.4 Combination properties
+===========================
+
+ -- Function: size_t gsl_combination_n (const gsl_combination * C)
+     This function returns the range (n) of the combination C.
+
+ -- Function: size_t gsl_combination_k (const gsl_combination * C)
+     This function returns the number of elements (k) in the combination
+     C.
+
+ -- Function: size_t * gsl_combination_data (const gsl_combination * C)
+     This function returns a pointer to the array of elements in the
+     combination C.
+
+ -- Function: int gsl_combination_valid (gsl_combination * C)
+     This function checks that the combination C is valid.  The K
+     elements should lie in the range 0 to N-1, with each value
+     occurring once at most and in increasing order.
+
+
+File: gsl-ref.info,  Node: Combination functions,  Next: Reading and writing combinations,  Prev: Combination properties,  Up: Combinations
+
+10.5 Combination functions
+==========================
+
+ -- Function: int gsl_combination_next (gsl_combination * C)
+     This function advances the combination C to the next combination in
+     lexicographic order and returns 'GSL_SUCCESS'.  If no further
+     combinations are available it returns 'GSL_FAILURE' and leaves C
+     unmodified.  Starting with the first combination and repeatedly
+     applying this function will iterate through all possible
+     combinations of a given order.
+
+ -- Function: int gsl_combination_prev (gsl_combination * C)
+     This function steps backwards from the combination C to the
+     previous combination in lexicographic order, returning
+     'GSL_SUCCESS'.  If no previous combination is available it returns
+     'GSL_FAILURE' and leaves C unmodified.
+
+
 File: gsl-ref.info,  Node: Reading and writing combinations,  Next: Combination Examples,  Prev: Combination functions,  Up: Combinations
 
 10.6 Reading and writing combinations
@@ -359,7 +625,7 @@
 Here is the output from the program,
 
      $ ./a.out
-     all multisets of {0,1,2,3} by size:
+     All multisets of {0,1,2,3} by size:
      { }
      { 0 }
      { 1 }
@@ -749,11 +1015,11 @@
 
        gsl_sort_smallest (small, k, x, 1, N);
 
-       printf ("%d smallest values from %d\n", k, N);
+       printf ("%zu smallest values from %zu\n", k, N);
 
        for (i = 0; i < k; i++)
          {
-           printf ("%d: %.18f\n", i, small[i]);
+           printf ("%zu: %.18f\n", i, small[i]);
          }
 
        free (x);
@@ -1527,17 +1793,22 @@
 
 * LU Decomposition::            
 * QR Decomposition::            
-* QR Decomposition with Column Pivoting::  
+* QR Decomposition with Column Pivoting::
+* Complete Orthogonal Decomposition::
 * Singular Value Decomposition::  
 * Cholesky Decomposition::      
+* Pivoted Cholesky Decomposition::      
+* Modified Cholesky Decomposition::      
 * Tridiagonal Decomposition of Real Symmetric Matrices::  
 * Tridiagonal Decomposition of Hermitian Matrices::  
 * Hessenberg Decomposition of Real Matrices::
 * Hessenberg-Triangular Decomposition of Real Matrices::
 * Bidiagonalization::           
+* Givens Rotations::  
 * Householder Transformations::  
 * Householder solver for linear systems::  
-* Tridiagonal Systems::         
+* Tridiagonal Systems::
+* Triangular Systems::
 * Balancing::
 * Linear Algebra Examples::     
 * Linear Algebra References and Further Reading::  
@@ -1548,8 +1819,8 @@
 14.1 LU Decomposition
 =====================
 
-A general square matrix A has an LU decomposition into upper and lower
-triangular matrices,
+A general N-by-N square matrix A has an LU decomposition into upper and
+lower triangular matrices,
 
      P A = L U
 
@@ -1571,11 +1842,12 @@
      contains L.  The diagonal elements of L are unity, and are not
      stored.
 
-     The permutation matrix P is encoded in the permutation P.  The j-th
-     column of the matrix P is given by the k-th column of the identity
-     matrix, where k = p_j the j-th element of the permutation vector.
-     The sign of the permutation is given by SIGNUM.  It has the value
-     (-1)^n, where n is the number of interchanges in the permutation.
+     The permutation matrix P is encoded in the permutation P on output.
+     The j-th column of the matrix P is given by the k-th column of the
+     identity matrix, where k = p_j the j-th element of the permutation
+     vector.  The sign of the permutation is given by SIGNUM.  It has
+     the value (-1)^n, where n is the number of interchanges in the
+     permutation.
 
      The algorithm used in the decomposition is Gaussian Elimination
      with partial pivoting (Golub & Van Loan, 'Matrix Computations',
@@ -1601,15 +1873,14 @@
 
  -- Function: int gsl_linalg_LU_refine (const gsl_matrix * A, const
           gsl_matrix * LU, const gsl_permutation * P, const gsl_vector *
-          B, gsl_vector * X, gsl_vector * RESIDUAL)
+          B, gsl_vector * X, gsl_vector * WORK)
  -- Function: int gsl_linalg_complex_LU_refine (const gsl_matrix_complex
           * A, const gsl_matrix_complex * LU, const gsl_permutation * P,
           const gsl_vector_complex * B, gsl_vector_complex * X,
-          gsl_vector_complex * RESIDUAL)
+          gsl_vector_complex * WORK)
      These functions apply an iterative improvement to X, the solution
      of A x = b, from the precomputed LU decomposition of A into (LU,P).
-     The initial residual r = A x - b is also computed and stored in
-     RESIDUAL.
+     Additional workspace of length N is required in WORK.
 
  -- Function: int gsl_linalg_LU_invert (const gsl_matrix * LU, const
           gsl_permutation * P, gsl_matrix * INVERSE)
@@ -1773,13 +2044,13 @@
      the solution on output.
 
 
-File: gsl-ref.info,  Node: QR Decomposition with Column Pivoting,  Next: Singular Value Decomposition,  Prev: QR Decomposition,  Up: Linear Algebra
+File: gsl-ref.info,  Node: QR Decomposition with Column Pivoting,  Next: Complete Orthogonal Decomposition,  Prev: QR Decomposition,  Up: Linear Algebra
 
 14.3 QR Decomposition with Column Pivoting
 ==========================================
 
-The QR decomposition can be extended to the rank deficient case by
-introducing a column permutation P,
+The QR decomposition of an M-by-N matrix A can be extended to the rank
+deficient case by introducing a column permutation P,
 
      A P = Q R
 
@@ -1788,7 +2059,20 @@
 convert the linear system A x = b into the triangular system R y = Q^T
 b, x = P y, which can be solved by back-substitution and permutation.
 We denote the QR decomposition with column pivoting by QRP^T since A = Q
-R P^T.
+R P^T.  When A is rank deficient with r = {\rm rank}(A), the matrix R
+can be partitioned as
+
+     R = [ R11 R12; 0 R22 ] =~ [ R11 R12; 0 0 ]
+
+   where R_{11} is r-by-r and nonsingular.  In this case, a "basic"
+least squares solution for the overdetermined system A x = b can be
+obtained as
+
+     x = P [ R11^-1 c1 ; 0 ]
+
+   where c_1 consists of the first r elements of Q^T b.  This basic
+solution is not guaranteed to be the minimum norm solution unless R_{12}
+= 0 (see *note Complete Orthogonal Decomposition::).
 
  -- Function: int gsl_linalg_QRPT_decomp (gsl_matrix * A, gsl_vector *
           TAU, gsl_permutation * P, int * SIGNUM, gsl_vector * NORM)
@@ -1832,6 +2116,33 @@
      contain the right-hand side b, which is replaced by the solution on
      output.
 
+ -- Function: int gsl_linalg_QRPT_lssolve (const gsl_matrix * QR, const
+          gsl_vector * TAU, const gsl_permutation * P, const gsl_vector
+          * B, gsl_vector * X, gsl_vector * RESIDUAL)
+     This function finds the least squares solution to the
+     overdetermined system A x = b where the matrix A has more rows than
+     columns and is assumed to have full rank.  The least squares
+     solution minimizes the Euclidean norm of the residual, ||b - A x||.
+     The routine requires as input the QR decomposition of A into (QR,
+     TAU, P) given by 'gsl_linalg_QRPT_decomp'.  The solution is
+     returned in X.  The residual is computed as a by-product and stored
+     in RESIDUAL.  For rank deficient matrices,
+     'gsl_linalg_QRPT_lssolve2' should be used instead.
+
+ -- Function: int gsl_linalg_QRPT_lssolve2 (const gsl_matrix * QR, const
+          gsl_vector * TAU, const gsl_permutation * P, const gsl_vector
+          * B, const size_t RANK, gsl_vector * X, gsl_vector * RESIDUAL)
+     This function finds the least squares solution to the
+     overdetermined system A x = b where the matrix A has more rows than
+     columns and has rank given by the input RANK.  If the user does not
+     know the rank of A, the routine 'gsl_linalg_QRPT_rank' can be
+     called to estimate it.  The least squares solution is the so-called
+     "basic" solution discussed above and may not be the minimum norm
+     solution.  The routine requires as input the QR decomposition of A
+     into (QR, TAU, P) given by 'gsl_linalg_QRPT_decomp'.  The solution
+     is returned in X.  The residual is computed as a by-product and
+     stored in RESIDUAL.
+
  -- Function: int gsl_linalg_QRPT_QRsolve (const gsl_matrix * Q, const
           gsl_matrix * R, const gsl_permutation * P, const gsl_vector *
           B, gsl_vector * X)
@@ -1859,10 +2170,96 @@
      the N-by-N matrix R contained in QR.  On input X should contain the
      right-hand side b, which is replaced by the solution on output.
 
+ -- Function: size_t gsl_linalg_QRPT_rank (const gsl_matrix * QR, const
+          double TOL)
+     This function estimates the rank of the triangular matrix R
+     contained in QR.  The algorithm simply counts the number of
+     diagonal elements of R whose absolute value is greater than the
+     specified tolerance TOL.  If the input TOL is negative, a default
+     value of 20 (M + N) eps(max(|diag(R)|)) is used.
+
+ -- Function: int gsl_linalg_QRPT_rcond (const gsl_matrix * QR, double *
+          RCOND, gsl_vector * WORK)
+     This function estimates the reciprocal condition number (using the
+     1-norm) of the R factor, stored in the upper triangle of QR.  The
+     reciprocal condition number estimate, defined as 1 / (||R||_1 \cdot
+     ||R^{-1}||_1), is stored in RCOND.  Additional workspace of size 3
+     N is required in WORK.
+
+
+File: gsl-ref.info,  Node: Complete Orthogonal Decomposition,  Next: Singular Value Decomposition,  Prev: QR Decomposition with Column Pivoting,  Up: Linear Algebra
+
+14.4 Complete Orthogonal Decomposition
+======================================
+
+The complete orthogonal decomposition of a M-by-N matrix A is a
+generalization of the QR decomposition with column pivoting, given by
+
+     A P = Q [ R11 0 ] Z
+             [  0  0 ]
+
+where P is a N-by-N permutation matrix, Q is M-by-M orthogonal, R_{11}
+is r-by-r upper triangular, with r = {\rm rank}(A), and Z is N-by-N
+orthogonal.  If A has full rank, then R_{11} = R, Z = I and this reduces
+to the QR decomposition with column pivoting.  The advantage of using
+the complete orthogonal decomposition for rank deficient matrices is the
+ability to compute the minimum norm solution to the linear least squares
+problem Ax = b, which is given by
+
+     x = P Z^T [ R11^-1 c1 ]
+               [    0      ]
+
+   and the vector c_1 is the first r elements of Q^T b.
+
+ -- Function: int gsl_linalg_COD_decomp (gsl_matrix * A, gsl_vector *
+          TAU_Q, gsl_vector * TAU_Z, gsl_permutation * P, size_t * RANK,
+          gsl_vector * WORK)
+ -- Function: int gsl_linalg_COD_decomp_e (gsl_matrix * A, gsl_vector *
+          TAU_Q, gsl_vector * TAU_Z, gsl_permutation * P, double TOL,
+          size_t * RANK, gsl_vector * WORK)
+     These functions factor the M-by-N matrix A into the decomposition A
+     = Q R Z P^T.  The rank of A is computed as the number of diagonal
+     elements of R greater than the tolerance TOL and output in RANK.
+     If TOL is not specified, a default value is used (see
+     'gsl_linalg_QRPT_rank').  On output, the permutation matrix P is
+     stored in P.  The matrix R_{11} is stored in the upper RANK-by-RANK
+     block of A.  The matrices Q and Z are encoded in packed storage in
+     A on output.  The vectors TAU_Q and TAU_Z contain the Householder
+     scalars corresponding to the matrices Q and Z respectively and must
+     be of length k = \min(M,N).  The vector WORK is additional
+     workspace of length N.
+
+ -- Function: int gsl_linalg_COD_lssolve (const gsl_matrix * QRZ, const
+          gsl_vector * TAU_Q, const gsl_vector * TAU_Z, const
+          gsl_permutation * P, const size_t RANK, const gsl_vector * B,
+          gsl_vector * X, gsl_vector * RESIDUAL)
+     This function finds the least squares solution to the
+     overdetermined system A x = b where the matrix A has more rows than
+     columns.  The least squares solution minimizes the Euclidean norm
+     of the residual, ||b - A x||.  The routine requires as input the
+     QRZ decomposition of A into (QRZ, TAU_Q, TAU_Z, P, RANK) given by
+     'gsl_linalg_COD_decomp'.  The solution is returned in X.  The
+     residual is computed as a by-product and stored in RESIDUAL.
+
+ -- Function: int gsl_linalg_COD_unpack (const gsl_matrix * QRZ, const
+          gsl_vector * TAU_Q, const gsl_vector * TAU_Z, const size_t
+          RANK, gsl_matrix * Q, gsl_matrix * R, gsl_matrix * Z)
+     This function unpacks the encoded QRZ decomposition (QRZ, TAU_Q,
+     TAU_Z, RANK) into the matrices Q, R, and Z, where Q is M-by-M, R is
+     M-by-N, and Z is N-by-N.
+
+ -- Function: int gsl_linalg_COD_matZ (const gsl_matrix * QRZ, const
+          gsl_vector * TAU_Z, const size_t RANK, gsl_matrix * A,
+          gsl_vector * WORK)
+     This function multiplies the input matrix A on the right by Z, A' =
+     A Z using the encoded QRZ decomposition (QRZ, TAU_Z, RANK).  A must
+     have N columns but may have any number of rows.  Additional
+     workspace of length M is provided in WORK.
+
 
-File: gsl-ref.info,  Node: Singular Value Decomposition,  Next: Cholesky Decomposition,  Prev: QR Decomposition with Column Pivoting,  Up: Linear Algebra
+File: gsl-ref.info,  Node: Singular Value Decomposition,  Next: Cholesky Decomposition,  Prev: Complete Orthogonal Decomposition,  Up: Linear Algebra
 
-14.4 Singular Value Decomposition
+14.5 Singular Value Decomposition
 =================================
 
 A general rectangular M-by-N matrix A has a singular value decomposition
@@ -1947,9 +2344,9 @@
      the matrix U which is the input to this function.
 
 
-File: gsl-ref.info,  Node: Cholesky Decomposition,  Next: Tridiagonal Decomposition of Real Symmetric Matrices,  Prev: Singular Value Decomposition,  Up: Linear Algebra
+File: gsl-ref.info,  Node: Cholesky Decomposition,  Next: Pivoted Cholesky Decomposition,  Prev: Singular Value Decomposition,  Up: Linear Algebra
 
-14.5 Cholesky Decomposition
+14.6 Cholesky Decomposition
 ===========================
 
 A symmetric, positive definite square matrix A has a Cholesky
@@ -1965,7 +2362,17 @@
 (L y = b, L^T x = y), which can be solved by forward and
 back-substitution.
 
- -- Function: int gsl_linalg_cholesky_decomp (gsl_matrix * A)
+   If the matrix A is near singular, it is sometimes possible to reduce
+the condition number and recover a more accurate solution vector x by
+scaling as
+
+     ( S A S ) ( S^(-1) x ) = S b
+
+   where S is a diagonal matrix whose elements are given by S_{ii} =
+1/\sqrt{A_{ii}}.  This scaling is also known as Jacobi preconditioning.
+There are routines below to solve both the scaled and unscaled systems.
+
+ -- Function: int gsl_linalg_cholesky_decomp1 (gsl_matrix * A)
  -- Function: int gsl_linalg_complex_cholesky_decomp (gsl_matrix_complex
           * A)
      These functions factorize the symmetric, positive-definite square
@@ -1974,14 +2381,17 @@
      lower-triangular part of the matrix A are used (the upper
      triangular part is ignored).  On output the diagonal and lower
      triangular part of the input matrix A contain the matrix L, while
-     the upper triangular part of the input matrix is overwritten with
-     L^T (the diagonal terms being identical for both L and L^T).  If
-     the matrix is not positive-definite then the decomposition will
-     fail, returning the error code 'GSL_EDOM'.
+     the upper triangular part is unmodified.  If the matrix is not
+     positive-definite then the decomposition will fail, returning the
+     error code 'GSL_EDOM'.
 
      When testing whether a matrix is positive-definite, disable the
      error handler first to avoid triggering an error.
 
+ -- Function: int gsl_linalg_cholesky_decomp (gsl_matrix * A)
+     This function is now deprecated and is provided only for backward
+     compatibility.
+
  -- Function: int gsl_linalg_cholesky_solve (const gsl_matrix *
           CHOLESKY, const gsl_vector * B, gsl_vector * X)
  -- Function: int gsl_linalg_complex_cholesky_solve (const
@@ -2011,10 +2421,229 @@
      'gsl_linalg_complex_cholesky_decomp'.  On output, the inverse is
      stored in-place in CHOLESKY.
 
+ -- Function: int gsl_linalg_cholesky_decomp2 (gsl_matrix * A,
+          gsl_vector * S)
+     This function calculates a diagonal scaling transformation S for
+     the symmetric, positive-definite square matrix A, and then computes
+     the Cholesky decomposition S A S = L L^T.  On input, the values
+     from the diagonal and lower-triangular part of the matrix A are
+     used (the upper triangular part is ignored).  On output the
+     diagonal and lower triangular part of the input matrix A contain
+     the matrix L, while the upper triangular part of the input matrix
+     is overwritten with L^T (the diagonal terms being identical for
+     both L and L^T).  If the matrix is not positive-definite then the
+     decomposition will fail, returning the error code 'GSL_EDOM'.  The
+     diagonal scale factors are stored in S on output.
+
+     When testing whether a matrix is positive-definite, disable the
+     error handler first to avoid triggering an error.
+
+ -- Function: int gsl_linalg_cholesky_solve2 (const gsl_matrix *
+          CHOLESKY, const gsl_vector * S, const gsl_vector * B,
+          gsl_vector * X)
+     This function solves the system (S A S) (S^{-1} x) = S b using the
+     Cholesky decomposition of S A S held in the matrix CHOLESKY which
+     must have been previously computed by
+     'gsl_linalg_cholesky_decomp2'.
+
+ -- Function: int gsl_linalg_cholesky_svx2 (const gsl_matrix * CHOLESKY,
+          const gsl_vector * S, gsl_vector * X)
+     This function solves the system (S A S) (S^{-1} x) = S b in-place
+     using the Cholesky decomposition of S A S held in the matrix
+     CHOLESKY which must have been previously computed by
+     'gsl_linalg_cholesky_decomp2'.  On input X should contain the
+     right-hand side b, which is replaced by the solution on output.
+
+ -- Function: int gsl_linalg_cholesky_scale (const gsl_matrix * A,
+          gsl_vector * S)
+     This function calculates a diagonal scaling transformation of the
+     symmetric, positive definite matrix A, such that S A S has a
+     condition number within a factor of N of the matrix of smallest
+     possible condition number over all possible diagonal scalings.  On
+     output, S contains the scale factors, given by S_i =
+     1/\sqrt{A_{ii}}.  For any A_{ii} \le 0, the corresponding scale
+     factor S_i is set to 1.
+
+ -- Function: int gsl_linalg_cholesky_scale_apply (gsl_matrix * A, const
+          gsl_vector * S)
+     This function applies the scaling transformation S to the matrix A.
+     On output, A is replaced by S A S.
+
+ -- Function: int gsl_linalg_cholesky_rcond (const gsl_matrix *
+          CHOLESKY, double * RCOND, gsl_vector * WORK)
+     This function estimates the reciprocal condition number (using the
+     1-norm) of the symmetric positive definite matrix A, using its
+     Cholesky decomposition provided in CHOLESKY.  The reciprocal
+     condition number estimate, defined as 1 / (||A||_1 \cdot
+     ||A^{-1}||_1), is stored in RCOND.  Additional workspace of size 3
+     N is required in WORK.
+
 
-File: gsl-ref.info,  Node: Tridiagonal Decomposition of Real Symmetric Matrices,  Next: Tridiagonal Decomposition of Hermitian Matrices,  Prev: Cholesky Decomposition,  Up: Linear Algebra
+File: gsl-ref.info,  Node: Pivoted Cholesky Decomposition,  Next: Modified Cholesky Decomposition,  Prev: Cholesky Decomposition,  Up: Linear Algebra
+
+14.7 Pivoted Cholesky Decomposition
+===================================
+
+A symmetric, positive definite square matrix A has an alternate Cholesky
+decomposition into a product of a lower unit triangular matrix L, a
+diagonal matrix D and L^T, given by L D L^T.  This is equivalent to the
+Cholesky formulation discussed above, with the standard Cholesky lower
+triangular factor given by L D^{1 \over 2}.  For ill-conditioned
+matrices, it can help to use a pivoting strategy to prevent the entries
+of D and L from growing too large, and also ensure D_1 \ge D_2 \ge
+\cdots \ge D_n > 0, where D_i are the diagonal entries of D.  The final
+decomposition is given by
+
+     P A P^T = L D L^T
+
+   where P is a permutation matrix.
+
+ -- Function: int gsl_linalg_pcholesky_decomp (gsl_matrix * A,
+          gsl_permutation * P)
+     This function factors the symmetric, positive-definite square
+     matrix A into the Pivoted Cholesky decomposition P A P^T = L D L^T.
+     On input, the values from the diagonal and lower-triangular part of
+     the matrix A are used to construct the factorization.  On output
+     the diagonal of the input matrix A stores the diagonal elements of
+     D, and the lower triangular portion of A contains the matrix L.
+     Since L has ones on its diagonal these do not need to be
+     explicitely stored.  The upper triangular portion of A is
+     unmodified.  The permutation matrix P is stored in P on output.
 
-14.6 Tridiagonal Decomposition of Real Symmetric Matrices
+ -- Function: int gsl_linalg_pcholesky_solve (const gsl_matrix * LDLT,
+          const gsl_permutation * P, const gsl_vector * B, gsl_vector *
+          X)
+     This function solves the system A x = b using the Pivoted Cholesky
+     decomposition of A held in the matrix LDLT and permutation P which
+     must have been previously computed by
+     'gsl_linalg_pcholesky_decomp'.
+
+ -- Function: int gsl_linalg_pcholesky_svx (const gsl_matrix * LDLT,
+          const gsl_permutation * P, gsl_vector * X)
+     This function solves the system A x = b in-place using the Pivoted
+     Cholesky decomposition of A held in the matrix LDLT and permutation
+     P which must have been previously computed by
+     'gsl_linalg_pcholesky_decomp'.  On input, X contains the right hand
+     side vector b which is replaced by the solution vector on output.
+
+ -- Function: int gsl_linalg_pcholesky_decomp2 (gsl_matrix * A,
+          gsl_permutation * P, gsl_vector * S)
+     This function computes the pivoted Cholesky factorization of the
+     matrix S A S, where the input matrix A is symmetric and positive
+     definite, and the diagonal scaling matrix S is computed to reduce
+     the condition number of A as much as possible.  See *note Cholesky
+     Decomposition:: for more information on the matrix S.  The Pivoted
+     Cholesky decomposition satisfies P S A S P^T = L D L^T.  On input,
+     the values from the diagonal and lower-triangular part of the
+     matrix A are used to construct the factorization.  On output the
+     diagonal of the input matrix A stores the diagonal elements of D,
+     and the lower triangular portion of A contains the matrix L.  Since
+     L has ones on its diagonal these do not need to be explicitely
+     stored.  The upper triangular portion of A is unmodified.  The
+     permutation matrix P is stored in P on output.  The diagonal
+     scaling transformation is stored in S on output.
+
+ -- Function: int gsl_linalg_pcholesky_solve2 (const gsl_matrix * LDLT,
+          const gsl_permutation * P, const gsl_vector * S, const
+          gsl_vector * B, gsl_vector * X)
+     This function solves the system (S A S) (S^{-1} x) = S b using the
+     Pivoted Cholesky decomposition of S A S held in the matrix LDLT,
+     permutation P, and vector S, which must have been previously
+     computed by 'gsl_linalg_pcholesky_decomp2'.
+
+ -- Function: int gsl_linalg_pcholesky_svx2 (const gsl_matrix * LDLT,
+          const gsl_permutation * P, const gsl_vector * S, gsl_vector *
+          X)
+     This function solves the system (S A S) (S^{-1} x) = S b in-place
+     using the Pivoted Cholesky decomposition of S A S held in the
+     matrix LDLT, permutation P and vector S, which must have been
+     previously computed by 'gsl_linalg_pcholesky_decomp2'.  On input, X
+     contains the right hand side vector b which is replaced by the
+     solution vector on output.
+
+ -- Function: int gsl_linalg_pcholesky_invert (const gsl_matrix * LDLT,
+          const gsl_permutation * P, gsl_matrix * AINV)
+     This function computes the inverse of the matrix A, using the
+     Pivoted Cholesky decomposition stored in LDLT and P.  On output,
+     the matrix AINV contains A^{-1}.
+
+ -- Function: int gsl_linalg_pcholesky_rcond (const gsl_matrix * LDLT,
+          const gsl_permutation * P, double * RCOND, gsl_vector * WORK)
+     This function estimates the reciprocal condition number (using the
+     1-norm) of the symmetric positive definite matrix A, using its
+     pivoted Cholesky decomposition provided in LDLT.  The reciprocal
+     condition number estimate, defined as 1 / (||A||_1 \cdot
+     ||A^{-1}||_1), is stored in RCOND.  Additional workspace of size 3
+     N is required in WORK.
+
+
+File: gsl-ref.info,  Node: Modified Cholesky Decomposition,  Next: Tridiagonal Decomposition of Real Symmetric Matrices,  Prev: Pivoted Cholesky Decomposition,  Up: Linear Algebra
+
+14.8 Modified Cholesky Decomposition
+====================================
+
+The modified Cholesky decomposition is suitable for solving systems A x
+= b where A is a symmetric indefinite matrix.  Such matrices arise in
+nonlinear optimization algorithms.  The standard Cholesky decomposition
+requires a positive definite matrix and would fail in this case.
+Instead of resorting to a method like QR or SVD, which do not take into
+account the symmetry of the matrix, we can instead introduce a small
+perturbation to the matrix A to make it positive definite, and then use
+a Cholesky decomposition on the perturbed matrix.  The resulting
+decomposition satisfies
+
+     P (A + E) P^T = L D L^T
+
+   where P is a permutation matrix, E is a diagonal perturbation matrix,
+L is unit lower triangular, and D is diagonal.  If A is sufficiently
+positive definite, then the perturbation matrix E will be zero and this
+method is equivalent to the pivoted Cholesky algorithm.  For indefinite
+matrices, the perturbation matrix E is computed to ensure that A + E is
+positive definite and well conditioned.
+
+ -- Function: int gsl_linalg_mcholesky_decomp (gsl_matrix * A,
+          gsl_permutation * P, gsl_vector * E)
+     This function factors the symmetric, indefinite square matrix A
+     into the Modified Cholesky decomposition P (A + E) P^T = L D L^T.
+     On input, the values from the diagonal and lower-triangular part of
+     the matrix A are used to construct the factorization.  On output
+     the diagonal of the input matrix A stores the diagonal elements of
+     D, and the lower triangular portion of A contains the matrix L.
+     Since L has ones on its diagonal these do not need to be
+     explicitely stored.  The upper triangular portion of A is
+     unmodified.  The permutation matrix P is stored in P on output.
+     The diagonal perturbation matrix is stored in E on output.  The
+     parameter E may be set to NULL if it is not required.
+
+ -- Function: int gsl_linalg_mcholesky_solve (const gsl_matrix * LDLT,
+          const gsl_permutation * P, const gsl_vector * B, gsl_vector *
+          X)
+     This function solves the perturbed system (A + E) x = b using the
+     Cholesky decomposition of A + E held in the matrix LDLT and
+     permutation P which must have been previously computed by
+     'gsl_linalg_mcholesky_decomp'.
+
+ -- Function: int gsl_linalg_mcholesky_svx (const gsl_matrix * LDLT,
+          const gsl_permutation * P, gsl_vector * X)
+     This function solves the perturbed system (A + E) x = b in-place
+     using the Cholesky decomposition of A + E held in the matrix LDLT
+     and permutation P which must have been previously computed by
+     'gsl_linalg_mcholesky_decomp'.  On input, X contains the right hand
+     side vector b which is replaced by the solution vector on output.
+
+ -- Function: int gsl_linalg_mcholesky_rcond (const gsl_matrix * LDLT,
+          const gsl_permutation * P, double * RCOND, gsl_vector * WORK)
+     This function estimates the reciprocal condition number (using the
+     1-norm) of the perturbed matrix A + E, using its pivoted Cholesky
+     decomposition provided in LDLT.  The reciprocal condition number
+     estimate, defined as 1 / (||A + E||_1 \cdot ||(A + E)^{-1}||_1), is
+     stored in RCOND.  Additional workspace of size 3 N is required in
+     WORK.
+
+
+File: gsl-ref.info,  Node: Tridiagonal Decomposition of Real Symmetric Matrices,  Next: Tridiagonal Decomposition of Hermitian Matrices,  Prev: Modified Cholesky Decomposition,  Up: Linear Algebra
+
+14.9 Tridiagonal Decomposition of Real Symmetric Matrices
 =========================================================
 
 A symmetric matrix A can be factorized by similarity transformations
@@ -2052,8 +2681,8 @@
 
 File: gsl-ref.info,  Node: Tridiagonal Decomposition of Hermitian Matrices,  Next: Hessenberg Decomposition of Real Matrices,  Prev: Tridiagonal Decomposition of Real Symmetric Matrices,  Up: Linear Algebra
 
-14.7 Tridiagonal Decomposition of Hermitian Matrices
-====================================================
+14.10 Tridiagonal Decomposition of Hermitian Matrices
+=====================================================
 
 A hermitian matrix A can be factorized by similarity transformations
 into the form,
@@ -2092,8 +2721,8 @@
 
 File: gsl-ref.info,  Node: Hessenberg Decomposition of Real Matrices,  Next: Hessenberg-Triangular Decomposition of Real Matrices,  Prev: Tridiagonal Decomposition of Hermitian Matrices,  Up: Linear Algebra
 
-14.8 Hessenberg Decomposition of Real Matrices
-==============================================
+14.11 Hessenberg Decomposition of Real Matrices
+===============================================
 
 A general real matrix A can be decomposed by orthogonal similarity
 transformations into the form
@@ -2139,8 +2768,8 @@
 
 File: gsl-ref.info,  Node: Hessenberg-Triangular Decomposition of Real Matrices,  Next: Bidiagonalization,  Prev: Hessenberg Decomposition of Real Matrices,  Up: Linear Algebra
 
-14.9 Hessenberg-Triangular Decomposition of Real Matrices
-=========================================================
+14.12 Hessenberg-Triangular Decomposition of Real Matrices
+==========================================================
 
 A general real matrix pair (A, B) can be decomposed by orthogonal
 similarity transformations into the form
@@ -2162,9 +2791,9 @@
      workspace of length N is needed in WORK.
 
 
-File: gsl-ref.info,  Node: Bidiagonalization,  Next: Householder Transformations,  Prev: Hessenberg-Triangular Decomposition of Real Matrices,  Up: Linear Algebra
+File: gsl-ref.info,  Node: Bidiagonalization,  Next: Givens Rotations,  Prev: Hessenberg-Triangular Decomposition of Real Matrices,  Up: Linear Algebra
 
-14.10 Bidiagonalization
+14.13 Bidiagonalization
 =======================
 
 A general matrix A can be factorized by similarity transformations into
@@ -2210,9 +2839,37 @@
      the diagonal vector DIAG and superdiagonal vector SUPERDIAG.
 
 
-File: gsl-ref.info,  Node: Householder Transformations,  Next: Householder solver for linear systems,  Prev: Bidiagonalization,  Up: Linear Algebra
+File: gsl-ref.info,  Node: Givens Rotations,  Next: Householder Transformations,  Prev: Bidiagonalization,  Up: Linear Algebra
+
+14.14 Givens Rotations
+======================
+
+A Givens rotation is a rotation in the plane acting on two elements of a
+given vector.  It can be represented in matrix form as
+   where the \cos{\theta} and \sin{\theta} appear at the intersection of
+the ith and jth rows and columns.  When acting on a vector x,
+G(i,j,\theta) x performs a rotation of the (i,j) elements of x.  Givens
+rotations are typically used to introduce zeros in vectors, such as
+during the QR decomposition of a matrix.  In this case, it is typically
+desired to find c and s such that
+   with r = \sqrt{a^2 + b^2}.
+
+ -- Function: void gsl_linalg_givens (const double A, const double B,
+          double * C, double * S)
+     This function computes c = \cos{\theta} and s = \sin{\theta} so
+     that the Givens matrix G(\theta) acting on the vector (a,b)
+     produces (r, 0), with r = \sqrt{a^2 + b^2}.
+
+ -- Function: void gsl_linalg_givens_gv (gsl_vector * V, const size_t I,
+          const size_t J, const double C, const double S)
+     This function applies the Givens rotation defined by c =
+     \cos{\theta} and s = \sin{\theta} to the I and J elements of V.  On
+     output, (v(i),v(j)) \leftarrow G(\theta) (v(i),v(j)).
 
-14.11 Householder Transformations
+
+File: gsl-ref.info,  Node: Householder Transformations,  Next: Householder solver for linear systems,  Prev: Givens Rotations,  Up: Linear Algebra
+
+14.15 Householder Transformations
 =================================
 
 A Householder transformation is a rank-1 modification of the identity
@@ -2226,13 +2883,17 @@
 the Householder matrix to create and apply Householder transformations
 efficiently.
 
- -- Function: double gsl_linalg_householder_transform (gsl_vector * V)
+ -- Function: double gsl_linalg_householder_transform (gsl_vector * W)
  -- Function: gsl_complex gsl_linalg_complex_householder_transform
-          (gsl_vector_complex * V)
+          (gsl_vector_complex * W)
      This function prepares a Householder transformation P = I - \tau v
      v^T which can be used to zero all the elements of the input vector
-     except the first.  On output the transformation is stored in the
-     vector V and the scalar \tau is returned.
+     W except the first.  On output the Householder vector V is stored
+     in W and the scalar \tau is returned.  The householder vector V is
+     normalized so that V[0] = 1, however this 1 is not stored in the
+     output vector.  Instead, W[0] is set to the first element of the
+     transformed vector, so that if u = P w, W[0] = u[0] on output and
+     the remainder of u is zero.
 
  -- Function: int gsl_linalg_householder_hm (double TAU, const
           gsl_vector * V, gsl_matrix * A)
@@ -2261,7 +2922,7 @@
 
 File: gsl-ref.info,  Node: Householder solver for linear systems,  Next: Tridiagonal Systems,  Prev: Householder Transformations,  Up: Linear Algebra
 
-14.12 Householder solver for linear systems
+14.16 Householder solver for linear systems
 ===========================================
 
  -- Function: int gsl_linalg_HH_solve (gsl_matrix * A, const gsl_vector
@@ -2278,9 +2939,9 @@
      destroyed by the Householder transformations.
 
 
-File: gsl-ref.info,  Node: Tridiagonal Systems,  Next: Balancing,  Prev: Householder solver for linear systems,  Up: Linear Algebra
+File: gsl-ref.info,  Node: Tridiagonal Systems,  Next: Triangular Systems,  Prev: Householder solver for linear systems,  Up: Linear Algebra
 
-14.13 Tridiagonal Systems
+14.17 Tridiagonal Systems
 =========================
 
 The functions described in this section efficiently solve symmetric,
@@ -2344,9 +3005,37 @@
               ( e_3  0  e_2 d_3 )
 
 
-File: gsl-ref.info,  Node: Balancing,  Next: Linear Algebra Examples,  Prev: Tridiagonal Systems,  Up: Linear Algebra
+File: gsl-ref.info,  Node: Triangular Systems,  Next: Balancing,  Prev: Tridiagonal Systems,  Up: Linear Algebra
+
+14.18 Triangular Systems
+========================
+
+ -- Function: int gsl_linalg_tri_upper_invert (gsl_matrix * T)
+ -- Function: int gsl_linalg_tri_lower_invert (gsl_matrix * T)
+ -- Function: int gsl_linalg_tri_upper_unit_invert (gsl_matrix * T)
+ -- Function: int gsl_linalg_tri_lower_unit_invert (gsl_matrix * T)
+     These functions calculate the in-place inverse of the triangular
+     matrix T.  When the 'upper' prefix is specified, then the upper
+     triangle of T is used, and when the 'lower' prefix is specified,
+     the lower triangle is used.  If the 'unit' prefix is specified,
+     then the diagonal elements of the matrix T are taken as unity and
+     are not referenced.  Otherwise the diagonal elements are used in
+     the inversion.
+
+ -- Function: int gsl_linalg_tri_upper_rcond (const gsl_matrix * T,
+          double * RCOND, gsl_vector * WORK)
+ -- Function: int gsl_linalg_tri_lower_rcond (const gsl_matrix * T,
+          double * RCOND, gsl_vector * WORK)
+     These functions estimate the reciprocal condition number, in the
+     1-norm, of the upper or lower N-by-N triangular matrix T.  The
+     reciprocal condition number is stored in RCOND on output, and is
+     defined by 1 / (||T||_1 \cdot ||T^{-1}||_1).  Additional workspace
+     of size 3 N is required in WORK.
+
+
+File: gsl-ref.info,  Node: Balancing,  Next: Linear Algebra Examples,  Prev: Triangular Systems,  Up: Linear Algebra
 
-14.14 Balancing
+14.19 Balancing
 ===============
 
 The process of balancing a matrix applies similarity transformations to
@@ -2369,7 +3058,7 @@
 
 File: gsl-ref.info,  Node: Linear Algebra Examples,  Next: Linear Algebra References and Further Reading,  Prev: Balancing,  Up: Linear Algebra
 
-14.15 Examples
+14.20 Examples
 ==============
 
 The following program solves the linear system A x = b.  The system to
@@ -2421,7 +3110,8 @@
 
 Here is the output from the program,
 
-     x = -4.05205
+     x =
+     -4.05205
      -12.6056
      1.66091
      8.69377
@@ -2449,7 +3139,7 @@
 
 File: gsl-ref.info,  Node: Linear Algebra References and Further Reading,  Prev: Linear Algebra Examples,  Up: Linear Algebra
 
-14.16 References and Further Reading
+14.21 References and Further Reading
 ====================================
 
 Further information on the algorithms described in this section can be
@@ -2491,6 +3181,14 @@
      Available from netlib, <http://www.netlib.org/lapack/> in the
      'lawns' or 'lawnspdf' directories.
 
+The algorithm for estimating a matrix condition number is described in
+the following paper,
+
+     N. J. Higham, "FORTRAN codes for estimating the one-norm of a real
+     or complex matrix, with applications to condition estimation", ACM
+     Trans.  Math.  Soft., vol.  14, no.  4, pp.  381-396, December
+     1988.
+
 
 File: gsl-ref.info,  Node: Eigensystems,  Next: Fast Fourier Transforms,  Prev: Linear Algebra,  Up: Top
 
@@ -3748,9 +4446,9 @@
        wavetable = gsl_fft_complex_wavetable_alloc (n);
        workspace = gsl_fft_complex_workspace_alloc (n);
 
-       for (i = 0; i < wavetable->nf; i++)
+       for (i = 0; i < (int) wavetable->nf; i++)
          {
-            printf ("# factor %d: %d\n", i,
+            printf ("# factor %d: %zu\n", i,
                     wavetable->factor[i]);
          }
 
@@ -5001,7 +5699,7 @@
        printf ("exact result    = % .18f\n", expected);
        printf ("estimated error = % .18f\n", error);
        printf ("actual error    = % .18f\n", result - expected);
-       printf ("intervals =  %d\n", w->size);
+       printf ("intervals       = %zu\n", w->size);
 
        gsl_integration_workspace_free (w);
 
@@ -5012,11 +5710,11 @@
 subdivisions.
 
      $ ./a.out
-     result          = -3.999999999999973799
+     result          = -4.000000000000085265
      exact result    = -4.000000000000000000
-     estimated error =  0.000000000000246025
-     actual error    =  0.000000000000026201
-     intervals =  8
+     estimated error =  0.000000000000135447
+     actual error    = -0.000000000000085265
+     intervals       = 8
 
 In fact, the extrapolation procedure used by 'QAGS' produces an accuracy
 of almost twice as many digits.  The error estimate returned by the
@@ -6006,8 +6704,6 @@
 'mrg',
 
      $ GSL_RNG_SEED=123 GSL_RNG_TYPE=mrg ./a.out
-     GSL_RNG_TYPE=mrg
-     GSL_RNG_SEED=123
      0.33050
      0.86631
      0.32982
@@ -6088,7 +6784,7 @@
 * Quasi-random number generator initialization::  
 * Sampling from a quasi-random number generator::  
 * Auxiliary quasi-random number generator functions::  
-* Saving and resorting quasi-random number generator state::  
+* Saving and restoring quasi-random number generator state::  
 * Quasi-random number generator algorithms::  
 * Quasi-random number generator examples::  
 * Quasi-random number references::  
@@ -6129,7 +6825,7 @@
      'HAVE_INLINE' is defined.
 
 
-File: gsl-ref.info,  Node: Auxiliary quasi-random number generator functions,  Next: Saving and resorting quasi-random number generator state,  Prev: Sampling from a quasi-random number generator,  Up: Quasi-Random Sequences
+File: gsl-ref.info,  Node: Auxiliary quasi-random number generator functions,  Next: Saving and restoring quasi-random number generator state,  Prev: Sampling from a quasi-random number generator,  Up: Quasi-Random Sequences
 
 19.3 Auxiliary quasi-random number generator functions
 ======================================================
@@ -6149,9 +6845,9 @@
           fwrite (state, n, 1, stream);
 
 
-File: gsl-ref.info,  Node: Saving and resorting quasi-random number generator state,  Next: Quasi-random number generator algorithms,  Prev: Auxiliary quasi-random number generator functions,  Up: Quasi-Random Sequences
+File: gsl-ref.info,  Node: Saving and restoring quasi-random number generator state,  Next: Quasi-random number generator algorithms,  Prev: Auxiliary quasi-random number generator functions,  Up: Quasi-Random Sequences
 
-19.4 Saving and resorting quasi-random number generator state
+19.4 Saving and restoring quasi-random number generator state
 =============================================================
 
  -- Function: int gsl_qrng_memcpy (gsl_qrng * DEST, const gsl_qrng *
@@ -6164,801 +6860,3 @@
      This function returns a pointer to a newly created generator which
      is an exact copy of the generator Q.
 
-
-File: gsl-ref.info,  Node: Quasi-random number generator algorithms,  Next: Quasi-random number generator examples,  Prev: Saving and resorting quasi-random number generator state,  Up: Quasi-Random Sequences
-
-19.5 Quasi-random number generator algorithms
-=============================================
-
-The following quasi-random sequence algorithms are available,
-
- -- Generator: gsl_qrng_niederreiter_2
-     This generator uses the algorithm described in Bratley, Fox,
-     Niederreiter, 'ACM Trans. Model. Comp. Sim.' 2, 195 (1992).  It is
-     valid up to 12 dimensions.
-
- -- Generator: gsl_qrng_sobol
-     This generator uses the Sobol sequence described in Antonov,
-     Saleev, 'USSR Comput. Maths. Math. Phys.' 19, 252 (1980).  It is
-     valid up to 40 dimensions.
-
- -- Generator: gsl_qrng_halton
- -- Generator: gsl_qrng_reversehalton
-     These generators use the Halton and reverse Halton sequences
-     described in J.H. Halton, 'Numerische Mathematik' 2, 84-90 (1960)
-     and B. Vandewoestyne and R. Cools 'Computational and Applied
-     Mathematics' 189, 1&2, 341-361 (2006).  They are valid up to 1229
-     dimensions.
-
-
-File: gsl-ref.info,  Node: Quasi-random number generator examples,  Next: Quasi-random number references,  Prev: Quasi-random number generator algorithms,  Up: Quasi-Random Sequences
-
-19.6 Examples
-=============
-
-The following program prints the first 1024 points of the 2-dimensional
-Sobol sequence.
-
-     #include <stdio.h>
-     #include <gsl/gsl_qrng.h>
-
-     int
-     main (void)
-     {
-       int i;
-       gsl_qrng * q = gsl_qrng_alloc (gsl_qrng_sobol, 2);
-
-       for (i = 0; i < 1024; i++)
-         {
-           double v[2];
-           gsl_qrng_get (q, v);
-           printf ("%.5f %.5f\n", v[0], v[1]);
-         }
-
-       gsl_qrng_free (q);
-       return 0;
-     }
-
-Here is the output from the program,
-
-     $ ./a.out
-     0.50000 0.50000
-     0.75000 0.25000
-     0.25000 0.75000
-     0.37500 0.37500
-     0.87500 0.87500
-     0.62500 0.12500
-     0.12500 0.62500
-     ....
-
-It can be seen that successive points progressively fill-in the spaces
-between previous points.
-
-
-File: gsl-ref.info,  Node: Quasi-random number references,  Prev: Quasi-random number generator examples,  Up: Quasi-Random Sequences
-
-19.7 References
-===============
-
-The implementations of the quasi-random sequence routines are based on
-the algorithms described in the following paper,
-
-     P. Bratley and B.L. Fox and H. Niederreiter, "Algorithm 738:
-     Programs to Generate Niederreiter's Low-discrepancy Sequences",
-     'ACM Transactions on Mathematical Software', Vol. 20, No. 4,
-     December, 1994, p. 494-495.
-
-
-File: gsl-ref.info,  Node: Random Number Distributions,  Next: Statistics,  Prev: Quasi-Random Sequences,  Up: Top
-
-20 Random Number Distributions
-******************************
-
-This chapter describes functions for generating random variates and
-computing their probability distributions.  Samples from the
-distributions described in this chapter can be obtained using any of the
-random number generators in the library as an underlying source of
-randomness.
-
-   In the simplest cases a non-uniform distribution can be obtained
-analytically from the uniform distribution of a random number generator
-by applying an appropriate transformation.  This method uses one call to
-the random number generator.  More complicated distributions are created
-by the "acceptance-rejection" method, which compares the desired
-distribution against a distribution which is similar and known
-analytically.  This usually requires several samples from the generator.
-
-   The library also provides cumulative distribution functions and
-inverse cumulative distribution functions, sometimes referred to as
-quantile functions.  The cumulative distribution functions and their
-inverses are computed separately for the upper and lower tails of the
-distribution, allowing full accuracy to be retained for small results.
-
-   The functions for random variates and probability density functions
-described in this section are declared in 'gsl_randist.h'.  The
-corresponding cumulative distribution functions are declared in
-'gsl_cdf.h'.
-
-   Note that the discrete random variate functions always return a value
-of type 'unsigned int', and on most platforms this has a maximum value
-of 2^32-1 ~=~ 4.29e9.  They should only be called with a safe range of
-parameters (where there is a negligible probability of a variate
-exceeding this limit) to prevent incorrect results due to overflow.
-
-* Menu:
-
-* Random Number Distribution Introduction::  
-* The Gaussian Distribution::   
-* The Gaussian Tail Distribution::  
-* The Bivariate Gaussian Distribution::  
-* The Exponential Distribution::  
-* The Laplace Distribution::    
-* The Exponential Power Distribution::  
-* The Cauchy Distribution::     
-* The Rayleigh Distribution::   
-* The Rayleigh Tail Distribution::  
-* The Landau Distribution::     
-* The Levy alpha-Stable Distributions::  
-* The Levy skew alpha-Stable Distribution::  
-* The Gamma Distribution::      
-* The Flat (Uniform) Distribution::  
-* The Lognormal Distribution::  
-* The Chi-squared Distribution::  
-* The F-distribution::          
-* The t-distribution::          
-* The Beta Distribution::       
-* The Logistic Distribution::   
-* The Pareto Distribution::     
-* Spherical Vector Distributions::  
-* The Weibull Distribution::    
-* The Type-1 Gumbel Distribution::  
-* The Type-2 Gumbel Distribution::  
-* The Dirichlet Distribution::  
-* General Discrete Distributions::  
-* The Poisson Distribution::    
-* The Bernoulli Distribution::  
-* The Binomial Distribution::   
-* The Multinomial Distribution::  
-* The Negative Binomial Distribution::  
-* The Pascal Distribution::     
-* The Geometric Distribution::  
-* The Hypergeometric Distribution::  
-* The Logarithmic Distribution::  
-* Shuffling and Sampling::      
-* Random Number Distribution Examples::  
-* Random Number Distribution References and Further Reading::  
-
-
-File: gsl-ref.info,  Node: Random Number Distribution Introduction,  Next: The Gaussian Distribution,  Up: Random Number Distributions
-
-20.1 Introduction
-=================
-
-Continuous random number distributions are defined by a probability
-density function, p(x), such that the probability of x occurring in the
-infinitesimal range x to x+dx is p dx.
-
-   The cumulative distribution function for the lower tail P(x) is
-defined by the integral,
-
-     P(x) = \int_{-\infty}^{x} dx' p(x')
-
-and gives the probability of a variate taking a value less than x.
-
-   The cumulative distribution function for the upper tail Q(x) is
-defined by the integral,
-
-     Q(x) = \int_{x}^{+\infty} dx' p(x')
-
-and gives the probability of a variate taking a value greater than x.
-
-   The upper and lower cumulative distribution functions are related by
-P(x) + Q(x) = 1 and satisfy 0 <= P(x) <= 1, 0 <= Q(x) <= 1.
-
-   The inverse cumulative distributions, x=P^{-1}(P) and x=Q^{-1}(Q)
-give the values of x which correspond to a specific value of P or Q.
-They can be used to find confidence limits from probability values.
-
-   For discrete distributions the probability of sampling the integer
-value k is given by p(k), where \sum_k p(k) = 1.  The cumulative
-distribution for the lower tail P(k) of a discrete distribution is
-defined as,
-
-     P(k) = \sum_{i <= k} p(i)
-
-where the sum is over the allowed range of the distribution less than or
-equal to k.
-
-   The cumulative distribution for the upper tail of a discrete
-distribution Q(k) is defined as
-
-     Q(k) = \sum_{i > k} p(i)
-
-giving the sum of probabilities for all values greater than k.  These
-two definitions satisfy the identity P(k)+Q(k)=1.
-
-   If the range of the distribution is 1 to n inclusive then P(n)=1,
-Q(n)=0 while P(1) = p(1), Q(1)=1-p(1).
-
-
-File: gsl-ref.info,  Node: The Gaussian Distribution,  Next: The Gaussian Tail Distribution,  Prev: Random Number Distribution Introduction,  Up: Random Number Distributions
-
-20.2 The Gaussian Distribution
-==============================
-
- -- Function: double gsl_ran_gaussian (const gsl_rng * R, double SIGMA)
-     This function returns a Gaussian random variate, with mean zero and
-     standard deviation SIGMA.  The probability distribution for
-     Gaussian random variates is,
-
-          p(x) dx = {1 \over \sqrt{2 \pi \sigma^2}} \exp (-x^2 / 2\sigma^2) dx
-
-     for x in the range -\infty to +\infty.  Use the transformation z =
-     \mu + x on the numbers returned by 'gsl_ran_gaussian' to obtain a
-     Gaussian distribution with mean \mu.  This function uses the
-     Box-Muller algorithm which requires two calls to the random number
-     generator R.
-
- -- Function: double gsl_ran_gaussian_pdf (double X, double SIGMA)
-     This function computes the probability density p(x) at X for a
-     Gaussian distribution with standard deviation SIGMA, using the
-     formula given above.
-
-
- -- Function: double gsl_ran_gaussian_ziggurat (const gsl_rng * R,
-          double SIGMA)
- -- Function: double gsl_ran_gaussian_ratio_method (const gsl_rng * R,
-          double SIGMA)
-     This function computes a Gaussian random variate using the
-     alternative Marsaglia-Tsang ziggurat and Kinderman-Monahan-Leva
-     ratio methods.  The Ziggurat algorithm is the fastest available
-     algorithm in most cases.
-
- -- Function: double gsl_ran_ugaussian (const gsl_rng * R)
- -- Function: double gsl_ran_ugaussian_pdf (double X)
- -- Function: double gsl_ran_ugaussian_ratio_method (const gsl_rng * R)
-     These functions compute results for the unit Gaussian distribution.
-     They are equivalent to the functions above with a standard
-     deviation of one, SIGMA = 1.
-
- -- Function: double gsl_cdf_gaussian_P (double X, double SIGMA)
- -- Function: double gsl_cdf_gaussian_Q (double X, double SIGMA)
- -- Function: double gsl_cdf_gaussian_Pinv (double P, double SIGMA)
- -- Function: double gsl_cdf_gaussian_Qinv (double Q, double SIGMA)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the Gaussian distribution with standard
-     deviation SIGMA.
-
- -- Function: double gsl_cdf_ugaussian_P (double X)
- -- Function: double gsl_cdf_ugaussian_Q (double X)
- -- Function: double gsl_cdf_ugaussian_Pinv (double P)
- -- Function: double gsl_cdf_ugaussian_Qinv (double Q)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the unit Gaussian distribution.
-
-
-File: gsl-ref.info,  Node: The Gaussian Tail Distribution,  Next: The Bivariate Gaussian Distribution,  Prev: The Gaussian Distribution,  Up: Random Number Distributions
-
-20.3 The Gaussian Tail Distribution
-===================================
-
- -- Function: double gsl_ran_gaussian_tail (const gsl_rng * R, double A,
-          double SIGMA)
-     This function provides random variates from the upper tail of a
-     Gaussian distribution with standard deviation SIGMA.  The values
-     returned are larger than the lower limit A, which must be positive.
-     The method is based on Marsaglia's famous rectangle-wedge-tail
-     algorithm (Ann.  Math.  Stat.  32, 894-899 (1961)), with this
-     aspect explained in Knuth, v2, 3rd ed, p139,586 (exercise 11).
-
-     The probability distribution for Gaussian tail random variates is,
-
-          p(x) dx = {1 \over N(a;\sigma) \sqrt{2 \pi \sigma^2}} \exp (- x^2/(2 \sigma^2)) dx
-
-     for x > a where N(a;\sigma) is the normalization constant,
-
-          N(a;\sigma) = (1/2) erfc(a / sqrt(2 sigma^2)).
-
- -- Function: double gsl_ran_gaussian_tail_pdf (double X, double A,
-          double SIGMA)
-     This function computes the probability density p(x) at X for a
-     Gaussian tail distribution with standard deviation SIGMA and lower
-     limit A, using the formula given above.
-
-
- -- Function: double gsl_ran_ugaussian_tail (const gsl_rng * R, double
-          A)
- -- Function: double gsl_ran_ugaussian_tail_pdf (double X, double A)
-     These functions compute results for the tail of a unit Gaussian
-     distribution.  They are equivalent to the functions above with a
-     standard deviation of one, SIGMA = 1.
-
-
-File: gsl-ref.info,  Node: The Bivariate Gaussian Distribution,  Next: The Exponential Distribution,  Prev: The Gaussian Tail Distribution,  Up: Random Number Distributions
-
-20.4 The Bivariate Gaussian Distribution
-========================================
-
- -- Function: void gsl_ran_bivariate_gaussian (const gsl_rng * R, double
-          SIGMA_X, double SIGMA_Y, double RHO, double * X, double * Y)
-     This function generates a pair of correlated Gaussian variates,
-     with mean zero, correlation coefficient RHO and standard deviations
-     SIGMA_X and SIGMA_Y in the x and y directions.  The probability
-     distribution for bivariate Gaussian random variates is,
-
-          p(x,y) dx dy = {1 \over 2 \pi \sigma_x \sigma_y \sqrt{1-\rho^2}} \exp (-(x^2/\sigma_x^2 + y^2/\sigma_y^2 - 2 \rho x y/(\sigma_x\sigma_y))/2(1-\rho^2)) dx dy
-
-     for x,y in the range -\infty to +\infty.  The correlation
-     coefficient RHO should lie between 1 and -1.
-
- -- Function: double gsl_ran_bivariate_gaussian_pdf (double X, double Y,
-          double SIGMA_X, double SIGMA_Y, double RHO)
-     This function computes the probability density p(x,y) at (X,Y) for
-     a bivariate Gaussian distribution with standard deviations SIGMA_X,
-     SIGMA_Y and correlation coefficient RHO, using the formula given
-     above.
-
-
-
-File: gsl-ref.info,  Node: The Exponential Distribution,  Next: The Laplace Distribution,  Prev: The Bivariate Gaussian Distribution,  Up: Random Number Distributions
-
-20.5 The Exponential Distribution
-=================================
-
- -- Function: double gsl_ran_exponential (const gsl_rng * R, double MU)
-     This function returns a random variate from the exponential
-     distribution with mean MU.  The distribution is,
-
-          p(x) dx = {1 \over \mu} \exp(-x/\mu) dx
-
-     for x >= 0.
-
- -- Function: double gsl_ran_exponential_pdf (double X, double MU)
-     This function computes the probability density p(x) at X for an
-     exponential distribution with mean MU, using the formula given
-     above.
-
-
- -- Function: double gsl_cdf_exponential_P (double X, double MU)
- -- Function: double gsl_cdf_exponential_Q (double X, double MU)
- -- Function: double gsl_cdf_exponential_Pinv (double P, double MU)
- -- Function: double gsl_cdf_exponential_Qinv (double Q, double MU)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the exponential distribution with mean
-     MU.
-
-
-File: gsl-ref.info,  Node: The Laplace Distribution,  Next: The Exponential Power Distribution,  Prev: The Exponential Distribution,  Up: Random Number Distributions
-
-20.6 The Laplace Distribution
-=============================
-
- -- Function: double gsl_ran_laplace (const gsl_rng * R, double A)
-     This function returns a random variate from the Laplace
-     distribution with width A.  The distribution is,
-
-          p(x) dx = {1 \over 2 a}  \exp(-|x/a|) dx
-
-     for -\infty < x < \infty.
-
- -- Function: double gsl_ran_laplace_pdf (double X, double A)
-     This function computes the probability density p(x) at X for a
-     Laplace distribution with width A, using the formula given above.
-
-
- -- Function: double gsl_cdf_laplace_P (double X, double A)
- -- Function: double gsl_cdf_laplace_Q (double X, double A)
- -- Function: double gsl_cdf_laplace_Pinv (double P, double A)
- -- Function: double gsl_cdf_laplace_Qinv (double Q, double A)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the Laplace distribution with width A.
-
-
-File: gsl-ref.info,  Node: The Exponential Power Distribution,  Next: The Cauchy Distribution,  Prev: The Laplace Distribution,  Up: Random Number Distributions
-
-20.7 The Exponential Power Distribution
-=======================================
-
- -- Function: double gsl_ran_exppow (const gsl_rng * R, double A, double
-          B)
-     This function returns a random variate from the exponential power
-     distribution with scale parameter A and exponent B.  The
-     distribution is,
-
-          p(x) dx = {1 \over 2 a \Gamma(1+1/b)} \exp(-|x/a|^b) dx
-
-     for x >= 0.  For b = 1 this reduces to the Laplace distribution.
-     For b = 2 it has the same form as a Gaussian distribution, but with
-     a = \sqrt{2} \sigma.
-
- -- Function: double gsl_ran_exppow_pdf (double X, double A, double B)
-     This function computes the probability density p(x) at X for an
-     exponential power distribution with scale parameter A and exponent
-     B, using the formula given above.
-
-
- -- Function: double gsl_cdf_exppow_P (double X, double A, double B)
- -- Function: double gsl_cdf_exppow_Q (double X, double A, double B)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) for the exponential power distribution with parameters A and
-     B.
-
-
-File: gsl-ref.info,  Node: The Cauchy Distribution,  Next: The Rayleigh Distribution,  Prev: The Exponential Power Distribution,  Up: Random Number Distributions
-
-20.8 The Cauchy Distribution
-============================
-
- -- Function: double gsl_ran_cauchy (const gsl_rng * R, double A)
-     This function returns a random variate from the Cauchy distribution
-     with scale parameter A.  The probability distribution for Cauchy
-     random variates is,
-
-          p(x) dx = {1 \over a\pi (1 + (x/a)^2) } dx
-
-     for x in the range -\infty to +\infty.  The Cauchy distribution is
-     also known as the Lorentz distribution.
-
- -- Function: double gsl_ran_cauchy_pdf (double X, double A)
-     This function computes the probability density p(x) at X for a
-     Cauchy distribution with scale parameter A, using the formula given
-     above.
-
-
- -- Function: double gsl_cdf_cauchy_P (double X, double A)
- -- Function: double gsl_cdf_cauchy_Q (double X, double A)
- -- Function: double gsl_cdf_cauchy_Pinv (double P, double A)
- -- Function: double gsl_cdf_cauchy_Qinv (double Q, double A)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the Cauchy distribution with scale
-     parameter A.
-
-
-File: gsl-ref.info,  Node: The Rayleigh Distribution,  Next: The Rayleigh Tail Distribution,  Prev: The Cauchy Distribution,  Up: Random Number Distributions
-
-20.9 The Rayleigh Distribution
-==============================
-
- -- Function: double gsl_ran_rayleigh (const gsl_rng * R, double SIGMA)
-     This function returns a random variate from the Rayleigh
-     distribution with scale parameter SIGMA.  The distribution is,
-
-          p(x) dx = {x \over \sigma^2} \exp(- x^2/(2 \sigma^2)) dx
-
-     for x > 0.
-
- -- Function: double gsl_ran_rayleigh_pdf (double X, double SIGMA)
-     This function computes the probability density p(x) at X for a
-     Rayleigh distribution with scale parameter SIGMA, using the formula
-     given above.
-
-
- -- Function: double gsl_cdf_rayleigh_P (double X, double SIGMA)
- -- Function: double gsl_cdf_rayleigh_Q (double X, double SIGMA)
- -- Function: double gsl_cdf_rayleigh_Pinv (double P, double SIGMA)
- -- Function: double gsl_cdf_rayleigh_Qinv (double Q, double SIGMA)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the Rayleigh distribution with scale
-     parameter SIGMA.
-
-
-File: gsl-ref.info,  Node: The Rayleigh Tail Distribution,  Next: The Landau Distribution,  Prev: The Rayleigh Distribution,  Up: Random Number Distributions
-
-20.10 The Rayleigh Tail Distribution
-====================================
-
- -- Function: double gsl_ran_rayleigh_tail (const gsl_rng * R, double A,
-          double SIGMA)
-     This function returns a random variate from the tail of the
-     Rayleigh distribution with scale parameter SIGMA and a lower limit
-     of A.  The distribution is,
-
-          p(x) dx = {x \over \sigma^2} \exp ((a^2 - x^2) /(2 \sigma^2)) dx
-
-     for x > a.
-
- -- Function: double gsl_ran_rayleigh_tail_pdf (double X, double A,
-          double SIGMA)
-     This function computes the probability density p(x) at X for a
-     Rayleigh tail distribution with scale parameter SIGMA and lower
-     limit A, using the formula given above.
-
-
-
-File: gsl-ref.info,  Node: The Landau Distribution,  Next: The Levy alpha-Stable Distributions,  Prev: The Rayleigh Tail Distribution,  Up: Random Number Distributions
-
-20.11 The Landau Distribution
-=============================
-
- -- Function: double gsl_ran_landau (const gsl_rng * R)
-     This function returns a random variate from the Landau
-     distribution.  The probability distribution for Landau random
-     variates is defined analytically by the complex integral,
-
-          p(x) = (1/(2 \pi i)) \int_{c-i\infty}^{c+i\infty} ds exp(s log(s) + x s)
-     For numerical purposes it is more convenient to use the following
-     equivalent form of the integral,
-
-          p(x) = (1/\pi) \int_0^\infty dt \exp(-t \log(t) - x t) \sin(\pi t).
-
- -- Function: double gsl_ran_landau_pdf (double X)
-     This function computes the probability density p(x) at X for the
-     Landau distribution using an approximation to the formula given
-     above.
-
-
-
-File: gsl-ref.info,  Node: The Levy alpha-Stable Distributions,  Next: The Levy skew alpha-Stable Distribution,  Prev: The Landau Distribution,  Up: Random Number Distributions
-
-20.12 The Levy alpha-Stable Distributions
-=========================================
-
- -- Function: double gsl_ran_levy (const gsl_rng * R, double C, double
-          ALPHA)
-     This function returns a random variate from the Levy symmetric
-     stable distribution with scale C and exponent ALPHA.  The symmetric
-     stable probability distribution is defined by a Fourier transform,
-
-          p(x) = {1 \over 2 \pi} \int_{-\infty}^{+\infty} dt \exp(-it x - |c t|^alpha)
-
-     There is no explicit solution for the form of p(x) and the library
-     does not define a corresponding 'pdf' function.  For \alpha = 1 the
-     distribution reduces to the Cauchy distribution.  For \alpha = 2 it
-     is a Gaussian distribution with \sigma = \sqrt{2} c.  For \alpha <
-     1 the tails of the distribution become extremely wide.
-
-     The algorithm only works for 0 < alpha <= 2.
-
-
-
-File: gsl-ref.info,  Node: The Levy skew alpha-Stable Distribution,  Next: The Gamma Distribution,  Prev: The Levy alpha-Stable Distributions,  Up: Random Number Distributions
-
-20.13 The Levy skew alpha-Stable Distribution
-=============================================
-
- -- Function: double gsl_ran_levy_skew (const gsl_rng * R, double C,
-          double ALPHA, double BETA)
-     This function returns a random variate from the Levy skew stable
-     distribution with scale C, exponent ALPHA and skewness parameter
-     BETA.  The skewness parameter must lie in the range [-1,1].  The
-     Levy skew stable probability distribution is defined by a Fourier
-     transform,
-
-          p(x) = {1 \over 2 \pi} \int_{-\infty}^{+\infty} dt \exp(-it x - |c t|^alpha (1-i beta sign(t) tan(pi alpha/2)))
-
-     When \alpha = 1 the term \tan(\pi \alpha/2) is replaced by
-     -(2/\pi)\log|t|.  There is no explicit solution for the form of
-     p(x) and the library does not define a corresponding 'pdf'
-     function.  For \alpha = 2 the distribution reduces to a Gaussian
-     distribution with \sigma = \sqrt{2} c and the skewness parameter
-     has no effect.  For \alpha < 1 the tails of the distribution become
-     extremely wide.  The symmetric distribution corresponds to \beta =
-     0.
-
-     The algorithm only works for 0 < alpha <= 2.
-
-   The Levy alpha-stable distributions have the property that if N
-alpha-stable variates are drawn from the distribution p(c, \alpha,
-\beta) then the sum Y = X_1 + X_2 + \dots + X_N will also be distributed
-as an alpha-stable variate, p(N^(1/\alpha) c, \alpha, \beta).
-
-
-
-File: gsl-ref.info,  Node: The Gamma Distribution,  Next: The Flat (Uniform) Distribution,  Prev: The Levy skew alpha-Stable Distribution,  Up: Random Number Distributions
-
-20.14 The Gamma Distribution
-============================
-
- -- Function: double gsl_ran_gamma (const gsl_rng * R, double A, double
-          B)
-     This function returns a random variate from the gamma distribution.
-     The distribution function is,
-
-          p(x) dx = {1 \over \Gamma(a) b^a} x^{a-1} e^{-x/b} dx
-
-     for x > 0.
-
-     The gamma distribution with an integer parameter A is known as the
-     Erlang distribution.
-
-     The variates are computed using the Marsaglia-Tsang fast gamma
-     method.  This function for this method was previously called
-     'gsl_ran_gamma_mt' and can still be accessed using this name.
-
- -- Function: double gsl_ran_gamma_knuth (const gsl_rng * R, double A,
-          double B)
-     This function returns a gamma variate using the algorithms from
-     Knuth (vol 2).
-
- -- Function: double gsl_ran_gamma_pdf (double X, double A, double B)
-     This function computes the probability density p(x) at X for a
-     gamma distribution with parameters A and B, using the formula given
-     above.
-
-
- -- Function: double gsl_cdf_gamma_P (double X, double A, double B)
- -- Function: double gsl_cdf_gamma_Q (double X, double A, double B)
- -- Function: double gsl_cdf_gamma_Pinv (double P, double A, double B)
- -- Function: double gsl_cdf_gamma_Qinv (double Q, double A, double B)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the gamma distribution with parameters
-     A and B.
-
-
-File: gsl-ref.info,  Node: The Flat (Uniform) Distribution,  Next: The Lognormal Distribution,  Prev: The Gamma Distribution,  Up: Random Number Distributions
-
-20.15 The Flat (Uniform) Distribution
-=====================================
-
- -- Function: double gsl_ran_flat (const gsl_rng * R, double A, double
-          B)
-     This function returns a random variate from the flat (uniform)
-     distribution from A to B.  The distribution is,
-
-          p(x) dx = {1 \over (b-a)} dx
-
-     if a <= x < b and 0 otherwise.
-
- -- Function: double gsl_ran_flat_pdf (double X, double A, double B)
-     This function computes the probability density p(x) at X for a
-     uniform distribution from A to B, using the formula given above.
-
-
- -- Function: double gsl_cdf_flat_P (double X, double A, double B)
- -- Function: double gsl_cdf_flat_Q (double X, double A, double B)
- -- Function: double gsl_cdf_flat_Pinv (double P, double A, double B)
- -- Function: double gsl_cdf_flat_Qinv (double Q, double A, double B)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for a uniform distribution from A to B.
-
-
-File: gsl-ref.info,  Node: The Lognormal Distribution,  Next: The Chi-squared Distribution,  Prev: The Flat (Uniform) Distribution,  Up: Random Number Distributions
-
-20.16 The Lognormal Distribution
-================================
-
- -- Function: double gsl_ran_lognormal (const gsl_rng * R, double ZETA,
-          double SIGMA)
-     This function returns a random variate from the lognormal
-     distribution.  The distribution function is,
-
-          p(x) dx = {1 \over x \sqrt{2 \pi \sigma^2} } \exp(-(\ln(x) - \zeta)^2/2 \sigma^2) dx
-
-     for x > 0.
-
- -- Function: double gsl_ran_lognormal_pdf (double X, double ZETA,
-          double SIGMA)
-     This function computes the probability density p(x) at X for a
-     lognormal distribution with parameters ZETA and SIGMA, using the
-     formula given above.
-
-
- -- Function: double gsl_cdf_lognormal_P (double X, double ZETA, double
-          SIGMA)
- -- Function: double gsl_cdf_lognormal_Q (double X, double ZETA, double
-          SIGMA)
- -- Function: double gsl_cdf_lognormal_Pinv (double P, double ZETA,
-          double SIGMA)
- -- Function: double gsl_cdf_lognormal_Qinv (double Q, double ZETA,
-          double SIGMA)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the lognormal distribution with
-     parameters ZETA and SIGMA.
-
-
-File: gsl-ref.info,  Node: The Chi-squared Distribution,  Next: The F-distribution,  Prev: The Lognormal Distribution,  Up: Random Number Distributions
-
-20.17 The Chi-squared Distribution
-==================================
-
-The chi-squared distribution arises in statistics.  If Y_i are n
-independent Gaussian random variates with unit variance then the
-sum-of-squares,
-
-     X_i = \sum_i Y_i^2
-
-has a chi-squared distribution with n degrees of freedom.
-
- -- Function: double gsl_ran_chisq (const gsl_rng * R, double NU)
-     This function returns a random variate from the chi-squared
-     distribution with NU degrees of freedom.  The distribution function
-     is,
-
-          p(x) dx = {1 \over 2 \Gamma(\nu/2) } (x/2)^{\nu/2 - 1} \exp(-x/2) dx
-
-     for x >= 0.
-
- -- Function: double gsl_ran_chisq_pdf (double X, double NU)
-     This function computes the probability density p(x) at X for a
-     chi-squared distribution with NU degrees of freedom, using the
-     formula given above.
-
-
- -- Function: double gsl_cdf_chisq_P (double X, double NU)
- -- Function: double gsl_cdf_chisq_Q (double X, double NU)
- -- Function: double gsl_cdf_chisq_Pinv (double P, double NU)
- -- Function: double gsl_cdf_chisq_Qinv (double Q, double NU)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the chi-squared distribution with NU
-     degrees of freedom.
-
-
-File: gsl-ref.info,  Node: The F-distribution,  Next: The t-distribution,  Prev: The Chi-squared Distribution,  Up: Random Number Distributions
-
-20.18 The F-distribution
-========================
-
-The F-distribution arises in statistics.  If Y_1 and Y_2 are chi-squared
-deviates with \nu_1 and \nu_2 degrees of freedom then the ratio,
-
-     X = { (Y_1 / \nu_1) \over (Y_2 / \nu_2) }
-
-has an F-distribution F(x;\nu_1,\nu_2).
-
- -- Function: double gsl_ran_fdist (const gsl_rng * R, double NU1,
-          double NU2)
-     This function returns a random variate from the F-distribution with
-     degrees of freedom NU1 and NU2.  The distribution function is,
-
-          p(x) dx =
-             { \Gamma((\nu_1 + \nu_2)/2)
-                  \over \Gamma(\nu_1/2) \Gamma(\nu_2/2) }
-             \nu_1^{\nu_1/2} \nu_2^{\nu_2/2}
-             x^{\nu_1/2 - 1} (\nu_2 + \nu_1 x)^{-\nu_1/2 -\nu_2/2}
-
-     for x >= 0.
-
- -- Function: double gsl_ran_fdist_pdf (double X, double NU1, double
-          NU2)
-     This function computes the probability density p(x) at X for an
-     F-distribution with NU1 and NU2 degrees of freedom, using the
-     formula given above.
-
-
- -- Function: double gsl_cdf_fdist_P (double X, double NU1, double NU2)
- -- Function: double gsl_cdf_fdist_Q (double X, double NU1, double NU2)
- -- Function: double gsl_cdf_fdist_Pinv (double P, double NU1, double
-          NU2)
- -- Function: double gsl_cdf_fdist_Qinv (double Q, double NU1, double
-          NU2)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the F-distribution with NU1 and NU2
-     degrees of freedom.
-
-
-File: gsl-ref.info,  Node: The t-distribution,  Next: The Beta Distribution,  Prev: The F-distribution,  Up: Random Number Distributions
-
-20.19 The t-distribution
-========================
-
-The t-distribution arises in statistics.  If Y_1 has a normal
-distribution and Y_2 has a chi-squared distribution with \nu degrees of
-freedom then the ratio,
-
-     X = { Y_1 \over \sqrt{Y_2 / \nu} }
-
-has a t-distribution t(x;\nu) with \nu degrees of freedom.
-
- -- Function: double gsl_ran_tdist (const gsl_rng * R, double NU)
-     This function returns a random variate from the t-distribution.
-     The distribution function is,
-
-          p(x) dx = {\Gamma((\nu + 1)/2) \over \sqrt{\pi \nu} \Gamma(\nu/2)}
-             (1 + x^2/\nu)^{-(\nu + 1)/2} dx
-
-     for -\infty < x < +\infty.
-
- -- Function: double gsl_ran_tdist_pdf (double X, double NU)
-     This function computes the probability density p(x) at X for a
-     t-distribution with NU degrees of freedom, using the formula given
-     above.
-
-
- -- Function: double gsl_cdf_tdist_P (double X, double NU)
- -- Function: double gsl_cdf_tdist_Q (double X, double NU)
- -- Function: double gsl_cdf_tdist_Pinv (double P, double NU)
- -- Function: double gsl_cdf_tdist_Qinv (double Q, double NU)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the t-distribution with NU degrees of
-     freedom.
-
diff -Nru gsl-doc-1.16/doc/gsl-ref.info-3 gsl-doc-2.3/doc/gsl-ref.info-3
--- gsl-doc-1.16/doc/gsl-ref.info-3	2013-07-19 15:17:44.000000000 +0000
+++ gsl-doc-2.3/doc/gsl-ref.info-3	2016-12-09 00:08:06.000000000 +0000
@@ -2,7384 +2,7276 @@
 gsl-ref.texi.
 
 Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,
-2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 The GSL Team.
+2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016
+The GSL Team.
 
    Permission is granted to copy, distribute and/or modify this document
 under the terms of the GNU Free Documentation License, Version 1.3 or
-any later version published by the Free Software Foundation; with no
-Invariant Sections and no cover texts.  A copy of the license is
-included in the section entitled "GNU Free Documentation License".
+any later version published by the Free Software Foundation; with the
+Invariant Sections being "GNU General Public License" and "Free Software
+Needs Free Documentation", the Front-Cover text being "A GNU Manual",
+and with the Back-Cover Text being (a) (see below).  A copy of the
+license is included in the section entitled "GNU Free Documentation
+License".
+
+   (a) The Back-Cover Text is: "You have the freedom to copy and modify
+this GNU Manual."
 INFO-DIR-SECTION Software libraries
 START-INFO-DIR-ENTRY
 * gsl-ref: (gsl-ref).                   GNU Scientific Library - Reference
 END-INFO-DIR-ENTRY
 
 
-File: gsl-ref.info,  Node: The Beta Distribution,  Next: The Logistic Distribution,  Prev: The t-distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: Quasi-random number generator algorithms,  Next: Quasi-random number generator examples,  Prev: Saving and restoring quasi-random number generator state,  Up: Quasi-Random Sequences
 
-20.20 The Beta Distribution
-===========================
+19.5 Quasi-random number generator algorithms
+=============================================
 
- -- Function: double gsl_ran_beta (const gsl_rng * R, double A, double
-          B)
-     This function returns a random variate from the beta distribution.
-     The distribution function is,
+The following quasi-random sequence algorithms are available,
 
-          p(x) dx = {\Gamma(a+b) \over \Gamma(a) \Gamma(b)} x^{a-1} (1-x)^{b-1} dx
+ -- Generator: gsl_qrng_niederreiter_2
+     This generator uses the algorithm described in Bratley, Fox,
+     Niederreiter, 'ACM Trans. Model. Comp. Sim.' 2, 195 (1992).  It is
+     valid up to 12 dimensions.
 
-     for 0 <= x <= 1.
+ -- Generator: gsl_qrng_sobol
+     This generator uses the Sobol sequence described in Antonov,
+     Saleev, 'USSR Comput. Maths. Math. Phys.' 19, 252 (1980).  It is
+     valid up to 40 dimensions.
 
- -- Function: double gsl_ran_beta_pdf (double X, double A, double B)
-     This function computes the probability density p(x) at X for a beta
-     distribution with parameters A and B, using the formula given
-     above.
+ -- Generator: gsl_qrng_halton
+ -- Generator: gsl_qrng_reversehalton
+     These generators use the Halton and reverse Halton sequences
+     described in J.H. Halton, 'Numerische Mathematik' 2, 84-90 (1960)
+     and B. Vandewoestyne and R. Cools 'Computational and Applied
+     Mathematics' 189, 1&2, 341-361 (2006).  They are valid up to 1229
+     dimensions.
 
+
+File: gsl-ref.info,  Node: Quasi-random number generator examples,  Next: Quasi-random number references,  Prev: Quasi-random number generator algorithms,  Up: Quasi-Random Sequences
 
- -- Function: double gsl_cdf_beta_P (double X, double A, double B)
- -- Function: double gsl_cdf_beta_Q (double X, double A, double B)
- -- Function: double gsl_cdf_beta_Pinv (double P, double A, double B)
- -- Function: double gsl_cdf_beta_Qinv (double Q, double A, double B)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the beta distribution with parameters A
-     and B.
+19.6 Examples
+=============
 
-
-File: gsl-ref.info,  Node: The Logistic Distribution,  Next: The Pareto Distribution,  Prev: The Beta Distribution,  Up: Random Number Distributions
+The following program prints the first 1024 points of the 2-dimensional
+Sobol sequence.
 
-20.21 The Logistic Distribution
-===============================
+     #include <stdio.h>
+     #include <gsl/gsl_qrng.h>
 
- -- Function: double gsl_ran_logistic (const gsl_rng * R, double A)
-     This function returns a random variate from the logistic
-     distribution.  The distribution function is,
+     int
+     main (void)
+     {
+       int i;
+       gsl_qrng * q = gsl_qrng_alloc (gsl_qrng_sobol, 2);
 
-          p(x) dx = { \exp(-x/a) \over a (1 + \exp(-x/a))^2 } dx
+       for (i = 0; i < 1024; i++)
+         {
+           double v[2];
+           gsl_qrng_get (q, v);
+           printf ("%.5f %.5f\n", v[0], v[1]);
+         }
 
-     for -\infty < x < +\infty.
+       gsl_qrng_free (q);
+       return 0;
+     }
 
- -- Function: double gsl_ran_logistic_pdf (double X, double A)
-     This function computes the probability density p(x) at X for a
-     logistic distribution with scale parameter A, using the formula
-     given above.
+Here is the output from the program,
 
+     $ ./a.out
+     0.50000 0.50000
+     0.75000 0.25000
+     0.25000 0.75000
+     0.37500 0.37500
+     0.87500 0.87500
+     0.62500 0.12500
+     0.12500 0.62500
+     ....
 
- -- Function: double gsl_cdf_logistic_P (double X, double A)
- -- Function: double gsl_cdf_logistic_Q (double X, double A)
- -- Function: double gsl_cdf_logistic_Pinv (double P, double A)
- -- Function: double gsl_cdf_logistic_Qinv (double Q, double A)
-     These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the logistic distribution with scale
-     parameter A.
+It can be seen that successive points progressively fill-in the spaces
+between previous points.
 
 
-File: gsl-ref.info,  Node: The Pareto Distribution,  Next: Spherical Vector Distributions,  Prev: The Logistic Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: Quasi-random number references,  Prev: Quasi-random number generator examples,  Up: Quasi-Random Sequences
 
-20.22 The Pareto Distribution
-=============================
+19.7 References
+===============
 
- -- Function: double gsl_ran_pareto (const gsl_rng * R, double A, double
-          B)
-     This function returns a random variate from the Pareto distribution
-     of order A.  The distribution function is,
+The implementations of the quasi-random sequence routines are based on
+the algorithms described in the following paper,
 
-          p(x) dx = (a/b) / (x/b)^{a+1} dx
+     P. Bratley and B.L. Fox and H. Niederreiter, "Algorithm 738:
+     Programs to Generate Niederreiter's Low-discrepancy Sequences",
+     'ACM Transactions on Mathematical Software', Vol. 20, No. 4,
+     December, 1994, p. 494-495.
+
+
+File: gsl-ref.info,  Node: Random Number Distributions,  Next: Statistics,  Prev: Quasi-Random Sequences,  Up: Top
+
+20 Random Number Distributions
+******************************
+
+This chapter describes functions for generating random variates and
+computing their probability distributions.  Samples from the
+distributions described in this chapter can be obtained using any of the
+random number generators in the library as an underlying source of
+randomness.
+
+   In the simplest cases a non-uniform distribution can be obtained
+analytically from the uniform distribution of a random number generator
+by applying an appropriate transformation.  This method uses one call to
+the random number generator.  More complicated distributions are created
+by the "acceptance-rejection" method, which compares the desired
+distribution against a distribution which is similar and known
+analytically.  This usually requires several samples from the generator.
+
+   The library also provides cumulative distribution functions and
+inverse cumulative distribution functions, sometimes referred to as
+quantile functions.  The cumulative distribution functions and their
+inverses are computed separately for the upper and lower tails of the
+distribution, allowing full accuracy to be retained for small results.
+
+   The functions for random variates and probability density functions
+described in this section are declared in 'gsl_randist.h'.  The
+corresponding cumulative distribution functions are declared in
+'gsl_cdf.h'.
+
+   Note that the discrete random variate functions always return a value
+of type 'unsigned int', and on most platforms this has a maximum value
+of 2^32-1 ~=~ 4.29e9.  They should only be called with a safe range of
+parameters (where there is a negligible probability of a variate
+exceeding this limit) to prevent incorrect results due to overflow.
 
-     for x >= b.
+* Menu:
 
- -- Function: double gsl_ran_pareto_pdf (double X, double A, double B)
+* Random Number Distribution Introduction::  
+* The Gaussian Distribution::   
+* The Gaussian Tail Distribution::  
+* The Bivariate Gaussian Distribution::  
+* The Multivariate Gaussian Distribution::  
+* The Exponential Distribution::  
+* The Laplace Distribution::    
+* The Exponential Power Distribution::  
+* The Cauchy Distribution::     
+* The Rayleigh Distribution::   
+* The Rayleigh Tail Distribution::  
+* The Landau Distribution::     
+* The Levy alpha-Stable Distributions::  
+* The Levy skew alpha-Stable Distribution::  
+* The Gamma Distribution::      
+* The Flat (Uniform) Distribution::  
+* The Lognormal Distribution::  
+* The Chi-squared Distribution::  
+* The F-distribution::          
+* The t-distribution::          
+* The Beta Distribution::       
+* The Logistic Distribution::   
+* The Pareto Distribution::     
+* Spherical Vector Distributions::  
+* The Weibull Distribution::    
+* The Type-1 Gumbel Distribution::  
+* The Type-2 Gumbel Distribution::  
+* The Dirichlet Distribution::  
+* General Discrete Distributions::  
+* The Poisson Distribution::    
+* The Bernoulli Distribution::  
+* The Binomial Distribution::   
+* The Multinomial Distribution::  
+* The Negative Binomial Distribution::  
+* The Pascal Distribution::     
+* The Geometric Distribution::  
+* The Hypergeometric Distribution::  
+* The Logarithmic Distribution::  
+* Shuffling and Sampling::      
+* Random Number Distribution Examples::  
+* Random Number Distribution References and Further Reading::  
+
+
+File: gsl-ref.info,  Node: Random Number Distribution Introduction,  Next: The Gaussian Distribution,  Up: Random Number Distributions
+
+20.1 Introduction
+=================
+
+Continuous random number distributions are defined by a probability
+density function, p(x), such that the probability of x occurring in the
+infinitesimal range x to x+dx is p dx.
+
+   The cumulative distribution function for the lower tail P(x) is
+defined by the integral,
+
+     P(x) = \int_{-\infty}^{x} dx' p(x')
+
+and gives the probability of a variate taking a value less than x.
+
+   The cumulative distribution function for the upper tail Q(x) is
+defined by the integral,
+
+     Q(x) = \int_{x}^{+\infty} dx' p(x')
+
+and gives the probability of a variate taking a value greater than x.
+
+   The upper and lower cumulative distribution functions are related by
+P(x) + Q(x) = 1 and satisfy 0 <= P(x) <= 1, 0 <= Q(x) <= 1.
+
+   The inverse cumulative distributions, x=P^{-1}(P) and x=Q^{-1}(Q)
+give the values of x which correspond to a specific value of P or Q.
+They can be used to find confidence limits from probability values.
+
+   For discrete distributions the probability of sampling the integer
+value k is given by p(k), where \sum_k p(k) = 1.  The cumulative
+distribution for the lower tail P(k) of a discrete distribution is
+defined as,
+
+     P(k) = \sum_{i <= k} p(i)
+
+where the sum is over the allowed range of the distribution less than or
+equal to k.
+
+   The cumulative distribution for the upper tail of a discrete
+distribution Q(k) is defined as
+
+     Q(k) = \sum_{i > k} p(i)
+
+giving the sum of probabilities for all values greater than k.  These
+two definitions satisfy the identity P(k)+Q(k)=1.
+
+   If the range of the distribution is 1 to n inclusive then P(n)=1,
+Q(n)=0 while P(1) = p(1), Q(1)=1-p(1).
+
+
+File: gsl-ref.info,  Node: The Gaussian Distribution,  Next: The Gaussian Tail Distribution,  Prev: Random Number Distribution Introduction,  Up: Random Number Distributions
+
+20.2 The Gaussian Distribution
+==============================
+
+ -- Function: double gsl_ran_gaussian (const gsl_rng * R, double SIGMA)
+     This function returns a Gaussian random variate, with mean zero and
+     standard deviation SIGMA.  The probability distribution for
+     Gaussian random variates is,
+
+          p(x) dx = {1 \over \sqrt{2 \pi \sigma^2}} \exp (-x^2 / 2\sigma^2) dx
+
+     for x in the range -\infty to +\infty.  Use the transformation z =
+     \mu + x on the numbers returned by 'gsl_ran_gaussian' to obtain a
+     Gaussian distribution with mean \mu.  This function uses the
+     Box-Muller algorithm which requires two calls to the random number
+     generator R.
+
+ -- Function: double gsl_ran_gaussian_pdf (double X, double SIGMA)
      This function computes the probability density p(x) at X for a
-     Pareto distribution with exponent A and scale B, using the formula
-     given above.
+     Gaussian distribution with standard deviation SIGMA, using the
+     formula given above.
 
 
- -- Function: double gsl_cdf_pareto_P (double X, double A, double B)
- -- Function: double gsl_cdf_pareto_Q (double X, double A, double B)
- -- Function: double gsl_cdf_pareto_Pinv (double P, double A, double B)
- -- Function: double gsl_cdf_pareto_Qinv (double Q, double A, double B)
+ -- Function: double gsl_ran_gaussian_ziggurat (const gsl_rng * R,
+          double SIGMA)
+ -- Function: double gsl_ran_gaussian_ratio_method (const gsl_rng * R,
+          double SIGMA)
+     This function computes a Gaussian random variate using the
+     alternative Marsaglia-Tsang ziggurat and Kinderman-Monahan-Leva
+     ratio methods.  The Ziggurat algorithm is the fastest available
+     algorithm in most cases.
+
+ -- Function: double gsl_ran_ugaussian (const gsl_rng * R)
+ -- Function: double gsl_ran_ugaussian_pdf (double X)
+ -- Function: double gsl_ran_ugaussian_ratio_method (const gsl_rng * R)
+     These functions compute results for the unit Gaussian distribution.
+     They are equivalent to the functions above with a standard
+     deviation of one, SIGMA = 1.
+
+ -- Function: double gsl_cdf_gaussian_P (double X, double SIGMA)
+ -- Function: double gsl_cdf_gaussian_Q (double X, double SIGMA)
+ -- Function: double gsl_cdf_gaussian_Pinv (double P, double SIGMA)
+ -- Function: double gsl_cdf_gaussian_Qinv (double Q, double SIGMA)
      These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the Pareto distribution with exponent A
-     and scale B.
+     Q(x) and their inverses for the Gaussian distribution with standard
+     deviation SIGMA.
+
+ -- Function: double gsl_cdf_ugaussian_P (double X)
+ -- Function: double gsl_cdf_ugaussian_Q (double X)
+ -- Function: double gsl_cdf_ugaussian_Pinv (double P)
+ -- Function: double gsl_cdf_ugaussian_Qinv (double Q)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the unit Gaussian distribution.
 
 
-File: gsl-ref.info,  Node: Spherical Vector Distributions,  Next: The Weibull Distribution,  Prev: The Pareto Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The Gaussian Tail Distribution,  Next: The Bivariate Gaussian Distribution,  Prev: The Gaussian Distribution,  Up: Random Number Distributions
 
-20.23 Spherical Vector Distributions
-====================================
+20.3 The Gaussian Tail Distribution
+===================================
 
-The spherical distributions generate random vectors, located on a
-spherical surface.  They can be used as random directions, for example
-in the steps of a random walk.
+ -- Function: double gsl_ran_gaussian_tail (const gsl_rng * R, double A,
+          double SIGMA)
+     This function provides random variates from the upper tail of a
+     Gaussian distribution with standard deviation SIGMA.  The values
+     returned are larger than the lower limit A, which must be positive.
+     The method is based on Marsaglia's famous rectangle-wedge-tail
+     algorithm (Ann.  Math.  Stat.  32, 894-899 (1961)), with this
+     aspect explained in Knuth, v2, 3rd ed, p139,586 (exercise 11).
 
- -- Function: void gsl_ran_dir_2d (const gsl_rng * R, double * X, double
-          * Y)
- -- Function: void gsl_ran_dir_2d_trig_method (const gsl_rng * R, double
-          * X, double * Y)
-     This function returns a random direction vector v = (X,Y) in two
-     dimensions.  The vector is normalized such that |v|^2 = x^2 + y^2 =
-     1.  The obvious way to do this is to take a uniform random number
-     between 0 and 2\pi and let X and Y be the sine and cosine
-     respectively.  Two trig functions would have been expensive in the
-     old days, but with modern hardware implementations, this is
-     sometimes the fastest way to go.  This is the case for the Pentium
-     (but not the case for the Sun Sparcstation).  One can avoid the
-     trig evaluations by choosing X and Y in the interior of a unit
-     circle (choose them at random from the interior of the enclosing
-     square, and then reject those that are outside the unit circle),
-     and then dividing by \sqrt{x^2 + y^2}.  A much cleverer approach,
-     attributed to von Neumann (See Knuth, v2, 3rd ed, p140, exercise
-     23), requires neither trig nor a square root.  In this approach, U
-     and V are chosen at random from the interior of a unit circle, and
-     then x=(u^2-v^2)/(u^2+v^2) and y=2uv/(u^2+v^2).
+     The probability distribution for Gaussian tail random variates is,
 
- -- Function: void gsl_ran_dir_3d (const gsl_rng * R, double * X, double
-          * Y, double * Z)
-     This function returns a random direction vector v = (X,Y,Z) in
-     three dimensions.  The vector is normalized such that |v|^2 = x^2 +
-     y^2 + z^2 = 1.  The method employed is due to Robert E. Knop (CACM
-     13, 326 (1970)), and explained in Knuth, v2, 3rd ed, p136.  It uses
-     the surprising fact that the distribution projected along any axis
-     is actually uniform (this is only true for 3 dimensions).
+          p(x) dx = {1 \over N(a;\sigma) \sqrt{2 \pi \sigma^2}} \exp (- x^2/(2 \sigma^2)) dx
 
- -- Function: void gsl_ran_dir_nd (const gsl_rng * R, size_t N, double *
-          X)
+     for x > a where N(a;\sigma) is the normalization constant,
+
+          N(a;\sigma) = (1/2) erfc(a / sqrt(2 sigma^2)).
+
+ -- Function: double gsl_ran_gaussian_tail_pdf (double X, double A,
+          double SIGMA)
+     This function computes the probability density p(x) at X for a
+     Gaussian tail distribution with standard deviation SIGMA and lower
+     limit A, using the formula given above.
 
-     This function returns a random direction vector v =
-     (x_1,x_2,...,x_n) in N dimensions.  The vector is normalized such
-     that |v|^2 = x_1^2 + x_2^2 + ... + x_n^2 = 1.  The method uses the
-     fact that a multivariate Gaussian distribution is spherically
-     symmetric.  Each component is generated to have a Gaussian
-     distribution, and then the components are normalized.  The method
-     is described by Knuth, v2, 3rd ed, p135-136, and attributed to G.
-     W. Brown, Modern Mathematics for the Engineer (1956).
+
+ -- Function: double gsl_ran_ugaussian_tail (const gsl_rng * R, double
+          A)
+ -- Function: double gsl_ran_ugaussian_tail_pdf (double X, double A)
+     These functions compute results for the tail of a unit Gaussian
+     distribution.  They are equivalent to the functions above with a
+     standard deviation of one, SIGMA = 1.
 
 
-File: gsl-ref.info,  Node: The Weibull Distribution,  Next: The Type-1 Gumbel Distribution,  Prev: Spherical Vector Distributions,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The Bivariate Gaussian Distribution,  Next: The Multivariate Gaussian Distribution,  Prev: The Gaussian Tail Distribution,  Up: Random Number Distributions
 
-20.24 The Weibull Distribution
-==============================
+20.4 The Bivariate Gaussian Distribution
+========================================
 
- -- Function: double gsl_ran_weibull (const gsl_rng * R, double A,
-          double B)
-     This function returns a random variate from the Weibull
-     distribution.  The distribution function is,
+ -- Function: void gsl_ran_bivariate_gaussian (const gsl_rng * R, double
+          SIGMA_X, double SIGMA_Y, double RHO, double * X, double * Y)
+     This function generates a pair of correlated Gaussian variates,
+     with mean zero, correlation coefficient RHO and standard deviations
+     SIGMA_X and SIGMA_Y in the x and y directions.  The probability
+     distribution for bivariate Gaussian random variates is,
+
+          p(x,y) dx dy = {1 \over 2 \pi \sigma_x \sigma_y \sqrt{1-\rho^2}} \exp (-(x^2/\sigma_x^2 + y^2/\sigma_y^2 - 2 \rho x y/(\sigma_x\sigma_y))/2(1-\rho^2)) dx dy
+
+     for x,y in the range -\infty to +\infty.  The correlation
+     coefficient RHO should lie between 1 and -1.
+
+ -- Function: double gsl_ran_bivariate_gaussian_pdf (double X, double Y,
+          double SIGMA_X, double SIGMA_Y, double RHO)
+     This function computes the probability density p(x,y) at (X,Y) for
+     a bivariate Gaussian distribution with standard deviations SIGMA_X,
+     SIGMA_Y and correlation coefficient RHO, using the formula given
+     above.
 
-          p(x) dx = {b \over a^b} x^{b-1}  \exp(-(x/a)^b) dx
+
+
+File: gsl-ref.info,  Node: The Multivariate Gaussian Distribution,  Next: The Exponential Distribution,  Prev: The Bivariate Gaussian Distribution,  Up: Random Number Distributions
+
+20.5 The Multivariate Gaussian Distribution
+===========================================
+
+ -- Function: int gsl_ran_multivariate_gaussian (const gsl_rng * R,
+          const gsl_vector * MU, const gsl_matrix * L, gsl_vector *
+          RESULT)
+     This function generates a random vector satisfying the
+     k-dimensional multivariate Gaussian distribution with mean \mu and
+     variance-covariance matrix \Sigma.  On input, the k-vector \mu is
+     given in MU, and the Cholesky factor of the k-by-k matrix \Sigma =
+     L L^T is given in the lower triangle of L, as output from
+     'gsl_linalg_cholesky_decomp'.  The random vector is stored in
+     RESULT on output.  The probability distribution for multivariate
+     Gaussian random variates is
+
+          p(x_1,...,x_k) dx_1 ... dx_k = {1 \over \sqrt{(2 \pi)^k |\Sigma|} \exp \left(-{1 \over 2} (x - \mu)^T \Sigma^{-1} (x - \mu)\right) dx_1 \dots dx_k
+
+ -- Function: int gsl_ran_multivariate_gaussian_pdf (const gsl_vector *
+          X, const gsl_vector * MU, const gsl_matrix * L, double *
+          RESULT, gsl_vector * WORK)
+ -- Function: int gsl_ran_multivariate_gaussian_log_pdf (const
+          gsl_vector * X, const gsl_vector * MU, const gsl_matrix * L,
+          double * RESULT, gsl_vector * WORK)
+     These functions compute p(x) or \log{p(x)} at the point X, using
+     mean vector MU and variance-covariance matrix specified by its
+     Cholesky factor L using the formula above.  Additional workspace of
+     length k is required in WORK.
+
+ -- Function: int gsl_ran_multivariate_gaussian_mean (const gsl_matrix *
+          X, gsl_vector * MU_HAT)
+     Given a set of n samples X_j from a k-dimensional multivariate
+     Gaussian distribution, this function computes the maximum
+     likelihood estimate of the mean of the distribution, given by
+
+          \Hat{\mu} = {1 \over n} \sum_{j=1}^n X_j
+
+     The samples X_1,X_2,\dots,X_n are given in the n-by-k matrix X, and
+     the maximum likelihood estimate of the mean is stored in MU_HAT on
+     output.
+
+ -- Function: int gsl_ran_multivariate_gaussian_vcov (const gsl_matrix *
+          X, gsl_matrix * SIGMA_HAT)
+     Given a set of n samples X_j from a k-dimensional multivariate
+     Gaussian distribution, this function computes the maximum
+     likelihood estimate of the variance-covariance matrix of the
+     distribution, given by
+
+          \Hat{\Sigma} = {1 \over n} \sum_{j=1}^n \left( X_j - \Hat{\mu} \right) \left( X_j - \Hat{\mu} \right)^T
+
+     The samples X_1,X_2,\dots,X_n are given in the n-by-k matrix X and
+     the maximum likelihood estimate of the variance-covariance matrix
+     is stored in SIGMA_HAT on output.
+
+
+File: gsl-ref.info,  Node: The Exponential Distribution,  Next: The Laplace Distribution,  Prev: The Multivariate Gaussian Distribution,  Up: Random Number Distributions
+
+20.6 The Exponential Distribution
+=================================
+
+ -- Function: double gsl_ran_exponential (const gsl_rng * R, double MU)
+     This function returns a random variate from the exponential
+     distribution with mean MU.  The distribution is,
+
+          p(x) dx = {1 \over \mu} \exp(-x/\mu) dx
 
      for x >= 0.
 
- -- Function: double gsl_ran_weibull_pdf (double X, double A, double B)
-     This function computes the probability density p(x) at X for a
-     Weibull distribution with scale A and exponent B, using the formula
-     given above.
+ -- Function: double gsl_ran_exponential_pdf (double X, double MU)
+     This function computes the probability density p(x) at X for an
+     exponential distribution with mean MU, using the formula given
+     above.
 
 
- -- Function: double gsl_cdf_weibull_P (double X, double A, double B)
- -- Function: double gsl_cdf_weibull_Q (double X, double A, double B)
- -- Function: double gsl_cdf_weibull_Pinv (double P, double A, double B)
- -- Function: double gsl_cdf_weibull_Qinv (double Q, double A, double B)
+ -- Function: double gsl_cdf_exponential_P (double X, double MU)
+ -- Function: double gsl_cdf_exponential_Q (double X, double MU)
+ -- Function: double gsl_cdf_exponential_Pinv (double P, double MU)
+ -- Function: double gsl_cdf_exponential_Qinv (double Q, double MU)
      These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the Weibull distribution with scale A
-     and exponent B.
+     Q(x) and their inverses for the exponential distribution with mean
+     MU.
 
 
-File: gsl-ref.info,  Node: The Type-1 Gumbel Distribution,  Next: The Type-2 Gumbel Distribution,  Prev: The Weibull Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The Laplace Distribution,  Next: The Exponential Power Distribution,  Prev: The Exponential Distribution,  Up: Random Number Distributions
 
-20.25 The Type-1 Gumbel Distribution
-====================================
+20.7 The Laplace Distribution
+=============================
 
- -- Function: double gsl_ran_gumbel1 (const gsl_rng * R, double A,
-          double B)
-     This function returns a random variate from the Type-1 Gumbel
-     distribution.  The Type-1 Gumbel distribution function is,
+ -- Function: double gsl_ran_laplace (const gsl_rng * R, double A)
+     This function returns a random variate from the Laplace
+     distribution with width A.  The distribution is,
 
-          p(x) dx = a b \exp(-(b \exp(-ax) + ax)) dx
+          p(x) dx = {1 \over 2 a}  \exp(-|x/a|) dx
 
      for -\infty < x < \infty.
 
- -- Function: double gsl_ran_gumbel1_pdf (double X, double A, double B)
+ -- Function: double gsl_ran_laplace_pdf (double X, double A)
      This function computes the probability density p(x) at X for a
-     Type-1 Gumbel distribution with parameters A and B, using the
-     formula given above.
+     Laplace distribution with width A, using the formula given above.
 
 
- -- Function: double gsl_cdf_gumbel1_P (double X, double A, double B)
- -- Function: double gsl_cdf_gumbel1_Q (double X, double A, double B)
- -- Function: double gsl_cdf_gumbel1_Pinv (double P, double A, double B)
- -- Function: double gsl_cdf_gumbel1_Qinv (double Q, double A, double B)
+ -- Function: double gsl_cdf_laplace_P (double X, double A)
+ -- Function: double gsl_cdf_laplace_Q (double X, double A)
+ -- Function: double gsl_cdf_laplace_Pinv (double P, double A)
+ -- Function: double gsl_cdf_laplace_Qinv (double Q, double A)
      These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the Type-1 Gumbel distribution with
-     parameters A and B.
+     Q(x) and their inverses for the Laplace distribution with width A.
 
 
-File: gsl-ref.info,  Node: The Type-2 Gumbel Distribution,  Next: The Dirichlet Distribution,  Prev: The Type-1 Gumbel Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The Exponential Power Distribution,  Next: The Cauchy Distribution,  Prev: The Laplace Distribution,  Up: Random Number Distributions
 
-20.26 The Type-2 Gumbel Distribution
-====================================
+20.8 The Exponential Power Distribution
+=======================================
 
- -- Function: double gsl_ran_gumbel2 (const gsl_rng * R, double A,
-          double B)
-     This function returns a random variate from the Type-2 Gumbel
-     distribution.  The Type-2 Gumbel distribution function is,
+ -- Function: double gsl_ran_exppow (const gsl_rng * R, double A, double
+          B)
+     This function returns a random variate from the exponential power
+     distribution with scale parameter A and exponent B.  The
+     distribution is,
 
-          p(x) dx = a b x^{-a-1} \exp(-b x^{-a}) dx
+          p(x) dx = {1 \over 2 a \Gamma(1+1/b)} \exp(-|x/a|^b) dx
 
-     for 0 < x < \infty.
+     for x >= 0.  For b = 1 this reduces to the Laplace distribution.
+     For b = 2 it has the same form as a Gaussian distribution, but with
+     a = \sqrt{2} \sigma.
 
- -- Function: double gsl_ran_gumbel2_pdf (double X, double A, double B)
-     This function computes the probability density p(x) at X for a
-     Type-2 Gumbel distribution with parameters A and B, using the
-     formula given above.
+ -- Function: double gsl_ran_exppow_pdf (double X, double A, double B)
+     This function computes the probability density p(x) at X for an
+     exponential power distribution with scale parameter A and exponent
+     B, using the formula given above.
 
 
- -- Function: double gsl_cdf_gumbel2_P (double X, double A, double B)
- -- Function: double gsl_cdf_gumbel2_Q (double X, double A, double B)
- -- Function: double gsl_cdf_gumbel2_Pinv (double P, double A, double B)
- -- Function: double gsl_cdf_gumbel2_Qinv (double Q, double A, double B)
+ -- Function: double gsl_cdf_exppow_P (double X, double A, double B)
+ -- Function: double gsl_cdf_exppow_Q (double X, double A, double B)
      These functions compute the cumulative distribution functions P(x),
-     Q(x) and their inverses for the Type-2 Gumbel distribution with
-     parameters A and B.
+     Q(x) for the exponential power distribution with parameters A and
+     B.
 
 
-File: gsl-ref.info,  Node: The Dirichlet Distribution,  Next: General Discrete Distributions,  Prev: The Type-2 Gumbel Distribution,  Up: Random Number Distributions
-
-20.27 The Dirichlet Distribution
-================================
+File: gsl-ref.info,  Node: The Cauchy Distribution,  Next: The Rayleigh Distribution,  Prev: The Exponential Power Distribution,  Up: Random Number Distributions
 
- -- Function: void gsl_ran_dirichlet (const gsl_rng * R, size_t K, const
-          double ALPHA[], double THETA[])
-     This function returns an array of K random variates from a
-     Dirichlet distribution of order K-1.  The distribution function is
+20.9 The Cauchy Distribution
+============================
 
-          p(\theta_1, ..., \theta_K) d\theta_1 ... d\theta_K =
-            (1/Z) \prod_{i=1}^K \theta_i^{\alpha_i - 1} \delta(1 -\sum_{i=1}^K \theta_i) d\theta_1 ... d\theta_K
+ -- Function: double gsl_ran_cauchy (const gsl_rng * R, double A)
+     This function returns a random variate from the Cauchy distribution
+     with scale parameter A.  The probability distribution for Cauchy
+     random variates is,
 
-     for theta_i >= 0 and alpha_i > 0.  The delta function ensures that
-     \sum \theta_i = 1.  The normalization factor Z is
+          p(x) dx = {1 \over a\pi (1 + (x/a)^2) } dx
 
-          Z = {\prod_{i=1}^K \Gamma(\alpha_i)} / {\Gamma( \sum_{i=1}^K \alpha_i)}
+     for x in the range -\infty to +\infty.  The Cauchy distribution is
+     also known as the Lorentz distribution.
 
-     The random variates are generated by sampling K values from gamma
-     distributions with parameters a=alpha_i, b=1, and renormalizing.
-     See A.M. Law, W.D. Kelton, 'Simulation Modeling and Analysis'
-     (1991).
+ -- Function: double gsl_ran_cauchy_pdf (double X, double A)
+     This function computes the probability density p(x) at X for a
+     Cauchy distribution with scale parameter A, using the formula given
+     above.
 
- -- Function: double gsl_ran_dirichlet_pdf (size_t K, const double
-          ALPHA[], const double THETA[])
-     This function computes the probability density p(\theta_1, ... ,
-     \theta_K) at THETA[K] for a Dirichlet distribution with parameters
-     ALPHA[K], using the formula given above.
 
- -- Function: double gsl_ran_dirichlet_lnpdf (size_t K, const double
-          ALPHA[], const double THETA[])
-     This function computes the logarithm of the probability density
-     p(\theta_1, ... , \theta_K) for a Dirichlet distribution with
-     parameters ALPHA[K].
+ -- Function: double gsl_cdf_cauchy_P (double X, double A)
+ -- Function: double gsl_cdf_cauchy_Q (double X, double A)
+ -- Function: double gsl_cdf_cauchy_Pinv (double P, double A)
+ -- Function: double gsl_cdf_cauchy_Qinv (double Q, double A)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the Cauchy distribution with scale
+     parameter A.
 
 
-File: gsl-ref.info,  Node: General Discrete Distributions,  Next: The Poisson Distribution,  Prev: The Dirichlet Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The Rayleigh Distribution,  Next: The Rayleigh Tail Distribution,  Prev: The Cauchy Distribution,  Up: Random Number Distributions
 
-20.28 General Discrete Distributions
-====================================
+20.10 The Rayleigh Distribution
+===============================
 
-Given K discrete events with different probabilities P[k], produce a
-random value k consistent with its probability.
+ -- Function: double gsl_ran_rayleigh (const gsl_rng * R, double SIGMA)
+     This function returns a random variate from the Rayleigh
+     distribution with scale parameter SIGMA.  The distribution is,
 
-   The obvious way to do this is to preprocess the probability list by
-generating a cumulative probability array with K+1 elements:
+          p(x) dx = {x \over \sigma^2} \exp(- x^2/(2 \sigma^2)) dx
 
-       C[0] = 0
-     C[k+1] = C[k]+P[k].
+     for x > 0.
 
-Note that this construction produces C[K]=1.  Now choose a uniform
-deviate u between 0 and 1, and find the value of k such that C[k] <= u <
-C[k+1].  Although this in principle requires of order \log K steps per
-random number generation, they are fast steps, and if you use something
-like \lfloor uK \rfloor as a starting point, you can often do pretty
-well.
-
-   But faster methods have been devised.  Again, the idea is to
-preprocess the probability list, and save the result in some form of
-lookup table; then the individual calls for a random discrete event can
-go rapidly.  An approach invented by G. Marsaglia (Generating discrete
-random variables in a computer, Comm ACM 6, 37-38 (1963)) is very
-clever, and readers interested in examples of good algorithm design are
-directed to this short and well-written paper.  Unfortunately, for large
-K, Marsaglia's lookup table can be quite large.
-
-   A much better approach is due to Alastair J. Walker (An efficient
-method for generating discrete random variables with general
-distributions, ACM Trans on Mathematical Software 3, 253-256 (1977); see
-also Knuth, v2, 3rd ed, p120-121,139).  This requires two lookup tables,
-one floating point and one integer, but both only of size K.  After
-preprocessing, the random numbers are generated in O(1) time, even for
-large K.  The preprocessing suggested by Walker requires O(K^2) effort,
-but that is not actually necessary, and the implementation provided here
-only takes O(K) effort.  In general, more preprocessing leads to faster
-generation of the individual random numbers, but a diminishing return is
-reached pretty early.  Knuth points out that the optimal preprocessing
-is combinatorially difficult for large K.
+ -- Function: double gsl_ran_rayleigh_pdf (double X, double SIGMA)
+     This function computes the probability density p(x) at X for a
+     Rayleigh distribution with scale parameter SIGMA, using the formula
+     given above.
 
-   This method can be used to speed up some of the discrete random
-number generators below, such as the binomial distribution.  To use it
-for something like the Poisson Distribution, a modification would have
-to be made, since it only takes a finite set of K outcomes.
 
- -- Function: gsl_ran_discrete_t * gsl_ran_discrete_preproc (size_t K,
-          const double * P)
-     This function returns a pointer to a structure that contains the
-     lookup table for the discrete random number generator.  The array
-     P[] contains the probabilities of the discrete events; these array
-     elements must all be positive, but they needn't add up to one (so
-     you can think of them more generally as "weights")--the
-     preprocessor will normalize appropriately.  This return value is
-     used as an argument for the 'gsl_ran_discrete' function below.
+ -- Function: double gsl_cdf_rayleigh_P (double X, double SIGMA)
+ -- Function: double gsl_cdf_rayleigh_Q (double X, double SIGMA)
+ -- Function: double gsl_cdf_rayleigh_Pinv (double P, double SIGMA)
+ -- Function: double gsl_cdf_rayleigh_Qinv (double Q, double SIGMA)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the Rayleigh distribution with scale
+     parameter SIGMA.
 
- -- Function: size_t gsl_ran_discrete (const gsl_rng * R, const
-          gsl_ran_discrete_t * G)
-     After the preprocessor, above, has been called, you use this
-     function to get the discrete random numbers.
+
+File: gsl-ref.info,  Node: The Rayleigh Tail Distribution,  Next: The Landau Distribution,  Prev: The Rayleigh Distribution,  Up: Random Number Distributions
 
- -- Function: double gsl_ran_discrete_pdf (size_t K, const
-          gsl_ran_discrete_t * G)
-     Returns the probability P[k] of observing the variable K.  Since
-     P[k] is not stored as part of the lookup table, it must be
-     recomputed; this computation takes O(K), so if K is large and you
-     care about the original array P[k] used to create the lookup table,
-     then you should just keep this original array P[k] around.
+20.11 The Rayleigh Tail Distribution
+====================================
 
- -- Function: void gsl_ran_discrete_free (gsl_ran_discrete_t * G)
-     De-allocates the lookup table pointed to by G.
+ -- Function: double gsl_ran_rayleigh_tail (const gsl_rng * R, double A,
+          double SIGMA)
+     This function returns a random variate from the tail of the
+     Rayleigh distribution with scale parameter SIGMA and a lower limit
+     of A.  The distribution is,
 
-
-File: gsl-ref.info,  Node: The Poisson Distribution,  Next: The Bernoulli Distribution,  Prev: General Discrete Distributions,  Up: Random Number Distributions
+          p(x) dx = {x \over \sigma^2} \exp ((a^2 - x^2) /(2 \sigma^2)) dx
 
-20.29 The Poisson Distribution
-==============================
+     for x > a.
 
- -- Function: unsigned int gsl_ran_poisson (const gsl_rng * R, double
-          MU)
-     This function returns a random integer from the Poisson
-     distribution with mean MU.  The probability distribution for
-     Poisson variates is,
+ -- Function: double gsl_ran_rayleigh_tail_pdf (double X, double A,
+          double SIGMA)
+     This function computes the probability density p(x) at X for a
+     Rayleigh tail distribution with scale parameter SIGMA and lower
+     limit A, using the formula given above.
 
-          p(k) = {\mu^k \over k!} \exp(-\mu)
 
-     for k >= 0.
+
+File: gsl-ref.info,  Node: The Landau Distribution,  Next: The Levy alpha-Stable Distributions,  Prev: The Rayleigh Tail Distribution,  Up: Random Number Distributions
 
- -- Function: double gsl_ran_poisson_pdf (unsigned int K, double MU)
-     This function computes the probability p(k) of obtaining K from a
-     Poisson distribution with mean MU, using the formula given above.
+20.12 The Landau Distribution
+=============================
 
+ -- Function: double gsl_ran_landau (const gsl_rng * R)
+     This function returns a random variate from the Landau
+     distribution.  The probability distribution for Landau random
+     variates is defined analytically by the complex integral,
+
+          p(x) = (1/(2 \pi i)) \int_{c-i\infty}^{c+i\infty} ds exp(s log(s) + x s)
+     For numerical purposes it is more convenient to use the following
+     equivalent form of the integral,
+
+          p(x) = (1/\pi) \int_0^\infty dt \exp(-t \log(t) - x t) \sin(\pi t).
+
+ -- Function: double gsl_ran_landau_pdf (double X)
+     This function computes the probability density p(x) at X for the
+     Landau distribution using an approximation to the formula given
+     above.
 
- -- Function: double gsl_cdf_poisson_P (unsigned int K, double MU)
- -- Function: double gsl_cdf_poisson_Q (unsigned int K, double MU)
-     These functions compute the cumulative distribution functions P(k),
-     Q(k) for the Poisson distribution with parameter MU.
 
 
-File: gsl-ref.info,  Node: The Bernoulli Distribution,  Next: The Binomial Distribution,  Prev: The Poisson Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The Levy alpha-Stable Distributions,  Next: The Levy skew alpha-Stable Distribution,  Prev: The Landau Distribution,  Up: Random Number Distributions
 
-20.30 The Bernoulli Distribution
-================================
+20.13 The Levy alpha-Stable Distributions
+=========================================
 
- -- Function: unsigned int gsl_ran_bernoulli (const gsl_rng * R, double
-          P)
-     This function returns either 0 or 1, the result of a Bernoulli
-     trial with probability P.  The probability distribution for a
-     Bernoulli trial is,
+ -- Function: double gsl_ran_levy (const gsl_rng * R, double C, double
+          ALPHA)
+     This function returns a random variate from the Levy symmetric
+     stable distribution with scale C and exponent ALPHA.  The symmetric
+     stable probability distribution is defined by a Fourier transform,
 
-          p(0) = 1 - p
-          p(1) = p
+          p(x) = {1 \over 2 \pi} \int_{-\infty}^{+\infty} dt \exp(-it x - |c t|^alpha)
 
- -- Function: double gsl_ran_bernoulli_pdf (unsigned int K, double P)
-     This function computes the probability p(k) of obtaining K from a
-     Bernoulli distribution with probability parameter P, using the
-     formula given above.
+     There is no explicit solution for the form of p(x) and the library
+     does not define a corresponding 'pdf' function.  For \alpha = 1 the
+     distribution reduces to the Cauchy distribution.  For \alpha = 2 it
+     is a Gaussian distribution with \sigma = \sqrt{2} c.  For \alpha <
+     1 the tails of the distribution become extremely wide.
+
+     The algorithm only works for 0 < alpha <= 2.
 
 
 
-File: gsl-ref.info,  Node: The Binomial Distribution,  Next: The Multinomial Distribution,  Prev: The Bernoulli Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The Levy skew alpha-Stable Distribution,  Next: The Gamma Distribution,  Prev: The Levy alpha-Stable Distributions,  Up: Random Number Distributions
 
-20.31 The Binomial Distribution
-===============================
+20.14 The Levy skew alpha-Stable Distribution
+=============================================
 
- -- Function: unsigned int gsl_ran_binomial (const gsl_rng * R, double
-          P, unsigned int N)
-     This function returns a random integer from the binomial
-     distribution, the number of successes in N independent trials with
-     probability P.  The probability distribution for binomial variates
-     is,
+ -- Function: double gsl_ran_levy_skew (const gsl_rng * R, double C,
+          double ALPHA, double BETA)
+     This function returns a random variate from the Levy skew stable
+     distribution with scale C, exponent ALPHA and skewness parameter
+     BETA.  The skewness parameter must lie in the range [-1,1].  The
+     Levy skew stable probability distribution is defined by a Fourier
+     transform,
 
-          p(k) = {n! \over k! (n-k)! } p^k (1-p)^{n-k}
+          p(x) = {1 \over 2 \pi} \int_{-\infty}^{+\infty} dt \exp(-it x - |c t|^alpha (1-i beta sign(t) tan(pi alpha/2)))
 
-     for 0 <= k <= n.
+     When \alpha = 1 the term \tan(\pi \alpha/2) is replaced by
+     -(2/\pi)\log|t|.  There is no explicit solution for the form of
+     p(x) and the library does not define a corresponding 'pdf'
+     function.  For \alpha = 2 the distribution reduces to a Gaussian
+     distribution with \sigma = \sqrt{2} c and the skewness parameter
+     has no effect.  For \alpha < 1 the tails of the distribution become
+     extremely wide.  The symmetric distribution corresponds to \beta =
+     0.
 
- -- Function: double gsl_ran_binomial_pdf (unsigned int K, double P,
-          unsigned int N)
-     This function computes the probability p(k) of obtaining K from a
-     binomial distribution with parameters P and N, using the formula
-     given above.
+     The algorithm only works for 0 < alpha <= 2.
 
+   The Levy alpha-stable distributions have the property that if N
+alpha-stable variates are drawn from the distribution p(c, \alpha,
+\beta) then the sum Y = X_1 + X_2 + \dots + X_N will also be distributed
+as an alpha-stable variate, p(N^(1/\alpha) c, \alpha, \beta).
 
- -- Function: double gsl_cdf_binomial_P (unsigned int K, double P,
-          unsigned int N)
- -- Function: double gsl_cdf_binomial_Q (unsigned int K, double P,
-          unsigned int N)
-     These functions compute the cumulative distribution functions P(k),
-     Q(k) for the binomial distribution with parameters P and N.
 
 
-File: gsl-ref.info,  Node: The Multinomial Distribution,  Next: The Negative Binomial Distribution,  Prev: The Binomial Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The Gamma Distribution,  Next: The Flat (Uniform) Distribution,  Prev: The Levy skew alpha-Stable Distribution,  Up: Random Number Distributions
 
-20.32 The Multinomial Distribution
-==================================
+20.15 The Gamma Distribution
+============================
 
- -- Function: void gsl_ran_multinomial (const gsl_rng * R, size_t K,
-          unsigned int N, const double P[], unsigned int N[])
+ -- Function: double gsl_ran_gamma (const gsl_rng * R, double A, double
+          B)
+     This function returns a random variate from the gamma distribution.
+     The distribution function is,
 
-     This function computes a random sample N[] from the multinomial
-     distribution formed by N trials from an underlying distribution
-     P[K].  The distribution function for N[] is,
+          p(x) dx = {1 \over \Gamma(a) b^a} x^{a-1} e^{-x/b} dx
 
-          P(n_1, n_2, ..., n_K) =
-            (N!/(n_1! n_2! ... n_K!)) p_1^n_1 p_2^n_2 ... p_K^n_K
+     for x > 0.
 
-     where (n_1, n_2, ..., n_K) are nonnegative integers with
-     sum_{k=1}^K n_k = N, and (p_1, p_2, ..., p_K) is a probability
-     distribution with \sum p_i = 1.  If the array P[K] is not
-     normalized then its entries will be treated as weights and
-     normalized appropriately.  The arrays N[] and P[] must both be of
-     length K.
+     The gamma distribution with an integer parameter A is known as the
+     Erlang distribution.
 
-     Random variates are generated using the conditional binomial method
-     (see C.S. Davis, 'The computer generation of multinomial random
-     variates', Comp.  Stat.  Data Anal.  16 (1993) 205-217 for
-     details).
+     The variates are computed using the Marsaglia-Tsang fast gamma
+     method.  This function for this method was previously called
+     'gsl_ran_gamma_mt' and can still be accessed using this name.
 
- -- Function: double gsl_ran_multinomial_pdf (size_t K, const double
-          P[], const unsigned int N[])
-     This function computes the probability P(n_1, n_2, ..., n_K) of
-     sampling N[K] from a multinomial distribution with parameters P[K],
-     using the formula given above.
+ -- Function: double gsl_ran_gamma_knuth (const gsl_rng * R, double A,
+          double B)
+     This function returns a gamma variate using the algorithms from
+     Knuth (vol 2).
 
- -- Function: double gsl_ran_multinomial_lnpdf (size_t K, const double
-          P[], const unsigned int N[])
-     This function returns the logarithm of the probability for the
-     multinomial distribution P(n_1, n_2, ..., n_K) with parameters
-     P[K].
+ -- Function: double gsl_ran_gamma_pdf (double X, double A, double B)
+     This function computes the probability density p(x) at X for a
+     gamma distribution with parameters A and B, using the formula given
+     above.
+
+
+ -- Function: double gsl_cdf_gamma_P (double X, double A, double B)
+ -- Function: double gsl_cdf_gamma_Q (double X, double A, double B)
+ -- Function: double gsl_cdf_gamma_Pinv (double P, double A, double B)
+ -- Function: double gsl_cdf_gamma_Qinv (double Q, double A, double B)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the gamma distribution with parameters
+     A and B.
 
 
-File: gsl-ref.info,  Node: The Negative Binomial Distribution,  Next: The Pascal Distribution,  Prev: The Multinomial Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The Flat (Uniform) Distribution,  Next: The Lognormal Distribution,  Prev: The Gamma Distribution,  Up: Random Number Distributions
 
-20.33 The Negative Binomial Distribution
-========================================
+20.16 The Flat (Uniform) Distribution
+=====================================
 
- -- Function: unsigned int gsl_ran_negative_binomial (const gsl_rng * R,
-          double P, double N)
-     This function returns a random integer from the negative binomial
-     distribution, the number of failures occurring before N successes
-     in independent trials with probability P of success.  The
-     probability distribution for negative binomial variates is,
+ -- Function: double gsl_ran_flat (const gsl_rng * R, double A, double
+          B)
+     This function returns a random variate from the flat (uniform)
+     distribution from A to B.  The distribution is,
 
-          p(k) = {\Gamma(n + k) \over \Gamma(k+1) \Gamma(n) } p^n (1-p)^k
+          p(x) dx = {1 \over (b-a)} dx
 
-     Note that n is not required to be an integer.
+     if a <= x < b and 0 otherwise.
 
- -- Function: double gsl_ran_negative_binomial_pdf (unsigned int K,
-          double P, double N)
-     This function computes the probability p(k) of obtaining K from a
-     negative binomial distribution with parameters P and N, using the
-     formula given above.
+ -- Function: double gsl_ran_flat_pdf (double X, double A, double B)
+     This function computes the probability density p(x) at X for a
+     uniform distribution from A to B, using the formula given above.
 
 
- -- Function: double gsl_cdf_negative_binomial_P (unsigned int K, double
-          P, double N)
- -- Function: double gsl_cdf_negative_binomial_Q (unsigned int K, double
-          P, double N)
-     These functions compute the cumulative distribution functions P(k),
-     Q(k) for the negative binomial distribution with parameters P and
-     N.
+ -- Function: double gsl_cdf_flat_P (double X, double A, double B)
+ -- Function: double gsl_cdf_flat_Q (double X, double A, double B)
+ -- Function: double gsl_cdf_flat_Pinv (double P, double A, double B)
+ -- Function: double gsl_cdf_flat_Qinv (double Q, double A, double B)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for a uniform distribution from A to B.
 
 
-File: gsl-ref.info,  Node: The Pascal Distribution,  Next: The Geometric Distribution,  Prev: The Negative Binomial Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The Lognormal Distribution,  Next: The Chi-squared Distribution,  Prev: The Flat (Uniform) Distribution,  Up: Random Number Distributions
 
-20.34 The Pascal Distribution
-=============================
+20.17 The Lognormal Distribution
+================================
 
- -- Function: unsigned int gsl_ran_pascal (const gsl_rng * R, double P,
-          unsigned int N)
-     This function returns a random integer from the Pascal
-     distribution.  The Pascal distribution is simply a negative
-     binomial distribution with an integer value of n.
+ -- Function: double gsl_ran_lognormal (const gsl_rng * R, double ZETA,
+          double SIGMA)
+     This function returns a random variate from the lognormal
+     distribution.  The distribution function is,
 
-          p(k) = {(n + k - 1)! \over k! (n - 1)! } p^n (1-p)^k
+          p(x) dx = {1 \over x \sqrt{2 \pi \sigma^2} } \exp(-(\ln(x) - \zeta)^2/2 \sigma^2) dx
 
-     for k >= 0
+     for x > 0.
 
- -- Function: double gsl_ran_pascal_pdf (unsigned int K, double P,
-          unsigned int N)
-     This function computes the probability p(k) of obtaining K from a
-     Pascal distribution with parameters P and N, using the formula
-     given above.
+ -- Function: double gsl_ran_lognormal_pdf (double X, double ZETA,
+          double SIGMA)
+     This function computes the probability density p(x) at X for a
+     lognormal distribution with parameters ZETA and SIGMA, using the
+     formula given above.
 
 
- -- Function: double gsl_cdf_pascal_P (unsigned int K, double P,
-          unsigned int N)
- -- Function: double gsl_cdf_pascal_Q (unsigned int K, double P,
-          unsigned int N)
-     These functions compute the cumulative distribution functions P(k),
-     Q(k) for the Pascal distribution with parameters P and N.
+ -- Function: double gsl_cdf_lognormal_P (double X, double ZETA, double
+          SIGMA)
+ -- Function: double gsl_cdf_lognormal_Q (double X, double ZETA, double
+          SIGMA)
+ -- Function: double gsl_cdf_lognormal_Pinv (double P, double ZETA,
+          double SIGMA)
+ -- Function: double gsl_cdf_lognormal_Qinv (double Q, double ZETA,
+          double SIGMA)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the lognormal distribution with
+     parameters ZETA and SIGMA.
 
 
-File: gsl-ref.info,  Node: The Geometric Distribution,  Next: The Hypergeometric Distribution,  Prev: The Pascal Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The Chi-squared Distribution,  Next: The F-distribution,  Prev: The Lognormal Distribution,  Up: Random Number Distributions
 
-20.35 The Geometric Distribution
-================================
+20.18 The Chi-squared Distribution
+==================================
 
- -- Function: unsigned int gsl_ran_geometric (const gsl_rng * R, double
-          P)
-     This function returns a random integer from the geometric
-     distribution, the number of independent trials with probability P
-     until the first success.  The probability distribution for
-     geometric variates is,
+The chi-squared distribution arises in statistics.  If Y_i are n
+independent Gaussian random variates with unit variance then the
+sum-of-squares,
 
-          p(k) =  p (1-p)^(k-1)
+     X_i = \sum_i Y_i^2
 
-     for k >= 1.  Note that the distribution begins with k=1 with this
-     definition.  There is another convention in which the exponent k-1
-     is replaced by k.
+has a chi-squared distribution with n degrees of freedom.
 
- -- Function: double gsl_ran_geometric_pdf (unsigned int K, double P)
-     This function computes the probability p(k) of obtaining K from a
-     geometric distribution with probability parameter P, using the
+ -- Function: double gsl_ran_chisq (const gsl_rng * R, double NU)
+     This function returns a random variate from the chi-squared
+     distribution with NU degrees of freedom.  The distribution function
+     is,
+
+          p(x) dx = {1 \over 2 \Gamma(\nu/2) } (x/2)^{\nu/2 - 1} \exp(-x/2) dx
+
+     for x >= 0.
+
+ -- Function: double gsl_ran_chisq_pdf (double X, double NU)
+     This function computes the probability density p(x) at X for a
+     chi-squared distribution with NU degrees of freedom, using the
      formula given above.
 
 
- -- Function: double gsl_cdf_geometric_P (unsigned int K, double P)
- -- Function: double gsl_cdf_geometric_Q (unsigned int K, double P)
-     These functions compute the cumulative distribution functions P(k),
-     Q(k) for the geometric distribution with parameter P.
+ -- Function: double gsl_cdf_chisq_P (double X, double NU)
+ -- Function: double gsl_cdf_chisq_Q (double X, double NU)
+ -- Function: double gsl_cdf_chisq_Pinv (double P, double NU)
+ -- Function: double gsl_cdf_chisq_Qinv (double Q, double NU)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the chi-squared distribution with NU
+     degrees of freedom.
 
 
-File: gsl-ref.info,  Node: The Hypergeometric Distribution,  Next: The Logarithmic Distribution,  Prev: The Geometric Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The F-distribution,  Next: The t-distribution,  Prev: The Chi-squared Distribution,  Up: Random Number Distributions
 
-20.36 The Hypergeometric Distribution
-=====================================
+20.19 The F-distribution
+========================
 
- -- Function: unsigned int gsl_ran_hypergeometric (const gsl_rng * R,
-          unsigned int N1, unsigned int N2, unsigned int T)
-     This function returns a random integer from the hypergeometric
-     distribution.  The probability distribution for hypergeometric
-     random variates is,
+The F-distribution arises in statistics.  If Y_1 and Y_2 are chi-squared
+deviates with \nu_1 and \nu_2 degrees of freedom then the ratio,
 
-          p(k) =  C(n_1, k) C(n_2, t - k) / C(n_1 + n_2, t)
+     X = { (Y_1 / \nu_1) \over (Y_2 / \nu_2) }
 
-     where C(a,b) = a!/(b!(a-b)!) and t <= n_1 + n_2.  The domain of k
-     is max(0,t-n_2), ..., min(t,n_1).
+has an F-distribution F(x;\nu_1,\nu_2).
 
-     If a population contains n_1 elements of "type 1" and n_2 elements
-     of "type 2" then the hypergeometric distribution gives the
-     probability of obtaining k elements of "type 1" in t samples from
-     the population without replacement.
+ -- Function: double gsl_ran_fdist (const gsl_rng * R, double NU1,
+          double NU2)
+     This function returns a random variate from the F-distribution with
+     degrees of freedom NU1 and NU2.  The distribution function is,
+
+          p(x) dx =
+             { \Gamma((\nu_1 + \nu_2)/2)
+                  \over \Gamma(\nu_1/2) \Gamma(\nu_2/2) }
+             \nu_1^{\nu_1/2} \nu_2^{\nu_2/2}
+             x^{\nu_1/2 - 1} (\nu_2 + \nu_1 x)^{-\nu_1/2 -\nu_2/2}
 
- -- Function: double gsl_ran_hypergeometric_pdf (unsigned int K,
-          unsigned int N1, unsigned int N2, unsigned int T)
-     This function computes the probability p(k) of obtaining K from a
-     hypergeometric distribution with parameters N1, N2, T, using the
+     for x >= 0.
+
+ -- Function: double gsl_ran_fdist_pdf (double X, double NU1, double
+          NU2)
+     This function computes the probability density p(x) at X for an
+     F-distribution with NU1 and NU2 degrees of freedom, using the
      formula given above.
 
 
- -- Function: double gsl_cdf_hypergeometric_P (unsigned int K, unsigned
-          int N1, unsigned int N2, unsigned int T)
- -- Function: double gsl_cdf_hypergeometric_Q (unsigned int K, unsigned
-          int N1, unsigned int N2, unsigned int T)
-     These functions compute the cumulative distribution functions P(k),
-     Q(k) for the hypergeometric distribution with parameters N1, N2 and
-     T.
+ -- Function: double gsl_cdf_fdist_P (double X, double NU1, double NU2)
+ -- Function: double gsl_cdf_fdist_Q (double X, double NU1, double NU2)
+ -- Function: double gsl_cdf_fdist_Pinv (double P, double NU1, double
+          NU2)
+ -- Function: double gsl_cdf_fdist_Qinv (double Q, double NU1, double
+          NU2)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the F-distribution with NU1 and NU2
+     degrees of freedom.
 
 
-File: gsl-ref.info,  Node: The Logarithmic Distribution,  Next: Shuffling and Sampling,  Prev: The Hypergeometric Distribution,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The t-distribution,  Next: The Beta Distribution,  Prev: The F-distribution,  Up: Random Number Distributions
 
-20.37 The Logarithmic Distribution
-==================================
-
- -- Function: unsigned int gsl_ran_logarithmic (const gsl_rng * R,
-          double P)
-     This function returns a random integer from the logarithmic
-     distribution.  The probability distribution for logarithmic random
-     variates is,
+20.20 The t-distribution
+========================
 
-          p(k) = {-1 \over \log(1-p)} {(p^k \over k)}
+The t-distribution arises in statistics.  If Y_1 has a normal
+distribution and Y_2 has a chi-squared distribution with \nu degrees of
+freedom then the ratio,
 
-     for k >= 1.
+     X = { Y_1 \over \sqrt{Y_2 / \nu} }
 
- -- Function: double gsl_ran_logarithmic_pdf (unsigned int K, double P)
-     This function computes the probability p(k) of obtaining K from a
-     logarithmic distribution with probability parameter P, using the
-     formula given above.
+has a t-distribution t(x;\nu) with \nu degrees of freedom.
 
+ -- Function: double gsl_ran_tdist (const gsl_rng * R, double NU)
+     This function returns a random variate from the t-distribution.
+     The distribution function is,
 
-
-File: gsl-ref.info,  Node: Shuffling and Sampling,  Next: Random Number Distribution Examples,  Prev: The Logarithmic Distribution,  Up: Random Number Distributions
+          p(x) dx = {\Gamma((\nu + 1)/2) \over \sqrt{\pi \nu} \Gamma(\nu/2)}
+             (1 + x^2/\nu)^{-(\nu + 1)/2} dx
 
-20.38 Shuffling and Sampling
-============================
+     for -\infty < x < +\infty.
 
-The following functions allow the shuffling and sampling of a set of
-objects.  The algorithms rely on a random number generator as a source
-of randomness and a poor quality generator can lead to correlations in
-the output.  In particular it is important to avoid generators with a
-short period.  For more information see Knuth, v2, 3rd ed, Section
-3.4.2, "Random Sampling and Shuffling".
+ -- Function: double gsl_ran_tdist_pdf (double X, double NU)
+     This function computes the probability density p(x) at X for a
+     t-distribution with NU degrees of freedom, using the formula given
+     above.
 
- -- Function: void gsl_ran_shuffle (const gsl_rng * R, void * BASE,
-          size_t N, size_t SIZE)
 
-     This function randomly shuffles the order of N objects, each of
-     size SIZE, stored in the array BASE[0..N-1].  The output of the
-     random number generator R is used to produce the permutation.  The
-     algorithm generates all possible n! permutations with equal
-     probability, assuming a perfect source of random numbers.
+ -- Function: double gsl_cdf_tdist_P (double X, double NU)
+ -- Function: double gsl_cdf_tdist_Q (double X, double NU)
+ -- Function: double gsl_cdf_tdist_Pinv (double P, double NU)
+ -- Function: double gsl_cdf_tdist_Qinv (double Q, double NU)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the t-distribution with NU degrees of
+     freedom.
 
-     The following code shows how to shuffle the numbers from 0 to 51,
+
+File: gsl-ref.info,  Node: The Beta Distribution,  Next: The Logistic Distribution,  Prev: The t-distribution,  Up: Random Number Distributions
 
-          int a[52];
+20.21 The Beta Distribution
+===========================
 
-          for (i = 0; i < 52; i++)
-            {
-              a[i] = i;
-            }
+ -- Function: double gsl_ran_beta (const gsl_rng * R, double A, double
+          B)
+     This function returns a random variate from the beta distribution.
+     The distribution function is,
 
-          gsl_ran_shuffle (r, a, 52, sizeof (int));
+          p(x) dx = {\Gamma(a+b) \over \Gamma(a) \Gamma(b)} x^{a-1} (1-x)^{b-1} dx
 
- -- Function: int gsl_ran_choose (const gsl_rng * R, void * DEST, size_t
-          K, void * SRC, size_t N, size_t SIZE)
-     This function fills the array DEST[k] with K objects taken randomly
-     from the N elements of the array SRC[0..N-1].  The objects are each
-     of size SIZE.  The output of the random number generator R is used
-     to make the selection.  The algorithm ensures all possible samples
-     are equally likely, assuming a perfect source of randomness.
+     for 0 <= x <= 1.
 
-     The objects are sampled _without_ replacement, thus each object can
-     only appear once in DEST[k].  It is required that K be less than or
-     equal to 'n'.  The objects in DEST will be in the same relative
-     order as those in SRC.  You will need to call 'gsl_ran_shuffle(r,
-     dest, n, size)' if you want to randomize the order.
+ -- Function: double gsl_ran_beta_pdf (double X, double A, double B)
+     This function computes the probability density p(x) at X for a beta
+     distribution with parameters A and B, using the formula given
+     above.
 
-     The following code shows how to select a random sample of three
-     unique numbers from the set 0 to 99,
 
-          double a[3], b[100];
+ -- Function: double gsl_cdf_beta_P (double X, double A, double B)
+ -- Function: double gsl_cdf_beta_Q (double X, double A, double B)
+ -- Function: double gsl_cdf_beta_Pinv (double P, double A, double B)
+ -- Function: double gsl_cdf_beta_Qinv (double Q, double A, double B)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the beta distribution with parameters A
+     and B.
 
-          for (i = 0; i < 100; i++)
-            {
-              b[i] = (double) i;
-            }
+
+File: gsl-ref.info,  Node: The Logistic Distribution,  Next: The Pareto Distribution,  Prev: The Beta Distribution,  Up: Random Number Distributions
 
-          gsl_ran_choose (r, a, 3, b, 100, sizeof (double));
+20.22 The Logistic Distribution
+===============================
 
- -- Function: void gsl_ran_sample (const gsl_rng * R, void * DEST,
-          size_t K, void * SRC, size_t N, size_t SIZE)
-     This function is like 'gsl_ran_choose' but samples K items from the
-     original array of N items SRC with replacement, so the same object
-     can appear more than once in the output sequence DEST.  There is no
-     requirement that K be less than N in this case.
+ -- Function: double gsl_ran_logistic (const gsl_rng * R, double A)
+     This function returns a random variate from the logistic
+     distribution.  The distribution function is,
 
-
-File: gsl-ref.info,  Node: Random Number Distribution Examples,  Next: Random Number Distribution References and Further Reading,  Prev: Shuffling and Sampling,  Up: Random Number Distributions
+          p(x) dx = { \exp(-x/a) \over a (1 + \exp(-x/a))^2 } dx
 
-20.39 Examples
-==============
+     for -\infty < x < +\infty.
 
-The following program demonstrates the use of a random number generator
-to produce variates from a distribution.  It prints 10 samples from the
-Poisson distribution with a mean of 3.
+ -- Function: double gsl_ran_logistic_pdf (double X, double A)
+     This function computes the probability density p(x) at X for a
+     logistic distribution with scale parameter A, using the formula
+     given above.
 
-     #include <stdio.h>
-     #include <gsl/gsl_rng.h>
-     #include <gsl/gsl_randist.h>
 
-     int
-     main (void)
-     {
-       const gsl_rng_type * T;
-       gsl_rng * r;
+ -- Function: double gsl_cdf_logistic_P (double X, double A)
+ -- Function: double gsl_cdf_logistic_Q (double X, double A)
+ -- Function: double gsl_cdf_logistic_Pinv (double P, double A)
+ -- Function: double gsl_cdf_logistic_Qinv (double Q, double A)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the logistic distribution with scale
+     parameter A.
 
-       int i, n = 10;
-       double mu = 3.0;
+
+File: gsl-ref.info,  Node: The Pareto Distribution,  Next: Spherical Vector Distributions,  Prev: The Logistic Distribution,  Up: Random Number Distributions
 
-       /* create a generator chosen by the
-          environment variable GSL_RNG_TYPE */
+20.23 The Pareto Distribution
+=============================
 
-       gsl_rng_env_setup();
+ -- Function: double gsl_ran_pareto (const gsl_rng * R, double A, double
+          B)
+     This function returns a random variate from the Pareto distribution
+     of order A.  The distribution function is,
 
-       T = gsl_rng_default;
-       r = gsl_rng_alloc (T);
+          p(x) dx = (a/b) / (x/b)^{a+1} dx
 
-       /* print n random variates chosen from
-          the poisson distribution with mean
-          parameter mu */
+     for x >= b.
 
-       for (i = 0; i < n; i++)
-         {
-           unsigned int k = gsl_ran_poisson (r, mu);
-           printf (" %u", k);
-         }
+ -- Function: double gsl_ran_pareto_pdf (double X, double A, double B)
+     This function computes the probability density p(x) at X for a
+     Pareto distribution with exponent A and scale B, using the formula
+     given above.
 
-       printf ("\n");
-       gsl_rng_free (r);
-       return 0;
-     }
 
-If the library and header files are installed under '/usr/local' (the
-default location) then the program can be compiled with these options,
+ -- Function: double gsl_cdf_pareto_P (double X, double A, double B)
+ -- Function: double gsl_cdf_pareto_Q (double X, double A, double B)
+ -- Function: double gsl_cdf_pareto_Pinv (double P, double A, double B)
+ -- Function: double gsl_cdf_pareto_Qinv (double Q, double A, double B)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the Pareto distribution with exponent A
+     and scale B.
 
-     $ gcc -Wall demo.c -lgsl -lgslcblas -lm
+
+File: gsl-ref.info,  Node: Spherical Vector Distributions,  Next: The Weibull Distribution,  Prev: The Pareto Distribution,  Up: Random Number Distributions
 
-Here is the output of the program,
+20.24 Spherical Vector Distributions
+====================================
 
-     $ ./a.out
-      2 5 5 2 1 0 3 4 1 1
+The spherical distributions generate random vectors, located on a
+spherical surface.  They can be used as random directions, for example
+in the steps of a random walk.
 
-The variates depend on the seed used by the generator.  The seed for the
-default generator type 'gsl_rng_default' can be changed with the
-'GSL_RNG_SEED' environment variable to produce a different stream of
-variates,
+ -- Function: void gsl_ran_dir_2d (const gsl_rng * R, double * X, double
+          * Y)
+ -- Function: void gsl_ran_dir_2d_trig_method (const gsl_rng * R, double
+          * X, double * Y)
+     This function returns a random direction vector v = (X,Y) in two
+     dimensions.  The vector is normalized such that |v|^2 = x^2 + y^2 =
+     1.  The obvious way to do this is to take a uniform random number
+     between 0 and 2\pi and let X and Y be the sine and cosine
+     respectively.  Two trig functions would have been expensive in the
+     old days, but with modern hardware implementations, this is
+     sometimes the fastest way to go.  This is the case for the Pentium
+     (but not the case for the Sun Sparcstation).  One can avoid the
+     trig evaluations by choosing X and Y in the interior of a unit
+     circle (choose them at random from the interior of the enclosing
+     square, and then reject those that are outside the unit circle),
+     and then dividing by \sqrt{x^2 + y^2}.  A much cleverer approach,
+     attributed to von Neumann (See Knuth, v2, 3rd ed, p140, exercise
+     23), requires neither trig nor a square root.  In this approach, U
+     and V are chosen at random from the interior of a unit circle, and
+     then x=(u^2-v^2)/(u^2+v^2) and y=2uv/(u^2+v^2).
 
-     $ GSL_RNG_SEED=123 ./a.out
-     GSL_RNG_SEED=123
-      4 5 6 3 3 1 4 2 5 5
+ -- Function: void gsl_ran_dir_3d (const gsl_rng * R, double * X, double
+          * Y, double * Z)
+     This function returns a random direction vector v = (X,Y,Z) in
+     three dimensions.  The vector is normalized such that |v|^2 = x^2 +
+     y^2 + z^2 = 1.  The method employed is due to Robert E. Knop (CACM
+     13, 326 (1970)), and explained in Knuth, v2, 3rd ed, p136.  It uses
+     the surprising fact that the distribution projected along any axis
+     is actually uniform (this is only true for 3 dimensions).
 
-The following program generates a random walk in two dimensions.
+ -- Function: void gsl_ran_dir_nd (const gsl_rng * R, size_t N, double *
+          X)
 
-     #include <stdio.h>
-     #include <gsl/gsl_rng.h>
-     #include <gsl/gsl_randist.h>
+     This function returns a random direction vector v =
+     (x_1,x_2,...,x_n) in N dimensions.  The vector is normalized such
+     that |v|^2 = x_1^2 + x_2^2 + ... + x_n^2 = 1.  The method uses the
+     fact that a multivariate Gaussian distribution is spherically
+     symmetric.  Each component is generated to have a Gaussian
+     distribution, and then the components are normalized.  The method
+     is described by Knuth, v2, 3rd ed, p135-136, and attributed to G.
+     W. Brown, Modern Mathematics for the Engineer (1956).
 
-     int
-     main (void)
-     {
-       int i;
-       double x = 0, y = 0, dx, dy;
+
+File: gsl-ref.info,  Node: The Weibull Distribution,  Next: The Type-1 Gumbel Distribution,  Prev: Spherical Vector Distributions,  Up: Random Number Distributions
 
-       const gsl_rng_type * T;
-       gsl_rng * r;
+20.25 The Weibull Distribution
+==============================
 
-       gsl_rng_env_setup();
-       T = gsl_rng_default;
-       r = gsl_rng_alloc (T);
+ -- Function: double gsl_ran_weibull (const gsl_rng * R, double A,
+          double B)
+     This function returns a random variate from the Weibull
+     distribution.  The distribution function is,
 
-       printf ("%g %g\n", x, y);
+          p(x) dx = {b \over a^b} x^{b-1}  \exp(-(x/a)^b) dx
 
-       for (i = 0; i < 10; i++)
-         {
-           gsl_ran_dir_2d (r, &dx, &dy);
-           x += dx; y += dy;
-           printf ("%g %g\n", x, y);
-         }
+     for x >= 0.
 
-       gsl_rng_free (r);
-       return 0;
-     }
+ -- Function: double gsl_ran_weibull_pdf (double X, double A, double B)
+     This function computes the probability density p(x) at X for a
+     Weibull distribution with scale A and exponent B, using the formula
+     given above.
 
-Here is some output from the program, four 10-step random walks from the
-origin,
 
-   The following program computes the upper and lower cumulative
-distribution functions for the standard normal distribution at x=2.
-
-     #include <stdio.h>
-     #include <gsl/gsl_cdf.h>
+ -- Function: double gsl_cdf_weibull_P (double X, double A, double B)
+ -- Function: double gsl_cdf_weibull_Q (double X, double A, double B)
+ -- Function: double gsl_cdf_weibull_Pinv (double P, double A, double B)
+ -- Function: double gsl_cdf_weibull_Qinv (double Q, double A, double B)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the Weibull distribution with scale A
+     and exponent B.
 
-     int
-     main (void)
-     {
-       double P, Q;
-       double x = 2.0;
+
+File: gsl-ref.info,  Node: The Type-1 Gumbel Distribution,  Next: The Type-2 Gumbel Distribution,  Prev: The Weibull Distribution,  Up: Random Number Distributions
 
-       P = gsl_cdf_ugaussian_P (x);
-       printf ("prob(x < %f) = %f\n", x, P);
+20.26 The Type-1 Gumbel Distribution
+====================================
 
-       Q = gsl_cdf_ugaussian_Q (x);
-       printf ("prob(x > %f) = %f\n", x, Q);
+ -- Function: double gsl_ran_gumbel1 (const gsl_rng * R, double A,
+          double B)
+     This function returns a random variate from the Type-1 Gumbel
+     distribution.  The Type-1 Gumbel distribution function is,
 
-       x = gsl_cdf_ugaussian_Pinv (P);
-       printf ("Pinv(%f) = %f\n", P, x);
+          p(x) dx = a b \exp(-(b \exp(-ax) + ax)) dx
 
-       x = gsl_cdf_ugaussian_Qinv (Q);
-       printf ("Qinv(%f) = %f\n", Q, x);
+     for -\infty < x < \infty.
 
-       return 0;
-     }
+ -- Function: double gsl_ran_gumbel1_pdf (double X, double A, double B)
+     This function computes the probability density p(x) at X for a
+     Type-1 Gumbel distribution with parameters A and B, using the
+     formula given above.
 
-Here is the output of the program,
 
-     prob(x < 2.000000) = 0.977250
-     prob(x > 2.000000) = 0.022750
-     Pinv(0.977250) = 2.000000
-     Qinv(0.022750) = 2.000000
+ -- Function: double gsl_cdf_gumbel1_P (double X, double A, double B)
+ -- Function: double gsl_cdf_gumbel1_Q (double X, double A, double B)
+ -- Function: double gsl_cdf_gumbel1_Pinv (double P, double A, double B)
+ -- Function: double gsl_cdf_gumbel1_Qinv (double Q, double A, double B)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the Type-1 Gumbel distribution with
+     parameters A and B.
 
 
-File: gsl-ref.info,  Node: Random Number Distribution References and Further Reading,  Prev: Random Number Distribution Examples,  Up: Random Number Distributions
+File: gsl-ref.info,  Node: The Type-2 Gumbel Distribution,  Next: The Dirichlet Distribution,  Prev: The Type-1 Gumbel Distribution,  Up: Random Number Distributions
 
-20.40 References and Further Reading
+20.27 The Type-2 Gumbel Distribution
 ====================================
 
-For an encyclopaedic coverage of the subject readers are advised to
-consult the book 'Non-Uniform Random Variate Generation' by Luc Devroye.
-It covers every imaginable distribution and provides hundreds of
-algorithms.
+ -- Function: double gsl_ran_gumbel2 (const gsl_rng * R, double A,
+          double B)
+     This function returns a random variate from the Type-2 Gumbel
+     distribution.  The Type-2 Gumbel distribution function is,
 
-     Luc Devroye, 'Non-Uniform Random Variate Generation',
-     Springer-Verlag, ISBN 0-387-96305-7.  Available online at
-     <http://cg.scs.carleton.ca/~luc/rnbookindex.html>.
+          p(x) dx = a b x^{-a-1} \exp(-b x^{-a}) dx
 
-The subject of random variate generation is also reviewed by Knuth, who
-describes algorithms for all the major distributions.
+     for 0 < x < \infty.
 
-     Donald E. Knuth, 'The Art of Computer Programming: Seminumerical
-     Algorithms' (Vol 2, 3rd Ed, 1997), Addison-Wesley, ISBN 0201896842.
+ -- Function: double gsl_ran_gumbel2_pdf (double X, double A, double B)
+     This function computes the probability density p(x) at X for a
+     Type-2 Gumbel distribution with parameters A and B, using the
+     formula given above.
 
-The Particle Data Group provides a short review of techniques for
-generating distributions of random numbers in the "Monte Carlo" section
-of its Annual Review of Particle Physics.
 
-     'Review of Particle Properties' R.M. Barnett et al., Physical
-     Review D54, 1 (1996) <http://pdg.lbl.gov/>.
+ -- Function: double gsl_cdf_gumbel2_P (double X, double A, double B)
+ -- Function: double gsl_cdf_gumbel2_Q (double X, double A, double B)
+ -- Function: double gsl_cdf_gumbel2_Pinv (double P, double A, double B)
+ -- Function: double gsl_cdf_gumbel2_Qinv (double Q, double A, double B)
+     These functions compute the cumulative distribution functions P(x),
+     Q(x) and their inverses for the Type-2 Gumbel distribution with
+     parameters A and B.
 
-The Review of Particle Physics is available online in postscript and pdf
-format.
+
+File: gsl-ref.info,  Node: The Dirichlet Distribution,  Next: General Discrete Distributions,  Prev: The Type-2 Gumbel Distribution,  Up: Random Number Distributions
 
-An overview of methods used to compute cumulative distribution functions
-can be found in 'Statistical Computing' by W.J. Kennedy and J.E. Gentle.
-Another general reference is 'Elements of Statistical Computing' by R.A.
-Thisted.
+20.28 The Dirichlet Distribution
+================================
 
-     William E. Kennedy and James E. Gentle, 'Statistical Computing'
-     (1980), Marcel Dekker, ISBN 0-8247-6898-1.
+ -- Function: void gsl_ran_dirichlet (const gsl_rng * R, size_t K, const
+          double ALPHA[], double THETA[])
+     This function returns an array of K random variates from a
+     Dirichlet distribution of order K-1.  The distribution function is
 
-     Ronald A. Thisted, 'Elements of Statistical Computing' (1988),
-     Chapman & Hall, ISBN 0-412-01371-1.
+          p(\theta_1, ..., \theta_K) d\theta_1 ... d\theta_K =
+            (1/Z) \prod_{i=1}^K \theta_i^{\alpha_i - 1} \delta(1 -\sum_{i=1}^K \theta_i) d\theta_1 ... d\theta_K
 
-The cumulative distribution functions for the Gaussian distribution are
-based on the following papers,
+     for theta_i >= 0 and alpha_i > 0.  The delta function ensures that
+     \sum \theta_i = 1.  The normalization factor Z is
 
-     'Rational Chebyshev Approximations Using Linear Equations', W.J.
-     Cody, W. Fraser, J.F. Hart.  Numerische Mathematik 12, 242-251
-     (1968).
+          Z = {\prod_{i=1}^K \Gamma(\alpha_i)} / {\Gamma( \sum_{i=1}^K \alpha_i)}
 
-     'Rational Chebyshev Approximations for the Error Function', W.J.
-     Cody.  Mathematics of Computation 23, n107, 631-637 (July 1969).
+     The random variates are generated by sampling K values from gamma
+     distributions with parameters a=alpha_i, b=1, and renormalizing.
+     See A.M. Law, W.D. Kelton, 'Simulation Modeling and Analysis'
+     (1991).
 
-
-File: gsl-ref.info,  Node: Statistics,  Next: Histograms,  Prev: Random Number Distributions,  Up: Top
+ -- Function: double gsl_ran_dirichlet_pdf (size_t K, const double
+          ALPHA[], const double THETA[])
+     This function computes the probability density p(\theta_1, ... ,
+     \theta_K) at THETA[K] for a Dirichlet distribution with parameters
+     ALPHA[K], using the formula given above.
 
-21 Statistics
-*************
+ -- Function: double gsl_ran_dirichlet_lnpdf (size_t K, const double
+          ALPHA[], const double THETA[])
+     This function computes the logarithm of the probability density
+     p(\theta_1, ... , \theta_K) for a Dirichlet distribution with
+     parameters ALPHA[K].
 
-This chapter describes the statistical functions in the library.  The
-basic statistical functions include routines to compute the mean,
-variance and standard deviation.  More advanced functions allow you to
-calculate absolute deviations, skewness, and kurtosis as well as the
-median and arbitrary percentiles.  The algorithms use recurrence
-relations to compute average quantities in a stable way, without large
-intermediate values that might overflow.
+
+File: gsl-ref.info,  Node: General Discrete Distributions,  Next: The Poisson Distribution,  Prev: The Dirichlet Distribution,  Up: Random Number Distributions
 
-   The functions are available in versions for datasets in the standard
-floating-point and integer types.  The versions for double precision
-floating-point data have the prefix 'gsl_stats' and are declared in the
-header file 'gsl_statistics_double.h'.  The versions for integer data
-have the prefix 'gsl_stats_int' and are declared in the header file
-'gsl_statistics_int.h'.  All the functions operate on C arrays with a
-STRIDE parameter specifying the spacing between elements.
+20.29 General Discrete Distributions
+====================================
 
-* Menu:
+Given K discrete events with different probabilities P[k], produce a
+random value k consistent with its probability.
 
-* Mean and standard deviation and variance::  
-* Absolute deviation::          
-* Higher moments (skewness and kurtosis)::  
-* Autocorrelation::             
-* Covariance::                  
-* Correlation::                  
-* Weighted Samples::            
-* Maximum and Minimum values::  
-* Median and Percentiles::      
-* Example statistical programs::  
-* Statistics References and Further Reading::  
+   The obvious way to do this is to preprocess the probability list by
+generating a cumulative probability array with K+1 elements:
 
-
-File: gsl-ref.info,  Node: Mean and standard deviation and variance,  Next: Absolute deviation,  Up: Statistics
+       C[0] = 0
+     C[k+1] = C[k]+P[k].
 
-21.1 Mean, Standard Deviation and Variance
-==========================================
+Note that this construction produces C[K]=1.  Now choose a uniform
+deviate u between 0 and 1, and find the value of k such that C[k] <= u <
+C[k+1].  Although this in principle requires of order \log K steps per
+random number generation, they are fast steps, and if you use something
+like \lfloor uK \rfloor as a starting point, you can often do pretty
+well.
 
- -- Function: double gsl_stats_mean (const double DATA[], size_t STRIDE,
-          size_t N)
-     This function returns the arithmetic mean of DATA, a dataset of
-     length N with stride STRIDE.  The arithmetic mean, or "sample
-     mean", is denoted by \Hat\mu and defined as,
+   But faster methods have been devised.  Again, the idea is to
+preprocess the probability list, and save the result in some form of
+lookup table; then the individual calls for a random discrete event can
+go rapidly.  An approach invented by G. Marsaglia (Generating discrete
+random variables in a computer, Comm ACM 6, 37-38 (1963)) is very
+clever, and readers interested in examples of good algorithm design are
+directed to this short and well-written paper.  Unfortunately, for large
+K, Marsaglia's lookup table can be quite large.
 
-          \Hat\mu = (1/N) \sum x_i
+   A much better approach is due to Alastair J. Walker (An efficient
+method for generating discrete random variables with general
+distributions, ACM Trans on Mathematical Software 3, 253-256 (1977); see
+also Knuth, v2, 3rd ed, p120-121,139).  This requires two lookup tables,
+one floating point and one integer, but both only of size K.  After
+preprocessing, the random numbers are generated in O(1) time, even for
+large K.  The preprocessing suggested by Walker requires O(K^2) effort,
+but that is not actually necessary, and the implementation provided here
+only takes O(K) effort.  In general, more preprocessing leads to faster
+generation of the individual random numbers, but a diminishing return is
+reached pretty early.  Knuth points out that the optimal preprocessing
+is combinatorially difficult for large K.
 
-     where x_i are the elements of the dataset DATA.  For samples drawn
-     from a gaussian distribution the variance of \Hat\mu is \sigma^2 /
-     N.
+   This method can be used to speed up some of the discrete random
+number generators below, such as the binomial distribution.  To use it
+for something like the Poisson Distribution, a modification would have
+to be made, since it only takes a finite set of K outcomes.
 
- -- Function: double gsl_stats_variance (const double DATA[], size_t
-          STRIDE, size_t N)
-     This function returns the estimated, or "sample", variance of DATA,
-     a dataset of length N with stride STRIDE.  The estimated variance
-     is denoted by \Hat\sigma^2 and is defined by,
+ -- Function: gsl_ran_discrete_t * gsl_ran_discrete_preproc (size_t K,
+          const double * P)
+     This function returns a pointer to a structure that contains the
+     lookup table for the discrete random number generator.  The array
+     P[] contains the probabilities of the discrete events; these array
+     elements must all be positive, but they needn't add up to one (so
+     you can think of them more generally as "weights")--the
+     preprocessor will normalize appropriately.  This return value is
+     used as an argument for the 'gsl_ran_discrete' function below.
 
-          \Hat\sigma^2 = (1/(N-1)) \sum (x_i - \Hat\mu)^2
+ -- Function: size_t gsl_ran_discrete (const gsl_rng * R, const
+          gsl_ran_discrete_t * G)
+     After the preprocessor, above, has been called, you use this
+     function to get the discrete random numbers.
 
-     where x_i are the elements of the dataset DATA.  Note that the
-     normalization factor of 1/(N-1) results from the derivation of
-     \Hat\sigma^2 as an unbiased estimator of the population variance
-     \sigma^2.  For samples drawn from a Gaussian distribution the
-     variance of \Hat\sigma^2 itself is 2 \sigma^4 / N.
+ -- Function: double gsl_ran_discrete_pdf (size_t K, const
+          gsl_ran_discrete_t * G)
+     Returns the probability P[k] of observing the variable K.  Since
+     P[k] is not stored as part of the lookup table, it must be
+     recomputed; this computation takes O(K), so if K is large and you
+     care about the original array P[k] used to create the lookup table,
+     then you should just keep this original array P[k] around.
 
-     This function computes the mean via a call to 'gsl_stats_mean'.  If
-     you have already computed the mean then you can pass it directly to
-     'gsl_stats_variance_m'.
+ -- Function: void gsl_ran_discrete_free (gsl_ran_discrete_t * G)
+     De-allocates the lookup table pointed to by G.
 
- -- Function: double gsl_stats_variance_m (const double DATA[], size_t
-          STRIDE, size_t N, double MEAN)
-     This function returns the sample variance of DATA relative to the
-     given value of MEAN.  The function is computed with \Hat\mu
-     replaced by the value of MEAN that you supply,
+
+File: gsl-ref.info,  Node: The Poisson Distribution,  Next: The Bernoulli Distribution,  Prev: General Discrete Distributions,  Up: Random Number Distributions
 
-          \Hat\sigma^2 = (1/(N-1)) \sum (x_i - mean)^2
+20.30 The Poisson Distribution
+==============================
 
- -- Function: double gsl_stats_sd (const double DATA[], size_t STRIDE,
-          size_t N)
- -- Function: double gsl_stats_sd_m (const double DATA[], size_t STRIDE,
-          size_t N, double MEAN)
-     The standard deviation is defined as the square root of the
-     variance.  These functions return the square root of the
-     corresponding variance functions above.
+ -- Function: unsigned int gsl_ran_poisson (const gsl_rng * R, double
+          MU)
+     This function returns a random integer from the Poisson
+     distribution with mean MU.  The probability distribution for
+     Poisson variates is,
 
- -- Function: double gsl_stats_tss (const double DATA[], size_t STRIDE,
-          size_t N)
- -- Function: double gsl_stats_tss_m (const double DATA[], size_t
-          STRIDE, size_t N, double MEAN)
-     These functions return the total sum of squares (TSS) of DATA about
-     the mean.  For 'gsl_stats_tss_m' the user-supplied value of MEAN is
-     used, and for 'gsl_stats_tss' it is computed using
-     'gsl_stats_mean'.
+          p(k) = {\mu^k \over k!} \exp(-\mu)
 
-          TSS =  \sum (x_i - mean)^2
+     for k >= 0.
 
- -- Function: double gsl_stats_variance_with_fixed_mean (const double
-          DATA[], size_t STRIDE, size_t N, double MEAN)
-     This function computes an unbiased estimate of the variance of DATA
-     when the population mean MEAN of the underlying distribution is
-     known _a priori_.  In this case the estimator for the variance uses
-     the factor 1/N and the sample mean \Hat\mu is replaced by the known
-     population mean \mu,
+ -- Function: double gsl_ran_poisson_pdf (unsigned int K, double MU)
+     This function computes the probability p(k) of obtaining K from a
+     Poisson distribution with mean MU, using the formula given above.
 
-          \Hat\sigma^2 = (1/N) \sum (x_i - \mu)^2
 
- -- Function: double gsl_stats_sd_with_fixed_mean (const double DATA[],
-          size_t STRIDE, size_t N, double MEAN)
-     This function calculates the standard deviation of DATA for a fixed
-     population mean MEAN.  The result is the square root of the
-     corresponding variance function.
+ -- Function: double gsl_cdf_poisson_P (unsigned int K, double MU)
+ -- Function: double gsl_cdf_poisson_Q (unsigned int K, double MU)
+     These functions compute the cumulative distribution functions P(k),
+     Q(k) for the Poisson distribution with parameter MU.
 
 
-File: gsl-ref.info,  Node: Absolute deviation,  Next: Higher moments (skewness and kurtosis),  Prev: Mean and standard deviation and variance,  Up: Statistics
-
-21.2 Absolute deviation
-=======================
-
- -- Function: double gsl_stats_absdev (const double DATA[], size_t
-          STRIDE, size_t N)
-     This function computes the absolute deviation from the mean of
-     DATA, a dataset of length N with stride STRIDE.  The absolute
-     deviation from the mean is defined as,
+File: gsl-ref.info,  Node: The Bernoulli Distribution,  Next: The Binomial Distribution,  Prev: The Poisson Distribution,  Up: Random Number Distributions
 
-          absdev  = (1/N) \sum |x_i - \Hat\mu|
+20.31 The Bernoulli Distribution
+================================
 
-     where x_i are the elements of the dataset DATA.  The absolute
-     deviation from the mean provides a more robust measure of the width
-     of a distribution than the variance.  This function computes the
-     mean of DATA via a call to 'gsl_stats_mean'.
+ -- Function: unsigned int gsl_ran_bernoulli (const gsl_rng * R, double
+          P)
+     This function returns either 0 or 1, the result of a Bernoulli
+     trial with probability P.  The probability distribution for a
+     Bernoulli trial is,
 
- -- Function: double gsl_stats_absdev_m (const double DATA[], size_t
-          STRIDE, size_t N, double MEAN)
-     This function computes the absolute deviation of the dataset DATA
-     relative to the given value of MEAN,
+          p(0) = 1 - p
+          p(1) = p
 
-          absdev  = (1/N) \sum |x_i - mean|
+ -- Function: double gsl_ran_bernoulli_pdf (unsigned int K, double P)
+     This function computes the probability p(k) of obtaining K from a
+     Bernoulli distribution with probability parameter P, using the
+     formula given above.
 
-     This function is useful if you have already computed the mean of
-     DATA (and want to avoid recomputing it), or wish to calculate the
-     absolute deviation relative to another value (such as zero, or the
-     median).
 
 
-File: gsl-ref.info,  Node: Higher moments (skewness and kurtosis),  Next: Autocorrelation,  Prev: Absolute deviation,  Up: Statistics
+File: gsl-ref.info,  Node: The Binomial Distribution,  Next: The Multinomial Distribution,  Prev: The Bernoulli Distribution,  Up: Random Number Distributions
 
-21.3 Higher moments (skewness and kurtosis)
-===========================================
+20.32 The Binomial Distribution
+===============================
 
- -- Function: double gsl_stats_skew (const double DATA[], size_t STRIDE,
-          size_t N)
-     This function computes the skewness of DATA, a dataset of length N
-     with stride STRIDE.  The skewness is defined as,
+ -- Function: unsigned int gsl_ran_binomial (const gsl_rng * R, double
+          P, unsigned int N)
+     This function returns a random integer from the binomial
+     distribution, the number of successes in N independent trials with
+     probability P.  The probability distribution for binomial variates
+     is,
 
-          skew = (1/N) \sum ((x_i - \Hat\mu)/\Hat\sigma)^3
+          p(k) = {n! \over k! (n-k)! } p^k (1-p)^{n-k}
 
-     where x_i are the elements of the dataset DATA.  The skewness
-     measures the asymmetry of the tails of a distribution.
+     for 0 <= k <= n.
 
-     The function computes the mean and estimated standard deviation of
-     DATA via calls to 'gsl_stats_mean' and 'gsl_stats_sd'.
+ -- Function: double gsl_ran_binomial_pdf (unsigned int K, double P,
+          unsigned int N)
+     This function computes the probability p(k) of obtaining K from a
+     binomial distribution with parameters P and N, using the formula
+     given above.
 
- -- Function: double gsl_stats_skew_m_sd (const double DATA[], size_t
-          STRIDE, size_t N, double MEAN, double SD)
-     This function computes the skewness of the dataset DATA using the
-     given values of the mean MEAN and standard deviation SD,
 
-          skew = (1/N) \sum ((x_i - mean)/sd)^3
+ -- Function: double gsl_cdf_binomial_P (unsigned int K, double P,
+          unsigned int N)
+ -- Function: double gsl_cdf_binomial_Q (unsigned int K, double P,
+          unsigned int N)
+     These functions compute the cumulative distribution functions P(k),
+     Q(k) for the binomial distribution with parameters P and N.
 
-     These functions are useful if you have already computed the mean
-     and standard deviation of DATA and want to avoid recomputing them.
+
+File: gsl-ref.info,  Node: The Multinomial Distribution,  Next: The Negative Binomial Distribution,  Prev: The Binomial Distribution,  Up: Random Number Distributions
 
- -- Function: double gsl_stats_kurtosis (const double DATA[], size_t
-          STRIDE, size_t N)
-     This function computes the kurtosis of DATA, a dataset of length N
-     with stride STRIDE.  The kurtosis is defined as,
+20.33 The Multinomial Distribution
+==================================
 
-          kurtosis = ((1/N) \sum ((x_i - \Hat\mu)/\Hat\sigma)^4)  - 3
+ -- Function: void gsl_ran_multinomial (const gsl_rng * R, size_t K,
+          unsigned int N, const double P[], unsigned int N[])
 
-     The kurtosis measures how sharply peaked a distribution is,
-     relative to its width.  The kurtosis is normalized to zero for a
-     Gaussian distribution.
+     This function computes a random sample N[] from the multinomial
+     distribution formed by N trials from an underlying distribution
+     P[K].  The distribution function for N[] is,
 
- -- Function: double gsl_stats_kurtosis_m_sd (const double DATA[],
-          size_t STRIDE, size_t N, double MEAN, double SD)
-     This function computes the kurtosis of the dataset DATA using the
-     given values of the mean MEAN and standard deviation SD,
+          P(n_1, n_2, ..., n_K) =
+            (N!/(n_1! n_2! ... n_K!)) p_1^n_1 p_2^n_2 ... p_K^n_K
 
-          kurtosis = ((1/N) \sum ((x_i - mean)/sd)^4) - 3
+     where (n_1, n_2, ..., n_K) are nonnegative integers with
+     sum_{k=1}^K n_k = N, and (p_1, p_2, ..., p_K) is a probability
+     distribution with \sum p_i = 1.  If the array P[K] is not
+     normalized then its entries will be treated as weights and
+     normalized appropriately.  The arrays N[] and P[] must both be of
+     length K.
 
-     This function is useful if you have already computed the mean and
-     standard deviation of DATA and want to avoid recomputing them.
+     Random variates are generated using the conditional binomial method
+     (see C.S. Davis, 'The computer generation of multinomial random
+     variates', Comp.  Stat.  Data Anal.  16 (1993) 205-217 for
+     details).
 
-
-File: gsl-ref.info,  Node: Autocorrelation,  Next: Covariance,  Prev: Higher moments (skewness and kurtosis),  Up: Statistics
+ -- Function: double gsl_ran_multinomial_pdf (size_t K, const double
+          P[], const unsigned int N[])
+     This function computes the probability P(n_1, n_2, ..., n_K) of
+     sampling N[K] from a multinomial distribution with parameters P[K],
+     using the formula given above.
 
-21.4 Autocorrelation
-====================
+ -- Function: double gsl_ran_multinomial_lnpdf (size_t K, const double
+          P[], const unsigned int N[])
+     This function returns the logarithm of the probability for the
+     multinomial distribution P(n_1, n_2, ..., n_K) with parameters
+     P[K].
 
- -- Function: double gsl_stats_lag1_autocorrelation (const double
-          DATA[], const size_t STRIDE, const size_t N)
-     This function computes the lag-1 autocorrelation of the dataset
-     DATA.
+
+File: gsl-ref.info,  Node: The Negative Binomial Distribution,  Next: The Pascal Distribution,  Prev: The Multinomial Distribution,  Up: Random Number Distributions
 
-          a_1 = {\sum_{i = 1}^{n} (x_{i} - \Hat\mu) (x_{i-1} - \Hat\mu)
-                 \over
-                 \sum_{i = 1}^{n} (x_{i} - \Hat\mu) (x_{i} - \Hat\mu)}
+20.34 The Negative Binomial Distribution
+========================================
 
- -- Function: double gsl_stats_lag1_autocorrelation_m (const double
-          DATA[], const size_t STRIDE, const size_t N, const double
-          MEAN)
-     This function computes the lag-1 autocorrelation of the dataset
-     DATA using the given value of the mean MEAN.
+ -- Function: unsigned int gsl_ran_negative_binomial (const gsl_rng * R,
+          double P, double N)
+     This function returns a random integer from the negative binomial
+     distribution, the number of failures occurring before N successes
+     in independent trials with probability P of success.  The
+     probability distribution for negative binomial variates is,
 
-
-File: gsl-ref.info,  Node: Covariance,  Next: Correlation,  Prev: Autocorrelation,  Up: Statistics
+          p(k) = {\Gamma(n + k) \over \Gamma(k+1) \Gamma(n) } p^n (1-p)^k
 
-21.5 Covariance
-===============
+     Note that n is not required to be an integer.
 
- -- Function: double gsl_stats_covariance (const double DATA1[], const
-          size_t STRIDE1, const double DATA2[], const size_t STRIDE2,
-          const size_t N)
-     This function computes the covariance of the datasets DATA1 and
-     DATA2 which must both be of the same length N.
+ -- Function: double gsl_ran_negative_binomial_pdf (unsigned int K,
+          double P, double N)
+     This function computes the probability p(k) of obtaining K from a
+     negative binomial distribution with parameters P and N, using the
+     formula given above.
 
-          covar = (1/(n - 1)) \sum_{i = 1}^{n} (x_i - \Hat x) (y_i - \Hat y)
 
- -- Function: double gsl_stats_covariance_m (const double DATA1[], const
-          size_t STRIDE1, const double DATA2[], const size_t STRIDE2,
-          const size_t N, const double MEAN1, const double MEAN2)
-     This function computes the covariance of the datasets DATA1 and
-     DATA2 using the given values of the means, MEAN1 and MEAN2.  This
-     is useful if you have already computed the means of DATA1 and DATA2
-     and want to avoid recomputing them.
+ -- Function: double gsl_cdf_negative_binomial_P (unsigned int K, double
+          P, double N)
+ -- Function: double gsl_cdf_negative_binomial_Q (unsigned int K, double
+          P, double N)
+     These functions compute the cumulative distribution functions P(k),
+     Q(k) for the negative binomial distribution with parameters P and
+     N.
 
 
-File: gsl-ref.info,  Node: Correlation,  Next: Weighted Samples,  Prev: Covariance,  Up: Statistics
+File: gsl-ref.info,  Node: The Pascal Distribution,  Next: The Geometric Distribution,  Prev: The Negative Binomial Distribution,  Up: Random Number Distributions
 
-21.6 Correlation
-================
+20.35 The Pascal Distribution
+=============================
 
- -- Function: double gsl_stats_correlation (const double DATA1[], const
-          size_t STRIDE1, const double DATA2[], const size_t STRIDE2,
-          const size_t N)
-     This function efficiently computes the Pearson correlation
-     coefficient between the datasets DATA1 and DATA2 which must both be
-     of the same length N.
-          r = cov(x, y) / (\Hat\sigma_x \Hat\sigma_y)
-            = {1/(n-1) \sum (x_i - \Hat x) (y_i - \Hat y)
-               \over
-               \sqrt{1/(n-1) \sum (x_i - \Hat x)^2} \sqrt{1/(n-1) \sum (y_i - \Hat y)^2}
-              }
+ -- Function: unsigned int gsl_ran_pascal (const gsl_rng * R, double P,
+          unsigned int N)
+     This function returns a random integer from the Pascal
+     distribution.  The Pascal distribution is simply a negative
+     binomial distribution with an integer value of n.
 
- -- Function: double gsl_stats_spearman (const double DATA1[], const
-          size_t STRIDE1, const double DATA2[], const size_t STRIDE2,
-          const size_t N, double WORK[])
-     This function computes the Spearman rank correlation coefficient
-     between the datasets DATA1 and DATA2 which must both be of the same
-     length N.  Additional workspace of size 2*N is required in WORK.
-     The Spearman rank correlation between vectors x and y is equivalent
-     to the Pearson correlation between the ranked vectors x_R and y_R,
-     where ranks are defined to be the average of the positions of an
-     element in the ascending order of the values.
+          p(k) = {(n + k - 1)! \over k! (n - 1)! } p^n (1-p)^k
 
-
-File: gsl-ref.info,  Node: Weighted Samples,  Next: Maximum and Minimum values,  Prev: Correlation,  Up: Statistics
+     for k >= 0
 
-21.7 Weighted Samples
-=====================
+ -- Function: double gsl_ran_pascal_pdf (unsigned int K, double P,
+          unsigned int N)
+     This function computes the probability p(k) of obtaining K from a
+     Pascal distribution with parameters P and N, using the formula
+     given above.
 
-The functions described in this section allow the computation of
-statistics for weighted samples.  The functions accept an array of
-samples, x_i, with associated weights, w_i.  Each sample x_i is
-considered as having been drawn from a Gaussian distribution with
-variance \sigma_i^2.  The sample weight w_i is defined as the reciprocal
-of this variance, w_i = 1/\sigma_i^2.  Setting a weight to zero
-corresponds to removing a sample from a dataset.
 
- -- Function: double gsl_stats_wmean (const double W[], size_t WSTRIDE,
-          const double DATA[], size_t STRIDE, size_t N)
-     This function returns the weighted mean of the dataset DATA with
-     stride STRIDE and length N, using the set of weights W with stride
-     WSTRIDE and length N.  The weighted mean is defined as,
+ -- Function: double gsl_cdf_pascal_P (unsigned int K, double P,
+          unsigned int N)
+ -- Function: double gsl_cdf_pascal_Q (unsigned int K, double P,
+          unsigned int N)
+     These functions compute the cumulative distribution functions P(k),
+     Q(k) for the Pascal distribution with parameters P and N.
 
-          \Hat\mu = (\sum w_i x_i) / (\sum w_i)
+
+File: gsl-ref.info,  Node: The Geometric Distribution,  Next: The Hypergeometric Distribution,  Prev: The Pascal Distribution,  Up: Random Number Distributions
 
- -- Function: double gsl_stats_wvariance (const double W[], size_t
-          WSTRIDE, const double DATA[], size_t STRIDE, size_t N)
-     This function returns the estimated variance of the dataset DATA
-     with stride STRIDE and length N, using the set of weights W with
-     stride WSTRIDE and length N.  The estimated variance of a weighted
-     dataset is calculated as,
+20.36 The Geometric Distribution
+================================
 
-          \Hat\sigma^2 = ((\sum w_i)/((\sum w_i)^2 - \sum (w_i^2)))
-                          \sum w_i (x_i - \Hat\mu)^2
+ -- Function: unsigned int gsl_ran_geometric (const gsl_rng * R, double
+          P)
+     This function returns a random integer from the geometric
+     distribution, the number of independent trials with probability P
+     until the first success.  The probability distribution for
+     geometric variates is,
 
-     Note that this expression reduces to an unweighted variance with
-     the familiar 1/(N-1) factor when there are N equal non-zero
-     weights.
+          p(k) =  p (1-p)^(k-1)
 
- -- Function: double gsl_stats_wvariance_m (const double W[], size_t
-          WSTRIDE, const double DATA[], size_t STRIDE, size_t N, double
-          WMEAN)
-     This function returns the estimated variance of the weighted
-     dataset DATA using the given weighted mean WMEAN.
+     for k >= 1.  Note that the distribution begins with k=1 with this
+     definition.  There is another convention in which the exponent k-1
+     is replaced by k.
 
- -- Function: double gsl_stats_wsd (const double W[], size_t WSTRIDE,
-          const double DATA[], size_t STRIDE, size_t N)
-     The standard deviation is defined as the square root of the
-     variance.  This function returns the square root of the
-     corresponding variance function 'gsl_stats_wvariance' above.
+ -- Function: double gsl_ran_geometric_pdf (unsigned int K, double P)
+     This function computes the probability p(k) of obtaining K from a
+     geometric distribution with probability parameter P, using the
+     formula given above.
 
- -- Function: double gsl_stats_wsd_m (const double W[], size_t WSTRIDE,
-          const double DATA[], size_t STRIDE, size_t N, double WMEAN)
-     This function returns the square root of the corresponding variance
-     function 'gsl_stats_wvariance_m' above.
 
- -- Function: double gsl_stats_wvariance_with_fixed_mean (const double
-          W[], size_t WSTRIDE, const double DATA[], size_t STRIDE,
-          size_t N, const double MEAN)
-     This function computes an unbiased estimate of the variance of the
-     weighted dataset DATA when the population mean MEAN of the
-     underlying distribution is known _a priori_.  In this case the
-     estimator for the variance replaces the sample mean \Hat\mu by the
-     known population mean \mu,
+ -- Function: double gsl_cdf_geometric_P (unsigned int K, double P)
+ -- Function: double gsl_cdf_geometric_Q (unsigned int K, double P)
+     These functions compute the cumulative distribution functions P(k),
+     Q(k) for the geometric distribution with parameter P.
 
-          \Hat\sigma^2 = (\sum w_i (x_i - \mu)^2) / (\sum w_i)
+
+File: gsl-ref.info,  Node: The Hypergeometric Distribution,  Next: The Logarithmic Distribution,  Prev: The Geometric Distribution,  Up: Random Number Distributions
 
- -- Function: double gsl_stats_wsd_with_fixed_mean (const double W[],
-          size_t WSTRIDE, const double DATA[], size_t STRIDE, size_t N,
-          const double MEAN)
-     The standard deviation is defined as the square root of the
-     variance.  This function returns the square root of the
-     corresponding variance function above.
+20.37 The Hypergeometric Distribution
+=====================================
 
- -- Function: double gsl_stats_wtss (const double W[], const size_t
-          WSTRIDE, const double DATA[], size_t STRIDE, size_t N)
- -- Function: double gsl_stats_wtss_m (const double W[], const size_t
-          WSTRIDE, const double DATA[], size_t STRIDE, size_t N, double
-          WMEAN)
-     These functions return the weighted total sum of squares (TSS) of
-     DATA about the weighted mean.  For 'gsl_stats_wtss_m' the
-     user-supplied value of WMEAN is used, and for 'gsl_stats_wtss' it
-     is computed using 'gsl_stats_wmean'.
+ -- Function: unsigned int gsl_ran_hypergeometric (const gsl_rng * R,
+          unsigned int N1, unsigned int N2, unsigned int T)
+     This function returns a random integer from the hypergeometric
+     distribution.  The probability distribution for hypergeometric
+     random variates is,
 
-          TSS =  \sum w_i (x_i - wmean)^2
+          p(k) =  C(n_1, k) C(n_2, t - k) / C(n_1 + n_2, t)
 
- -- Function: double gsl_stats_wabsdev (const double W[], size_t
-          WSTRIDE, const double DATA[], size_t STRIDE, size_t N)
-     This function computes the weighted absolute deviation from the
-     weighted mean of DATA.  The absolute deviation from the mean is
-     defined as,
+     where C(a,b) = a!/(b!(a-b)!) and t <= n_1 + n_2.  The domain of k
+     is max(0,t-n_2), ..., min(t,n_1).
 
-          absdev = (\sum w_i |x_i - \Hat\mu|) / (\sum w_i)
+     If a population contains n_1 elements of "type 1" and n_2 elements
+     of "type 2" then the hypergeometric distribution gives the
+     probability of obtaining k elements of "type 1" in t samples from
+     the population without replacement.
 
- -- Function: double gsl_stats_wabsdev_m (const double W[], size_t
-          WSTRIDE, const double DATA[], size_t STRIDE, size_t N, double
-          WMEAN)
-     This function computes the absolute deviation of the weighted
-     dataset DATA about the given weighted mean WMEAN.
+ -- Function: double gsl_ran_hypergeometric_pdf (unsigned int K,
+          unsigned int N1, unsigned int N2, unsigned int T)
+     This function computes the probability p(k) of obtaining K from a
+     hypergeometric distribution with parameters N1, N2, T, using the
+     formula given above.
 
- -- Function: double gsl_stats_wskew (const double W[], size_t WSTRIDE,
-          const double DATA[], size_t STRIDE, size_t N)
-     This function computes the weighted skewness of the dataset DATA.
 
-          skew = (\sum w_i ((x_i - \Hat x)/\Hat \sigma)^3) / (\sum w_i)
+ -- Function: double gsl_cdf_hypergeometric_P (unsigned int K, unsigned
+          int N1, unsigned int N2, unsigned int T)
+ -- Function: double gsl_cdf_hypergeometric_Q (unsigned int K, unsigned
+          int N1, unsigned int N2, unsigned int T)
+     These functions compute the cumulative distribution functions P(k),
+     Q(k) for the hypergeometric distribution with parameters N1, N2 and
+     T.
 
- -- Function: double gsl_stats_wskew_m_sd (const double W[], size_t
-          WSTRIDE, const double DATA[], size_t STRIDE, size_t N, double
-          WMEAN, double WSD)
-     This function computes the weighted skewness of the dataset DATA
-     using the given values of the weighted mean and weighted standard
-     deviation, WMEAN and WSD.
+
+File: gsl-ref.info,  Node: The Logarithmic Distribution,  Next: Shuffling and Sampling,  Prev: The Hypergeometric Distribution,  Up: Random Number Distributions
 
- -- Function: double gsl_stats_wkurtosis (const double W[], size_t
-          WSTRIDE, const double DATA[], size_t STRIDE, size_t N)
-     This function computes the weighted kurtosis of the dataset DATA.
+20.38 The Logarithmic Distribution
+==================================
 
-          kurtosis = ((\sum w_i ((x_i - \Hat x)/\Hat \sigma)^4) / (\sum w_i)) - 3
+ -- Function: unsigned int gsl_ran_logarithmic (const gsl_rng * R,
+          double P)
+     This function returns a random integer from the logarithmic
+     distribution.  The probability distribution for logarithmic random
+     variates is,
 
- -- Function: double gsl_stats_wkurtosis_m_sd (const double W[], size_t
-          WSTRIDE, const double DATA[], size_t STRIDE, size_t N, double
-          WMEAN, double WSD)
-     This function computes the weighted kurtosis of the dataset DATA
-     using the given values of the weighted mean and weighted standard
-     deviation, WMEAN and WSD.
+          p(k) = {-1 \over \log(1-p)} {(p^k \over k)}
 
-
-File: gsl-ref.info,  Node: Maximum and Minimum values,  Next: Median and Percentiles,  Prev: Weighted Samples,  Up: Statistics
+     for k >= 1.
 
-21.8 Maximum and Minimum values
-===============================
+ -- Function: double gsl_ran_logarithmic_pdf (unsigned int K, double P)
+     This function computes the probability p(k) of obtaining K from a
+     logarithmic distribution with probability parameter P, using the
+     formula given above.
 
-The following functions find the maximum and minimum values of a dataset
-(or their indices).  If the data contains 'NaN's then a 'NaN' will be
-returned, since the maximum or minimum value is undefined.  For
-functions which return an index, the location of the first 'NaN' in the
-array is returned.
 
- -- Function: double gsl_stats_max (const double DATA[], size_t STRIDE,
-          size_t N)
-     This function returns the maximum value in DATA, a dataset of
-     length N with stride STRIDE.  The maximum value is defined as the
-     value of the element x_i which satisfies x_i >= x_j for all j.
+
+File: gsl-ref.info,  Node: Shuffling and Sampling,  Next: Random Number Distribution Examples,  Prev: The Logarithmic Distribution,  Up: Random Number Distributions
 
-     If you want instead to find the element with the largest absolute
-     magnitude you will need to apply 'fabs' or 'abs' to your data
-     before calling this function.
+20.39 Shuffling and Sampling
+============================
 
- -- Function: double gsl_stats_min (const double DATA[], size_t STRIDE,
-          size_t N)
-     This function returns the minimum value in DATA, a dataset of
-     length N with stride STRIDE.  The minimum value is defined as the
-     value of the element x_i which satisfies x_i <= x_j for all j.
+The following functions allow the shuffling and sampling of a set of
+objects.  The algorithms rely on a random number generator as a source
+of randomness and a poor quality generator can lead to correlations in
+the output.  In particular it is important to avoid generators with a
+short period.  For more information see Knuth, v2, 3rd ed, Section
+3.4.2, "Random Sampling and Shuffling".
 
-     If you want instead to find the element with the smallest absolute
-     magnitude you will need to apply 'fabs' or 'abs' to your data
-     before calling this function.
+ -- Function: void gsl_ran_shuffle (const gsl_rng * R, void * BASE,
+          size_t N, size_t SIZE)
 
- -- Function: void gsl_stats_minmax (double * MIN, double * MAX, const
-          double DATA[], size_t STRIDE, size_t N)
-     This function finds both the minimum and maximum values MIN, MAX in
-     DATA in a single pass.
+     This function randomly shuffles the order of N objects, each of
+     size SIZE, stored in the array BASE[0..N-1].  The output of the
+     random number generator R is used to produce the permutation.  The
+     algorithm generates all possible n! permutations with equal
+     probability, assuming a perfect source of random numbers.
 
- -- Function: size_t gsl_stats_max_index (const double DATA[], size_t
-          STRIDE, size_t N)
-     This function returns the index of the maximum value in DATA, a
-     dataset of length N with stride STRIDE.  The maximum value is
-     defined as the value of the element x_i which satisfies x_i >= x_j
-     for all j.  When there are several equal maximum elements then the
-     first one is chosen.
+     The following code shows how to shuffle the numbers from 0 to 51,
 
- -- Function: size_t gsl_stats_min_index (const double DATA[], size_t
-          STRIDE, size_t N)
-     This function returns the index of the minimum value in DATA, a
-     dataset of length N with stride STRIDE.  The minimum value is
-     defined as the value of the element x_i which satisfies x_i >= x_j
-     for all j.  When there are several equal minimum elements then the
-     first one is chosen.
+          int a[52];
 
- -- Function: void gsl_stats_minmax_index (size_t * MIN_INDEX, size_t *
-          MAX_INDEX, const double DATA[], size_t STRIDE, size_t N)
-     This function returns the indexes MIN_INDEX, MAX_INDEX of the
-     minimum and maximum values in DATA in a single pass.
+          for (i = 0; i < 52; i++)
+            {
+              a[i] = i;
+            }
 
-
-File: gsl-ref.info,  Node: Median and Percentiles,  Next: Example statistical programs,  Prev: Maximum and Minimum values,  Up: Statistics
+          gsl_ran_shuffle (r, a, 52, sizeof (int));
 
-21.9 Median and Percentiles
-===========================
+ -- Function: int gsl_ran_choose (const gsl_rng * R, void * DEST, size_t
+          K, void * SRC, size_t N, size_t SIZE)
+     This function fills the array DEST[k] with K objects taken randomly
+     from the N elements of the array SRC[0..N-1].  The objects are each
+     of size SIZE.  The output of the random number generator R is used
+     to make the selection.  The algorithm ensures all possible samples
+     are equally likely, assuming a perfect source of randomness.
 
-The median and percentile functions described in this section operate on
-sorted data.  For convenience we use "quantiles", measured on a scale of
-0 to 1, instead of percentiles (which use a scale of 0 to 100).
+     The objects are sampled _without_ replacement, thus each object can
+     only appear once in DEST[k].  It is required that K be less than or
+     equal to 'n'.  The objects in DEST will be in the same relative
+     order as those in SRC.  You will need to call 'gsl_ran_shuffle(r,
+     dest, n, size)' if you want to randomize the order.
 
- -- Function: double gsl_stats_median_from_sorted_data (const double
-          SORTED_DATA[], size_t STRIDE, size_t N)
-     This function returns the median value of SORTED_DATA, a dataset of
-     length N with stride STRIDE.  The elements of the array must be in
-     ascending numerical order.  There are no checks to see whether the
-     data are sorted, so the function 'gsl_sort' should always be used
-     first.
-
-     When the dataset has an odd number of elements the median is the
-     value of element (n-1)/2.  When the dataset has an even number of
-     elements the median is the mean of the two nearest middle values,
-     elements (n-1)/2 and n/2.  Since the algorithm for computing the
-     median involves interpolation this function always returns a
-     floating-point number, even for integer data types.
-
- -- Function: double gsl_stats_quantile_from_sorted_data (const double
-          SORTED_DATA[], size_t STRIDE, size_t N, double F)
-     This function returns a quantile value of SORTED_DATA, a
-     double-precision array of length N with stride STRIDE.  The
-     elements of the array must be in ascending numerical order.  The
-     quantile is determined by the F, a fraction between 0 and 1.  For
-     example, to compute the value of the 75th percentile F should have
-     the value 0.75.
-
-     There are no checks to see whether the data are sorted, so the
-     function 'gsl_sort' should always be used first.
+     The following code shows how to select a random sample of three
+     unique numbers from the set 0 to 99,
 
-     The quantile is found by interpolation, using the formula
+          double a[3], b[100];
 
-          quantile = (1 - \delta) x_i + \delta x_{i+1}
+          for (i = 0; i < 100; i++)
+            {
+              b[i] = (double) i;
+            }
 
-     where i is 'floor'((n - 1)f) and \delta is (n-1)f - i.
+          gsl_ran_choose (r, a, 3, b, 100, sizeof (double));
 
-     Thus the minimum value of the array ('data[0*stride]') is given by
-     F equal to zero, the maximum value ('data[(n-1)*stride]') is given
-     by F equal to one and the median value is given by F equal to 0.5.
-     Since the algorithm for computing quantiles involves interpolation
-     this function always returns a floating-point number, even for
-     integer data types.
+ -- Function: void gsl_ran_sample (const gsl_rng * R, void * DEST,
+          size_t K, void * SRC, size_t N, size_t SIZE)
+     This function is like 'gsl_ran_choose' but samples K items from the
+     original array of N items SRC with replacement, so the same object
+     can appear more than once in the output sequence DEST.  There is no
+     requirement that K be less than N in this case.
 
 
-File: gsl-ref.info,  Node: Example statistical programs,  Next: Statistics References and Further Reading,  Prev: Median and Percentiles,  Up: Statistics
+File: gsl-ref.info,  Node: Random Number Distribution Examples,  Next: Random Number Distribution References and Further Reading,  Prev: Shuffling and Sampling,  Up: Random Number Distributions
 
-21.10 Examples
+20.40 Examples
 ==============
 
-Here is a basic example of how to use the statistical functions:
+The following program demonstrates the use of a random number generator
+to produce variates from a distribution.  It prints 10 samples from the
+Poisson distribution with a mean of 3.
 
      #include <stdio.h>
-     #include <gsl/gsl_statistics.h>
+     #include <gsl/gsl_rng.h>
+     #include <gsl/gsl_randist.h>
 
      int
-     main(void)
+     main (void)
      {
-       double data[5] = {17.2, 18.1, 16.5, 18.3, 12.6};
-       double mean, variance, largest, smallest;
+       const gsl_rng_type * T;
+       gsl_rng * r;
 
-       mean     = gsl_stats_mean(data, 1, 5);
-       variance = gsl_stats_variance(data, 1, 5);
-       largest  = gsl_stats_max(data, 1, 5);
-       smallest = gsl_stats_min(data, 1, 5);
+       int i, n = 10;
+       double mu = 3.0;
 
-       printf ("The dataset is %g, %g, %g, %g, %g\n",
-              data[0], data[1], data[2], data[3], data[4]);
+       /* create a generator chosen by the
+          environment variable GSL_RNG_TYPE */
 
-       printf ("The sample mean is %g\n", mean);
-       printf ("The estimated variance is %g\n", variance);
-       printf ("The largest value is %g\n", largest);
-       printf ("The smallest value is %g\n", smallest);
+       gsl_rng_env_setup();
+
+       T = gsl_rng_default;
+       r = gsl_rng_alloc (T);
+
+       /* print n random variates chosen from
+          the poisson distribution with mean
+          parameter mu */
+
+       for (i = 0; i < n; i++)
+         {
+           unsigned int k = gsl_ran_poisson (r, mu);
+           printf (" %u", k);
+         }
+
+       printf ("\n");
+       gsl_rng_free (r);
        return 0;
      }
 
-   The program should produce the following output,
+If the library and header files are installed under '/usr/local' (the
+default location) then the program can be compiled with these options,
 
-     The dataset is 17.2, 18.1, 16.5, 18.3, 12.6
-     The sample mean is 16.54
-     The estimated variance is 5.373
-     The largest value is 18.3
-     The smallest value is 12.6
+     $ gcc -Wall demo.c -lgsl -lgslcblas -lm
 
-   Here is an example using sorted data,
+Here is the output of the program,
+
+     $ ./a.out
+      2 5 5 2 1 0 3 4 1 1
+
+The variates depend on the seed used by the generator.  The seed for the
+default generator type 'gsl_rng_default' can be changed with the
+'GSL_RNG_SEED' environment variable to produce a different stream of
+variates,
+
+     $ GSL_RNG_SEED=123 ./a.out
+      4 5 6 3 3 1 4 2 5 5
+
+The following program generates a random walk in two dimensions.
 
      #include <stdio.h>
-     #include <gsl/gsl_sort.h>
-     #include <gsl/gsl_statistics.h>
+     #include <gsl/gsl_rng.h>
+     #include <gsl/gsl_randist.h>
 
      int
-     main(void)
+     main (void)
      {
-       double data[5] = {17.2, 18.1, 16.5, 18.3, 12.6};
-       double median, upperq, lowerq;
-
-       printf ("Original dataset:  %g, %g, %g, %g, %g\n",
-              data[0], data[1], data[2], data[3], data[4]);
+       int i;
+       double x = 0, y = 0, dx, dy;
 
-       gsl_sort (data, 1, 5);
+       const gsl_rng_type * T;
+       gsl_rng * r;
 
-       printf ("Sorted dataset: %g, %g, %g, %g, %g\n",
-              data[0], data[1], data[2], data[3], data[4]);
+       gsl_rng_env_setup();
+       T = gsl_rng_default;
+       r = gsl_rng_alloc (T);
 
-       median
-         = gsl_stats_median_from_sorted_data (data,
-                                              1, 5);
+       printf ("%g %g\n", x, y);
 
-       upperq
-         = gsl_stats_quantile_from_sorted_data (data,
-                                                1, 5,
-                                                0.75);
-       lowerq
-         = gsl_stats_quantile_from_sorted_data (data,
-                                                1, 5,
-                                                0.25);
+       for (i = 0; i < 10; i++)
+         {
+           gsl_ran_dir_2d (r, &dx, &dy);
+           x += dx; y += dy;
+           printf ("%g %g\n", x, y);
+         }
 
-       printf ("The median is %g\n", median);
-       printf ("The upper quartile is %g\n", upperq);
-       printf ("The lower quartile is %g\n", lowerq);
+       gsl_rng_free (r);
        return 0;
      }
 
-   This program should produce the following output,
+Here is some output from the program, four 10-step random walks from the
+origin,
 
-     Original dataset: 17.2, 18.1, 16.5, 18.3, 12.6
-     Sorted dataset: 12.6, 16.5, 17.2, 18.1, 18.3
-     The median is 17.2
-     The upper quartile is 18.1
-     The lower quartile is 16.5
+   The following program computes the upper and lower cumulative
+distribution functions for the standard normal distribution at x=2.
 
-
-File: gsl-ref.info,  Node: Statistics References and Further Reading,  Prev: Example statistical programs,  Up: Statistics
+     #include <stdio.h>
+     #include <gsl/gsl_cdf.h>
 
-21.11 References and Further Reading
-====================================
+     int
+     main (void)
+     {
+       double P, Q;
+       double x = 2.0;
 
-The standard reference for almost any topic in statistics is the
-multi-volume 'Advanced Theory of Statistics' by Kendall and Stuart.
+       P = gsl_cdf_ugaussian_P (x);
+       printf ("prob(x < %f) = %f\n", x, P);
 
-     Maurice Kendall, Alan Stuart, and J. Keith Ord.  'The Advanced
-     Theory of Statistics' (multiple volumes) reprinted as 'Kendall's
-     Advanced Theory of Statistics'.  Wiley, ISBN 047023380X.
+       Q = gsl_cdf_ugaussian_Q (x);
+       printf ("prob(x > %f) = %f\n", x, Q);
 
-Many statistical concepts can be more easily understood by a Bayesian
-approach.  The following book by Gelman, Carlin, Stern and Rubin gives a
-comprehensive coverage of the subject.
+       x = gsl_cdf_ugaussian_Pinv (P);
+       printf ("Pinv(%f) = %f\n", P, x);
 
-     Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin.
-     'Bayesian Data Analysis'.  Chapman & Hall, ISBN 0412039915.
+       x = gsl_cdf_ugaussian_Qinv (Q);
+       printf ("Qinv(%f) = %f\n", Q, x);
 
-For physicists the Particle Data Group provides useful reviews of
-Probability and Statistics in the "Mathematical Tools" section of its
-Annual Review of Particle Physics.
+       return 0;
+     }
 
-     'Review of Particle Properties' R.M. Barnett et al., Physical
-     Review D54, 1 (1996)
+Here is the output of the program,
 
-The Review of Particle Physics is available online at the website
-<http://pdg.lbl.gov/>.
+     prob(x < 2.000000) = 0.977250
+     prob(x > 2.000000) = 0.022750
+     Pinv(0.977250) = 2.000000
+     Qinv(0.022750) = 2.000000
 
 
-File: gsl-ref.info,  Node: Histograms,  Next: N-tuples,  Prev: Statistics,  Up: Top
+File: gsl-ref.info,  Node: Random Number Distribution References and Further Reading,  Prev: Random Number Distribution Examples,  Up: Random Number Distributions
 
-22 Histograms
-*************
+20.41 References and Further Reading
+====================================
 
-This chapter describes functions for creating histograms.  Histograms
-provide a convenient way of summarizing the distribution of a set of
-data.  A histogram consists of a set of "bins" which count the number of
-events falling into a given range of a continuous variable x.  In GSL
-the bins of a histogram contain floating-point numbers, so they can be
-used to record both integer and non-integer distributions.  The bins can
-use arbitrary sets of ranges (uniformly spaced bins are the default).
-Both one and two-dimensional histograms are supported.
+For an encyclopaedic coverage of the subject readers are advised to
+consult the book 'Non-Uniform Random Variate Generation' by Luc Devroye.
+It covers every imaginable distribution and provides hundreds of
+algorithms.
 
-   Once a histogram has been created it can also be converted into a
-probability distribution function.  The library provides efficient
-routines for selecting random samples from probability distributions.
-This can be useful for generating simulations based on real data.
+     Luc Devroye, 'Non-Uniform Random Variate Generation',
+     Springer-Verlag, ISBN 0-387-96305-7.  Available online at
+     <http://cg.scs.carleton.ca/~luc/rnbookindex.html>.
 
-   The functions are declared in the header files 'gsl_histogram.h' and
-'gsl_histogram2d.h'.
+The subject of random variate generation is also reviewed by Knuth, who
+describes algorithms for all the major distributions.
 
-* Menu:
+     Donald E. Knuth, 'The Art of Computer Programming: Seminumerical
+     Algorithms' (Vol 2, 3rd Ed, 1997), Addison-Wesley, ISBN 0201896842.
 
-* The histogram struct::        
-* Histogram allocation::        
-* Copying Histograms::          
-* Updating and accessing histogram elements::  
-* Searching histogram ranges::  
-* Histogram Statistics::        
-* Histogram Operations::        
-* Reading and writing histograms::  
-* Resampling from histograms::  
-* The histogram probability distribution struct::  
-* Example programs for histograms::  
-* Two dimensional histograms::  
-* The 2D histogram struct::     
-* 2D Histogram allocation::     
-* Copying 2D Histograms::       
-* Updating and accessing 2D histogram elements::  
-* Searching 2D histogram ranges::  
-* 2D Histogram Statistics::     
-* 2D Histogram Operations::     
-* Reading and writing 2D histograms::  
-* Resampling from 2D histograms::  
-* Example programs for 2D histograms::  
+The Particle Data Group provides a short review of techniques for
+generating distributions of random numbers in the "Monte Carlo" section
+of its Annual Review of Particle Physics.
 
-
-File: gsl-ref.info,  Node: The histogram struct,  Next: Histogram allocation,  Up: Histograms
+     'Review of Particle Properties' R.M. Barnett et al., Physical
+     Review D54, 1 (1996) <http://pdg.lbl.gov/>.
 
-22.1 The histogram struct
-=========================
+The Review of Particle Physics is available online in postscript and pdf
+format.
 
-A histogram is defined by the following struct,
+An overview of methods used to compute cumulative distribution functions
+can be found in 'Statistical Computing' by W.J. Kennedy and J.E. Gentle.
+Another general reference is 'Elements of Statistical Computing' by R.A.
+Thisted.
 
- -- Data Type: gsl_histogram
-     'size_t n'
-          This is the number of histogram bins
-     'double * range'
-          The ranges of the bins are stored in an array of N+1 elements
-          pointed to by RANGE.
-     'double * bin'
-          The counts for each bin are stored in an array of N elements
-          pointed to by BIN.  The bins are floating-point numbers, so
-          you can increment them by non-integer values if necessary.
+     William E. Kennedy and James E. Gentle, 'Statistical Computing'
+     (1980), Marcel Dekker, ISBN 0-8247-6898-1.
 
-The range for BIN[i] is given by RANGE[i] to RANGE[i+1].  For n bins
-there are n+1 entries in the array RANGE.  Each bin is inclusive at the
-lower end and exclusive at the upper end.  Mathematically this means
-that the bins are defined by the following inequality,
-     bin[i] corresponds to range[i] <= x < range[i+1]
+     Ronald A. Thisted, 'Elements of Statistical Computing' (1988),
+     Chapman & Hall, ISBN 0-412-01371-1.
 
-Here is a diagram of the correspondence between ranges and bins on the
-number-line for x,
+The cumulative distribution functions for the Gaussian distribution are
+based on the following papers,
 
+     'Rational Chebyshev Approximations Using Linear Equations', W.J.
+     Cody, W. Fraser, J.F. Hart.  Numerische Mathematik 12, 242-251
+     (1968).
 
-          [ bin[0] )[ bin[1] )[ bin[2] )[ bin[3] )[ bin[4] )
-       ---|---------|---------|---------|---------|---------|---  x
-        r[0]      r[1]      r[2]      r[3]      r[4]      r[5]
+     'Rational Chebyshev Approximations for the Error Function', W.J.
+     Cody.  Mathematics of Computation 23, n107, 631-637 (July 1969).
 
-In this picture the values of the RANGE array are denoted by r.  On the
-left-hand side of each bin the square bracket '[' denotes an inclusive
-lower bound (r <= x), and the round parentheses ')' on the right-hand
-side denote an exclusive upper bound (x < r).  Thus any samples which
-fall on the upper end of the histogram are excluded.  If you want to
-include this value for the last bin you will need to add an extra bin to
-your histogram.
+
+File: gsl-ref.info,  Node: Statistics,  Next: Running Statistics,  Prev: Random Number Distributions,  Up: Top
 
-   The 'gsl_histogram' struct and its associated functions are defined
-in the header file 'gsl_histogram.h'.
+21 Statistics
+*************
+
+This chapter describes the statistical functions in the library.  The
+basic statistical functions include routines to compute the mean,
+variance and standard deviation.  More advanced functions allow you to
+calculate absolute deviations, skewness, and kurtosis as well as the
+median and arbitrary percentiles.  The algorithms use recurrence
+relations to compute average quantities in a stable way, without large
+intermediate values that might overflow.
+
+   The functions are available in versions for datasets in the standard
+floating-point and integer types.  The versions for double precision
+floating-point data have the prefix 'gsl_stats' and are declared in the
+header file 'gsl_statistics_double.h'.  The versions for integer data
+have the prefix 'gsl_stats_int' and are declared in the header file
+'gsl_statistics_int.h'.  All the functions operate on C arrays with a
+STRIDE parameter specifying the spacing between elements.
+
+* Menu:
+
+* Mean and standard deviation and variance::  
+* Absolute deviation::          
+* Higher moments (skewness and kurtosis)::  
+* Autocorrelation::             
+* Covariance::                  
+* Correlation::                  
+* Weighted Samples::            
+* Maximum and Minimum values::  
+* Median and Percentiles::      
+* Example statistical programs::  
+* Statistics References and Further Reading::  
 
 
-File: gsl-ref.info,  Node: Histogram allocation,  Next: Copying Histograms,  Prev: The histogram struct,  Up: Histograms
+File: gsl-ref.info,  Node: Mean and standard deviation and variance,  Next: Absolute deviation,  Up: Statistics
 
-22.2 Histogram allocation
-=========================
+21.1 Mean, Standard Deviation and Variance
+==========================================
 
-The functions for allocating memory to a histogram follow the style of
-'malloc' and 'free'.  In addition they also perform their own error
-checking.  If there is insufficient memory available to allocate a
-histogram then the functions call the error handler (with an error
-number of 'GSL_ENOMEM') in addition to returning a null pointer.  Thus
-if you use the library error handler to abort your program then it isn't
-necessary to check every histogram 'alloc'.
+ -- Function: double gsl_stats_mean (const double DATA[], size_t STRIDE,
+          size_t N)
+     This function returns the arithmetic mean of DATA, a dataset of
+     length N with stride STRIDE.  The arithmetic mean, or "sample
+     mean", is denoted by \Hat\mu and defined as,
 
- -- Function: gsl_histogram * gsl_histogram_alloc (size_t N)
-     This function allocates memory for a histogram with N bins, and
-     returns a pointer to a newly created 'gsl_histogram' struct.  If
-     insufficient memory is available a null pointer is returned and the
-     error handler is invoked with an error code of 'GSL_ENOMEM'.  The
-     bins and ranges are not initialized, and should be prepared using
-     one of the range-setting functions below in order to make the
-     histogram ready for use.
+          \Hat\mu = (1/N) \sum x_i
 
- -- Function: int gsl_histogram_set_ranges (gsl_histogram * H, const
-          double RANGE[], size_t SIZE)
-     This function sets the ranges of the existing histogram H using the
-     array RANGE of size SIZE.  The values of the histogram bins are
-     reset to zero.  The 'range' array should contain the desired bin
-     limits.  The ranges can be arbitrary, subject to the restriction
-     that they are monotonically increasing.
+     where x_i are the elements of the dataset DATA.  For samples drawn
+     from a gaussian distribution the variance of \Hat\mu is \sigma^2 /
+     N.
 
-     The following example shows how to create a histogram with
-     logarithmic bins with ranges [1,10), [10,100) and [100,1000).
+ -- Function: double gsl_stats_variance (const double DATA[], size_t
+          STRIDE, size_t N)
+     This function returns the estimated, or "sample", variance of DATA,
+     a dataset of length N with stride STRIDE.  The estimated variance
+     is denoted by \Hat\sigma^2 and is defined by,
 
-          gsl_histogram * h = gsl_histogram_alloc (3);
+          \Hat\sigma^2 = (1/(N-1)) \sum (x_i - \Hat\mu)^2
 
-          /* bin[0] covers the range 1 <= x < 10 */
-          /* bin[1] covers the range 10 <= x < 100 */
-          /* bin[2] covers the range 100 <= x < 1000 */
+     where x_i are the elements of the dataset DATA.  Note that the
+     normalization factor of 1/(N-1) results from the derivation of
+     \Hat\sigma^2 as an unbiased estimator of the population variance
+     \sigma^2.  For samples drawn from a Gaussian distribution the
+     variance of \Hat\sigma^2 itself is 2 \sigma^4 / N.
 
-          double range[4] = { 1.0, 10.0, 100.0, 1000.0 };
+     This function computes the mean via a call to 'gsl_stats_mean'.  If
+     you have already computed the mean then you can pass it directly to
+     'gsl_stats_variance_m'.
 
-          gsl_histogram_set_ranges (h, range, 4);
+ -- Function: double gsl_stats_variance_m (const double DATA[], size_t
+          STRIDE, size_t N, double MEAN)
+     This function returns the sample variance of DATA relative to the
+     given value of MEAN.  The function is computed with \Hat\mu
+     replaced by the value of MEAN that you supply,
 
-     Note that the size of the RANGE array should be defined to be one
-     element bigger than the number of bins.  The additional element is
-     required for the upper value of the final bin.
+          \Hat\sigma^2 = (1/(N-1)) \sum (x_i - mean)^2
 
- -- Function: int gsl_histogram_set_ranges_uniform (gsl_histogram * H,
-          double XMIN, double XMAX)
-     This function sets the ranges of the existing histogram H to cover
-     the range XMIN to XMAX uniformly.  The values of the histogram bins
-     are reset to zero.  The bin ranges are shown in the table below,
-          bin[0] corresponds to xmin <= x < xmin + d
-          bin[1] corresponds to xmin + d <= x < xmin + 2 d
-          ......
-          bin[n-1] corresponds to xmin + (n-1)d <= x < xmax
+ -- Function: double gsl_stats_sd (const double DATA[], size_t STRIDE,
+          size_t N)
+ -- Function: double gsl_stats_sd_m (const double DATA[], size_t STRIDE,
+          size_t N, double MEAN)
+     The standard deviation is defined as the square root of the
+     variance.  These functions return the square root of the
+     corresponding variance functions above.
 
-     where d is the bin spacing, d = (xmax-xmin)/n.
+ -- Function: double gsl_stats_tss (const double DATA[], size_t STRIDE,
+          size_t N)
+ -- Function: double gsl_stats_tss_m (const double DATA[], size_t
+          STRIDE, size_t N, double MEAN)
+     These functions return the total sum of squares (TSS) of DATA about
+     the mean.  For 'gsl_stats_tss_m' the user-supplied value of MEAN is
+     used, and for 'gsl_stats_tss' it is computed using
+     'gsl_stats_mean'.
 
- -- Function: void gsl_histogram_free (gsl_histogram * H)
-     This function frees the histogram H and all of the memory
-     associated with it.
+          TSS =  \sum (x_i - mean)^2
+
+ -- Function: double gsl_stats_variance_with_fixed_mean (const double
+          DATA[], size_t STRIDE, size_t N, double MEAN)
+     This function computes an unbiased estimate of the variance of DATA
+     when the population mean MEAN of the underlying distribution is
+     known _a priori_.  In this case the estimator for the variance uses
+     the factor 1/N and the sample mean \Hat\mu is replaced by the known
+     population mean \mu,
+
+          \Hat\sigma^2 = (1/N) \sum (x_i - \mu)^2
+
+ -- Function: double gsl_stats_sd_with_fixed_mean (const double DATA[],
+          size_t STRIDE, size_t N, double MEAN)
+     This function calculates the standard deviation of DATA for a fixed
+     population mean MEAN.  The result is the square root of the
+     corresponding variance function.
 
 
-File: gsl-ref.info,  Node: Copying Histograms,  Next: Updating and accessing histogram elements,  Prev: Histogram allocation,  Up: Histograms
+File: gsl-ref.info,  Node: Absolute deviation,  Next: Higher moments (skewness and kurtosis),  Prev: Mean and standard deviation and variance,  Up: Statistics
 
-22.3 Copying Histograms
+21.2 Absolute deviation
 =======================
 
- -- Function: int gsl_histogram_memcpy (gsl_histogram * DEST, const
-          gsl_histogram * SRC)
-     This function copies the histogram SRC into the pre-existing
-     histogram DEST, making DEST into an exact copy of SRC.  The two
-     histograms must be of the same size.
+ -- Function: double gsl_stats_absdev (const double DATA[], size_t
+          STRIDE, size_t N)
+     This function computes the absolute deviation from the mean of
+     DATA, a dataset of length N with stride STRIDE.  The absolute
+     deviation from the mean is defined as,
 
- -- Function: gsl_histogram * gsl_histogram_clone (const gsl_histogram *
-          SRC)
-     This function returns a pointer to a newly created histogram which
-     is an exact copy of the histogram SRC.
+          absdev  = (1/N) \sum |x_i - \Hat\mu|
 
-
-File: gsl-ref.info,  Node: Updating and accessing histogram elements,  Next: Searching histogram ranges,  Prev: Copying Histograms,  Up: Histograms
+     where x_i are the elements of the dataset DATA.  The absolute
+     deviation from the mean provides a more robust measure of the width
+     of a distribution than the variance.  This function computes the
+     mean of DATA via a call to 'gsl_stats_mean'.
 
-22.4 Updating and accessing histogram elements
-==============================================
+ -- Function: double gsl_stats_absdev_m (const double DATA[], size_t
+          STRIDE, size_t N, double MEAN)
+     This function computes the absolute deviation of the dataset DATA
+     relative to the given value of MEAN,
 
-There are two ways to access histogram bins, either by specifying an x
-coordinate or by using the bin-index directly.  The functions for
-accessing the histogram through x coordinates use a binary search to
-identify the bin which covers the appropriate range.
+          absdev  = (1/N) \sum |x_i - mean|
 
- -- Function: int gsl_histogram_increment (gsl_histogram * H, double X)
-     This function updates the histogram H by adding one (1.0) to the
-     bin whose range contains the coordinate X.
+     This function is useful if you have already computed the mean of
+     DATA (and want to avoid recomputing it), or wish to calculate the
+     absolute deviation relative to another value (such as zero, or the
+     median).
 
-     If X lies in the valid range of the histogram then the function
-     returns zero to indicate success.  If X is less than the lower
-     limit of the histogram then the function returns 'GSL_EDOM', and
-     none of bins are modified.  Similarly, if the value of X is greater
-     than or equal to the upper limit of the histogram then the function
-     returns 'GSL_EDOM', and none of the bins are modified.  The error
-     handler is not called, however, since it is often necessary to
-     compute histograms for a small range of a larger dataset, ignoring
-     the values outside the range of interest.
+
+File: gsl-ref.info,  Node: Higher moments (skewness and kurtosis),  Next: Autocorrelation,  Prev: Absolute deviation,  Up: Statistics
 
- -- Function: int gsl_histogram_accumulate (gsl_histogram * H, double X,
-          double WEIGHT)
-     This function is similar to 'gsl_histogram_increment' but increases
-     the value of the appropriate bin in the histogram H by the
-     floating-point number WEIGHT.
+21.3 Higher moments (skewness and kurtosis)
+===========================================
 
- -- Function: double gsl_histogram_get (const gsl_histogram * H, size_t
-          I)
-     This function returns the contents of the I-th bin of the histogram
-     H.  If I lies outside the valid range of indices for the histogram
-     then the error handler is called with an error code of 'GSL_EDOM'
-     and the function returns 0.
+ -- Function: double gsl_stats_skew (const double DATA[], size_t STRIDE,
+          size_t N)
+     This function computes the skewness of DATA, a dataset of length N
+     with stride STRIDE.  The skewness is defined as,
 
- -- Function: int gsl_histogram_get_range (const gsl_histogram * H,
-          size_t I, double * LOWER, double * UPPER)
-     This function finds the upper and lower range limits of the I-th
-     bin of the histogram H.  If the index I is valid then the
-     corresponding range limits are stored in LOWER and UPPER.  The
-     lower limit is inclusive (i.e.  events with this coordinate are
-     included in the bin) and the upper limit is exclusive (i.e.  events
-     with the coordinate of the upper limit are excluded and fall in the
-     neighboring higher bin, if it exists).  The function returns 0 to
-     indicate success.  If I lies outside the valid range of indices for
-     the histogram then the error handler is called and the function
-     returns an error code of 'GSL_EDOM'.
+          skew = (1/N) \sum ((x_i - \Hat\mu)/\Hat\sigma)^3
 
- -- Function: double gsl_histogram_max (const gsl_histogram * H)
- -- Function: double gsl_histogram_min (const gsl_histogram * H)
- -- Function: size_t gsl_histogram_bins (const gsl_histogram * H)
-     These functions return the maximum upper and minimum lower range
-     limits and the number of bins of the histogram H.  They provide a
-     way of determining these values without accessing the
-     'gsl_histogram' struct directly.
+     where x_i are the elements of the dataset DATA.  The skewness
+     measures the asymmetry of the tails of a distribution.
 
- -- Function: void gsl_histogram_reset (gsl_histogram * H)
-     This function resets all the bins in the histogram H to zero.
+     The function computes the mean and estimated standard deviation of
+     DATA via calls to 'gsl_stats_mean' and 'gsl_stats_sd'.
 
-
-File: gsl-ref.info,  Node: Searching histogram ranges,  Next: Histogram Statistics,  Prev: Updating and accessing histogram elements,  Up: Histograms
+ -- Function: double gsl_stats_skew_m_sd (const double DATA[], size_t
+          STRIDE, size_t N, double MEAN, double SD)
+     This function computes the skewness of the dataset DATA using the
+     given values of the mean MEAN and standard deviation SD,
 
-22.5 Searching histogram ranges
-===============================
+          skew = (1/N) \sum ((x_i - mean)/sd)^3
 
-The following functions are used by the access and update routines to
-locate the bin which corresponds to a given x coordinate.
+     These functions are useful if you have already computed the mean
+     and standard deviation of DATA and want to avoid recomputing them.
 
- -- Function: int gsl_histogram_find (const gsl_histogram * H, double X,
-          size_t * I)
-     This function finds and sets the index I to the bin number which
-     covers the coordinate X in the histogram H.  The bin is located
-     using a binary search.  The search includes an optimization for
-     histograms with uniform range, and will return the correct bin
-     immediately in this case.  If X is found in the range of the
-     histogram then the function sets the index I and returns
-     'GSL_SUCCESS'.  If X lies outside the valid range of the histogram
-     then the function returns 'GSL_EDOM' and the error handler is
-     invoked.
+ -- Function: double gsl_stats_kurtosis (const double DATA[], size_t
+          STRIDE, size_t N)
+     This function computes the kurtosis of DATA, a dataset of length N
+     with stride STRIDE.  The kurtosis is defined as,
 
-
-File: gsl-ref.info,  Node: Histogram Statistics,  Next: Histogram Operations,  Prev: Searching histogram ranges,  Up: Histograms
+          kurtosis = ((1/N) \sum ((x_i - \Hat\mu)/\Hat\sigma)^4)  - 3
 
-22.6 Histogram Statistics
-=========================
+     The kurtosis measures how sharply peaked a distribution is,
+     relative to its width.  The kurtosis is normalized to zero for a
+     Gaussian distribution.
 
- -- Function: double gsl_histogram_max_val (const gsl_histogram * H)
-     This function returns the maximum value contained in the histogram
-     bins.
+ -- Function: double gsl_stats_kurtosis_m_sd (const double DATA[],
+          size_t STRIDE, size_t N, double MEAN, double SD)
+     This function computes the kurtosis of the dataset DATA using the
+     given values of the mean MEAN and standard deviation SD,
 
- -- Function: size_t gsl_histogram_max_bin (const gsl_histogram * H)
-     This function returns the index of the bin containing the maximum
-     value.  In the case where several bins contain the same maximum
-     value the smallest index is returned.
+          kurtosis = ((1/N) \sum ((x_i - mean)/sd)^4) - 3
 
- -- Function: double gsl_histogram_min_val (const gsl_histogram * H)
-     This function returns the minimum value contained in the histogram
-     bins.
+     This function is useful if you have already computed the mean and
+     standard deviation of DATA and want to avoid recomputing them.
 
- -- Function: size_t gsl_histogram_min_bin (const gsl_histogram * H)
-     This function returns the index of the bin containing the minimum
-     value.  In the case where several bins contain the same maximum
-     value the smallest index is returned.
+
+File: gsl-ref.info,  Node: Autocorrelation,  Next: Covariance,  Prev: Higher moments (skewness and kurtosis),  Up: Statistics
 
- -- Function: double gsl_histogram_mean (const gsl_histogram * H)
-     This function returns the mean of the histogrammed variable, where
-     the histogram is regarded as a probability distribution.  Negative
-     bin values are ignored for the purposes of this calculation.  The
-     accuracy of the result is limited by the bin width.
+21.4 Autocorrelation
+====================
 
- -- Function: double gsl_histogram_sigma (const gsl_histogram * H)
-     This function returns the standard deviation of the histogrammed
-     variable, where the histogram is regarded as a probability
-     distribution.  Negative bin values are ignored for the purposes of
-     this calculation.  The accuracy of the result is limited by the bin
-     width.
+ -- Function: double gsl_stats_lag1_autocorrelation (const double
+          DATA[], const size_t STRIDE, const size_t N)
+     This function computes the lag-1 autocorrelation of the dataset
+     DATA.
 
- -- Function: double gsl_histogram_sum (const gsl_histogram * H)
-     This function returns the sum of all bin values.  Negative bin
-     values are included in the sum.
+          a_1 = {\sum_{i = 2}^{n} (x_{i} - \Hat\mu) (x_{i-1} - \Hat\mu)
+                 \over
+                 \sum_{i = 1}^{n} (x_{i} - \Hat\mu) (x_{i} - \Hat\mu)}
+
+ -- Function: double gsl_stats_lag1_autocorrelation_m (const double
+          DATA[], const size_t STRIDE, const size_t N, const double
+          MEAN)
+     This function computes the lag-1 autocorrelation of the dataset
+     DATA using the given value of the mean MEAN.
 
 
-File: gsl-ref.info,  Node: Histogram Operations,  Next: Reading and writing histograms,  Prev: Histogram Statistics,  Up: Histograms
+File: gsl-ref.info,  Node: Covariance,  Next: Correlation,  Prev: Autocorrelation,  Up: Statistics
 
-22.7 Histogram Operations
-=========================
+21.5 Covariance
+===============
 
- -- Function: int gsl_histogram_equal_bins_p (const gsl_histogram * H1,
-          const gsl_histogram * H2)
-     This function returns 1 if the all of the individual bin ranges of
-     the two histograms are identical, and 0 otherwise.
+ -- Function: double gsl_stats_covariance (const double DATA1[], const
+          size_t STRIDE1, const double DATA2[], const size_t STRIDE2,
+          const size_t N)
+     This function computes the covariance of the datasets DATA1 and
+     DATA2 which must both be of the same length N.
 
- -- Function: int gsl_histogram_add (gsl_histogram * H1, const
-          gsl_histogram * H2)
-     This function adds the contents of the bins in histogram H2 to the
-     corresponding bins of histogram H1, i.e.  h'_1(i) = h_1(i) +
-     h_2(i).  The two histograms must have identical bin ranges.
+          covar = (1/(n - 1)) \sum_{i = 1}^{n} (x_i - \Hat x) (y_i - \Hat y)
 
- -- Function: int gsl_histogram_sub (gsl_histogram * H1, const
-          gsl_histogram * H2)
-     This function subtracts the contents of the bins in histogram H2
-     from the corresponding bins of histogram H1, i.e.  h'_1(i) = h_1(i)
-     - h_2(i).  The two histograms must have identical bin ranges.
+ -- Function: double gsl_stats_covariance_m (const double DATA1[], const
+          size_t STRIDE1, const double DATA2[], const size_t STRIDE2,
+          const size_t N, const double MEAN1, const double MEAN2)
+     This function computes the covariance of the datasets DATA1 and
+     DATA2 using the given values of the means, MEAN1 and MEAN2.  This
+     is useful if you have already computed the means of DATA1 and DATA2
+     and want to avoid recomputing them.
 
- -- Function: int gsl_histogram_mul (gsl_histogram * H1, const
-          gsl_histogram * H2)
-     This function multiplies the contents of the bins of histogram H1
-     by the contents of the corresponding bins in histogram H2, i.e.
-     h'_1(i) = h_1(i) * h_2(i).  The two histograms must have identical
-     bin ranges.
+
+File: gsl-ref.info,  Node: Correlation,  Next: Weighted Samples,  Prev: Covariance,  Up: Statistics
 
- -- Function: int gsl_histogram_div (gsl_histogram * H1, const
-          gsl_histogram * H2)
-     This function divides the contents of the bins of histogram H1 by
-     the contents of the corresponding bins in histogram H2, i.e.
-     h'_1(i) = h_1(i) / h_2(i).  The two histograms must have identical
-     bin ranges.
+21.6 Correlation
+================
 
- -- Function: int gsl_histogram_scale (gsl_histogram * H, double SCALE)
-     This function multiplies the contents of the bins of histogram H by
-     the constant SCALE, i.e.  h'_1(i) = h_1(i) * scale.
+ -- Function: double gsl_stats_correlation (const double DATA1[], const
+          size_t STRIDE1, const double DATA2[], const size_t STRIDE2,
+          const size_t N)
+     This function efficiently computes the Pearson correlation
+     coefficient between the datasets DATA1 and DATA2 which must both be
+     of the same length N.
+          r = cov(x, y) / (\Hat\sigma_x \Hat\sigma_y)
+            = {1/(n-1) \sum (x_i - \Hat x) (y_i - \Hat y)
+               \over
+               \sqrt{1/(n-1) \sum (x_i - \Hat x)^2} \sqrt{1/(n-1) \sum (y_i - \Hat y)^2}
+              }
 
- -- Function: int gsl_histogram_shift (gsl_histogram * H, double OFFSET)
-     This function shifts the contents of the bins of histogram H by the
-     constant OFFSET, i.e.  h'_1(i) = h_1(i) + offset.
+ -- Function: double gsl_stats_spearman (const double DATA1[], const
+          size_t STRIDE1, const double DATA2[], const size_t STRIDE2,
+          const size_t N, double WORK[])
+     This function computes the Spearman rank correlation coefficient
+     between the datasets DATA1 and DATA2 which must both be of the same
+     length N.  Additional workspace of size 2*N is required in WORK.
+     The Spearman rank correlation between vectors x and y is equivalent
+     to the Pearson correlation between the ranked vectors x_R and y_R,
+     where ranks are defined to be the average of the positions of an
+     element in the ascending order of the values.
 
 
-File: gsl-ref.info,  Node: Reading and writing histograms,  Next: Resampling from histograms,  Prev: Histogram Operations,  Up: Histograms
-
-22.8 Reading and writing histograms
-===================================
+File: gsl-ref.info,  Node: Weighted Samples,  Next: Maximum and Minimum values,  Prev: Correlation,  Up: Statistics
 
-The library provides functions for reading and writing histograms to a
-file as binary data or formatted text.
+21.7 Weighted Samples
+=====================
 
- -- Function: int gsl_histogram_fwrite (FILE * STREAM, const
-          gsl_histogram * H)
-     This function writes the ranges and bins of the histogram H to the
-     stream STREAM in binary format.  The return value is 0 for success
-     and 'GSL_EFAILED' if there was a problem writing to the file.
-     Since the data is written in the native binary format it may not be
-     portable between different architectures.
+The functions described in this section allow the computation of
+statistics for weighted samples.  The functions accept an array of
+samples, x_i, with associated weights, w_i.  Each sample x_i is
+considered as having been drawn from a Gaussian distribution with
+variance \sigma_i^2.  The sample weight w_i is defined as the reciprocal
+of this variance, w_i = 1/\sigma_i^2.  Setting a weight to zero
+corresponds to removing a sample from a dataset.
 
- -- Function: int gsl_histogram_fread (FILE * STREAM, gsl_histogram * H)
-     This function reads into the histogram H from the open stream
-     STREAM in binary format.  The histogram H must be preallocated with
-     the correct size since the function uses the number of bins in H to
-     determine how many bytes to read.  The return value is 0 for
-     success and 'GSL_EFAILED' if there was a problem reading from the
-     file.  The data is assumed to have been written in the native
-     binary format on the same architecture.
+ -- Function: double gsl_stats_wmean (const double W[], size_t WSTRIDE,
+          const double DATA[], size_t STRIDE, size_t N)
+     This function returns the weighted mean of the dataset DATA with
+     stride STRIDE and length N, using the set of weights W with stride
+     WSTRIDE and length N.  The weighted mean is defined as,
 
- -- Function: int gsl_histogram_fprintf (FILE * STREAM, const
-          gsl_histogram * H, const char * RANGE_FORMAT, const char *
-          BIN_FORMAT)
-     This function writes the ranges and bins of the histogram H
-     line-by-line to the stream STREAM using the format specifiers
-     RANGE_FORMAT and BIN_FORMAT.  These should be one of the '%g', '%e'
-     or '%f' formats for floating point numbers.  The function returns 0
-     for success and 'GSL_EFAILED' if there was a problem writing to the
-     file.  The histogram output is formatted in three columns, and the
-     columns are separated by spaces, like this,
+          \Hat\mu = (\sum w_i x_i) / (\sum w_i)
 
-          range[0] range[1] bin[0]
-          range[1] range[2] bin[1]
-          range[2] range[3] bin[2]
-          ....
-          range[n-1] range[n] bin[n-1]
+ -- Function: double gsl_stats_wvariance (const double W[], size_t
+          WSTRIDE, const double DATA[], size_t STRIDE, size_t N)
+     This function returns the estimated variance of the dataset DATA
+     with stride STRIDE and length N, using the set of weights W with
+     stride WSTRIDE and length N.  The estimated variance of a weighted
+     dataset is calculated as,
 
-     The values of the ranges are formatted using RANGE_FORMAT and the
-     value of the bins are formatted using BIN_FORMAT.  Each line
-     contains the lower and upper limit of the range of the bins and the
-     value of the bin itself.  Since the upper limit of one bin is the
-     lower limit of the next there is duplication of these values
-     between lines but this allows the histogram to be manipulated with
-     line-oriented tools.
+          \Hat\sigma^2 = ((\sum w_i)/((\sum w_i)^2 - \sum (w_i^2)))
+                          \sum w_i (x_i - \Hat\mu)^2
 
- -- Function: int gsl_histogram_fscanf (FILE * STREAM, gsl_histogram *
-          H)
-     This function reads formatted data from the stream STREAM into the
-     histogram H.  The data is assumed to be in the three-column format
-     used by 'gsl_histogram_fprintf'.  The histogram H must be
-     preallocated with the correct length since the function uses the
-     size of H to determine how many numbers to read.  The function
-     returns 0 for success and 'GSL_EFAILED' if there was a problem
-     reading from the file.
+     Note that this expression reduces to an unweighted variance with
+     the familiar 1/(N-1) factor when there are N equal non-zero
+     weights.
 
-
-File: gsl-ref.info,  Node: Resampling from histograms,  Next: The histogram probability distribution struct,  Prev: Reading and writing histograms,  Up: Histograms
+ -- Function: double gsl_stats_wvariance_m (const double W[], size_t
+          WSTRIDE, const double DATA[], size_t STRIDE, size_t N, double
+          WMEAN)
+     This function returns the estimated variance of the weighted
+     dataset DATA using the given weighted mean WMEAN.
 
-22.9 Resampling from histograms
-===============================
+ -- Function: double gsl_stats_wsd (const double W[], size_t WSTRIDE,
+          const double DATA[], size_t STRIDE, size_t N)
+     The standard deviation is defined as the square root of the
+     variance.  This function returns the square root of the
+     corresponding variance function 'gsl_stats_wvariance' above.
 
-A histogram made by counting events can be regarded as a measurement of
-a probability distribution.  Allowing for statistical error, the height
-of each bin represents the probability of an event where the value of x
-falls in the range of that bin.  The probability distribution function
-has the one-dimensional form p(x)dx where,
+ -- Function: double gsl_stats_wsd_m (const double W[], size_t WSTRIDE,
+          const double DATA[], size_t STRIDE, size_t N, double WMEAN)
+     This function returns the square root of the corresponding variance
+     function 'gsl_stats_wvariance_m' above.
 
-     p(x) = n_i/ (N w_i)
+ -- Function: double gsl_stats_wvariance_with_fixed_mean (const double
+          W[], size_t WSTRIDE, const double DATA[], size_t STRIDE,
+          size_t N, const double MEAN)
+     This function computes an unbiased estimate of the variance of the
+     weighted dataset DATA when the population mean MEAN of the
+     underlying distribution is known _a priori_.  In this case the
+     estimator for the variance replaces the sample mean \Hat\mu by the
+     known population mean \mu,
 
-In this equation n_i is the number of events in the bin which contains
-x, w_i is the width of the bin and N is the total number of events.  The
-distribution of events within each bin is assumed to be uniform.
+          \Hat\sigma^2 = (\sum w_i (x_i - \mu)^2) / (\sum w_i)
 
-
-File: gsl-ref.info,  Node: The histogram probability distribution struct,  Next: Example programs for histograms,  Prev: Resampling from histograms,  Up: Histograms
+ -- Function: double gsl_stats_wsd_with_fixed_mean (const double W[],
+          size_t WSTRIDE, const double DATA[], size_t STRIDE, size_t N,
+          const double MEAN)
+     The standard deviation is defined as the square root of the
+     variance.  This function returns the square root of the
+     corresponding variance function above.
 
-22.10 The histogram probability distribution struct
-===================================================
+ -- Function: double gsl_stats_wtss (const double W[], const size_t
+          WSTRIDE, const double DATA[], size_t STRIDE, size_t N)
+ -- Function: double gsl_stats_wtss_m (const double W[], const size_t
+          WSTRIDE, const double DATA[], size_t STRIDE, size_t N, double
+          WMEAN)
+     These functions return the weighted total sum of squares (TSS) of
+     DATA about the weighted mean.  For 'gsl_stats_wtss_m' the
+     user-supplied value of WMEAN is used, and for 'gsl_stats_wtss' it
+     is computed using 'gsl_stats_wmean'.
 
-The probability distribution function for a histogram consists of a set
-of "bins" which measure the probability of an event falling into a given
-range of a continuous variable x.  A probability distribution function
-is defined by the following struct, which actually stores the cumulative
-probability distribution function.  This is the natural quantity for
-generating samples via the inverse transform method, because there is a
-one-to-one mapping between the cumulative probability distribution and
-the range [0,1].  It can be shown that by taking a uniform random number
-in this range and finding its corresponding coordinate in the cumulative
-probability distribution we obtain samples with the desired probability
-distribution.
+          TSS =  \sum w_i (x_i - wmean)^2
 
- -- Data Type: gsl_histogram_pdf
-     'size_t n'
-          This is the number of bins used to approximate the probability
-          distribution function.
-     'double * range'
-          The ranges of the bins are stored in an array of N+1 elements
-          pointed to by RANGE.
-     'double * sum'
-          The cumulative probability for the bins is stored in an array
-          of N elements pointed to by SUM.
+ -- Function: double gsl_stats_wabsdev (const double W[], size_t
+          WSTRIDE, const double DATA[], size_t STRIDE, size_t N)
+     This function computes the weighted absolute deviation from the
+     weighted mean of DATA.  The absolute deviation from the mean is
+     defined as,
 
-The following functions allow you to create a 'gsl_histogram_pdf' struct
-which represents this probability distribution and generate random
-samples from it.
+          absdev = (\sum w_i |x_i - \Hat\mu|) / (\sum w_i)
 
- -- Function: gsl_histogram_pdf * gsl_histogram_pdf_alloc (size_t N)
-     This function allocates memory for a probability distribution with
-     N bins and returns a pointer to a newly initialized
-     'gsl_histogram_pdf' struct.  If insufficient memory is available a
-     null pointer is returned and the error handler is invoked with an
-     error code of 'GSL_ENOMEM'.
+ -- Function: double gsl_stats_wabsdev_m (const double W[], size_t
+          WSTRIDE, const double DATA[], size_t STRIDE, size_t N, double
+          WMEAN)
+     This function computes the absolute deviation of the weighted
+     dataset DATA about the given weighted mean WMEAN.
 
- -- Function: int gsl_histogram_pdf_init (gsl_histogram_pdf * P, const
-          gsl_histogram * H)
-     This function initializes the probability distribution P with the
-     contents of the histogram H.  If any of the bins of H are negative
-     then the error handler is invoked with an error code of 'GSL_EDOM'
-     because a probability distribution cannot contain negative values.
+ -- Function: double gsl_stats_wskew (const double W[], size_t WSTRIDE,
+          const double DATA[], size_t STRIDE, size_t N)
+     This function computes the weighted skewness of the dataset DATA.
 
- -- Function: void gsl_histogram_pdf_free (gsl_histogram_pdf * P)
-     This function frees the probability distribution function P and all
-     of the memory associated with it.
+          skew = (\sum w_i ((x_i - \Hat x)/\Hat \sigma)^3) / (\sum w_i)
 
- -- Function: double gsl_histogram_pdf_sample (const gsl_histogram_pdf *
-          P, double R)
-     This function uses R, a uniform random number between zero and one,
-     to compute a single random sample from the probability distribution
-     P.  The algorithm used to compute the sample s is given by the
-     following formula,
+ -- Function: double gsl_stats_wskew_m_sd (const double W[], size_t
+          WSTRIDE, const double DATA[], size_t STRIDE, size_t N, double
+          WMEAN, double WSD)
+     This function computes the weighted skewness of the dataset DATA
+     using the given values of the weighted mean and weighted standard
+     deviation, WMEAN and WSD.
 
-          s = range[i] + delta * (range[i+1] - range[i])
+ -- Function: double gsl_stats_wkurtosis (const double W[], size_t
+          WSTRIDE, const double DATA[], size_t STRIDE, size_t N)
+     This function computes the weighted kurtosis of the dataset DATA.
 
-     where i is the index which satisfies sum[i] <= r < sum[i+1] and
-     delta is (r - sum[i])/(sum[i+1] - sum[i]).
+          kurtosis = ((\sum w_i ((x_i - \Hat x)/\Hat \sigma)^4) / (\sum w_i)) - 3
 
-
-File: gsl-ref.info,  Node: Example programs for histograms,  Next: Two dimensional histograms,  Prev: The histogram probability distribution struct,  Up: Histograms
+ -- Function: double gsl_stats_wkurtosis_m_sd (const double W[], size_t
+          WSTRIDE, const double DATA[], size_t STRIDE, size_t N, double
+          WMEAN, double WSD)
+     This function computes the weighted kurtosis of the dataset DATA
+     using the given values of the weighted mean and weighted standard
+     deviation, WMEAN and WSD.
 
-22.11 Example programs for histograms
-=====================================
+
+File: gsl-ref.info,  Node: Maximum and Minimum values,  Next: Median and Percentiles,  Prev: Weighted Samples,  Up: Statistics
 
-The following program shows how to make a simple histogram of a column
-of numerical data supplied on 'stdin'.  The program takes three
-arguments, specifying the upper and lower bounds of the histogram and
-the number of bins.  It then reads numbers from 'stdin', one line at a
-time, and adds them to the histogram.  When there is no more data to
-read it prints out the accumulated histogram using
-'gsl_histogram_fprintf'.
+21.8 Maximum and Minimum values
+===============================
 
-     #include <stdio.h>
-     #include <stdlib.h>
-     #include <gsl/gsl_histogram.h>
+The following functions find the maximum and minimum values of a dataset
+(or their indices).  If the data contains 'NaN's then a 'NaN' will be
+returned, since the maximum or minimum value is undefined.  For
+functions which return an index, the location of the first 'NaN' in the
+array is returned.
 
-     int
-     main (int argc, char **argv)
-     {
-       double a, b;
-       size_t n;
+ -- Function: double gsl_stats_max (const double DATA[], size_t STRIDE,
+          size_t N)
+     This function returns the maximum value in DATA, a dataset of
+     length N with stride STRIDE.  The maximum value is defined as the
+     value of the element x_i which satisfies x_i >= x_j for all j.
 
-       if (argc != 4)
-         {
-           printf ("Usage: gsl-histogram xmin xmax n\n"
-                   "Computes a histogram of the data "
-                   "on stdin using n bins from xmin "
-                   "to xmax\n");
-           exit (0);
-         }
+     If you want instead to find the element with the largest absolute
+     magnitude you will need to apply 'fabs' or 'abs' to your data
+     before calling this function.
 
-       a = atof (argv[1]);
-       b = atof (argv[2]);
-       n = atoi (argv[3]);
+ -- Function: double gsl_stats_min (const double DATA[], size_t STRIDE,
+          size_t N)
+     This function returns the minimum value in DATA, a dataset of
+     length N with stride STRIDE.  The minimum value is defined as the
+     value of the element x_i which satisfies x_i <= x_j for all j.
 
-       {
-         double x;
-         gsl_histogram * h = gsl_histogram_alloc (n);
-         gsl_histogram_set_ranges_uniform (h, a, b);
+     If you want instead to find the element with the smallest absolute
+     magnitude you will need to apply 'fabs' or 'abs' to your data
+     before calling this function.
 
-         while (fscanf (stdin, "%lg", &x) == 1)
-           {
-             gsl_histogram_increment (h, x);
-           }
-         gsl_histogram_fprintf (stdout, h, "%g", "%g");
-         gsl_histogram_free (h);
-       }
-       exit (0);
-     }
+ -- Function: void gsl_stats_minmax (double * MIN, double * MAX, const
+          double DATA[], size_t STRIDE, size_t N)
+     This function finds both the minimum and maximum values MIN, MAX in
+     DATA in a single pass.
 
-Here is an example of the program in use.  We generate 10000 random
-samples from a Cauchy distribution with a width of 30 and histogram them
-over the range -100 to 100, using 200 bins.
+ -- Function: size_t gsl_stats_max_index (const double DATA[], size_t
+          STRIDE, size_t N)
+     This function returns the index of the maximum value in DATA, a
+     dataset of length N with stride STRIDE.  The maximum value is
+     defined as the value of the element x_i which satisfies x_i >= x_j
+     for all j.  When there are several equal maximum elements then the
+     first one is chosen.
 
-     $ gsl-randist 0 10000 cauchy 30
-        | gsl-histogram -100 100 200 > histogram.dat
+ -- Function: size_t gsl_stats_min_index (const double DATA[], size_t
+          STRIDE, size_t N)
+     This function returns the index of the minimum value in DATA, a
+     dataset of length N with stride STRIDE.  The minimum value is
+     defined as the value of the element x_i which satisfies x_i >= x_j
+     for all j.  When there are several equal minimum elements then the
+     first one is chosen.
 
-A plot of the resulting histogram shows the familiar shape of the Cauchy
-distribution and the fluctuations caused by the finite sample size.
-
-     $ awk '{print $1, $3 ; print $2, $3}' histogram.dat
-        | graph -T X
+ -- Function: void gsl_stats_minmax_index (size_t * MIN_INDEX, size_t *
+          MAX_INDEX, const double DATA[], size_t STRIDE, size_t N)
+     This function returns the indexes MIN_INDEX, MAX_INDEX of the
+     minimum and maximum values in DATA in a single pass.
 
 
-File: gsl-ref.info,  Node: Two dimensional histograms,  Next: The 2D histogram struct,  Prev: Example programs for histograms,  Up: Histograms
+File: gsl-ref.info,  Node: Median and Percentiles,  Next: Example statistical programs,  Prev: Maximum and Minimum values,  Up: Statistics
 
-22.12 Two dimensional histograms
-================================
+21.9 Median and Percentiles
+===========================
 
-A two dimensional histogram consists of a set of "bins" which count the
-number of events falling in a given area of the (x,y) plane.  The
-simplest way to use a two dimensional histogram is to record
-two-dimensional position information, n(x,y).  Another possibility is to
-form a "joint distribution" by recording related variables.  For example
-a detector might record both the position of an event (x) and the amount
-of energy it deposited E.  These could be histogrammed as the joint
-distribution n(x,E).
+The median and percentile functions described in this section operate on
+sorted data.  For convenience we use "quantiles", measured on a scale of
+0 to 1, instead of percentiles (which use a scale of 0 to 100).
 
-
-File: gsl-ref.info,  Node: The 2D histogram struct,  Next: 2D Histogram allocation,  Prev: Two dimensional histograms,  Up: Histograms
+ -- Function: double gsl_stats_median_from_sorted_data (const double
+          SORTED_DATA[], size_t STRIDE, size_t N)
+     This function returns the median value of SORTED_DATA, a dataset of
+     length N with stride STRIDE.  The elements of the array must be in
+     ascending numerical order.  There are no checks to see whether the
+     data are sorted, so the function 'gsl_sort' should always be used
+     first.
 
-22.13 The 2D histogram struct
-=============================
+     When the dataset has an odd number of elements the median is the
+     value of element (n-1)/2.  When the dataset has an even number of
+     elements the median is the mean of the two nearest middle values,
+     elements (n-1)/2 and n/2.  Since the algorithm for computing the
+     median involves interpolation this function always returns a
+     floating-point number, even for integer data types.
 
-Two dimensional histograms are defined by the following struct,
+ -- Function: double gsl_stats_quantile_from_sorted_data (const double
+          SORTED_DATA[], size_t STRIDE, size_t N, double F)
+     This function returns a quantile value of SORTED_DATA, a
+     double-precision array of length N with stride STRIDE.  The
+     elements of the array must be in ascending numerical order.  The
+     quantile is determined by the F, a fraction between 0 and 1.  For
+     example, to compute the value of the 75th percentile F should have
+     the value 0.75.
 
- -- Data Type: gsl_histogram2d
-     'size_t nx, ny'
-          This is the number of histogram bins in the x and y
-          directions.
-     'double * xrange'
-          The ranges of the bins in the x-direction are stored in an
-          array of NX + 1 elements pointed to by XRANGE.
-     'double * yrange'
-          The ranges of the bins in the y-direction are stored in an
-          array of NY + 1 elements pointed to by YRANGE.
-     'double * bin'
-          The counts for each bin are stored in an array pointed to by
-          BIN.  The bins are floating-point numbers, so you can
-          increment them by non-integer values if necessary.  The array
-          BIN stores the two dimensional array of bins in a single block
-          of memory according to the mapping 'bin(i,j)' = 'bin[i * ny +
-          j]'.
+     There are no checks to see whether the data are sorted, so the
+     function 'gsl_sort' should always be used first.
 
-The range for 'bin(i,j)' is given by 'xrange[i]' to 'xrange[i+1]' in the
-x-direction and 'yrange[j]' to 'yrange[j+1]' in the y-direction.  Each
-bin is inclusive at the lower end and exclusive at the upper end.
-Mathematically this means that the bins are defined by the following
-inequality,
-     bin(i,j) corresponds to xrange[i] <= x < xrange[i+1]
-                         and yrange[j] <= y < yrange[j+1]
+     The quantile is found by interpolation, using the formula
 
-Note that any samples which fall on the upper sides of the histogram are
-excluded.  If you want to include these values for the side bins you
-will need to add an extra row or column to your histogram.
+          quantile = (1 - \delta) x_i + \delta x_{i+1}
 
-   The 'gsl_histogram2d' struct and its associated functions are defined
-in the header file 'gsl_histogram2d.h'.
+     where i is 'floor'((n - 1)f) and \delta is (n-1)f - i.
+
+     Thus the minimum value of the array ('data[0*stride]') is given by
+     F equal to zero, the maximum value ('data[(n-1)*stride]') is given
+     by F equal to one and the median value is given by F equal to 0.5.
+     Since the algorithm for computing quantiles involves interpolation
+     this function always returns a floating-point number, even for
+     integer data types.
 
 
-File: gsl-ref.info,  Node: 2D Histogram allocation,  Next: Copying 2D Histograms,  Prev: The 2D histogram struct,  Up: Histograms
+File: gsl-ref.info,  Node: Example statistical programs,  Next: Statistics References and Further Reading,  Prev: Median and Percentiles,  Up: Statistics
 
-22.14 2D Histogram allocation
-=============================
+21.10 Examples
+==============
 
-The functions for allocating memory to a 2D histogram follow the style
-of 'malloc' and 'free'.  In addition they also perform their own error
-checking.  If there is insufficient memory available to allocate a
-histogram then the functions call the error handler (with an error
-number of 'GSL_ENOMEM') in addition to returning a null pointer.  Thus
-if you use the library error handler to abort your program then it isn't
-necessary to check every 2D histogram 'alloc'.
+Here is a basic example of how to use the statistical functions:
 
- -- Function: gsl_histogram2d * gsl_histogram2d_alloc (size_t NX, size_t
-          NY)
-     This function allocates memory for a two-dimensional histogram with
-     NX bins in the x direction and NY bins in the y direction.  The
-     function returns a pointer to a newly created 'gsl_histogram2d'
-     struct.  If insufficient memory is available a null pointer is
-     returned and the error handler is invoked with an error code of
-     'GSL_ENOMEM'.  The bins and ranges must be initialized with one of
-     the functions below before the histogram is ready for use.
+     #include <stdio.h>
+     #include <gsl/gsl_statistics.h>
 
- -- Function: int gsl_histogram2d_set_ranges (gsl_histogram2d * H, const
-          double XRANGE[], size_t XSIZE, const double YRANGE[], size_t
-          YSIZE)
-     This function sets the ranges of the existing histogram H using the
-     arrays XRANGE and YRANGE of size XSIZE and YSIZE respectively.  The
-     values of the histogram bins are reset to zero.
+     int
+     main(void)
+     {
+       double data[5] = {17.2, 18.1, 16.5, 18.3, 12.6};
+       double mean, variance, largest, smallest;
 
- -- Function: int gsl_histogram2d_set_ranges_uniform (gsl_histogram2d *
-          H, double XMIN, double XMAX, double YMIN, double YMAX)
-     This function sets the ranges of the existing histogram H to cover
-     the ranges XMIN to XMAX and YMIN to YMAX uniformly.  The values of
-     the histogram bins are reset to zero.
+       mean     = gsl_stats_mean(data, 1, 5);
+       variance = gsl_stats_variance(data, 1, 5);
+       largest  = gsl_stats_max(data, 1, 5);
+       smallest = gsl_stats_min(data, 1, 5);
 
- -- Function: void gsl_histogram2d_free (gsl_histogram2d * H)
-     This function frees the 2D histogram H and all of the memory
-     associated with it.
+       printf ("The dataset is %g, %g, %g, %g, %g\n",
+              data[0], data[1], data[2], data[3], data[4]);
 
-
-File: gsl-ref.info,  Node: Copying 2D Histograms,  Next: Updating and accessing 2D histogram elements,  Prev: 2D Histogram allocation,  Up: Histograms
+       printf ("The sample mean is %g\n", mean);
+       printf ("The estimated variance is %g\n", variance);
+       printf ("The largest value is %g\n", largest);
+       printf ("The smallest value is %g\n", smallest);
+       return 0;
+     }
 
-22.15 Copying 2D Histograms
-===========================
+   The program should produce the following output,
 
- -- Function: int gsl_histogram2d_memcpy (gsl_histogram2d * DEST, const
-          gsl_histogram2d * SRC)
-     This function copies the histogram SRC into the pre-existing
-     histogram DEST, making DEST into an exact copy of SRC.  The two
-     histograms must be of the same size.
+     The dataset is 17.2, 18.1, 16.5, 18.3, 12.6
+     The sample mean is 16.54
+     The estimated variance is 5.373
+     The largest value is 18.3
+     The smallest value is 12.6
 
- -- Function: gsl_histogram2d * gsl_histogram2d_clone (const
-          gsl_histogram2d * SRC)
-     This function returns a pointer to a newly created histogram which
-     is an exact copy of the histogram SRC.
+   Here is an example using sorted data,
 
-
-File: gsl-ref.info,  Node: Updating and accessing 2D histogram elements,  Next: Searching 2D histogram ranges,  Prev: Copying 2D Histograms,  Up: Histograms
+     #include <stdio.h>
+     #include <gsl/gsl_sort.h>
+     #include <gsl/gsl_statistics.h>
 
-22.16 Updating and accessing 2D histogram elements
-==================================================
+     int
+     main(void)
+     {
+       double data[5] = {17.2, 18.1, 16.5, 18.3, 12.6};
+       double median, upperq, lowerq;
 
-You can access the bins of a two-dimensional histogram either by
-specifying a pair of (x,y) coordinates or by using the bin indices (i,j)
-directly.  The functions for accessing the histogram through (x,y)
-coordinates use binary searches in the x and y directions to identify
-the bin which covers the appropriate range.
+       printf ("Original dataset:  %g, %g, %g, %g, %g\n",
+              data[0], data[1], data[2], data[3], data[4]);
 
- -- Function: int gsl_histogram2d_increment (gsl_histogram2d * H, double
-          X, double Y)
-     This function updates the histogram H by adding one (1.0) to the
-     bin whose x and y ranges contain the coordinates (X,Y).
+       gsl_sort (data, 1, 5);
 
-     If the point (x,y) lies inside the valid ranges of the histogram
-     then the function returns zero to indicate success.  If (x,y) lies
-     outside the limits of the histogram then the function returns
-     'GSL_EDOM', and none of the bins are modified.  The error handler
-     is not called, since it is often necessary to compute histograms
-     for a small range of a larger dataset, ignoring any coordinates
-     outside the range of interest.
+       printf ("Sorted dataset: %g, %g, %g, %g, %g\n",
+              data[0], data[1], data[2], data[3], data[4]);
 
- -- Function: int gsl_histogram2d_accumulate (gsl_histogram2d * H,
-          double X, double Y, double WEIGHT)
-     This function is similar to 'gsl_histogram2d_increment' but
-     increases the value of the appropriate bin in the histogram H by
-     the floating-point number WEIGHT.
+       median
+         = gsl_stats_median_from_sorted_data (data,
+                                              1, 5);
 
- -- Function: double gsl_histogram2d_get (const gsl_histogram2d * H,
-          size_t I, size_t J)
-     This function returns the contents of the (I,J)-th bin of the
-     histogram H.  If (I,J) lies outside the valid range of indices for
-     the histogram then the error handler is called with an error code
-     of 'GSL_EDOM' and the function returns 0.
+       upperq
+         = gsl_stats_quantile_from_sorted_data (data,
+                                                1, 5,
+                                                0.75);
+       lowerq
+         = gsl_stats_quantile_from_sorted_data (data,
+                                                1, 5,
+                                                0.25);
 
- -- Function: int gsl_histogram2d_get_xrange (const gsl_histogram2d * H,
-          size_t I, double * XLOWER, double * XUPPER)
- -- Function: int gsl_histogram2d_get_yrange (const gsl_histogram2d * H,
-          size_t J, double * YLOWER, double * YUPPER)
-     These functions find the upper and lower range limits of the I-th
-     and J-th bins in the x and y directions of the histogram H.  The
-     range limits are stored in XLOWER and XUPPER or YLOWER and YUPPER.
-     The lower limits are inclusive (i.e.  events with these coordinates
-     are included in the bin) and the upper limits are exclusive (i.e.
-     events with the value of the upper limit are not included and fall
-     in the neighboring higher bin, if it exists).  The functions return
-     0 to indicate success.  If I or J lies outside the valid range of
-     indices for the histogram then the error handler is called with an
-     error code of 'GSL_EDOM'.
+       printf ("The median is %g\n", median);
+       printf ("The upper quartile is %g\n", upperq);
+       printf ("The lower quartile is %g\n", lowerq);
+       return 0;
+     }
 
- -- Function: double gsl_histogram2d_xmax (const gsl_histogram2d * H)
- -- Function: double gsl_histogram2d_xmin (const gsl_histogram2d * H)
- -- Function: size_t gsl_histogram2d_nx (const gsl_histogram2d * H)
- -- Function: double gsl_histogram2d_ymax (const gsl_histogram2d * H)
- -- Function: double gsl_histogram2d_ymin (const gsl_histogram2d * H)
- -- Function: size_t gsl_histogram2d_ny (const gsl_histogram2d * H)
-     These functions return the maximum upper and minimum lower range
-     limits and the number of bins for the x and y directions of the
-     histogram H.  They provide a way of determining these values
-     without accessing the 'gsl_histogram2d' struct directly.
+   This program should produce the following output,
 
- -- Function: void gsl_histogram2d_reset (gsl_histogram2d * H)
-     This function resets all the bins of the histogram H to zero.
+     Original dataset:  17.2, 18.1, 16.5, 18.3, 12.6
+     Sorted dataset: 12.6, 16.5, 17.2, 18.1, 18.3
+     The median is 17.2
+     The upper quartile is 18.1
+     The lower quartile is 16.5
 
 
-File: gsl-ref.info,  Node: Searching 2D histogram ranges,  Next: 2D Histogram Statistics,  Prev: Updating and accessing 2D histogram elements,  Up: Histograms
+File: gsl-ref.info,  Node: Statistics References and Further Reading,  Prev: Example statistical programs,  Up: Statistics
 
-22.17 Searching 2D histogram ranges
-===================================
-
-The following functions are used by the access and update routines to
-locate the bin which corresponds to a given (x,y) coordinate.
+21.11 References and Further Reading
+====================================
 
- -- Function: int gsl_histogram2d_find (const gsl_histogram2d * H,
-          double X, double Y, size_t * I, size_t * J)
-     This function finds and sets the indices I and J to the bin which
-     covers the coordinates (X,Y).  The bin is located using a binary
-     search.  The search includes an optimization for histograms with
-     uniform ranges, and will return the correct bin immediately in this
-     case.  If (x,y) is found then the function sets the indices (I,J)
-     and returns 'GSL_SUCCESS'.  If (x,y) lies outside the valid range
-     of the histogram then the function returns 'GSL_EDOM' and the error
-     handler is invoked.
+The standard reference for almost any topic in statistics is the
+multi-volume 'Advanced Theory of Statistics' by Kendall and Stuart.
 
-
-File: gsl-ref.info,  Node: 2D Histogram Statistics,  Next: 2D Histogram Operations,  Prev: Searching 2D histogram ranges,  Up: Histograms
+     Maurice Kendall, Alan Stuart, and J. Keith Ord.  'The Advanced
+     Theory of Statistics' (multiple volumes) reprinted as 'Kendall's
+     Advanced Theory of Statistics'.  Wiley, ISBN 047023380X.
 
-22.18 2D Histogram Statistics
-=============================
+Many statistical concepts can be more easily understood by a Bayesian
+approach.  The following book by Gelman, Carlin, Stern and Rubin gives a
+comprehensive coverage of the subject.
 
- -- Function: double gsl_histogram2d_max_val (const gsl_histogram2d * H)
-     This function returns the maximum value contained in the histogram
-     bins.
+     Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin.
+     'Bayesian Data Analysis'.  Chapman & Hall, ISBN 0412039915.
 
- -- Function: void gsl_histogram2d_max_bin (const gsl_histogram2d * H,
-          size_t * I, size_t * J)
-     This function finds the indices of the bin containing the maximum
-     value in the histogram H and stores the result in (I,J).  In the
-     case where several bins contain the same maximum value the first
-     bin found is returned.
+For physicists the Particle Data Group provides useful reviews of
+Probability and Statistics in the "Mathematical Tools" section of its
+Annual Review of Particle Physics.
 
- -- Function: double gsl_histogram2d_min_val (const gsl_histogram2d * H)
-     This function returns the minimum value contained in the histogram
-     bins.
+     'Review of Particle Properties' R.M. Barnett et al., Physical
+     Review D54, 1 (1996)
 
- -- Function: void gsl_histogram2d_min_bin (const gsl_histogram2d * H,
-          size_t * I, size_t * J)
-     This function finds the indices of the bin containing the minimum
-     value in the histogram H and stores the result in (I,J).  In the
-     case where several bins contain the same maximum value the first
-     bin found is returned.
+The Review of Particle Physics is available online at the website
+<http://pdg.lbl.gov/>.
 
- -- Function: double gsl_histogram2d_xmean (const gsl_histogram2d * H)
-     This function returns the mean of the histogrammed x variable,
-     where the histogram is regarded as a probability distribution.
-     Negative bin values are ignored for the purposes of this
-     calculation.
+
+File: gsl-ref.info,  Node: Running Statistics,  Next: Histograms,  Prev: Statistics,  Up: Top
 
- -- Function: double gsl_histogram2d_ymean (const gsl_histogram2d * H)
-     This function returns the mean of the histogrammed y variable,
-     where the histogram is regarded as a probability distribution.
-     Negative bin values are ignored for the purposes of this
-     calculation.
+22 Running Statistics
+*********************
 
- -- Function: double gsl_histogram2d_xsigma (const gsl_histogram2d * H)
-     This function returns the standard deviation of the histogrammed x
-     variable, where the histogram is regarded as a probability
-     distribution.  Negative bin values are ignored for the purposes of
-     this calculation.
+This chapter describes routines for computing running statistics, also
+known as online statistics, of data.  These routines are suitable for
+handling large datasets for which it may be inconvenient or impractical
+to store in memory all at once.  The data can be processed in a single
+pass, one point at a time.  Each time a data point is added to the
+accumulator, internal parameters are updated in order to compute the
+current mean, variance, standard deviation, skewness, and kurtosis.
+These statistics are exact, and are updated with numerically stable
+single-pass algorithms.  The median and arbitrary quantiles are also
+available, however these calculations use algorithms which provide
+approximations, and grow more accurate as more data is added to the
+accumulator.
 
- -- Function: double gsl_histogram2d_ysigma (const gsl_histogram2d * H)
-     This function returns the standard deviation of the histogrammed y
-     variable, where the histogram is regarded as a probability
-     distribution.  Negative bin values are ignored for the purposes of
-     this calculation.
+   The functions described in this chapter are declared in the header
+file 'gsl_rstat.h'.
 
- -- Function: double gsl_histogram2d_cov (const gsl_histogram2d * H)
-     This function returns the covariance of the histogrammed x and y
-     variables, where the histogram is regarded as a probability
-     distribution.  Negative bin values are ignored for the purposes of
-     this calculation.
+* Menu:
 
- -- Function: double gsl_histogram2d_sum (const gsl_histogram2d * H)
-     This function returns the sum of all bin values.  Negative bin
-     values are included in the sum.
+* Running Statistics Initializing the Accumulator::
+* Running Statistics Adding Data to the Accumulator::
+* Running Statistics Current Statistics::
+* Running Statistics Quantiles::      
+* Running Statistics Example programs::  
+* Running Statistics References and Further Reading::  
 
 
-File: gsl-ref.info,  Node: 2D Histogram Operations,  Next: Reading and writing 2D histograms,  Prev: 2D Histogram Statistics,  Up: Histograms
+File: gsl-ref.info,  Node: Running Statistics Initializing the Accumulator,  Next: Running Statistics Adding Data to the Accumulator,  Up: Running Statistics
 
-22.19 2D Histogram Operations
-=============================
+22.1 Initializing the Accumulator
+=================================
 
- -- Function: int gsl_histogram2d_equal_bins_p (const gsl_histogram2d *
-          H1, const gsl_histogram2d * H2)
-     This function returns 1 if all the individual bin ranges of the two
-     histograms are identical, and 0 otherwise.
+ -- Function: gsl_rstat_workspace * gsl_rstat_alloc (void)
+     This function allocates a workspace for computing running
+     statistics.  The size of the workspace is O(1).
 
- -- Function: int gsl_histogram2d_add (gsl_histogram2d * H1, const
-          gsl_histogram2d * H2)
-     This function adds the contents of the bins in histogram H2 to the
-     corresponding bins of histogram H1, i.e.  h'_1(i,j) = h_1(i,j) +
-     h_2(i,j).  The two histograms must have identical bin ranges.
+ -- Function: void gsl_rstat_free (gsl_rstat_workspace * W)
+     This function frees the memory associated with the workspace W.
 
- -- Function: int gsl_histogram2d_sub (gsl_histogram2d * H1, const
-          gsl_histogram2d * H2)
-     This function subtracts the contents of the bins in histogram H2
-     from the corresponding bins of histogram H1, i.e.  h'_1(i,j) =
-     h_1(i,j) - h_2(i,j).  The two histograms must have identical bin
-     ranges.
+ -- Function: int gsl_rstat_reset (gsl_rstat_workspace * W)
+     This function resets the workspace W to its initial state, so it
+     can begin working on a new set of data.
 
- -- Function: int gsl_histogram2d_mul (gsl_histogram2d * H1, const
-          gsl_histogram2d * H2)
-     This function multiplies the contents of the bins of histogram H1
-     by the contents of the corresponding bins in histogram H2, i.e.
-     h'_1(i,j) = h_1(i,j) * h_2(i,j).  The two histograms must have
-     identical bin ranges.
+
+File: gsl-ref.info,  Node: Running Statistics Adding Data to the Accumulator,  Next: Running Statistics Current Statistics,  Prev: Running Statistics Initializing the Accumulator,  Up: Running Statistics
 
- -- Function: int gsl_histogram2d_div (gsl_histogram2d * H1, const
-          gsl_histogram2d * H2)
-     This function divides the contents of the bins of histogram H1 by
-     the contents of the corresponding bins in histogram H2, i.e.
-     h'_1(i,j) = h_1(i,j) / h_2(i,j).  The two histograms must have
-     identical bin ranges.
+22.2 Adding Data to the Accumulator
+===================================
 
- -- Function: int gsl_histogram2d_scale (gsl_histogram2d * H, double
-          SCALE)
-     This function multiplies the contents of the bins of histogram H by
-     the constant SCALE, i.e.  h'_1(i,j) = h_1(i,j) scale.
+ -- Function: int gsl_rstat_add (const double X, gsl_rstat_workspace *
+          W)
+     This function adds the data point X to the statistical accumulator,
+     updating calculations of the mean, variance, standard deviation,
+     skewness, kurtosis, and median.
 
- -- Function: int gsl_histogram2d_shift (gsl_histogram2d * H, double
-          OFFSET)
-     This function shifts the contents of the bins of histogram H by the
-     constant OFFSET, i.e.  h'_1(i,j) = h_1(i,j) + offset.
+ -- Function: size_t gsl_rstat_n (gsl_rstat_workspace * W)
+     This function returns the number of data so far added to the
+     accumulator.
 
 
-File: gsl-ref.info,  Node: Reading and writing 2D histograms,  Next: Resampling from 2D histograms,  Prev: 2D Histogram Operations,  Up: Histograms
+File: gsl-ref.info,  Node: Running Statistics Current Statistics,  Next: Running Statistics Quantiles,  Prev: Running Statistics Adding Data to the Accumulator,  Up: Running Statistics
 
-22.20 Reading and writing 2D histograms
-=======================================
+22.3 Current Statistics
+=======================
 
-The library provides functions for reading and writing two dimensional
-histograms to a file as binary data or formatted text.
+ -- Function: double gsl_rstat_min (gsl_rstat_workspace * W)
+     This function returns the minimum value added to the accumulator.
 
- -- Function: int gsl_histogram2d_fwrite (FILE * STREAM, const
-          gsl_histogram2d * H)
-     This function writes the ranges and bins of the histogram H to the
-     stream STREAM in binary format.  The return value is 0 for success
-     and 'GSL_EFAILED' if there was a problem writing to the file.
-     Since the data is written in the native binary format it may not be
-     portable between different architectures.
+ -- Function: double gsl_rstat_max (gsl_rstat_workspace * W)
+     This function returns the maximum value added to the accumulator.
 
- -- Function: int gsl_histogram2d_fread (FILE * STREAM, gsl_histogram2d
-          * H)
-     This function reads into the histogram H from the stream STREAM in
-     binary format.  The histogram H must be preallocated with the
-     correct size since the function uses the number of x and y bins in
-     H to determine how many bytes to read.  The return value is 0 for
-     success and 'GSL_EFAILED' if there was a problem reading from the
-     file.  The data is assumed to have been written in the native
-     binary format on the same architecture.
+ -- Function: double gsl_rstat_mean (gsl_rstat_workspace * W)
+     This function returns the mean of all data added to the
+     accumulator, defined as
 
- -- Function: int gsl_histogram2d_fprintf (FILE * STREAM, const
-          gsl_histogram2d * H, const char * RANGE_FORMAT, const char *
-          BIN_FORMAT)
-     This function writes the ranges and bins of the histogram H
-     line-by-line to the stream STREAM using the format specifiers
-     RANGE_FORMAT and BIN_FORMAT.  These should be one of the '%g', '%e'
-     or '%f' formats for floating point numbers.  The function returns 0
-     for success and 'GSL_EFAILED' if there was a problem writing to the
-     file.  The histogram output is formatted in five columns, and the
-     columns are separated by spaces, like this,
+          \Hat\mu = (1/N) \sum x_i
 
-          xrange[0] xrange[1] yrange[0] yrange[1] bin(0,0)
-          xrange[0] xrange[1] yrange[1] yrange[2] bin(0,1)
-          xrange[0] xrange[1] yrange[2] yrange[3] bin(0,2)
-          ....
-          xrange[0] xrange[1] yrange[ny-1] yrange[ny] bin(0,ny-1)
+ -- Function: double gsl_rstat_variance (gsl_rstat_workspace * W)
+     This function returns the variance of all data added to the
+     accumulator, defined as
 
-          xrange[1] xrange[2] yrange[0] yrange[1] bin(1,0)
-          xrange[1] xrange[2] yrange[1] yrange[2] bin(1,1)
-          xrange[1] xrange[2] yrange[1] yrange[2] bin(1,2)
-          ....
-          xrange[1] xrange[2] yrange[ny-1] yrange[ny] bin(1,ny-1)
+          \Hat\sigma^2 = (1/(N-1)) \sum (x_i - \Hat\mu)^2
 
-          ....
+ -- Function: double gsl_rstat_sd (gsl_rstat_workspace * W)
+     This function returns the standard deviation of all data added to
+     the accumulator, defined as the square root of the variance given
+     above.
 
-          xrange[nx-1] xrange[nx] yrange[0] yrange[1] bin(nx-1,0)
-          xrange[nx-1] xrange[nx] yrange[1] yrange[2] bin(nx-1,1)
-          xrange[nx-1] xrange[nx] yrange[1] yrange[2] bin(nx-1,2)
-          ....
-          xrange[nx-1] xrange[nx] yrange[ny-1] yrange[ny] bin(nx-1,ny-1)
+ -- Function: double gsl_rstat_sd_mean (gsl_rstat_workspace * W)
+     This function returns the standard deviation of the mean, defined
+     as
 
-     Each line contains the lower and upper limits of the bin and the
-     contents of the bin.  Since the upper limits of the each bin are
-     the lower limits of the neighboring bins there is duplication of
-     these values but this allows the histogram to be manipulated with
-     line-oriented tools.
+          sd_mean = \Hat\sigma / \sqrt{N}
 
- -- Function: int gsl_histogram2d_fscanf (FILE * STREAM, gsl_histogram2d
-          * H)
-     This function reads formatted data from the stream STREAM into the
-     histogram H.  The data is assumed to be in the five-column format
-     used by 'gsl_histogram2d_fprintf'.  The histogram H must be
-     preallocated with the correct lengths since the function uses the
-     sizes of H to determine how many numbers to read.  The function
-     returns 0 for success and 'GSL_EFAILED' if there was a problem
-     reading from the file.
+ -- Function: double gsl_rstat_rms (gsl_rstat_workspace * W)
+     This function returns the root mean square of all data added to the
+     accumulator, defined as
 
-
-File: gsl-ref.info,  Node: Resampling from 2D histograms,  Next: Example programs for 2D histograms,  Prev: Reading and writing 2D histograms,  Up: Histograms
+          rms = \sqrt ( 1/N \sum x_i^2 )
 
-22.21 Resampling from 2D histograms
-===================================
+ -- Function: double gsl_rstat_skew (gsl_rstat_workspace * W)
+     This function returns the skewness of all data added to the
+     accumulator, defined as
 
-As in the one-dimensional case, a two-dimensional histogram made by
-counting events can be regarded as a measurement of a probability
-distribution.  Allowing for statistical error, the height of each bin
-represents the probability of an event where (x,y) falls in the range of
-that bin.  For a two-dimensional histogram the probability distribution
-takes the form p(x,y) dx dy where,
+          skew = (1/N) \sum ((x_i - \Hat\mu)/\Hat\sigma)^3
 
-     p(x,y) = n_{ij}/ (N A_{ij})
+ -- Function: double gsl_rstat_kurtosis (gsl_rstat_workspace * W)
+     This function returns the kurtosis of all data added to the
+     accumulator, defined as
 
-In this equation n_{ij} is the number of events in the bin which
-contains (x,y), A_{ij} is the area of the bin and N is the total number
-of events.  The distribution of events within each bin is assumed to be
-uniform.
+          kurtosis = ((1/N) \sum ((x_i - \Hat\mu)/\Hat\sigma)^4)  - 3
 
- -- Data Type: gsl_histogram2d_pdf
-     'size_t nx, ny'
-          This is the number of histogram bins used to approximate the
-          probability distribution function in the x and y directions.
-     'double * xrange'
-          The ranges of the bins in the x-direction are stored in an
-          array of NX + 1 elements pointed to by XRANGE.
-     'double * yrange'
-          The ranges of the bins in the y-direction are stored in an
-          array of NY + 1 pointed to by YRANGE.
-     'double * sum'
-          The cumulative probability for the bins is stored in an array
-          of NX*NY elements pointed to by SUM.
+ -- Function: double gsl_rstat_median (gsl_rstat_workspace * W)
+     This function returns an estimate of the median of the data added
+     to the accumulator.
 
-The following functions allow you to create a 'gsl_histogram2d_pdf'
-struct which represents a two dimensional probability distribution and
-generate random samples from it.
+
+File: gsl-ref.info,  Node: Running Statistics Quantiles,  Next: Running Statistics Example programs,  Prev: Running Statistics Current Statistics,  Up: Running Statistics
 
- -- Function: gsl_histogram2d_pdf * gsl_histogram2d_pdf_alloc (size_t
-          NX, size_t NY)
-     This function allocates memory for a two-dimensional probability
-     distribution of size NX-by-NY and returns a pointer to a newly
-     initialized 'gsl_histogram2d_pdf' struct.  If insufficient memory
-     is available a null pointer is returned and the error handler is
-     invoked with an error code of 'GSL_ENOMEM'.
+22.4 Quantiles
+==============
 
- -- Function: int gsl_histogram2d_pdf_init (gsl_histogram2d_pdf * P,
-          const gsl_histogram2d * H)
-     This function initializes the two-dimensional probability
-     distribution calculated P from the histogram H.  If any of the bins
-     of H are negative then the error handler is invoked with an error
-     code of 'GSL_EDOM' because a probability distribution cannot
-     contain negative values.
+The functions in this section estimate quantiles dynamically without
+storing the entire dataset, using the algorithm of Jain and Chlamtec,
+1985.  Only five points (markers) are stored which represent the minimum
+and maximum of the data, as well as current estimates of the p/2-, p-,
+and (1+p)/2-quantiles.  Each time a new data point is added, the marker
+positions and heights are updated.
+
+ -- Function: gsl_rstat_quantile_workspace * gsl_rstat_quantile_alloc
+          (const double P)
+     This function allocates a workspace for the dynamic estimation of
+     P-quantiles, where P is between 0 and 1.  The median corresponds to
+     p = 0.5.  The size of the workspace is O(1).
 
- -- Function: void gsl_histogram2d_pdf_free (gsl_histogram2d_pdf * P)
-     This function frees the two-dimensional probability distribution
-     function P and all of the memory associated with it.
+ -- Function: void gsl_rstat_quantile_free (gsl_rstat_quantile_workspace
+          * W)
+     This function frees the memory associated with the workspace W.
 
- -- Function: int gsl_histogram2d_pdf_sample (const gsl_histogram2d_pdf
-          * P, double R1, double R2, double * X, double * Y)
-     This function uses two uniform random numbers between zero and one,
-     R1 and R2, to compute a single random sample from the
-     two-dimensional probability distribution P.
+ -- Function: int gsl_rstat_quantile_reset (gsl_rstat_quantile_workspace
+          * W)
+     This function resets the workspace W to its initial state, so it
+     can begin working on a new set of data.
+
+ -- Function: int gsl_rstat_quantile_add (const double X,
+          gsl_rstat_quantile_workspace * W)
+     This function updates the estimate of the p-quantile with the new
+     data point X.
+
+ -- Function: double gsl_rstat_quantile_get
+          (gsl_rstat_quantile_workspace * W)
+     This function returns the current estimate of the p-quantile.
 
 
-File: gsl-ref.info,  Node: Example programs for 2D histograms,  Prev: Resampling from 2D histograms,  Up: Histograms
+File: gsl-ref.info,  Node: Running Statistics Example programs,  Next: Running Statistics References and Further Reading,  Prev: Running Statistics Quantiles,  Up: Running Statistics
 
-22.22 Example programs for 2D histograms
-========================================
+22.5 Examples
+=============
 
-This program demonstrates two features of two-dimensional histograms.
-First a 10-by-10 two-dimensional histogram is created with x and y
-running from 0 to 1.  Then a few sample points are added to the
-histogram, at (0.3,0.3) with a height of 1, at (0.8,0.1) with a height
-of 5 and at (0.7,0.9) with a height of 0.5.  This histogram with three
-events is used to generate a random sample of 1000 simulated events,
-which are printed out.
+Here is a basic example of how to use the statistical functions:
 
      #include <stdio.h>
-     #include <gsl/gsl_rng.h>
-     #include <gsl/gsl_histogram2d.h>
+     #include <gsl/gsl_rstat.h>
 
      int
-     main (void)
+     main(void)
      {
-       const gsl_rng_type * T;
-       gsl_rng * r;
-
-       gsl_histogram2d * h = gsl_histogram2d_alloc (10, 10);
-
-       gsl_histogram2d_set_ranges_uniform (h,
-                                           0.0, 1.0,
-                                           0.0, 1.0);
+       double data[5] = {17.2, 18.1, 16.5, 18.3, 12.6};
+       double mean, variance, largest, smallest, sd,
+              rms, sd_mean, median, skew, kurtosis;
+       gsl_rstat_workspace *rstat_p = gsl_rstat_alloc();
+       size_t i, n;
+
+       /* add data to rstat accumulator */
+       for (i = 0; i < 5; ++i)
+         gsl_rstat_add(data[i], rstat_p);
+
+       mean     = gsl_rstat_mean(rstat_p);
+       variance = gsl_rstat_variance(rstat_p);
+       largest  = gsl_rstat_max(rstat_p);
+       smallest = gsl_rstat_min(rstat_p);
+       median   = gsl_rstat_median(rstat_p);
+       sd       = gsl_rstat_sd(rstat_p);
+       sd_mean  = gsl_rstat_sd_mean(rstat_p);
+       skew     = gsl_rstat_skew(rstat_p);
+       rms      = gsl_rstat_rms(rstat_p);
+       kurtosis = gsl_rstat_kurtosis(rstat_p);
+       n        = gsl_rstat_n(rstat_p);
 
-       gsl_histogram2d_accumulate (h, 0.3, 0.3, 1);
-       gsl_histogram2d_accumulate (h, 0.8, 0.1, 5);
-       gsl_histogram2d_accumulate (h, 0.7, 0.9, 0.5);
+       printf ("The dataset is %g, %g, %g, %g, %g\n",
+              data[0], data[1], data[2], data[3], data[4]);
 
-       gsl_rng_env_setup ();
+       printf ("The sample mean is %g\n", mean);
+       printf ("The estimated variance is %g\n", variance);
+       printf ("The largest value is %g\n", largest);
+       printf ("The smallest value is %g\n", smallest);
+       printf( "The median is %g\n", median);
+       printf( "The standard deviation is %g\n", sd);
+       printf( "The root mean square is %g\n", rms);
+       printf( "The standard devation of the mean is %g\n", sd_mean);
+       printf( "The skew is %g\n", skew);
+       printf( "The kurtosis %g\n", kurtosis);
+       printf( "There are %zu items in the accumulator\n", n);
+
+       gsl_rstat_reset(rstat_p);
+       n = gsl_rstat_n(rstat_p);
+       printf( "There are %zu items in the accumulator\n", n);
 
-       T = gsl_rng_default;
-       r = gsl_rng_alloc (T);
+       gsl_rstat_free(rstat_p);
 
-       {
-         int i;
-         gsl_histogram2d_pdf * p
-           = gsl_histogram2d_pdf_alloc (h->nx, h->ny);
+       return 0;
+     }
 
-         gsl_histogram2d_pdf_init (p, h);
+   The program should produce the following output,
 
-         for (i = 0; i < 1000; i++) {
-           double x, y;
-           double u = gsl_rng_uniform (r);
-           double v = gsl_rng_uniform (r);
+     The dataset is 17.2, 18.1, 16.5, 18.3, 12.6
+     The sample mean is 16.54
+     The estimated variance is 5.373
+     The largest value is 18.3
+     The smallest value is 12.6
+     The median is 16.5
+     The standard deviation is 2.31797
+     The root mean square is 16.6694
+     The standard devation of the mean is 1.03663
+     The skew is -0.829058
+     The kurtosis -1.2217
+     There are 5 items in the accumulator
+     There are 0 items in the accumulator
+
+This next program estimates the lower quartile, median and upper
+quartile from 10,000 samples of a random Rayleigh distribution, using
+the P^2 algorithm of Jain and Chlamtec.  For comparison, the exact
+values are also computed from the sorted dataset.
 
-           gsl_histogram2d_pdf_sample (p, u, v, &x, &y);
+     #include <stdio.h>
+     #include <stdlib.h>
+     #include <gsl/gsl_rstat.h>
+     #include <gsl/gsl_statistics.h>
+     #include <gsl/gsl_rng.h>
+     #include <gsl/gsl_randist.h>
+     #include <gsl/gsl_sort.h>
 
-           printf ("%g %g\n", x, y);
+     int
+     main(void)
+     {
+       const size_t N = 10000;
+       double *data = malloc(N * sizeof(double));
+       gsl_rstat_quantile_workspace *work_25 = gsl_rstat_quantile_alloc(0.25);
+       gsl_rstat_quantile_workspace *work_50 = gsl_rstat_quantile_alloc(0.5);
+       gsl_rstat_quantile_workspace *work_75 = gsl_rstat_quantile_alloc(0.75);
+       gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+       double exact_p25, exact_p50, exact_p75;
+       double val_p25, val_p50, val_p75;
+       size_t i;
+
+       /* add data to quantile accumulators; also store data for exact
+        * comparisons */
+       for (i = 0; i < N; ++i)
+         {
+           data[i] = gsl_ran_rayleigh(r, 1.0);
+           gsl_rstat_quantile_add(data[i], work_25);
+           gsl_rstat_quantile_add(data[i], work_50);
+           gsl_rstat_quantile_add(data[i], work_75);
          }
 
-         gsl_histogram2d_pdf_free (p);
-       }
+       /* exact values */
+       gsl_sort(data, 1, N);
+       exact_p25 = gsl_stats_quantile_from_sorted_data(data, 1, N, 0.25);
+       exact_p50 = gsl_stats_quantile_from_sorted_data(data, 1, N, 0.5);
+       exact_p75 = gsl_stats_quantile_from_sorted_data(data, 1, N, 0.75);
+
+       /* estimated values */
+       val_p25 = gsl_rstat_quantile_get(work_25);
+       val_p50 = gsl_rstat_quantile_get(work_50);
+       val_p75 = gsl_rstat_quantile_get(work_75);
 
-       gsl_histogram2d_free (h);
-       gsl_rng_free (r);
+       printf ("The dataset is %g, %g, %g, %g, %g, ...\n",
+              data[0], data[1], data[2], data[3], data[4]);
+
+       printf ("0.25 quartile: exact = %.5f, estimated = %.5f, error = %.6e\n",
+               exact_p25, val_p25, (val_p25 - exact_p25) / exact_p25);
+       printf ("0.50 quartile: exact = %.5f, estimated = %.5f, error = %.6e\n",
+               exact_p50, val_p50, (val_p50 - exact_p50) / exact_p50);
+       printf ("0.75 quartile: exact = %.5f, estimated = %.5f, error = %.6e\n",
+               exact_p75, val_p75, (val_p75 - exact_p75) / exact_p75);
+
+       gsl_rstat_quantile_free(work_25);
+       gsl_rstat_quantile_free(work_50);
+       gsl_rstat_quantile_free(work_75);
+       gsl_rng_free(r);
+       free(data);
 
        return 0;
      }
 
-
-File: gsl-ref.info,  Node: N-tuples,  Next: Monte Carlo Integration,  Prev: Histograms,  Up: Top
+   The program should produce the following output,
 
-23 N-tuples
-***********
+     The dataset is 0.00645272, 0.0074002, 0.0120706, 0.0207256, 0.0227282, ...
+     0.25 quartile: exact = 0.75766, estimated = 0.75580, error = -2.450209e-03
+     0.50 quartile: exact = 1.17508, estimated = 1.17438, error = -5.995912e-04
+     0.75 quartile: exact = 1.65347, estimated = 1.65696, error = 2.110571e-03
 
-This chapter describes functions for creating and manipulating
-"ntuples", sets of values associated with events.  The ntuples are
-stored in files.  Their values can be extracted in any combination and
-"booked" in a histogram using a selection function.
+
+File: gsl-ref.info,  Node: Running Statistics References and Further Reading,  Prev: Running Statistics Example programs,  Up: Running Statistics
 
-   The values to be stored are held in a user-defined data structure,
-and an ntuple is created associating this data structure with a file.
-The values are then written to the file (normally inside a loop) using
-the ntuple functions described below.
+22.6 References and Further Reading
+===================================
 
-   A histogram can be created from ntuple data by providing a selection
-function and a value function.  The selection function specifies whether
-an event should be included in the subset to be analyzed or not.  The
-value function computes the entry to be added to the histogram for each
-event.
+The algorithm used to dynamically estimate p-quantiles is described in
+the paper,
+     R. Jain and I. Chlamtac.  'The P^2 algorithm for dynamic
+     calculation of quantiles and histograms without storing
+     observations', Communications of the ACM, Volume 28 (October),
+     Number 10, 1985, p.  1076-1085.
 
-   All the ntuple functions are defined in the header file
-'gsl_ntuple.h'
+
+File: gsl-ref.info,  Node: Histograms,  Next: N-tuples,  Prev: Running Statistics,  Up: Top
 
-* Menu:
+23 Histograms
+*************
 
-* The ntuple struct::           
-* Creating ntuples::            
-* Opening an existing ntuple file::  
-* Writing ntuples::             
-* Reading ntuples ::            
-* Closing an ntuple file::      
-* Histogramming ntuple values::  
-* Example ntuple programs::     
-* Ntuple References and Further Reading::  
+This chapter describes functions for creating histograms.  Histograms
+provide a convenient way of summarizing the distribution of a set of
+data.  A histogram consists of a set of "bins" which count the number of
+events falling into a given range of a continuous variable x.  In GSL
+the bins of a histogram contain floating-point numbers, so they can be
+used to record both integer and non-integer distributions.  The bins can
+use arbitrary sets of ranges (uniformly spaced bins are the default).
+Both one and two-dimensional histograms are supported.
 
-
-File: gsl-ref.info,  Node: The ntuple struct,  Next: Creating ntuples,  Up: N-tuples
+   Once a histogram has been created it can also be converted into a
+probability distribution function.  The library provides efficient
+routines for selecting random samples from probability distributions.
+This can be useful for generating simulations based on real data.
 
-23.1 The ntuple struct
-======================
+   The functions are declared in the header files 'gsl_histogram.h' and
+'gsl_histogram2d.h'.
 
-Ntuples are manipulated using the 'gsl_ntuple' struct.  This struct
-contains information on the file where the ntuple data is stored, a
-pointer to the current ntuple data row and the size of the user-defined
-ntuple data struct.
+* Menu:
 
-     typedef struct {
-         FILE * file;
-         void * ntuple_data;
-         size_t size;
-     } gsl_ntuple;
+* The histogram struct::        
+* Histogram allocation::        
+* Copying Histograms::          
+* Updating and accessing histogram elements::  
+* Searching histogram ranges::  
+* Histogram Statistics::        
+* Histogram Operations::        
+* Reading and writing histograms::  
+* Resampling from histograms::  
+* The histogram probability distribution struct::  
+* Example programs for histograms::  
+* Two dimensional histograms::  
+* The 2D histogram struct::     
+* 2D Histogram allocation::     
+* Copying 2D Histograms::       
+* Updating and accessing 2D histogram elements::  
+* Searching 2D histogram ranges::  
+* 2D Histogram Statistics::     
+* 2D Histogram Operations::     
+* Reading and writing 2D histograms::  
+* Resampling from 2D histograms::  
+* Example programs for 2D histograms::  
 
 
-File: gsl-ref.info,  Node: Creating ntuples,  Next: Opening an existing ntuple file,  Prev: The ntuple struct,  Up: N-tuples
+File: gsl-ref.info,  Node: The histogram struct,  Next: Histogram allocation,  Up: Histograms
 
-23.2 Creating ntuples
-=====================
+23.1 The histogram struct
+=========================
 
- -- Function: gsl_ntuple * gsl_ntuple_create (char * FILENAME, void *
-          NTUPLE_DATA, size_t SIZE)
-     This function creates a new write-only ntuple file FILENAME for
-     ntuples of size SIZE and returns a pointer to the newly created
-     ntuple struct.  Any existing file with the same name is truncated
-     to zero length and overwritten.  A pointer to memory for the
-     current ntuple row NTUPLE_DATA must be supplied--this is used to
-     copy ntuples in and out of the file.
+A histogram is defined by the following struct,
 
-
-File: gsl-ref.info,  Node: Opening an existing ntuple file,  Next: Writing ntuples,  Prev: Creating ntuples,  Up: N-tuples
+ -- Data Type: gsl_histogram
+     'size_t n'
+          This is the number of histogram bins
+     'double * range'
+          The ranges of the bins are stored in an array of N+1 elements
+          pointed to by RANGE.
+     'double * bin'
+          The counts for each bin are stored in an array of N elements
+          pointed to by BIN.  The bins are floating-point numbers, so
+          you can increment them by non-integer values if necessary.
 
-23.3 Opening an existing ntuple file
-====================================
+The range for BIN[i] is given by RANGE[i] to RANGE[i+1].  For n bins
+there are n+1 entries in the array RANGE.  Each bin is inclusive at the
+lower end and exclusive at the upper end.  Mathematically this means
+that the bins are defined by the following inequality,
+     bin[i] corresponds to range[i] <= x < range[i+1]
 
- -- Function: gsl_ntuple * gsl_ntuple_open (char * FILENAME, void *
-          NTUPLE_DATA, size_t SIZE)
-     This function opens an existing ntuple file FILENAME for reading
-     and returns a pointer to a corresponding ntuple struct.  The
-     ntuples in the file must have size SIZE.  A pointer to memory for
-     the current ntuple row NTUPLE_DATA must be supplied--this is used
-     to copy ntuples in and out of the file.
+Here is a diagram of the correspondence between ranges and bins on the
+number-line for x,
 
-
-File: gsl-ref.info,  Node: Writing ntuples,  Next: Reading ntuples,  Prev: Opening an existing ntuple file,  Up: N-tuples
 
-23.4 Writing ntuples
-====================
+          [ bin[0] )[ bin[1] )[ bin[2] )[ bin[3] )[ bin[4] )
+       ---|---------|---------|---------|---------|---------|---  x
+        r[0]      r[1]      r[2]      r[3]      r[4]      r[5]
 
- -- Function: int gsl_ntuple_write (gsl_ntuple * NTUPLE)
-     This function writes the current ntuple NTUPLE->NTUPLE_DATA of size
-     NTUPLE->SIZE to the corresponding file.
+In this picture the values of the RANGE array are denoted by r.  On the
+left-hand side of each bin the square bracket '[' denotes an inclusive
+lower bound (r <= x), and the round parentheses ')' on the right-hand
+side denote an exclusive upper bound (x < r).  Thus any samples which
+fall on the upper end of the histogram are excluded.  If you want to
+include this value for the last bin you will need to add an extra bin to
+your histogram.
 
- -- Function: int gsl_ntuple_bookdata (gsl_ntuple * NTUPLE)
-     This function is a synonym for 'gsl_ntuple_write'.
+   The 'gsl_histogram' struct and its associated functions are defined
+in the header file 'gsl_histogram.h'.
 
 
-File: gsl-ref.info,  Node: Reading ntuples,  Next: Closing an ntuple file,  Prev: Writing ntuples,  Up: N-tuples
+File: gsl-ref.info,  Node: Histogram allocation,  Next: Copying Histograms,  Prev: The histogram struct,  Up: Histograms
 
-23.5 Reading ntuples
-====================
+23.2 Histogram allocation
+=========================
 
- -- Function: int gsl_ntuple_read (gsl_ntuple * NTUPLE)
-     This function reads the current row of the ntuple file for NTUPLE
-     and stores the values in NTUPLE->DATA.
+The functions for allocating memory to a histogram follow the style of
+'malloc' and 'free'.  In addition they also perform their own error
+checking.  If there is insufficient memory available to allocate a
+histogram then the functions call the error handler (with an error
+number of 'GSL_ENOMEM') in addition to returning a null pointer.  Thus
+if you use the library error handler to abort your program then it isn't
+necessary to check every histogram 'alloc'.
 
-
-File: gsl-ref.info,  Node: Closing an ntuple file,  Next: Histogramming ntuple values,  Prev: Reading ntuples,  Up: N-tuples
+ -- Function: gsl_histogram * gsl_histogram_alloc (size_t N)
+     This function allocates memory for a histogram with N bins, and
+     returns a pointer to a newly created 'gsl_histogram' struct.  If
+     insufficient memory is available a null pointer is returned and the
+     error handler is invoked with an error code of 'GSL_ENOMEM'.  The
+     bins and ranges are not initialized, and should be prepared using
+     one of the range-setting functions below in order to make the
+     histogram ready for use.
 
-23.6 Closing an ntuple file
-===========================
+ -- Function: int gsl_histogram_set_ranges (gsl_histogram * H, const
+          double RANGE[], size_t SIZE)
+     This function sets the ranges of the existing histogram H using the
+     array RANGE of size SIZE.  The values of the histogram bins are
+     reset to zero.  The 'range' array should contain the desired bin
+     limits.  The ranges can be arbitrary, subject to the restriction
+     that they are monotonically increasing.
 
- -- Function: int gsl_ntuple_close (gsl_ntuple * NTUPLE)
-     This function closes the ntuple file NTUPLE and frees its
-     associated allocated memory.
+     The following example shows how to create a histogram with
+     logarithmic bins with ranges [1,10), [10,100) and [100,1000).
 
-
-File: gsl-ref.info,  Node: Histogramming ntuple values,  Next: Example ntuple programs,  Prev: Closing an ntuple file,  Up: N-tuples
+          gsl_histogram * h = gsl_histogram_alloc (3);
 
-23.7 Histogramming ntuple values
-================================
+          /* bin[0] covers the range 1 <= x < 10 */
+          /* bin[1] covers the range 10 <= x < 100 */
+          /* bin[2] covers the range 100 <= x < 1000 */
 
-Once an ntuple has been created its contents can be histogrammed in
-various ways using the function 'gsl_ntuple_project'.  Two user-defined
-functions must be provided, a function to select events and a function
-to compute scalar values.  The selection function and the value function
-both accept the ntuple row as a first argument and other parameters as a
-second argument.
+          double range[4] = { 1.0, 10.0, 100.0, 1000.0 };
 
-   The "selection function" determines which ntuple rows are selected
-for histogramming.  It is defined by the following struct,
-
-     typedef struct {
-       int (* function) (void * ntuple_data, void * params);
-       void * params;
-     } gsl_ntuple_select_fn;
-
-The struct component FUNCTION should return a non-zero value for each
-ntuple row that is to be included in the histogram.
+          gsl_histogram_set_ranges (h, range, 4);
 
-   The "value function" computes scalar values for those ntuple rows
-selected by the selection function,
+     Note that the size of the RANGE array should be defined to be one
+     element bigger than the number of bins.  The additional element is
+     required for the upper value of the final bin.
 
-     typedef struct {
-       double (* function) (void * ntuple_data, void * params);
-       void * params;
-     } gsl_ntuple_value_fn;
+ -- Function: int gsl_histogram_set_ranges_uniform (gsl_histogram * H,
+          double XMIN, double XMAX)
+     This function sets the ranges of the existing histogram H to cover
+     the range XMIN to XMAX uniformly.  The values of the histogram bins
+     are reset to zero.  The bin ranges are shown in the table below,
+          bin[0] corresponds to xmin <= x < xmin + d
+          bin[1] corresponds to xmin + d <= x < xmin + 2 d
+          ......
+          bin[n-1] corresponds to xmin + (n-1)d <= x < xmax
 
-In this case the struct component FUNCTION should return the value to be
-added to the histogram for the ntuple row.
+     where d is the bin spacing, d = (xmax-xmin)/n.
 
- -- Function: int gsl_ntuple_project (gsl_histogram * H, gsl_ntuple *
-          NTUPLE, gsl_ntuple_value_fn * VALUE_FUNC, gsl_ntuple_select_fn
-          * SELECT_FUNC)
-     This function updates the histogram H from the ntuple NTUPLE using
-     the functions VALUE_FUNC and SELECT_FUNC.  For each ntuple row
-     where the selection function SELECT_FUNC is non-zero the
-     corresponding value of that row is computed using the function
-     VALUE_FUNC and added to the histogram.  Those ntuple rows where
-     SELECT_FUNC returns zero are ignored.  New entries are added to the
-     histogram, so subsequent calls can be used to accumulate further
-     data in the same histogram.
+ -- Function: void gsl_histogram_free (gsl_histogram * H)
+     This function frees the histogram H and all of the memory
+     associated with it.
 
 
-File: gsl-ref.info,  Node: Example ntuple programs,  Next: Ntuple References and Further Reading,  Prev: Histogramming ntuple values,  Up: N-tuples
+File: gsl-ref.info,  Node: Copying Histograms,  Next: Updating and accessing histogram elements,  Prev: Histogram allocation,  Up: Histograms
 
-23.8 Examples
-=============
+23.3 Copying Histograms
+=======================
 
-The following example programs demonstrate the use of ntuples in
-managing a large dataset.  The first program creates a set of 10,000
-simulated "events", each with 3 associated values (x,y,z).  These are
-generated from a Gaussian distribution with unit variance, for
-demonstration purposes, and written to the ntuple file 'test.dat'.
+ -- Function: int gsl_histogram_memcpy (gsl_histogram * DEST, const
+          gsl_histogram * SRC)
+     This function copies the histogram SRC into the pre-existing
+     histogram DEST, making DEST into an exact copy of SRC.  The two
+     histograms must be of the same size.
 
-     #include <gsl/gsl_ntuple.h>
-     #include <gsl/gsl_rng.h>
-     #include <gsl/gsl_randist.h>
+ -- Function: gsl_histogram * gsl_histogram_clone (const gsl_histogram *
+          SRC)
+     This function returns a pointer to a newly created histogram which
+     is an exact copy of the histogram SRC.
 
-     struct data
-     {
-       double x;
-       double y;
-       double z;
-     };
+
+File: gsl-ref.info,  Node: Updating and accessing histogram elements,  Next: Searching histogram ranges,  Prev: Copying Histograms,  Up: Histograms
 
-     int
-     main (void)
-     {
-       const gsl_rng_type * T;
-       gsl_rng * r;
+23.4 Updating and accessing histogram elements
+==============================================
 
-       struct data ntuple_row;
-       int i;
+There are two ways to access histogram bins, either by specifying an x
+coordinate or by using the bin-index directly.  The functions for
+accessing the histogram through x coordinates use a binary search to
+identify the bin which covers the appropriate range.
 
-       gsl_ntuple *ntuple
-         = gsl_ntuple_create ("test.dat", &ntuple_row,
-                              sizeof (ntuple_row));
+ -- Function: int gsl_histogram_increment (gsl_histogram * H, double X)
+     This function updates the histogram H by adding one (1.0) to the
+     bin whose range contains the coordinate X.
 
-       gsl_rng_env_setup ();
+     If X lies in the valid range of the histogram then the function
+     returns zero to indicate success.  If X is less than the lower
+     limit of the histogram then the function returns 'GSL_EDOM', and
+     none of bins are modified.  Similarly, if the value of X is greater
+     than or equal to the upper limit of the histogram then the function
+     returns 'GSL_EDOM', and none of the bins are modified.  The error
+     handler is not called, however, since it is often necessary to
+     compute histograms for a small range of a larger dataset, ignoring
+     the values outside the range of interest.
 
-       T = gsl_rng_default;
-       r = gsl_rng_alloc (T);
+ -- Function: int gsl_histogram_accumulate (gsl_histogram * H, double X,
+          double WEIGHT)
+     This function is similar to 'gsl_histogram_increment' but increases
+     the value of the appropriate bin in the histogram H by the
+     floating-point number WEIGHT.
 
-       for (i = 0; i < 10000; i++)
-         {
-           ntuple_row.x = gsl_ran_ugaussian (r);
-           ntuple_row.y = gsl_ran_ugaussian (r);
-           ntuple_row.z = gsl_ran_ugaussian (r);
+ -- Function: double gsl_histogram_get (const gsl_histogram * H, size_t
+          I)
+     This function returns the contents of the I-th bin of the histogram
+     H.  If I lies outside the valid range of indices for the histogram
+     then the error handler is called with an error code of 'GSL_EDOM'
+     and the function returns 0.
 
-           gsl_ntuple_write (ntuple);
-         }
+ -- Function: int gsl_histogram_get_range (const gsl_histogram * H,
+          size_t I, double * LOWER, double * UPPER)
+     This function finds the upper and lower range limits of the I-th
+     bin of the histogram H.  If the index I is valid then the
+     corresponding range limits are stored in LOWER and UPPER.  The
+     lower limit is inclusive (i.e.  events with this coordinate are
+     included in the bin) and the upper limit is exclusive (i.e.  events
+     with the coordinate of the upper limit are excluded and fall in the
+     neighboring higher bin, if it exists).  The function returns 0 to
+     indicate success.  If I lies outside the valid range of indices for
+     the histogram then the error handler is called and the function
+     returns an error code of 'GSL_EDOM'.
 
-       gsl_ntuple_close (ntuple);
-       gsl_rng_free (r);
+ -- Function: double gsl_histogram_max (const gsl_histogram * H)
+ -- Function: double gsl_histogram_min (const gsl_histogram * H)
+ -- Function: size_t gsl_histogram_bins (const gsl_histogram * H)
+     These functions return the maximum upper and minimum lower range
+     limits and the number of bins of the histogram H.  They provide a
+     way of determining these values without accessing the
+     'gsl_histogram' struct directly.
 
-       return 0;
-     }
+ -- Function: void gsl_histogram_reset (gsl_histogram * H)
+     This function resets all the bins in the histogram H to zero.
 
-The next program analyses the ntuple data in the file 'test.dat'.  The
-analysis procedure is to compute the squared-magnitude of each event,
-E^2=x^2+y^2+z^2, and select only those which exceed a lower limit of
-1.5.  The selected events are then histogrammed using their E^2 values.
+
+File: gsl-ref.info,  Node: Searching histogram ranges,  Next: Histogram Statistics,  Prev: Updating and accessing histogram elements,  Up: Histograms
 
-     #include <math.h>
-     #include <gsl/gsl_ntuple.h>
-     #include <gsl/gsl_histogram.h>
+23.5 Searching histogram ranges
+===============================
 
-     struct data
-     {
-       double x;
-       double y;
-       double z;
-     };
+The following functions are used by the access and update routines to
+locate the bin which corresponds to a given x coordinate.
 
-     int sel_func (void *ntuple_data, void *params);
-     double val_func (void *ntuple_data, void *params);
+ -- Function: int gsl_histogram_find (const gsl_histogram * H, double X,
+          size_t * I)
+     This function finds and sets the index I to the bin number which
+     covers the coordinate X in the histogram H.  The bin is located
+     using a binary search.  The search includes an optimization for
+     histograms with uniform range, and will return the correct bin
+     immediately in this case.  If X is found in the range of the
+     histogram then the function sets the index I and returns
+     'GSL_SUCCESS'.  If X lies outside the valid range of the histogram
+     then the function returns 'GSL_EDOM' and the error handler is
+     invoked.
 
-     int
-     main (void)
-     {
-       struct data ntuple_row;
+
+File: gsl-ref.info,  Node: Histogram Statistics,  Next: Histogram Operations,  Prev: Searching histogram ranges,  Up: Histograms
 
-       gsl_ntuple *ntuple
-         = gsl_ntuple_open ("test.dat", &ntuple_row,
-                            sizeof (ntuple_row));
-       double lower = 1.5;
+23.6 Histogram Statistics
+=========================
 
-       gsl_ntuple_select_fn S;
-       gsl_ntuple_value_fn V;
+ -- Function: double gsl_histogram_max_val (const gsl_histogram * H)
+     This function returns the maximum value contained in the histogram
+     bins.
 
-       gsl_histogram *h = gsl_histogram_alloc (100);
-       gsl_histogram_set_ranges_uniform(h, 0.0, 10.0);
+ -- Function: size_t gsl_histogram_max_bin (const gsl_histogram * H)
+     This function returns the index of the bin containing the maximum
+     value.  In the case where several bins contain the same maximum
+     value the smallest index is returned.
 
-       S.function = &sel_func;
-       S.params = &lower;
+ -- Function: double gsl_histogram_min_val (const gsl_histogram * H)
+     This function returns the minimum value contained in the histogram
+     bins.
 
-       V.function = &val_func;
-       V.params = 0;
+ -- Function: size_t gsl_histogram_min_bin (const gsl_histogram * H)
+     This function returns the index of the bin containing the minimum
+     value.  In the case where several bins contain the same maximum
+     value the smallest index is returned.
 
-       gsl_ntuple_project (h, ntuple, &V, &S);
-       gsl_histogram_fprintf (stdout, h, "%f", "%f");
-       gsl_histogram_free (h);
-       gsl_ntuple_close (ntuple);
+ -- Function: double gsl_histogram_mean (const gsl_histogram * H)
+     This function returns the mean of the histogrammed variable, where
+     the histogram is regarded as a probability distribution.  Negative
+     bin values are ignored for the purposes of this calculation.  The
+     accuracy of the result is limited by the bin width.
 
-       return 0;
-     }
+ -- Function: double gsl_histogram_sigma (const gsl_histogram * H)
+     This function returns the standard deviation of the histogrammed
+     variable, where the histogram is regarded as a probability
+     distribution.  Negative bin values are ignored for the purposes of
+     this calculation.  The accuracy of the result is limited by the bin
+     width.
 
-     int
-     sel_func (void *ntuple_data, void *params)
-     {
-       struct data * data = (struct data *) ntuple_data;
-       double x, y, z, E2, scale;
-       scale = *(double *) params;
+ -- Function: double gsl_histogram_sum (const gsl_histogram * H)
+     This function returns the sum of all bin values.  Negative bin
+     values are included in the sum.
 
-       x = data->x;
-       y = data->y;
-       z = data->z;
+
+File: gsl-ref.info,  Node: Histogram Operations,  Next: Reading and writing histograms,  Prev: Histogram Statistics,  Up: Histograms
 
-       E2 = x * x + y * y + z * z;
+23.7 Histogram Operations
+=========================
 
-       return E2 > scale;
-     }
+ -- Function: int gsl_histogram_equal_bins_p (const gsl_histogram * H1,
+          const gsl_histogram * H2)
+     This function returns 1 if the all of the individual bin ranges of
+     the two histograms are identical, and 0 otherwise.
 
-     double
-     val_func (void *ntuple_data, void *params)
-     {
-       struct data * data = (struct data *) ntuple_data;
-       double x, y, z;
-
-       x = data->x;
-       y = data->y;
-       z = data->z;
+ -- Function: int gsl_histogram_add (gsl_histogram * H1, const
+          gsl_histogram * H2)
+     This function adds the contents of the bins in histogram H2 to the
+     corresponding bins of histogram H1, i.e.  h'_1(i) = h_1(i) +
+     h_2(i).  The two histograms must have identical bin ranges.
 
-       return x * x + y * y + z * z;
-     }
+ -- Function: int gsl_histogram_sub (gsl_histogram * H1, const
+          gsl_histogram * H2)
+     This function subtracts the contents of the bins in histogram H2
+     from the corresponding bins of histogram H1, i.e.  h'_1(i) = h_1(i)
+     - h_2(i).  The two histograms must have identical bin ranges.
 
-   The following plot shows the distribution of the selected events.
-Note the cut-off at the lower bound.
+ -- Function: int gsl_histogram_mul (gsl_histogram * H1, const
+          gsl_histogram * H2)
+     This function multiplies the contents of the bins of histogram H1
+     by the contents of the corresponding bins in histogram H2, i.e.
+     h'_1(i) = h_1(i) * h_2(i).  The two histograms must have identical
+     bin ranges.
 
-
-File: gsl-ref.info,  Node: Ntuple References and Further Reading,  Prev: Example ntuple programs,  Up: N-tuples
+ -- Function: int gsl_histogram_div (gsl_histogram * H1, const
+          gsl_histogram * H2)
+     This function divides the contents of the bins of histogram H1 by
+     the contents of the corresponding bins in histogram H2, i.e.
+     h'_1(i) = h_1(i) / h_2(i).  The two histograms must have identical
+     bin ranges.
 
-23.9 References and Further Reading
-===================================
+ -- Function: int gsl_histogram_scale (gsl_histogram * H, double SCALE)
+     This function multiplies the contents of the bins of histogram H by
+     the constant SCALE, i.e.  h'_1(i) = h_1(i) * scale.
 
-Further information on the use of ntuples can be found in the
-documentation for the CERN packages PAW and HBOOK (available online).
+ -- Function: int gsl_histogram_shift (gsl_histogram * H, double OFFSET)
+     This function shifts the contents of the bins of histogram H by the
+     constant OFFSET, i.e.  h'_1(i) = h_1(i) + offset.
 
 
-File: gsl-ref.info,  Node: Monte Carlo Integration,  Next: Simulated Annealing,  Prev: N-tuples,  Up: Top
-
-24 Monte Carlo Integration
-**************************
+File: gsl-ref.info,  Node: Reading and writing histograms,  Next: Resampling from histograms,  Prev: Histogram Operations,  Up: Histograms
 
-This chapter describes routines for multidimensional Monte Carlo
-integration.  These include the traditional Monte Carlo method and
-adaptive algorithms such as VEGAS and MISER which use importance
-sampling and stratified sampling techniques.  Each algorithm computes an
-estimate of a multidimensional definite integral of the form,
+23.8 Reading and writing histograms
+===================================
 
-     I = \int_xl^xu dx \int_yl^yu  dy ...  f(x, y, ...)
+The library provides functions for reading and writing histograms to a
+file as binary data or formatted text.
 
-over a hypercubic region ((x_l,x_u), (y_l,y_u), ...) using a fixed
-number of function calls.  The routines also provide a statistical
-estimate of the error on the result.  This error estimate should be
-taken as a guide rather than as a strict error bound--random sampling of
-the region may not uncover all the important features of the function,
-resulting in an underestimate of the error.
+ -- Function: int gsl_histogram_fwrite (FILE * STREAM, const
+          gsl_histogram * H)
+     This function writes the ranges and bins of the histogram H to the
+     stream STREAM in binary format.  The return value is 0 for success
+     and 'GSL_EFAILED' if there was a problem writing to the file.
+     Since the data is written in the native binary format it may not be
+     portable between different architectures.
 
-   The functions are defined in separate header files for each routine,
-'gsl_monte_plain.h', 'gsl_monte_miser.h' and 'gsl_monte_vegas.h'.
+ -- Function: int gsl_histogram_fread (FILE * STREAM, gsl_histogram * H)
+     This function reads into the histogram H from the open stream
+     STREAM in binary format.  The histogram H must be preallocated with
+     the correct size since the function uses the number of bins in H to
+     determine how many bytes to read.  The return value is 0 for
+     success and 'GSL_EFAILED' if there was a problem reading from the
+     file.  The data is assumed to have been written in the native
+     binary format on the same architecture.
 
-* Menu:
+ -- Function: int gsl_histogram_fprintf (FILE * STREAM, const
+          gsl_histogram * H, const char * RANGE_FORMAT, const char *
+          BIN_FORMAT)
+     This function writes the ranges and bins of the histogram H
+     line-by-line to the stream STREAM using the format specifiers
+     RANGE_FORMAT and BIN_FORMAT.  These should be one of the '%g', '%e'
+     or '%f' formats for floating point numbers.  The function returns 0
+     for success and 'GSL_EFAILED' if there was a problem writing to the
+     file.  The histogram output is formatted in three columns, and the
+     columns are separated by spaces, like this,
 
-* Monte Carlo Interface::       
-* PLAIN Monte Carlo::  
-* MISER::                       
-* VEGAS::                       
-* Monte Carlo Examples::        
-* Monte Carlo Integration References and Further Reading::  
+          range[0] range[1] bin[0]
+          range[1] range[2] bin[1]
+          range[2] range[3] bin[2]
+          ....
+          range[n-1] range[n] bin[n-1]
 
-
-File: gsl-ref.info,  Node: Monte Carlo Interface,  Next: PLAIN Monte Carlo,  Up: Monte Carlo Integration
+     The values of the ranges are formatted using RANGE_FORMAT and the
+     value of the bins are formatted using BIN_FORMAT.  Each line
+     contains the lower and upper limit of the range of the bins and the
+     value of the bin itself.  Since the upper limit of one bin is the
+     lower limit of the next there is duplication of these values
+     between lines but this allows the histogram to be manipulated with
+     line-oriented tools.
 
-24.1 Interface
-==============
+ -- Function: int gsl_histogram_fscanf (FILE * STREAM, gsl_histogram *
+          H)
+     This function reads formatted data from the stream STREAM into the
+     histogram H.  The data is assumed to be in the three-column format
+     used by 'gsl_histogram_fprintf'.  The histogram H must be
+     preallocated with the correct length since the function uses the
+     size of H to determine how many numbers to read.  The function
+     returns 0 for success and 'GSL_EFAILED' if there was a problem
+     reading from the file.
 
-All of the Monte Carlo integration routines use the same general form of
-interface.  There is an allocator to allocate memory for control
-variables and workspace, a routine to initialize those control
-variables, the integrator itself, and a function to free the space when
-done.
+
+File: gsl-ref.info,  Node: Resampling from histograms,  Next: The histogram probability distribution struct,  Prev: Reading and writing histograms,  Up: Histograms
 
-   Each integration function requires a random number generator to be
-supplied, and returns an estimate of the integral and its standard
-deviation.  The accuracy of the result is determined by the number of
-function calls specified by the user.  If a known level of accuracy is
-required this can be achieved by calling the integrator several times
-and averaging the individual results until the desired accuracy is
-obtained.
+23.9 Resampling from histograms
+===============================
 
-   Random sample points used within the Monte Carlo routines are always
-chosen strictly within the integration region, so that endpoint
-singularities are automatically avoided.
+A histogram made by counting events can be regarded as a measurement of
+a probability distribution.  Allowing for statistical error, the height
+of each bin represents the probability of an event where the value of x
+falls in the range of that bin.  The probability distribution function
+has the one-dimensional form p(x)dx where,
 
-   The function to be integrated has its own datatype, defined in the
-header file 'gsl_monte.h'.
+     p(x) = n_i/ (N w_i)
 
- -- Data Type: gsl_monte_function
+In this equation n_i is the number of events in the bin which contains
+x, w_i is the width of the bin and N is the total number of events.  The
+distribution of events within each bin is assumed to be uniform.
 
-     This data type defines a general function with parameters for Monte
-     Carlo integration.
+
+File: gsl-ref.info,  Node: The histogram probability distribution struct,  Next: Example programs for histograms,  Prev: Resampling from histograms,  Up: Histograms
 
-     'double (* f) (double * X, size_t DIM, void * PARAMS)'
-          this function should return the value f(x,params) for the
-          argument X and parameters PARAMS, where X is an array of size
-          DIM giving the coordinates of the point where the function is
-          to be evaluated.
+23.10 The histogram probability distribution struct
+===================================================
 
-     'size_t dim'
-          the number of dimensions for X.
+The probability distribution function for a histogram consists of a set
+of "bins" which measure the probability of an event falling into a given
+range of a continuous variable x.  A probability distribution function
+is defined by the following struct, which actually stores the cumulative
+probability distribution function.  This is the natural quantity for
+generating samples via the inverse transform method, because there is a
+one-to-one mapping between the cumulative probability distribution and
+the range [0,1].  It can be shown that by taking a uniform random number
+in this range and finding its corresponding coordinate in the cumulative
+probability distribution we obtain samples with the desired probability
+distribution.
 
-     'void * params'
-          a pointer to the parameters of the function.
+ -- Data Type: gsl_histogram_pdf
+     'size_t n'
+          This is the number of bins used to approximate the probability
+          distribution function.
+     'double * range'
+          The ranges of the bins are stored in an array of N+1 elements
+          pointed to by RANGE.
+     'double * sum'
+          The cumulative probability for the bins is stored in an array
+          of N elements pointed to by SUM.
 
-Here is an example for a quadratic function in two dimensions,
+The following functions allow you to create a 'gsl_histogram_pdf' struct
+which represents this probability distribution and generate random
+samples from it.
 
-     f(x,y) = a x^2 + b x y + c y^2
+ -- Function: gsl_histogram_pdf * gsl_histogram_pdf_alloc (size_t N)
+     This function allocates memory for a probability distribution with
+     N bins and returns a pointer to a newly initialized
+     'gsl_histogram_pdf' struct.  If insufficient memory is available a
+     null pointer is returned and the error handler is invoked with an
+     error code of 'GSL_ENOMEM'.
 
-with a = 3, b = 2, c = 1.  The following code defines a
-'gsl_monte_function' 'F' which you could pass to an integrator:
+ -- Function: int gsl_histogram_pdf_init (gsl_histogram_pdf * P, const
+          gsl_histogram * H)
+     This function initializes the probability distribution P with the
+     contents of the histogram H.  If any of the bins of H are negative
+     then the error handler is invoked with an error code of 'GSL_EDOM'
+     because a probability distribution cannot contain negative values.
 
-     struct my_f_params { double a; double b; double c; };
+ -- Function: void gsl_histogram_pdf_free (gsl_histogram_pdf * P)
+     This function frees the probability distribution function P and all
+     of the memory associated with it.
 
-     double
-     my_f (double x[], size_t dim, void * p) {
-        struct my_f_params * fp = (struct my_f_params *)p;
+ -- Function: double gsl_histogram_pdf_sample (const gsl_histogram_pdf *
+          P, double R)
+     This function uses R, a uniform random number between zero and one,
+     to compute a single random sample from the probability distribution
+     P.  The algorithm used to compute the sample s is given by the
+     following formula,
 
-        if (dim != 2)
-           {
-             fprintf (stderr, "error: dim != 2");
-             abort ();
-           }
+          s = range[i] + delta * (range[i+1] - range[i])
 
-        return  fp->a * x[0] * x[0]
-                  + fp->b * x[0] * x[1]
-                    + fp->c * x[1] * x[1];
-     }
+     where i is the index which satisfies sum[i] <= r < sum[i+1] and
+     delta is (r - sum[i])/(sum[i+1] - sum[i]).
 
-     gsl_monte_function F;
-     struct my_f_params params = { 3.0, 2.0, 1.0 };
+
+File: gsl-ref.info,  Node: Example programs for histograms,  Next: Two dimensional histograms,  Prev: The histogram probability distribution struct,  Up: Histograms
 
-     F.f = &my_f;
-     F.dim = 2;
-     F.params = &params;
+23.11 Example programs for histograms
+=====================================
 
-The function f(x) can be evaluated using the following macro,
+The following program shows how to make a simple histogram of a column
+of numerical data supplied on 'stdin'.  The program takes three
+arguments, specifying the upper and lower bounds of the histogram and
+the number of bins.  It then reads numbers from 'stdin', one line at a
+time, and adds them to the histogram.  When there is no more data to
+read it prints out the accumulated histogram using
+'gsl_histogram_fprintf'.
 
-     #define GSL_MONTE_FN_EVAL(F,x)
-         (*((F)->f))(x,(F)->dim,(F)->params)
+     #include <stdio.h>
+     #include <stdlib.h>
+     #include <gsl/gsl_histogram.h>
 
-
-File: gsl-ref.info,  Node: PLAIN Monte Carlo,  Next: MISER,  Prev: Monte Carlo Interface,  Up: Monte Carlo Integration
+     int
+     main (int argc, char **argv)
+     {
+       double a, b;
+       size_t n;
 
-24.2 PLAIN Monte Carlo
-======================
+       if (argc != 4)
+         {
+           printf ("Usage: gsl-histogram xmin xmax n\n"
+                   "Computes a histogram of the data "
+                   "on stdin using n bins from xmin "
+                   "to xmax\n");
+           exit (0);
+         }
 
-The plain Monte Carlo algorithm samples points randomly from the
-integration region to estimate the integral and its error.  Using this
-algorithm the estimate of the integral E(f; N) for N randomly
-distributed points x_i is given by,
+       a = atof (argv[1]);
+       b = atof (argv[2]);
+       n = atoi (argv[3]);
 
-     E(f; N) = =  V <f> = (V / N) \sum_i^N f(x_i)
+       {
+         double x;
+         gsl_histogram * h = gsl_histogram_alloc (n);
+         gsl_histogram_set_ranges_uniform (h, a, b);
 
-where V is the volume of the integration region.  The error on this
-estimate \sigma(E;N) is calculated from the estimated variance of the
-mean,
+         while (fscanf (stdin, "%lg", &x) == 1)
+           {
+             gsl_histogram_increment (h, x);
+           }
+         gsl_histogram_fprintf (stdout, h, "%g", "%g");
+         gsl_histogram_free (h);
+       }
+       exit (0);
+     }
 
-     \sigma^2 (E; N) = (V^2 / N^2) \sum_i^N (f(x_i) -  <f>)^2.
+Here is an example of the program in use.  We generate 10000 random
+samples from a Cauchy distribution with a width of 30 and histogram them
+over the range -100 to 100, using 200 bins.
 
-For large N this variance decreases asymptotically as \Var(f)/N, where
-\Var(f) is the true variance of the function over the integration
-region.  The error estimate itself should decrease as
-\sigma(f)/\sqrt{N}.  The familiar law of errors decreasing as 1/\sqrt{N}
-applies--to reduce the error by a factor of 10 requires a 100-fold
-increase in the number of sample points.
+     $ gsl-randist 0 10000 cauchy 30
+        | gsl-histogram -100 100 200 > histogram.dat
 
-   The functions described in this section are declared in the header
-file 'gsl_monte_plain.h'.
+A plot of the resulting histogram shows the familiar shape of the Cauchy
+distribution and the fluctuations caused by the finite sample size.
 
- -- Function: gsl_monte_plain_state * gsl_monte_plain_alloc (size_t DIM)
-     This function allocates and initializes a workspace for Monte Carlo
-     integration in DIM dimensions.
+     $ awk '{print $1, $3 ; print $2, $3}' histogram.dat
+        | graph -T X
 
- -- Function: int gsl_monte_plain_init (gsl_monte_plain_state* S)
-     This function initializes a previously allocated integration state.
-     This allows an existing workspace to be reused for different
-     integrations.
+
+File: gsl-ref.info,  Node: Two dimensional histograms,  Next: The 2D histogram struct,  Prev: Example programs for histograms,  Up: Histograms
 
- -- Function: int gsl_monte_plain_integrate (gsl_monte_function * F,
-          const double XL[], const double XU[], size_t DIM, size_t
-          CALLS, gsl_rng * R, gsl_monte_plain_state * S, double *
-          RESULT, double * ABSERR)
-     This routines uses the plain Monte Carlo algorithm to integrate the
-     function F over the DIM-dimensional hypercubic region defined by
-     the lower and upper limits in the arrays XL and XU, each of size
-     DIM.  The integration uses a fixed number of function calls CALLS,
-     and obtains random sampling points using the random number
-     generator R.  A previously allocated workspace S must be supplied.
-     The result of the integration is returned in RESULT, with an
-     estimated absolute error ABSERR.
+23.12 Two dimensional histograms
+================================
 
- -- Function: void gsl_monte_plain_free (gsl_monte_plain_state * S)
-     This function frees the memory associated with the integrator state
-     S.
+A two dimensional histogram consists of a set of "bins" which count the
+number of events falling in a given area of the (x,y) plane.  The
+simplest way to use a two dimensional histogram is to record
+two-dimensional position information, n(x,y).  Another possibility is to
+form a "joint distribution" by recording related variables.  For example
+a detector might record both the position of an event (x) and the amount
+of energy it deposited E.  These could be histogrammed as the joint
+distribution n(x,E).
 
 
-File: gsl-ref.info,  Node: MISER,  Next: VEGAS,  Prev: PLAIN Monte Carlo,  Up: Monte Carlo Integration
-
-24.3 MISER
-==========
+File: gsl-ref.info,  Node: The 2D histogram struct,  Next: 2D Histogram allocation,  Prev: Two dimensional histograms,  Up: Histograms
 
-The MISER algorithm of Press and Farrar is based on recursive stratified
-sampling.  This technique aims to reduce the overall integration error
-by concentrating integration points in the regions of highest variance.
+23.13 The 2D histogram struct
+=============================
 
-   The idea of stratified sampling begins with the observation that for
-two disjoint regions a and b with Monte Carlo estimates of the integral
-E_a(f) and E_b(f) and variances \sigma_a^2(f) and \sigma_b^2(f), the
-variance \Var(f) of the combined estimate E(f) = (1/2) (E_a(f) + E_b(f))
-is given by,
+Two dimensional histograms are defined by the following struct,
 
-     \Var(f) = (\sigma_a^2(f) / 4 N_a) + (\sigma_b^2(f) / 4 N_b).
+ -- Data Type: gsl_histogram2d
+     'size_t nx, ny'
+          This is the number of histogram bins in the x and y
+          directions.
+     'double * xrange'
+          The ranges of the bins in the x-direction are stored in an
+          array of NX + 1 elements pointed to by XRANGE.
+     'double * yrange'
+          The ranges of the bins in the y-direction are stored in an
+          array of NY + 1 elements pointed to by YRANGE.
+     'double * bin'
+          The counts for each bin are stored in an array pointed to by
+          BIN.  The bins are floating-point numbers, so you can
+          increment them by non-integer values if necessary.  The array
+          BIN stores the two dimensional array of bins in a single block
+          of memory according to the mapping 'bin(i,j)' = 'bin[i * ny +
+          j]'.
 
-It can be shown that this variance is minimized by distributing the
-points such that,
+The range for 'bin(i,j)' is given by 'xrange[i]' to 'xrange[i+1]' in the
+x-direction and 'yrange[j]' to 'yrange[j+1]' in the y-direction.  Each
+bin is inclusive at the lower end and exclusive at the upper end.
+Mathematically this means that the bins are defined by the following
+inequality,
+     bin(i,j) corresponds to xrange[i] <= x < xrange[i+1]
+                         and yrange[j] <= y < yrange[j+1]
 
-     N_a / (N_a + N_b) = \sigma_a / (\sigma_a + \sigma_b).
+Note that any samples which fall on the upper sides of the histogram are
+excluded.  If you want to include these values for the side bins you
+will need to add an extra row or column to your histogram.
 
-Hence the smallest error estimate is obtained by allocating sample
-points in proportion to the standard deviation of the function in each
-sub-region.
+   The 'gsl_histogram2d' struct and its associated functions are defined
+in the header file 'gsl_histogram2d.h'.
 
-   The MISER algorithm proceeds by bisecting the integration region
-along one coordinate axis to give two sub-regions at each step.  The
-direction is chosen by examining all d possible bisections and selecting
-the one which will minimize the combined variance of the two
-sub-regions.  The variance in the sub-regions is estimated by sampling
-with a fraction of the total number of points available to the current
-step.  The same procedure is then repeated recursively for each of the
-two half-spaces from the best bisection.  The remaining sample points
-are allocated to the sub-regions using the formula for N_a and N_b.
-This recursive allocation of integration points continues down to a
-user-specified depth where each sub-region is integrated using a plain
-Monte Carlo estimate.  These individual values and their error estimates
-are then combined upwards to give an overall result and an estimate of
-its error.
+
+File: gsl-ref.info,  Node: 2D Histogram allocation,  Next: Copying 2D Histograms,  Prev: The 2D histogram struct,  Up: Histograms
 
-   The functions described in this section are declared in the header
-file 'gsl_monte_miser.h'.
+23.14 2D Histogram allocation
+=============================
 
- -- Function: gsl_monte_miser_state * gsl_monte_miser_alloc (size_t DIM)
-     This function allocates and initializes a workspace for Monte Carlo
-     integration in DIM dimensions.  The workspace is used to maintain
-     the state of the integration.
+The functions for allocating memory to a 2D histogram follow the style
+of 'malloc' and 'free'.  In addition they also perform their own error
+checking.  If there is insufficient memory available to allocate a
+histogram then the functions call the error handler (with an error
+number of 'GSL_ENOMEM') in addition to returning a null pointer.  Thus
+if you use the library error handler to abort your program then it isn't
+necessary to check every 2D histogram 'alloc'.
 
- -- Function: int gsl_monte_miser_init (gsl_monte_miser_state* S)
-     This function initializes a previously allocated integration state.
-     This allows an existing workspace to be reused for different
-     integrations.
+ -- Function: gsl_histogram2d * gsl_histogram2d_alloc (size_t NX, size_t
+          NY)
+     This function allocates memory for a two-dimensional histogram with
+     NX bins in the x direction and NY bins in the y direction.  The
+     function returns a pointer to a newly created 'gsl_histogram2d'
+     struct.  If insufficient memory is available a null pointer is
+     returned and the error handler is invoked with an error code of
+     'GSL_ENOMEM'.  The bins and ranges must be initialized with one of
+     the functions below before the histogram is ready for use.
 
- -- Function: int gsl_monte_miser_integrate (gsl_monte_function * F,
-          const double XL[], const double XU[], size_t DIM, size_t
-          CALLS, gsl_rng * R, gsl_monte_miser_state * S, double *
-          RESULT, double * ABSERR)
-     This routines uses the MISER Monte Carlo algorithm to integrate the
-     function F over the DIM-dimensional hypercubic region defined by
-     the lower and upper limits in the arrays XL and XU, each of size
-     DIM.  The integration uses a fixed number of function calls CALLS,
-     and obtains random sampling points using the random number
-     generator R.  A previously allocated workspace S must be supplied.
-     The result of the integration is returned in RESULT, with an
-     estimated absolute error ABSERR.
+ -- Function: int gsl_histogram2d_set_ranges (gsl_histogram2d * H, const
+          double XRANGE[], size_t XSIZE, const double YRANGE[], size_t
+          YSIZE)
+     This function sets the ranges of the existing histogram H using the
+     arrays XRANGE and YRANGE of size XSIZE and YSIZE respectively.  The
+     values of the histogram bins are reset to zero.
 
- -- Function: void gsl_monte_miser_free (gsl_monte_miser_state * S)
-     This function frees the memory associated with the integrator state
-     S.
+ -- Function: int gsl_histogram2d_set_ranges_uniform (gsl_histogram2d *
+          H, double XMIN, double XMAX, double YMIN, double YMAX)
+     This function sets the ranges of the existing histogram H to cover
+     the ranges XMIN to XMAX and YMIN to YMAX uniformly.  The values of
+     the histogram bins are reset to zero.
 
-   The MISER algorithm has several configurable parameters which can be
-changed using the following two functions.(1)
+ -- Function: void gsl_histogram2d_free (gsl_histogram2d * H)
+     This function frees the 2D histogram H and all of the memory
+     associated with it.
 
- -- Function: void gsl_monte_miser_params_get (const
-          gsl_monte_miser_state * S, gsl_monte_miser_params * PARAMS)
-     This function copies the parameters of the integrator state into
-     the user-supplied PARAMS structure.
+
+File: gsl-ref.info,  Node: Copying 2D Histograms,  Next: Updating and accessing 2D histogram elements,  Prev: 2D Histogram allocation,  Up: Histograms
 
- -- Function: void gsl_monte_miser_params_set (gsl_monte_miser_state *
-          S, const gsl_monte_miser_params * PARAMS)
-     This function sets the integrator parameters based on values
-     provided in the PARAMS structure.
+23.15 Copying 2D Histograms
+===========================
 
-   Typically the values of the parameters are first read using
-'gsl_monte_miser_params_get', the necessary changes are made to the
-fields of the PARAMS structure, and the values are copied back into the
-integrator state using 'gsl_monte_miser_params_set'.  The functions use
-the 'gsl_monte_miser_params' structure which contains the following
-fields:
+ -- Function: int gsl_histogram2d_memcpy (gsl_histogram2d * DEST, const
+          gsl_histogram2d * SRC)
+     This function copies the histogram SRC into the pre-existing
+     histogram DEST, making DEST into an exact copy of SRC.  The two
+     histograms must be of the same size.
 
- -- Variable: double estimate_frac
-     This parameter specifies the fraction of the currently available
-     number of function calls which are allocated to estimating the
-     variance at each recursive step.  The default value is 0.1.
+ -- Function: gsl_histogram2d * gsl_histogram2d_clone (const
+          gsl_histogram2d * SRC)
+     This function returns a pointer to a newly created histogram which
+     is an exact copy of the histogram SRC.
 
- -- Variable: size_t min_calls
-     This parameter specifies the minimum number of function calls
-     required for each estimate of the variance.  If the number of
-     function calls allocated to the estimate using ESTIMATE_FRAC falls
-     below MIN_CALLS then MIN_CALLS are used instead.  This ensures that
-     each estimate maintains a reasonable level of accuracy.  The
-     default value of MIN_CALLS is '16 * dim'.
+
+File: gsl-ref.info,  Node: Updating and accessing 2D histogram elements,  Next: Searching 2D histogram ranges,  Prev: Copying 2D Histograms,  Up: Histograms
 
- -- Variable: size_t min_calls_per_bisection
-     This parameter specifies the minimum number of function calls
-     required to proceed with a bisection step.  When a recursive step
-     has fewer calls available than MIN_CALLS_PER_BISECTION it performs
-     a plain Monte Carlo estimate of the current sub-region and
-     terminates its branch of the recursion.  The default value of this
-     parameter is '32 * min_calls'.
+23.16 Updating and accessing 2D histogram elements
+==================================================
 
- -- Variable: double alpha
-     This parameter controls how the estimated variances for the two
-     sub-regions of a bisection are combined when allocating points.
-     With recursive sampling the overall variance should scale better
-     than 1/N, since the values from the sub-regions will be obtained
-     using a procedure which explicitly minimizes their variance.  To
-     accommodate this behavior the MISER algorithm allows the total
-     variance to depend on a scaling parameter \alpha,
+You can access the bins of a two-dimensional histogram either by
+specifying a pair of (x,y) coordinates or by using the bin indices (i,j)
+directly.  The functions for accessing the histogram through (x,y)
+coordinates use binary searches in the x and y directions to identify
+the bin which covers the appropriate range.
 
-          \Var(f) = {\sigma_a \over N_a^\alpha} + {\sigma_b \over N_b^\alpha}.
+ -- Function: int gsl_histogram2d_increment (gsl_histogram2d * H, double
+          X, double Y)
+     This function updates the histogram H by adding one (1.0) to the
+     bin whose x and y ranges contain the coordinates (X,Y).
 
-     The authors of the original paper describing MISER recommend the
-     value \alpha = 2 as a good choice, obtained from numerical
-     experiments, and this is used as the default value in this
-     implementation.
+     If the point (x,y) lies inside the valid ranges of the histogram
+     then the function returns zero to indicate success.  If (x,y) lies
+     outside the limits of the histogram then the function returns
+     'GSL_EDOM', and none of the bins are modified.  The error handler
+     is not called, since it is often necessary to compute histograms
+     for a small range of a larger dataset, ignoring any coordinates
+     outside the range of interest.
 
- -- Variable: double dither
-     This parameter introduces a random fractional variation of size
-     DITHER into each bisection, which can be used to break the symmetry
-     of integrands which are concentrated near the exact center of the
-     hypercubic integration region.  The default value of dither is
-     zero, so no variation is introduced.  If needed, a typical value of
-     DITHER is 0.1.
+ -- Function: int gsl_histogram2d_accumulate (gsl_histogram2d * H,
+          double X, double Y, double WEIGHT)
+     This function is similar to 'gsl_histogram2d_increment' but
+     increases the value of the appropriate bin in the histogram H by
+     the floating-point number WEIGHT.
 
-   ---------- Footnotes ----------
+ -- Function: double gsl_histogram2d_get (const gsl_histogram2d * H,
+          size_t I, size_t J)
+     This function returns the contents of the (I,J)-th bin of the
+     histogram H.  If (I,J) lies outside the valid range of indices for
+     the histogram then the error handler is called with an error code
+     of 'GSL_EDOM' and the function returns 0.
 
-   (1) The previous method of accessing these fields directly through
-the 'gsl_monte_miser_state' struct is now deprecated.
+ -- Function: int gsl_histogram2d_get_xrange (const gsl_histogram2d * H,
+          size_t I, double * XLOWER, double * XUPPER)
+ -- Function: int gsl_histogram2d_get_yrange (const gsl_histogram2d * H,
+          size_t J, double * YLOWER, double * YUPPER)
+     These functions find the upper and lower range limits of the I-th
+     and J-th bins in the x and y directions of the histogram H.  The
+     range limits are stored in XLOWER and XUPPER or YLOWER and YUPPER.
+     The lower limits are inclusive (i.e.  events with these coordinates
+     are included in the bin) and the upper limits are exclusive (i.e.
+     events with the value of the upper limit are not included and fall
+     in the neighboring higher bin, if it exists).  The functions return
+     0 to indicate success.  If I or J lies outside the valid range of
+     indices for the histogram then the error handler is called with an
+     error code of 'GSL_EDOM'.
 
-
-File: gsl-ref.info,  Node: VEGAS,  Next: Monte Carlo Examples,  Prev: MISER,  Up: Monte Carlo Integration
+ -- Function: double gsl_histogram2d_xmax (const gsl_histogram2d * H)
+ -- Function: double gsl_histogram2d_xmin (const gsl_histogram2d * H)
+ -- Function: size_t gsl_histogram2d_nx (const gsl_histogram2d * H)
+ -- Function: double gsl_histogram2d_ymax (const gsl_histogram2d * H)
+ -- Function: double gsl_histogram2d_ymin (const gsl_histogram2d * H)
+ -- Function: size_t gsl_histogram2d_ny (const gsl_histogram2d * H)
+     These functions return the maximum upper and minimum lower range
+     limits and the number of bins for the x and y directions of the
+     histogram H.  They provide a way of determining these values
+     without accessing the 'gsl_histogram2d' struct directly.
 
-24.4 VEGAS
-==========
+ -- Function: void gsl_histogram2d_reset (gsl_histogram2d * H)
+     This function resets all the bins of the histogram H to zero.
 
-The VEGAS algorithm of Lepage is based on importance sampling.  It
-samples points from the probability distribution described by the
-function |f|, so that the points are concentrated in the regions that
-make the largest contribution to the integral.
+
+File: gsl-ref.info,  Node: Searching 2D histogram ranges,  Next: 2D Histogram Statistics,  Prev: Updating and accessing 2D histogram elements,  Up: Histograms
 
-   In general, if the Monte Carlo integral of f is sampled with points
-distributed according to a probability distribution described by the
-function g, we obtain an estimate E_g(f; N),
+23.17 Searching 2D histogram ranges
+===================================
 
-     E_g(f; N) = E(f/g; N)
+The following functions are used by the access and update routines to
+locate the bin which corresponds to a given (x,y) coordinate.
 
-with a corresponding variance,
+ -- Function: int gsl_histogram2d_find (const gsl_histogram2d * H,
+          double X, double Y, size_t * I, size_t * J)
+     This function finds and sets the indices I and J to the bin which
+     covers the coordinates (X,Y).  The bin is located using a binary
+     search.  The search includes an optimization for histograms with
+     uniform ranges, and will return the correct bin immediately in this
+     case.  If (x,y) is found then the function sets the indices (I,J)
+     and returns 'GSL_SUCCESS'.  If (x,y) lies outside the valid range
+     of the histogram then the function returns 'GSL_EDOM' and the error
+     handler is invoked.
 
-     \Var_g(f; N) = \Var(f/g; N).
+
+File: gsl-ref.info,  Node: 2D Histogram Statistics,  Next: 2D Histogram Operations,  Prev: Searching 2D histogram ranges,  Up: Histograms
 
-If the probability distribution is chosen as g = |f|/I(|f|) then it can
-be shown that the variance V_g(f; N) vanishes, and the error in the
-estimate will be zero.  In practice it is not possible to sample from
-the exact distribution g for an arbitrary function, so importance
-sampling algorithms aim to produce efficient approximations to the
-desired distribution.
+23.18 2D Histogram Statistics
+=============================
 
-   The VEGAS algorithm approximates the exact distribution by making a
-number of passes over the integration region while histogramming the
-function f.  Each histogram is used to define a sampling distribution
-for the next pass.  Asymptotically this procedure converges to the
-desired distribution.  In order to avoid the number of histogram bins
-growing like K^d the probability distribution is approximated by a
-separable function: g(x_1, x_2, ...) = g_1(x_1) g_2(x_2) ... so that the
-number of bins required is only Kd.  This is equivalent to locating the
-peaks of the function from the projections of the integrand onto the
-coordinate axes.  The efficiency of VEGAS depends on the validity of
-this assumption.  It is most efficient when the peaks of the integrand
-are well-localized.  If an integrand can be rewritten in a form which is
-approximately separable this will increase the efficiency of integration
-with VEGAS.
+ -- Function: double gsl_histogram2d_max_val (const gsl_histogram2d * H)
+     This function returns the maximum value contained in the histogram
+     bins.
 
-   VEGAS incorporates a number of additional features, and combines both
-stratified sampling and importance sampling.  The integration region is
-divided into a number of "boxes", with each box getting a fixed number
-of points (the goal is 2).  Each box can then have a fractional number
-of bins, but if the ratio of bins-per-box is less than two, Vegas
-switches to a kind variance reduction (rather than importance sampling).
+ -- Function: void gsl_histogram2d_max_bin (const gsl_histogram2d * H,
+          size_t * I, size_t * J)
+     This function finds the indices of the bin containing the maximum
+     value in the histogram H and stores the result in (I,J).  In the
+     case where several bins contain the same maximum value the first
+     bin found is returned.
 
- -- Function: gsl_monte_vegas_state * gsl_monte_vegas_alloc (size_t DIM)
-     This function allocates and initializes a workspace for Monte Carlo
-     integration in DIM dimensions.  The workspace is used to maintain
-     the state of the integration.
+ -- Function: double gsl_histogram2d_min_val (const gsl_histogram2d * H)
+     This function returns the minimum value contained in the histogram
+     bins.
 
- -- Function: int gsl_monte_vegas_init (gsl_monte_vegas_state* S)
-     This function initializes a previously allocated integration state.
-     This allows an existing workspace to be reused for different
-     integrations.
+ -- Function: void gsl_histogram2d_min_bin (const gsl_histogram2d * H,
+          size_t * I, size_t * J)
+     This function finds the indices of the bin containing the minimum
+     value in the histogram H and stores the result in (I,J).  In the
+     case where several bins contain the same maximum value the first
+     bin found is returned.
 
- -- Function: int gsl_monte_vegas_integrate (gsl_monte_function * F,
-          double XL[], double XU[], size_t DIM, size_t CALLS, gsl_rng *
-          R, gsl_monte_vegas_state * S, double * RESULT, double *
-          ABSERR)
-     This routines uses the VEGAS Monte Carlo algorithm to integrate the
-     function F over the DIM-dimensional hypercubic region defined by
-     the lower and upper limits in the arrays XL and XU, each of size
-     DIM.  The integration uses a fixed number of function calls CALLS,
-     and obtains random sampling points using the random number
-     generator R.  A previously allocated workspace S must be supplied.
-     The result of the integration is returned in RESULT, with an
-     estimated absolute error ABSERR.  The result and its error estimate
-     are based on a weighted average of independent samples.  The
-     chi-squared per degree of freedom for the weighted average is
-     returned via the state struct component, S->CHISQ, and must be
-     consistent with 1 for the weighted average to be reliable.
+ -- Function: double gsl_histogram2d_xmean (const gsl_histogram2d * H)
+     This function returns the mean of the histogrammed x variable,
+     where the histogram is regarded as a probability distribution.
+     Negative bin values are ignored for the purposes of this
+     calculation.
 
- -- Function: void gsl_monte_vegas_free (gsl_monte_vegas_state * S)
-     This function frees the memory associated with the integrator state
-     S.
+ -- Function: double gsl_histogram2d_ymean (const gsl_histogram2d * H)
+     This function returns the mean of the histogrammed y variable,
+     where the histogram is regarded as a probability distribution.
+     Negative bin values are ignored for the purposes of this
+     calculation.
 
-   The VEGAS algorithm computes a number of independent estimates of the
-integral internally, according to the 'iterations' parameter described
-below, and returns their weighted average.  Random sampling of the
-integrand can occasionally produce an estimate where the error is zero,
-particularly if the function is constant in some regions.  An estimate
-with zero error causes the weighted average to break down and must be
-handled separately.  In the original Fortran implementations of VEGAS
-the error estimate is made non-zero by substituting a small value
-(typically '1e-30').  The implementation in GSL differs from this and
-avoids the use of an arbitrary constant--it either assigns the value a
-weight which is the average weight of the preceding estimates or
-discards it according to the following procedure,
+ -- Function: double gsl_histogram2d_xsigma (const gsl_histogram2d * H)
+     This function returns the standard deviation of the histogrammed x
+     variable, where the histogram is regarded as a probability
+     distribution.  Negative bin values are ignored for the purposes of
+     this calculation.
 
-current estimate has zero error, weighted average has finite error
+ -- Function: double gsl_histogram2d_ysigma (const gsl_histogram2d * H)
+     This function returns the standard deviation of the histogrammed y
+     variable, where the histogram is regarded as a probability
+     distribution.  Negative bin values are ignored for the purposes of
+     this calculation.
 
-     The current estimate is assigned a weight which is the average
-     weight of the preceding estimates.
+ -- Function: double gsl_histogram2d_cov (const gsl_histogram2d * H)
+     This function returns the covariance of the histogrammed x and y
+     variables, where the histogram is regarded as a probability
+     distribution.  Negative bin values are ignored for the purposes of
+     this calculation.
 
-current estimate has finite error, previous estimates had zero error
+ -- Function: double gsl_histogram2d_sum (const gsl_histogram2d * H)
+     This function returns the sum of all bin values.  Negative bin
+     values are included in the sum.
 
-     The previous estimates are discarded and the weighted averaging
-     procedure begins with the current estimate.
+
+File: gsl-ref.info,  Node: 2D Histogram Operations,  Next: Reading and writing 2D histograms,  Prev: 2D Histogram Statistics,  Up: Histograms
 
-current estimate has zero error, previous estimates had zero error
+23.19 2D Histogram Operations
+=============================
 
-     The estimates are averaged using the arithmetic mean, but no error
-     is computed.
+ -- Function: int gsl_histogram2d_equal_bins_p (const gsl_histogram2d *
+          H1, const gsl_histogram2d * H2)
+     This function returns 1 if all the individual bin ranges of the two
+     histograms are identical, and 0 otherwise.
 
-   The convergence of the algorithm can be tested using the overall
-chi-squared value of the results, which is available from the following
-function:
+ -- Function: int gsl_histogram2d_add (gsl_histogram2d * H1, const
+          gsl_histogram2d * H2)
+     This function adds the contents of the bins in histogram H2 to the
+     corresponding bins of histogram H1, i.e.  h'_1(i,j) = h_1(i,j) +
+     h_2(i,j).  The two histograms must have identical bin ranges.
 
- -- Function: double gsl_monte_vegas_chisq (const gsl_monte_vegas_state
-          * S)
-     This function returns the chi-squared per degree of freedom for the
-     weighted estimate of the integral.  The returned value should be
-     close to 1.  A value which differs significantly from 1 indicates
-     that the values from different iterations are inconsistent.  In
-     this case the weighted error will be under-estimated, and further
-     iterations of the algorithm are needed to obtain reliable results.
+ -- Function: int gsl_histogram2d_sub (gsl_histogram2d * H1, const
+          gsl_histogram2d * H2)
+     This function subtracts the contents of the bins in histogram H2
+     from the corresponding bins of histogram H1, i.e.  h'_1(i,j) =
+     h_1(i,j) - h_2(i,j).  The two histograms must have identical bin
+     ranges.
 
- -- Function: void gsl_monte_vegas_runval (const gsl_monte_vegas_state *
-          S, double * RESULT, double * SIGMA)
-     This function returns the raw (unaveraged) values of the integral
-     RESULT and its error SIGMA from the most recent iteration of the
-     algorithm.
+ -- Function: int gsl_histogram2d_mul (gsl_histogram2d * H1, const
+          gsl_histogram2d * H2)
+     This function multiplies the contents of the bins of histogram H1
+     by the contents of the corresponding bins in histogram H2, i.e.
+     h'_1(i,j) = h_1(i,j) * h_2(i,j).  The two histograms must have
+     identical bin ranges.
 
-   The VEGAS algorithm is highly configurable.  Several parameters can
-be changed using the following two functions.
+ -- Function: int gsl_histogram2d_div (gsl_histogram2d * H1, const
+          gsl_histogram2d * H2)
+     This function divides the contents of the bins of histogram H1 by
+     the contents of the corresponding bins in histogram H2, i.e.
+     h'_1(i,j) = h_1(i,j) / h_2(i,j).  The two histograms must have
+     identical bin ranges.
 
- -- Function: void gsl_monte_vegas_params_get (const
-          gsl_monte_vegas_state * S, gsl_monte_vegas_params * PARAMS)
-     This function copies the parameters of the integrator state into
-     the user-supplied PARAMS structure.
+ -- Function: int gsl_histogram2d_scale (gsl_histogram2d * H, double
+          SCALE)
+     This function multiplies the contents of the bins of histogram H by
+     the constant SCALE, i.e.  h'_1(i,j) = h_1(i,j) scale.
 
- -- Function: void gsl_monte_vegas_params_set (gsl_monte_vegas_state *
-          S, const gsl_monte_vegas_params * PARAMS)
-     This function sets the integrator parameters based on values
-     provided in the PARAMS structure.
+ -- Function: int gsl_histogram2d_shift (gsl_histogram2d * H, double
+          OFFSET)
+     This function shifts the contents of the bins of histogram H by the
+     constant OFFSET, i.e.  h'_1(i,j) = h_1(i,j) + offset.
 
-   Typically the values of the parameters are first read using
-'gsl_monte_vegas_params_get', the necessary changes are made to the
-fields of the PARAMS structure, and the values are copied back into the
-integrator state using 'gsl_monte_vegas_params_set'.  The functions use
-the 'gsl_monte_vegas_params' structure which contains the following
-fields:
+
+File: gsl-ref.info,  Node: Reading and writing 2D histograms,  Next: Resampling from 2D histograms,  Prev: 2D Histogram Operations,  Up: Histograms
 
- -- Variable: double alpha
-     The parameter 'alpha' controls the stiffness of the rebinning
-     algorithm.  It is typically set between one and two.  A value of
-     zero prevents rebinning of the grid.  The default value is 1.5.
+23.20 Reading and writing 2D histograms
+=======================================
 
- -- Variable: size_t iterations
-     The number of iterations to perform for each call to the routine.
-     The default value is 5 iterations.
+The library provides functions for reading and writing two dimensional
+histograms to a file as binary data or formatted text.
 
- -- Variable: int stage
-     Setting this determines the "stage" of the calculation.  Normally,
-     'stage = 0' which begins with a new uniform grid and empty weighted
-     average.  Calling VEGAS with 'stage = 1' retains the grid from the
-     previous run but discards the weighted average, so that one can
-     "tune" the grid using a relatively small number of points and then
-     do a large run with 'stage = 1' on the optimized grid.  Setting
-     'stage = 2' keeps the grid and the weighted average from the
-     previous run, but may increase (or decrease) the number of
-     histogram bins in the grid depending on the number of calls
-     available.  Choosing 'stage = 3' enters at the main loop, so that
-     nothing is changed, and is equivalent to performing additional
-     iterations in a previous call.
+ -- Function: int gsl_histogram2d_fwrite (FILE * STREAM, const
+          gsl_histogram2d * H)
+     This function writes the ranges and bins of the histogram H to the
+     stream STREAM in binary format.  The return value is 0 for success
+     and 'GSL_EFAILED' if there was a problem writing to the file.
+     Since the data is written in the native binary format it may not be
+     portable between different architectures.
 
- -- Variable: int mode
-     The possible choices are 'GSL_VEGAS_MODE_IMPORTANCE',
-     'GSL_VEGAS_MODE_STRATIFIED', 'GSL_VEGAS_MODE_IMPORTANCE_ONLY'.
-     This determines whether VEGAS will use importance sampling or
-     stratified sampling, or whether it can pick on its own.  In low
-     dimensions VEGAS uses strict stratified sampling (more precisely,
-     stratified sampling is chosen if there are fewer than 2 bins per
-     box).
+ -- Function: int gsl_histogram2d_fread (FILE * STREAM, gsl_histogram2d
+          * H)
+     This function reads into the histogram H from the stream STREAM in
+     binary format.  The histogram H must be preallocated with the
+     correct size since the function uses the number of x and y bins in
+     H to determine how many bytes to read.  The return value is 0 for
+     success and 'GSL_EFAILED' if there was a problem reading from the
+     file.  The data is assumed to have been written in the native
+     binary format on the same architecture.
 
- -- Variable: int verbose
- -- Variable: FILE * ostream
-     These parameters set the level of information printed by VEGAS.
-     All information is written to the stream OSTREAM.  The default
-     setting of VERBOSE is '-1', which turns off all output.  A VERBOSE
-     value of '0' prints summary information about the weighted average
-     and final result, while a value of '1' also displays the grid
-     coordinates.  A value of '2' prints information from the rebinning
-     procedure for each iteration.
+ -- Function: int gsl_histogram2d_fprintf (FILE * STREAM, const
+          gsl_histogram2d * H, const char * RANGE_FORMAT, const char *
+          BIN_FORMAT)
+     This function writes the ranges and bins of the histogram H
+     line-by-line to the stream STREAM using the format specifiers
+     RANGE_FORMAT and BIN_FORMAT.  These should be one of the '%g', '%e'
+     or '%f' formats for floating point numbers.  The function returns 0
+     for success and 'GSL_EFAILED' if there was a problem writing to the
+     file.  The histogram output is formatted in five columns, and the
+     columns are separated by spaces, like this,
 
-   The above fields and the CHISQ value can also be accessed directly in
-the 'gsl_monte_vegas_state' but such use is deprecated.
+          xrange[0] xrange[1] yrange[0] yrange[1] bin(0,0)
+          xrange[0] xrange[1] yrange[1] yrange[2] bin(0,1)
+          xrange[0] xrange[1] yrange[2] yrange[3] bin(0,2)
+          ....
+          xrange[0] xrange[1] yrange[ny-1] yrange[ny] bin(0,ny-1)
 
-
-File: gsl-ref.info,  Node: Monte Carlo Examples,  Next: Monte Carlo Integration References and Further Reading,  Prev: VEGAS,  Up: Monte Carlo Integration
+          xrange[1] xrange[2] yrange[0] yrange[1] bin(1,0)
+          xrange[1] xrange[2] yrange[1] yrange[2] bin(1,1)
+          xrange[1] xrange[2] yrange[1] yrange[2] bin(1,2)
+          ....
+          xrange[1] xrange[2] yrange[ny-1] yrange[ny] bin(1,ny-1)
 
-24.5 Examples
-=============
+          ....
 
-The example program below uses the Monte Carlo routines to estimate the
-value of the following 3-dimensional integral from the theory of random
-walks,
+          xrange[nx-1] xrange[nx] yrange[0] yrange[1] bin(nx-1,0)
+          xrange[nx-1] xrange[nx] yrange[1] yrange[2] bin(nx-1,1)
+          xrange[nx-1] xrange[nx] yrange[1] yrange[2] bin(nx-1,2)
+          ....
+          xrange[nx-1] xrange[nx] yrange[ny-1] yrange[ny] bin(nx-1,ny-1)
 
-     I = \int_{-pi}^{+pi} {dk_x/(2 pi)}
-         \int_{-pi}^{+pi} {dk_y/(2 pi)}
-         \int_{-pi}^{+pi} {dk_z/(2 pi)}
-          1 / (1 - cos(k_x)cos(k_y)cos(k_z)).
+     Each line contains the lower and upper limits of the bin and the
+     contents of the bin.  Since the upper limits of the each bin are
+     the lower limits of the neighboring bins there is duplication of
+     these values but this allows the histogram to be manipulated with
+     line-oriented tools.
 
-The analytic value of this integral can be shown to be I =
-\Gamma(1/4)^4/(4 \pi^3) = 1.393203929685676859....  The integral gives
-the mean time spent at the origin by a random walk on a body-centered
-cubic lattice in three dimensions.
+ -- Function: int gsl_histogram2d_fscanf (FILE * STREAM, gsl_histogram2d
+          * H)
+     This function reads formatted data from the stream STREAM into the
+     histogram H.  The data is assumed to be in the five-column format
+     used by 'gsl_histogram2d_fprintf'.  The histogram H must be
+     preallocated with the correct lengths since the function uses the
+     sizes of H to determine how many numbers to read.  The function
+     returns 0 for success and 'GSL_EFAILED' if there was a problem
+     reading from the file.
 
-   For simplicity we will compute the integral over the region (0,0,0)
-to (\pi,\pi,\pi) and multiply by 8 to obtain the full result.  The
-integral is slowly varying in the middle of the region but has
-integrable singularities at the corners (0,0,0), (0,\pi,\pi),
-(\pi,0,\pi) and (\pi,\pi,0).  The Monte Carlo routines only select
-points which are strictly within the integration region and so no
-special measures are needed to avoid these singularities.
+
+File: gsl-ref.info,  Node: Resampling from 2D histograms,  Next: Example programs for 2D histograms,  Prev: Reading and writing 2D histograms,  Up: Histograms
 
-     #include <stdlib.h>
-     #include <gsl/gsl_math.h>
-     #include <gsl/gsl_monte.h>
-     #include <gsl/gsl_monte_plain.h>
-     #include <gsl/gsl_monte_miser.h>
-     #include <gsl/gsl_monte_vegas.h>
+23.21 Resampling from 2D histograms
+===================================
 
-     /* Computation of the integral,
+As in the one-dimensional case, a two-dimensional histogram made by
+counting events can be regarded as a measurement of a probability
+distribution.  Allowing for statistical error, the height of each bin
+represents the probability of an event where (x,y) falls in the range of
+that bin.  For a two-dimensional histogram the probability distribution
+takes the form p(x,y) dx dy where,
 
-           I = int (dx dy dz)/(2pi)^3  1/(1-cos(x)cos(y)cos(z))
+     p(x,y) = n_{ij}/ (N A_{ij})
 
-        over (-pi,-pi,-pi) to (+pi, +pi, +pi).  The exact answer
-        is Gamma(1/4)^4/(4 pi^3).  This example is taken from
-        C.Itzykson, J.M.Drouffe, "Statistical Field Theory -
-        Volume 1", Section 1.1, p21, which cites the original
-        paper M.L.Glasser, I.J.Zucker, Proc.Natl.Acad.Sci.USA 74
-        1800 (1977) */
+In this equation n_{ij} is the number of events in the bin which
+contains (x,y), A_{ij} is the area of the bin and N is the total number
+of events.  The distribution of events within each bin is assumed to be
+uniform.
 
-     /* For simplicity we compute the integral over the region
-        (0,0,0) -> (pi,pi,pi) and multiply by 8 */
+ -- Data Type: gsl_histogram2d_pdf
+     'size_t nx, ny'
+          This is the number of histogram bins used to approximate the
+          probability distribution function in the x and y directions.
+     'double * xrange'
+          The ranges of the bins in the x-direction are stored in an
+          array of NX + 1 elements pointed to by XRANGE.
+     'double * yrange'
+          The ranges of the bins in the y-direction are stored in an
+          array of NY + 1 pointed to by YRANGE.
+     'double * sum'
+          The cumulative probability for the bins is stored in an array
+          of NX*NY elements pointed to by SUM.
 
-     double exact = 1.3932039296856768591842462603255;
+The following functions allow you to create a 'gsl_histogram2d_pdf'
+struct which represents a two dimensional probability distribution and
+generate random samples from it.
 
-     double
-     g (double *k, size_t dim, void *params)
-     {
-       double A = 1.0 / (M_PI * M_PI * M_PI);
-       return A / (1.0 - cos (k[0]) * cos (k[1]) * cos (k[2]));
-     }
+ -- Function: gsl_histogram2d_pdf * gsl_histogram2d_pdf_alloc (size_t
+          NX, size_t NY)
+     This function allocates memory for a two-dimensional probability
+     distribution of size NX-by-NY and returns a pointer to a newly
+     initialized 'gsl_histogram2d_pdf' struct.  If insufficient memory
+     is available a null pointer is returned and the error handler is
+     invoked with an error code of 'GSL_ENOMEM'.
 
-     void
-     display_results (char *title, double result, double error)
-     {
-       printf ("%s ==================\n", title);
-       printf ("result = % .6f\n", result);
-       printf ("sigma  = % .6f\n", error);
-       printf ("exact  = % .6f\n", exact);
-       printf ("error  = % .6f = %.2g sigma\n", result - exact,
-               fabs (result - exact) / error);
-     }
+ -- Function: int gsl_histogram2d_pdf_init (gsl_histogram2d_pdf * P,
+          const gsl_histogram2d * H)
+     This function initializes the two-dimensional probability
+     distribution calculated P from the histogram H.  If any of the bins
+     of H are negative then the error handler is invoked with an error
+     code of 'GSL_EDOM' because a probability distribution cannot
+     contain negative values.
 
-     int
-     main (void)
-     {
-       double res, err;
+ -- Function: void gsl_histogram2d_pdf_free (gsl_histogram2d_pdf * P)
+     This function frees the two-dimensional probability distribution
+     function P and all of the memory associated with it.
 
-       double xl[3] = { 0, 0, 0 };
-       double xu[3] = { M_PI, M_PI, M_PI };
+ -- Function: int gsl_histogram2d_pdf_sample (const gsl_histogram2d_pdf
+          * P, double R1, double R2, double * X, double * Y)
+     This function uses two uniform random numbers between zero and one,
+     R1 and R2, to compute a single random sample from the
+     two-dimensional probability distribution P.
 
-       const gsl_rng_type *T;
-       gsl_rng *r;
+
+File: gsl-ref.info,  Node: Example programs for 2D histograms,  Prev: Resampling from 2D histograms,  Up: Histograms
 
-       gsl_monte_function G = { &g, 3, 0 };
+23.22 Example programs for 2D histograms
+========================================
 
-       size_t calls = 500000;
+This program demonstrates two features of two-dimensional histograms.
+First a 10-by-10 two-dimensional histogram is created with x and y
+running from 0 to 1.  Then a few sample points are added to the
+histogram, at (0.3,0.3) with a height of 1, at (0.8,0.1) with a height
+of 5 and at (0.7,0.9) with a height of 0.5.  This histogram with three
+events is used to generate a random sample of 1000 simulated events,
+which are printed out.
 
-       gsl_rng_env_setup ();
+     #include <stdio.h>
+     #include <gsl/gsl_rng.h>
+     #include <gsl/gsl_histogram2d.h>
 
-       T = gsl_rng_default;
-       r = gsl_rng_alloc (T);
+     int
+     main (void)
+     {
+       const gsl_rng_type * T;
+       gsl_rng * r;
 
-       {
-         gsl_monte_plain_state *s = gsl_monte_plain_alloc (3);
-         gsl_monte_plain_integrate (&G, xl, xu, 3, calls, r, s,
-                                    &res, &err);
-         gsl_monte_plain_free (s);
+       gsl_histogram2d * h = gsl_histogram2d_alloc (10, 10);
 
-         display_results ("plain", res, err);
-       }
+       gsl_histogram2d_set_ranges_uniform (h,
+                                           0.0, 1.0,
+                                           0.0, 1.0);
 
-       {
-         gsl_monte_miser_state *s = gsl_monte_miser_alloc (3);
-         gsl_monte_miser_integrate (&G, xl, xu, 3, calls, r, s,
-                                    &res, &err);
-         gsl_monte_miser_free (s);
+       gsl_histogram2d_accumulate (h, 0.3, 0.3, 1);
+       gsl_histogram2d_accumulate (h, 0.8, 0.1, 5);
+       gsl_histogram2d_accumulate (h, 0.7, 0.9, 0.5);
 
-         display_results ("miser", res, err);
-       }
+       gsl_rng_env_setup ();
+
+       T = gsl_rng_default;
+       r = gsl_rng_alloc (T);
 
        {
-         gsl_monte_vegas_state *s = gsl_monte_vegas_alloc (3);
+         int i;
+         gsl_histogram2d_pdf * p
+           = gsl_histogram2d_pdf_alloc (h->nx, h->ny);
 
-         gsl_monte_vegas_integrate (&G, xl, xu, 3, 10000, r, s,
-                                    &res, &err);
-         display_results ("vegas warm-up", res, err);
+         gsl_histogram2d_pdf_init (p, h);
 
-         printf ("converging...\n");
+         for (i = 0; i < 1000; i++) {
+           double x, y;
+           double u = gsl_rng_uniform (r);
+           double v = gsl_rng_uniform (r);
 
-         do
-           {
-             gsl_monte_vegas_integrate (&G, xl, xu, 3, calls/5, r, s,
-                                        &res, &err);
-             printf ("result = % .6f sigma = % .6f "
-                     "chisq/dof = %.1f\n", res, err, gsl_monte_vegas_chisq (s));
-           }
-         while (fabs (gsl_monte_vegas_chisq (s) - 1.0) > 0.5);
+           gsl_histogram2d_pdf_sample (p, u, v, &x, &y);
 
-         display_results ("vegas final", res, err);
+           printf ("%g %g\n", x, y);
+         }
 
-         gsl_monte_vegas_free (s);
+         gsl_histogram2d_pdf_free (p);
        }
 
+       gsl_histogram2d_free (h);
        gsl_rng_free (r);
 
        return 0;
      }
 
-With 500,000 function calls the plain Monte Carlo algorithm achieves a
-fractional error of 1%.  The estimated error 'sigma' is roughly
-consistent with the actual error-the computed result differs from the
-true result by about 1.4 standard deviations,
+
+File: gsl-ref.info,  Node: N-tuples,  Next: Monte Carlo Integration,  Prev: Histograms,  Up: Top
 
-     plain ==================
-     result =  1.412209
-     sigma  =  0.013436
-     exact  =  1.393204
-     error  =  0.019005 = 1.4 sigma
+24 N-tuples
+***********
 
-The MISER algorithm reduces the error by a factor of four, and also
-correctly estimates the error,
+This chapter describes functions for creating and manipulating
+"ntuples", sets of values associated with events.  The ntuples are
+stored in files.  Their values can be extracted in any combination and
+"booked" in a histogram using a selection function.
 
-     miser ==================
-     result =  1.391322
-     sigma  =  0.003461
-     exact  =  1.393204
-     error  = -0.001882 = 0.54 sigma
+   The values to be stored are held in a user-defined data structure,
+and an ntuple is created associating this data structure with a file.
+The values are then written to the file (normally inside a loop) using
+the ntuple functions described below.
 
-In the case of the VEGAS algorithm the program uses an initial warm-up
-run of 10,000 function calls to prepare, or "warm up", the grid.  This
-is followed by a main run with five iterations of 100,000 function
-calls.  The chi-squared per degree of freedom for the five iterations
-are checked for consistency with 1, and the run is repeated if the
-results have not converged.  In this case the estimates are consistent
-on the first pass.
+   A histogram can be created from ntuple data by providing a selection
+function and a value function.  The selection function specifies whether
+an event should be included in the subset to be analyzed or not.  The
+value function computes the entry to be added to the histogram for each
+event.
 
-     vegas warm-up ==================
-     result =  1.392673
-     sigma  =  0.003410
-     exact  =  1.393204
-     error  = -0.000531 = 0.16 sigma
-     converging...
-     result =  1.393281 sigma =  0.000362 chisq/dof = 1.5
-     vegas final ==================
-     result =  1.393281
-     sigma  =  0.000362
-     exact  =  1.393204
-     error  =  0.000077 = 0.21 sigma
+   All the ntuple functions are defined in the header file
+'gsl_ntuple.h'
 
-If the value of 'chisq' had differed significantly from 1 it would
-indicate inconsistent results, with a correspondingly underestimated
-error.  The final estimate from VEGAS (using a similar number of
-function calls) is significantly more accurate than the other two
-algorithms.
+* Menu:
+
+* The ntuple struct::           
+* Creating ntuples::            
+* Opening an existing ntuple file::  
+* Writing ntuples::             
+* Reading ntuples ::            
+* Closing an ntuple file::      
+* Histogramming ntuple values::  
+* Example ntuple programs::     
+* Ntuple References and Further Reading::  
 
 
-File: gsl-ref.info,  Node: Monte Carlo Integration References and Further Reading,  Prev: Monte Carlo Examples,  Up: Monte Carlo Integration
+File: gsl-ref.info,  Node: The ntuple struct,  Next: Creating ntuples,  Up: N-tuples
 
-24.6 References and Further Reading
-===================================
+24.1 The ntuple struct
+======================
 
-The MISER algorithm is described in the following article by Press and
-Farrar,
+Ntuples are manipulated using the 'gsl_ntuple' struct.  This struct
+contains information on the file where the ntuple data is stored, a
+pointer to the current ntuple data row and the size of the user-defined
+ntuple data struct.
 
-     W.H. Press, G.R. Farrar, 'Recursive Stratified Sampling for
-     Multidimensional Monte Carlo Integration', Computers in Physics, v4
-     (1990), pp190-195.
+     typedef struct {
+         FILE * file;
+         void * ntuple_data;
+         size_t size;
+     } gsl_ntuple;
 
-The VEGAS algorithm is described in the following papers,
+
+File: gsl-ref.info,  Node: Creating ntuples,  Next: Opening an existing ntuple file,  Prev: The ntuple struct,  Up: N-tuples
 
-     G.P. Lepage, 'A New Algorithm for Adaptive Multidimensional
-     Integration', Journal of Computational Physics 27, 192-203, (1978)
+24.2 Creating ntuples
+=====================
 
-     G.P. Lepage, 'VEGAS: An Adaptive Multi-dimensional Integration
-     Program', Cornell preprint CLNS 80-447, March 1980
+ -- Function: gsl_ntuple * gsl_ntuple_create (char * FILENAME, void *
+          NTUPLE_DATA, size_t SIZE)
+     This function creates a new write-only ntuple file FILENAME for
+     ntuples of size SIZE and returns a pointer to the newly created
+     ntuple struct.  Any existing file with the same name is truncated
+     to zero length and overwritten.  A pointer to memory for the
+     current ntuple row NTUPLE_DATA must be supplied--this is used to
+     copy ntuples in and out of the file.
 
 
-File: gsl-ref.info,  Node: Simulated Annealing,  Next: Ordinary Differential Equations,  Prev: Monte Carlo Integration,  Up: Top
+File: gsl-ref.info,  Node: Opening an existing ntuple file,  Next: Writing ntuples,  Prev: Creating ntuples,  Up: N-tuples
 
-25 Simulated Annealing
-**********************
+24.3 Opening an existing ntuple file
+====================================
 
-Stochastic search techniques are used when the structure of a space is
-not well understood or is not smooth, so that techniques like Newton's
-method (which requires calculating Jacobian derivative matrices) cannot
-be used.  In particular, these techniques are frequently used to solve
-combinatorial optimization problems, such as the traveling salesman
-problem.
+ -- Function: gsl_ntuple * gsl_ntuple_open (char * FILENAME, void *
+          NTUPLE_DATA, size_t SIZE)
+     This function opens an existing ntuple file FILENAME for reading
+     and returns a pointer to a corresponding ntuple struct.  The
+     ntuples in the file must have size SIZE.  A pointer to memory for
+     the current ntuple row NTUPLE_DATA must be supplied--this is used
+     to copy ntuples in and out of the file.
 
-   The goal is to find a point in the space at which a real valued
-"energy function" (or "cost function") is minimized.  Simulated
-annealing is a minimization technique which has given good results in
-avoiding local minima; it is based on the idea of taking a random walk
-through the space at successively lower temperatures, where the
-probability of taking a step is given by a Boltzmann distribution.
+
+File: gsl-ref.info,  Node: Writing ntuples,  Next: Reading ntuples,  Prev: Opening an existing ntuple file,  Up: N-tuples
 
-   The functions described in this chapter are declared in the header
-file 'gsl_siman.h'.
+24.4 Writing ntuples
+====================
 
-* Menu:
+ -- Function: int gsl_ntuple_write (gsl_ntuple * NTUPLE)
+     This function writes the current ntuple NTUPLE->NTUPLE_DATA of size
+     NTUPLE->SIZE to the corresponding file.
 
-* Simulated Annealing algorithm::  
-* Simulated Annealing functions::  
-* Examples with Simulated Annealing::  
-* Simulated Annealing References and Further Reading::  
+ -- Function: int gsl_ntuple_bookdata (gsl_ntuple * NTUPLE)
+     This function is a synonym for 'gsl_ntuple_write'.
 
 
-File: gsl-ref.info,  Node: Simulated Annealing algorithm,  Next: Simulated Annealing functions,  Up: Simulated Annealing
-
-25.1 Simulated Annealing algorithm
-==================================
-
-The simulated annealing algorithm takes random walks through the problem
-space, looking for points with low energies; in these random walks, the
-probability of taking a step is determined by the Boltzmann
-distribution,
+File: gsl-ref.info,  Node: Reading ntuples,  Next: Closing an ntuple file,  Prev: Writing ntuples,  Up: N-tuples
 
-     p = e^{-(E_{i+1} - E_i)/(kT)}
+24.5 Reading ntuples
+====================
 
-if E_{i+1} > E_i, and p = 1 when E_{i+1} <= E_i.
+ -- Function: int gsl_ntuple_read (gsl_ntuple * NTUPLE)
+     This function reads the current row of the ntuple file for NTUPLE
+     and stores the values in NTUPLE->DATA.
 
-   In other words, a step will occur if the new energy is lower.  If the
-new energy is higher, the transition can still occur, and its likelihood
-is proportional to the temperature T and inversely proportional to the
-energy difference E_{i+1} - E_i.
+
+File: gsl-ref.info,  Node: Closing an ntuple file,  Next: Histogramming ntuple values,  Prev: Reading ntuples,  Up: N-tuples
 
-   The temperature T is initially set to a high value, and a random walk
-is carried out at that temperature.  Then the temperature is lowered
-very slightly according to a "cooling schedule", for example: T ->
-T/mu_T where \mu_T is slightly greater than 1.
+24.6 Closing an ntuple file
+===========================
 
-   The slight probability of taking a step that gives higher energy is
-what allows simulated annealing to frequently get out of local minima.
+ -- Function: int gsl_ntuple_close (gsl_ntuple * NTUPLE)
+     This function closes the ntuple file NTUPLE and frees its
+     associated allocated memory.
 
 
-File: gsl-ref.info,  Node: Simulated Annealing functions,  Next: Examples with Simulated Annealing,  Prev: Simulated Annealing algorithm,  Up: Simulated Annealing
-
-25.2 Simulated Annealing functions
-==================================
+File: gsl-ref.info,  Node: Histogramming ntuple values,  Next: Example ntuple programs,  Prev: Closing an ntuple file,  Up: N-tuples
 
- -- Function: void gsl_siman_solve (const gsl_rng * R, void * X0_P,
-          gsl_siman_Efunc_t EF, gsl_siman_step_t TAKE_STEP,
-          gsl_siman_metric_t DISTANCE, gsl_siman_print_t PRINT_POSITION,
-          gsl_siman_copy_t COPYFUNC, gsl_siman_copy_construct_t
-          COPY_CONSTRUCTOR, gsl_siman_destroy_t DESTRUCTOR, size_t
-          ELEMENT_SIZE, gsl_siman_params_t PARAMS)
+24.7 Histogramming ntuple values
+================================
 
-     This function performs a simulated annealing search through a given
-     space.  The space is specified by providing the functions EF and
-     DISTANCE.  The simulated annealing steps are generated using the
-     random number generator R and the function TAKE_STEP.
+Once an ntuple has been created its contents can be histogrammed in
+various ways using the function 'gsl_ntuple_project'.  Two user-defined
+functions must be provided, a function to select events and a function
+to compute scalar values.  The selection function and the value function
+both accept the ntuple row as a first argument and other parameters as a
+second argument.
 
-     The starting configuration of the system should be given by X0_P.
-     The routine offers two modes for updating configurations, a
-     fixed-size mode and a variable-size mode.  In the fixed-size mode
-     the configuration is stored as a single block of memory of size
-     ELEMENT_SIZE.  Copies of this configuration are created, copied and
-     destroyed internally using the standard library functions 'malloc',
-     'memcpy' and 'free'.  The function pointers COPYFUNC,
-     COPY_CONSTRUCTOR and DESTRUCTOR should be null pointers in
-     fixed-size mode.  In the variable-size mode the functions COPYFUNC,
-     COPY_CONSTRUCTOR and DESTRUCTOR are used to create, copy and
-     destroy configurations internally.  The variable ELEMENT_SIZE
-     should be zero in the variable-size mode.
+   The "selection function" determines which ntuple rows are selected
+for histogramming.  It is defined by the following struct,
 
-     The PARAMS structure (described below) controls the run by
-     providing the temperature schedule and other tunable parameters to
-     the algorithm.
+     typedef struct {
+       int (* function) (void * ntuple_data, void * params);
+       void * params;
+     } gsl_ntuple_select_fn;
 
-     On exit the best result achieved during the search is placed in
-     '*X0_P'.  If the annealing process has been successful this should
-     be a good approximation to the optimal point in the space.
+The struct component FUNCTION should return a non-zero value for each
+ntuple row that is to be included in the histogram.
 
-     If the function pointer PRINT_POSITION is not null, a debugging log
-     will be printed to 'stdout' with the following columns:
+   The "value function" computes scalar values for those ntuple rows
+selected by the selection function,
 
-          #-iter  #-evals  temperature  position  energy  best_energy
+     typedef struct {
+       double (* function) (void * ntuple_data, void * params);
+       void * params;
+     } gsl_ntuple_value_fn;
 
-     and the output of the function PRINT_POSITION itself.  If
-     PRINT_POSITION is null then no information is printed.
+In this case the struct component FUNCTION should return the value to be
+added to the histogram for the ntuple row.
 
-The simulated annealing routines require several user-specified
-functions to define the configuration space and energy function.  The
-prototypes for these functions are given below.
+ -- Function: int gsl_ntuple_project (gsl_histogram * H, gsl_ntuple *
+          NTUPLE, gsl_ntuple_value_fn * VALUE_FUNC, gsl_ntuple_select_fn
+          * SELECT_FUNC)
+     This function updates the histogram H from the ntuple NTUPLE using
+     the functions VALUE_FUNC and SELECT_FUNC.  For each ntuple row
+     where the selection function SELECT_FUNC is non-zero the
+     corresponding value of that row is computed using the function
+     VALUE_FUNC and added to the histogram.  Those ntuple rows where
+     SELECT_FUNC returns zero are ignored.  New entries are added to the
+     histogram, so subsequent calls can be used to accumulate further
+     data in the same histogram.
 
- -- Data Type: gsl_siman_Efunc_t
-     This function type should return the energy of a configuration XP.
+
+File: gsl-ref.info,  Node: Example ntuple programs,  Next: Ntuple References and Further Reading,  Prev: Histogramming ntuple values,  Up: N-tuples
 
-          double (*gsl_siman_Efunc_t) (void *xp)
+24.8 Examples
+=============
 
- -- Data Type: gsl_siman_step_t
-     This function type should modify the configuration XP using a
-     random step taken from the generator R, up to a maximum distance of
-     STEP_SIZE.
+The following example programs demonstrate the use of ntuples in
+managing a large dataset.  The first program creates a set of 10,000
+simulated "events", each with 3 associated values (x,y,z).  These are
+generated from a Gaussian distribution with unit variance, for
+demonstration purposes, and written to the ntuple file 'test.dat'.
 
-          void (*gsl_siman_step_t) (const gsl_rng *r, void *xp,
-                                    double step_size)
+     #include <gsl/gsl_ntuple.h>
+     #include <gsl/gsl_rng.h>
+     #include <gsl/gsl_randist.h>
 
- -- Data Type: gsl_siman_metric_t
-     This function type should return the distance between two
-     configurations XP and YP.
+     struct data
+     {
+       double x;
+       double y;
+       double z;
+     };
 
-          double (*gsl_siman_metric_t) (void *xp, void *yp)
+     int
+     main (void)
+     {
+       const gsl_rng_type * T;
+       gsl_rng * r;
 
- -- Data Type: gsl_siman_print_t
-     This function type should print the contents of the configuration
-     XP.
+       struct data ntuple_row;
+       int i;
 
-          void (*gsl_siman_print_t) (void *xp)
+       gsl_ntuple *ntuple
+         = gsl_ntuple_create ("test.dat", &ntuple_row,
+                              sizeof (ntuple_row));
 
- -- Data Type: gsl_siman_copy_t
-     This function type should copy the configuration SOURCE into DEST.
+       gsl_rng_env_setup ();
 
-          void (*gsl_siman_copy_t) (void *source, void *dest)
+       T = gsl_rng_default;
+       r = gsl_rng_alloc (T);
 
- -- Data Type: gsl_siman_copy_construct_t
-     This function type should create a new copy of the configuration
-     XP.
+       for (i = 0; i < 10000; i++)
+         {
+           ntuple_row.x = gsl_ran_ugaussian (r);
+           ntuple_row.y = gsl_ran_ugaussian (r);
+           ntuple_row.z = gsl_ran_ugaussian (r);
 
-          void * (*gsl_siman_copy_construct_t) (void *xp)
+           gsl_ntuple_write (ntuple);
+         }
 
- -- Data Type: gsl_siman_destroy_t
-     This function type should destroy the configuration XP, freeing its
-     memory.
+       gsl_ntuple_close (ntuple);
+       gsl_rng_free (r);
 
-          void (*gsl_siman_destroy_t) (void *xp)
+       return 0;
+     }
 
- -- Data Type: gsl_siman_params_t
-     These are the parameters that control a run of 'gsl_siman_solve'.
-     This structure contains all the information needed to control the
-     search, beyond the energy function, the step function and the
-     initial guess.
+The next program analyses the ntuple data in the file 'test.dat'.  The
+analysis procedure is to compute the squared-magnitude of each event,
+E^2=x^2+y^2+z^2, and select only those which exceed a lower limit of
+1.5.  The selected events are then histogrammed using their E^2 values.
 
-     'int n_tries'
-          The number of points to try for each step.
+     #include <math.h>
+     #include <gsl/gsl_ntuple.h>
+     #include <gsl/gsl_histogram.h>
 
-     'int iters_fixed_T'
-          The number of iterations at each temperature.
+     struct data
+     {
+       double x;
+       double y;
+       double z;
+     };
 
-     'double step_size'
-          The maximum step size in the random walk.
+     int sel_func (void *ntuple_data, void *params);
+     double val_func (void *ntuple_data, void *params);
 
-     'double k, t_initial, mu_t, t_min'
-          The parameters of the Boltzmann distribution and cooling
-          schedule.
+     int
+     main (void)
+     {
+       struct data ntuple_row;
 
-
-File: gsl-ref.info,  Node: Examples with Simulated Annealing,  Next: Simulated Annealing References and Further Reading,  Prev: Simulated Annealing functions,  Up: Simulated Annealing
+       gsl_ntuple *ntuple
+         = gsl_ntuple_open ("test.dat", &ntuple_row,
+                            sizeof (ntuple_row));
+       double lower = 1.5;
 
-25.3 Examples
-=============
+       gsl_ntuple_select_fn S;
+       gsl_ntuple_value_fn V;
 
-The simulated annealing package is clumsy, and it has to be because it
-is written in C, for C callers, and tries to be polymorphic at the same
-time.  But here we provide some examples which can be pasted into your
-application with little change and should make things easier.
+       gsl_histogram *h = gsl_histogram_alloc (100);
+       gsl_histogram_set_ranges_uniform(h, 0.0, 10.0);
 
-* Menu:
+       S.function = &sel_func;
+       S.params = &lower;
 
-* Trivial example::             
-* Traveling Salesman Problem::  
+       V.function = &val_func;
+       V.params = 0;
 
-
-File: gsl-ref.info,  Node: Trivial example,  Next: Traveling Salesman Problem,  Up: Examples with Simulated Annealing
+       gsl_ntuple_project (h, ntuple, &V, &S);
+       gsl_histogram_fprintf (stdout, h, "%f", "%f");
+       gsl_histogram_free (h);
+       gsl_ntuple_close (ntuple);
 
-25.3.1 Trivial example
-----------------------
+       return 0;
+     }
 
-The first example, in one dimensional Cartesian space, sets up an energy
-function which is a damped sine wave; this has many local minima, but
-only one global minimum, somewhere between 1.0 and 1.5.  The initial
-guess given is 15.5, which is several local minima away from the global
-minimum.
+     int
+     sel_func (void *ntuple_data, void *params)
+     {
+       struct data * data = (struct data *) ntuple_data;
+       double x, y, z, E2, scale;
+       scale = *(double *) params;
 
-     #include <math.h>
-     #include <stdlib.h>
-     #include <string.h>
-     #include <gsl/gsl_siman.h>
+       x = data->x;
+       y = data->y;
+       z = data->z;
 
-     /* set up parameters for this simulated annealing run */
+       E2 = x * x + y * y + z * z;
 
-     /* how many points do we try before stepping */
-     #define N_TRIES 200
+       return E2 > scale;
+     }
 
-     /* how many iterations for each T? */
-     #define ITERS_FIXED_T 1000
+     double
+     val_func (void *ntuple_data, void *params)
+     {
+       (void)(params); /* avoid unused parameter warning */
+       struct data * data = (struct data *) ntuple_data;
+       double x, y, z;
 
-     /* max step size in random walk */
-     #define STEP_SIZE 1.0
+       x = data->x;
+       y = data->y;
+       z = data->z;
 
-     /* Boltzmann constant */
-     #define K 1.0
+       return x * x + y * y + z * z;
+     }
 
-     /* initial temperature */
-     #define T_INITIAL 0.008
+   The following plot shows the distribution of the selected events.
+Note the cut-off at the lower bound.
 
-     /* damping factor for temperature */
-     #define MU_T 1.003
-     #define T_MIN 2.0e-6
+
+File: gsl-ref.info,  Node: Ntuple References and Further Reading,  Prev: Example ntuple programs,  Up: N-tuples
 
-     gsl_siman_params_t params
-       = {N_TRIES, ITERS_FIXED_T, STEP_SIZE,
-          K, T_INITIAL, MU_T, T_MIN};
+24.9 References and Further Reading
+===================================
 
-     /* now some functions to test in one dimension */
-     double E1(void *xp)
-     {
-       double x = * ((double *) xp);
+Further information on the use of ntuples can be found in the
+documentation for the CERN packages PAW and HBOOK (available online).
 
-       return exp(-pow((x-1.0),2.0))*sin(8*x);
-     }
+
+File: gsl-ref.info,  Node: Monte Carlo Integration,  Next: Simulated Annealing,  Prev: N-tuples,  Up: Top
 
-     double M1(void *xp, void *yp)
-     {
-       double x = *((double *) xp);
-       double y = *((double *) yp);
+25 Monte Carlo Integration
+**************************
 
-       return fabs(x - y);
-     }
+This chapter describes routines for multidimensional Monte Carlo
+integration.  These include the traditional Monte Carlo method and
+adaptive algorithms such as VEGAS and MISER which use importance
+sampling and stratified sampling techniques.  Each algorithm computes an
+estimate of a multidimensional definite integral of the form,
 
-     void S1(const gsl_rng * r, void *xp, double step_size)
-     {
-       double old_x = *((double *) xp);
-       double new_x;
+     I = \int_xl^xu dx \int_yl^yu  dy ...  f(x, y, ...)
 
-       double u = gsl_rng_uniform(r);
-       new_x = u * 2 * step_size - step_size + old_x;
+over a hypercubic region ((x_l,x_u), (y_l,y_u), ...) using a fixed
+number of function calls.  The routines also provide a statistical
+estimate of the error on the result.  This error estimate should be
+taken as a guide rather than as a strict error bound--random sampling of
+the region may not uncover all the important features of the function,
+resulting in an underestimate of the error.
 
-       memcpy(xp, &new_x, sizeof(new_x));
-     }
+   The functions are defined in separate header files for each routine,
+'gsl_monte_plain.h', 'gsl_monte_miser.h' and 'gsl_monte_vegas.h'.
 
-     void P1(void *xp)
-     {
-       printf ("%12g", *((double *) xp));
-     }
+* Menu:
 
-     int
-     main(int argc, char *argv[])
-     {
-       const gsl_rng_type * T;
-       gsl_rng * r;
+* Monte Carlo Interface::       
+* PLAIN Monte Carlo::  
+* MISER::                       
+* VEGAS::                       
+* Monte Carlo Examples::        
+* Monte Carlo Integration References and Further Reading::  
 
-       double x_initial = 15.5;
+
+File: gsl-ref.info,  Node: Monte Carlo Interface,  Next: PLAIN Monte Carlo,  Up: Monte Carlo Integration
 
-       gsl_rng_env_setup();
+25.1 Interface
+==============
 
-       T = gsl_rng_default;
-       r = gsl_rng_alloc(T);
+All of the Monte Carlo integration routines use the same general form of
+interface.  There is an allocator to allocate memory for control
+variables and workspace, a routine to initialize those control
+variables, the integrator itself, and a function to free the space when
+done.
 
-       gsl_siman_solve(r, &x_initial, E1, S1, M1, P1,
-                       NULL, NULL, NULL,
-                       sizeof(double), params);
+   Each integration function requires a random number generator to be
+supplied, and returns an estimate of the integral and its standard
+deviation.  The accuracy of the result is determined by the number of
+function calls specified by the user.  If a known level of accuracy is
+required this can be achieved by calling the integrator several times
+and averaging the individual results until the desired accuracy is
+obtained.
 
-       gsl_rng_free (r);
-       return 0;
-     }
+   Random sample points used within the Monte Carlo routines are always
+chosen strictly within the integration region, so that endpoint
+singularities are automatically avoided.
 
-   Here are a couple of plots that are generated by running 'siman_test'
-in the following way:
+   The function to be integrated has its own datatype, defined in the
+header file 'gsl_monte.h'.
 
-     $ ./siman_test | awk '!/^#/ {print $1, $4}'
-      | graph -y 1.34 1.4 -W0 -X generation -Y position
-      | plot -Tps > siman-test.eps
-     $ ./siman_test | awk '!/^#/ {print $1, $5}'
-      | graph -y -0.88 -0.83 -W0 -X generation -Y energy
-      | plot -Tps > siman-energy.eps
+ -- Data Type: gsl_monte_function
 
-
-File: gsl-ref.info,  Node: Traveling Salesman Problem,  Prev: Trivial example,  Up: Examples with Simulated Annealing
+     This data type defines a general function with parameters for Monte
+     Carlo integration.
 
-25.3.2 Traveling Salesman Problem
----------------------------------
+     'double (* f) (double * X, size_t DIM, void * PARAMS)'
+          this function should return the value f(x,params) for the
+          argument X and parameters PARAMS, where X is an array of size
+          DIM giving the coordinates of the point where the function is
+          to be evaluated.
 
-The TSP ("Traveling Salesman Problem") is the classic combinatorial
-optimization problem.  I have provided a very simple version of it,
-based on the coordinates of twelve cities in the southwestern United
-States.  This should maybe be called the "Flying Salesman Problem",
-since I am using the great-circle distance between cities, rather than
-the driving distance.  Also: I assume the earth is a sphere, so I don't
-use geoid distances.
+     'size_t dim'
+          the number of dimensions for X.
 
-   The 'gsl_siman_solve' routine finds a route which is 3490.62
-Kilometers long; this is confirmed by an exhaustive search of all
-possible routes with the same initial city.
+     'void * params'
+          a pointer to the parameters of the function.
 
-   The full code can be found in 'siman/siman_tsp.c', but I include here
-some plots generated in the following way:
+Here is an example for a quadratic function in two dimensions,
 
-     $ ./siman_tsp > tsp.output
-     $ grep -v "^#" tsp.output
-      | awk '{print $1, $NF}'
-      | graph -y 3300 6500 -W0 -X generation -Y distance
-         -L "TSP - 12 southwest cities"
-      | plot -Tps > 12-cities.eps
-     $ grep initial_city_coord tsp.output
-       | awk '{print $2, $3}'
-       | graph -X "longitude (- means west)" -Y "latitude"
-          -L "TSP - initial-order" -f 0.03 -S 1 0.1
-       | plot -Tps > initial-route.eps
-     $ grep final_city_coord tsp.output
-       | awk '{print $2, $3}'
-       | graph -X "longitude (- means west)" -Y "latitude"
-          -L "TSP - final-order" -f 0.03 -S 1 0.1
-       | plot -Tps > final-route.eps
+     f(x,y) = a x^2 + b x y + c y^2
 
-This is the output showing the initial order of the cities; longitude is
-negative, since it is west and I want the plot to look like a map.
+with a = 3, b = 2, c = 1.  The following code defines a
+'gsl_monte_function' 'F' which you could pass to an integrator:
 
-     # initial coordinates of cities (longitude and latitude)
-     ###initial_city_coord: -105.95 35.68 Santa Fe
-     ###initial_city_coord: -112.07 33.54 Phoenix
-     ###initial_city_coord: -106.62 35.12 Albuquerque
-     ###initial_city_coord: -103.2 34.41 Clovis
-     ###initial_city_coord: -107.87 37.29 Durango
-     ###initial_city_coord: -96.77 32.79 Dallas
-     ###initial_city_coord: -105.92 35.77 Tesuque
-     ###initial_city_coord: -107.84 35.15 Grants
-     ###initial_city_coord: -106.28 35.89 Los Alamos
-     ###initial_city_coord: -106.76 32.34 Las Cruces
-     ###initial_city_coord: -108.58 37.35 Cortez
-     ###initial_city_coord: -108.74 35.52 Gallup
-     ###initial_city_coord: -105.95 35.68 Santa Fe
+     struct my_f_params { double a; double b; double c; };
 
-   The optimal route turns out to be:
+     double
+     my_f (double x[], size_t dim, void * p) {
+        struct my_f_params * fp = (struct my_f_params *)p;
 
-     # final coordinates of cities (longitude and latitude)
-     ###final_city_coord: -105.95 35.68 Santa Fe
-     ###final_city_coord: -103.2 34.41 Clovis
-     ###final_city_coord: -96.77 32.79 Dallas
-     ###final_city_coord: -106.76 32.34 Las Cruces
-     ###final_city_coord: -112.07 33.54 Phoenix
-     ###final_city_coord: -108.74 35.52 Gallup
-     ###final_city_coord: -108.58 37.35 Cortez
-     ###final_city_coord: -107.87 37.29 Durango
-     ###final_city_coord: -107.84 35.15 Grants
-     ###final_city_coord: -106.62 35.12 Albuquerque
-     ###final_city_coord: -106.28 35.89 Los Alamos
-     ###final_city_coord: -105.92 35.77 Tesuque
-     ###final_city_coord: -105.95 35.68 Santa Fe
+        if (dim != 2)
+           {
+             fprintf (stderr, "error: dim != 2");
+             abort ();
+           }
 
-Here's a plot of the cost function (energy) versus generation (point in
-the calculation at which a new temperature is set) for this problem:
+        return  fp->a * x[0] * x[0]
+                  + fp->b * x[0] * x[1]
+                    + fp->c * x[1] * x[1];
+     }
 
-
-File: gsl-ref.info,  Node: Simulated Annealing References and Further Reading,  Prev: Examples with Simulated Annealing,  Up: Simulated Annealing
+     gsl_monte_function F;
+     struct my_f_params params = { 3.0, 2.0, 1.0 };
 
-25.4 References and Further Reading
-===================================
+     F.f = &my_f;
+     F.dim = 2;
+     F.params = &params;
 
-Further information is available in the following book,
+The function f(x) can be evaluated using the following macro,
 
-     'Modern Heuristic Techniques for Combinatorial Problems', Colin R.
-     Reeves (ed.), McGraw-Hill, 1995 (ISBN 0-07-709239-2).
+     #define GSL_MONTE_FN_EVAL(F,x)
+         (*((F)->f))(x,(F)->dim,(F)->params)
 
 
-File: gsl-ref.info,  Node: Ordinary Differential Equations,  Next: Interpolation,  Prev: Simulated Annealing,  Up: Top
-
-26 Ordinary Differential Equations
-**********************************
-
-This chapter describes functions for solving ordinary differential
-equation (ODE) initial value problems.  The library provides a variety
-of low-level methods, such as Runge-Kutta and Bulirsch-Stoer routines,
-and higher-level components for adaptive step-size control.  The
-components can be combined by the user to achieve the desired solution,
-with full access to any intermediate steps.  A driver object can be used
-as a high level wrapper for easy use of low level functions.
+File: gsl-ref.info,  Node: PLAIN Monte Carlo,  Next: MISER,  Prev: Monte Carlo Interface,  Up: Monte Carlo Integration
 
-   These functions are declared in the header file 'gsl_odeiv2.h'.  This
-is a new interface in version 1.15 and uses the prefix 'gsl_odeiv2' for
-all functions.  It is recommended over the previous 'gsl_odeiv'
-implementation defined in 'gsl_odeiv.h' The old interface has been
-retained under the original name for backwards compatibility.
+25.2 PLAIN Monte Carlo
+======================
 
-* Menu:
+The plain Monte Carlo algorithm samples points randomly from the
+integration region to estimate the integral and its error.  Using this
+algorithm the estimate of the integral E(f; N) for N randomly
+distributed points x_i is given by,
 
-* Defining the ODE System::     
-* Stepping Functions::          
-* Adaptive Step-size Control::  
-* Evolution::                   
-* Driver::
-* ODE Example programs::        
-* ODE References and Further Reading::  
+     E(f; N) = =  V <f> = (V / N) \sum_i^N f(x_i)
 
-
-File: gsl-ref.info,  Node: Defining the ODE System,  Next: Stepping Functions,  Up: Ordinary Differential Equations
+where V is the volume of the integration region.  The error on this
+estimate \sigma(E;N) is calculated from the estimated variance of the
+mean,
 
-26.1 Defining the ODE System
-============================
+     \sigma^2 (E; N) = (V^2 / N^2) \sum_i^N (f(x_i) -  <f>)^2.
 
-The routines solve the general n-dimensional first-order system,
+For large N this variance decreases asymptotically as \Var(f)/N, where
+\Var(f) is the true variance of the function over the integration
+region.  The error estimate itself should decrease as
+\sigma(f)/\sqrt{N}.  The familiar law of errors decreasing as 1/\sqrt{N}
+applies--to reduce the error by a factor of 10 requires a 100-fold
+increase in the number of sample points.
 
-     dy_i(t)/dt = f_i(t, y_1(t), ..., y_n(t))
+   The functions described in this section are declared in the header
+file 'gsl_monte_plain.h'.
 
-for i = 1, \dots, n.  The stepping functions rely on the vector of
-derivatives f_i and the Jacobian matrix, J_{ij} = df_i(t,y(t)) / dy_j.
-A system of equations is defined using the 'gsl_odeiv2_system' datatype.
+ -- Function: gsl_monte_plain_state * gsl_monte_plain_alloc (size_t DIM)
+     This function allocates and initializes a workspace for Monte Carlo
+     integration in DIM dimensions.
 
- -- Data Type: gsl_odeiv2_system
-     This data type defines a general ODE system with arbitrary
-     parameters.
+ -- Function: int gsl_monte_plain_init (gsl_monte_plain_state* S)
+     This function initializes a previously allocated integration state.
+     This allows an existing workspace to be reused for different
+     integrations.
 
-     'int (* function) (double t, const double y[], double dydt[], void * params)'
-          This function should store the vector elements f_i(t,y,params)
-          in the array DYDT, for arguments (T,Y) and parameters PARAMS.
+ -- Function: int gsl_monte_plain_integrate (gsl_monte_function * F,
+          const double XL[], const double XU[], size_t DIM, size_t
+          CALLS, gsl_rng * R, gsl_monte_plain_state * S, double *
+          RESULT, double * ABSERR)
+     This routines uses the plain Monte Carlo algorithm to integrate the
+     function F over the DIM-dimensional hypercubic region defined by
+     the lower and upper limits in the arrays XL and XU, each of size
+     DIM.  The integration uses a fixed number of function calls CALLS,
+     and obtains random sampling points using the random number
+     generator R.  A previously allocated workspace S must be supplied.
+     The result of the integration is returned in RESULT, with an
+     estimated absolute error ABSERR.
 
-          The function should return 'GSL_SUCCESS' if the calculation
-          was completed successfully.  Any other return value indicates
-          an error.  A special return value 'GSL_EBADFUNC' causes
-          'gsl_odeiv2' routines to immediately stop and return.  The
-          user must call an appropriate reset function (e.g.
-          'gsl_odeiv2_driver_reset' or 'gsl_odeiv2_step_reset') before
-          continuing.  Use return values distinct from standard GSL
-          error codes to distinguish your function as the source of the
-          error.
+ -- Function: void gsl_monte_plain_free (gsl_monte_plain_state * S)
+     This function frees the memory associated with the integrator state
+     S.
 
-     'int (* jacobian) (double t, const double y[], double * dfdy, double dfdt[], void * params);'
-          This function should store the vector of derivative elements
-          in the array DFDT and the Jacobian matrix J_{ij} in the array
-          DFDY, regarded as a row-ordered matrix 'J(i,j) = dfdy[i *
-          dimension + j]' where 'dimension' is the dimension of the
-          system.
+
+File: gsl-ref.info,  Node: MISER,  Next: VEGAS,  Prev: PLAIN Monte Carlo,  Up: Monte Carlo Integration
 
-          Not all of the stepper algorithms of 'gsl_odeiv2' make use of
-          the Jacobian matrix, so it may not be necessary to provide
-          this function (the 'jacobian' element of the struct can be
-          replaced by a null pointer for those algorithms).
+25.3 MISER
+==========
 
-          The function should return 'GSL_SUCCESS' if the calculation
-          was completed successfully.  Any other return value indicates
-          an error.  A special return value 'GSL_EBADFUNC' causes
-          'gsl_odeiv2' routines to immediately stop and return.  The
-          user must call an appropriate reset function (e.g.
-          'gsl_odeiv2_driver_reset' or 'gsl_odeiv2_step_reset') before
-          continuing.  Use return values distinct from standard GSL
-          error codes to distinguish your function as the source of the
-          error.
+The MISER algorithm of Press and Farrar is based on recursive stratified
+sampling.  This technique aims to reduce the overall integration error
+by concentrating integration points in the regions of highest variance.
 
-     'size_t dimension;'
-          This is the dimension of the system of equations.
+   The idea of stratified sampling begins with the observation that for
+two disjoint regions a and b with Monte Carlo estimates of the integral
+E_a(f) and E_b(f) and variances \sigma_a^2(f) and \sigma_b^2(f), the
+variance \Var(f) of the combined estimate E(f) = (1/2) (E_a(f) + E_b(f))
+is given by,
 
-     'void * params'
-          This is a pointer to the arbitrary parameters of the system.
+     \Var(f) = (\sigma_a^2(f) / 4 N_a) + (\sigma_b^2(f) / 4 N_b).
 
-
-File: gsl-ref.info,  Node: Stepping Functions,  Next: Adaptive Step-size Control,  Prev: Defining the ODE System,  Up: Ordinary Differential Equations
+It can be shown that this variance is minimized by distributing the
+points such that,
 
-26.2 Stepping Functions
-=======================
+     N_a / (N_a + N_b) = \sigma_a / (\sigma_a + \sigma_b).
 
-The lowest level components are the "stepping functions" which advance a
-solution from time t to t+h for a fixed step-size h and estimate the
-resulting local error.
+Hence the smallest error estimate is obtained by allocating sample
+points in proportion to the standard deviation of the function in each
+sub-region.
 
- -- Function: gsl_odeiv2_step * gsl_odeiv2_step_alloc (const
-          gsl_odeiv2_step_type * T, size_t DIM)
-     This function returns a pointer to a newly allocated instance of a
-     stepping function of type T for a system of DIM dimensions.  Please
-     note that if you use a stepper method that requires access to a
-     driver object, it is advisable to use a driver allocation method,
-     which automatically allocates a stepper, too.
+   The MISER algorithm proceeds by bisecting the integration region
+along one coordinate axis to give two sub-regions at each step.  The
+direction is chosen by examining all d possible bisections and selecting
+the one which will minimize the combined variance of the two
+sub-regions.  The variance in the sub-regions is estimated by sampling
+with a fraction of the total number of points available to the current
+step.  The same procedure is then repeated recursively for each of the
+two half-spaces from the best bisection.  The remaining sample points
+are allocated to the sub-regions using the formula for N_a and N_b.
+This recursive allocation of integration points continues down to a
+user-specified depth where each sub-region is integrated using a plain
+Monte Carlo estimate.  These individual values and their error estimates
+are then combined upwards to give an overall result and an estimate of
+its error.
 
- -- Function: int gsl_odeiv2_step_reset (gsl_odeiv2_step * S)
-     This function resets the stepping function S.  It should be used
-     whenever the next use of S will not be a continuation of a previous
-     step.
+   The functions described in this section are declared in the header
+file 'gsl_monte_miser.h'.
 
- -- Function: void gsl_odeiv2_step_free (gsl_odeiv2_step * S)
-     This function frees all the memory associated with the stepping
-     function S.
+ -- Function: gsl_monte_miser_state * gsl_monte_miser_alloc (size_t DIM)
+     This function allocates and initializes a workspace for Monte Carlo
+     integration in DIM dimensions.  The workspace is used to maintain
+     the state of the integration.
 
- -- Function: const char * gsl_odeiv2_step_name (const gsl_odeiv2_step *
-          S)
-     This function returns a pointer to the name of the stepping
-     function.  For example,
+ -- Function: int gsl_monte_miser_init (gsl_monte_miser_state* S)
+     This function initializes a previously allocated integration state.
+     This allows an existing workspace to be reused for different
+     integrations.
 
-          printf ("step method is '%s'\n",
-                   gsl_odeiv2_step_name (s));
+ -- Function: int gsl_monte_miser_integrate (gsl_monte_function * F,
+          const double XL[], const double XU[], size_t DIM, size_t
+          CALLS, gsl_rng * R, gsl_monte_miser_state * S, double *
+          RESULT, double * ABSERR)
+     This routines uses the MISER Monte Carlo algorithm to integrate the
+     function F over the DIM-dimensional hypercubic region defined by
+     the lower and upper limits in the arrays XL and XU, each of size
+     DIM.  The integration uses a fixed number of function calls CALLS,
+     and obtains random sampling points using the random number
+     generator R.  A previously allocated workspace S must be supplied.
+     The result of the integration is returned in RESULT, with an
+     estimated absolute error ABSERR.
 
-     would print something like 'step method is 'rkf45''.
+ -- Function: void gsl_monte_miser_free (gsl_monte_miser_state * S)
+     This function frees the memory associated with the integrator state
+     S.
 
- -- Function: unsigned int gsl_odeiv2_step_order (const gsl_odeiv2_step
-          * S)
-     This function returns the order of the stepping function on the
-     previous step.  The order can vary if the stepping function itself
-     is adaptive.
+   The MISER algorithm has several configurable parameters which can be
+changed using the following two functions.(1)
 
- -- Function: int gsl_odeiv2_step_set_driver (gsl_odeiv2_step * S, const
-          gsl_odeiv2_driver * D)
-     This function sets a pointer of the driver object D for stepper S,
-     to allow the stepper to access control (and evolve) object through
-     the driver object.  This is a requirement for some steppers, to get
-     the desired error level for internal iteration of stepper.
-     Allocation of a driver object calls this function automatically.
+ -- Function: void gsl_monte_miser_params_get (const
+          gsl_monte_miser_state * S, gsl_monte_miser_params * PARAMS)
+     This function copies the parameters of the integrator state into
+     the user-supplied PARAMS structure.
 
- -- Function: int gsl_odeiv2_step_apply (gsl_odeiv2_step * S, double T,
-          double H, double Y[], double YERR[], const double DYDT_IN[],
-          double DYDT_OUT[], const gsl_odeiv2_system * SYS)
-     This function applies the stepping function S to the system of
-     equations defined by SYS, using the step-size H to advance the
-     system from time T and state Y to time T+H.  The new state of the
-     system is stored in Y on output, with an estimate of the absolute
-     error in each component stored in YERR.  If the argument DYDT_IN is
-     not null it should point an array containing the derivatives for
-     the system at time T on input.  This is optional as the derivatives
-     will be computed internally if they are not provided, but allows
-     the reuse of existing derivative information.  On output the new
-     derivatives of the system at time T+H will be stored in DYDT_OUT if
-     it is not null.
+ -- Function: void gsl_monte_miser_params_set (gsl_monte_miser_state *
+          S, const gsl_monte_miser_params * PARAMS)
+     This function sets the integrator parameters based on values
+     provided in the PARAMS structure.
 
-     The stepping function returns 'GSL_FAILURE' if it is unable to
-     compute the requested step.  Also, if the user-supplied functions
-     defined in the system SYS return a status other than 'GSL_SUCCESS'
-     the step will be aborted.  In that case, the elements of Y will be
-     restored to their pre-step values and the error code from the
-     user-supplied function will be returned.  Failure may be due to a
-     singularity in the system or too large step-size H.  In that case
-     the step should be attempted again with a smaller step-size, e.g.
-     H/2.
+   Typically the values of the parameters are first read using
+'gsl_monte_miser_params_get', the necessary changes are made to the
+fields of the PARAMS structure, and the values are copied back into the
+integrator state using 'gsl_monte_miser_params_set'.  The functions use
+the 'gsl_monte_miser_params' structure which contains the following
+fields:
 
-     If the driver object is not appropriately set via
-     'gsl_odeiv2_step_set_driver' for those steppers that need it, the
-     stepping function returns 'GSL_EFAULT'.  If the user-supplied
-     functions defined in the system SYS returns 'GSL_EBADFUNC', the
-     function returns immediately with the same return code.  In this
-     case the user must call 'gsl_odeiv2_step_reset' before calling this
-     function again.
+ -- Variable: double estimate_frac
+     This parameter specifies the fraction of the currently available
+     number of function calls which are allocated to estimating the
+     variance at each recursive step.  The default value is 0.1.
 
-   The following algorithms are available,
+ -- Variable: size_t min_calls
+     This parameter specifies the minimum number of function calls
+     required for each estimate of the variance.  If the number of
+     function calls allocated to the estimate using ESTIMATE_FRAC falls
+     below MIN_CALLS then MIN_CALLS are used instead.  This ensures that
+     each estimate maintains a reasonable level of accuracy.  The
+     default value of MIN_CALLS is '16 * dim'.
 
- -- Step Type: gsl_odeiv2_step_rk2
-     Explicit embedded Runge-Kutta (2, 3) method.
+ -- Variable: size_t min_calls_per_bisection
+     This parameter specifies the minimum number of function calls
+     required to proceed with a bisection step.  When a recursive step
+     has fewer calls available than MIN_CALLS_PER_BISECTION it performs
+     a plain Monte Carlo estimate of the current sub-region and
+     terminates its branch of the recursion.  The default value of this
+     parameter is '32 * min_calls'.
 
- -- Step Type: gsl_odeiv2_step_rk4
-     Explicit 4th order (classical) Runge-Kutta.  Error estimation is
-     carried out by the step doubling method.  For more efficient
-     estimate of the error, use the embedded methods described below.
+ -- Variable: double alpha
+     This parameter controls how the estimated variances for the two
+     sub-regions of a bisection are combined when allocating points.
+     With recursive sampling the overall variance should scale better
+     than 1/N, since the values from the sub-regions will be obtained
+     using a procedure which explicitly minimizes their variance.  To
+     accommodate this behavior the MISER algorithm allows the total
+     variance to depend on a scaling parameter \alpha,
 
- -- Step Type: gsl_odeiv2_step_rkf45
-     Explicit embedded Runge-Kutta-Fehlberg (4, 5) method.  This method
-     is a good general-purpose integrator.
+          \Var(f) = {\sigma_a \over N_a^\alpha} + {\sigma_b \over N_b^\alpha}.
 
- -- Step Type: gsl_odeiv2_step_rkck
-     Explicit embedded Runge-Kutta Cash-Karp (4, 5) method.
+     The authors of the original paper describing MISER recommend the
+     value \alpha = 2 as a good choice, obtained from numerical
+     experiments, and this is used as the default value in this
+     implementation.
 
- -- Step Type: gsl_odeiv2_step_rk8pd
-     Explicit embedded Runge-Kutta Prince-Dormand (8, 9) method.
+ -- Variable: double dither
+     This parameter introduces a random fractional variation of size
+     DITHER into each bisection, which can be used to break the symmetry
+     of integrands which are concentrated near the exact center of the
+     hypercubic integration region.  The default value of dither is
+     zero, so no variation is introduced.  If needed, a typical value of
+     DITHER is 0.1.
 
- -- Step Type: gsl_odeiv2_step_rk1imp
-     Implicit Gaussian first order Runge-Kutta.  Also known as implicit
-     Euler or backward Euler method.  Error estimation is carried out by
-     the step doubling method.  This algorithm requires the Jacobian and
-     access to the driver object via 'gsl_odeiv2_step_set_driver'.
+   ---------- Footnotes ----------
 
- -- Step Type: gsl_odeiv2_step_rk2imp
-     Implicit Gaussian second order Runge-Kutta.  Also known as implicit
-     mid-point rule.  Error estimation is carried out by the step
-     doubling method.  This stepper requires the Jacobian and access to
-     the driver object via 'gsl_odeiv2_step_set_driver'.
+   (1) The previous method of accessing these fields directly through
+the 'gsl_monte_miser_state' struct is now deprecated.
 
- -- Step Type: gsl_odeiv2_step_rk4imp
-     Implicit Gaussian 4th order Runge-Kutta.  Error estimation is
-     carried out by the step doubling method.  This algorithm requires
-     the Jacobian and access to the driver object via
-     'gsl_odeiv2_step_set_driver'.
+
+File: gsl-ref.info,  Node: VEGAS,  Next: Monte Carlo Examples,  Prev: MISER,  Up: Monte Carlo Integration
 
- -- Step Type: gsl_odeiv2_step_bsimp
-     Implicit Bulirsch-Stoer method of Bader and Deuflhard.  The method
-     is generally suitable for stiff problems.  This stepper requires
-     the Jacobian.
+25.4 VEGAS
+==========
 
- -- Step Type: gsl_odeiv2_step_msadams
-     A variable-coefficient linear multistep Adams method in Nordsieck
-     form.  This stepper uses explicit Adams-Bashforth (predictor) and
-     implicit Adams-Moulton (corrector) methods in P(EC)^m functional
-     iteration mode.  Method order varies dynamically between 1 and 12.
-     This stepper requires the access to the driver object via
-     'gsl_odeiv2_step_set_driver'.
-
- -- Step Type: gsl_odeiv2_step_msbdf
-     A variable-coefficient linear multistep backward differentiation
-     formula (BDF) method in Nordsieck form.  This stepper uses the
-     explicit BDF formula as predictor and implicit BDF formula as
-     corrector.  A modified Newton iteration method is used to solve the
-     system of non-linear equations.  Method order varies dynamically
-     between 1 and 5.  The method is generally suitable for stiff
-     problems.  This stepper requires the Jacobian and the access to the
-     driver object via 'gsl_odeiv2_step_set_driver'.
-
-
-File: gsl-ref.info,  Node: Adaptive Step-size Control,  Next: Evolution,  Prev: Stepping Functions,  Up: Ordinary Differential Equations
-
-26.3 Adaptive Step-size Control
-===============================
-
-The control function examines the proposed change to the solution
-produced by a stepping function and attempts to determine the optimal
-step-size for a user-specified level of error.
-
- -- Function: gsl_odeiv2_control * gsl_odeiv2_control_standard_new
-          (double EPS_ABS, double EPS_REL, double A_Y, double A_DYDT)
-     The standard control object is a four parameter heuristic based on
-     absolute and relative errors EPS_ABS and EPS_REL, and scaling
-     factors A_Y and A_DYDT for the system state y(t) and derivatives
-     y'(t) respectively.
-
-     The step-size adjustment procedure for this method begins by
-     computing the desired error level D_i for each component,
-
-          D_i = eps_abs + eps_rel * (a_y |y_i| + a_dydt h |y\prime_i|)
-
-     and comparing it with the observed error E_i = |yerr_i|.  If the
-     observed error E exceeds the desired error level D by more than 10%
-     for any component then the method reduces the step-size by an
-     appropriate factor,
-
-          h_new = h_old * S * (E/D)^(-1/q)
-
-     where q is the consistency order of the method (e.g.  q=4 for 4(5)
-     embedded RK), and S is a safety factor of 0.9.  The ratio E/D is
-     taken to be the maximum of the ratios E_i/D_i.
-
-     If the observed error E is less than 50% of the desired error level
-     D for the maximum ratio E_i/D_i then the algorithm takes the
-     opportunity to increase the step-size to bring the error in line
-     with the desired level,
-
-          h_new = h_old * S * (E/D)^(-1/(q+1))
-
-     This encompasses all the standard error scaling methods.  To avoid
-     uncontrolled changes in the stepsize, the overall scaling factor is
-     limited to the range 1/5 to 5.
-
- -- Function: gsl_odeiv2_control * gsl_odeiv2_control_y_new (double
-          EPS_ABS, double EPS_REL)
-     This function creates a new control object which will keep the
-     local error on each step within an absolute error of EPS_ABS and
-     relative error of EPS_REL with respect to the solution y_i(t).
-     This is equivalent to the standard control object with A_Y=1 and
-     A_DYDT=0.
-
- -- Function: gsl_odeiv2_control * gsl_odeiv2_control_yp_new (double
-          EPS_ABS, double EPS_REL)
-     This function creates a new control object which will keep the
-     local error on each step within an absolute error of EPS_ABS and
-     relative error of EPS_REL with respect to the derivatives of the
-     solution y'_i(t).  This is equivalent to the standard control
-     object with A_Y=0 and A_DYDT=1.
-
- -- Function: gsl_odeiv2_control * gsl_odeiv2_control_scaled_new (double
-          EPS_ABS, double EPS_REL, double A_Y, double A_DYDT, const
-          double SCALE_ABS[], size_t DIM)
-     This function creates a new control object which uses the same
-     algorithm as 'gsl_odeiv2_control_standard_new' but with an absolute
-     error which is scaled for each component by the array SCALE_ABS.
-     The formula for D_i for this control object is,
-
-          D_i = eps_abs * s_i + eps_rel * (a_y |y_i| + a_dydt h |y\prime_i|)
-
-     where s_i is the i-th component of the array SCALE_ABS.  The same
-     error control heuristic is used by the Matlab ODE suite.
-
- -- Function: gsl_odeiv2_control * gsl_odeiv2_control_alloc (const
-          gsl_odeiv2_control_type * T)
-     This function returns a pointer to a newly allocated instance of a
-     control function of type T.  This function is only needed for
-     defining new types of control functions.  For most purposes the
-     standard control functions described above should be sufficient.
-
- -- Function: int gsl_odeiv2_control_init (gsl_odeiv2_control * C,
-          double EPS_ABS, double EPS_REL, double A_Y, double A_DYDT)
-     This function initializes the control function C with the
-     parameters EPS_ABS (absolute error), EPS_REL (relative error), A_Y
-     (scaling factor for y) and A_DYDT (scaling factor for derivatives).
-
- -- Function: void gsl_odeiv2_control_free (gsl_odeiv2_control * C)
-     This function frees all the memory associated with the control
-     function C.
-
- -- Function: int gsl_odeiv2_control_hadjust (gsl_odeiv2_control * C,
-          gsl_odeiv2_step * S, const double Y[], const double YERR[],
-          const double DYDT[], double * H)
-     This function adjusts the step-size H using the control function C,
-     and the current values of Y, YERR and DYDT.  The stepping function
-     STEP is also needed to determine the order of the method.  If the
-     error in the y-values YERR is found to be too large then the
-     step-size H is reduced and the function returns
-     'GSL_ODEIV_HADJ_DEC'.  If the error is sufficiently small then H
-     may be increased and 'GSL_ODEIV_HADJ_INC' is returned.  The
-     function returns 'GSL_ODEIV_HADJ_NIL' if the step-size is
-     unchanged.  The goal of the function is to estimate the largest
-     step-size which satisfies the user-specified accuracy requirements
-     for the current point.
-
- -- Function: const char * gsl_odeiv2_control_name (const
-          gsl_odeiv2_control * C)
-     This function returns a pointer to the name of the control
-     function.  For example,
-
-          printf ("control method is '%s'\n",
-                  gsl_odeiv2_control_name (c));
-
-     would print something like 'control method is 'standard''
-
- -- Function: int gsl_odeiv2_control_errlevel (gsl_odeiv2_control * C,
-          const double Y, const double DYDT, const double H, const
-          size_t IND, double * ERRLEV)
-     This function calculates the desired error level of the IND-th
-     component to ERRLEV.  It requires the value (Y) and value of the
-     derivative (DYDT) of the component, and the current step size H.
-
- -- Function: int gsl_odeiv2_control_set_driver (gsl_odeiv2_control * C,
-          const gsl_odeiv2_driver * D)
-     This function sets a pointer of the driver object D for control
-     object C.
-
-
-File: gsl-ref.info,  Node: Evolution,  Next: Driver,  Prev: Adaptive Step-size Control,  Up: Ordinary Differential Equations
+The VEGAS algorithm of Lepage is based on importance sampling.  It
+samples points from the probability distribution described by the
+function |f|, so that the points are concentrated in the regions that
+make the largest contribution to the integral.
 
-26.4 Evolution
-==============
+   In general, if the Monte Carlo integral of f is sampled with points
+distributed according to a probability distribution described by the
+function g, we obtain an estimate E_g(f; N),
 
-The evolution function combines the results of a stepping function and
-control function to reliably advance the solution forward one step using
-an acceptable step-size.
+     E_g(f; N) = E(f/g; N)
 
- -- Function: gsl_odeiv2_evolve * gsl_odeiv2_evolve_alloc (size_t DIM)
-     This function returns a pointer to a newly allocated instance of an
-     evolution function for a system of DIM dimensions.
+with a corresponding variance,
 
- -- Function: int gsl_odeiv2_evolve_apply (gsl_odeiv2_evolve * E,
-          gsl_odeiv2_control * CON, gsl_odeiv2_step * STEP, const
-          gsl_odeiv2_system * SYS, double * T, double T1, double * H,
-          double Y[])
-     This function advances the system (E, SYS) from time T and position
-     Y using the stepping function STEP.  The new time and position are
-     stored in T and Y on output.
+     \Var_g(f; N) = \Var(f/g; N).
 
-     The initial step-size is taken as H.  The control function CON is
-     applied to check whether the local error estimated by the stepping
-     function STEP using step-size H exceeds the required error
-     tolerance.  If the error is too high, the step is retried by
-     calling STEP with a decreased step-size.  This process is continued
-     until an acceptable step-size is found.  An estimate of the local
-     error for the step can be obtained from the components of the array
-     'E->yerr[]'.
+If the probability distribution is chosen as g = |f|/I(|f|) then it can
+be shown that the variance V_g(f; N) vanishes, and the error in the
+estimate will be zero.  In practice it is not possible to sample from
+the exact distribution g for an arbitrary function, so importance
+sampling algorithms aim to produce efficient approximations to the
+desired distribution.
 
-     If the user-supplied functions defined in the system SYS returns
-     'GSL_EBADFUNC', the function returns immediately with the same
-     return code.  In this case the user must call
-     'gsl_odeiv2_step_reset' and 'gsl_odeiv2_evolve_reset' before
-     calling this function again.
+   The VEGAS algorithm approximates the exact distribution by making a
+number of passes over the integration region while histogramming the
+function f.  Each histogram is used to define a sampling distribution
+for the next pass.  Asymptotically this procedure converges to the
+desired distribution.  In order to avoid the number of histogram bins
+growing like K^d the probability distribution is approximated by a
+separable function: g(x_1, x_2, ...) = g_1(x_1) g_2(x_2) ... so that the
+number of bins required is only Kd.  This is equivalent to locating the
+peaks of the function from the projections of the integrand onto the
+coordinate axes.  The efficiency of VEGAS depends on the validity of
+this assumption.  It is most efficient when the peaks of the integrand
+are well-localized.  If an integrand can be rewritten in a form which is
+approximately separable this will increase the efficiency of integration
+with VEGAS.
 
-     Otherwise, if the user-supplied functions defined in the system SYS
-     or the stepping function STEP return a status other than
-     'GSL_SUCCESS', the step is retried with a decreased step-size.  If
-     the step-size decreases below machine precision, a status of
-     'GSL_FAILURE' is returned if the user functions returned
-     'GSL_SUCCESS'.  Otherwise the value returned by user function is
-     returned.  If no acceptable step can be made, T and Y will be
-     restored to their pre-step values and H contains the final
-     attempted step-size.
+   VEGAS incorporates a number of additional features, and combines both
+stratified sampling and importance sampling.  The integration region is
+divided into a number of "boxes", with each box getting a fixed number
+of points (the goal is 2).  Each box can then have a fractional number
+of bins, but if the ratio of bins-per-box is less than two, Vegas
+switches to a kind variance reduction (rather than importance sampling).
 
-     If the step is successful the function returns a suggested
-     step-size for the next step in H.  The maximum time T1 is
-     guaranteed not to be exceeded by the time-step.  On the final
-     time-step the value of T will be set to T1 exactly.
+ -- Function: gsl_monte_vegas_state * gsl_monte_vegas_alloc (size_t DIM)
+     This function allocates and initializes a workspace for Monte Carlo
+     integration in DIM dimensions.  The workspace is used to maintain
+     the state of the integration.
 
- -- Function: int gsl_odeiv2_evolve_apply_fixed_step (gsl_odeiv2_evolve
-          * E, gsl_odeiv2_control * CON, gsl_odeiv2_step * STEP, const
-          gsl_odeiv2_system * SYS, double * T, const double H, double
-          Y[])
-     This function advances the ODE-system (E, SYS, CON) from time T and
-     position Y using the stepping function STEP by a specified step
-     size H.  If the local error estimated by the stepping function
-     exceeds the desired error level, the step is not taken and the
-     function returns 'GSL_FAILURE'.  Otherwise the value returned by
-     user function is returned.
+ -- Function: int gsl_monte_vegas_init (gsl_monte_vegas_state* S)
+     This function initializes a previously allocated integration state.
+     This allows an existing workspace to be reused for different
+     integrations.
 
- -- Function: int gsl_odeiv2_evolve_reset (gsl_odeiv2_evolve * E)
-     This function resets the evolution function E.  It should be used
-     whenever the next use of E will not be a continuation of a previous
-     step.
+ -- Function: int gsl_monte_vegas_integrate (gsl_monte_function * F,
+          double XL[], double XU[], size_t DIM, size_t CALLS, gsl_rng *
+          R, gsl_monte_vegas_state * S, double * RESULT, double *
+          ABSERR)
+     This routines uses the VEGAS Monte Carlo algorithm to integrate the
+     function F over the DIM-dimensional hypercubic region defined by
+     the lower and upper limits in the arrays XL and XU, each of size
+     DIM.  The integration uses a fixed number of function calls CALLS,
+     and obtains random sampling points using the random number
+     generator R.  A previously allocated workspace S must be supplied.
+     The result of the integration is returned in RESULT, with an
+     estimated absolute error ABSERR.  The result and its error estimate
+     are based on a weighted average of independent samples.  The
+     chi-squared per degree of freedom for the weighted average is
+     returned via the state struct component, S->CHISQ, and must be
+     consistent with 1 for the weighted average to be reliable.
 
- -- Function: void gsl_odeiv2_evolve_free (gsl_odeiv2_evolve * E)
-     This function frees all the memory associated with the evolution
-     function E.
+ -- Function: void gsl_monte_vegas_free (gsl_monte_vegas_state * S)
+     This function frees the memory associated with the integrator state
+     S.
 
- -- Function: int gsl_odeiv2_evolve_set_driver (gsl_odeiv2_evolve * E,
-          const gsl_odeiv2_driver * D)
-     This function sets a pointer of the driver object D for evolve
-     object E.
+   The VEGAS algorithm computes a number of independent estimates of the
+integral internally, according to the 'iterations' parameter described
+below, and returns their weighted average.  Random sampling of the
+integrand can occasionally produce an estimate where the error is zero,
+particularly if the function is constant in some regions.  An estimate
+with zero error causes the weighted average to break down and must be
+handled separately.  In the original Fortran implementations of VEGAS
+the error estimate is made non-zero by substituting a small value
+(typically '1e-30').  The implementation in GSL differs from this and
+avoids the use of an arbitrary constant--it either assigns the value a
+weight which is the average weight of the preceding estimates or
+discards it according to the following procedure,
 
-   If a system has discontinuous changes in the derivatives at known
-points, it is advisable to evolve the system between each discontinuity
-in sequence.  For example, if a step-change in an external driving force
-occurs at times t_a, t_b and t_c then evolution should be carried out
-over the ranges (t_0,t_a), (t_a,t_b), (t_b,t_c), and (t_c,t_1)
-separately and not directly over the range (t_0,t_1).
+current estimate has zero error, weighted average has finite error
 
-
-File: gsl-ref.info,  Node: Driver,  Next: ODE Example programs,  Prev: Evolution,  Up: Ordinary Differential Equations
+     The current estimate is assigned a weight which is the average
+     weight of the preceding estimates.
 
-26.5 Driver
-===========
+current estimate has finite error, previous estimates had zero error
 
-The driver object is a high level wrapper that combines the evolution,
-control and stepper objects for easy use.
+     The previous estimates are discarded and the weighted averaging
+     procedure begins with the current estimate.
 
- -- Function: gsl_odeiv2_driver * gsl_odeiv2_driver_alloc_y_new (const
-          gsl_odeiv2_system * SYS, const gsl_odeiv2_step_type * T, const
-          double HSTART, const double EPSABS, const double EPSREL)
- -- Function: gsl_odeiv2_driver * gsl_odeiv2_driver_alloc_yp_new (const
-          gsl_odeiv2_system * SYS, const gsl_odeiv2_step_type * T, const
-          double HSTART, const double EPSABS, const double EPSREL)
- -- Function: gsl_odeiv2_driver * gsl_odeiv2_driver_alloc_standard_new
-          (const gsl_odeiv2_system * SYS, const gsl_odeiv2_step_type *
-          T, const double HSTART, const double EPSABS, const double
-          EPSREL, const double A_Y, const double A_DYDT)
- -- Function: gsl_odeiv2_driver * gsl_odeiv2_driver_alloc_scaled_new
-          (const gsl_odeiv2_system * SYS, const gsl_odeiv2_step_type *
-          T, const double HSTART, const double EPSABS, const double
-          EPSREL, const double A_Y, const double A_DYDT, const double
-          SCALE_ABS[])
-     These functions return a pointer to a newly allocated instance of a
-     driver object.  The functions automatically allocate and initialise
-     the evolve, control and stepper objects for ODE system SYS using
-     stepper type T.  The initial step size is given in HSTART.  The
-     rest of the arguments follow the syntax and semantics of the
-     control functions with same name ('gsl_odeiv2_control_*_new').
+current estimate has zero error, previous estimates had zero error
 
- -- Function: int gsl_odeiv2_driver_set_hmin (gsl_odeiv2_driver * D,
-          const double HMIN)
-     The function sets a minimum for allowed step size HMIN for driver
-     D.  Default value is 0.
+     The estimates are averaged using the arithmetic mean, but no error
+     is computed.
 
- -- Function: int gsl_odeiv2_driver_set_hmax (gsl_odeiv2_driver * D,
-          const double HMAX)
-     The function sets a maximum for allowed step size HMAX for driver
-     D.  Default value is 'GSL_DBL_MAX'.
+   The convergence of the algorithm can be tested using the overall
+chi-squared value of the results, which is available from the following
+function:
 
- -- Function: int gsl_odeiv2_driver_set_nmax (gsl_odeiv2_driver * D,
-          const unsigned long int NMAX)
-     The function sets a maximum for allowed number of steps NMAX for
-     driver D.  Default value of 0 sets no limit for steps.
+ -- Function: double gsl_monte_vegas_chisq (const gsl_monte_vegas_state
+          * S)
+     This function returns the chi-squared per degree of freedom for the
+     weighted estimate of the integral.  The returned value should be
+     close to 1.  A value which differs significantly from 1 indicates
+     that the values from different iterations are inconsistent.  In
+     this case the weighted error will be under-estimated, and further
+     iterations of the algorithm are needed to obtain reliable results.
 
- -- Function: int gsl_odeiv2_driver_apply (gsl_odeiv2_driver * D, double
-          * T, const double T1, double Y[])
-     This function evolves the driver system D from T to T1.  Initially
-     vector Y should contain the values of dependent variables at point
-     T.  If the function is unable to complete the calculation, an error
-     code from 'gsl_odeiv2_evolve_apply' is returned, and T and Y
-     contain the values from last successful step.
+ -- Function: void gsl_monte_vegas_runval (const gsl_monte_vegas_state *
+          S, double * RESULT, double * SIGMA)
+     This function returns the raw (unaveraged) values of the integral
+     RESULT and its error SIGMA from the most recent iteration of the
+     algorithm.
 
-     If maximum number of steps is reached, a value of 'GSL_EMAXITER' is
-     returned.  If the step size drops below minimum value, the function
-     returns with 'GSL_ENOPROG'.  If the user-supplied functions defined
-     in the system SYS returns 'GSL_EBADFUNC', the function returns
-     immediately with the same return code.  In this case the user must
-     call 'gsl_odeiv2_driver_reset' before calling this function again.
+   The VEGAS algorithm is highly configurable.  Several parameters can
+be changed using the following two functions.
 
- -- Function: int gsl_odeiv2_driver_apply_fixed_step (gsl_odeiv2_driver
-          * D, double * T, const double H, const unsigned long int N,
-          double Y[])
-     This function evolves the driver system D from T with N steps of
-     size H.  If the function is unable to complete the calculation, an
-     error code from 'gsl_odeiv2_evolve_apply_fixed_step' is returned,
-     and T and Y contain the values from last successful step.
+ -- Function: void gsl_monte_vegas_params_get (const
+          gsl_monte_vegas_state * S, gsl_monte_vegas_params * PARAMS)
+     This function copies the parameters of the integrator state into
+     the user-supplied PARAMS structure.
 
- -- Function: int gsl_odeiv2_driver_reset (gsl_odeiv2_driver * D)
-     This function resets the evolution and stepper objects.
+ -- Function: void gsl_monte_vegas_params_set (gsl_monte_vegas_state *
+          S, const gsl_monte_vegas_params * PARAMS)
+     This function sets the integrator parameters based on values
+     provided in the PARAMS structure.
 
- -- Function: int gsl_odeiv2_driver_reset_hstart (gsl_odeiv2_driver * D,
-          const double HSTART)
-     The routine resets the evolution and stepper objects and sets new
-     initial step size to HSTART.  This function can be used e.g.  to
-     change the direction of integration.
+   Typically the values of the parameters are first read using
+'gsl_monte_vegas_params_get', the necessary changes are made to the
+fields of the PARAMS structure, and the values are copied back into the
+integrator state using 'gsl_monte_vegas_params_set'.  The functions use
+the 'gsl_monte_vegas_params' structure which contains the following
+fields:
 
- -- Function: int gsl_odeiv2_driver_free (gsl_odeiv2_driver * D)
-     This function frees the driver object, and the related evolution,
-     stepper and control objects.
+ -- Variable: double alpha
+     The parameter 'alpha' controls the stiffness of the rebinning
+     algorithm.  It is typically set between one and two.  A value of
+     zero prevents rebinning of the grid.  The default value is 1.5.
 
-
-File: gsl-ref.info,  Node: ODE Example programs,  Next: ODE References and Further Reading,  Prev: Driver,  Up: Ordinary Differential Equations
+ -- Variable: size_t iterations
+     The number of iterations to perform for each call to the routine.
+     The default value is 5 iterations.
 
-26.6 Examples
-=============
+ -- Variable: int stage
+     Setting this determines the "stage" of the calculation.  Normally,
+     'stage = 0' which begins with a new uniform grid and empty weighted
+     average.  Calling VEGAS with 'stage = 1' retains the grid from the
+     previous run but discards the weighted average, so that one can
+     "tune" the grid using a relatively small number of points and then
+     do a large run with 'stage = 1' on the optimized grid.  Setting
+     'stage = 2' keeps the grid and the weighted average from the
+     previous run, but may increase (or decrease) the number of
+     histogram bins in the grid depending on the number of calls
+     available.  Choosing 'stage = 3' enters at the main loop, so that
+     nothing is changed, and is equivalent to performing additional
+     iterations in a previous call.
 
-The following program solves the second-order nonlinear Van der Pol
-oscillator equation,
+ -- Variable: int mode
+     The possible choices are 'GSL_VEGAS_MODE_IMPORTANCE',
+     'GSL_VEGAS_MODE_STRATIFIED', 'GSL_VEGAS_MODE_IMPORTANCE_ONLY'.
+     This determines whether VEGAS will use importance sampling or
+     stratified sampling, or whether it can pick on its own.  In low
+     dimensions VEGAS uses strict stratified sampling (more precisely,
+     stratified sampling is chosen if there are fewer than 2 bins per
+     box).
 
-     u''(t) + \mu u'(t) (u(t)^2 - 1) + u(t) = 0
+ -- Variable: int verbose
+ -- Variable: FILE * ostream
+     These parameters set the level of information printed by VEGAS.
+     All information is written to the stream OSTREAM.  The default
+     setting of VERBOSE is '-1', which turns off all output.  A VERBOSE
+     value of '0' prints summary information about the weighted average
+     and final result, while a value of '1' also displays the grid
+     coordinates.  A value of '2' prints information from the rebinning
+     procedure for each iteration.
 
-This can be converted into a first order system suitable for use with
-the routines described in this chapter by introducing a separate
-variable for the velocity, v = u'(t),
+   The above fields and the CHISQ value can also be accessed directly in
+the 'gsl_monte_vegas_state' but such use is deprecated.
 
-     u' = v
-     v' = -u + \mu v (1-u^2)
+
+File: gsl-ref.info,  Node: Monte Carlo Examples,  Next: Monte Carlo Integration References and Further Reading,  Prev: VEGAS,  Up: Monte Carlo Integration
 
-The program begins by defining functions for these derivatives and their
-Jacobian.  The main function uses driver level functions to solve the
-problem.  The program evolves the solution from (u, v) = (1, 0) at t=0
-to t=100.  The step-size h is automatically adjusted by the controller
-to maintain an absolute accuracy of 10^{-6} in the function values (u,
-v).  The loop in the example prints the solution at the points t_i = 1,
-2, \dots, 100.
+25.5 Examples
+=============
 
-     #include <stdio.h>
-     #include <gsl/gsl_errno.h>
-     #include <gsl/gsl_matrix.h>
-     #include <gsl/gsl_odeiv2.h>
+The example program below uses the Monte Carlo routines to estimate the
+value of the following 3-dimensional integral from the theory of random
+walks,
 
-     int
-     func (double t, const double y[], double f[],
-           void *params)
-     {
-       double mu = *(double *)params;
-       f[0] = y[1];
-       f[1] = -y[0] - mu*y[1]*(y[0]*y[0] - 1);
-       return GSL_SUCCESS;
-     }
+     I = \int_{-pi}^{+pi} {dk_x/(2 pi)}
+         \int_{-pi}^{+pi} {dk_y/(2 pi)}
+         \int_{-pi}^{+pi} {dk_z/(2 pi)}
+          1 / (1 - cos(k_x)cos(k_y)cos(k_z)).
 
-     int
-     jac (double t, const double y[], double *dfdy,
-          double dfdt[], void *params)
-     {
-       double mu = *(double *)params;
-       gsl_matrix_view dfdy_mat
-         = gsl_matrix_view_array (dfdy, 2, 2);
-       gsl_matrix * m = &dfdy_mat.matrix;
-       gsl_matrix_set (m, 0, 0, 0.0);
-       gsl_matrix_set (m, 0, 1, 1.0);
-       gsl_matrix_set (m, 1, 0, -2.0*mu*y[0]*y[1] - 1.0);
-       gsl_matrix_set (m, 1, 1, -mu*(y[0]*y[0] - 1.0));
-       dfdt[0] = 0.0;
-       dfdt[1] = 0.0;
-       return GSL_SUCCESS;
-     }
+The analytic value of this integral can be shown to be I =
+\Gamma(1/4)^4/(4 \pi^3) = 1.393203929685676859....  The integral gives
+the mean time spent at the origin by a random walk on a body-centered
+cubic lattice in three dimensions.
 
-     int
-     main (void)
-     {
-       double mu = 10;
-       gsl_odeiv2_system sys = {func, jac, 2, &mu};
+   For simplicity we will compute the integral over the region (0,0,0)
+to (\pi,\pi,\pi) and multiply by 8 to obtain the full result.  The
+integral is slowly varying in the middle of the region but has
+integrable singularities at the corners (0,0,0), (0,\pi,\pi),
+(\pi,0,\pi) and (\pi,\pi,0).  The Monte Carlo routines only select
+points which are strictly within the integration region and so no
+special measures are needed to avoid these singularities.
 
-       gsl_odeiv2_driver * d =
-         gsl_odeiv2_driver_alloc_y_new (&sys, gsl_odeiv2_step_rk8pd,
-     				  1e-6, 1e-6, 0.0);
-       int i;
-       double t = 0.0, t1 = 100.0;
-       double y[2] = { 1.0, 0.0 };
+     #include <stdlib.h>
+     #include <gsl/gsl_math.h>
+     #include <gsl/gsl_monte.h>
+     #include <gsl/gsl_monte_plain.h>
+     #include <gsl/gsl_monte_miser.h>
+     #include <gsl/gsl_monte_vegas.h>
 
-       for (i = 1; i <= 100; i++)
-         {
-           double ti = i * t1 / 100.0;
-           int status = gsl_odeiv2_driver_apply (d, &t, ti, y);
+     /* Computation of the integral,
 
-           if (status != GSL_SUCCESS)
-     	{
-     	  printf ("error, return value=%d\n", status);
-     	  break;
-     	}
+           I = int (dx dy dz)/(2pi)^3  1/(1-cos(x)cos(y)cos(z))
 
-           printf ("%.5e %.5e %.5e\n", t, y[0], y[1]);
-         }
+        over (-pi,-pi,-pi) to (+pi, +pi, +pi).  The exact answer
+        is Gamma(1/4)^4/(4 pi^3).  This example is taken from
+        C.Itzykson, J.M.Drouffe, "Statistical Field Theory -
+        Volume 1", Section 1.1, p21, which cites the original
+        paper M.L.Glasser, I.J.Zucker, Proc.Natl.Acad.Sci.USA 74
+        1800 (1977) */
 
-       gsl_odeiv2_driver_free (d);
-       return 0;
+     /* For simplicity we compute the integral over the region
+        (0,0,0) -> (pi,pi,pi) and multiply by 8 */
+
+     double exact = 1.3932039296856768591842462603255;
+
+     double
+     g (double *k, size_t dim, void *params)
+     {
+       (void)(dim); /* avoid unused parameter warnings */
+       (void)(params);
+       double A = 1.0 / (M_PI * M_PI * M_PI);
+       return A / (1.0 - cos (k[0]) * cos (k[1]) * cos (k[2]));
      }
 
-The user can work with the lower level functions directly, as in the
-following example.  In this case an intermediate result is printed after
-each successful step instead of equidistant time points.
+     void
+     display_results (char *title, double result, double error)
+     {
+       printf ("%s ==================\n", title);
+       printf ("result = % .6f\n", result);
+       printf ("sigma  = % .6f\n", error);
+       printf ("exact  = % .6f\n", exact);
+       printf ("error  = % .6f = %.2g sigma\n", result - exact,
+               fabs (result - exact) / error);
+     }
 
      int
      main (void)
      {
-       const gsl_odeiv2_step_type * T
-         = gsl_odeiv2_step_rk8pd;
+       double res, err;
 
-       gsl_odeiv2_step * s
-         = gsl_odeiv2_step_alloc (T, 2);
-       gsl_odeiv2_control * c
-         = gsl_odeiv2_control_y_new (1e-6, 0.0);
-       gsl_odeiv2_evolve * e
-         = gsl_odeiv2_evolve_alloc (2);
+       double xl[3] = { 0, 0, 0 };
+       double xu[3] = { M_PI, M_PI, M_PI };
+
+       const gsl_rng_type *T;
+       gsl_rng *r;
 
-       double mu = 10;
-       gsl_odeiv2_system sys = {func, jac, 2, &mu};
+       gsl_monte_function G = { &g, 3, 0 };
 
-       double t = 0.0, t1 = 100.0;
-       double h = 1e-6;
-       double y[2] = { 1.0, 0.0 };
+       size_t calls = 500000;
 
-       while (t < t1)
-         {
-           int status = gsl_odeiv2_evolve_apply (e, c, s,
-                                                &sys,
-                                                &t, t1,
-                                                &h, y);
+       gsl_rng_env_setup ();
 
-           if (status != GSL_SUCCESS)
-               break;
+       T = gsl_rng_default;
+       r = gsl_rng_alloc (T);
 
-           printf ("%.5e %.5e %.5e\n", t, y[0], y[1]);
-         }
+       {
+         gsl_monte_plain_state *s = gsl_monte_plain_alloc (3);
+         gsl_monte_plain_integrate (&G, xl, xu, 3, calls, r, s,
+                                    &res, &err);
+         gsl_monte_plain_free (s);
 
-       gsl_odeiv2_evolve_free (e);
-       gsl_odeiv2_control_free (c);
-       gsl_odeiv2_step_free (s);
-       return 0;
-     }
+         display_results ("plain", res, err);
+       }
 
-For functions with multiple parameters, the appropriate information can
-be passed in through the PARAMS argument in 'gsl_odeiv2_system'
-definition (MU in this example) by using a pointer to a struct.
+       {
+         gsl_monte_miser_state *s = gsl_monte_miser_alloc (3);
+         gsl_monte_miser_integrate (&G, xl, xu, 3, calls, r, s,
+                                    &res, &err);
+         gsl_monte_miser_free (s);
 
-It is also possible to work with a non-adaptive integrator, using only
-the stepping function itself, 'gsl_odeiv2_driver_apply_fixed_step' or
-'gsl_odeiv2_evolve_apply_fixed_step'.  The following program uses the
-driver level function, with fourth-order Runge-Kutta stepping function
-with a fixed stepsize of 0.001.
+         display_results ("miser", res, err);
+       }
 
-     int
-     main (void)
-     {
-       double mu = 10;
-       gsl_odeiv2_system sys = { func, jac, 2, &mu };
+       {
+         gsl_monte_vegas_state *s = gsl_monte_vegas_alloc (3);
 
-       gsl_odeiv2_driver *d =
-         gsl_odeiv2_driver_alloc_y_new (&sys, gsl_odeiv2_step_rk4,
-                                        1e-3, 1e-8, 1e-8);
+         gsl_monte_vegas_integrate (&G, xl, xu, 3, 10000, r, s,
+                                    &res, &err);
+         display_results ("vegas warm-up", res, err);
 
-       double t = 0.0;
-       double y[2] = { 1.0, 0.0 };
-       int i, s;
+         printf ("converging...\n");
 
-       for (i = 0; i < 100; i++)
-         {
-           s = gsl_odeiv2_driver_apply_fixed_step (d, &t, 1e-3, 1000, y);
+         do
+           {
+             gsl_monte_vegas_integrate (&G, xl, xu, 3, calls/5, r, s,
+                                        &res, &err);
+             printf ("result = % .6f sigma = % .6f "
+                     "chisq/dof = %.1f\n", res, err, gsl_monte_vegas_chisq (s));
+           }
+         while (fabs (gsl_monte_vegas_chisq (s) - 1.0) > 0.5);
 
-           if (s != GSL_SUCCESS)
-             {
-               printf ("error: driver returned %d\n", s);
-               break;
-             }
+         display_results ("vegas final", res, err);
 
-           printf ("%.5e %.5e %.5e\n", t, y[0], y[1]);
-         }
+         gsl_monte_vegas_free (s);
+       }
 
-       gsl_odeiv2_driver_free (d);
-       return s;
+       gsl_rng_free (r);
+
+       return 0;
      }
 
-
-File: gsl-ref.info,  Node: ODE References and Further Reading,  Prev: ODE Example programs,  Up: Ordinary Differential Equations
+With 500,000 function calls the plain Monte Carlo algorithm achieves a
+fractional error of 1%.  The estimated error 'sigma' is roughly
+consistent with the actual error-the computed result differs from the
+true result by about 1.4 standard deviations,
 
-26.7 References and Further Reading
-===================================
+     plain ==================
+     result =  1.412209
+     sigma  =  0.013436
+     exact  =  1.393204
+     error  =  0.019005 = 1.4 sigma
 
-     Ascher, U.M., Petzold, L.R., 'Computer Methods for Ordinary
-     Differential and Differential-Algebraic Equations', SIAM,
-     Philadelphia, 1998.
+The MISER algorithm reduces the error by a factor of four, and also
+correctly estimates the error,
 
-     Hairer, E., Norsett, S. P., Wanner, G., 'Solving Ordinary
-     Differential Equations I: Nonstiff Problems', Springer, Berlin,
-     1993.
+     miser ==================
+     result =  1.391322
+     sigma  =  0.003461
+     exact  =  1.393204
+     error  = -0.001882 = 0.54 sigma
 
-     Hairer, E., Wanner, G., 'Solving Ordinary Differential Equations
-     II: Stiff and Differential-Algebraic Problems', Springer, Berlin,
-     1996.
+In the case of the VEGAS algorithm the program uses an initial warm-up
+run of 10,000 function calls to prepare, or "warm up", the grid.  This
+is followed by a main run with five iterations of 100,000 function
+calls.  The chi-squared per degree of freedom for the five iterations
+are checked for consistency with 1, and the run is repeated if the
+results have not converged.  In this case the estimates are consistent
+on the first pass.
 
-   Many of the basic Runge-Kutta formulas can be found in the Handbook
-of Mathematical Functions,
+     vegas warm-up ==================
+     result =  1.392673
+     sigma  =  0.003410
+     exact  =  1.393204
+     error  = -0.000531 = 0.16 sigma
+     converging...
+     result =  1.393281 sigma =  0.000362 chisq/dof = 1.5
+     vegas final ==================
+     result =  1.393281
+     sigma  =  0.000362
+     exact  =  1.393204
+     error  =  0.000077 = 0.21 sigma
 
-     Abramowitz & Stegun (eds.), 'Handbook of Mathematical Functions',
-     Section 25.5.
+If the value of 'chisq' had differed significantly from 1 it would
+indicate inconsistent results, with a correspondingly underestimated
+error.  The final estimate from VEGAS (using a similar number of
+function calls) is significantly more accurate than the other two
+algorithms.
 
-The implicit Bulirsch-Stoer algorithm 'bsimp' is described in the
-following paper,
+
+File: gsl-ref.info,  Node: Monte Carlo Integration References and Further Reading,  Prev: Monte Carlo Examples,  Up: Monte Carlo Integration
 
-     G. Bader and P. Deuflhard, "A Semi-Implicit Mid-Point Rule for
-     Stiff Systems of Ordinary Differential Equations.", Numer. Math.
-     41, 373-398, 1983.
+25.6 References and Further Reading
+===================================
 
-The Adams and BDF multistep methods 'msadams' and 'msbdf' are based on
-the following articles,
+The MISER algorithm is described in the following article by Press and
+Farrar,
 
-     G. D. Byrne and A. C. Hindmarsh, "A Polyalgorithm for the Numerical
-     Solution of Ordinary Differential Equations.", ACM Trans.  Math.
-     Software, 1, 71-96, 1975.
+     W.H. Press, G.R. Farrar, 'Recursive Stratified Sampling for
+     Multidimensional Monte Carlo Integration', Computers in Physics, v4
+     (1990), pp190-195.
 
-     P. N. Brown, G. D. Byrne and A. C. Hindmarsh, "VODE: A
-     Variable-coefficient ODE Solver.", SIAM J. Sci.  Stat.  Comput.
-     10, 1038-1051, 1989.
+The VEGAS algorithm is described in the following papers,
 
-     A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D.
-     E. Shumaker and C. S. Woodward, "SUNDIALS: Suite of Nonlinear and
-     Differential/Algebraic Equation Solvers.", ACM Trans.  Math.
-     Software 31, 363-396, 2005.
+     G.P. Lepage, 'A New Algorithm for Adaptive Multidimensional
+     Integration', Journal of Computational Physics 27, 192-203, (1978)
+
+     G.P. Lepage, 'VEGAS: An Adaptive Multi-dimensional Integration
+     Program', Cornell preprint CLNS 80-447, March 1980
 
 
-File: gsl-ref.info,  Node: Interpolation,  Next: Numerical Differentiation,  Prev: Ordinary Differential Equations,  Up: Top
+File: gsl-ref.info,  Node: Simulated Annealing,  Next: Ordinary Differential Equations,  Prev: Monte Carlo Integration,  Up: Top
 
-27 Interpolation
-****************
+26 Simulated Annealing
+**********************
 
-This chapter describes functions for performing interpolation.  The
-library provides a variety of interpolation methods, including Cubic
-splines and Akima splines.  The interpolation types are interchangeable,
-allowing different methods to be used without recompiling.
-Interpolations can be defined for both normal and periodic boundary
-conditions.  Additional functions are available for computing
-derivatives and integrals of interpolating functions.
+Stochastic search techniques are used when the structure of a space is
+not well understood or is not smooth, so that techniques like Newton's
+method (which requires calculating Jacobian derivative matrices) cannot
+be used.  In particular, these techniques are frequently used to solve
+combinatorial optimization problems, such as the traveling salesman
+problem.
 
-   These interpolation methods produce curves that pass through each
-datapoint.  To interpolate noisy data with a smoothing curve see *note
-Basis Splines::.
+   The goal is to find a point in the space at which a real valued
+"energy function" (or "cost function") is minimized.  Simulated
+annealing is a minimization technique which has given good results in
+avoiding local minima; it is based on the idea of taking a random walk
+through the space at successively lower temperatures, where the
+probability of taking a step is given by a Boltzmann distribution.
 
-   The functions described in this section are declared in the header
-files 'gsl_interp.h' and 'gsl_spline.h'.
+   The functions described in this chapter are declared in the header
+file 'gsl_siman.h'.
 
 * Menu:
 
-* Introduction to Interpolation::  
-* Interpolation Functions::     
-* Interpolation Types::         
-* Index Look-up and Acceleration::  
-* Evaluation of Interpolating Functions::  
-* Higher-level Interface::      
-* Interpolation Example programs::  
-* Interpolation References and Further Reading::  
-
-
-File: gsl-ref.info,  Node: Introduction to Interpolation,  Next: Interpolation Functions,  Up: Interpolation
-
-27.1 Introduction
-=================
-
-Given a set of data points (x_1, y_1) \dots (x_n, y_n) the routines
-described in this section compute a continuous interpolating function
-y(x) such that y(x_i) = y_i.  The interpolation is piecewise smooth, and
-its behavior at the end-points is determined by the type of
-interpolation used.
+* Simulated Annealing algorithm::  
+* Simulated Annealing functions::  
+* Examples with Simulated Annealing::  
+* Simulated Annealing References and Further Reading::  
 
 
-File: gsl-ref.info,  Node: Interpolation Functions,  Next: Interpolation Types,  Prev: Introduction to Interpolation,  Up: Interpolation
-
-27.2 Interpolation Functions
-============================
+File: gsl-ref.info,  Node: Simulated Annealing algorithm,  Next: Simulated Annealing functions,  Up: Simulated Annealing
 
-The interpolation function for a given dataset is stored in a
-'gsl_interp' object.  These are created by the following functions.
+26.1 Simulated Annealing algorithm
+==================================
 
- -- Function: gsl_interp * gsl_interp_alloc (const gsl_interp_type * T,
-          size_t SIZE)
-     This function returns a pointer to a newly allocated interpolation
-     object of type T for SIZE data-points.
+The simulated annealing algorithm takes random walks through the problem
+space, looking for points with low energies; in these random walks, the
+probability of taking a step is determined by the Boltzmann
+distribution,
 
- -- Function: int gsl_interp_init (gsl_interp * INTERP, const double
-          XA[], const double YA[], size_t SIZE)
-     This function initializes the interpolation object INTERP for the
-     data (XA,YA) where XA and YA are arrays of size SIZE.  The
-     interpolation object ('gsl_interp') does not save the data arrays
-     XA and YA and only stores the static state computed from the data.
-     The XA data array is always assumed to be strictly ordered, with
-     increasing x values; the behavior for other arrangements is not
-     defined.
+     p = e^{-(E_{i+1} - E_i)/(kT)}
 
- -- Function: void gsl_interp_free (gsl_interp * INTERP)
-     This function frees the interpolation object INTERP.
+if E_{i+1} > E_i, and p = 1 when E_{i+1} <= E_i.
 
-
-File: gsl-ref.info,  Node: Interpolation Types,  Next: Index Look-up and Acceleration,  Prev: Interpolation Functions,  Up: Interpolation
+   In other words, a step will occur if the new energy is lower.  If the
+new energy is higher, the transition can still occur, and its likelihood
+is proportional to the temperature T and inversely proportional to the
+energy difference E_{i+1} - E_i.
 
-27.3 Interpolation Types
-========================
+   The temperature T is initially set to a high value, and a random walk
+is carried out at that temperature.  Then the temperature is lowered
+very slightly according to a "cooling schedule", for example: T ->
+T/mu_T where \mu_T is slightly greater than 1.
 
-The interpolation library provides six interpolation types:
+   The slight probability of taking a step that gives higher energy is
+what allows simulated annealing to frequently get out of local minima.
 
- -- Interpolation Type: gsl_interp_linear
-     Linear interpolation.  This interpolation method does not require
-     any additional memory.
+
+File: gsl-ref.info,  Node: Simulated Annealing functions,  Next: Examples with Simulated Annealing,  Prev: Simulated Annealing algorithm,  Up: Simulated Annealing
 
- -- Interpolation Type: gsl_interp_polynomial
-     Polynomial interpolation.  This method should only be used for
-     interpolating small numbers of points because polynomial
-     interpolation introduces large oscillations, even for well-behaved
-     datasets.  The number of terms in the interpolating polynomial is
-     equal to the number of points.
+26.2 Simulated Annealing functions
+==================================
 
- -- Interpolation Type: gsl_interp_cspline
-     Cubic spline with natural boundary conditions.  The resulting curve
-     is piecewise cubic on each interval, with matching first and second
-     derivatives at the supplied data-points.  The second derivative is
-     chosen to be zero at the first point and last point.
+ -- Function: void gsl_siman_solve (const gsl_rng * R, void * X0_P,
+          gsl_siman_Efunc_t EF, gsl_siman_step_t TAKE_STEP,
+          gsl_siman_metric_t DISTANCE, gsl_siman_print_t PRINT_POSITION,
+          gsl_siman_copy_t COPYFUNC, gsl_siman_copy_construct_t
+          COPY_CONSTRUCTOR, gsl_siman_destroy_t DESTRUCTOR, size_t
+          ELEMENT_SIZE, gsl_siman_params_t PARAMS)
 
- -- Interpolation Type: gsl_interp_cspline_periodic
-     Cubic spline with periodic boundary conditions.  The resulting
-     curve is piecewise cubic on each interval, with matching first and
-     second derivatives at the supplied data-points.  The derivatives at
-     the first and last points are also matched.  Note that the last
-     point in the data must have the same y-value as the first point,
-     otherwise the resulting periodic interpolation will have a
-     discontinuity at the boundary.
+     This function performs a simulated annealing search through a given
+     space.  The space is specified by providing the functions EF and
+     DISTANCE.  The simulated annealing steps are generated using the
+     random number generator R and the function TAKE_STEP.
 
- -- Interpolation Type: gsl_interp_akima
-     Non-rounded Akima spline with natural boundary conditions.  This
-     method uses the non-rounded corner algorithm of Wodicka.
+     The starting configuration of the system should be given by X0_P.
+     The routine offers two modes for updating configurations, a
+     fixed-size mode and a variable-size mode.  In the fixed-size mode
+     the configuration is stored as a single block of memory of size
+     ELEMENT_SIZE.  Copies of this configuration are created, copied and
+     destroyed internally using the standard library functions 'malloc',
+     'memcpy' and 'free'.  The function pointers COPYFUNC,
+     COPY_CONSTRUCTOR and DESTRUCTOR should be null pointers in
+     fixed-size mode.  In the variable-size mode the functions COPYFUNC,
+     COPY_CONSTRUCTOR and DESTRUCTOR are used to create, copy and
+     destroy configurations internally.  The variable ELEMENT_SIZE
+     should be zero in the variable-size mode.
 
- -- Interpolation Type: gsl_interp_akima_periodic
-     Non-rounded Akima spline with periodic boundary conditions.  This
-     method uses the non-rounded corner algorithm of Wodicka.
+     The PARAMS structure (described below) controls the run by
+     providing the temperature schedule and other tunable parameters to
+     the algorithm.
 
-   The following related functions are available:
+     On exit the best result achieved during the search is placed in
+     '*X0_P'.  If the annealing process has been successful this should
+     be a good approximation to the optimal point in the space.
 
- -- Function: const char * gsl_interp_name (const gsl_interp * INTERP)
-     This function returns the name of the interpolation type used by
-     INTERP.  For example,
+     If the function pointer PRINT_POSITION is not null, a debugging log
+     will be printed to 'stdout' with the following columns:
 
-          printf ("interp uses '%s' interpolation.\n",
-                  gsl_interp_name (interp));
+          #-iter  #-evals  temperature  position  energy  best_energy
 
-     would print something like,
+     and the output of the function PRINT_POSITION itself.  If
+     PRINT_POSITION is null then no information is printed.
 
-          interp uses 'cspline' interpolation.
+The simulated annealing routines require several user-specified
+functions to define the configuration space and energy function.  The
+prototypes for these functions are given below.
 
- -- Function: unsigned int gsl_interp_min_size (const gsl_interp *
-          INTERP)
- -- Function: unsigned int gsl_interp_type_min_size (const
-          gsl_interp_type * T)
-     These functions return the minimum number of points required by the
-     interpolation object INTERP or interpolation type T.  For example,
-     Akima spline interpolation requires a minimum of 5 points.
+ -- Data Type: gsl_siman_Efunc_t
+     This function type should return the energy of a configuration XP.
 
-
-File: gsl-ref.info,  Node: Index Look-up and Acceleration,  Next: Evaluation of Interpolating Functions,  Prev: Interpolation Types,  Up: Interpolation
+          double (*gsl_siman_Efunc_t) (void *xp)
 
-27.4 Index Look-up and Acceleration
-===================================
+ -- Data Type: gsl_siman_step_t
+     This function type should modify the configuration XP using a
+     random step taken from the generator R, up to a maximum distance of
+     STEP_SIZE.
 
-The state of searches can be stored in a 'gsl_interp_accel' object,
-which is a kind of iterator for interpolation lookups.  It caches the
-previous value of an index lookup.  When the subsequent interpolation
-point falls in the same interval its index value can be returned
-immediately.
+          void (*gsl_siman_step_t) (const gsl_rng *r, void *xp,
+                                    double step_size)
 
- -- Function: size_t gsl_interp_bsearch (const double X_ARRAY[], double
-          X, size_t INDEX_LO, size_t INDEX_HI)
-     This function returns the index i of the array X_ARRAY such that
-     'x_array[i] <= x < x_array[i+1]'.  The index is searched for in the
-     range [INDEX_LO,INDEX_HI].  An inline version of this function is
-     used when 'HAVE_INLINE' is defined.
+ -- Data Type: gsl_siman_metric_t
+     This function type should return the distance between two
+     configurations XP and YP.
 
- -- Function: gsl_interp_accel * gsl_interp_accel_alloc (void)
-     This function returns a pointer to an accelerator object, which is
-     a kind of iterator for interpolation lookups.  It tracks the state
-     of lookups, thus allowing for application of various acceleration
-     strategies.
+          double (*gsl_siman_metric_t) (void *xp, void *yp)
 
- -- Function: size_t gsl_interp_accel_find (gsl_interp_accel * A, const
-          double X_ARRAY[], size_t SIZE, double X)
-     This function performs a lookup action on the data array X_ARRAY of
-     size SIZE, using the given accelerator A.  This is how lookups are
-     performed during evaluation of an interpolation.  The function
-     returns an index i such that 'x_array[i] <= x < x_array[i+1]'.  An
-     inline version of this function is used when 'HAVE_INLINE' is
-     defined.
+ -- Data Type: gsl_siman_print_t
+     This function type should print the contents of the configuration
+     XP.
 
- -- Function: int gsl_interp_accel_reset (gsl_interp_accel * ACC);
-     This function reinitializes the accelerator object ACC.  It should
-     be used when the cached information is no longer applicable--for
-     example, when switching to a new dataset.
+          void (*gsl_siman_print_t) (void *xp)
 
- -- Function: void gsl_interp_accel_free (gsl_interp_accel* ACC)
-     This function frees the accelerator object ACC.
+ -- Data Type: gsl_siman_copy_t
+     This function type should copy the configuration SOURCE into DEST.
 
-
-File: gsl-ref.info,  Node: Evaluation of Interpolating Functions,  Next: Higher-level Interface,  Prev: Index Look-up and Acceleration,  Up: Interpolation
+          void (*gsl_siman_copy_t) (void *source, void *dest)
 
-27.5 Evaluation of Interpolating Functions
-==========================================
+ -- Data Type: gsl_siman_copy_construct_t
+     This function type should create a new copy of the configuration
+     XP.
 
- -- Function: double gsl_interp_eval (const gsl_interp * INTERP, const
-          double XA[], const double YA[], double X, gsl_interp_accel *
-          ACC)
- -- Function: int gsl_interp_eval_e (const gsl_interp * INTERP, const
-          double XA[], const double YA[], double X, gsl_interp_accel *
-          ACC, double * Y)
-     These functions return the interpolated value of Y for a given
-     point X, using the interpolation object INTERP, data arrays XA and
-     YA and the accelerator ACC.  When X is outside the range of XA, the
-     error code 'GSL_EDOM' is returned with a value of 'GSL_NAN' for Y.
+          void * (*gsl_siman_copy_construct_t) (void *xp)
 
- -- Function: double gsl_interp_eval_deriv (const gsl_interp * INTERP,
-          const double XA[], const double YA[], double X,
-          gsl_interp_accel * ACC)
- -- Function: int gsl_interp_eval_deriv_e (const gsl_interp * INTERP,
-          const double XA[], const double YA[], double X,
-          gsl_interp_accel * ACC, double * D)
-     These functions return the derivative D of an interpolated function
-     for a given point X, using the interpolation object INTERP, data
-     arrays XA and YA and the accelerator ACC.
+ -- Data Type: gsl_siman_destroy_t
+     This function type should destroy the configuration XP, freeing its
+     memory.
 
- -- Function: double gsl_interp_eval_deriv2 (const gsl_interp * INTERP,
-          const double XA[], const double YA[], double X,
-          gsl_interp_accel * ACC)
- -- Function: int gsl_interp_eval_deriv2_e (const gsl_interp * INTERP,
-          const double XA[], const double YA[], double X,
-          gsl_interp_accel * ACC, double * D2)
-     These functions return the second derivative D2 of an interpolated
-     function for a given point X, using the interpolation object
-     INTERP, data arrays XA and YA and the accelerator ACC.
+          void (*gsl_siman_destroy_t) (void *xp)
 
- -- Function: double gsl_interp_eval_integ (const gsl_interp * INTERP,
-          const double XA[], const double YA[], double A, double B,
-          gsl_interp_accel * ACC)
- -- Function: int gsl_interp_eval_integ_e (const gsl_interp * INTERP,
-          const double XA[], const double YA[], double A, double B,
-          gsl_interp_accel * ACC, double * RESULT)
-     These functions return the numerical integral RESULT of an
-     interpolated function over the range [A, B], using the
-     interpolation object INTERP, data arrays XA and YA and the
-     accelerator ACC.
+ -- Data Type: gsl_siman_params_t
+     These are the parameters that control a run of 'gsl_siman_solve'.
+     This structure contains all the information needed to control the
+     search, beyond the energy function, the step function and the
+     initial guess.
 
-
-File: gsl-ref.info,  Node: Higher-level Interface,  Next: Interpolation Example programs,  Prev: Evaluation of Interpolating Functions,  Up: Interpolation
+     'int n_tries'
+          The number of points to try for each step.
 
-27.6 Higher-level Interface
-===========================
+     'int iters_fixed_T'
+          The number of iterations at each temperature.
 
-The functions described in the previous sections required the user to
-supply pointers to the x and y arrays on each call.  The following
-functions are equivalent to the corresponding 'gsl_interp' functions but
-maintain a copy of this data in the 'gsl_spline' object.  This removes
-the need to pass both XA and YA as arguments on each evaluation.  These
-functions are defined in the header file 'gsl_spline.h'.
+     'double step_size'
+          The maximum step size in the random walk.
 
- -- Function: gsl_spline * gsl_spline_alloc (const gsl_interp_type * T,
-          size_t SIZE)
+     'double k, t_initial, mu_t, t_min'
+          The parameters of the Boltzmann distribution and cooling
+          schedule.
 
- -- Function: int gsl_spline_init (gsl_spline * SPLINE, const double
-          XA[], const double YA[], size_t SIZE)
+
+File: gsl-ref.info,  Node: Examples with Simulated Annealing,  Next: Simulated Annealing References and Further Reading,  Prev: Simulated Annealing functions,  Up: Simulated Annealing
 
- -- Function: void gsl_spline_free (gsl_spline * SPLINE)
+26.3 Examples
+=============
 
- -- Function: const char * gsl_spline_name (const gsl_spline * SPLINE)
+The simulated annealing package is clumsy, and it has to be because it
+is written in C, for C callers, and tries to be polymorphic at the same
+time.  But here we provide some examples which can be pasted into your
+application with little change and should make things easier.
 
- -- Function: unsigned int gsl_spline_min_size (const gsl_spline *
-          SPLINE)
+* Menu:
 
- -- Function: double gsl_spline_eval (const gsl_spline * SPLINE, double
-          X, gsl_interp_accel * ACC)
- -- Function: int gsl_spline_eval_e (const gsl_spline * SPLINE, double
-          X, gsl_interp_accel * ACC, double * Y)
+* Trivial example::             
+* Traveling Salesman Problem::  
 
- -- Function: double gsl_spline_eval_deriv (const gsl_spline * SPLINE,
-          double X, gsl_interp_accel * ACC)
- -- Function: int gsl_spline_eval_deriv_e (const gsl_spline * SPLINE,
-          double X, gsl_interp_accel * ACC, double * D)
+
+File: gsl-ref.info,  Node: Trivial example,  Next: Traveling Salesman Problem,  Up: Examples with Simulated Annealing
 
- -- Function: double gsl_spline_eval_deriv2 (const gsl_spline * SPLINE,
-          double X, gsl_interp_accel * ACC)
- -- Function: int gsl_spline_eval_deriv2_e (const gsl_spline * SPLINE,
-          double X, gsl_interp_accel * ACC, double * D2)
+26.3.1 Trivial example
+----------------------
 
- -- Function: double gsl_spline_eval_integ (const gsl_spline * SPLINE,
-          double A, double B, gsl_interp_accel * ACC)
- -- Function: int gsl_spline_eval_integ_e (const gsl_spline * SPLINE,
-          double A, double B, gsl_interp_accel * ACC, double * RESULT)
+The first example, in one dimensional Cartesian space, sets up an energy
+function which is a damped sine wave; this has many local minima, but
+only one global minimum, somewhere between 1.0 and 1.5.  The initial
+guess given is 15.5, which is several local minima away from the global
+minimum.
 
-
-File: gsl-ref.info,  Node: Interpolation Example programs,  Next: Interpolation References and Further Reading,  Prev: Higher-level Interface,  Up: Interpolation
+     #include <math.h>
+     #include <stdlib.h>
+     #include <string.h>
+     #include <gsl/gsl_siman.h>
 
-27.7 Examples
-=============
+     /* set up parameters for this simulated annealing run */
 
-The following program demonstrates the use of the interpolation and
-spline functions.  It computes a cubic spline interpolation of the
-10-point dataset (x_i, y_i) where x_i = i + \sin(i)/2 and y_i = i +
-\cos(i^2) for i = 0 \dots 9.
+     /* how many points do we try before stepping */
+     #define N_TRIES 200
 
-     #include <stdlib.h>
-     #include <stdio.h>
-     #include <math.h>
-     #include <gsl/gsl_errno.h>
-     #include <gsl/gsl_spline.h>
+     /* how many iterations for each T? */
+     #define ITERS_FIXED_T 1000
 
-     int
-     main (void)
-     {
-       int i;
-       double xi, yi, x[10], y[10];
+     /* max step size in random walk */
+     #define STEP_SIZE 1.0
 
-       printf ("#m=0,S=2\n");
+     /* Boltzmann constant */
+     #define K 1.0
 
-       for (i = 0; i < 10; i++)
-         {
-           x[i] = i + 0.5 * sin (i);
-           y[i] = i + cos (i * i);
-           printf ("%g %g\n", x[i], y[i]);
-         }
+     /* initial temperature */
+     #define T_INITIAL 0.008
 
-       printf ("#m=1,S=0\n");
+     /* damping factor for temperature */
+     #define MU_T 1.003
+     #define T_MIN 2.0e-6
 
-       {
-         gsl_interp_accel *acc
-           = gsl_interp_accel_alloc ();
-         gsl_spline *spline
-           = gsl_spline_alloc (gsl_interp_cspline, 10);
+     gsl_siman_params_t params
+       = {N_TRIES, ITERS_FIXED_T, STEP_SIZE,
+          K, T_INITIAL, MU_T, T_MIN};
 
-         gsl_spline_init (spline, x, y, 10);
+     /* now some functions to test in one dimension */
+     double E1(void *xp)
+     {
+       double x = * ((double *) xp);
 
-         for (xi = x[0]; xi < x[9]; xi += 0.01)
-           {
-             yi = gsl_spline_eval (spline, xi, acc);
-             printf ("%g %g\n", xi, yi);
-           }
-         gsl_spline_free (spline);
-         gsl_interp_accel_free (acc);
-       }
-       return 0;
+       return exp(-pow((x-1.0),2.0))*sin(8*x);
      }
 
-The output is designed to be used with the GNU plotutils 'graph'
-program,
+     double M1(void *xp, void *yp)
+     {
+       double x = *((double *) xp);
+       double y = *((double *) yp);
 
-     $ ./a.out > interp.dat
-     $ graph -T ps < interp.dat > interp.ps
+       return fabs(x - y);
+     }
 
-The result shows a smooth interpolation of the original points.  The
-interpolation method can be changed simply by varying the first argument
-of 'gsl_spline_alloc'.
+     void S1(const gsl_rng * r, void *xp, double step_size)
+     {
+       double old_x = *((double *) xp);
+       double new_x;
 
-   The next program demonstrates a periodic cubic spline with 4 data
-points.  Note that the first and last points must be supplied with the
-same y-value for a periodic spline.
+       double u = gsl_rng_uniform(r);
+       new_x = u * 2 * step_size - step_size + old_x;
 
-     #include <stdlib.h>
-     #include <stdio.h>
-     #include <math.h>
-     #include <gsl/gsl_errno.h>
-     #include <gsl/gsl_spline.h>
+       memcpy(xp, &new_x, sizeof(new_x));
+     }
 
-     int
-     main (void)
+     void P1(void *xp)
      {
-       int N = 4;
-       double x[4] = {0.00, 0.10,  0.27,  0.30};
-       double y[4] = {0.15, 0.70, -0.10,  0.15};
-                  /* Note: y[0] == y[3] for periodic data */
+       printf ("%12g", *((double *) xp));
+     }
 
-       gsl_interp_accel *acc = gsl_interp_accel_alloc ();
-       const gsl_interp_type *t = gsl_interp_cspline_periodic;
-       gsl_spline *spline = gsl_spline_alloc (t, N);
+     int
+     main(void)
+     {
+       const gsl_rng_type * T;
+       gsl_rng * r;
 
-       int i; double xi, yi;
+       double x_initial = 15.5;
 
-       printf ("#m=0,S=5\n");
-       for (i = 0; i < N; i++)
-         {
-           printf ("%g %g\n", x[i], y[i]);
-         }
+       gsl_rng_env_setup();
 
-       printf ("#m=1,S=0\n");
-       gsl_spline_init (spline, x, y, N);
+       T = gsl_rng_default;
+       r = gsl_rng_alloc(T);
 
-       for (i = 0; i <= 100; i++)
-         {
-           xi = (1 - i / 100.0) * x[0] + (i / 100.0) * x[N-1];
-           yi = gsl_spline_eval (spline, xi, acc);
-           printf ("%g %g\n", xi, yi);
-         }
+       gsl_siman_solve(r, &x_initial, E1, S1, M1, P1,
+                       NULL, NULL, NULL,
+                       sizeof(double), params);
 
-       gsl_spline_free (spline);
-       gsl_interp_accel_free (acc);
+       gsl_rng_free (r);
        return 0;
      }
 
-   The output can be plotted with GNU 'graph'.
-
-     $ ./a.out > interp.dat
-     $ graph -T ps < interp.dat > interp.ps
+   Here are a couple of plots that are generated by running 'siman_test'
+in the following way:
 
-The result shows a periodic interpolation of the original points.  The
-slope of the fitted curve is the same at the beginning and end of the
-data, and the second derivative is also.
+     $ ./siman_test | awk '!/^#/ {print $1, $4}'
+      | graph -y 1.34 1.4 -W0 -X generation -Y position
+      | plot -Tps > siman-test.eps
+     $ ./siman_test | awk '!/^#/ {print $1, $5}'
+      | graph -y -0.88 -0.83 -W0 -X generation -Y energy
+      | plot -Tps > siman-energy.eps
 
 
-File: gsl-ref.info,  Node: Interpolation References and Further Reading,  Prev: Interpolation Example programs,  Up: Interpolation
+File: gsl-ref.info,  Node: Traveling Salesman Problem,  Prev: Trivial example,  Up: Examples with Simulated Annealing
 
-27.8 References and Further Reading
-===================================
+26.3.2 Traveling Salesman Problem
+---------------------------------
 
-Descriptions of the interpolation algorithms and further references can
-be found in the following books:
+The TSP ("Traveling Salesman Problem") is the classic combinatorial
+optimization problem.  I have provided a very simple version of it,
+based on the coordinates of twelve cities in the southwestern United
+States.  This should maybe be called the "Flying Salesman Problem",
+since I am using the great-circle distance between cities, rather than
+the driving distance.  Also: I assume the earth is a sphere, so I don't
+use geoid distances.
 
-     C.W. Ueberhuber, 'Numerical Computation (Volume 1), Chapter 9
-     "Interpolation"', Springer (1997), ISBN 3-540-62058-3.
+   The 'gsl_siman_solve' routine finds a route which is 3490.62
+Kilometers long; this is confirmed by an exhaustive search of all
+possible routes with the same initial city.
 
-     D.M. Young, R.T. Gregory 'A Survey of Numerical Mathematics (Volume
-     1), Chapter 6.8', Dover (1988), ISBN 0-486-65691-8.
+   The full code can be found in 'siman/siman_tsp.c', but I include here
+some plots generated in the following way:
 
-
-File: gsl-ref.info,  Node: Numerical Differentiation,  Next: Chebyshev Approximations,  Prev: Interpolation,  Up: Top
+     $ ./siman_tsp > tsp.output
+     $ grep -v "^#" tsp.output
+      | awk '{print $1, $NF}'
+      | graph -y 3300 6500 -W0 -X generation -Y distance
+         -L "TSP - 12 southwest cities"
+      | plot -Tps > 12-cities.eps
+     $ grep initial_city_coord tsp.output
+       | awk '{print $2, $3}'
+       | graph -X "longitude (- means west)" -Y "latitude"
+          -L "TSP - initial-order" -f 0.03 -S 1 0.1
+       | plot -Tps > initial-route.eps
+     $ grep final_city_coord tsp.output
+       | awk '{print $2, $3}'
+       | graph -X "longitude (- means west)" -Y "latitude"
+          -L "TSP - final-order" -f 0.03 -S 1 0.1
+       | plot -Tps > final-route.eps
 
-28 Numerical Differentiation
-****************************
+This is the output showing the initial order of the cities; longitude is
+negative, since it is west and I want the plot to look like a map.
 
-The functions described in this chapter compute numerical derivatives by
-finite differencing.  An adaptive algorithm is used to find the best
-choice of finite difference and to estimate the error in the derivative.
-These functions are declared in the header file 'gsl_deriv.h'.
+     # initial coordinates of cities (longitude and latitude)
+     ###initial_city_coord: -105.95 35.68 Santa Fe
+     ###initial_city_coord: -112.07 33.54 Phoenix
+     ###initial_city_coord: -106.62 35.12 Albuquerque
+     ###initial_city_coord: -103.2 34.41 Clovis
+     ###initial_city_coord: -107.87 37.29 Durango
+     ###initial_city_coord: -96.77 32.79 Dallas
+     ###initial_city_coord: -105.92 35.77 Tesuque
+     ###initial_city_coord: -107.84 35.15 Grants
+     ###initial_city_coord: -106.28 35.89 Los Alamos
+     ###initial_city_coord: -106.76 32.34 Las Cruces
+     ###initial_city_coord: -108.58 37.35 Cortez
+     ###initial_city_coord: -108.74 35.52 Gallup
+     ###initial_city_coord: -105.95 35.68 Santa Fe
 
-* Menu:
+   The optimal route turns out to be:
 
-* Numerical Differentiation functions::  
-* Numerical Differentiation Examples::  
-* Numerical Differentiation References::  
+     # final coordinates of cities (longitude and latitude)
+     ###final_city_coord: -105.95 35.68 Santa Fe
+     ###final_city_coord: -103.2 34.41 Clovis
+     ###final_city_coord: -96.77 32.79 Dallas
+     ###final_city_coord: -106.76 32.34 Las Cruces
+     ###final_city_coord: -112.07 33.54 Phoenix
+     ###final_city_coord: -108.74 35.52 Gallup
+     ###final_city_coord: -108.58 37.35 Cortez
+     ###final_city_coord: -107.87 37.29 Durango
+     ###final_city_coord: -107.84 35.15 Grants
+     ###final_city_coord: -106.62 35.12 Albuquerque
+     ###final_city_coord: -106.28 35.89 Los Alamos
+     ###final_city_coord: -105.92 35.77 Tesuque
+     ###final_city_coord: -105.95 35.68 Santa Fe
+
+Here's a plot of the cost function (energy) versus generation (point in
+the calculation at which a new temperature is set) for this problem:
 
 
-File: gsl-ref.info,  Node: Numerical Differentiation functions,  Next: Numerical Differentiation Examples,  Up: Numerical Differentiation
+File: gsl-ref.info,  Node: Simulated Annealing References and Further Reading,  Prev: Examples with Simulated Annealing,  Up: Simulated Annealing
 
-28.1 Functions
-==============
+26.4 References and Further Reading
+===================================
 
- -- Function: int gsl_deriv_central (const gsl_function * F, double X,
-          double H, double * RESULT, double * ABSERR)
-     This function computes the numerical derivative of the function F
-     at the point X using an adaptive central difference algorithm with
-     a step-size of H.  The derivative is returned in RESULT and an
-     estimate of its absolute error is returned in ABSERR.
+Further information is available in the following book,
 
-     The initial value of H is used to estimate an optimal step-size,
-     based on the scaling of the truncation error and round-off error in
-     the derivative calculation.  The derivative is computed using a
-     5-point rule for equally spaced abscissae at x-h, x-h/2, x, x+h/2,
-     x+h, with an error estimate taken from the difference between the
-     5-point rule and the corresponding 3-point rule x-h, x, x+h.  Note
-     that the value of the function at x does not contribute to the
-     derivative calculation, so only 4-points are actually used.
+     'Modern Heuristic Techniques for Combinatorial Problems', Colin R.
+     Reeves (ed.), McGraw-Hill, 1995 (ISBN 0-07-709239-2).
 
- -- Function: int gsl_deriv_forward (const gsl_function * F, double X,
-          double H, double * RESULT, double * ABSERR)
-     This function computes the numerical derivative of the function F
-     at the point X using an adaptive forward difference algorithm with
-     a step-size of H.  The function is evaluated only at points greater
-     than X, and never at X itself.  The derivative is returned in
-     RESULT and an estimate of its absolute error is returned in ABSERR.
-     This function should be used if f(x) has a discontinuity at X, or
-     is undefined for values less than X.
+
+File: gsl-ref.info,  Node: Ordinary Differential Equations,  Next: Interpolation,  Prev: Simulated Annealing,  Up: Top
+
+27 Ordinary Differential Equations
+**********************************
+
+This chapter describes functions for solving ordinary differential
+equation (ODE) initial value problems.  The library provides a variety
+of low-level methods, such as Runge-Kutta and Bulirsch-Stoer routines,
+and higher-level components for adaptive step-size control.  The
+components can be combined by the user to achieve the desired solution,
+with full access to any intermediate steps.  A driver object can be used
+as a high level wrapper for easy use of low level functions.
 
-     The initial value of H is used to estimate an optimal step-size,
-     based on the scaling of the truncation error and round-off error in
-     the derivative calculation.  The derivative at x is computed using
-     an "open" 4-point rule for equally spaced abscissae at x+h/4,
-     x+h/2, x+3h/4, x+h, with an error estimate taken from the
-     difference between the 4-point rule and the corresponding 2-point
-     rule x+h/2, x+h.
+   These functions are declared in the header file 'gsl_odeiv2.h'.  This
+is a new interface in version 1.15 and uses the prefix 'gsl_odeiv2' for
+all functions.  It is recommended over the previous 'gsl_odeiv'
+implementation defined in 'gsl_odeiv.h' The old interface has been
+retained under the original name for backwards compatibility.
 
- -- Function: int gsl_deriv_backward (const gsl_function * F, double X,
-          double H, double * RESULT, double * ABSERR)
-     This function computes the numerical derivative of the function F
-     at the point X using an adaptive backward difference algorithm with
-     a step-size of H.  The function is evaluated only at points less
-     than X, and never at X itself.  The derivative is returned in
-     RESULT and an estimate of its absolute error is returned in ABSERR.
-     This function should be used if f(x) has a discontinuity at X, or
-     is undefined for values greater than X.
+* Menu:
 
-     This function is equivalent to calling 'gsl_deriv_forward' with a
-     negative step-size.
+* Defining the ODE System::     
+* Stepping Functions::          
+* Adaptive Step-size Control::  
+* Evolution::                   
+* Driver::
+* ODE Example programs::        
+* ODE References and Further Reading::  
 
 
-File: gsl-ref.info,  Node: Numerical Differentiation Examples,  Next: Numerical Differentiation References,  Prev: Numerical Differentiation functions,  Up: Numerical Differentiation
-
-28.2 Examples
-=============
+File: gsl-ref.info,  Node: Defining the ODE System,  Next: Stepping Functions,  Up: Ordinary Differential Equations
 
-The following code estimates the derivative of the function f(x) =
-x^{3/2} at x=2 and at x=0.  The function f(x) is undefined for x<0 so
-the derivative at x=0 is computed using 'gsl_deriv_forward'.
+27.1 Defining the ODE System
+============================
 
-     #include <stdio.h>
-     #include <gsl/gsl_math.h>
-     #include <gsl/gsl_deriv.h>
+The routines solve the general n-dimensional first-order system,
 
-     double f (double x, void * params)
-     {
-       return pow (x, 1.5);
-     }
+     dy_i(t)/dt = f_i(t, y_1(t), ..., y_n(t))
 
-     int
-     main (void)
-     {
-       gsl_function F;
-       double result, abserr;
+for i = 1, \dots, n.  The stepping functions rely on the vector of
+derivatives f_i and the Jacobian matrix, J_{ij} = df_i(t,y(t)) / dy_j.
+A system of equations is defined using the 'gsl_odeiv2_system' datatype.
 
-       F.function = &f;
-       F.params = 0;
+ -- Data Type: gsl_odeiv2_system
+     This data type defines a general ODE system with arbitrary
+     parameters.
 
-       printf ("f(x) = x^(3/2)\n");
+     'int (* function) (double t, const double y[], double dydt[], void * params)'
+          This function should store the vector elements f_i(t,y,params)
+          in the array DYDT, for arguments (T,Y) and parameters PARAMS.
 
-       gsl_deriv_central (&F, 2.0, 1e-8, &result, &abserr);
-       printf ("x = 2.0\n");
-       printf ("f'(x) = %.10f +/- %.10f\n", result, abserr);
-       printf ("exact = %.10f\n\n", 1.5 * sqrt(2.0));
+          The function should return 'GSL_SUCCESS' if the calculation
+          was completed successfully.  Any other return value indicates
+          an error.  A special return value 'GSL_EBADFUNC' causes
+          'gsl_odeiv2' routines to immediately stop and return.  If
+          'function' is modified (for example contents of PARAMS), the
+          user must call an appropriate reset function
+          ('gsl_odeiv2_driver_reset', 'gsl_odeiv2_evolve_reset' or
+          'gsl_odeiv2_step_reset') before continuing.  Use return values
+          distinct from standard GSL error codes to distinguish your
+          function as the source of the error.
 
-       gsl_deriv_forward (&F, 0.0, 1e-8, &result, &abserr);
-       printf ("x = 0.0\n");
-       printf ("f'(x) = %.10f +/- %.10f\n", result, abserr);
-       printf ("exact = %.10f\n", 0.0);
+     'int (* jacobian) (double t, const double y[], double * dfdy, double dfdt[], void * params);'
+          This function should store the vector of derivative elements
+          in the array DFDT and the Jacobian matrix J_{ij} in the array
+          DFDY, regarded as a row-ordered matrix 'J(i,j) = dfdy[i *
+          dimension + j]' where 'dimension' is the dimension of the
+          system.
 
-       return 0;
-     }
+          Not all of the stepper algorithms of 'gsl_odeiv2' make use of
+          the Jacobian matrix, so it may not be necessary to provide
+          this function (the 'jacobian' element of the struct can be
+          replaced by a null pointer for those algorithms).
 
-Here is the output of the program,
+          The function should return 'GSL_SUCCESS' if the calculation
+          was completed successfully.  Any other return value indicates
+          an error.  A special return value 'GSL_EBADFUNC' causes
+          'gsl_odeiv2' routines to immediately stop and return.  If
+          'jacobian' is modified (for example contents of PARAMS), the
+          user must call an appropriate reset function
+          ('gsl_odeiv2_driver_reset', 'gsl_odeiv2_evolve_reset' or
+          'gsl_odeiv2_step_reset') before continuing.  Use return values
+          distinct from standard GSL error codes to distinguish your
+          function as the source of the error.
 
-     $ ./a.out
-     f(x) = x^(3/2)
-     x = 2.0
-     f'(x) = 2.1213203120 +/- 0.0000004064
-     exact = 2.1213203436
+     'size_t dimension;'
+          This is the dimension of the system of equations.
 
-     x = 0.0
-     f'(x) = 0.0000000160 +/- 0.0000000339
-     exact = 0.0000000000
+     'void * params'
+          This is a pointer to the arbitrary parameters of the system.
 
 
-File: gsl-ref.info,  Node: Numerical Differentiation References,  Prev: Numerical Differentiation Examples,  Up: Numerical Differentiation
+File: gsl-ref.info,  Node: Stepping Functions,  Next: Adaptive Step-size Control,  Prev: Defining the ODE System,  Up: Ordinary Differential Equations
 
-28.3 References and Further Reading
-===================================
+27.2 Stepping Functions
+=======================
 
-The algorithms used by these functions are described in the following
-sources:
+The lowest level components are the "stepping functions" which advance a
+solution from time t to t+h for a fixed step-size h and estimate the
+resulting local error.
 
-     Abramowitz and Stegun, 'Handbook of Mathematical Functions',
-     Section 25.3.4, and Table 25.5 (Coefficients for Differentiation).
+ -- Function: gsl_odeiv2_step * gsl_odeiv2_step_alloc (const
+          gsl_odeiv2_step_type * T, size_t DIM)
+     This function returns a pointer to a newly allocated instance of a
+     stepping function of type T for a system of DIM dimensions.  Please
+     note that if you use a stepper method that requires access to a
+     driver object, it is advisable to use a driver allocation method,
+     which automatically allocates a stepper, too.
 
-     S.D. Conte and Carl de Boor, 'Elementary Numerical Analysis: An
-     Algorithmic Approach', McGraw-Hill, 1972.
+ -- Function: int gsl_odeiv2_step_reset (gsl_odeiv2_step * S)
+     This function resets the stepping function S.  It should be used
+     whenever the next use of S will not be a continuation of a previous
+     step.
 
-
-File: gsl-ref.info,  Node: Chebyshev Approximations,  Next: Series Acceleration,  Prev: Numerical Differentiation,  Up: Top
+ -- Function: void gsl_odeiv2_step_free (gsl_odeiv2_step * S)
+     This function frees all the memory associated with the stepping
+     function S.
 
-29 Chebyshev Approximations
-***************************
+ -- Function: const char * gsl_odeiv2_step_name (const gsl_odeiv2_step *
+          S)
+     This function returns a pointer to the name of the stepping
+     function.  For example,
 
-This chapter describes routines for computing Chebyshev approximations
-to univariate functions.  A Chebyshev approximation is a truncation of
-the series f(x) = \sum c_n T_n(x), where the Chebyshev polynomials
-T_n(x) = \cos(n \arccos x) provide an orthogonal basis of polynomials on
-the interval [-1,1] with the weight function 1 / \sqrt{1-x^2}.  The
-first few Chebyshev polynomials are, T_0(x) = 1, T_1(x) = x, T_2(x) = 2
-x^2 - 1.  For further information see Abramowitz & Stegun, Chapter 22.
+          printf ("step method is '%s'\n",
+                   gsl_odeiv2_step_name (s));
 
-   The functions described in this chapter are declared in the header
-file 'gsl_chebyshev.h'.
+     would print something like 'step method is 'rkf45''.
 
-* Menu:
+ -- Function: unsigned int gsl_odeiv2_step_order (const gsl_odeiv2_step
+          * S)
+     This function returns the order of the stepping function on the
+     previous step.  The order can vary if the stepping function itself
+     is adaptive.
 
-* Chebyshev Definitions::       
-* Creation and Calculation of Chebyshev Series::  
-* Auxiliary Functions for Chebyshev Series::  
-* Chebyshev Series Evaluation::  
-* Derivatives and Integrals::   
-* Chebyshev Approximation Examples::  
-* Chebyshev Approximation References and Further Reading::  
+ -- Function: int gsl_odeiv2_step_set_driver (gsl_odeiv2_step * S, const
+          gsl_odeiv2_driver * D)
+     This function sets a pointer of the driver object D for stepper S,
+     to allow the stepper to access control (and evolve) object through
+     the driver object.  This is a requirement for some steppers, to get
+     the desired error level for internal iteration of stepper.
+     Allocation of a driver object calls this function automatically.
 
-
-File: gsl-ref.info,  Node: Chebyshev Definitions,  Next: Creation and Calculation of Chebyshev Series,  Up: Chebyshev Approximations
+ -- Function: int gsl_odeiv2_step_apply (gsl_odeiv2_step * S, double T,
+          double H, double Y[], double YERR[], const double DYDT_IN[],
+          double DYDT_OUT[], const gsl_odeiv2_system * SYS)
+     This function applies the stepping function S to the system of
+     equations defined by SYS, using the step-size H to advance the
+     system from time T and state Y to time T+H.  The new state of the
+     system is stored in Y on output, with an estimate of the absolute
+     error in each component stored in YERR.  If the argument DYDT_IN is
+     not null it should point an array containing the derivatives for
+     the system at time T on input.  This is optional as the derivatives
+     will be computed internally if they are not provided, but allows
+     the reuse of existing derivative information.  On output the new
+     derivatives of the system at time T+H will be stored in DYDT_OUT if
+     it is not null.
 
-29.1 Definitions
-================
+     The stepping function returns 'GSL_FAILURE' if it is unable to
+     compute the requested step.  Also, if the user-supplied functions
+     defined in the system SYS return a status other than 'GSL_SUCCESS'
+     the step will be aborted.  In that case, the elements of Y will be
+     restored to their pre-step values and the error code from the
+     user-supplied function will be returned.  Failure may be due to a
+     singularity in the system or too large step-size H.  In that case
+     the step should be attempted again with a smaller step-size, e.g.
+     H/2.
 
-A Chebyshev series is stored using the following structure,
+     If the driver object is not appropriately set via
+     'gsl_odeiv2_step_set_driver' for those steppers that need it, the
+     stepping function returns 'GSL_EFAULT'.  If the user-supplied
+     functions defined in the system SYS returns 'GSL_EBADFUNC', the
+     function returns immediately with the same return code.  In this
+     case the user must call 'gsl_odeiv2_step_reset' before calling this
+     function again.
 
-     typedef struct
-     {
-       double * c;   /* coefficients  c[0] .. c[order] */
-       int order;    /* order of expansion             */
-       double a;     /* lower interval point           */
-       double b;     /* upper interval point           */
-       ...
-     } gsl_cheb_series
+   The following algorithms are available,
 
-The approximation is made over the range [a,b] using ORDER+1 terms,
-including the coefficient c[0].  The series is computed using the
-following convention,
+ -- Step Type: gsl_odeiv2_step_rk2
+     Explicit embedded Runge-Kutta (2, 3) method.
 
-     f(x) = (c_0 / 2) + \sum_{n=1} c_n T_n(x)
+ -- Step Type: gsl_odeiv2_step_rk4
+     Explicit 4th order (classical) Runge-Kutta.  Error estimation is
+     carried out by the step doubling method.  For more efficient
+     estimate of the error, use the embedded methods described below.
 
-which is needed when accessing the coefficients directly.
+ -- Step Type: gsl_odeiv2_step_rkf45
+     Explicit embedded Runge-Kutta-Fehlberg (4, 5) method.  This method
+     is a good general-purpose integrator.
 
-
-File: gsl-ref.info,  Node: Creation and Calculation of Chebyshev Series,  Next: Auxiliary Functions for Chebyshev Series,  Prev: Chebyshev Definitions,  Up: Chebyshev Approximations
+ -- Step Type: gsl_odeiv2_step_rkck
+     Explicit embedded Runge-Kutta Cash-Karp (4, 5) method.
 
-29.2 Creation and Calculation of Chebyshev Series
-=================================================
+ -- Step Type: gsl_odeiv2_step_rk8pd
+     Explicit embedded Runge-Kutta Prince-Dormand (8, 9) method.
 
- -- Function: gsl_cheb_series * gsl_cheb_alloc (const size_t N)
-     This function allocates space for a Chebyshev series of order N and
-     returns a pointer to a new 'gsl_cheb_series' struct.
+ -- Step Type: gsl_odeiv2_step_rk1imp
+     Implicit Gaussian first order Runge-Kutta.  Also known as implicit
+     Euler or backward Euler method.  Error estimation is carried out by
+     the step doubling method.  This algorithm requires the Jacobian and
+     access to the driver object via 'gsl_odeiv2_step_set_driver'.
+
+ -- Step Type: gsl_odeiv2_step_rk2imp
+     Implicit Gaussian second order Runge-Kutta.  Also known as implicit
+     mid-point rule.  Error estimation is carried out by the step
+     doubling method.  This stepper requires the Jacobian and access to
+     the driver object via 'gsl_odeiv2_step_set_driver'.
+
+ -- Step Type: gsl_odeiv2_step_rk4imp
+     Implicit Gaussian 4th order Runge-Kutta.  Error estimation is
+     carried out by the step doubling method.  This algorithm requires
+     the Jacobian and access to the driver object via
+     'gsl_odeiv2_step_set_driver'.
 
- -- Function: void gsl_cheb_free (gsl_cheb_series * CS)
-     This function frees a previously allocated Chebyshev series CS.
+ -- Step Type: gsl_odeiv2_step_bsimp
+     Implicit Bulirsch-Stoer method of Bader and Deuflhard.  The method
+     is generally suitable for stiff problems.  This stepper requires
+     the Jacobian.
 
- -- Function: int gsl_cheb_init (gsl_cheb_series * CS, const
-          gsl_function * F, const double A, const double B)
-     This function computes the Chebyshev approximation CS for the
-     function F over the range (a,b) to the previously specified order.
-     The computation of the Chebyshev approximation is an O(n^2)
-     process, and requires n function evaluations.
+ -- Step Type: gsl_odeiv2_step_msadams
+     A variable-coefficient linear multistep Adams method in Nordsieck
+     form.  This stepper uses explicit Adams-Bashforth (predictor) and
+     implicit Adams-Moulton (corrector) methods in P(EC)^m functional
+     iteration mode.  Method order varies dynamically between 1 and 12.
+     This stepper requires the access to the driver object via
+     'gsl_odeiv2_step_set_driver'.
+
+ -- Step Type: gsl_odeiv2_step_msbdf
+     A variable-coefficient linear multistep backward differentiation
+     formula (BDF) method in Nordsieck form.  This stepper uses the
+     explicit BDF formula as predictor and implicit BDF formula as
+     corrector.  A modified Newton iteration method is used to solve the
+     system of non-linear equations.  Method order varies dynamically
+     between 1 and 5.  The method is generally suitable for stiff
+     problems.  This stepper requires the Jacobian and the access to the
+     driver object via 'gsl_odeiv2_step_set_driver'.
 
 
-File: gsl-ref.info,  Node: Auxiliary Functions for Chebyshev Series,  Next: Chebyshev Series Evaluation,  Prev: Creation and Calculation of Chebyshev Series,  Up: Chebyshev Approximations
+File: gsl-ref.info,  Node: Adaptive Step-size Control,  Next: Evolution,  Prev: Stepping Functions,  Up: Ordinary Differential Equations
 
-29.3 Auxiliary Functions
-========================
+27.3 Adaptive Step-size Control
+===============================
 
-The following functions provide information about an existing Chebyshev
-series.
+The control function examines the proposed change to the solution
+produced by a stepping function and attempts to determine the optimal
+step-size for a user-specified level of error.
 
- -- Function: size_t gsl_cheb_order (const gsl_cheb_series * CS)
-     This function returns the order of Chebyshev series CS.
+ -- Function: gsl_odeiv2_control * gsl_odeiv2_control_standard_new
+          (double EPS_ABS, double EPS_REL, double A_Y, double A_DYDT)
+     The standard control object is a four parameter heuristic based on
+     absolute and relative errors EPS_ABS and EPS_REL, and scaling
+     factors A_Y and A_DYDT for the system state y(t) and derivatives
+     y'(t) respectively.
 
- -- Function: size_t gsl_cheb_size (const gsl_cheb_series * CS)
- -- Function: double * gsl_cheb_coeffs (const gsl_cheb_series * CS)
-     These functions return the size of the Chebyshev coefficient array
-     'c[]' and a pointer to its location in memory for the Chebyshev
-     series CS.
+     The step-size adjustment procedure for this method begins by
+     computing the desired error level D_i for each component,
 
-
-File: gsl-ref.info,  Node: Chebyshev Series Evaluation,  Next: Derivatives and Integrals,  Prev: Auxiliary Functions for Chebyshev Series,  Up: Chebyshev Approximations
+          D_i = eps_abs + eps_rel * (a_y |y_i| + a_dydt h |y\prime_i|)
 
-29.4 Chebyshev Series Evaluation
-================================
+     and comparing it with the observed error E_i = |yerr_i|.  If the
+     observed error E exceeds the desired error level D by more than 10%
+     for any component then the method reduces the step-size by an
+     appropriate factor,
 
- -- Function: double gsl_cheb_eval (const gsl_cheb_series * CS, double
-          X)
-     This function evaluates the Chebyshev series CS at a given point X.
+          h_new = h_old * S * (E/D)^(-1/q)
 
- -- Function: int gsl_cheb_eval_err (const gsl_cheb_series * CS, const
-          double X, double * RESULT, double * ABSERR)
-     This function computes the Chebyshev series CS at a given point X,
-     estimating both the series RESULT and its absolute error ABSERR.
-     The error estimate is made from the first neglected term in the
-     series.
+     where q is the consistency order of the method (e.g.  q=4 for 4(5)
+     embedded RK), and S is a safety factor of 0.9.  The ratio E/D is
+     taken to be the maximum of the ratios E_i/D_i.
 
- -- Function: double gsl_cheb_eval_n (const gsl_cheb_series * CS, size_t
-          ORDER, double X)
-     This function evaluates the Chebyshev series CS at a given point X,
-     to (at most) the given order ORDER.
+     If the observed error E is less than 50% of the desired error level
+     D for the maximum ratio E_i/D_i then the algorithm takes the
+     opportunity to increase the step-size to bring the error in line
+     with the desired level,
 
- -- Function: int gsl_cheb_eval_n_err (const gsl_cheb_series * CS, const
-          size_t ORDER, const double X, double * RESULT, double *
-          ABSERR)
-     This function evaluates a Chebyshev series CS at a given point X,
-     estimating both the series RESULT and its absolute error ABSERR, to
-     (at most) the given order ORDER.  The error estimate is made from
-     the first neglected term in the series.
+          h_new = h_old * S * (E/D)^(-1/(q+1))
 
-
-File: gsl-ref.info,  Node: Derivatives and Integrals,  Next: Chebyshev Approximation Examples,  Prev: Chebyshev Series Evaluation,  Up: Chebyshev Approximations
+     This encompasses all the standard error scaling methods.  To avoid
+     uncontrolled changes in the stepsize, the overall scaling factor is
+     limited to the range 1/5 to 5.
 
-29.5 Derivatives and Integrals
-==============================
+ -- Function: gsl_odeiv2_control * gsl_odeiv2_control_y_new (double
+          EPS_ABS, double EPS_REL)
+     This function creates a new control object which will keep the
+     local error on each step within an absolute error of EPS_ABS and
+     relative error of EPS_REL with respect to the solution y_i(t).
+     This is equivalent to the standard control object with A_Y=1 and
+     A_DYDT=0.
 
-The following functions allow a Chebyshev series to be differentiated or
-integrated, producing a new Chebyshev series.  Note that the error
-estimate produced by evaluating the derivative series will be
-underestimated due to the contribution of higher order terms being
-neglected.
+ -- Function: gsl_odeiv2_control * gsl_odeiv2_control_yp_new (double
+          EPS_ABS, double EPS_REL)
+     This function creates a new control object which will keep the
+     local error on each step within an absolute error of EPS_ABS and
+     relative error of EPS_REL with respect to the derivatives of the
+     solution y'_i(t).  This is equivalent to the standard control
+     object with A_Y=0 and A_DYDT=1.
 
- -- Function: int gsl_cheb_calc_deriv (gsl_cheb_series * DERIV, const
-          gsl_cheb_series * CS)
-     This function computes the derivative of the series CS, storing the
-     derivative coefficients in the previously allocated DERIV.  The two
-     series CS and DERIV must have been allocated with the same order.
+ -- Function: gsl_odeiv2_control * gsl_odeiv2_control_scaled_new (double
+          EPS_ABS, double EPS_REL, double A_Y, double A_DYDT, const
+          double SCALE_ABS[], size_t DIM)
+     This function creates a new control object which uses the same
+     algorithm as 'gsl_odeiv2_control_standard_new' but with an absolute
+     error which is scaled for each component by the array SCALE_ABS.
+     The formula for D_i for this control object is,
 
- -- Function: int gsl_cheb_calc_integ (gsl_cheb_series * INTEG, const
-          gsl_cheb_series * CS)
-     This function computes the integral of the series CS, storing the
-     integral coefficients in the previously allocated INTEG.  The two
-     series CS and INTEG must have been allocated with the same order.
-     The lower limit of the integration is taken to be the left hand end
-     of the range A.
+          D_i = eps_abs * s_i + eps_rel * (a_y |y_i| + a_dydt h |y\prime_i|)
 
-
-File: gsl-ref.info,  Node: Chebyshev Approximation Examples,  Next: Chebyshev Approximation References and Further Reading,  Prev: Derivatives and Integrals,  Up: Chebyshev Approximations
+     where s_i is the i-th component of the array SCALE_ABS.  The same
+     error control heuristic is used by the Matlab ODE suite.
 
-29.6 Examples
-=============
+ -- Function: gsl_odeiv2_control * gsl_odeiv2_control_alloc (const
+          gsl_odeiv2_control_type * T)
+     This function returns a pointer to a newly allocated instance of a
+     control function of type T.  This function is only needed for
+     defining new types of control functions.  For most purposes the
+     standard control functions described above should be sufficient.
 
-The following example program computes Chebyshev approximations to a
-step function.  This is an extremely difficult approximation to make,
-due to the discontinuity, and was chosen as an example where
-approximation error is visible.  For smooth functions the Chebyshev
-approximation converges extremely rapidly and errors would not be
-visible.
+ -- Function: int gsl_odeiv2_control_init (gsl_odeiv2_control * C,
+          double EPS_ABS, double EPS_REL, double A_Y, double A_DYDT)
+     This function initializes the control function C with the
+     parameters EPS_ABS (absolute error), EPS_REL (relative error), A_Y
+     (scaling factor for y) and A_DYDT (scaling factor for derivatives).
 
-     #include <stdio.h>
-     #include <gsl/gsl_math.h>
-     #include <gsl/gsl_chebyshev.h>
+ -- Function: void gsl_odeiv2_control_free (gsl_odeiv2_control * C)
+     This function frees all the memory associated with the control
+     function C.
 
-     double
-     f (double x, void *p)
-     {
-       if (x < 0.5)
-         return 0.25;
-       else
-         return 0.75;
-     }
+ -- Function: int gsl_odeiv2_control_hadjust (gsl_odeiv2_control * C,
+          gsl_odeiv2_step * S, const double Y[], const double YERR[],
+          const double DYDT[], double * H)
+     This function adjusts the step-size H using the control function C,
+     and the current values of Y, YERR and DYDT.  The stepping function
+     STEP is also needed to determine the order of the method.  If the
+     error in the y-values YERR is found to be too large then the
+     step-size H is reduced and the function returns
+     'GSL_ODEIV_HADJ_DEC'.  If the error is sufficiently small then H
+     may be increased and 'GSL_ODEIV_HADJ_INC' is returned.  The
+     function returns 'GSL_ODEIV_HADJ_NIL' if the step-size is
+     unchanged.  The goal of the function is to estimate the largest
+     step-size which satisfies the user-specified accuracy requirements
+     for the current point.
 
-     int
-     main (void)
-     {
-       int i, n = 10000;
+ -- Function: const char * gsl_odeiv2_control_name (const
+          gsl_odeiv2_control * C)
+     This function returns a pointer to the name of the control
+     function.  For example,
 
-       gsl_cheb_series *cs = gsl_cheb_alloc (40);
+          printf ("control method is '%s'\n",
+                  gsl_odeiv2_control_name (c));
 
-       gsl_function F;
+     would print something like 'control method is 'standard''
 
-       F.function = f;
-       F.params = 0;
+ -- Function: int gsl_odeiv2_control_errlevel (gsl_odeiv2_control * C,
+          const double Y, const double DYDT, const double H, const
+          size_t IND, double * ERRLEV)
+     This function calculates the desired error level of the IND-th
+     component to ERRLEV.  It requires the value (Y) and value of the
+     derivative (DYDT) of the component, and the current step size H.
 
-       gsl_cheb_init (cs, &F, 0.0, 1.0);
+ -- Function: int gsl_odeiv2_control_set_driver (gsl_odeiv2_control * C,
+          const gsl_odeiv2_driver * D)
+     This function sets a pointer of the driver object D for control
+     object C.
 
-       for (i = 0; i < n; i++)
-         {
-           double x = i / (double)n;
-           double r10 = gsl_cheb_eval_n (cs, 10, x);
-           double r40 = gsl_cheb_eval (cs, x);
-           printf ("%g %g %g %g\n",
-                   x, GSL_FN_EVAL (&F, x), r10, r40);
-         }
+
+File: gsl-ref.info,  Node: Evolution,  Next: Driver,  Prev: Adaptive Step-size Control,  Up: Ordinary Differential Equations
 
-       gsl_cheb_free (cs);
+27.4 Evolution
+==============
 
-       return 0;
-     }
+The evolution function combines the results of a stepping function and
+control function to reliably advance the solution forward one step using
+an acceptable step-size.
 
-The output from the program gives the original function, 10-th order
-approximation and 40-th order approximation, all sampled at intervals of
-0.001 in x.
+ -- Function: gsl_odeiv2_evolve * gsl_odeiv2_evolve_alloc (size_t DIM)
+     This function returns a pointer to a newly allocated instance of an
+     evolution function for a system of DIM dimensions.
 
-
-File: gsl-ref.info,  Node: Chebyshev Approximation References and Further Reading,  Prev: Chebyshev Approximation Examples,  Up: Chebyshev Approximations
+ -- Function: int gsl_odeiv2_evolve_apply (gsl_odeiv2_evolve * E,
+          gsl_odeiv2_control * CON, gsl_odeiv2_step * STEP, const
+          gsl_odeiv2_system * SYS, double * T, double T1, double * H,
+          double Y[])
+     This function advances the system (E, SYS) from time T and position
+     Y using the stepping function STEP.  The new time and position are
+     stored in T and Y on output.
 
-29.7 References and Further Reading
-===================================
+     The initial step-size is taken as H.  The control function CON is
+     applied to check whether the local error estimated by the stepping
+     function STEP using step-size H exceeds the required error
+     tolerance.  If the error is too high, the step is retried by
+     calling STEP with a decreased step-size.  This process is continued
+     until an acceptable step-size is found.  An estimate of the local
+     error for the step can be obtained from the components of the array
+     'E->yerr[]'.
 
-The following paper describes the use of Chebyshev series,
+     If the user-supplied functions defined in the system SYS returns
+     'GSL_EBADFUNC', the function returns immediately with the same
+     return code.  In this case the user must call
+     'gsl_odeiv2_step_reset' and 'gsl_odeiv2_evolve_reset' before
+     calling this function again.
 
-     R. Broucke, "Ten Subroutines for the Manipulation of Chebyshev
-     Series [C1] (Algorithm 446)".  'Communications of the ACM' 16(4),
-     254-256 (1973)
+     Otherwise, if the user-supplied functions defined in the system SYS
+     or the stepping function STEP return a status other than
+     'GSL_SUCCESS', the step is retried with a decreased step-size.  If
+     the step-size decreases below machine precision, a status of
+     'GSL_FAILURE' is returned if the user functions returned
+     'GSL_SUCCESS'.  Otherwise the value returned by user function is
+     returned.  If no acceptable step can be made, T and Y will be
+     restored to their pre-step values and H contains the final
+     attempted step-size.
 
-
-File: gsl-ref.info,  Node: Series Acceleration,  Next: Wavelet Transforms,  Prev: Chebyshev Approximations,  Up: Top
+     If the step is successful the function returns a suggested
+     step-size for the next step in H.  The maximum time T1 is
+     guaranteed not to be exceeded by the time-step.  On the final
+     time-step the value of T will be set to T1 exactly.
 
-30 Series Acceleration
-**********************
+ -- Function: int gsl_odeiv2_evolve_apply_fixed_step (gsl_odeiv2_evolve
+          * E, gsl_odeiv2_control * CON, gsl_odeiv2_step * STEP, const
+          gsl_odeiv2_system * SYS, double * T, const double H, double
+          Y[])
+     This function advances the ODE-system (E, SYS, CON) from time T and
+     position Y using the stepping function STEP by a specified step
+     size H.  If the local error estimated by the stepping function
+     exceeds the desired error level, the step is not taken and the
+     function returns 'GSL_FAILURE'.  Otherwise the value returned by
+     user function is returned.
 
-The functions described in this chapter accelerate the convergence of a
-series using the Levin u-transform.  This method takes a small number of
-terms from the start of a series and uses a systematic approximation to
-compute an extrapolated value and an estimate of its error.  The
-u-transform works for both convergent and divergent series, including
-asymptotic series.
+ -- Function: int gsl_odeiv2_evolve_reset (gsl_odeiv2_evolve * E)
+     This function resets the evolution function E.  It should be used
+     whenever the next use of E will not be a continuation of a previous
+     step.
 
-   These functions are declared in the header file 'gsl_sum.h'.
+ -- Function: void gsl_odeiv2_evolve_free (gsl_odeiv2_evolve * E)
+     This function frees all the memory associated with the evolution
+     function E.
 
-* Menu:
+ -- Function: int gsl_odeiv2_evolve_set_driver (gsl_odeiv2_evolve * E,
+          const gsl_odeiv2_driver * D)
+     This function sets a pointer of the driver object D for evolve
+     object E.
 
-* Acceleration functions::      
-* Acceleration functions without error estimation::  
-* Example of accelerating a series::  
-* Series Acceleration References::  
+   If a system has discontinuous changes in the derivatives at known
+points, it is advisable to evolve the system between each discontinuity
+in sequence.  For example, if a step-change in an external driving force
+occurs at times t_a, t_b and t_c then evolution should be carried out
+over the ranges (t_0,t_a), (t_a,t_b), (t_b,t_c), and (t_c,t_1)
+separately and not directly over the range (t_0,t_1).
 
 
-File: gsl-ref.info,  Node: Acceleration functions,  Next: Acceleration functions without error estimation,  Up: Series Acceleration
-
-30.1 Acceleration functions
-===========================
+File: gsl-ref.info,  Node: Driver,  Next: ODE Example programs,  Prev: Evolution,  Up: Ordinary Differential Equations
 
-The following functions compute the full Levin u-transform of a series
-with its error estimate.  The error estimate is computed by propagating
-rounding errors from each term through to the final extrapolation.
+27.5 Driver
+===========
 
-   These functions are intended for summing analytic series where each
-term is known to high accuracy, and the rounding errors are assumed to
-originate from finite precision.  They are taken to be relative errors
-of order 'GSL_DBL_EPSILON' for each term.
+The driver object is a high level wrapper that combines the evolution,
+control and stepper objects for easy use.
 
-   The calculation of the error in the extrapolated value is an O(N^2)
-process, which is expensive in time and memory.  A faster but less
-reliable method which estimates the error from the convergence of the
-extrapolated value is described in the next section.  For the method
-described here a full table of intermediate values and derivatives
-through to O(N) must be computed and stored, but this does give a
-reliable error estimate.
+ -- Function: gsl_odeiv2_driver * gsl_odeiv2_driver_alloc_y_new (const
+          gsl_odeiv2_system * SYS, const gsl_odeiv2_step_type * T, const
+          double HSTART, const double EPSABS, const double EPSREL)
+ -- Function: gsl_odeiv2_driver * gsl_odeiv2_driver_alloc_yp_new (const
+          gsl_odeiv2_system * SYS, const gsl_odeiv2_step_type * T, const
+          double HSTART, const double EPSABS, const double EPSREL)
+ -- Function: gsl_odeiv2_driver * gsl_odeiv2_driver_alloc_standard_new
+          (const gsl_odeiv2_system * SYS, const gsl_odeiv2_step_type *
+          T, const double HSTART, const double EPSABS, const double
+          EPSREL, const double A_Y, const double A_DYDT)
+ -- Function: gsl_odeiv2_driver * gsl_odeiv2_driver_alloc_scaled_new
+          (const gsl_odeiv2_system * SYS, const gsl_odeiv2_step_type *
+          T, const double HSTART, const double EPSABS, const double
+          EPSREL, const double A_Y, const double A_DYDT, const double
+          SCALE_ABS[])
+     These functions return a pointer to a newly allocated instance of a
+     driver object.  The functions automatically allocate and initialise
+     the evolve, control and stepper objects for ODE system SYS using
+     stepper type T.  The initial step size is given in HSTART.  The
+     rest of the arguments follow the syntax and semantics of the
+     control functions with same name ('gsl_odeiv2_control_*_new').
 
- -- Function: gsl_sum_levin_u_workspace * gsl_sum_levin_u_alloc (size_t
-          N)
-     This function allocates a workspace for a Levin u-transform of N
-     terms.  The size of the workspace is O(2n^2 + 3n).
+ -- Function: int gsl_odeiv2_driver_set_hmin (gsl_odeiv2_driver * D,
+          const double HMIN)
+     The function sets a minimum for allowed step size HMIN for driver
+     D.  Default value is 0.
 
- -- Function: void gsl_sum_levin_u_free (gsl_sum_levin_u_workspace * W)
-     This function frees the memory associated with the workspace W.
+ -- Function: int gsl_odeiv2_driver_set_hmax (gsl_odeiv2_driver * D,
+          const double HMAX)
+     The function sets a maximum for allowed step size HMAX for driver
+     D.  Default value is 'GSL_DBL_MAX'.
 
- -- Function: int gsl_sum_levin_u_accel (const double * ARRAY, size_t
-          ARRAY_SIZE, gsl_sum_levin_u_workspace * W, double * SUM_ACCEL,
-          double * ABSERR)
-     This function takes the terms of a series in ARRAY of size
-     ARRAY_SIZE and computes the extrapolated limit of the series using
-     a Levin u-transform.  Additional working space must be provided in
-     W.  The extrapolated sum is stored in SUM_ACCEL, with an estimate
-     of the absolute error stored in ABSERR.  The actual term-by-term
-     sum is returned in 'w->sum_plain'.  The algorithm calculates the
-     truncation error (the difference between two successive
-     extrapolations) and round-off error (propagated from the individual
-     terms) to choose an optimal number of terms for the extrapolation.
-     All the terms of the series passed in through ARRAY should be
-     non-zero.
+ -- Function: int gsl_odeiv2_driver_set_nmax (gsl_odeiv2_driver * D,
+          const unsigned long int NMAX)
+     The function sets a maximum for allowed number of steps NMAX for
+     driver D.  Default value of 0 sets no limit for steps.
 
-
-File: gsl-ref.info,  Node: Acceleration functions without error estimation,  Next: Example of accelerating a series,  Prev: Acceleration functions,  Up: Series Acceleration
+ -- Function: int gsl_odeiv2_driver_apply (gsl_odeiv2_driver * D, double
+          * T, const double T1, double Y[])
+     This function evolves the driver system D from T to T1.  Initially
+     vector Y should contain the values of dependent variables at point
+     T.  If the function is unable to complete the calculation, an error
+     code from 'gsl_odeiv2_evolve_apply' is returned, and T and Y
+     contain the values from last successful step.
 
-30.2 Acceleration functions without error estimation
-====================================================
+     If maximum number of steps is reached, a value of 'GSL_EMAXITER' is
+     returned.  If the step size drops below minimum value, the function
+     returns with 'GSL_ENOPROG'.  If the user-supplied functions defined
+     in the system SYS returns 'GSL_EBADFUNC', the function returns
+     immediately with the same return code.  In this case the user must
+     call 'gsl_odeiv2_driver_reset' before calling this function again.
 
-The functions described in this section compute the Levin u-transform of
-series and attempt to estimate the error from the "truncation error" in
-the extrapolation, the difference between the final two approximations.
-Using this method avoids the need to compute an intermediate table of
-derivatives because the error is estimated from the behavior of the
-extrapolated value itself.  Consequently this algorithm is an O(N)
-process and only requires O(N) terms of storage.  If the series
-converges sufficiently fast then this procedure can be acceptable.  It
-is appropriate to use this method when there is a need to compute many
-extrapolations of series with similar convergence properties at
-high-speed.  For example, when numerically integrating a function
-defined by a parameterized series where the parameter varies only
-slightly.  A reliable error estimate should be computed first using the
-full algorithm described above in order to verify the consistency of the
-results.
+ -- Function: int gsl_odeiv2_driver_apply_fixed_step (gsl_odeiv2_driver
+          * D, double * T, const double H, const unsigned long int N,
+          double Y[])
+     This function evolves the driver system D from T with N steps of
+     size H.  If the function is unable to complete the calculation, an
+     error code from 'gsl_odeiv2_evolve_apply_fixed_step' is returned,
+     and T and Y contain the values from last successful step.
 
- -- Function: gsl_sum_levin_utrunc_workspace *
-          gsl_sum_levin_utrunc_alloc (size_t N)
-     This function allocates a workspace for a Levin u-transform of N
-     terms, without error estimation.  The size of the workspace is
-     O(3n).
+ -- Function: int gsl_odeiv2_driver_reset (gsl_odeiv2_driver * D)
+     This function resets the evolution and stepper objects.
 
- -- Function: void gsl_sum_levin_utrunc_free
-          (gsl_sum_levin_utrunc_workspace * W)
-     This function frees the memory associated with the workspace W.
+ -- Function: int gsl_odeiv2_driver_reset_hstart (gsl_odeiv2_driver * D,
+          const double HSTART)
+     The routine resets the evolution and stepper objects and sets new
+     initial step size to HSTART.  This function can be used e.g.  to
+     change the direction of integration.
 
- -- Function: int gsl_sum_levin_utrunc_accel (const double * ARRAY,
-          size_t ARRAY_SIZE, gsl_sum_levin_utrunc_workspace * W, double
-          * SUM_ACCEL, double * ABSERR_TRUNC)
-     This function takes the terms of a series in ARRAY of size
-     ARRAY_SIZE and computes the extrapolated limit of the series using
-     a Levin u-transform.  Additional working space must be provided in
-     W.  The extrapolated sum is stored in SUM_ACCEL.  The actual
-     term-by-term sum is returned in 'w->sum_plain'.  The algorithm
-     terminates when the difference between two successive
-     extrapolations reaches a minimum or is sufficiently small.  The
-     difference between these two values is used as estimate of the
-     error and is stored in ABSERR_TRUNC.  To improve the reliability of
-     the algorithm the extrapolated values are replaced by moving
-     averages when calculating the truncation error, smoothing out any
-     fluctuations.
+ -- Function: int gsl_odeiv2_driver_free (gsl_odeiv2_driver * D)
+     This function frees the driver object, and the related evolution,
+     stepper and control objects.
 
 
-File: gsl-ref.info,  Node: Example of accelerating a series,  Next: Series Acceleration References,  Prev: Acceleration functions without error estimation,  Up: Series Acceleration
+File: gsl-ref.info,  Node: ODE Example programs,  Next: ODE References and Further Reading,  Prev: Driver,  Up: Ordinary Differential Equations
 
-30.3 Examples
+27.6 Examples
 =============
 
-The following code calculates an estimate of \zeta(2) = \pi^2 / 6 using
-the series,
+The following program solves the second-order nonlinear Van der Pol
+oscillator equation,
 
-     \zeta(2) = 1 + 1/2^2 + 1/3^2 + 1/4^2 + ...
+     u''(t) + \mu u'(t) (u(t)^2 - 1) + u(t) = 0
 
-After N terms the error in the sum is O(1/N), making direct summation of
-the series converge slowly.
+This can be converted into a first order system suitable for use with
+the routines described in this chapter by introducing a separate
+variable for the velocity, v = u'(t),
+
+     u' = v
+     v' = -u + \mu v (1-u^2)
+
+The program begins by defining functions for these derivatives and their
+Jacobian.  The main function uses driver level functions to solve the
+problem.  The program evolves the solution from (u, v) = (1, 0) at t=0
+to t=100.  The step-size h is automatically adjusted by the controller
+to maintain an absolute accuracy of 10^{-6} in the function values (u,
+v).  The loop in the example prints the solution at the points t_i = 1,
+2, \dots, 100.
 
      #include <stdio.h>
-     #include <gsl/gsl_math.h>
-     #include <gsl/gsl_sum.h>
+     #include <gsl/gsl_errno.h>
+     #include <gsl/gsl_matrix.h>
+     #include <gsl/gsl_odeiv2.h>
 
-     #define N 20
+     int
+     func (double t, const double y[], double f[],
+           void *params)
+     {
+       (void)(t); /* avoid unused parameter warning */
+       double mu = *(double *)params;
+       f[0] = y[1];
+       f[1] = -y[0] - mu*y[1]*(y[0]*y[0] - 1);
+       return GSL_SUCCESS;
+     }
+
+     int
+     jac (double t, const double y[], double *dfdy,
+          double dfdt[], void *params)
+     {
+       (void)(t); /* avoid unused parameter warning */
+       double mu = *(double *)params;
+       gsl_matrix_view dfdy_mat
+         = gsl_matrix_view_array (dfdy, 2, 2);
+       gsl_matrix * m = &dfdy_mat.matrix;
+       gsl_matrix_set (m, 0, 0, 0.0);
+       gsl_matrix_set (m, 0, 1, 1.0);
+       gsl_matrix_set (m, 1, 0, -2.0*mu*y[0]*y[1] - 1.0);
+       gsl_matrix_set (m, 1, 1, -mu*(y[0]*y[0] - 1.0));
+       dfdt[0] = 0.0;
+       dfdt[1] = 0.0;
+       return GSL_SUCCESS;
+     }
 
      int
      main (void)
      {
-       double t[N];
-       double sum_accel, err;
-       double sum = 0;
-       int n;
-
-       gsl_sum_levin_u_workspace * w
-         = gsl_sum_levin_u_alloc (N);
-
-       const double zeta_2 = M_PI * M_PI / 6.0;
+       double mu = 10;
+       gsl_odeiv2_system sys = {func, jac, 2, &mu};
 
-       /* terms for zeta(2) = \sum_{n=1}^{\infty} 1/n^2 */
+       gsl_odeiv2_driver * d =
+         gsl_odeiv2_driver_alloc_y_new (&sys, gsl_odeiv2_step_rk8pd,
+     				  1e-6, 1e-6, 0.0);
+       int i;
+       double t = 0.0, t1 = 100.0;
+       double y[2] = { 1.0, 0.0 };
 
-       for (n = 0; n < N; n++)
+       for (i = 1; i <= 100; i++)
          {
-           double np1 = n + 1.0;
-           t[n] = 1.0 / (np1 * np1);
-           sum += t[n];
-         }
-
-       gsl_sum_levin_u_accel (t, N, w, &sum_accel, &err);
-
-       printf ("term-by-term sum = % .16f using %d terms\n",
-               sum, N);
-
-       printf ("term-by-term sum = % .16f using %d terms\n",
-               w->sum_plain, w->terms_used);
+           double ti = i * t1 / 100.0;
+           int status = gsl_odeiv2_driver_apply (d, &t, ti, y);
 
-       printf ("exact value      = % .16f\n", zeta_2);
-       printf ("accelerated sum  = % .16f using %d terms\n",
-               sum_accel, w->terms_used);
+           if (status != GSL_SUCCESS)
+     	{
+     	  printf ("error, return value=%d\n", status);
+     	  break;
+     	}
 
-       printf ("estimated error  = % .16f\n", err);
-       printf ("actual error     = % .16f\n",
-               sum_accel - zeta_2);
+           printf ("%.5e %.5e %.5e\n", t, y[0], y[1]);
+         }
 
-       gsl_sum_levin_u_free (w);
+       gsl_odeiv2_driver_free (d);
        return 0;
      }
 
-The output below shows that the Levin u-transform is able to obtain an
-estimate of the sum to 1 part in 10^10 using the first eleven terms of
-the series.  The error estimate returned by the function is also
-accurate, giving the correct number of significant digits.
-
-     $ ./a.out
-     term-by-term sum =  1.5961632439130233 using 20 terms
-     term-by-term sum =  1.5759958390005426 using 13 terms
-     exact value      =  1.6449340668482264
-     accelerated sum  =  1.6449340668166479 using 13 terms
-     estimated error  =  0.0000000000508580
-     actual error     = -0.0000000000315785
-
-Note that a direct summation of this series would require 10^10 terms to
-achieve the same precision as the accelerated sum does in 13 terms.
-
-
-File: gsl-ref.info,  Node: Series Acceleration References,  Prev: Example of accelerating a series,  Up: Series Acceleration
-
-30.4 References and Further Reading
-===================================
-
-The algorithms used by these functions are described in the following
-papers,
-
-     T. Fessler, W.F. Ford, D.A. Smith, HURRY: An acceleration algorithm
-     for scalar sequences and series 'ACM Transactions on Mathematical
-     Software', 9(3):346-354, 1983.  and Algorithm 602 9(3):355-357,
-     1983.
+The user can work with the lower level functions directly, as in the
+following example.  In this case an intermediate result is printed after
+each successful step instead of equidistant time points.
 
-The theory of the u-transform was presented by Levin,
+     int
+     main (void)
+     {
+       const gsl_odeiv2_step_type * T
+         = gsl_odeiv2_step_rk8pd;
 
-     D. Levin, Development of Non-Linear Transformations for Improving
-     Convergence of Sequences, 'Intern. J. Computer Math.' B3:371-388,
-     1973.
+       gsl_odeiv2_step * s
+         = gsl_odeiv2_step_alloc (T, 2);
+       gsl_odeiv2_control * c
+         = gsl_odeiv2_control_y_new (1e-6, 0.0);
+       gsl_odeiv2_evolve * e
+         = gsl_odeiv2_evolve_alloc (2);
 
-A review paper on the Levin Transform is available online,
-     Herbert H. H. Homeier, Scalar Levin-Type Sequence Transformations,
-     <http://arxiv.org/abs/math/0005209>.
+       double mu = 10;
+       gsl_odeiv2_system sys = {func, jac, 2, &mu};
 
-
-File: gsl-ref.info,  Node: Wavelet Transforms,  Next: Discrete Hankel Transforms,  Prev: Series Acceleration,  Up: Top
+       double t = 0.0, t1 = 100.0;
+       double h = 1e-6;
+       double y[2] = { 1.0, 0.0 };
 
-31 Wavelet Transforms
-*********************
+       while (t < t1)
+         {
+           int status = gsl_odeiv2_evolve_apply (e, c, s,
+                                                &sys,
+                                                &t, t1,
+                                                &h, y);
 
-This chapter describes functions for performing Discrete Wavelet
-Transforms (DWTs).  The library includes wavelets for real data in both
-one and two dimensions.  The wavelet functions are declared in the
-header files 'gsl_wavelet.h' and 'gsl_wavelet2d.h'.
+           if (status != GSL_SUCCESS)
+               break;
 
-* Menu:
+           printf ("%.5e %.5e %.5e\n", t, y[0], y[1]);
+         }
 
-* DWT Definitions::             
-* DWT Initialization::          
-* DWT Transform Functions::     
-* DWT Examples::                
-* DWT References::              
+       gsl_odeiv2_evolve_free (e);
+       gsl_odeiv2_control_free (c);
+       gsl_odeiv2_step_free (s);
+       return 0;
+     }
 
-
-File: gsl-ref.info,  Node: DWT Definitions,  Next: DWT Initialization,  Up: Wavelet Transforms
+For functions with multiple parameters, the appropriate information can
+be passed in through the PARAMS argument in 'gsl_odeiv2_system'
+definition (MU in this example) by using a pointer to a struct.
 
-31.1 Definitions
-================
+It is also possible to work with a non-adaptive integrator, using only
+the stepping function itself, 'gsl_odeiv2_driver_apply_fixed_step' or
+'gsl_odeiv2_evolve_apply_fixed_step'.  The following program uses the
+driver level function, with fourth-order Runge-Kutta stepping function
+with a fixed stepsize of 0.001.
 
-The continuous wavelet transform and its inverse are defined by the
-relations,
+     int
+     main (void)
+     {
+       double mu = 10;
+       gsl_odeiv2_system sys = { func, jac, 2, &mu };
 
-     w(s,\tau) = \int f(t) * \psi^*_{s,\tau}(t) dt
+       gsl_odeiv2_driver *d =
+         gsl_odeiv2_driver_alloc_y_new (&sys, gsl_odeiv2_step_rk4,
+                                        1e-3, 1e-8, 1e-8);
 
-and,
+       double t = 0.0;
+       double y[2] = { 1.0, 0.0 };
+       int i, s;
 
-     f(t) = \int \int_{-\infty}^\infty w(s, \tau) * \psi_{s,\tau}(t) d\tau ds
+       for (i = 0; i < 100; i++)
+         {
+           s = gsl_odeiv2_driver_apply_fixed_step (d, &t, 1e-3, 1000, y);
 
-where the basis functions \psi_{s,\tau} are obtained by scaling and
-translation from a single function, referred to as the "mother wavelet".
+           if (s != GSL_SUCCESS)
+             {
+               printf ("error: driver returned %d\n", s);
+               break;
+             }
 
-   The discrete version of the wavelet transform acts on equally-spaced
-samples, with fixed scaling and translation steps (s, \tau).  The
-frequency and time axes are sampled "dyadically" on scales of 2^j
-through a level parameter j.  The resulting family of functions
-{\psi_{j,n}} constitutes an orthonormal basis for square-integrable
-signals.
+           printf ("%.5e %.5e %.5e\n", t, y[0], y[1]);
+         }
 
-   The discrete wavelet transform is an O(N) algorithm, and is also
-referred to as the "fast wavelet transform".
+       gsl_odeiv2_driver_free (d);
+       return s;
+     }
 
 
-File: gsl-ref.info,  Node: DWT Initialization,  Next: DWT Transform Functions,  Prev: DWT Definitions,  Up: Wavelet Transforms
-
-31.2 Initialization
-===================
+File: gsl-ref.info,  Node: ODE References and Further Reading,  Prev: ODE Example programs,  Up: Ordinary Differential Equations
 
-The 'gsl_wavelet' structure contains the filter coefficients defining
-the wavelet and any associated offset parameters.
+27.7 References and Further Reading
+===================================
 
- -- Function: gsl_wavelet * gsl_wavelet_alloc (const gsl_wavelet_type *
-          T, size_t K)
-     This function allocates and initializes a wavelet object of type T.
-     The parameter K selects the specific member of the wavelet family.
-     A null pointer is returned if insufficient memory is available or
-     if a unsupported member is selected.
+     Ascher, U.M., Petzold, L.R., 'Computer Methods for Ordinary
+     Differential and Differential-Algebraic Equations', SIAM,
+     Philadelphia, 1998.
 
-   The following wavelet types are implemented:
+     Hairer, E., Norsett, S. P., Wanner, G., 'Solving Ordinary
+     Differential Equations I: Nonstiff Problems', Springer, Berlin,
+     1993.
 
- -- Wavelet: gsl_wavelet_daubechies
- -- Wavelet: gsl_wavelet_daubechies_centered
-     This is the Daubechies wavelet family of maximum phase with k/2
-     vanishing moments.  The implemented wavelets are k=4, 6, ..., 20,
-     with K even.
+     Hairer, E., Wanner, G., 'Solving Ordinary Differential Equations
+     II: Stiff and Differential-Algebraic Problems', Springer, Berlin,
+     1996.
 
- -- Wavelet: gsl_wavelet_haar
- -- Wavelet: gsl_wavelet_haar_centered
-     This is the Haar wavelet.  The only valid choice of k for the Haar
-     wavelet is k=2.
+   Many of the basic Runge-Kutta formulas can be found in the Handbook
+of Mathematical Functions,
 
- -- Wavelet: gsl_wavelet_bspline
- -- Wavelet: gsl_wavelet_bspline_centered
-     This is the biorthogonal B-spline wavelet family of order (i,j).
-     The implemented values of k = 100*i + j are 103, 105, 202, 204,
-     206, 208, 301, 303, 305 307, 309.
+     Abramowitz & Stegun (eds.), 'Handbook of Mathematical Functions',
+     Section 25.5.
 
-The centered forms of the wavelets align the coefficients of the various
-sub-bands on edges.  Thus the resulting visualization of the
-coefficients of the wavelet transform in the phase plane is easier to
-understand.
+The implicit Bulirsch-Stoer algorithm 'bsimp' is described in the
+following paper,
 
- -- Function: const char * gsl_wavelet_name (const gsl_wavelet * W)
-     This function returns a pointer to the name of the wavelet family
-     for W.
+     G. Bader and P. Deuflhard, "A Semi-Implicit Mid-Point Rule for
+     Stiff Systems of Ordinary Differential Equations.", Numer. Math.
+     41, 373-398, 1983.
 
- -- Function: void gsl_wavelet_free (gsl_wavelet * W)
-     This function frees the wavelet object W.
+The Adams and BDF multistep methods 'msadams' and 'msbdf' are based on
+the following articles,
 
-   The 'gsl_wavelet_workspace' structure contains scratch space of the
-same size as the input data and is used to hold intermediate results
-during the transform.
+     G. D. Byrne and A. C. Hindmarsh, "A Polyalgorithm for the Numerical
+     Solution of Ordinary Differential Equations.", ACM Trans.  Math.
+     Software, 1, 71-96, 1975.
 
- -- Function: gsl_wavelet_workspace * gsl_wavelet_workspace_alloc
-          (size_t N)
-     This function allocates a workspace for the discrete wavelet
-     transform.  To perform a one-dimensional transform on N elements, a
-     workspace of size N must be provided.  For two-dimensional
-     transforms of N-by-N matrices it is sufficient to allocate a
-     workspace of size N, since the transform operates on individual
-     rows and columns.  A null pointer is returned if insufficient
-     memory is available.
+     P. N. Brown, G. D. Byrne and A. C. Hindmarsh, "VODE: A
+     Variable-coefficient ODE Solver.", SIAM J. Sci.  Stat.  Comput.
+     10, 1038-1051, 1989.
 
- -- Function: void gsl_wavelet_workspace_free (gsl_wavelet_workspace *
-          WORK)
-     This function frees the allocated workspace WORK.
+     A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D.
+     E. Shumaker and C. S. Woodward, "SUNDIALS: Suite of Nonlinear and
+     Differential/Algebraic Equation Solvers.", ACM Trans.  Math.
+     Software 31, 363-396, 2005.
 
 
-File: gsl-ref.info,  Node: DWT Transform Functions,  Next: DWT Examples,  Prev: DWT Initialization,  Up: Wavelet Transforms
-
-31.3 Transform Functions
-========================
-
-This sections describes the actual functions performing the discrete
-wavelet transform.  Note that the transforms use periodic boundary
-conditions.  If the signal is not periodic in the sample length then
-spurious coefficients will appear at the beginning and end of each level
-of the transform.
-
-* Menu:
-
-* DWT in one dimension::        
-* DWT in two dimension::        
+File: gsl-ref.info,  Node: Interpolation,  Next: Numerical Differentiation,  Prev: Ordinary Differential Equations,  Up: Top
 
-
-File: gsl-ref.info,  Node: DWT in one dimension,  Next: DWT in two dimension,  Up: DWT Transform Functions
+28 Interpolation
+****************
 
-31.3.1 Wavelet transforms in one dimension
-------------------------------------------
+This chapter describes functions for performing interpolation.  The
+library provides a variety of interpolation methods, including Cubic,
+Akima, and Steffen splines.  The interpolation types are
+interchangeable, allowing different methods to be used without
+recompiling.  Interpolations can be defined for both normal and periodic
+boundary conditions.  Additional functions are available for computing
+derivatives and integrals of interpolating functions.  Routines are
+provided for interpolating both one and two dimensional datasets.
 
- -- Function: int gsl_wavelet_transform (const gsl_wavelet * W, double *
-          DATA, size_t STRIDE, size_t N, gsl_wavelet_direction DIR,
-          gsl_wavelet_workspace * WORK)
- -- Function: int gsl_wavelet_transform_forward (const gsl_wavelet * W,
-          double * DATA, size_t STRIDE, size_t N, gsl_wavelet_workspace
-          * WORK)
- -- Function: int gsl_wavelet_transform_inverse (const gsl_wavelet * W,
-          double * DATA, size_t STRIDE, size_t N, gsl_wavelet_workspace
-          * WORK)
-
-     These functions compute in-place forward and inverse discrete
-     wavelet transforms of length N with stride STRIDE on the array
-     DATA.  The length of the transform N is restricted to powers of
-     two.  For the 'transform' version of the function the argument DIR
-     can be either 'forward' (+1) or 'backward' (-1).  A workspace WORK
-     of length N must be provided.
-
-     For the forward transform, the elements of the original array are
-     replaced by the discrete wavelet transform f_i -> w_{j,k} in a
-     packed triangular storage layout, where J is the index of the level
-     j = 0 ... J-1 and K is the index of the coefficient within each
-     level, k = 0 ... (2^j)-1.  The total number of levels is J =
-     \log_2(n).  The output data has the following form,
-
-          (s_{-1,0}, d_{0,0}, d_{1,0}, d_{1,1}, d_{2,0}, ...,
-            d_{j,k}, ..., d_{J-1,2^{J-1}-1})
-
-     where the first element is the smoothing coefficient s_{-1,0},
-     followed by the detail coefficients d_{j,k} for each level j.  The
-     backward transform inverts these coefficients to obtain the
-     original data.
-
-     These functions return a status of 'GSL_SUCCESS' upon successful
-     completion.  'GSL_EINVAL' is returned if N is not an integer power
-     of 2 or if insufficient workspace is provided.
-
-
-File: gsl-ref.info,  Node: DWT in two dimension,  Prev: DWT in one dimension,  Up: DWT Transform Functions
-
-31.3.2 Wavelet transforms in two dimension
-------------------------------------------
-
-The library provides functions to perform two-dimensional discrete
-wavelet transforms on square matrices.  The matrix dimensions must be an
-integer power of two.  There are two possible orderings of the rows and
-columns in the two-dimensional wavelet transform, referred to as the
-"standard" and "non-standard" forms.
-
-   The "standard" transform performs a complete discrete wavelet
-transform on the rows of the matrix, followed by a separate complete
-discrete wavelet transform on the columns of the resulting
-row-transformed matrix.  This procedure uses the same ordering as a
-two-dimensional Fourier transform.
-
-   The "non-standard" transform is performed in interleaved passes on
-the rows and columns of the matrix for each level of the transform.  The
-first level of the transform is applied to the matrix rows, and then to
-the matrix columns.  This procedure is then repeated across the rows and
-columns of the data for the subsequent levels of the transform, until
-the full discrete wavelet transform is complete.  The non-standard form
-of the discrete wavelet transform is typically used in image analysis.
+   These interpolation methods produce curves that pass through each
+datapoint.  To interpolate noisy data with a smoothing curve see *note
+Basis Splines::.
 
    The functions described in this section are declared in the header
-file 'gsl_wavelet2d.h'.
-
- -- Function: int gsl_wavelet2d_transform (const gsl_wavelet * W, double
-          * DATA, size_t TDA, size_t SIZE1, size_t SIZE2,
-          gsl_wavelet_direction DIR, gsl_wavelet_workspace * WORK)
- -- Function: int gsl_wavelet2d_transform_forward (const gsl_wavelet *
-          W, double * DATA, size_t TDA, size_t SIZE1, size_t SIZE2,
-          gsl_wavelet_workspace * WORK)
- -- Function: int gsl_wavelet2d_transform_inverse (const gsl_wavelet *
-          W, double * DATA, size_t TDA, size_t SIZE1, size_t SIZE2,
-          gsl_wavelet_workspace * WORK)
-
-     These functions compute two-dimensional in-place forward and
-     inverse discrete wavelet transforms in standard form on the array
-     DATA stored in row-major form with dimensions SIZE1 and SIZE2 and
-     physical row length TDA.  The dimensions must be equal (square
-     matrix) and are restricted to powers of two.  For the 'transform'
-     version of the function the argument DIR can be either 'forward'
-     (+1) or 'backward' (-1).  A workspace WORK of the appropriate size
-     must be provided.  On exit, the appropriate elements of the array
-     DATA are replaced by their two-dimensional wavelet transform.
-
-     The functions return a status of 'GSL_SUCCESS' upon successful
-     completion.  'GSL_EINVAL' is returned if SIZE1 and SIZE2 are not
-     equal and integer powers of 2, or if insufficient workspace is
-     provided.
-
- -- Function: int gsl_wavelet2d_transform_matrix (const gsl_wavelet * W,
-          gsl_matrix * M, gsl_wavelet_direction DIR,
-          gsl_wavelet_workspace * WORK)
- -- Function: int gsl_wavelet2d_transform_matrix_forward (const
-          gsl_wavelet * W, gsl_matrix * M, gsl_wavelet_workspace * WORK)
- -- Function: int gsl_wavelet2d_transform_matrix_inverse (const
-          gsl_wavelet * W, gsl_matrix * M, gsl_wavelet_workspace * WORK)
-     These functions compute the two-dimensional in-place wavelet
-     transform on a matrix A.
-
- -- Function: int gsl_wavelet2d_nstransform (const gsl_wavelet * W,
-          double * DATA, size_t TDA, size_t SIZE1, size_t SIZE2,
-          gsl_wavelet_direction DIR, gsl_wavelet_workspace * WORK)
- -- Function: int gsl_wavelet2d_nstransform_forward (const gsl_wavelet *
-          W, double * DATA, size_t TDA, size_t SIZE1, size_t SIZE2,
-          gsl_wavelet_workspace * WORK)
- -- Function: int gsl_wavelet2d_nstransform_inverse (const gsl_wavelet *
-          W, double * DATA, size_t TDA, size_t SIZE1, size_t SIZE2,
-          gsl_wavelet_workspace * WORK)
-     These functions compute the two-dimensional wavelet transform in
-     non-standard form.
-
- -- Function: int gsl_wavelet2d_nstransform_matrix (const gsl_wavelet *
-          W, gsl_matrix * M, gsl_wavelet_direction DIR,
-          gsl_wavelet_workspace * WORK)
- -- Function: int gsl_wavelet2d_nstransform_matrix_forward (const
-          gsl_wavelet * W, gsl_matrix * M, gsl_wavelet_workspace * WORK)
- -- Function: int gsl_wavelet2d_nstransform_matrix_inverse (const
-          gsl_wavelet * W, gsl_matrix * M, gsl_wavelet_workspace * WORK)
-     These functions compute the non-standard form of the
-     two-dimensional in-place wavelet transform on a matrix A.
-
-
-File: gsl-ref.info,  Node: DWT Examples,  Next: DWT References,  Prev: DWT Transform Functions,  Up: Wavelet Transforms
-
-31.4 Examples
-=============
-
-The following program demonstrates the use of the one-dimensional
-wavelet transform functions.  It computes an approximation to an input
-signal (of length 256) using the 20 largest components of the wavelet
-transform, while setting the others to zero.
+files 'gsl_interp.h' and 'gsl_spline.h'.
 
-     #include <stdio.h>
-     #include <math.h>
-     #include <gsl/gsl_sort.h>
-     #include <gsl/gsl_wavelet.h>
+* Menu:
 
-     int
-     main (int argc, char **argv)
-     {
-       int i, n = 256, nc = 20;
-       double *data = malloc (n * sizeof (double));
-       double *abscoeff = malloc (n * sizeof (double));
-       size_t *p = malloc (n * sizeof (size_t));
-
-       FILE * f;
-       gsl_wavelet *w;
-       gsl_wavelet_workspace *work;
+* 1D Introduction to Interpolation::  
+* 1D Interpolation Functions::     
+* 1D Interpolation Types::         
+* 1D Index Look-up and Acceleration::  
+* 1D Evaluation of Interpolating Functions::  
+* 1D Higher-level Interface::      
+* 1D Interpolation Example programs::  
+* 1D Interpolation References and Further Reading::  
+* 2D Introduction to Interpolation::  
+* 2D Interpolation Functions::     
+* 2D Interpolation Grids::     
+* 2D Interpolation Types::         
+* 2D Evaluation of Interpolating Functions::  
+* 2D Higher-level Interface::      
+* 2D Interpolation Example programs::  
 
-       w = gsl_wavelet_alloc (gsl_wavelet_daubechies, 4);
-       work = gsl_wavelet_workspace_alloc (n);
+
+File: gsl-ref.info,  Node: 1D Introduction to Interpolation,  Next: 1D Interpolation Functions,  Up: Interpolation
 
-       f = fopen (argv[1], "r");
-       for (i = 0; i < n; i++)
-         {
-           fscanf (f, "%lg", &data[i]);
-         }
-       fclose (f);
+28.1 Introduction to 1D Interpolation
+=====================================
 
-       gsl_wavelet_transform_forward (w, data, 1, n, work);
+Given a set of data points (x_1, y_1) \dots (x_n, y_n) the routines
+described in this section compute a continuous interpolating function
+y(x) such that y(x_i) = y_i.  The interpolation is piecewise smooth, and
+its behavior at the end-points is determined by the type of
+interpolation used.
 
-       for (i = 0; i < n; i++)
-         {
-           abscoeff[i] = fabs (data[i]);
-         }
+
+File: gsl-ref.info,  Node: 1D Interpolation Functions,  Next: 1D Interpolation Types,  Prev: 1D Introduction to Interpolation,  Up: Interpolation
 
-       gsl_sort_index (p, abscoeff, 1, n);
+28.2 1D Interpolation Functions
+===============================
 
-       for (i = 0; (i + nc) < n; i++)
-         data[p[i]] = 0;
+The interpolation function for a given dataset is stored in a
+'gsl_interp' object.  These are created by the following functions.
 
-       gsl_wavelet_transform_inverse (w, data, 1, n, work);
+ -- Function: gsl_interp * gsl_interp_alloc (const gsl_interp_type * T,
+          size_t SIZE)
+     This function returns a pointer to a newly allocated interpolation
+     object of type T for SIZE data-points.
 
-       for (i = 0; i < n; i++)
-         {
-           printf ("%g\n", data[i]);
-         }
+ -- Function: int gsl_interp_init (gsl_interp * INTERP, const double
+          XA[], const double YA[], size_t SIZE)
+     This function initializes the interpolation object INTERP for the
+     data (XA,YA) where XA and YA are arrays of size SIZE.  The
+     interpolation object ('gsl_interp') does not save the data arrays
+     XA and YA and only stores the static state computed from the data.
+     The XA data array is always assumed to be strictly ordered, with
+     increasing x values; the behavior for other arrangements is not
+     defined.
 
-       gsl_wavelet_free (w);
-       gsl_wavelet_workspace_free (work);
+ -- Function: void gsl_interp_free (gsl_interp * INTERP)
+     This function frees the interpolation object INTERP.
 
-       free (data);
-       free (abscoeff);
-       free (p);
-       return 0;
-     }
+
+File: gsl-ref.info,  Node: 1D Interpolation Types,  Next: 1D Index Look-up and Acceleration,  Prev: 1D Interpolation Functions,  Up: Interpolation
 
-The output can be used with the GNU plotutils 'graph' program,
+28.3 1D Interpolation Types
+===========================
 
-     $ ./a.out ecg.dat > dwt.dat
-     $ graph -T ps -x 0 256 32 -h 0.3 -a dwt.dat > dwt.ps
+The interpolation library provides the following interpolation types:
 
-
-File: gsl-ref.info,  Node: DWT References,  Prev: DWT Examples,  Up: Wavelet Transforms
+ -- Interpolation Type: gsl_interp_linear
+     Linear interpolation.  This interpolation method does not require
+     any additional memory.
 
-31.5 References and Further Reading
-===================================
+ -- Interpolation Type: gsl_interp_polynomial
+     Polynomial interpolation.  This method should only be used for
+     interpolating small numbers of points because polynomial
+     interpolation introduces large oscillations, even for well-behaved
+     datasets.  The number of terms in the interpolating polynomial is
+     equal to the number of points.
 
-The mathematical background to wavelet transforms is covered in the
-original lectures by Daubechies,
+ -- Interpolation Type: gsl_interp_cspline
+     Cubic spline with natural boundary conditions.  The resulting curve
+     is piecewise cubic on each interval, with matching first and second
+     derivatives at the supplied data-points.  The second derivative is
+     chosen to be zero at the first point and last point.
 
-     Ingrid Daubechies.  Ten Lectures on Wavelets.  'CBMS-NSF Regional
-     Conference Series in Applied Mathematics' (1992), SIAM, ISBN
-     0898712742.
+ -- Interpolation Type: gsl_interp_cspline_periodic
+     Cubic spline with periodic boundary conditions.  The resulting
+     curve is piecewise cubic on each interval, with matching first and
+     second derivatives at the supplied data-points.  The derivatives at
+     the first and last points are also matched.  Note that the last
+     point in the data must have the same y-value as the first point,
+     otherwise the resulting periodic interpolation will have a
+     discontinuity at the boundary.
 
-An easy to read introduction to the subject with an emphasis on the
-application of the wavelet transform in various branches of science is,
+ -- Interpolation Type: gsl_interp_akima
+     Non-rounded Akima spline with natural boundary conditions.  This
+     method uses the non-rounded corner algorithm of Wodicka.
 
-     Paul S. Addison.  'The Illustrated Wavelet Transform Handbook'.
-     Institute of Physics Publishing (2002), ISBN 0750306920.
+ -- Interpolation Type: gsl_interp_akima_periodic
+     Non-rounded Akima spline with periodic boundary conditions.  This
+     method uses the non-rounded corner algorithm of Wodicka.
 
-For extensive coverage of signal analysis by wavelets, wavelet packets
-and local cosine bases see,
+ -- Interpolation Type: gsl_interp_steffen
+     Steffen's method guarantees the monotonicity of the interpolating
+     function between the given data points.  Therefore, minima and
+     maxima can only occur exactly at the data points, and there can
+     never be spurious oscillations between data points.  The
+     interpolated function is piecewise cubic in each interval.  The
+     resulting curve and its first derivative are guaranteed to be
+     continuous, but the second derivative may be discontinuous.
 
-     S. G. Mallat.  'A wavelet tour of signal processing' (Second
-     edition).  Academic Press (1999), ISBN 012466606X.
+The following related functions are available:
 
-The concept of multiresolution analysis underlying the wavelet transform
-is described in,
+ -- Function: const char * gsl_interp_name (const gsl_interp * INTERP)
+     This function returns the name of the interpolation type used by
+     INTERP.  For example,
 
-     S. G. Mallat.  Multiresolution Approximations and Wavelet
-     Orthonormal Bases of L^2(R). 'Transactions of the American
-     Mathematical Society', 315(1), 1989, 69-87.
+          printf ("interp uses '%s' interpolation.\n",
+                  gsl_interp_name (interp));
 
-     S. G. Mallat.  A Theory for Multiresolution Signal
-     Decomposition--The Wavelet Representation.  'IEEE Transactions on
-     Pattern Analysis and Machine Intelligence', 11, 1989, 674-693.
+     would print something like,
 
-The coefficients for the individual wavelet families implemented by the
-library can be found in the following papers,
+          interp uses 'cspline' interpolation.
 
-     I. Daubechies.  Orthonormal Bases of Compactly Supported Wavelets.
-     'Communications on Pure and Applied Mathematics', 41 (1988)
-     909-996.
+ -- Function: unsigned int gsl_interp_min_size (const gsl_interp *
+          INTERP)
+ -- Function: unsigned int gsl_interp_type_min_size (const
+          gsl_interp_type * T)
+     These functions return the minimum number of points required by the
+     interpolation object INTERP or interpolation type T.  For example,
+     Akima spline interpolation requires a minimum of 5 points.
 
-     A. Cohen, I. Daubechies, and J.-C. Feauveau.  Biorthogonal Bases of
-     Compactly Supported Wavelets.  'Communications on Pure and Applied
-     Mathematics', 45 (1992) 485-560.
+
+File: gsl-ref.info,  Node: 1D Index Look-up and Acceleration,  Next: 1D Evaluation of Interpolating Functions,  Prev: 1D Interpolation Types,  Up: Interpolation
 
-The PhysioNet archive of physiological datasets can be found online at
-<http://www.physionet.org/> and is described in the following paper,
+28.4 1D Index Look-up and Acceleration
+======================================
 
-     Goldberger et al.  PhysioBank, PhysioToolkit, and PhysioNet:
-     Components of a New Research Resource for Complex Physiologic
-     Signals.  'Circulation' 101(23):e215-e220 2000.
+The state of searches can be stored in a 'gsl_interp_accel' object,
+which is a kind of iterator for interpolation lookups.  It caches the
+previous value of an index lookup.  When the subsequent interpolation
+point falls in the same interval its index value can be returned
+immediately.
 
-
-File: gsl-ref.info,  Node: Discrete Hankel Transforms,  Next: One dimensional Root-Finding,  Prev: Wavelet Transforms,  Up: Top
+ -- Function: size_t gsl_interp_bsearch (const double X_ARRAY[], double
+          X, size_t INDEX_LO, size_t INDEX_HI)
+     This function returns the index i of the array X_ARRAY such that
+     'x_array[i] <= x < x_array[i+1]'.  The index is searched for in the
+     range [INDEX_LO,INDEX_HI].  An inline version of this function is
+     used when 'HAVE_INLINE' is defined.
 
-32 Discrete Hankel Transforms
-*****************************
+ -- Function: gsl_interp_accel * gsl_interp_accel_alloc (void)
+     This function returns a pointer to an accelerator object, which is
+     a kind of iterator for interpolation lookups.  It tracks the state
+     of lookups, thus allowing for application of various acceleration
+     strategies.
 
-This chapter describes functions for performing Discrete Hankel
-Transforms (DHTs).  The functions are declared in the header file
-'gsl_dht.h'.
+ -- Function: size_t gsl_interp_accel_find (gsl_interp_accel * A, const
+          double X_ARRAY[], size_t SIZE, double X)
+     This function performs a lookup action on the data array X_ARRAY of
+     size SIZE, using the given accelerator A.  This is how lookups are
+     performed during evaluation of an interpolation.  The function
+     returns an index i such that 'x_array[i] <= x < x_array[i+1]'.  An
+     inline version of this function is used when 'HAVE_INLINE' is
+     defined.
 
-* Menu:
+ -- Function: int gsl_interp_accel_reset (gsl_interp_accel * ACC);
+     This function reinitializes the accelerator object ACC.  It should
+     be used when the cached information is no longer applicable--for
+     example, when switching to a new dataset.
 
-* Discrete Hankel Transform Definition::  
-* Discrete Hankel Transform Functions::  
-* Discrete Hankel Transform References::  
+ -- Function: void gsl_interp_accel_free (gsl_interp_accel* ACC)
+     This function frees the accelerator object ACC.
 
 
-File: gsl-ref.info,  Node: Discrete Hankel Transform Definition,  Next: Discrete Hankel Transform Functions,  Up: Discrete Hankel Transforms
+File: gsl-ref.info,  Node: 1D Evaluation of Interpolating Functions,  Next: 1D Higher-level Interface,  Prev: 1D Index Look-up and Acceleration,  Up: Interpolation
 
-32.1 Definitions
-================
+28.5 1D Evaluation of Interpolating Functions
+=============================================
 
-The discrete Hankel transform acts on a vector of sampled data, where
-the samples are assumed to have been taken at points related to the
-zeroes of a Bessel function of fixed order; compare this to the case of
-the discrete Fourier transform, where samples are taken at points
-related to the zeroes of the sine or cosine function.
-
-   Specifically, let f(t) be a function on the unit interval and
-j_(\nu,m) the m-th zero of the Bessel function J_\nu(x).  Then the
-finite \nu-Hankel transform of f(t) is defined to be the set of numbers
-g_m given by,
-     g_m = \int_0^1 t dt J_\nu(j_(\nu,m)t) f(t),
-
-so that,
-     f(t) = \sum_{m=1}^\infty (2 J_\nu(j_(\nu,m)t) / J_(\nu+1)(j_(\nu,m))^2) g_m.
-
-Suppose that f is band-limited in the sense that g_m=0 for m > M.  Then
-we have the following fundamental sampling theorem.
-     g_m = (2 / j_(\nu,M)^2)
-           \sum_{k=1}^{M-1} f(j_(\nu,k)/j_(\nu,M))
-               (J_\nu(j_(\nu,m) j_(\nu,k) / j_(\nu,M)) / J_(\nu+1)(j_(\nu,k))^2).
-
-It is this discrete expression which defines the discrete Hankel
-transform.  The kernel in the summation above defines the matrix of the
-\nu-Hankel transform of size M-1.  The coefficients of this matrix,
-being dependent on \nu and M, must be precomputed and stored; the
-'gsl_dht' object encapsulates this data.  The allocation function
-'gsl_dht_alloc' returns a 'gsl_dht' object which must be properly
-initialized with 'gsl_dht_init' before it can be used to perform
-transforms on data sample vectors, for fixed \nu and M, using the
-'gsl_dht_apply' function.  The implementation allows a scaling of the
-fundamental interval, for convenience, so that one can assume the
-function is defined on the interval [0,X], rather than the unit
-interval.
-
-   Notice that by assumption f(t) vanishes at the endpoints of the
-interval, consistent with the inversion formula and the sampling formula
-given above.  Therefore, this transform corresponds to an orthogonal
-expansion in eigenfunctions of the Dirichlet problem for the Bessel
-differential equation.
+ -- Function: double gsl_interp_eval (const gsl_interp * INTERP, const
+          double XA[], const double YA[], double X, gsl_interp_accel *
+          ACC)
+ -- Function: int gsl_interp_eval_e (const gsl_interp * INTERP, const
+          double XA[], const double YA[], double X, gsl_interp_accel *
+          ACC, double * Y)
+     These functions return the interpolated value of Y for a given
+     point X, using the interpolation object INTERP, data arrays XA and
+     YA and the accelerator ACC.  When X is outside the range of XA, the
+     error code 'GSL_EDOM' is returned with a value of 'GSL_NAN' for Y.
 
-
-File: gsl-ref.info,  Node: Discrete Hankel Transform Functions,  Next: Discrete Hankel Transform References,  Prev: Discrete Hankel Transform Definition,  Up: Discrete Hankel Transforms
+ -- Function: double gsl_interp_eval_deriv (const gsl_interp * INTERP,
+          const double XA[], const double YA[], double X,
+          gsl_interp_accel * ACC)
+ -- Function: int gsl_interp_eval_deriv_e (const gsl_interp * INTERP,
+          const double XA[], const double YA[], double X,
+          gsl_interp_accel * ACC, double * D)
+     These functions return the derivative D of an interpolated function
+     for a given point X, using the interpolation object INTERP, data
+     arrays XA and YA and the accelerator ACC.
 
-32.2 Functions
-==============
+ -- Function: double gsl_interp_eval_deriv2 (const gsl_interp * INTERP,
+          const double XA[], const double YA[], double X,
+          gsl_interp_accel * ACC)
+ -- Function: int gsl_interp_eval_deriv2_e (const gsl_interp * INTERP,
+          const double XA[], const double YA[], double X,
+          gsl_interp_accel * ACC, double * D2)
+     These functions return the second derivative D2 of an interpolated
+     function for a given point X, using the interpolation object
+     INTERP, data arrays XA and YA and the accelerator ACC.
 
- -- Function: gsl_dht * gsl_dht_alloc (size_t SIZE)
-     This function allocates a Discrete Hankel transform object of size
-     SIZE.
+ -- Function: double gsl_interp_eval_integ (const gsl_interp * INTERP,
+          const double XA[], const double YA[], double A, double B,
+          gsl_interp_accel * ACC)
+ -- Function: int gsl_interp_eval_integ_e (const gsl_interp * INTERP,
+          const double XA[], const double YA[], double A, double B,
+          gsl_interp_accel * ACC, double * RESULT)
+     These functions return the numerical integral RESULT of an
+     interpolated function over the range [A, B], using the
+     interpolation object INTERP, data arrays XA and YA and the
+     accelerator ACC.
 
- -- Function: int gsl_dht_init (gsl_dht * T, double NU, double XMAX)
-     This function initializes the transform T for the given values of
-     NU and XMAX.
+
+File: gsl-ref.info,  Node: 1D Higher-level Interface,  Next: 1D Interpolation Example programs,  Prev: 1D Evaluation of Interpolating Functions,  Up: Interpolation
 
- -- Function: gsl_dht * gsl_dht_new (size_t SIZE, double NU, double
-          XMAX)
-     This function allocates a Discrete Hankel transform object of size
-     SIZE and initializes it for the given values of NU and XMAX.
+28.6 1D Higher-level Interface
+==============================
 
- -- Function: void gsl_dht_free (gsl_dht * T)
-     This function frees the transform T.
+The functions described in the previous sections required the user to
+supply pointers to the x and y arrays on each call.  The following
+functions are equivalent to the corresponding 'gsl_interp' functions but
+maintain a copy of this data in the 'gsl_spline' object.  This removes
+the need to pass both XA and YA as arguments on each evaluation.  These
+functions are defined in the header file 'gsl_spline.h'.
 
- -- Function: int gsl_dht_apply (const gsl_dht * T, double * F_IN,
-          double * F_OUT)
-     This function applies the transform T to the array F_IN whose size
-     is equal to the size of the transform.  The result is stored in the
-     array F_OUT which must be of the same length.
+ -- Function: gsl_spline * gsl_spline_alloc (const gsl_interp_type * T,
+          size_t SIZE)
 
-     Applying this function to its output gives the original data
-     multiplied by (1/j_(\nu,M))^2, up to numerical errors.
+ -- Function: int gsl_spline_init (gsl_spline * SPLINE, const double
+          XA[], const double YA[], size_t SIZE)
 
- -- Function: double gsl_dht_x_sample (const gsl_dht * T, int N)
-     This function returns the value of the N-th sample point in the
-     unit interval, (j_{\nu,n+1}/j_{\nu,M}) X.  These are the points
-     where the function f(t) is assumed to be sampled.
+ -- Function: void gsl_spline_free (gsl_spline * SPLINE)
 
- -- Function: double gsl_dht_k_sample (const gsl_dht * T, int N)
-     This function returns the value of the N-th sample point in
-     "k-space", j_{\nu,n+1}/X.
+ -- Function: const char * gsl_spline_name (const gsl_spline * SPLINE)
 
-
-File: gsl-ref.info,  Node: Discrete Hankel Transform References,  Prev: Discrete Hankel Transform Functions,  Up: Discrete Hankel Transforms
+ -- Function: unsigned int gsl_spline_min_size (const gsl_spline *
+          SPLINE)
 
-32.3 References and Further Reading
-===================================
+ -- Function: double gsl_spline_eval (const gsl_spline * SPLINE, double
+          X, gsl_interp_accel * ACC)
+ -- Function: int gsl_spline_eval_e (const gsl_spline * SPLINE, double
+          X, gsl_interp_accel * ACC, double * Y)
 
-The algorithms used by these functions are described in the following
-papers,
+ -- Function: double gsl_spline_eval_deriv (const gsl_spline * SPLINE,
+          double X, gsl_interp_accel * ACC)
+ -- Function: int gsl_spline_eval_deriv_e (const gsl_spline * SPLINE,
+          double X, gsl_interp_accel * ACC, double * D)
 
-     H. Fisk Johnson, Comp. Phys. Comm. 43, 181 (1987).
+ -- Function: double gsl_spline_eval_deriv2 (const gsl_spline * SPLINE,
+          double X, gsl_interp_accel * ACC)
+ -- Function: int gsl_spline_eval_deriv2_e (const gsl_spline * SPLINE,
+          double X, gsl_interp_accel * ACC, double * D2)
 
-     D. Lemoine, J. Chem. Phys. 101, 3936 (1994).
+ -- Function: double gsl_spline_eval_integ (const gsl_spline * SPLINE,
+          double A, double B, gsl_interp_accel * ACC)
+ -- Function: int gsl_spline_eval_integ_e (const gsl_spline * SPLINE,
+          double A, double B, gsl_interp_accel * ACC, double * RESULT)
 
 
-File: gsl-ref.info,  Node: One dimensional Root-Finding,  Next: One dimensional Minimization,  Prev: Discrete Hankel Transforms,  Up: Top
+File: gsl-ref.info,  Node: 1D Interpolation Example programs,  Next: 1D Interpolation References and Further Reading,  Prev: 1D Higher-level Interface,  Up: Interpolation
 
-33 One dimensional Root-Finding
-*******************************
+28.7 Examples of 1D Interpolation
+=================================
 
-This chapter describes routines for finding roots of arbitrary
-one-dimensional functions.  The library provides low level components
-for a variety of iterative solvers and convergence tests.  These can be
-combined by the user to achieve the desired solution, with full access
-to the intermediate steps of the iteration.  Each class of methods uses
-the same framework, so that you can switch between solvers at runtime
-without needing to recompile your program.  Each instance of a solver
-keeps track of its own state, allowing the solvers to be used in
-multi-threaded programs.
+The following program demonstrates the use of the interpolation and
+spline functions.  It computes a cubic spline interpolation of the
+10-point dataset (x_i, y_i) where x_i = i + \sin(i)/2 and y_i = i +
+\cos(i^2) for i = 0 \dots 9.
 
-   The header file 'gsl_roots.h' contains prototypes for the root
-finding functions and related declarations.
+     #include <stdlib.h>
+     #include <stdio.h>
+     #include <math.h>
+     #include <gsl/gsl_errno.h>
+     #include <gsl/gsl_spline.h>
 
-* Menu:
+     int
+     main (void)
+     {
+       int i;
+       double xi, yi, x[10], y[10];
 
-* Root Finding Overview::       
-* Root Finding Caveats::        
-* Initializing the Solver::     
-* Providing the function to solve::  
-* Search Bounds and Guesses::   
-* Root Finding Iteration::      
-* Search Stopping Parameters::  
-* Root Bracketing Algorithms::  
-* Root Finding Algorithms using Derivatives::  
-* Root Finding Examples::       
-* Root Finding References and Further Reading::  
+       printf ("#m=0,S=2\n");
 
-
-File: gsl-ref.info,  Node: Root Finding Overview,  Next: Root Finding Caveats,  Up: One dimensional Root-Finding
+       for (i = 0; i < 10; i++)
+         {
+           x[i] = i + 0.5 * sin (i);
+           y[i] = i + cos (i * i);
+           printf ("%g %g\n", x[i], y[i]);
+         }
 
-33.1 Overview
-=============
+       printf ("#m=1,S=0\n");
 
-One-dimensional root finding algorithms can be divided into two classes,
-"root bracketing" and "root polishing".  Algorithms which proceed by
-bracketing a root are guaranteed to converge.  Bracketing algorithms
-begin with a bounded region known to contain a root.  The size of this
-bounded region is reduced, iteratively, until it encloses the root to a
-desired tolerance.  This provides a rigorous error estimate for the
-location of the root.
-
-   The technique of "root polishing" attempts to improve an initial
-guess to the root.  These algorithms converge only if started "close
-enough" to a root, and sacrifice a rigorous error bound for speed.  By
-approximating the behavior of a function in the vicinity of a root they
-attempt to find a higher order improvement of an initial guess.  When
-the behavior of the function is compatible with the algorithm and a good
-initial guess is available a polishing algorithm can provide rapid
-convergence.
-
-   In GSL both types of algorithm are available in similar frameworks.
-The user provides a high-level driver for the algorithms, and the
-library provides the individual functions necessary for each of the
-steps.  There are three main phases of the iteration.  The steps are,
-
-   * initialize solver state, S, for algorithm T
-
-   * update S using the iteration T
-
-   * test S for convergence, and repeat iteration if necessary
-
-The state for bracketing solvers is held in a 'gsl_root_fsolver' struct.
-The updating procedure uses only function evaluations (not derivatives).
-The state for root polishing solvers is held in a 'gsl_root_fdfsolver'
-struct.  The updates require both the function and its derivative (hence
-the name 'fdf') to be supplied by the user.
-
-
-File: gsl-ref.info,  Node: Root Finding Caveats,  Next: Initializing the Solver,  Prev: Root Finding Overview,  Up: One dimensional Root-Finding
-
-33.2 Caveats
-============
-
-Note that root finding functions can only search for one root at a time.
-When there are several roots in the search area, the first root to be
-found will be returned; however it is difficult to predict which of the
-roots this will be.  _In most cases, no error will be reported if you
-try to find a root in an area where there is more than one._
-
-   Care must be taken when a function may have a multiple root (such as
-f(x) = (x-x_0)^2 or f(x) = (x-x_0)^3).  It is not possible to use
-root-bracketing algorithms on even-multiplicity roots.  For these
-algorithms the initial interval must contain a zero-crossing, where the
-function is negative at one end of the interval and positive at the
-other end.  Roots with even-multiplicity do not cross zero, but only
-touch it instantaneously.  Algorithms based on root bracketing will
-still work for odd-multiplicity roots (e.g.  cubic, quintic, ...).  Root
-polishing algorithms generally work with higher multiplicity roots, but
-at a reduced rate of convergence.  In these cases the "Steffenson
-algorithm" can be used to accelerate the convergence of multiple roots.
-
-   While it is not absolutely required that f have a root within the
-search region, numerical root finding functions should not be used
-haphazardly to check for the _existence_ of roots.  There are better
-ways to do this.  Because it is easy to create situations where
-numerical root finders can fail, it is a bad idea to throw a root finder
-at a function you do not know much about.  In general it is best to
-examine the function visually by plotting before searching for a root.
+       {
+         gsl_interp_accel *acc
+           = gsl_interp_accel_alloc ();
+         gsl_spline *spline
+           = gsl_spline_alloc (gsl_interp_cspline, 10);
 
-
-File: gsl-ref.info,  Node: Initializing the Solver,  Next: Providing the function to solve,  Prev: Root Finding Caveats,  Up: One dimensional Root-Finding
+         gsl_spline_init (spline, x, y, 10);
 
-33.3 Initializing the Solver
-============================
+         for (xi = x[0]; xi < x[9]; xi += 0.01)
+           {
+             yi = gsl_spline_eval (spline, xi, acc);
+             printf ("%g %g\n", xi, yi);
+           }
+         gsl_spline_free (spline);
+         gsl_interp_accel_free (acc);
+       }
+       return 0;
+     }
 
- -- Function: gsl_root_fsolver * gsl_root_fsolver_alloc (const
-          gsl_root_fsolver_type * T)
-     This function returns a pointer to a newly allocated instance of a
-     solver of type T.  For example, the following code creates an
-     instance of a bisection solver,
+The output is designed to be used with the GNU plotutils 'graph'
+program,
 
-          const gsl_root_fsolver_type * T
-            = gsl_root_fsolver_bisection;
-          gsl_root_fsolver * s
-            = gsl_root_fsolver_alloc (T);
-
-     If there is insufficient memory to create the solver then the
-     function returns a null pointer and the error handler is invoked
-     with an error code of 'GSL_ENOMEM'.
+     $ ./a.out > interp.dat
+     $ graph -T ps < interp.dat > interp.ps
 
- -- Function: gsl_root_fdfsolver * gsl_root_fdfsolver_alloc (const
-          gsl_root_fdfsolver_type * T)
-     This function returns a pointer to a newly allocated instance of a
-     derivative-based solver of type T.  For example, the following code
-     creates an instance of a Newton-Raphson solver,
+The result shows a smooth interpolation of the original points.  The
+interpolation method can be changed simply by varying the first argument
+of 'gsl_spline_alloc'.
 
-          const gsl_root_fdfsolver_type * T
-            = gsl_root_fdfsolver_newton;
-          gsl_root_fdfsolver * s
-            = gsl_root_fdfsolver_alloc (T);
-
-     If there is insufficient memory to create the solver then the
-     function returns a null pointer and the error handler is invoked
-     with an error code of 'GSL_ENOMEM'.
-
- -- Function: int gsl_root_fsolver_set (gsl_root_fsolver * S,
-          gsl_function * F, double X_LOWER, double X_UPPER)
-     This function initializes, or reinitializes, an existing solver S
-     to use the function F and the initial search interval [X_LOWER,
-     X_UPPER].
-
- -- Function: int gsl_root_fdfsolver_set (gsl_root_fdfsolver * S,
-          gsl_function_fdf * FDF, double ROOT)
-     This function initializes, or reinitializes, an existing solver S
-     to use the function and derivative FDF and the initial guess ROOT.
-
- -- Function: void gsl_root_fsolver_free (gsl_root_fsolver * S)
- -- Function: void gsl_root_fdfsolver_free (gsl_root_fdfsolver * S)
-     These functions free all the memory associated with the solver S.
+   The next program demonstrates a periodic cubic spline with 4 data
+points.  Note that the first and last points must be supplied with the
+same y-value for a periodic spline.
 
- -- Function: const char * gsl_root_fsolver_name (const gsl_root_fsolver
-          * S)
- -- Function: const char * gsl_root_fdfsolver_name (const
-          gsl_root_fdfsolver * S)
-     These functions return a pointer to the name of the solver.  For
-     example,
+     #include <stdlib.h>
+     #include <stdio.h>
+     #include <math.h>
+     #include <gsl/gsl_errno.h>
+     #include <gsl/gsl_spline.h>
 
-          printf ("s is a '%s' solver\n",
-                  gsl_root_fsolver_name (s));
+     int
+     main (void)
+     {
+       int N = 4;
+       double x[4] = {0.00, 0.10,  0.27,  0.30};
+       double y[4] = {0.15, 0.70, -0.10,  0.15};
+                  /* Note: y[0] == y[3] for periodic data */
 
-     would print something like 's is a 'bisection' solver'.
+       gsl_interp_accel *acc = gsl_interp_accel_alloc ();
+       const gsl_interp_type *t = gsl_interp_cspline_periodic;
+       gsl_spline *spline = gsl_spline_alloc (t, N);
 
-
-File: gsl-ref.info,  Node: Providing the function to solve,  Next: Search Bounds and Guesses,  Prev: Initializing the Solver,  Up: One dimensional Root-Finding
+       int i; double xi, yi;
 
-33.4 Providing the function to solve
-====================================
+       printf ("#m=0,S=5\n");
+       for (i = 0; i < N; i++)
+         {
+           printf ("%g %g\n", x[i], y[i]);
+         }
 
-You must provide a continuous function of one variable for the root
-finders to operate on, and, sometimes, its first derivative.  In order
-to allow for general parameters the functions are defined by the
-following data types:
-
- -- Data Type: gsl_function
-     This data type defines a general function with parameters.
-
-     'double (* function) (double X, void * PARAMS)'
-          this function should return the value f(x,params) for argument
-          X and parameters PARAMS
+       printf ("#m=1,S=0\n");
+       gsl_spline_init (spline, x, y, N);
 
-     'void * params'
-          a pointer to the parameters of the function
+       for (i = 0; i <= 100; i++)
+         {
+           xi = (1 - i / 100.0) * x[0] + (i / 100.0) * x[N-1];
+           yi = gsl_spline_eval (spline, xi, acc);
+           printf ("%g %g\n", xi, yi);
+         }
 
-   Here is an example for the general quadratic function,
+       gsl_spline_free (spline);
+       gsl_interp_accel_free (acc);
+       return 0;
+     }
 
-     f(x) = a x^2 + b x + c
+   The output can be plotted with GNU 'graph'.
 
-with a = 3, b = 2, c = 1.  The following code defines a 'gsl_function'
-'F' which you could pass to a root finder as a function pointer:
+     $ ./a.out > interp.dat
+     $ graph -T ps < interp.dat > interp.ps
 
-     struct my_f_params { double a; double b; double c; };
+The result shows a periodic interpolation of the original points.  The
+slope of the fitted curve is the same at the beginning and end of the
+data, and the second derivative is also.
 
-     double
-     my_f (double x, void * p) {
-        struct my_f_params * params
-          = (struct my_f_params *)p;
-        double a = (params->a);
-        double b = (params->b);
-        double c = (params->c);
+   The next program illustrates the difference between the cubic spline,
+Akima, and Steffen interpolation types on a difficult dataset.
 
-        return  (a * x + b) * x + c;
-     }
+     #include <stdio.h>
+     #include <stdlib.h>
+     #include <math.h>
 
-     gsl_function F;
-     struct my_f_params params = { 3.0, 2.0, 1.0 };
+     #include <gsl/gsl_math.h>
+     #include <gsl/gsl_spline.h>
 
-     F.function = &my_f;
-     F.params = &params;
+     int
+     main(void)
+     {
+       size_t i;
+       const size_t N = 9;
 
-The function f(x) can be evaluated using the macro 'GSL_FN_EVAL(&F,x)'
-defined in 'gsl_math.h'.
+       /* this dataset is taken from
+        * J. M. Hyman, Accurate Monotonicity preserving cubic interpolation,
+        * SIAM J. Sci. Stat. Comput. 4, 4, 1983. */
+       const double x[] = { 7.99, 8.09, 8.19, 8.7, 9.2,
+                            10.0, 12.0, 15.0, 20.0 };
+       const double y[] = { 0.0, 2.76429e-5, 4.37498e-2,
+                            0.169183, 0.469428, 0.943740,
+                            0.998636, 0.999919, 0.999994 };
+
+       gsl_interp_accel *acc = gsl_interp_accel_alloc();
+       gsl_spline *spline_cubic = gsl_spline_alloc(gsl_interp_cspline, N);
+       gsl_spline *spline_akima = gsl_spline_alloc(gsl_interp_akima, N);
+       gsl_spline *spline_steffen = gsl_spline_alloc(gsl_interp_steffen, N);
+
+       gsl_spline_init(spline_cubic, x, y, N);
+       gsl_spline_init(spline_akima, x, y, N);
+       gsl_spline_init(spline_steffen, x, y, N);
 
- -- Data Type: gsl_function_fdf
-     This data type defines a general function with parameters and its
-     first derivative.
-
-     'double (* f) (double X, void * PARAMS)'
-          this function should return the value of f(x,params) for
-          argument X and parameters PARAMS
-
-     'double (* df) (double X, void * PARAMS)'
-          this function should return the value of the derivative of F
-          with respect to X, f'(x,params), for argument X and parameters
-          PARAMS
-
-     'void (* fdf) (double X, void * PARAMS, double * F, double * DF)'
-          this function should set the values of the function F to
-          f(x,params) and its derivative DF to f'(x,params) for argument
-          X and parameters PARAMS.  This function provides an
-          optimization of the separate functions for f(x) and f'(x)--it
-          is always faster to compute the function and its derivative at
-          the same time.
+       for (i = 0; i < N; ++i)
+         printf("%g %g\n", x[i], y[i]);
 
-     'void * params'
-          a pointer to the parameters of the function
+       printf("\n\n");
 
-   Here is an example where f(x) = 2\exp(2x):
+       for (i = 0; i <= 100; ++i)
+         {
+           double xi = (1 - i / 100.0) * x[0] + (i / 100.0) * x[N-1];
+           double yi_cubic = gsl_spline_eval(spline_cubic, xi, acc);
+           double yi_akima = gsl_spline_eval(spline_akima, xi, acc);
+           double yi_steffen = gsl_spline_eval(spline_steffen, xi, acc);
 
-     double
-     my_f (double x, void * params)
-     {
-        return exp (2 * x);
-     }
+           printf("%g %g %g %g\n", xi, yi_cubic, yi_akima, yi_steffen);
+         }
 
-     double
-     my_df (double x, void * params)
-     {
-        return 2 * exp (2 * x);
+       gsl_spline_free(spline_cubic);
+       gsl_spline_free(spline_akima);
+       gsl_spline_free(spline_steffen);
+       gsl_interp_accel_free(acc);
+
+       return 0;
      }
 
-     void
-     my_fdf (double x, void * params,
-             double * f, double * df)
-     {
-        double t = exp (2 * x);
+The cubic method exhibits a local maxima between the 6th and 7th data
+points and continues oscillating for the rest of the data.  Akima also
+shows a local maxima but recovers and follows the data well after the
+7th grid point.  Steffen preserves monotonicity in all intervals and
+does not exhibit oscillations, at the expense of having a discontinuous
+second derivative.
 
-        *f = t;
-        *df = 2 * t;   /* uses existing value */
-     }
+
+File: gsl-ref.info,  Node: 1D Interpolation References and Further Reading,  Next: 2D Introduction to Interpolation,  Prev: 1D Interpolation Example programs,  Up: Interpolation
 
-     gsl_function_fdf FDF;
+28.8 References and Further Reading
+===================================
 
-     FDF.f = &my_f;
-     FDF.df = &my_df;
-     FDF.fdf = &my_fdf;
-     FDF.params = 0;
+Descriptions of the interpolation algorithms and further references can
+be found in the following publications:
 
-The function f(x) can be evaluated using the macro
-'GSL_FN_FDF_EVAL_F(&FDF,x)' and the derivative f'(x) can be evaluated
-using the macro 'GSL_FN_FDF_EVAL_DF(&FDF,x)'.  Both the function y =
-f(x) and its derivative dy = f'(x) can be evaluated at the same time
-using the macro 'GSL_FN_FDF_EVAL_F_DF(&FDF,x,y,dy)'.  The macro stores
-f(x) in its Y argument and f'(x) in its DY argument--both of these
-should be pointers to 'double'.
+     C.W. Ueberhuber, 'Numerical Computation (Volume 1), Chapter 9
+     "Interpolation"', Springer (1997), ISBN 3-540-62058-3.
 
-
-File: gsl-ref.info,  Node: Search Bounds and Guesses,  Next: Root Finding Iteration,  Prev: Providing the function to solve,  Up: One dimensional Root-Finding
+     D.M. Young, R.T. Gregory, 'A Survey of Numerical Mathematics
+     (Volume 1), Chapter 6.8', Dover (1988), ISBN 0-486-65691-8.
 
-33.5 Search Bounds and Guesses
-==============================
+     M. Steffen, 'A simple method for monotonic interpolation in one
+     dimension', Astron.  Astrophys.  239, 443-450, 1990.
 
-You provide either search bounds or an initial guess; this section
-explains how search bounds and guesses work and how function arguments
-control them.
+
+File: gsl-ref.info,  Node: 2D Introduction to Interpolation,  Next: 2D Interpolation Functions,  Prev: 1D Interpolation References and Further Reading,  Up: Interpolation
 
-   A guess is simply an x value which is iterated until it is within the
-desired precision of a root.  It takes the form of a 'double'.
+28.9 Introduction to 2D Interpolation
+=====================================
 
-   Search bounds are the endpoints of an interval which is iterated
-until the length of the interval is smaller than the requested
-precision.  The interval is defined by two values, the lower limit and
-the upper limit.  Whether the endpoints are intended to be included in
-the interval or not depends on the context in which the interval is
-used.
+Given a set of x coordinates x_1,...,x_m and a set of y coordinates
+y_1,...,y_n, each in increasing order, plus a set of function values
+z_{ij} for each grid point (x_i,y_j), the routines described in this
+section compute a continuous interpolation function z(x,y) such that
+z(x_i,y_j) = z_{ij}.
 
 
-File: gsl-ref.info,  Node: Root Finding Iteration,  Next: Search Stopping Parameters,  Prev: Search Bounds and Guesses,  Up: One dimensional Root-Finding
+File: gsl-ref.info,  Node: 2D Interpolation Functions,  Next: 2D Interpolation Grids,  Prev: 2D Introduction to Interpolation,  Up: Interpolation
 
-33.6 Iteration
-==============
+28.10 2D Interpolation Functions
+================================
 
-The following functions drive the iteration of each algorithm.  Each
-function performs one iteration to update the state of any solver of the
-corresponding type.  The same functions work for all solvers so that
-different methods can be substituted at runtime without modifications to
-the code.
-
- -- Function: int gsl_root_fsolver_iterate (gsl_root_fsolver * S)
- -- Function: int gsl_root_fdfsolver_iterate (gsl_root_fdfsolver * S)
-     These functions perform a single iteration of the solver S.  If the
-     iteration encounters an unexpected problem then an error code will
-     be returned,
-
-     'GSL_EBADFUNC'
-          the iteration encountered a singular point where the function
-          or its derivative evaluated to 'Inf' or 'NaN'.
-
-     'GSL_EZERODIV'
-          the derivative of the function vanished at the iteration
-          point, preventing the algorithm from continuing without a
-          division by zero.
-
-   The solver maintains a current best estimate of the root at all
-times.  The bracketing solvers also keep track of the current best
-interval bounding the root.  This information can be accessed with the
-following auxiliary functions,
+The interpolation function for a given dataset is stored in a
+'gsl_interp2d' object.  These are created by the following functions.
 
- -- Function: double gsl_root_fsolver_root (const gsl_root_fsolver * S)
- -- Function: double gsl_root_fdfsolver_root (const gsl_root_fdfsolver *
-          S)
-     These functions return the current estimate of the root for the
-     solver S.
+ -- Function: gsl_interp2d * gsl_interp2d_alloc (const gsl_interp2d_type
+          * T, const size_t XSIZE, const size_t YSIZE)
+     This function returns a pointer to a newly allocated interpolation
+     object of type T for XSIZE grid points in the x direction and YSIZE
+     grid points in the y direction.
 
- -- Function: double gsl_root_fsolver_x_lower (const gsl_root_fsolver *
-          S)
- -- Function: double gsl_root_fsolver_x_upper (const gsl_root_fsolver *
-          S)
-     These functions return the current bracketing interval for the
-     solver S.
+ -- Function: int gsl_interp2d_init (gsl_interp2d * INTERP, const double
+          XA[], const double YA[], const double ZA[], const size_t
+          XSIZE, const size_t YSIZE)
+     This function initializes the interpolation object INTERP for the
+     data (XA,YA,ZA) where XA and YA are arrays of the x and y grid
+     points of size XSIZE and YSIZE respectively, and ZA is an array of
+     function values of size XSIZE*YSIZE.  The interpolation object
+     ('gsl_interp2d') does not save the data arrays XA, YA, and ZA and
+     only stores the static state computed from the data.  The XA and YA
+     data arrays are always assumed to be strictly ordered, with
+     increasing x,y values; the behavior for other arrangements is not
+     defined.
+
+ -- Function: void gsl_interp2d_free (gsl_interp2d * INTERP)
+     This function frees the interpolation object INTERP.
 
 
-File: gsl-ref.info,  Node: Search Stopping Parameters,  Next: Root Bracketing Algorithms,  Prev: Root Finding Iteration,  Up: One dimensional Root-Finding
+File: gsl-ref.info,  Node: 2D Interpolation Grids,  Next: 2D Interpolation Types,  Prev: 2D Interpolation Functions,  Up: Interpolation
 
-33.7 Search Stopping Parameters
-===============================
+28.11 2D Interpolation Grids
+============================
 
-A root finding procedure should stop when one of the following
-conditions is true:
+The 2D interpolation routines access the function values z_{ij} with the
+following ordering:
 
-   * A root has been found to within the user-specified precision.
+     z_ij = za[j*xsize + i]
 
-   * A user-specified maximum number of iterations has been reached.
+   with i = 0,...,xsize-1 and j = 0,...,ysize-1.  However, for ease of
+use, the following functions are provided to add and retrieve elements
+from the function grid without requiring knowledge of the internal
+ordering.
 
-   * An error has occurred.
+ -- Function: int gsl_interp2d_set (const gsl_interp2d * INTERP, double
+          ZA[], const size_t I, const size_t J, const double Z)
+     This function sets the value z_{ij} for grid point (I,J) of the
+     array ZA to Z.
 
-The handling of these conditions is under user control.  The functions
-below allow the user to test the precision of the current result in
-several standard ways.
+ -- Function: double gsl_interp2d_get (const gsl_interp2d * INTERP,
+          const double ZA[], const size_t I, const size_t J)
+     This function returns the value z_{ij} for grid point (I,J) stored
+     in the array ZA.
 
- -- Function: int gsl_root_test_interval (double X_LOWER, double
-          X_UPPER, double EPSABS, double EPSREL)
-     This function tests for the convergence of the interval [X_LOWER,
-     X_UPPER] with absolute error EPSABS and relative error EPSREL.  The
-     test returns 'GSL_SUCCESS' if the following condition is achieved,
+ -- Function: size_t gsl_interp2d_idx (const gsl_interp2d * INTERP,
+          const size_t I, const size_t J)
+     This function returns the index corresponding to the grid point
+     (I,J).  The index is given by j*xsize + i.
+
+
+File: gsl-ref.info,  Node: 2D Interpolation Types,  Next: 2D Evaluation of Interpolating Functions,  Prev: 2D Interpolation Grids,  Up: Interpolation
 
-          |a - b| < epsabs + epsrel min(|a|,|b|)
+28.12 2D Interpolation Types
+============================
 
-     when the interval x = [a,b] does not include the origin.  If the
-     interval includes the origin then \min(|a|,|b|) is replaced by zero
-     (which is the minimum value of |x| over the interval).  This
-     ensures that the relative error is accurately estimated for roots
-     close to the origin.
+The interpolation library provides the following 2D interpolation types:
 
-     This condition on the interval also implies that any estimate of
-     the root r in the interval satisfies the same condition with
-     respect to the true root r^*,
+ -- Interpolation Type: gsl_interp2d_bilinear
+     Bilinear interpolation.  This interpolation method does not require
+     any additional memory.
 
-          |r - r^*| < epsabs + epsrel r^*
+ -- Interpolation Type: gsl_interp2d_bicubic
+     Bicubic interpolation.
 
-     assuming that the true root r^* is contained within the interval.
+ -- Function: const char * gsl_interp2d_name (const gsl_interp2d *
+          INTERP)
+     This function returns the name of the interpolation type used by
+     INTERP.  For example,
 
- -- Function: int gsl_root_test_delta (double X1, double X0, double
-          EPSABS, double EPSREL)
+          printf ("interp uses '%s' interpolation.\n",
+                  gsl_interp2d_name (interp));
 
-     This function tests for the convergence of the sequence ..., X0, X1
-     with absolute error EPSABS and relative error EPSREL.  The test
-     returns 'GSL_SUCCESS' if the following condition is achieved,
+     would print something like,
 
-          |x_1 - x_0| < epsabs + epsrel |x_1|
+          interp uses 'bilinear' interpolation.
 
-     and returns 'GSL_CONTINUE' otherwise.
+ -- Function: unsigned int gsl_interp2d_min_size (const gsl_interp2d *
+          INTERP)
+ -- Function: unsigned int gsl_interp2d_type_min_size (const
+          gsl_interp2d_type * T)
+     These functions return the minimum number of points required by the
+     interpolation object INTERP or interpolation type T.  For example,
+     bicubic interpolation requires a minimum of 4 points.
 
- -- Function: int gsl_root_test_residual (double F, double EPSABS)
-     This function tests the residual value F against the absolute error
-     bound EPSABS.  The test returns 'GSL_SUCCESS' if the following
-     condition is achieved,
+
+File: gsl-ref.info,  Node: 2D Evaluation of Interpolating Functions,  Next: 2D Higher-level Interface,  Prev: 2D Interpolation Types,  Up: Interpolation
 
-          |f| < epsabs
+28.13 2D Evaluation of Interpolating Functions
+==============================================
 
-     and returns 'GSL_CONTINUE' otherwise.  This criterion is suitable
-     for situations where the precise location of the root, x, is
-     unimportant provided a value can be found where the residual,
-     |f(x)|, is small enough.
+ -- Function: double gsl_interp2d_eval (const gsl_interp2d * INTERP,
+          const double XA[], const double YA[], const double ZA[], const
+          double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC)
+ -- Function: int gsl_interp2d_eval_e (const gsl_interp2d * INTERP,
+          const double XA[], const double YA[], const double ZA[], const
+          double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC, double * Z)
+     These functions return the interpolated value of Z for a given
+     point (X,Y), using the interpolation object INTERP, data arrays XA,
+     YA, and ZA and the accelerators XACC and YACC.  When X is outside
+     the range of XA or Y is outside the range of YA, the error code
+     'GSL_EDOM' is returned.
+
+ -- Function: double gsl_interp2d_eval_extrap (const gsl_interp2d *
+          INTERP, const double XA[], const double YA[], const double
+          ZA[], const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC)
+ -- Function: int gsl_interp2d_eval_extrap_e (const gsl_interp2d *
+          INTERP, const double XA[], const double YA[], const double
+          ZA[], const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC, double * Z)
+     These functions return the interpolated value of Z for a given
+     point (X,Y), using the interpolation object INTERP, data arrays XA,
+     YA, and ZA and the accelerators XACC and YACC.  The functions
+     perform no bounds checking, so when X is outside the range of XA or
+     Y is outside the range of YA, extrapolation is performed.
+
+ -- Function: double gsl_interp2d_eval_deriv_x (const gsl_interp2d *
+          INTERP, const double XA[], const double YA[], const double
+          ZA[], const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC)
+ -- Function: int gsl_interp2d_eval_deriv_x_e (const gsl_interp2d *
+          INTERP, const double XA[], const double YA[], const double
+          ZA[], const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC, double * D)
+     These functions return the interpolated value D = \partial z /
+     \partial x for a given point (X,Y), using the interpolation object
+     INTERP, data arrays XA, YA, and ZA and the accelerators XACC and
+     YACC.  When X is outside the range of XA or Y is outside the range
+     of YA, the error code 'GSL_EDOM' is returned.
+
+ -- Function: double gsl_interp2d_eval_deriv_y (const gsl_interp2d *
+          INTERP, const double XA[], const double YA[], const double
+          ZA[], const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC)
+ -- Function: int gsl_interp2d_eval_deriv_y_e (const gsl_interp2d *
+          INTERP, const double XA[], const double YA[], const double
+          ZA[], const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC, double * D)
+     These functions return the interpolated value D = \partial z /
+     \partial y for a given point (X,Y), using the interpolation object
+     INTERP, data arrays XA, YA, and ZA and the accelerators XACC and
+     YACC.  When X is outside the range of XA or Y is outside the range
+     of YA, the error code 'GSL_EDOM' is returned.
+
+ -- Function: double gsl_interp2d_eval_deriv_xx (const gsl_interp2d *
+          INTERP, const double XA[], const double YA[], const double
+          ZA[], const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC)
+ -- Function: int gsl_interp2d_eval_deriv_xx_e (const gsl_interp2d *
+          INTERP, const double XA[], const double YA[], const double
+          ZA[], const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC, double * D)
+     These functions return the interpolated value D = \partial^2 z /
+     \partial x^2 for a given point (X,Y), using the interpolation
+     object INTERP, data arrays XA, YA, and ZA and the accelerators XACC
+     and YACC.  When X is outside the range of XA or Y is outside the
+     range of YA, the error code 'GSL_EDOM' is returned.
+
+ -- Function: double gsl_interp2d_eval_deriv_yy (const gsl_interp2d *
+          INTERP, const double XA[], const double YA[], const double
+          ZA[], const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC)
+ -- Function: int gsl_interp2d_eval_deriv_yy_e (const gsl_interp2d *
+          INTERP, const double XA[], const double YA[], const double
+          ZA[], const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC, double * D)
+     These functions return the interpolated value D = \partial^2 z /
+     \partial y^2 for a given point (X,Y), using the interpolation
+     object INTERP, data arrays XA, YA, and ZA and the accelerators XACC
+     and YACC.  When X is outside the range of XA or Y is outside the
+     range of YA, the error code 'GSL_EDOM' is returned.
+
+ -- Function: double gsl_interp2d_eval_deriv_xy (const gsl_interp2d *
+          INTERP, const double XA[], const double YA[], const double
+          ZA[], const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC)
+ -- Function: int gsl_interp2d_eval_deriv_xy_e (const gsl_interp2d *
+          INTERP, const double XA[], const double YA[], const double
+          ZA[], const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC, double * D)
+     These functions return the interpolated value D = \partial^2 z /
+     \partial x \partial y for a given point (X,Y), using the
+     interpolation object INTERP, data arrays XA, YA, and ZA and the
+     accelerators XACC and YACC.  When X is outside the range of XA or Y
+     is outside the range of YA, the error code 'GSL_EDOM' is returned.
 
 
-File: gsl-ref.info,  Node: Root Bracketing Algorithms,  Next: Root Finding Algorithms using Derivatives,  Prev: Search Stopping Parameters,  Up: One dimensional Root-Finding
+File: gsl-ref.info,  Node: 2D Higher-level Interface,  Next: 2D Interpolation Example programs,  Prev: 2D Evaluation of Interpolating Functions,  Up: Interpolation
 
-33.8 Root Bracketing Algorithms
+28.14 2D Higher-level Interface
 ===============================
 
-The root bracketing algorithms described in this section require an
-initial interval which is guaranteed to contain a root--if a and b are
-the endpoints of the interval then f(a) must differ in sign from f(b).
-This ensures that the function crosses zero at least once in the
-interval.  If a valid initial interval is used then these algorithm
-cannot fail, provided the function is well-behaved.
-
-   Note that a bracketing algorithm cannot find roots of even degree,
-since these do not cross the x-axis.
-
- -- Solver: gsl_root_fsolver_bisection
-
-     The "bisection algorithm" is the simplest method of bracketing the
-     roots of a function.  It is the slowest algorithm provided by the
-     library, with linear convergence.
-
-     On each iteration, the interval is bisected and the value of the
-     function at the midpoint is calculated.  The sign of this value is
-     used to determine which half of the interval does not contain a
-     root.  That half is discarded to give a new, smaller interval
-     containing the root.  This procedure can be continued indefinitely
-     until the interval is sufficiently small.
-
-     At any time the current estimate of the root is taken as the
-     midpoint of the interval.
-
- -- Solver: gsl_root_fsolver_falsepos
-
-     The "false position algorithm" is a method of finding roots based
-     on linear interpolation.  Its convergence is linear, but it is
-     usually faster than bisection.
-
-     On each iteration a line is drawn between the endpoints (a,f(a))
-     and (b,f(b)) and the point where this line crosses the x-axis taken
-     as a "midpoint".  The value of the function at this point is
-     calculated and its sign is used to determine which side of the
-     interval does not contain a root.  That side is discarded to give a
-     new, smaller interval containing the root.  This procedure can be
-     continued indefinitely until the interval is sufficiently small.
-
-     The best estimate of the root is taken from the linear
-     interpolation of the interval on the current iteration.
-
- -- Solver: gsl_root_fsolver_brent
-
-     The "Brent-Dekker method" (referred to here as "Brent's method")
-     combines an interpolation strategy with the bisection algorithm.
-     This produces a fast algorithm which is still robust.
-
-     On each iteration Brent's method approximates the function using an
-     interpolating curve.  On the first iteration this is a linear
-     interpolation of the two endpoints.  For subsequent iterations the
-     algorithm uses an inverse quadratic fit to the last three points,
-     for higher accuracy.  The intercept of the interpolating curve with
-     the x-axis is taken as a guess for the root.  If it lies within the
-     bounds of the current interval then the interpolating point is
-     accepted, and used to generate a smaller interval.  If the
-     interpolating point is not accepted then the algorithm falls back
-     to an ordinary bisection step.
+The functions described in the previous sections required the user to
+supply pointers to the x, y, and z arrays on each call.  The following
+functions are equivalent to the corresponding 'gsl_interp2d' functions
+but maintain a copy of this data in the 'gsl_spline2d' object.  This
+removes the need to pass XA, YA, and ZA as arguments on each evaluation.
+These functions are defined in the header file 'gsl_spline2d.h'.
+
+ -- Function: gsl_spline2d * gsl_spline2d_alloc (const gsl_interp2d_type
+          * T, size_t XSIZE, size_t YSIZE)
+
+ -- Function: int gsl_spline2d_init (gsl_spline2d * SPLINE, const double
+          XA[], const double YA[], const double ZA[], size_t XSIZE,
+          size_t YSIZE)
 
-     The best estimate of the root is taken from the most recent
-     interpolation or bisection.
+ -- Function: void gsl_spline2d_free (gsl_spline2d * SPLINE)
 
-
-File: gsl-ref.info,  Node: Root Finding Algorithms using Derivatives,  Next: Root Finding Examples,  Prev: Root Bracketing Algorithms,  Up: One dimensional Root-Finding
+ -- Function: const char * gsl_spline2d_name (const gsl_spline2d *
+          SPLINE)
 
-33.9 Root Finding Algorithms using Derivatives
-==============================================
+ -- Function: unsigned int gsl_spline2d_min_size (const gsl_spline2d *
+          SPLINE)
 
-The root polishing algorithms described in this section require an
-initial guess for the location of the root.  There is no absolute
-guarantee of convergence--the function must be suitable for this
-technique and the initial guess must be sufficiently close to the root
-for it to work.  When these conditions are satisfied then convergence is
-quadratic.
+ -- Function: double gsl_spline2d_eval (const gsl_spline2d * SPLINE,
+          const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC)
+ -- Function: int gsl_spline2d_eval_e (const gsl_spline2d * SPLINE,
+          const double X, const double Y, gsl_interp_accel * XACC,
+          gsl_interp_accel * YACC, double * Z)
+
+ -- Function: double gsl_spline2d_eval_deriv_x (const gsl_spline2d *
+          SPLINE, const double X, const double Y, gsl_interp_accel *
+          XACC, gsl_interp_accel * YACC)
+ -- Function: int gsl_spline2d_eval_deriv_x_e (const gsl_spline2d *
+          SPLINE, const double X, const double Y, gsl_interp_accel *
+          XACC, gsl_interp_accel * YACC, double * D)
+
+ -- Function: double gsl_spline2d_eval_deriv_y (const gsl_spline2d *
+          SPLINE, const double X, const double Y, gsl_interp_accel *
+          XACC, gsl_interp_accel * YACC)
+ -- Function: int gsl_spline2d_eval_deriv_y_e (const gsl_spline2d *
+          SPLINE, const double X, const double Y, gsl_interp_accel *
+          XACC, gsl_interp_accel * YACC, double * D)
+
+ -- Function: double gsl_spline2d_eval_deriv_xx (const gsl_spline2d *
+          SPLINE, const double X, const double Y, gsl_interp_accel *
+          XACC, gsl_interp_accel * YACC)
+ -- Function: int gsl_spline2d_eval_deriv_xx_e (const gsl_spline2d *
+          SPLINE, const double X, const double Y, gsl_interp_accel *
+          XACC, gsl_interp_accel * YACC, double * D)
+
+ -- Function: double gsl_spline2d_eval_deriv_yy (const gsl_spline2d *
+          SPLINE, const double X, const double Y, gsl_interp_accel *
+          XACC, gsl_interp_accel * YACC)
+ -- Function: int gsl_spline2d_eval_deriv_yy_e (const gsl_spline2d *
+          SPLINE, const double X, const double Y, gsl_interp_accel *
+          XACC, gsl_interp_accel * YACC, double * D)
+
+ -- Function: double gsl_spline2d_eval_deriv_xy (const gsl_spline2d *
+          SPLINE, const double X, const double Y, gsl_interp_accel *
+          XACC, gsl_interp_accel * YACC)
+ -- Function: int gsl_spline2d_eval_deriv_xy_e (const gsl_spline2d *
+          SPLINE, const double X, const double Y, gsl_interp_accel *
+          XACC, gsl_interp_accel * YACC, double * D)
+
+ -- Function: int gsl_spline2d_set (const gsl_spline2d * SPLINE, double
+          ZA[], const size_t I, const size_t J, const double Z)
+
+ -- Function: double gsl_spline2d_get (const gsl_spline2d * SPLINE,
+          const double ZA[], const size_t I, const size_t J)
+     This function returns the value z_{ij} for grid point (I,J) stored
+     in the array ZA.
 
-   These algorithms make use of both the function and its derivative.
+
+File: gsl-ref.info,  Node: 2D Interpolation Example programs,  Prev: 2D Higher-level Interface,  Up: Interpolation
 
- -- Derivative Solver: gsl_root_fdfsolver_newton
+28.15 2D Interpolation Example programs
+=======================================
 
-     Newton's Method is the standard root-polishing algorithm.  The
-     algorithm begins with an initial guess for the location of the
-     root.  On each iteration, a line tangent to the function f is drawn
-     at that position.  The point where this line crosses the x-axis
-     becomes the new guess.  The iteration is defined by the following
-     sequence,
+The following example performs bilinear interpolation on the unit
+square, using z values of (0,1,0.5,1) going clockwise around the square.
 
-          x_{i+1} = x_i - f(x_i)/f'(x_i)
+     #include <stdio.h>
+     #include <stdlib.h>
 
-     Newton's method converges quadratically for single roots, and
-     linearly for multiple roots.
+     #include <gsl/gsl_math.h>
+     #include <gsl/gsl_interp2d.h>
+     #include <gsl/gsl_spline2d.h>
 
- -- Derivative Solver: gsl_root_fdfsolver_secant
+     int
+     main()
+     {
+       const gsl_interp2d_type *T = gsl_interp2d_bilinear;
+       const size_t N = 100;             /* number of points to interpolate */
+       const double xa[] = { 0.0, 1.0 }; /* define unit square */
+       const double ya[] = { 0.0, 1.0 };
+       const size_t nx = sizeof(xa) / sizeof(double); /* x grid points */
+       const size_t ny = sizeof(ya) / sizeof(double); /* y grid points */
+       double *za = malloc(nx * ny * sizeof(double));
+       gsl_spline2d *spline = gsl_spline2d_alloc(T, nx, ny);
+       gsl_interp_accel *xacc = gsl_interp_accel_alloc();
+       gsl_interp_accel *yacc = gsl_interp_accel_alloc();
+       size_t i, j;
+
+       /* set z grid values */
+       gsl_spline2d_set(spline, za, 0, 0, 0.0);
+       gsl_spline2d_set(spline, za, 0, 1, 1.0);
+       gsl_spline2d_set(spline, za, 1, 1, 0.5);
+       gsl_spline2d_set(spline, za, 1, 0, 1.0);
 
-     The "secant method" is a simplified version of Newton's method
-     which does not require the computation of the derivative on every
-     step.
+       /* initialize interpolation */
+       gsl_spline2d_init(spline, xa, ya, za, nx, ny);
 
-     On its first iteration the algorithm begins with Newton's method,
-     using the derivative to compute a first step,
+       /* interpolate N values in x and y and print out grid for plotting */
+       for (i = 0; i < N; ++i)
+         {
+           double xi = i / (N - 1.0);
 
-          x_1 = x_0 - f(x_0)/f'(x_0)
+           for (j = 0; j < N; ++j)
+             {
+               double yj = j / (N - 1.0);
+               double zij = gsl_spline2d_eval(spline, xi, yj, xacc, yacc);
 
-     Subsequent iterations avoid the evaluation of the derivative by
-     replacing it with a numerical estimate, the slope of the line
-     through the previous two points,
-
-          x_{i+1} = x_i f(x_i) / f'_{est} where
-           f'_{est} = (f(x_i) - f(x_{i-1})/(x_i - x_{i-1})
-
-     When the derivative does not change significantly in the vicinity
-     of the root the secant method gives a useful saving.
-     Asymptotically the secant method is faster than Newton's method
-     whenever the cost of evaluating the derivative is more than 0.44
-     times the cost of evaluating the function itself.  As with all
-     methods of computing a numerical derivative the estimate can suffer
-     from cancellation errors if the separation of the points becomes
-     too small.
-
-     On single roots, the method has a convergence of order (1 + \sqrt
-     5)/2 (approximately 1.62).  It converges linearly for multiple
-     roots.
-
- -- Derivative Solver: gsl_root_fdfsolver_steffenson
-
-     The "Steffenson Method"(1) provides the fastest convergence of all
-     the routines.  It combines the basic Newton algorithm with an
-     Aitken "delta-squared" acceleration.  If the Newton iterates are
-     x_i then the acceleration procedure generates a new sequence R_i,
-
-          R_i = x_i - (x_{i+1} - x_i)^2 / (x_{i+2} - 2 x_{i+1} + x_{i})
-
-     which converges faster than the original sequence under reasonable
-     conditions.  The new sequence requires three terms before it can
-     produce its first value so the method returns accelerated values on
-     the second and subsequent iterations.  On the first iteration it
-     returns the ordinary Newton estimate.  The Newton iterate is also
-     returned if the denominator of the acceleration term ever becomes
-     zero.
+               printf("%f %f %f\n", xi, yj, zij);
+             }
+           printf("\n");
+         }
 
-     As with all acceleration procedures this method can become unstable
-     if the function is not well-behaved.
+       gsl_spline2d_free(spline);
+       gsl_interp_accel_free(xacc);
+       gsl_interp_accel_free(yacc);
+       free(za);
 
-   ---------- Footnotes ----------
+       return 0;
+     }
 
-   (1) J.F. Steffensen (1873-1961).  The spelling used in the name of
-the function is slightly incorrect, but has been preserved to avoid
-incompatibility.
+The results of the interpolation are shown in the following plot, where
+the corners are labeled with their fixed z values.
 
 
-File: gsl-ref.info,  Node: Root Finding Examples,  Next: Root Finding References and Further Reading,  Prev: Root Finding Algorithms using Derivatives,  Up: One dimensional Root-Finding
-
-33.10 Examples
-==============
-
-For any root finding algorithm we need to prepare the function to be
-solved.  For this example we will use the general quadratic equation
-described earlier.  We first need a header file ('demo_fn.h') to define
-the function parameters,
+File: gsl-ref.info,  Node: Numerical Differentiation,  Next: Chebyshev Approximations,  Prev: Interpolation,  Up: Top
 
-     struct quadratic_params
-       {
-         double a, b, c;
-       };
+29 Numerical Differentiation
+****************************
 
-     double quadratic (double x, void *params);
-     double quadratic_deriv (double x, void *params);
-     void quadratic_fdf (double x, void *params,
-                         double *y, double *dy);
+The functions described in this chapter compute numerical derivatives by
+finite differencing.  An adaptive algorithm is used to find the best
+choice of finite difference and to estimate the error in the derivative.
+These functions are declared in the header file 'gsl_deriv.h'.
 
-We place the function definitions in a separate file ('demo_fn.c'),
+* Menu:
 
-     double
-     quadratic (double x, void *params)
-     {
-       struct quadratic_params *p
-         = (struct quadratic_params *) params;
+* Numerical Differentiation functions::  
+* Numerical Differentiation Examples::  
+* Numerical Differentiation References::  
 
-       double a = p->a;
-       double b = p->b;
-       double c = p->c;
+
+File: gsl-ref.info,  Node: Numerical Differentiation functions,  Next: Numerical Differentiation Examples,  Up: Numerical Differentiation
 
-       return (a * x + b) * x + c;
-     }
+29.1 Functions
+==============
 
-     double
-     quadratic_deriv (double x, void *params)
-     {
-       struct quadratic_params *p
-         = (struct quadratic_params *) params;
+ -- Function: int gsl_deriv_central (const gsl_function * F, double X,
+          double H, double * RESULT, double * ABSERR)
+     This function computes the numerical derivative of the function F
+     at the point X using an adaptive central difference algorithm with
+     a step-size of H.  The derivative is returned in RESULT and an
+     estimate of its absolute error is returned in ABSERR.
 
-       double a = p->a;
-       double b = p->b;
-       double c = p->c;
+     The initial value of H is used to estimate an optimal step-size,
+     based on the scaling of the truncation error and round-off error in
+     the derivative calculation.  The derivative is computed using a
+     5-point rule for equally spaced abscissae at x-h, x-h/2, x, x+h/2,
+     x+h, with an error estimate taken from the difference between the
+     5-point rule and the corresponding 3-point rule x-h, x, x+h.  Note
+     that the value of the function at x does not contribute to the
+     derivative calculation, so only 4-points are actually used.
 
-       return 2.0 * a * x + b;
-     }
+ -- Function: int gsl_deriv_forward (const gsl_function * F, double X,
+          double H, double * RESULT, double * ABSERR)
+     This function computes the numerical derivative of the function F
+     at the point X using an adaptive forward difference algorithm with
+     a step-size of H.  The function is evaluated only at points greater
+     than X, and never at X itself.  The derivative is returned in
+     RESULT and an estimate of its absolute error is returned in ABSERR.
+     This function should be used if f(x) has a discontinuity at X, or
+     is undefined for values less than X.
 
-     void
-     quadratic_fdf (double x, void *params,
-                    double *y, double *dy)
-     {
-       struct quadratic_params *p
-         = (struct quadratic_params *) params;
+     The initial value of H is used to estimate an optimal step-size,
+     based on the scaling of the truncation error and round-off error in
+     the derivative calculation.  The derivative at x is computed using
+     an "open" 4-point rule for equally spaced abscissae at x+h/4,
+     x+h/2, x+3h/4, x+h, with an error estimate taken from the
+     difference between the 4-point rule and the corresponding 2-point
+     rule x+h/2, x+h.
 
-       double a = p->a;
-       double b = p->b;
-       double c = p->c;
+ -- Function: int gsl_deriv_backward (const gsl_function * F, double X,
+          double H, double * RESULT, double * ABSERR)
+     This function computes the numerical derivative of the function F
+     at the point X using an adaptive backward difference algorithm with
+     a step-size of H.  The function is evaluated only at points less
+     than X, and never at X itself.  The derivative is returned in
+     RESULT and an estimate of its absolute error is returned in ABSERR.
+     This function should be used if f(x) has a discontinuity at X, or
+     is undefined for values greater than X.
 
-       *y = (a * x + b) * x + c;
-       *dy = 2.0 * a * x + b;
-     }
+     This function is equivalent to calling 'gsl_deriv_forward' with a
+     negative step-size.
 
-The first program uses the function solver 'gsl_root_fsolver_brent' for
-Brent's method and the general quadratic defined above to solve the
-following equation,
+
+File: gsl-ref.info,  Node: Numerical Differentiation Examples,  Next: Numerical Differentiation References,  Prev: Numerical Differentiation functions,  Up: Numerical Differentiation
 
-     x^2 - 5 = 0
+29.2 Examples
+=============
 
-with solution x = \sqrt 5 = 2.236068...
+The following code estimates the derivative of the function f(x) =
+x^{3/2} at x=2 and at x=0.  The function f(x) is undefined for x<0 so
+the derivative at x=0 is computed using 'gsl_deriv_forward'.
 
      #include <stdio.h>
-     #include <gsl/gsl_errno.h>
      #include <gsl/gsl_math.h>
-     #include <gsl/gsl_roots.h>
+     #include <gsl/gsl_deriv.h>
 
-     #include "demo_fn.h"
-     #include "demo_fn.c"
+     double f (double x, void * params)
+     {
+       (void)(params); /* avoid unused parameter warning */
+       return pow (x, 1.5);
+     }
 
      int
      main (void)
      {
-       int status;
-       int iter = 0, max_iter = 100;
-       const gsl_root_fsolver_type *T;
-       gsl_root_fsolver *s;
-       double r = 0, r_expected = sqrt (5.0);
-       double x_lo = 0.0, x_hi = 5.0;
        gsl_function F;
-       struct quadratic_params params = {1.0, 0.0, -5.0};
-
-       F.function = &quadratic;
-       F.params = &params;
-
-       T = gsl_root_fsolver_brent;
-       s = gsl_root_fsolver_alloc (T);
-       gsl_root_fsolver_set (s, &F, x_lo, x_hi);
+       double result, abserr;
 
-       printf ("using %s method\n",
-               gsl_root_fsolver_name (s));
+       F.function = &f;
+       F.params = 0;
 
-       printf ("%5s [%9s, %9s] %9s %10s %9s\n",
-               "iter", "lower", "upper", "root",
-               "err", "err(est)");
+       printf ("f(x) = x^(3/2)\n");
 
-       do
-         {
-           iter++;
-           status = gsl_root_fsolver_iterate (s);
-           r = gsl_root_fsolver_root (s);
-           x_lo = gsl_root_fsolver_x_lower (s);
-           x_hi = gsl_root_fsolver_x_upper (s);
-           status = gsl_root_test_interval (x_lo, x_hi,
-                                            0, 0.001);
-
-           if (status == GSL_SUCCESS)
-             printf ("Converged:\n");
-
-           printf ("%5d [%.7f, %.7f] %.7f %+.7f %.7f\n",
-                   iter, x_lo, x_hi,
-                   r, r - r_expected,
-                   x_hi - x_lo);
-         }
-       while (status == GSL_CONTINUE && iter < max_iter);
+       gsl_deriv_central (&F, 2.0, 1e-8, &result, &abserr);
+       printf ("x = 2.0\n");
+       printf ("f'(x) = %.10f +/- %.10f\n", result, abserr);
+       printf ("exact = %.10f\n\n", 1.5 * sqrt(2.0));
 
-       gsl_root_fsolver_free (s);
+       gsl_deriv_forward (&F, 0.0, 1e-8, &result, &abserr);
+       printf ("x = 0.0\n");
+       printf ("f'(x) = %.10f +/- %.10f\n", result, abserr);
+       printf ("exact = %.10f\n", 0.0);
 
-       return status;
+       return 0;
      }
 
-Here are the results of the iterations,
+Here is the output of the program,
 
      $ ./a.out
-     using brent method
-      iter [    lower,     upper]      root        err  err(est)
-         1 [1.0000000, 5.0000000] 1.0000000 -1.2360680 4.0000000
-         2 [1.0000000, 3.0000000] 3.0000000 +0.7639320 2.0000000
-         3 [2.0000000, 3.0000000] 2.0000000 -0.2360680 1.0000000
-         4 [2.2000000, 3.0000000] 2.2000000 -0.0360680 0.8000000
-         5 [2.2000000, 2.2366300] 2.2366300 +0.0005621 0.0366300
-     Converged:
-         6 [2.2360634, 2.2366300] 2.2360634 -0.0000046 0.0005666
-
-If the program is modified to use the bisection solver instead of
-Brent's method, by changing 'gsl_root_fsolver_brent' to
-'gsl_root_fsolver_bisection' the slower convergence of the Bisection
-method can be observed,
+     f(x) = x^(3/2)
+     x = 2.0
+     f'(x) = 2.1213203120 +/- 0.0000005006
+     exact = 2.1213203436
 
-     $ ./a.out
-     using bisection method
-      iter [    lower,     upper]      root        err  err(est)
-         1 [0.0000000, 2.5000000] 1.2500000 -0.9860680 2.5000000
-         2 [1.2500000, 2.5000000] 1.8750000 -0.3610680 1.2500000
-         3 [1.8750000, 2.5000000] 2.1875000 -0.0485680 0.6250000
-         4 [2.1875000, 2.5000000] 2.3437500 +0.1076820 0.3125000
-         5 [2.1875000, 2.3437500] 2.2656250 +0.0295570 0.1562500
-         6 [2.1875000, 2.2656250] 2.2265625 -0.0095055 0.0781250
-         7 [2.2265625, 2.2656250] 2.2460938 +0.0100258 0.0390625
-         8 [2.2265625, 2.2460938] 2.2363281 +0.0002601 0.0195312
-         9 [2.2265625, 2.2363281] 2.2314453 -0.0046227 0.0097656
-        10 [2.2314453, 2.2363281] 2.2338867 -0.0021813 0.0048828
-        11 [2.2338867, 2.2363281] 2.2351074 -0.0009606 0.0024414
-     Converged:
-        12 [2.2351074, 2.2363281] 2.2357178 -0.0003502 0.0012207
+     x = 0.0
+     f'(x) = 0.0000000160 +/- 0.0000000339
+     exact = 0.0000000000
 
-   The next program solves the same function using a derivative solver
-instead.
+
+File: gsl-ref.info,  Node: Numerical Differentiation References,  Prev: Numerical Differentiation Examples,  Up: Numerical Differentiation
 
-     #include <stdio.h>
-     #include <gsl/gsl_errno.h>
-     #include <gsl/gsl_math.h>
-     #include <gsl/gsl_roots.h>
+29.3 References and Further Reading
+===================================
+
+The algorithms used by these functions are described in the following
+sources:
 
-     #include "demo_fn.h"
-     #include "demo_fn.c"
+     Abramowitz and Stegun, 'Handbook of Mathematical Functions',
+     Section 25.3.4, and Table 25.5 (Coefficients for Differentiation).
 
-     int
-     main (void)
-     {
-       int status;
-       int iter = 0, max_iter = 100;
-       const gsl_root_fdfsolver_type *T;
-       gsl_root_fdfsolver *s;
-       double x0, x = 5.0, r_expected = sqrt (5.0);
-       gsl_function_fdf FDF;
-       struct quadratic_params params = {1.0, 0.0, -5.0};
-
-       FDF.f = &quadratic;
-       FDF.df = &quadratic_deriv;
-       FDF.fdf = &quadratic_fdf;
-       FDF.params = &params;
-
-       T = gsl_root_fdfsolver_newton;
-       s = gsl_root_fdfsolver_alloc (T);
-       gsl_root_fdfsolver_set (s, &FDF, x);
-
-       printf ("using %s method\n",
-               gsl_root_fdfsolver_name (s));
-
-       printf ("%-5s %10s %10s %10s\n",
-               "iter", "root", "err", "err(est)");
-       do
-         {
-           iter++;
-           status = gsl_root_fdfsolver_iterate (s);
-           x0 = x;
-           x = gsl_root_fdfsolver_root (s);
-           status = gsl_root_test_delta (x, x0, 0, 1e-3);
+     S.D. Conte and Carl de Boor, 'Elementary Numerical Analysis: An
+     Algorithmic Approach', McGraw-Hill, 1972.
 
-           if (status == GSL_SUCCESS)
-             printf ("Converged:\n");
+
+File: gsl-ref.info,  Node: Chebyshev Approximations,  Next: Series Acceleration,  Prev: Numerical Differentiation,  Up: Top
 
-           printf ("%5d %10.7f %+10.7f %10.7f\n",
-                   iter, x, x - r_expected, x - x0);
-         }
-       while (status == GSL_CONTINUE && iter < max_iter);
+30 Chebyshev Approximations
+***************************
 
-       gsl_root_fdfsolver_free (s);
-       return status;
-     }
+This chapter describes routines for computing Chebyshev approximations
+to univariate functions.  A Chebyshev approximation is a truncation of
+the series f(x) = \sum c_n T_n(x), where the Chebyshev polynomials
+T_n(x) = \cos(n \arccos x) provide an orthogonal basis of polynomials on
+the interval [-1,1] with the weight function 1 / \sqrt{1-x^2}.  The
+first few Chebyshev polynomials are, T_0(x) = 1, T_1(x) = x, T_2(x) = 2
+x^2 - 1.  For further information see Abramowitz & Stegun, Chapter 22.
 
-Here are the results for Newton's method,
+   The functions described in this chapter are declared in the header
+file 'gsl_chebyshev.h'.
 
-     $ ./a.out
-     using newton method
-     iter        root        err   err(est)
-         1  3.0000000 +0.7639320 -2.0000000
-         2  2.3333333 +0.0972654 -0.6666667
-         3  2.2380952 +0.0020273 -0.0952381
-     Converged:
-         4  2.2360689 +0.0000009 -0.0020263
-
-Note that the error can be estimated more accurately by taking the
-difference between the current iterate and next iterate rather than the
-previous iterate.  The other derivative solvers can be investigated by
-changing 'gsl_root_fdfsolver_newton' to 'gsl_root_fdfsolver_secant' or
-'gsl_root_fdfsolver_steffenson'.
+* Menu:
+
+* Chebyshev Definitions::       
+* Creation and Calculation of Chebyshev Series::  
+* Auxiliary Functions for Chebyshev Series::  
+* Chebyshev Series Evaluation::  
+* Derivatives and Integrals::   
+* Chebyshev Approximation Examples::  
+* Chebyshev Approximation References and Further Reading::  
 
 
-File: gsl-ref.info,  Node: Root Finding References and Further Reading,  Prev: Root Finding Examples,  Up: One dimensional Root-Finding
+File: gsl-ref.info,  Node: Chebyshev Definitions,  Next: Creation and Calculation of Chebyshev Series,  Up: Chebyshev Approximations
 
-33.11 References and Further Reading
-====================================
+30.1 Definitions
+================
+
+A Chebyshev series is stored using the following structure,
+
+     typedef struct
+     {
+       double * c;   /* coefficients  c[0] .. c[order] */
+       int order;    /* order of expansion             */
+       double a;     /* lower interval point           */
+       double b;     /* upper interval point           */
+       ...
+     } gsl_cheb_series
+
+The approximation is made over the range [a,b] using ORDER+1 terms,
+including the coefficient c[0].  The series is computed using the
+following convention,
 
-For information on the Brent-Dekker algorithm see the following two
-papers,
+     f(x) = (c_0 / 2) + \sum_{n=1} c_n T_n(x)
 
-     R. P. Brent, "An algorithm with guaranteed convergence for finding
-     a zero of a function", 'Computer Journal', 14 (1971) 422-425
+which is needed when accessing the coefficients directly.
 
-     J. C. P. Bus and T. J. Dekker, "Two Efficient Algorithms with
-     Guaranteed Convergence for Finding a Zero of a Function", 'ACM
-     Transactions of Mathematical Software', Vol. 1 No. 4 (1975) 330-345
-
-
-File: gsl-ref.info,  Node: One dimensional Minimization,  Next: Multidimensional Root-Finding,  Prev: One dimensional Root-Finding,  Up: Top
-
-34 One dimensional Minimization
-*******************************
-
-This chapter describes routines for finding minima of arbitrary
-one-dimensional functions.  The library provides low level components
-for a variety of iterative minimizers and convergence tests.  These can
-be combined by the user to achieve the desired solution, with full
-access to the intermediate steps of the algorithms.  Each class of
-methods uses the same framework, so that you can switch between
-minimizers at runtime without needing to recompile your program.  Each
-instance of a minimizer keeps track of its own state, allowing the
-minimizers to be used in multi-threaded programs.
-
-   The header file 'gsl_min.h' contains prototypes for the minimization
-functions and related declarations.  To use the minimization algorithms
-to find the maximum of a function simply invert its sign.
+
+File: gsl-ref.info,  Node: Creation and Calculation of Chebyshev Series,  Next: Auxiliary Functions for Chebyshev Series,  Prev: Chebyshev Definitions,  Up: Chebyshev Approximations
 
-* Menu:
+30.2 Creation and Calculation of Chebyshev Series
+=================================================
+
+ -- Function: gsl_cheb_series * gsl_cheb_alloc (const size_t N)
+     This function allocates space for a Chebyshev series of order N and
+     returns a pointer to a new 'gsl_cheb_series' struct.
+
+ -- Function: void gsl_cheb_free (gsl_cheb_series * CS)
+     This function frees a previously allocated Chebyshev series CS.
+
+ -- Function: int gsl_cheb_init (gsl_cheb_series * CS, const
+          gsl_function * F, const double A, const double B)
+     This function computes the Chebyshev approximation CS for the
+     function F over the range (a,b) to the previously specified order.
+     The computation of the Chebyshev approximation is an O(n^2)
+     process, and requires n function evaluations.
+
+
+File: gsl-ref.info,  Node: Auxiliary Functions for Chebyshev Series,  Next: Chebyshev Series Evaluation,  Prev: Creation and Calculation of Chebyshev Series,  Up: Chebyshev Approximations
+
+30.3 Auxiliary Functions
+========================
+
+The following functions provide information about an existing Chebyshev
+series.
+
+ -- Function: size_t gsl_cheb_order (const gsl_cheb_series * CS)
+     This function returns the order of Chebyshev series CS.
 
-* Minimization Overview::       
-* Minimization Caveats::        
-* Initializing the Minimizer::  
-* Providing the function to minimize::  
-* Minimization Iteration::      
-* Minimization Stopping Parameters::  
-* Minimization Algorithms::     
-* Minimization Examples::       
-* Minimization References and Further Reading::  
+ -- Function: size_t gsl_cheb_size (const gsl_cheb_series * CS)
+ -- Function: double * gsl_cheb_coeffs (const gsl_cheb_series * CS)
+     These functions return the size of the Chebyshev coefficient array
+     'c[]' and a pointer to its location in memory for the Chebyshev
+     series CS.
 
 
-File: gsl-ref.info,  Node: Minimization Overview,  Next: Minimization Caveats,  Up: One dimensional Minimization
+File: gsl-ref.info,  Node: Chebyshev Series Evaluation,  Next: Derivatives and Integrals,  Prev: Auxiliary Functions for Chebyshev Series,  Up: Chebyshev Approximations
 
-34.1 Overview
-=============
+30.4 Chebyshev Series Evaluation
+================================
 
-The minimization algorithms begin with a bounded region known to contain
-a minimum.  The region is described by a lower bound a and an upper
-bound b, with an estimate of the location of the minimum x.
+ -- Function: double gsl_cheb_eval (const gsl_cheb_series * CS, double
+          X)
+     This function evaluates the Chebyshev series CS at a given point X.
 
-The value of the function at x must be less than the value of the
-function at the ends of the interval,
+ -- Function: int gsl_cheb_eval_err (const gsl_cheb_series * CS, const
+          double X, double * RESULT, double * ABSERR)
+     This function computes the Chebyshev series CS at a given point X,
+     estimating both the series RESULT and its absolute error ABSERR.
+     The error estimate is made from the first neglected term in the
+     series.
 
-     f(a) > f(x) < f(b)
+ -- Function: double gsl_cheb_eval_n (const gsl_cheb_series * CS, size_t
+          ORDER, double X)
+     This function evaluates the Chebyshev series CS at a given point X,
+     to (at most) the given order ORDER.
 
-This condition guarantees that a minimum is contained somewhere within
-the interval.  On each iteration a new point x' is selected using one of
-the available algorithms.  If the new point is a better estimate of the
-minimum, i.e. where f(x') < f(x), then the current estimate of the
-minimum x is updated.  The new point also allows the size of the bounded
-interval to be reduced, by choosing the most compact set of points which
-satisfies the constraint f(a) > f(x) < f(b).  The interval is reduced
-until it encloses the true minimum to a desired tolerance.  This
-provides a best estimate of the location of the minimum and a rigorous
-error estimate.
+ -- Function: int gsl_cheb_eval_n_err (const gsl_cheb_series * CS, const
+          size_t ORDER, const double X, double * RESULT, double *
+          ABSERR)
+     This function evaluates a Chebyshev series CS at a given point X,
+     estimating both the series RESULT and its absolute error ABSERR, to
+     (at most) the given order ORDER.  The error estimate is made from
+     the first neglected term in the series.
 
-   Several bracketing algorithms are available within a single
-framework.  The user provides a high-level driver for the algorithm, and
-the library provides the individual functions necessary for each of the
-steps.  There are three main phases of the iteration.  The steps are,
+
+File: gsl-ref.info,  Node: Derivatives and Integrals,  Next: Chebyshev Approximation Examples,  Prev: Chebyshev Series Evaluation,  Up: Chebyshev Approximations
 
-   * initialize minimizer state, S, for algorithm T
+30.5 Derivatives and Integrals
+==============================
 
-   * update S using the iteration T
+The following functions allow a Chebyshev series to be differentiated or
+integrated, producing a new Chebyshev series.  Note that the error
+estimate produced by evaluating the derivative series will be
+underestimated due to the contribution of higher order terms being
+neglected.
 
-   * test S for convergence, and repeat iteration if necessary
+ -- Function: int gsl_cheb_calc_deriv (gsl_cheb_series * DERIV, const
+          gsl_cheb_series * CS)
+     This function computes the derivative of the series CS, storing the
+     derivative coefficients in the previously allocated DERIV.  The two
+     series CS and DERIV must have been allocated with the same order.
 
-The state for the minimizers is held in a 'gsl_min_fminimizer' struct.
-The updating procedure uses only function evaluations (not derivatives).
+ -- Function: int gsl_cheb_calc_integ (gsl_cheb_series * INTEG, const
+          gsl_cheb_series * CS)
+     This function computes the integral of the series CS, storing the
+     integral coefficients in the previously allocated INTEG.  The two
+     series CS and INTEG must have been allocated with the same order.
+     The lower limit of the integration is taken to be the left hand end
+     of the range A.
 
 
-File: gsl-ref.info,  Node: Minimization Caveats,  Next: Initializing the Minimizer,  Prev: Minimization Overview,  Up: One dimensional Minimization
+File: gsl-ref.info,  Node: Chebyshev Approximation Examples,  Next: Chebyshev Approximation References and Further Reading,  Prev: Derivatives and Integrals,  Up: Chebyshev Approximations
+
+30.6 Examples
+=============
 
-34.2 Caveats
-============
+The following example program computes Chebyshev approximations to a
+step function.  This is an extremely difficult approximation to make,
+due to the discontinuity, and was chosen as an example where
+approximation error is visible.  For smooth functions the Chebyshev
+approximation converges extremely rapidly and errors would not be
+visible.
 
-Note that minimization functions can only search for one minimum at a
-time.  When there are several minima in the search area, the first
-minimum to be found will be returned; however it is difficult to predict
-which of the minima this will be.  _In most cases, no error will be
-reported if you try to find a minimum in an area where there is more
-than one._
+     #include <stdio.h>
+     #include <gsl/gsl_math.h>
+     #include <gsl/gsl_chebyshev.h>
 
-   With all minimization algorithms it can be difficult to determine the
-location of the minimum to full numerical precision.  The behavior of
-the function in the region of the minimum x^* can be approximated by a
-Taylor expansion,
+     double
+     f (double x, void *p)
+     {
+       (void)(p); /* avoid unused parameter warning */
 
-     y = f(x^*) + (1/2) f''(x^*) (x - x^*)^2
+       if (x < 0.5)
+         return 0.25;
+       else
+         return 0.75;
+     }
 
-and the second term of this expansion can be lost when added to the
-first term at finite precision.  This magnifies the error in locating
-x^*, making it proportional to \sqrt \epsilon (where \epsilon is the
-relative accuracy of the floating point numbers).  For functions with
-higher order minima, such as x^4, the magnification of the error is
-correspondingly worse.  The best that can be achieved is to converge to
-the limit of numerical accuracy in the function values, rather than the
-location of the minimum itself.
+     int
+     main (void)
+     {
+       int i, n = 10000;
 
-
-File: gsl-ref.info,  Node: Initializing the Minimizer,  Next: Providing the function to minimize,  Prev: Minimization Caveats,  Up: One dimensional Minimization
+       gsl_cheb_series *cs = gsl_cheb_alloc (40);
 
-34.3 Initializing the Minimizer
-===============================
+       gsl_function F;
 
- -- Function: gsl_min_fminimizer * gsl_min_fminimizer_alloc (const
-          gsl_min_fminimizer_type * T)
-     This function returns a pointer to a newly allocated instance of a
-     minimizer of type T.  For example, the following code creates an
-     instance of a golden section minimizer,
+       F.function = f;
+       F.params = 0;
 
-          const gsl_min_fminimizer_type * T
-            = gsl_min_fminimizer_goldensection;
-          gsl_min_fminimizer * s
-            = gsl_min_fminimizer_alloc (T);
+       gsl_cheb_init (cs, &F, 0.0, 1.0);
 
-     If there is insufficient memory to create the minimizer then the
-     function returns a null pointer and the error handler is invoked
-     with an error code of 'GSL_ENOMEM'.
+       for (i = 0; i < n; i++)
+         {
+           double x = i / (double)n;
+           double r10 = gsl_cheb_eval_n (cs, 10, x);
+           double r40 = gsl_cheb_eval (cs, x);
+           printf ("%g %g %g %g\n",
+                   x, GSL_FN_EVAL (&F, x), r10, r40);
+         }
 
- -- Function: int gsl_min_fminimizer_set (gsl_min_fminimizer * S,
-          gsl_function * F, double X_MINIMUM, double X_LOWER, double
-          X_UPPER)
-     This function sets, or resets, an existing minimizer S to use the
-     function F and the initial search interval [X_LOWER, X_UPPER], with
-     a guess for the location of the minimum X_MINIMUM.
+       gsl_cheb_free (cs);
 
-     If the interval given does not contain a minimum, then the function
-     returns an error code of 'GSL_EINVAL'.
+       return 0;
+     }
 
- -- Function: int gsl_min_fminimizer_set_with_values (gsl_min_fminimizer
-          * S, gsl_function * F, double X_MINIMUM, double F_MINIMUM,
-          double X_LOWER, double F_LOWER, double X_UPPER, double
-          F_UPPER)
-     This function is equivalent to 'gsl_min_fminimizer_set' but uses
-     the values F_MINIMUM, F_LOWER and F_UPPER instead of computing
-     'f(x_minimum)', 'f(x_lower)' and 'f(x_upper)'.
+The output from the program gives the original function, 10-th order
+approximation and 40-th order approximation, all sampled at intervals of
+0.001 in x.
 
- -- Function: void gsl_min_fminimizer_free (gsl_min_fminimizer * S)
-     This function frees all the memory associated with the minimizer S.
+
+File: gsl-ref.info,  Node: Chebyshev Approximation References and Further Reading,  Prev: Chebyshev Approximation Examples,  Up: Chebyshev Approximations
 
- -- Function: const char * gsl_min_fminimizer_name (const
-          gsl_min_fminimizer * S)
-     This function returns a pointer to the name of the minimizer.  For
-     example,
+30.7 References and Further Reading
+===================================
 
-          printf ("s is a '%s' minimizer\n",
-                  gsl_min_fminimizer_name (s));
+The following paper describes the use of Chebyshev series,
 
-     would print something like 's is a 'brent' minimizer'.
+     R. Broucke, "Ten Subroutines for the Manipulation of Chebyshev
+     Series [C1] (Algorithm 446)".  'Communications of the ACM' 16(4),
+     254-256 (1973)
 
 
-File: gsl-ref.info,  Node: Providing the function to minimize,  Next: Minimization Iteration,  Prev: Initializing the Minimizer,  Up: One dimensional Minimization
+File: gsl-ref.info,  Node: Series Acceleration,  Next: Wavelet Transforms,  Prev: Chebyshev Approximations,  Up: Top
 
-34.4 Providing the function to minimize
-=======================================
+31 Series Acceleration
+**********************
 
-You must provide a continuous function of one variable for the
-minimizers to operate on.  In order to allow for general parameters the
-functions are defined by a 'gsl_function' data type (*note Providing the
-function to solve::).
+The functions described in this chapter accelerate the convergence of a
+series using the Levin u-transform.  This method takes a small number of
+terms from the start of a series and uses a systematic approximation to
+compute an extrapolated value and an estimate of its error.  The
+u-transform works for both convergent and divergent series, including
+asymptotic series.
 
-
-File: gsl-ref.info,  Node: Minimization Iteration,  Next: Minimization Stopping Parameters,  Prev: Providing the function to minimize,  Up: One dimensional Minimization
+   These functions are declared in the header file 'gsl_sum.h'.
 
-34.5 Iteration
-==============
+* Menu:
 
-The following functions drive the iteration of each algorithm.  Each
-function performs one iteration to update the state of any minimizer of
-the corresponding type.  The same functions work for all minimizers so
-that different methods can be substituted at runtime without
-modifications to the code.
-
- -- Function: int gsl_min_fminimizer_iterate (gsl_min_fminimizer * S)
-     This function performs a single iteration of the minimizer S.  If
-     the iteration encounters an unexpected problem then an error code
-     will be returned,
-
-     'GSL_EBADFUNC'
-          the iteration encountered a singular point where the function
-          evaluated to 'Inf' or 'NaN'.
-
-     'GSL_FAILURE'
-          the algorithm could not improve the current best approximation
-          or bounding interval.
-
-   The minimizer maintains a current best estimate of the position of
-the minimum at all times, and the current interval bounding the minimum.
-This information can be accessed with the following auxiliary functions,
-
- -- Function: double gsl_min_fminimizer_x_minimum (const
-          gsl_min_fminimizer * S)
-     This function returns the current estimate of the position of the
-     minimum for the minimizer S.
-
- -- Function: double gsl_min_fminimizer_x_upper (const
-          gsl_min_fminimizer * S)
- -- Function: double gsl_min_fminimizer_x_lower (const
-          gsl_min_fminimizer * S)
-     These functions return the current upper and lower bound of the
-     interval for the minimizer S.
-
- -- Function: double gsl_min_fminimizer_f_minimum (const
-          gsl_min_fminimizer * S)
- -- Function: double gsl_min_fminimizer_f_upper (const
-          gsl_min_fminimizer * S)
- -- Function: double gsl_min_fminimizer_f_lower (const
-          gsl_min_fminimizer * S)
-     These functions return the value of the function at the current
-     estimate of the minimum and at the upper and lower bounds of the
-     interval for the minimizer S.
+* Acceleration functions::      
+* Acceleration functions without error estimation::  
+* Example of accelerating a series::  
+* Series Acceleration References::  
 
 
-File: gsl-ref.info,  Node: Minimization Stopping Parameters,  Next: Minimization Algorithms,  Prev: Minimization Iteration,  Up: One dimensional Minimization
-
-34.6 Stopping Parameters
-========================
-
-A minimization procedure should stop when one of the following
-conditions is true:
+File: gsl-ref.info,  Node: Acceleration functions,  Next: Acceleration functions without error estimation,  Up: Series Acceleration
 
-   * A minimum has been found to within the user-specified precision.
+31.1 Acceleration functions
+===========================
 
-   * A user-specified maximum number of iterations has been reached.
+The following functions compute the full Levin u-transform of a series
+with its error estimate.  The error estimate is computed by propagating
+rounding errors from each term through to the final extrapolation.
 
-   * An error has occurred.
+   These functions are intended for summing analytic series where each
+term is known to high accuracy, and the rounding errors are assumed to
+originate from finite precision.  They are taken to be relative errors
+of order 'GSL_DBL_EPSILON' for each term.
 
-The handling of these conditions is under user control.  The function
-below allows the user to test the precision of the current result.
+   The calculation of the error in the extrapolated value is an O(N^2)
+process, which is expensive in time and memory.  A faster but less
+reliable method which estimates the error from the convergence of the
+extrapolated value is described in the next section.  For the method
+described here a full table of intermediate values and derivatives
+through to O(N) must be computed and stored, but this does give a
+reliable error estimate.
 
- -- Function: int gsl_min_test_interval (double X_LOWER, double X_UPPER,
-          double EPSABS, double EPSREL)
-     This function tests for the convergence of the interval [X_LOWER,
-     X_UPPER] with absolute error EPSABS and relative error EPSREL.  The
-     test returns 'GSL_SUCCESS' if the following condition is achieved,
+ -- Function: gsl_sum_levin_u_workspace * gsl_sum_levin_u_alloc (size_t
+          N)
+     This function allocates a workspace for a Levin u-transform of N
+     terms.  The size of the workspace is O(2n^2 + 3n).
 
-          |a - b| < epsabs + epsrel min(|a|,|b|)
+ -- Function: void gsl_sum_levin_u_free (gsl_sum_levin_u_workspace * W)
+     This function frees the memory associated with the workspace W.
 
-     when the interval x = [a,b] does not include the origin.  If the
-     interval includes the origin then \min(|a|,|b|) is replaced by zero
-     (which is the minimum value of |x| over the interval).  This
-     ensures that the relative error is accurately estimated for minima
-     close to the origin.
+ -- Function: int gsl_sum_levin_u_accel (const double * ARRAY, size_t
+          ARRAY_SIZE, gsl_sum_levin_u_workspace * W, double * SUM_ACCEL,
+          double * ABSERR)
+     This function takes the terms of a series in ARRAY of size
+     ARRAY_SIZE and computes the extrapolated limit of the series using
+     a Levin u-transform.  Additional working space must be provided in
+     W.  The extrapolated sum is stored in SUM_ACCEL, with an estimate
+     of the absolute error stored in ABSERR.  The actual term-by-term
+     sum is returned in 'w->sum_plain'.  The algorithm calculates the
+     truncation error (the difference between two successive
+     extrapolations) and round-off error (propagated from the individual
+     terms) to choose an optimal number of terms for the extrapolation.
+     All the terms of the series passed in through ARRAY should be
+     non-zero.
 
-     This condition on the interval also implies that any estimate of
-     the minimum x_m in the interval satisfies the same condition with
-     respect to the true minimum x_m^*,
+
+File: gsl-ref.info,  Node: Acceleration functions without error estimation,  Next: Example of accelerating a series,  Prev: Acceleration functions,  Up: Series Acceleration
 
-          |x_m - x_m^*| < epsabs + epsrel x_m^*
+31.2 Acceleration functions without error estimation
+====================================================
 
-     assuming that the true minimum x_m^* is contained within the
-     interval.
+The functions described in this section compute the Levin u-transform of
+series and attempt to estimate the error from the "truncation error" in
+the extrapolation, the difference between the final two approximations.
+Using this method avoids the need to compute an intermediate table of
+derivatives because the error is estimated from the behavior of the
+extrapolated value itself.  Consequently this algorithm is an O(N)
+process and only requires O(N) terms of storage.  If the series
+converges sufficiently fast then this procedure can be acceptable.  It
+is appropriate to use this method when there is a need to compute many
+extrapolations of series with similar convergence properties at
+high-speed.  For example, when numerically integrating a function
+defined by a parameterized series where the parameter varies only
+slightly.  A reliable error estimate should be computed first using the
+full algorithm described above in order to verify the consistency of the
+results.
 
-
-File: gsl-ref.info,  Node: Minimization Algorithms,  Next: Minimization Examples,  Prev: Minimization Stopping Parameters,  Up: One dimensional Minimization
+ -- Function: gsl_sum_levin_utrunc_workspace *
+          gsl_sum_levin_utrunc_alloc (size_t N)
+     This function allocates a workspace for a Levin u-transform of N
+     terms, without error estimation.  The size of the workspace is
+     O(3n).
 
-34.7 Minimization Algorithms
-============================
+ -- Function: void gsl_sum_levin_utrunc_free
+          (gsl_sum_levin_utrunc_workspace * W)
+     This function frees the memory associated with the workspace W.
 
-The minimization algorithms described in this section require an initial
-interval which is guaranteed to contain a minimum--if a and b are the
-endpoints of the interval and x is an estimate of the minimum then f(a)
-> f(x) < f(b).  This ensures that the function has at least one minimum
-somewhere in the interval.  If a valid initial interval is used then
-these algorithm cannot fail, provided the function is well-behaved.
-
- -- Minimizer: gsl_min_fminimizer_goldensection
-
-     The "golden section algorithm" is the simplest method of bracketing
-     the minimum of a function.  It is the slowest algorithm provided by
-     the library, with linear convergence.
-
-     On each iteration, the algorithm first compares the subintervals
-     from the endpoints to the current minimum.  The larger subinterval
-     is divided in a golden section (using the famous ratio (3-\sqrt
-     5)/2 = 0.3189660...) and the value of the function at this new
-     point is calculated.  The new value is used with the constraint
-     f(a') > f(x') < f(b') to a select new interval containing the
-     minimum, by discarding the least useful point.  This procedure can
-     be continued indefinitely until the interval is sufficiently small.
-     Choosing the golden section as the bisection ratio can be shown to
-     provide the fastest convergence for this type of algorithm.
-
- -- Minimizer: gsl_min_fminimizer_brent
-
-     The "Brent minimization algorithm" combines a parabolic
-     interpolation with the golden section algorithm.  This produces a
-     fast algorithm which is still robust.
-
-     The outline of the algorithm can be summarized as follows: on each
-     iteration Brent's method approximates the function using an
-     interpolating parabola through three existing points.  The minimum
-     of the parabola is taken as a guess for the minimum.  If it lies
-     within the bounds of the current interval then the interpolating
-     point is accepted, and used to generate a smaller interval.  If the
-     interpolating point is not accepted then the algorithm falls back
-     to an ordinary golden section step.  The full details of Brent's
-     method include some additional checks to improve convergence.
-
- -- Minimizer: gsl_min_fminimizer_quad_golden
-     This is a variant of Brent's algorithm which uses the safeguarded
-     step-length algorithm of Gill and Murray.
+ -- Function: int gsl_sum_levin_utrunc_accel (const double * ARRAY,
+          size_t ARRAY_SIZE, gsl_sum_levin_utrunc_workspace * W, double
+          * SUM_ACCEL, double * ABSERR_TRUNC)
+     This function takes the terms of a series in ARRAY of size
+     ARRAY_SIZE and computes the extrapolated limit of the series using
+     a Levin u-transform.  Additional working space must be provided in
+     W.  The extrapolated sum is stored in SUM_ACCEL.  The actual
+     term-by-term sum is returned in 'w->sum_plain'.  The algorithm
+     terminates when the difference between two successive
+     extrapolations reaches a minimum or is sufficiently small.  The
+     difference between these two values is used as estimate of the
+     error and is stored in ABSERR_TRUNC.  To improve the reliability of
+     the algorithm the extrapolated values are replaced by moving
+     averages when calculating the truncation error, smoothing out any
+     fluctuations.
 
 
-File: gsl-ref.info,  Node: Minimization Examples,  Next: Minimization References and Further Reading,  Prev: Minimization Algorithms,  Up: One dimensional Minimization
+File: gsl-ref.info,  Node: Example of accelerating a series,  Next: Series Acceleration References,  Prev: Acceleration functions without error estimation,  Up: Series Acceleration
 
-34.8 Examples
+31.3 Examples
 =============
 
-The following program uses the Brent algorithm to find the minimum of
-the function f(x) = \cos(x) + 1, which occurs at x = \pi.  The starting
-interval is (0,6), with an initial guess for the minimum of 2.
+The following code calculates an estimate of \zeta(2) = \pi^2 / 6 using
+the series,
+
+     \zeta(2) = 1 + 1/2^2 + 1/3^2 + 1/4^2 + ...
+
+After N terms the error in the sum is O(1/N), making direct summation of
+the series converge slowly.
 
      #include <stdio.h>
-     #include <gsl/gsl_errno.h>
      #include <gsl/gsl_math.h>
-     #include <gsl/gsl_min.h>
+     #include <gsl/gsl_sum.h>
 
-     double fn1 (double x, void * params)
-     {
-       return cos(x) + 1.0;
-     }
+     #define N 20
 
      int
      main (void)
      {
-       int status;
-       int iter = 0, max_iter = 100;
-       const gsl_min_fminimizer_type *T;
-       gsl_min_fminimizer *s;
-       double m = 2.0, m_expected = M_PI;
-       double a = 0.0, b = 6.0;
-       gsl_function F;
+       double t[N];
+       double sum_accel, err;
+       double sum = 0;
+       int n;
 
-       F.function = &fn1;
-       F.params = 0;
+       gsl_sum_levin_u_workspace * w
+         = gsl_sum_levin_u_alloc (N);
+
+       const double zeta_2 = M_PI * M_PI / 6.0;
 
-       T = gsl_min_fminimizer_brent;
-       s = gsl_min_fminimizer_alloc (T);
-       gsl_min_fminimizer_set (s, &F, m, a, b);
-
-       printf ("using %s method\n",
-               gsl_min_fminimizer_name (s));
-
-       printf ("%5s [%9s, %9s] %9s %10s %9s\n",
-               "iter", "lower", "upper", "min",
-               "err", "err(est)");
-
-       printf ("%5d [%.7f, %.7f] %.7f %+.7f %.7f\n",
-               iter, a, b,
-               m, m - m_expected, b - a);
+       /* terms for zeta(2) = \sum_{n=1}^{\infty} 1/n^2 */
 
-       do
+       for (n = 0; n < N; n++)
          {
-           iter++;
-           status = gsl_min_fminimizer_iterate (s);
-
-           m = gsl_min_fminimizer_x_minimum (s);
-           a = gsl_min_fminimizer_x_lower (s);
-           b = gsl_min_fminimizer_x_upper (s);
-
-           status
-             = gsl_min_test_interval (a, b, 0.001, 0.0);
-
-           if (status == GSL_SUCCESS)
-             printf ("Converged:\n");
-
-           printf ("%5d [%.7f, %.7f] "
-                   "%.7f %+.7f %.7f\n",
-                   iter, a, b,
-                   m, m - m_expected, b - a);
+           double np1 = n + 1.0;
+           t[n] = 1.0 / (np1 * np1);
+           sum += t[n];
          }
-       while (status == GSL_CONTINUE && iter < max_iter);
 
-       gsl_min_fminimizer_free (s);
+       gsl_sum_levin_u_accel (t, N, w, &sum_accel, &err);
+
+       printf ("term-by-term sum = % .16f using %d terms\n",
+               sum, N);
+
+       printf ("term-by-term sum = % .16f using %zu terms\n",
+               w->sum_plain, w->terms_used);
+
+       printf ("exact value      = % .16f\n", zeta_2);
+       printf ("accelerated sum  = % .16f using %zu terms\n",
+               sum_accel, w->terms_used);
+
+       printf ("estimated error  = % .16f\n", err);
+       printf ("actual error     = % .16f\n",
+               sum_accel - zeta_2);
 
-       return status;
+       gsl_sum_levin_u_free (w);
+       return 0;
      }
 
-Here are the results of the minimization procedure.
+The output below shows that the Levin u-transform is able to obtain an
+estimate of the sum to 1 part in 10^10 using the first eleven terms of
+the series.  The error estimate returned by the function is also
+accurate, giving the correct number of significant digits.
 
      $ ./a.out
-         0 [0.0000000, 6.0000000] 2.0000000 -1.1415927 6.0000000
-         1 [2.0000000, 6.0000000] 3.2758640 +0.1342713 4.0000000
-         2 [2.0000000, 3.2831929] 3.2758640 +0.1342713 1.2831929
-         3 [2.8689068, 3.2831929] 3.2758640 +0.1342713 0.4142862
-         4 [2.8689068, 3.2831929] 3.2758640 +0.1342713 0.4142862
-         5 [2.8689068, 3.2758640] 3.1460585 +0.0044658 0.4069572
-         6 [3.1346075, 3.2758640] 3.1460585 +0.0044658 0.1412565
-         7 [3.1346075, 3.1874620] 3.1460585 +0.0044658 0.0528545
-         8 [3.1346075, 3.1460585] 3.1460585 +0.0044658 0.0114510
-         9 [3.1346075, 3.1460585] 3.1424060 +0.0008133 0.0114510
-        10 [3.1346075, 3.1424060] 3.1415885 -0.0000041 0.0077985
-     Converged:
-        11 [3.1415885, 3.1424060] 3.1415927 -0.0000000 0.0008175
+     term-by-term sum =  1.5961632439130233 using 20 terms
+     term-by-term sum =  1.5759958390005426 using 13 terms
+     exact value      =  1.6449340668482264
+     accelerated sum  =  1.6449340669228176 using 13 terms
+     estimated error  =  0.0000000000888360
+     actual error     =  0.0000000000745912
+
+Note that a direct summation of this series would require 10^10 terms to
+achieve the same precision as the accelerated sum does in 13 terms.
 
diff -Nru gsl-doc-1.16/doc/gsl-ref.info-4 gsl-doc-2.3/doc/gsl-ref.info-4
--- gsl-doc-1.16/doc/gsl-ref.info-4	2013-07-19 15:17:48.000000000 +0000
+++ gsl-doc-2.3/doc/gsl-ref.info-4	2016-12-09 00:08:08.000000000 +0000
@@ -2,947 +2,1450 @@
 gsl-ref.texi.
 
 Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,
-2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 The GSL Team.
+2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016
+The GSL Team.
 
    Permission is granted to copy, distribute and/or modify this document
 under the terms of the GNU Free Documentation License, Version 1.3 or
-any later version published by the Free Software Foundation; with no
-Invariant Sections and no cover texts.  A copy of the license is
-included in the section entitled "GNU Free Documentation License".
+any later version published by the Free Software Foundation; with the
+Invariant Sections being "GNU General Public License" and "Free Software
+Needs Free Documentation", the Front-Cover text being "A GNU Manual",
+and with the Back-Cover Text being (a) (see below).  A copy of the
+license is included in the section entitled "GNU Free Documentation
+License".
+
+   (a) The Back-Cover Text is: "You have the freedom to copy and modify
+this GNU Manual."
 INFO-DIR-SECTION Software libraries
 START-INFO-DIR-ENTRY
 * gsl-ref: (gsl-ref).                   GNU Scientific Library - Reference
 END-INFO-DIR-ENTRY
 
 
-File: gsl-ref.info,  Node: Minimization References and Further Reading,  Prev: Minimization Examples,  Up: One dimensional Minimization
+File: gsl-ref.info,  Node: Series Acceleration References,  Prev: Example of accelerating a series,  Up: Series Acceleration
 
-34.9 References and Further Reading
+31.4 References and Further Reading
 ===================================
 
-Further information on Brent's algorithm is available in the following
-book,
+The algorithms used by these functions are described in the following
+papers,
 
-     Richard Brent, 'Algorithms for minimization without derivatives',
-     Prentice-Hall (1973), republished by Dover in paperback (2002),
-     ISBN 0-486-41998-3.
+     T. Fessler, W.F. Ford, D.A. Smith, HURRY: An acceleration algorithm
+     for scalar sequences and series 'ACM Transactions on Mathematical
+     Software', 9(3):346-354, 1983.  and Algorithm 602 9(3):355-357,
+     1983.
 
-
-File: gsl-ref.info,  Node: Multidimensional Root-Finding,  Next: Multidimensional Minimization,  Prev: One dimensional Minimization,  Up: Top
+The theory of the u-transform was presented by Levin,
 
-35 Multidimensional Root-Finding
-********************************
+     D. Levin, Development of Non-Linear Transformations for Improving
+     Convergence of Sequences, 'Intern. J. Computer Math.' B3:371-388,
+     1973.
 
-This chapter describes functions for multidimensional root-finding
-(solving nonlinear systems with n equations in n unknowns).  The library
-provides low level components for a variety of iterative solvers and
-convergence tests.  These can be combined by the user to achieve the
-desired solution, with full access to the intermediate steps of the
-iteration.  Each class of methods uses the same framework, so that you
-can switch between solvers at runtime without needing to recompile your
-program.  Each instance of a solver keeps track of its own state,
-allowing the solvers to be used in multi-threaded programs.  The solvers
-are based on the original Fortran library MINPACK.
+A review paper on the Levin Transform is available online,
+     Herbert H. H. Homeier, Scalar Levin-Type Sequence Transformations,
+     <http://arxiv.org/abs/math/0005209>.
 
-   The header file 'gsl_multiroots.h' contains prototypes for the
-multidimensional root finding functions and related declarations.
+
+File: gsl-ref.info,  Node: Wavelet Transforms,  Next: Discrete Hankel Transforms,  Prev: Series Acceleration,  Up: Top
+
+32 Wavelet Transforms
+*********************
+
+This chapter describes functions for performing Discrete Wavelet
+Transforms (DWTs).  The library includes wavelets for real data in both
+one and two dimensions.  The wavelet functions are declared in the
+header files 'gsl_wavelet.h' and 'gsl_wavelet2d.h'.
 
 * Menu:
 
-* Overview of Multidimensional Root Finding::  
-* Initializing the Multidimensional Solver::  
-* Providing the multidimensional system of equations to solve::  
-* Iteration of the multidimensional solver::  
-* Search Stopping Parameters for the multidimensional solver::  
-* Algorithms using Derivatives::  
-* Algorithms without Derivatives::  
-* Example programs for Multidimensional Root finding::  
-* References and Further Reading for Multidimensional Root Finding::  
+* DWT Definitions::             
+* DWT Initialization::          
+* DWT Transform Functions::     
+* DWT Examples::                
+* DWT References::              
 
 
-File: gsl-ref.info,  Node: Overview of Multidimensional Root Finding,  Next: Initializing the Multidimensional Solver,  Up: Multidimensional Root-Finding
+File: gsl-ref.info,  Node: DWT Definitions,  Next: DWT Initialization,  Up: Wavelet Transforms
 
-35.1 Overview
-=============
-
-The problem of multidimensional root finding requires the simultaneous
-solution of n equations, f_i, in n variables, x_i,
+32.1 Definitions
+================
 
-     f_i (x_1, ..., x_n) = 0    for i = 1 ... n.
+The continuous wavelet transform and its inverse are defined by the
+relations,
 
-In general there are no bracketing methods available for n dimensional
-systems, and no way of knowing whether any solutions exist.  All
-algorithms proceed from an initial guess using a variant of the Newton
-iteration,
+     w(s,\tau) = \int f(t) * \psi^*_{s,\tau}(t) dt
 
-     x -> x' = x - J^{-1} f(x)
+and,
 
-where x, f are vector quantities and J is the Jacobian matrix J_{ij} = d
-f_i / d x_j.  Additional strategies can be used to enlarge the region of
-convergence.  These include requiring a decrease in the norm |f| on each
-step proposed by Newton's method, or taking steepest-descent steps in
-the direction of the negative gradient of |f|.
+     f(t) = \int \int_{-\infty}^\infty w(s, \tau) * \psi_{s,\tau}(t) d\tau ds
 
-   Several root-finding algorithms are available within a single
-framework.  The user provides a high-level driver for the algorithms,
-and the library provides the individual functions necessary for each of
-the steps.  There are three main phases of the iteration.  The steps
-are,
+where the basis functions \psi_{s,\tau} are obtained by scaling and
+translation from a single function, referred to as the "mother wavelet".
 
-   * initialize solver state, S, for algorithm T
+   The discrete version of the wavelet transform acts on equally-spaced
+samples, with fixed scaling and translation steps (s, \tau).  The
+frequency and time axes are sampled "dyadically" on scales of 2^j
+through a level parameter j.  The resulting family of functions
+{\psi_{j,n}} constitutes an orthonormal basis for square-integrable
+signals.
 
-   * update S using the iteration T
+   The discrete wavelet transform is an O(N) algorithm, and is also
+referred to as the "fast wavelet transform".
 
-   * test S for convergence, and repeat iteration if necessary
+
+File: gsl-ref.info,  Node: DWT Initialization,  Next: DWT Transform Functions,  Prev: DWT Definitions,  Up: Wavelet Transforms
 
-The evaluation of the Jacobian matrix can be problematic, either because
-programming the derivatives is intractable or because computation of the
-n^2 terms of the matrix becomes too expensive.  For these reasons the
-algorithms provided by the library are divided into two classes
-according to whether the derivatives are available or not.
+32.2 Initialization
+===================
 
-   The state for solvers with an analytic Jacobian matrix is held in a
-'gsl_multiroot_fdfsolver' struct.  The updating procedure requires both
-the function and its derivatives to be supplied by the user.
+The 'gsl_wavelet' structure contains the filter coefficients defining
+the wavelet and any associated offset parameters.
 
-   The state for solvers which do not use an analytic Jacobian matrix is
-held in a 'gsl_multiroot_fsolver' struct.  The updating procedure uses
-only function evaluations (not derivatives).  The algorithms estimate
-the matrix J or J^{-1} by approximate methods.
+ -- Function: gsl_wavelet * gsl_wavelet_alloc (const gsl_wavelet_type *
+          T, size_t K)
+     This function allocates and initializes a wavelet object of type T.
+     The parameter K selects the specific member of the wavelet family.
+     A null pointer is returned if insufficient memory is available or
+     if a unsupported member is selected.
+
+   The following wavelet types are implemented:
+
+ -- Wavelet: gsl_wavelet_daubechies
+ -- Wavelet: gsl_wavelet_daubechies_centered
+     This is the Daubechies wavelet family of maximum phase with k/2
+     vanishing moments.  The implemented wavelets are k=4, 6, ..., 20,
+     with K even.
+
+ -- Wavelet: gsl_wavelet_haar
+ -- Wavelet: gsl_wavelet_haar_centered
+     This is the Haar wavelet.  The only valid choice of k for the Haar
+     wavelet is k=2.
+
+ -- Wavelet: gsl_wavelet_bspline
+ -- Wavelet: gsl_wavelet_bspline_centered
+     This is the biorthogonal B-spline wavelet family of order (i,j).
+     The implemented values of k = 100*i + j are 103, 105, 202, 204,
+     206, 208, 301, 303, 305 307, 309.
+
+The centered forms of the wavelets align the coefficients of the various
+sub-bands on edges.  Thus the resulting visualization of the
+coefficients of the wavelet transform in the phase plane is easier to
+understand.
+
+ -- Function: const char * gsl_wavelet_name (const gsl_wavelet * W)
+     This function returns a pointer to the name of the wavelet family
+     for W.
+
+ -- Function: void gsl_wavelet_free (gsl_wavelet * W)
+     This function frees the wavelet object W.
+
+   The 'gsl_wavelet_workspace' structure contains scratch space of the
+same size as the input data and is used to hold intermediate results
+during the transform.
+
+ -- Function: gsl_wavelet_workspace * gsl_wavelet_workspace_alloc
+          (size_t N)
+     This function allocates a workspace for the discrete wavelet
+     transform.  To perform a one-dimensional transform on N elements, a
+     workspace of size N must be provided.  For two-dimensional
+     transforms of N-by-N matrices it is sufficient to allocate a
+     workspace of size N, since the transform operates on individual
+     rows and columns.  A null pointer is returned if insufficient
+     memory is available.
+
+ -- Function: void gsl_wavelet_workspace_free (gsl_wavelet_workspace *
+          WORK)
+     This function frees the allocated workspace WORK.
 
 
-File: gsl-ref.info,  Node: Initializing the Multidimensional Solver,  Next: Providing the multidimensional system of equations to solve,  Prev: Overview of Multidimensional Root Finding,  Up: Multidimensional Root-Finding
+File: gsl-ref.info,  Node: DWT Transform Functions,  Next: DWT Examples,  Prev: DWT Initialization,  Up: Wavelet Transforms
 
-35.2 Initializing the Solver
-============================
+32.3 Transform Functions
+========================
 
-The following functions initialize a multidimensional solver, either
-with or without derivatives.  The solver itself depends only on the
-dimension of the problem and the algorithm and can be reused for
-different problems.
+This sections describes the actual functions performing the discrete
+wavelet transform.  Note that the transforms use periodic boundary
+conditions.  If the signal is not periodic in the sample length then
+spurious coefficients will appear at the beginning and end of each level
+of the transform.
 
- -- Function: gsl_multiroot_fsolver * gsl_multiroot_fsolver_alloc (const
-          gsl_multiroot_fsolver_type * T, size_t N)
-     This function returns a pointer to a newly allocated instance of a
-     solver of type T for a system of N dimensions.  For example, the
-     following code creates an instance of a hybrid solver, to solve a
-     3-dimensional system of equations.
+* Menu:
 
-          const gsl_multiroot_fsolver_type * T
-              = gsl_multiroot_fsolver_hybrid;
-          gsl_multiroot_fsolver * s
-              = gsl_multiroot_fsolver_alloc (T, 3);
+* DWT in one dimension::        
+* DWT in two dimension::        
 
-     If there is insufficient memory to create the solver then the
-     function returns a null pointer and the error handler is invoked
-     with an error code of 'GSL_ENOMEM'.
+
+File: gsl-ref.info,  Node: DWT in one dimension,  Next: DWT in two dimension,  Up: DWT Transform Functions
 
- -- Function: gsl_multiroot_fdfsolver * gsl_multiroot_fdfsolver_alloc
-          (const gsl_multiroot_fdfsolver_type * T, size_t N)
-     This function returns a pointer to a newly allocated instance of a
-     derivative solver of type T for a system of N dimensions.  For
-     example, the following code creates an instance of a Newton-Raphson
-     solver, for a 2-dimensional system of equations.
+32.3.1 Wavelet transforms in one dimension
+------------------------------------------
 
-          const gsl_multiroot_fdfsolver_type * T
-              = gsl_multiroot_fdfsolver_newton;
-          gsl_multiroot_fdfsolver * s =
-              gsl_multiroot_fdfsolver_alloc (T, 2);
+ -- Function: int gsl_wavelet_transform (const gsl_wavelet * W, double *
+          DATA, size_t STRIDE, size_t N, gsl_wavelet_direction DIR,
+          gsl_wavelet_workspace * WORK)
+ -- Function: int gsl_wavelet_transform_forward (const gsl_wavelet * W,
+          double * DATA, size_t STRIDE, size_t N, gsl_wavelet_workspace
+          * WORK)
+ -- Function: int gsl_wavelet_transform_inverse (const gsl_wavelet * W,
+          double * DATA, size_t STRIDE, size_t N, gsl_wavelet_workspace
+          * WORK)
+
+     These functions compute in-place forward and inverse discrete
+     wavelet transforms of length N with stride STRIDE on the array
+     DATA.  The length of the transform N is restricted to powers of
+     two.  For the 'transform' version of the function the argument DIR
+     can be either 'forward' (+1) or 'backward' (-1).  A workspace WORK
+     of length N must be provided.
+
+     For the forward transform, the elements of the original array are
+     replaced by the discrete wavelet transform f_i -> w_{j,k} in a
+     packed triangular storage layout, where J is the index of the level
+     j = 0 ... J-1 and K is the index of the coefficient within each
+     level, k = 0 ... (2^j)-1.  The total number of levels is J =
+     \log_2(n).  The output data has the following form,
+
+          (s_{-1,0}, d_{0,0}, d_{1,0}, d_{1,1}, d_{2,0}, ...,
+            d_{j,k}, ..., d_{J-1,2^{J-1}-1})
+
+     where the first element is the smoothing coefficient s_{-1,0},
+     followed by the detail coefficients d_{j,k} for each level j.  The
+     backward transform inverts these coefficients to obtain the
+     original data.
+
+     These functions return a status of 'GSL_SUCCESS' upon successful
+     completion.  'GSL_EINVAL' is returned if N is not an integer power
+     of 2 or if insufficient workspace is provided.
+
+
+File: gsl-ref.info,  Node: DWT in two dimension,  Prev: DWT in one dimension,  Up: DWT Transform Functions
+
+32.3.2 Wavelet transforms in two dimension
+------------------------------------------
+
+The library provides functions to perform two-dimensional discrete
+wavelet transforms on square matrices.  The matrix dimensions must be an
+integer power of two.  There are two possible orderings of the rows and
+columns in the two-dimensional wavelet transform, referred to as the
+"standard" and "non-standard" forms.
+
+   The "standard" transform performs a complete discrete wavelet
+transform on the rows of the matrix, followed by a separate complete
+discrete wavelet transform on the columns of the resulting
+row-transformed matrix.  This procedure uses the same ordering as a
+two-dimensional Fourier transform.
+
+   The "non-standard" transform is performed in interleaved passes on
+the rows and columns of the matrix for each level of the transform.  The
+first level of the transform is applied to the matrix rows, and then to
+the matrix columns.  This procedure is then repeated across the rows and
+columns of the data for the subsequent levels of the transform, until
+the full discrete wavelet transform is complete.  The non-standard form
+of the discrete wavelet transform is typically used in image analysis.
 
-     If there is insufficient memory to create the solver then the
-     function returns a null pointer and the error handler is invoked
-     with an error code of 'GSL_ENOMEM'.
+   The functions described in this section are declared in the header
+file 'gsl_wavelet2d.h'.
 
- -- Function: int gsl_multiroot_fsolver_set (gsl_multiroot_fsolver * S,
-          gsl_multiroot_function * F, const gsl_vector * X)
- -- Function: int gsl_multiroot_fdfsolver_set (gsl_multiroot_fdfsolver *
-          S, gsl_multiroot_function_fdf * FDF, const gsl_vector * X)
-     These functions set, or reset, an existing solver S to use the
-     function F or function and derivative FDF, and the initial guess X.
-     Note that the initial position is copied from X, this argument is
-     not modified by subsequent iterations.
+ -- Function: int gsl_wavelet2d_transform (const gsl_wavelet * W, double
+          * DATA, size_t TDA, size_t SIZE1, size_t SIZE2,
+          gsl_wavelet_direction DIR, gsl_wavelet_workspace * WORK)
+ -- Function: int gsl_wavelet2d_transform_forward (const gsl_wavelet *
+          W, double * DATA, size_t TDA, size_t SIZE1, size_t SIZE2,
+          gsl_wavelet_workspace * WORK)
+ -- Function: int gsl_wavelet2d_transform_inverse (const gsl_wavelet *
+          W, double * DATA, size_t TDA, size_t SIZE1, size_t SIZE2,
+          gsl_wavelet_workspace * WORK)
+
+     These functions compute two-dimensional in-place forward and
+     inverse discrete wavelet transforms in standard form on the array
+     DATA stored in row-major form with dimensions SIZE1 and SIZE2 and
+     physical row length TDA.  The dimensions must be equal (square
+     matrix) and are restricted to powers of two.  For the 'transform'
+     version of the function the argument DIR can be either 'forward'
+     (+1) or 'backward' (-1).  A workspace WORK of the appropriate size
+     must be provided.  On exit, the appropriate elements of the array
+     DATA are replaced by their two-dimensional wavelet transform.
+
+     The functions return a status of 'GSL_SUCCESS' upon successful
+     completion.  'GSL_EINVAL' is returned if SIZE1 and SIZE2 are not
+     equal and integer powers of 2, or if insufficient workspace is
+     provided.
+
+ -- Function: int gsl_wavelet2d_transform_matrix (const gsl_wavelet * W,
+          gsl_matrix * M, gsl_wavelet_direction DIR,
+          gsl_wavelet_workspace * WORK)
+ -- Function: int gsl_wavelet2d_transform_matrix_forward (const
+          gsl_wavelet * W, gsl_matrix * M, gsl_wavelet_workspace * WORK)
+ -- Function: int gsl_wavelet2d_transform_matrix_inverse (const
+          gsl_wavelet * W, gsl_matrix * M, gsl_wavelet_workspace * WORK)
+     These functions compute the two-dimensional in-place wavelet
+     transform on a matrix A.
+
+ -- Function: int gsl_wavelet2d_nstransform (const gsl_wavelet * W,
+          double * DATA, size_t TDA, size_t SIZE1, size_t SIZE2,
+          gsl_wavelet_direction DIR, gsl_wavelet_workspace * WORK)
+ -- Function: int gsl_wavelet2d_nstransform_forward (const gsl_wavelet *
+          W, double * DATA, size_t TDA, size_t SIZE1, size_t SIZE2,
+          gsl_wavelet_workspace * WORK)
+ -- Function: int gsl_wavelet2d_nstransform_inverse (const gsl_wavelet *
+          W, double * DATA, size_t TDA, size_t SIZE1, size_t SIZE2,
+          gsl_wavelet_workspace * WORK)
+     These functions compute the two-dimensional wavelet transform in
+     non-standard form.
+
+ -- Function: int gsl_wavelet2d_nstransform_matrix (const gsl_wavelet *
+          W, gsl_matrix * M, gsl_wavelet_direction DIR,
+          gsl_wavelet_workspace * WORK)
+ -- Function: int gsl_wavelet2d_nstransform_matrix_forward (const
+          gsl_wavelet * W, gsl_matrix * M, gsl_wavelet_workspace * WORK)
+ -- Function: int gsl_wavelet2d_nstransform_matrix_inverse (const
+          gsl_wavelet * W, gsl_matrix * M, gsl_wavelet_workspace * WORK)
+     These functions compute the non-standard form of the
+     two-dimensional in-place wavelet transform on a matrix A.
 
- -- Function: void gsl_multiroot_fsolver_free (gsl_multiroot_fsolver *
-          S)
- -- Function: void gsl_multiroot_fdfsolver_free (gsl_multiroot_fdfsolver
-          * S)
-     These functions free all the memory associated with the solver S.
+
+File: gsl-ref.info,  Node: DWT Examples,  Next: DWT References,  Prev: DWT Transform Functions,  Up: Wavelet Transforms
 
- -- Function: const char * gsl_multiroot_fsolver_name (const
-          gsl_multiroot_fsolver * S)
- -- Function: const char * gsl_multiroot_fdfsolver_name (const
-          gsl_multiroot_fdfsolver * S)
-     These functions return a pointer to the name of the solver.  For
-     example,
+32.4 Examples
+=============
 
-          printf ("s is a '%s' solver\n",
-                  gsl_multiroot_fdfsolver_name (s));
+The following program demonstrates the use of the one-dimensional
+wavelet transform functions.  It computes an approximation to an input
+signal (of length 256) using the 20 largest components of the wavelet
+transform, while setting the others to zero.
 
-     would print something like 's is a 'newton' solver'.
+     #include <stdio.h>
+     #include <math.h>
+     #include <gsl/gsl_sort.h>
+     #include <gsl/gsl_wavelet.h>
 
-
-File: gsl-ref.info,  Node: Providing the multidimensional system of equations to solve,  Next: Iteration of the multidimensional solver,  Prev: Initializing the Multidimensional Solver,  Up: Multidimensional Root-Finding
+     int
+     main (int argc, char **argv)
+     {
+       (void)(argc); /* avoid unused parameter warning */
+       int i, n = 256, nc = 20;
+       double *data = malloc (n * sizeof (double));
+       double *abscoeff = malloc (n * sizeof (double));
+       size_t *p = malloc (n * sizeof (size_t));
+
+       FILE * f;
+       gsl_wavelet *w;
+       gsl_wavelet_workspace *work;
 
-35.3 Providing the function to solve
-====================================
+       w = gsl_wavelet_alloc (gsl_wavelet_daubechies, 4);
+       work = gsl_wavelet_workspace_alloc (n);
 
-You must provide n functions of n variables for the root finders to
-operate on.  In order to allow for general parameters the functions are
-defined by the following data types:
+       f = fopen (argv[1], "r");
+       for (i = 0; i < n; i++)
+         {
+           fscanf (f, "%lg", &data[i]);
+         }
+       fclose (f);
 
- -- Data Type: gsl_multiroot_function
-     This data type defines a general system of functions with
-     parameters.
+       gsl_wavelet_transform_forward (w, data, 1, n, work);
 
-     'int (* f) (const gsl_vector * X, void * PARAMS, gsl_vector * F)'
-          this function should store the vector result f(x,params) in F
-          for argument X and parameters PARAMS, returning an appropriate
-          error code if the function cannot be computed.
+       for (i = 0; i < n; i++)
+         {
+           abscoeff[i] = fabs (data[i]);
+         }
 
-     'size_t n'
-          the dimension of the system, i.e.  the number of components of
-          the vectors X and F.
+       gsl_sort_index (p, abscoeff, 1, n);
 
-     'void * params'
-          a pointer to the parameters of the function.
+       for (i = 0; (i + nc) < n; i++)
+         data[p[i]] = 0;
 
-Here is an example using Powell's test function,
+       gsl_wavelet_transform_inverse (w, data, 1, n, work);
 
-     f_1(x) = A x_0 x_1 - 1,
-     f_2(x) = exp(-x_0) + exp(-x_1) - (1 + 1/A)
+       for (i = 0; i < n; i++)
+         {
+           printf ("%g\n", data[i]);
+         }
 
-with A = 10^4.  The following code defines a 'gsl_multiroot_function'
-system 'F' which you could pass to a solver:
+       gsl_wavelet_free (w);
+       gsl_wavelet_workspace_free (work);
 
-     struct powell_params { double A; };
+       free (data);
+       free (abscoeff);
+       free (p);
+       return 0;
+     }
 
-     int
-     powell (gsl_vector * x, void * p, gsl_vector * f) {
-        struct powell_params * params
-          = (struct powell_params *)p;
-        const double A = (params->A);
-        const double x0 = gsl_vector_get(x,0);
-        const double x1 = gsl_vector_get(x,1);
+The output can be used with the GNU plotutils 'graph' program,
 
-        gsl_vector_set (f, 0, A * x0 * x1 - 1);
-        gsl_vector_set (f, 1, (exp(-x0) + exp(-x1)
-                               - (1.0 + 1.0/A)));
-        return GSL_SUCCESS
-     }
+     $ ./a.out ecg.dat > dwt.txt
+     $ graph -T ps -x 0 256 32 -h 0.3 -a dwt.txt > dwt.ps
 
-     gsl_multiroot_function F;
-     struct powell_params params = { 10000.0 };
+
+File: gsl-ref.info,  Node: DWT References,  Prev: DWT Examples,  Up: Wavelet Transforms
 
-     F.f = &powell;
-     F.n = 2;
-     F.params = &params;
+32.5 References and Further Reading
+===================================
 
- -- Data Type: gsl_multiroot_function_fdf
-     This data type defines a general system of functions with
-     parameters and the corresponding Jacobian matrix of derivatives,
+The mathematical background to wavelet transforms is covered in the
+original lectures by Daubechies,
 
-     'int (* f) (const gsl_vector * X, void * PARAMS, gsl_vector * F)'
-          this function should store the vector result f(x,params) in F
-          for argument X and parameters PARAMS, returning an appropriate
-          error code if the function cannot be computed.
+     Ingrid Daubechies.  Ten Lectures on Wavelets.  'CBMS-NSF Regional
+     Conference Series in Applied Mathematics' (1992), SIAM, ISBN
+     0898712742.
 
-     'int (* df) (const gsl_vector * X, void * PARAMS, gsl_matrix * J)'
-          this function should store the N-by-N matrix result J_ij = d
-          f_i(x,params) / d x_j in J for argument X and parameters
-          PARAMS, returning an appropriate error code if the function
-          cannot be computed.
+An easy to read introduction to the subject with an emphasis on the
+application of the wavelet transform in various branches of science is,
 
-     'int (* fdf) (const gsl_vector * X, void * PARAMS, gsl_vector * F, gsl_matrix * J)'
-          This function should set the values of the F and J as above,
-          for arguments X and parameters PARAMS.  This function provides
-          an optimization of the separate functions for f(x) and
-          J(x)--it is always faster to compute the function and its
-          derivative at the same time.
+     Paul S. Addison.  'The Illustrated Wavelet Transform Handbook'.
+     Institute of Physics Publishing (2002), ISBN 0750306920.
 
-     'size_t n'
-          the dimension of the system, i.e.  the number of components of
-          the vectors X and F.
+For extensive coverage of signal analysis by wavelets, wavelet packets
+and local cosine bases see,
 
-     'void * params'
-          a pointer to the parameters of the function.
+     S. G. Mallat.  'A wavelet tour of signal processing' (Second
+     edition).  Academic Press (1999), ISBN 012466606X.
 
-The example of Powell's test function defined above can be extended to
-include analytic derivatives using the following code,
+The concept of multiresolution analysis underlying the wavelet transform
+is described in,
 
-     int
-     powell_df (gsl_vector * x, void * p, gsl_matrix * J)
-     {
-        struct powell_params * params
-          = (struct powell_params *)p;
-        const double A = (params->A);
-        const double x0 = gsl_vector_get(x,0);
-        const double x1 = gsl_vector_get(x,1);
-        gsl_matrix_set (J, 0, 0, A * x1);
-        gsl_matrix_set (J, 0, 1, A * x0);
-        gsl_matrix_set (J, 1, 0, -exp(-x0));
-        gsl_matrix_set (J, 1, 1, -exp(-x1));
-        return GSL_SUCCESS
-     }
+     S. G. Mallat.  Multiresolution Approximations and Wavelet
+     Orthonormal Bases of L^2(R). 'Transactions of the American
+     Mathematical Society', 315(1), 1989, 69-87.
 
-     int
-     powell_fdf (gsl_vector * x, void * p,
-                 gsl_matrix * f, gsl_matrix * J) {
-        struct powell_params * params
-          = (struct powell_params *)p;
-        const double A = (params->A);
-        const double x0 = gsl_vector_get(x,0);
-        const double x1 = gsl_vector_get(x,1);
+     S. G. Mallat.  A Theory for Multiresolution Signal
+     Decomposition--The Wavelet Representation.  'IEEE Transactions on
+     Pattern Analysis and Machine Intelligence', 11, 1989, 674-693.
 
-        const double u0 = exp(-x0);
-        const double u1 = exp(-x1);
+The coefficients for the individual wavelet families implemented by the
+library can be found in the following papers,
 
-        gsl_vector_set (f, 0, A * x0 * x1 - 1);
-        gsl_vector_set (f, 1, u0 + u1 - (1 + 1/A));
+     I. Daubechies.  Orthonormal Bases of Compactly Supported Wavelets.
+     'Communications on Pure and Applied Mathematics', 41 (1988)
+     909-996.
 
-        gsl_matrix_set (J, 0, 0, A * x1);
-        gsl_matrix_set (J, 0, 1, A * x0);
-        gsl_matrix_set (J, 1, 0, -u0);
-        gsl_matrix_set (J, 1, 1, -u1);
-        return GSL_SUCCESS
-     }
+     A. Cohen, I. Daubechies, and J.-C. Feauveau.  Biorthogonal Bases of
+     Compactly Supported Wavelets.  'Communications on Pure and Applied
+     Mathematics', 45 (1992) 485-560.
 
-     gsl_multiroot_function_fdf FDF;
+The PhysioNet archive of physiological datasets can be found online at
+<http://www.physionet.org/> and is described in the following paper,
 
-     FDF.f = &powell_f;
-     FDF.df = &powell_df;
-     FDF.fdf = &powell_fdf;
-     FDF.n = 2;
-     FDF.params = 0;
+     Goldberger et al.  PhysioBank, PhysioToolkit, and PhysioNet:
+     Components of a New Research Resource for Complex Physiologic
+     Signals.  'Circulation' 101(23):e215-e220 2000.
 
-Note that the function 'powell_fdf' is able to reuse existing terms from
-the function when calculating the Jacobian, thus saving time.
+
+File: gsl-ref.info,  Node: Discrete Hankel Transforms,  Next: One dimensional Root-Finding,  Prev: Wavelet Transforms,  Up: Top
+
+33 Discrete Hankel Transforms
+*****************************
+
+This chapter describes functions for performing Discrete Hankel
+Transforms (DHTs).  The functions are declared in the header file
+'gsl_dht.h'.
+
+* Menu:
+
+* Discrete Hankel Transform Definition::  
+* Discrete Hankel Transform Functions::  
+* Discrete Hankel Transform References::  
+
+
+File: gsl-ref.info,  Node: Discrete Hankel Transform Definition,  Next: Discrete Hankel Transform Functions,  Up: Discrete Hankel Transforms
+
+33.1 Definitions
+================
+
+The discrete Hankel transform acts on a vector of sampled data, where
+the samples are assumed to have been taken at points related to the
+zeros of a Bessel function of fixed order; compare this to the case of
+the discrete Fourier transform, where samples are taken at points
+related to the zeroes of the sine or cosine function.
+
+   Starting with its definition, the Hankel transform (or Bessel
+transform) of order \nu of a function f with \nu > -1/2 is defined as
+(see Johnson, 1987 and Lemoine, 1994)
+     F_\nu(u) = \int_0^\infty f(t) J_\nu(u t) t dt
+
+If the integral exists, F_\nu is called the Hankel transformation of f.
+The reverse transform is given by
+     f(t) = \int_0^\infty F_\nu(u) J_\nu(u t) u du ,
+
+where \int_0^\infty f(t) t^{1/2} dt must exist and be absolutely
+convergent, and where f(t) satisfies Dirichlet's conditions (of limited
+total fluctuations) in the interval [0,\infty].
+
+   Now the discrete Hankel transform works on a discrete function f,
+which is sampled on points n=1...M located at positions
+t_n=(j_{\nu,n}/j_{\nu,M}) X in real space and at u_n=j_{\nu,n}/X in
+reciprocal space.  Here, j_{\nu,m} are the m-th zeros of the Bessel
+function J_\nu(x) arranged in ascending order.  Moreover, the discrete
+functions are assumed to be band limited, so f(t_n)=0 and F(u_n)=0 for
+n>M.  Accordingly, the function f is defined on the interval [0,X].
+
+   Following the work of Johnson, 1987 and Lemoine, 1994, the discrete
+Hankel transform is given by
+     F_\nu(u_m) = (2 X^2 / j_(\nu,M)^2)
+           \sum_{k=1}^{M-1} f(j_(\nu,k) X/j_(\nu,M))
+               (J_\nu(j_(\nu,m) j_(\nu,k) / j_(\nu,M)) / J_(\nu+1)(j_(\nu,k))^2).
+
+It is this discrete expression which defines the discrete Hankel
+transform calculated by GSL. In GSL, forward and backward transforms are
+defined equally and calculate F_\nu(u_m).  Following Johnson, the
+backward transform reads
+     f(t_k) = (2 / X^2)
+           \sum_{m=1}^{M-1} F(j_(\nu,m)/X)
+               (J_\nu(j_(\nu,m) j_(\nu,k) / j_(\nu,M)) / J_(\nu+1)(j_(\nu,m))^2).
+
+Obviously, using the forward transform instead of the backward transform
+gives an additional factor X^4/j_{\nu,M}^2=t_m^2/u_m^2.
+
+   The kernel in the summation above defines the matrix of the
+\nu-Hankel transform of size M-1.  The coefficients of this matrix,
+being dependent on \nu and M, must be precomputed and stored; the
+'gsl_dht' object encapsulates this data.  The allocation function
+'gsl_dht_alloc' returns a 'gsl_dht' object which must be properly
+initialized with 'gsl_dht_init' before it can be used to perform
+transforms on data sample vectors, for fixed \nu and M, using the
+'gsl_dht_apply' function.  The implementation allows to define the
+length X of the fundamental interval, for convenience, while discrete
+Hankel transforms are often defined on the unit interval instead of
+[0,X].
+
+   Notice that by assumption f(t) vanishes at the endpoints of the
+interval, consistent with the inversion formula and the sampling formula
+given above.  Therefore, this transform corresponds to an orthogonal
+expansion in eigenfunctions of the Dirichlet problem for the Bessel
+differential equation.
 
 
-File: gsl-ref.info,  Node: Iteration of the multidimensional solver,  Next: Search Stopping Parameters for the multidimensional solver,  Prev: Providing the multidimensional system of equations to solve,  Up: Multidimensional Root-Finding
+File: gsl-ref.info,  Node: Discrete Hankel Transform Functions,  Next: Discrete Hankel Transform References,  Prev: Discrete Hankel Transform Definition,  Up: Discrete Hankel Transforms
 
-35.4 Iteration
+33.2 Functions
 ==============
 
-The following functions drive the iteration of each algorithm.  Each
-function performs one iteration to update the state of any solver of the
-corresponding type.  The same functions work for all solvers so that
-different methods can be substituted at runtime without modifications to
-the code.
+ -- Function: gsl_dht * gsl_dht_alloc (size_t SIZE)
+     This function allocates a Discrete Hankel transform object of size
+     SIZE.
 
- -- Function: int gsl_multiroot_fsolver_iterate (gsl_multiroot_fsolver *
-          S)
- -- Function: int gsl_multiroot_fdfsolver_iterate
-          (gsl_multiroot_fdfsolver * S)
-     These functions perform a single iteration of the solver S.  If the
-     iteration encounters an unexpected problem then an error code will
-     be returned,
+ -- Function: int gsl_dht_init (gsl_dht * T, double NU, double XMAX)
+     This function initializes the transform T for the given values of
+     NU and XMAX.
 
-     'GSL_EBADFUNC'
-          the iteration encountered a singular point where the function
-          or its derivative evaluated to 'Inf' or 'NaN'.
+ -- Function: gsl_dht * gsl_dht_new (size_t SIZE, double NU, double
+          XMAX)
+     This function allocates a Discrete Hankel transform object of size
+     SIZE and initializes it for the given values of NU and XMAX.
 
-     'GSL_ENOPROG'
-          the iteration is not making any progress, preventing the
-          algorithm from continuing.
+ -- Function: void gsl_dht_free (gsl_dht * T)
+     This function frees the transform T.
 
-   The solver maintains a current best estimate of the root 's->x' and
-its function value 's->f' at all times.  This information can be
-accessed with the following auxiliary functions,
+ -- Function: int gsl_dht_apply (const gsl_dht * T, double * F_IN,
+          double * F_OUT)
+     This function applies the transform T to the array F_IN whose size
+     is equal to the size of the transform.  The result is stored in the
+     array F_OUT which must be of the same length.
 
- -- Function: gsl_vector * gsl_multiroot_fsolver_root (const
-          gsl_multiroot_fsolver * S)
- -- Function: gsl_vector * gsl_multiroot_fdfsolver_root (const
-          gsl_multiroot_fdfsolver * S)
-     These functions return the current estimate of the root for the
-     solver S, given by 's->x'.
+     Applying this function to its output gives the original data
+     multiplied by (1/j_(\nu,M))^2, up to numerical errors.
 
- -- Function: gsl_vector * gsl_multiroot_fsolver_f (const
-          gsl_multiroot_fsolver * S)
- -- Function: gsl_vector * gsl_multiroot_fdfsolver_f (const
-          gsl_multiroot_fdfsolver * S)
-     These functions return the function value f(x) at the current
-     estimate of the root for the solver S, given by 's->f'.
+ -- Function: double gsl_dht_x_sample (const gsl_dht * T, int N)
+     This function returns the value of the N-th sample point in the
+     unit interval, (j_{\nu,n+1}/j_{\nu,M}) X.  These are the points
+     where the function f(t) is assumed to be sampled.
 
- -- Function: gsl_vector * gsl_multiroot_fsolver_dx (const
-          gsl_multiroot_fsolver * S)
- -- Function: gsl_vector * gsl_multiroot_fdfsolver_dx (const
-          gsl_multiroot_fdfsolver * S)
-     These functions return the last step dx taken by the solver S,
-     given by 's->dx'.
+ -- Function: double gsl_dht_k_sample (const gsl_dht * T, int N)
+     This function returns the value of the N-th sample point in
+     "k-space", j_{\nu,n+1}/X.
 
 
-File: gsl-ref.info,  Node: Search Stopping Parameters for the multidimensional solver,  Next: Algorithms using Derivatives,  Prev: Iteration of the multidimensional solver,  Up: Multidimensional Root-Finding
-
-35.5 Search Stopping Parameters
-===============================
+File: gsl-ref.info,  Node: Discrete Hankel Transform References,  Prev: Discrete Hankel Transform Functions,  Up: Discrete Hankel Transforms
 
-A root finding procedure should stop when one of the following
-conditions is true:
+33.3 References and Further Reading
+===================================
 
-   * A multidimensional root has been found to within the user-specified
-     precision.
+The algorithms used by these functions are described in the following
+papers,
 
-   * A user-specified maximum number of iterations has been reached.
+     H. Fisk Johnson, Comp. Phys. Comm. 43, 181 (1987).
 
-   * An error has occurred.
+     D. Lemoine, J. Chem. Phys. 101, 3936 (1994).
 
-The handling of these conditions is under user control.  The functions
-below allow the user to test the precision of the current result in
-several standard ways.
+
+File: gsl-ref.info,  Node: One dimensional Root-Finding,  Next: One dimensional Minimization,  Prev: Discrete Hankel Transforms,  Up: Top
 
- -- Function: int gsl_multiroot_test_delta (const gsl_vector * DX, const
-          gsl_vector * X, double EPSABS, double EPSREL)
+34 One dimensional Root-Finding
+*******************************
 
-     This function tests for the convergence of the sequence by
-     comparing the last step DX with the absolute error EPSABS and
-     relative error EPSREL to the current position X.  The test returns
-     'GSL_SUCCESS' if the following condition is achieved,
+This chapter describes routines for finding roots of arbitrary
+one-dimensional functions.  The library provides low level components
+for a variety of iterative solvers and convergence tests.  These can be
+combined by the user to achieve the desired solution, with full access
+to the intermediate steps of the iteration.  Each class of methods uses
+the same framework, so that you can switch between solvers at runtime
+without needing to recompile your program.  Each instance of a solver
+keeps track of its own state, allowing the solvers to be used in
+multi-threaded programs.
 
-          |dx_i| < epsabs + epsrel |x_i|
+   The header file 'gsl_roots.h' contains prototypes for the root
+finding functions and related declarations.
 
-     for each component of X and returns 'GSL_CONTINUE' otherwise.
+* Menu:
 
- -- Function: int gsl_multiroot_test_residual (const gsl_vector * F,
-          double EPSABS)
-     This function tests the residual value F against the absolute error
-     bound EPSABS.  The test returns 'GSL_SUCCESS' if the following
-     condition is achieved,
+* Root Finding Overview::       
+* Root Finding Caveats::        
+* Initializing the Solver::     
+* Providing the function to solve::  
+* Search Bounds and Guesses::   
+* Root Finding Iteration::      
+* Search Stopping Parameters::  
+* Root Bracketing Algorithms::  
+* Root Finding Algorithms using Derivatives::  
+* Root Finding Examples::       
+* Root Finding References and Further Reading::  
 
-          \sum_i |f_i| < epsabs
+
+File: gsl-ref.info,  Node: Root Finding Overview,  Next: Root Finding Caveats,  Up: One dimensional Root-Finding
 
-     and returns 'GSL_CONTINUE' otherwise.  This criterion is suitable
-     for situations where the precise location of the root, x, is
-     unimportant provided a value can be found where the residual is
-     small enough.
+34.1 Overview
+=============
 
-
-File: gsl-ref.info,  Node: Algorithms using Derivatives,  Next: Algorithms without Derivatives,  Prev: Search Stopping Parameters for the multidimensional solver,  Up: Multidimensional Root-Finding
+One-dimensional root finding algorithms can be divided into two classes,
+"root bracketing" and "root polishing".  Algorithms which proceed by
+bracketing a root are guaranteed to converge.  Bracketing algorithms
+begin with a bounded region known to contain a root.  The size of this
+bounded region is reduced, iteratively, until it encloses the root to a
+desired tolerance.  This provides a rigorous error estimate for the
+location of the root.
+
+   The technique of "root polishing" attempts to improve an initial
+guess to the root.  These algorithms converge only if started "close
+enough" to a root, and sacrifice a rigorous error bound for speed.  By
+approximating the behavior of a function in the vicinity of a root they
+attempt to find a higher order improvement of an initial guess.  When
+the behavior of the function is compatible with the algorithm and a good
+initial guess is available a polishing algorithm can provide rapid
+convergence.
+
+   In GSL both types of algorithm are available in similar frameworks.
+The user provides a high-level driver for the algorithms, and the
+library provides the individual functions necessary for each of the
+steps.  There are three main phases of the iteration.  The steps are,
 
-35.6 Algorithms using Derivatives
-=================================
+   * initialize solver state, S, for algorithm T
 
-The root finding algorithms described in this section make use of both
-the function and its derivative.  They require an initial guess for the
-location of the root, but there is no absolute guarantee of
-convergence--the function must be suitable for this technique and the
-initial guess must be sufficiently close to the root for it to work.
-When the conditions are satisfied then convergence is quadratic.
+   * update S using the iteration T
 
- -- Derivative Solver: gsl_multiroot_fdfsolver_hybridsj
-     This is a modified version of Powell's Hybrid method as implemented
-     in the HYBRJ algorithm in MINPACK.  Minpack was written by Jorge J.
-     More', Burton S. Garbow and Kenneth E. Hillstrom.  The Hybrid
-     algorithm retains the fast convergence of Newton's method but will
-     also reduce the residual when Newton's method is unreliable.
+   * test S for convergence, and repeat iteration if necessary
 
-     The algorithm uses a generalized trust region to keep each step
-     under control.  In order to be accepted a proposed new position x'
-     must satisfy the condition |D (x' - x)| < \delta, where D is a
-     diagonal scaling matrix and \delta is the size of the trust region.
-     The components of D are computed internally, using the column norms
-     of the Jacobian to estimate the sensitivity of the residual to each
-     component of x.  This improves the behavior of the algorithm for
-     badly scaled functions.
+The state for bracketing solvers is held in a 'gsl_root_fsolver' struct.
+The updating procedure uses only function evaluations (not derivatives).
+The state for root polishing solvers is held in a 'gsl_root_fdfsolver'
+struct.  The updates require both the function and its derivative (hence
+the name 'fdf') to be supplied by the user.
 
-     On each iteration the algorithm first determines the standard
-     Newton step by solving the system J dx = - f.  If this step falls
-     inside the trust region it is used as a trial step in the next
-     stage.  If not, the algorithm uses the linear combination of the
-     Newton and gradient directions which is predicted to minimize the
-     norm of the function while staying inside the trust region,
+
+File: gsl-ref.info,  Node: Root Finding Caveats,  Next: Initializing the Solver,  Prev: Root Finding Overview,  Up: One dimensional Root-Finding
 
-          dx = - \alpha J^{-1} f(x) - \beta \nabla |f(x)|^2.
+34.2 Caveats
+============
 
-     This combination of Newton and gradient directions is referred to
-     as a "dogleg step".
+Note that root finding functions can only search for one root at a time.
+When there are several roots in the search area, the first root to be
+found will be returned; however it is difficult to predict which of the
+roots this will be.  _In most cases, no error will be reported if you
+try to find a root in an area where there is more than one._
+
+   Care must be taken when a function may have a multiple root (such as
+f(x) = (x-x_0)^2 or f(x) = (x-x_0)^3).  It is not possible to use
+root-bracketing algorithms on even-multiplicity roots.  For these
+algorithms the initial interval must contain a zero-crossing, where the
+function is negative at one end of the interval and positive at the
+other end.  Roots with even-multiplicity do not cross zero, but only
+touch it instantaneously.  Algorithms based on root bracketing will
+still work for odd-multiplicity roots (e.g.  cubic, quintic, ...).  Root
+polishing algorithms generally work with higher multiplicity roots, but
+at a reduced rate of convergence.  In these cases the "Steffenson
+algorithm" can be used to accelerate the convergence of multiple roots.
+
+   While it is not absolutely required that f have a root within the
+search region, numerical root finding functions should not be used
+haphazardly to check for the _existence_ of roots.  There are better
+ways to do this.  Because it is easy to create situations where
+numerical root finders can fail, it is a bad idea to throw a root finder
+at a function you do not know much about.  In general it is best to
+examine the function visually by plotting before searching for a root.
 
-     The proposed step is now tested by evaluating the function at the
-     resulting point, x'.  If the step reduces the norm of the function
-     sufficiently then it is accepted and size of the trust region is
-     increased.  If the proposed step fails to improve the solution then
-     the size of the trust region is decreased and another trial step is
-     computed.
+
+File: gsl-ref.info,  Node: Initializing the Solver,  Next: Providing the function to solve,  Prev: Root Finding Caveats,  Up: One dimensional Root-Finding
 
-     The speed of the algorithm is increased by computing the changes to
-     the Jacobian approximately, using a rank-1 update.  If two
-     successive attempts fail to reduce the residual then the full
-     Jacobian is recomputed.  The algorithm also monitors the progress
-     of the solution and returns an error if several steps fail to make
-     any improvement,
+34.3 Initializing the Solver
+============================
 
-     'GSL_ENOPROG'
-          the iteration is not making any progress, preventing the
-          algorithm from continuing.
+ -- Function: gsl_root_fsolver * gsl_root_fsolver_alloc (const
+          gsl_root_fsolver_type * T)
+     This function returns a pointer to a newly allocated instance of a
+     solver of type T.  For example, the following code creates an
+     instance of a bisection solver,
 
-     'GSL_ENOPROGJ'
-          re-evaluations of the Jacobian indicate that the iteration is
-          not making any progress, preventing the algorithm from
-          continuing.
+          const gsl_root_fsolver_type * T
+            = gsl_root_fsolver_bisection;
+          gsl_root_fsolver * s
+            = gsl_root_fsolver_alloc (T);
 
- -- Derivative Solver: gsl_multiroot_fdfsolver_hybridj
-     This algorithm is an unscaled version of 'hybridsj'.  The steps are
-     controlled by a spherical trust region |x' - x| < \delta, instead
-     of a generalized region.  This can be useful if the generalized
-     region estimated by 'hybridsj' is inappropriate.
+     If there is insufficient memory to create the solver then the
+     function returns a null pointer and the error handler is invoked
+     with an error code of 'GSL_ENOMEM'.
 
- -- Derivative Solver: gsl_multiroot_fdfsolver_newton
+ -- Function: gsl_root_fdfsolver * gsl_root_fdfsolver_alloc (const
+          gsl_root_fdfsolver_type * T)
+     This function returns a pointer to a newly allocated instance of a
+     derivative-based solver of type T.  For example, the following code
+     creates an instance of a Newton-Raphson solver,
 
-     Newton's Method is the standard root-polishing algorithm.  The
-     algorithm begins with an initial guess for the location of the
-     solution.  On each iteration a linear approximation to the function
-     F is used to estimate the step which will zero all the components
-     of the residual.  The iteration is defined by the following
-     sequence,
+          const gsl_root_fdfsolver_type * T
+            = gsl_root_fdfsolver_newton;
+          gsl_root_fdfsolver * s
+            = gsl_root_fdfsolver_alloc (T);
 
-          x -> x' = x - J^{-1} f(x)
+     If there is insufficient memory to create the solver then the
+     function returns a null pointer and the error handler is invoked
+     with an error code of 'GSL_ENOMEM'.
 
-     where the Jacobian matrix J is computed from the derivative
-     functions provided by F.  The step dx is obtained by solving the
-     linear system,
+ -- Function: int gsl_root_fsolver_set (gsl_root_fsolver * S,
+          gsl_function * F, double X_LOWER, double X_UPPER)
+     This function initializes, or reinitializes, an existing solver S
+     to use the function F and the initial search interval [X_LOWER,
+     X_UPPER].
 
-          J dx = - f(x)
+ -- Function: int gsl_root_fdfsolver_set (gsl_root_fdfsolver * S,
+          gsl_function_fdf * FDF, double ROOT)
+     This function initializes, or reinitializes, an existing solver S
+     to use the function and derivative FDF and the initial guess ROOT.
 
-     using LU decomposition.  If the Jacobian matrix is singular, an
-     error code of 'GSL_EDOM' is returned.
+ -- Function: void gsl_root_fsolver_free (gsl_root_fsolver * S)
+ -- Function: void gsl_root_fdfsolver_free (gsl_root_fdfsolver * S)
+     These functions free all the memory associated with the solver S.
 
- -- Derivative Solver: gsl_multiroot_fdfsolver_gnewton
-     This is a modified version of Newton's method which attempts to
-     improve global convergence by requiring every step to reduce the
-     Euclidean norm of the residual, |f(x)|.  If the Newton step leads
-     to an increase in the norm then a reduced step of relative size,
+ -- Function: const char * gsl_root_fsolver_name (const gsl_root_fsolver
+          * S)
+ -- Function: const char * gsl_root_fdfsolver_name (const
+          gsl_root_fdfsolver * S)
+     These functions return a pointer to the name of the solver.  For
+     example,
 
-          t = (\sqrt(1 + 6 r) - 1) / (3 r)
+          printf ("s is a '%s' solver\n",
+                  gsl_root_fsolver_name (s));
 
-     is proposed, with r being the ratio of norms |f(x')|^2/|f(x)|^2.
-     This procedure is repeated until a suitable step size is found.
+     would print something like 's is a 'bisection' solver'.
 
 
-File: gsl-ref.info,  Node: Algorithms without Derivatives,  Next: Example programs for Multidimensional Root finding,  Prev: Algorithms using Derivatives,  Up: Multidimensional Root-Finding
+File: gsl-ref.info,  Node: Providing the function to solve,  Next: Search Bounds and Guesses,  Prev: Initializing the Solver,  Up: One dimensional Root-Finding
 
-35.7 Algorithms without Derivatives
-===================================
+34.4 Providing the function to solve
+====================================
 
-The algorithms described in this section do not require any derivative
-information to be supplied by the user.  Any derivatives needed are
-approximated by finite differences.  Note that if the
-finite-differencing step size chosen by these routines is inappropriate,
-an explicit user-supplied numerical derivative can always be used with
-the algorithms described in the previous section.
+You must provide a continuous function of one variable for the root
+finders to operate on, and, sometimes, its first derivative.  In order
+to allow for general parameters the functions are defined by the
+following data types:
+
+ -- Data Type: gsl_function
+     This data type defines a general function with parameters.
+
+     'double (* function) (double X, void * PARAMS)'
+          this function should return the value f(x,params) for argument
+          X and parameters PARAMS
 
- -- Solver: gsl_multiroot_fsolver_hybrids
-     This is a version of the Hybrid algorithm which replaces calls to
-     the Jacobian function by its finite difference approximation.  The
-     finite difference approximation is computed using
-     'gsl_multiroots_fdjac' with a relative step size of
-     'GSL_SQRT_DBL_EPSILON'.  Note that this step size will not be
-     suitable for all problems.
+     'void * params'
+          a pointer to the parameters of the function
 
- -- Solver: gsl_multiroot_fsolver_hybrid
-     This is a finite difference version of the Hybrid algorithm without
-     internal scaling.
+   Here is an example for the general quadratic function,
 
- -- Solver: gsl_multiroot_fsolver_dnewton
+     f(x) = a x^2 + b x + c
 
-     The "discrete Newton algorithm" is the simplest method of solving a
-     multidimensional system.  It uses the Newton iteration
+with a = 3, b = 2, c = 1.  The following code defines a 'gsl_function'
+'F' which you could pass to a root finder as a function pointer:
 
-          x -> x - J^{-1} f(x)
+     struct my_f_params { double a; double b; double c; };
 
-     where the Jacobian matrix J is approximated by taking finite
-     differences of the function F.  The approximation scheme used by
-     this implementation is,
+     double
+     my_f (double x, void * p) {
+        struct my_f_params * params
+          = (struct my_f_params *)p;
+        double a = (params->a);
+        double b = (params->b);
+        double c = (params->c);
 
-          J_{ij} = (f_i(x + \delta_j) - f_i(x)) /  \delta_j
+        return  (a * x + b) * x + c;
+     }
 
-     where \delta_j is a step of size \sqrt\epsilon |x_j| with \epsilon
-     being the machine precision (\epsilon \approx 2.22 \times 10^-16).
-     The order of convergence of Newton's algorithm is quadratic, but
-     the finite differences require n^2 function evaluations on each
-     iteration.  The algorithm may become unstable if the finite
-     differences are not a good approximation to the true derivatives.
+     gsl_function F;
+     struct my_f_params params = { 3.0, 2.0, 1.0 };
 
- -- Solver: gsl_multiroot_fsolver_broyden
+     F.function = &my_f;
+     F.params = &params;
 
-     The "Broyden algorithm" is a version of the discrete Newton
-     algorithm which attempts to avoids the expensive update of the
-     Jacobian matrix on each iteration.  The changes to the Jacobian are
-     also approximated, using a rank-1 update,
+The function f(x) can be evaluated using the macro 'GSL_FN_EVAL(&F,x)'
+defined in 'gsl_math.h'.
 
-          J^{-1} \to J^{-1} - (J^{-1} df - dx) dx^T J^{-1} / dx^T J^{-1} df
+ -- Data Type: gsl_function_fdf
+     This data type defines a general function with parameters and its
+     first derivative.
+
+     'double (* f) (double X, void * PARAMS)'
+          this function should return the value of f(x,params) for
+          argument X and parameters PARAMS
+
+     'double (* df) (double X, void * PARAMS)'
+          this function should return the value of the derivative of F
+          with respect to X, f'(x,params), for argument X and parameters
+          PARAMS
+
+     'void (* fdf) (double X, void * PARAMS, double * F, double * DF)'
+          this function should set the values of the function F to
+          f(x,params) and its derivative DF to f'(x,params) for argument
+          X and parameters PARAMS.  This function provides an
+          optimization of the separate functions for f(x) and f'(x)--it
+          is always faster to compute the function and its derivative at
+          the same time.
 
-     where the vectors dx and df are the changes in x and f.  On the
-     first iteration the inverse Jacobian is estimated using finite
-     differences, as in the discrete Newton algorithm.
+     'void * params'
+          a pointer to the parameters of the function
 
-     This approximation gives a fast update but is unreliable if the
-     changes are not small, and the estimate of the inverse Jacobian
-     becomes worse as time passes.  The algorithm has a tendency to
-     become unstable unless it starts close to the root.  The Jacobian
-     is refreshed if this instability is detected (consult the source
-     for details).
+   Here is an example where f(x) = 2\exp(2x):
 
-     This algorithm is included only for demonstration purposes, and is
-     not recommended for serious use.
+     double
+     my_f (double x, void * params)
+     {
+        return exp (2 * x);
+     }
 
-
-File: gsl-ref.info,  Node: Example programs for Multidimensional Root finding,  Next: References and Further Reading for Multidimensional Root Finding,  Prev: Algorithms without Derivatives,  Up: Multidimensional Root-Finding
+     double
+     my_df (double x, void * params)
+     {
+        return 2 * exp (2 * x);
+     }
 
-35.8 Examples
-=============
+     void
+     my_fdf (double x, void * params,
+             double * f, double * df)
+     {
+        double t = exp (2 * x);
 
-The multidimensional solvers are used in a similar way to the
-one-dimensional root finding algorithms.  This first example
-demonstrates the 'hybrids' scaled-hybrid algorithm, which does not
-require derivatives.  The program solves the Rosenbrock system of
-equations,
+        *f = t;
+        *df = 2 * t;   /* uses existing value */
+     }
 
-     f_1 (x, y) = a (1 - x)
-     f_2 (x, y) = b (y - x^2)
+     gsl_function_fdf FDF;
 
-with a = 1, b = 10.  The solution of this system lies at (x,y) = (1,1)
-in a narrow valley.
+     FDF.f = &my_f;
+     FDF.df = &my_df;
+     FDF.fdf = &my_fdf;
+     FDF.params = 0;
 
-   The first stage of the program is to define the system of equations,
+The function f(x) can be evaluated using the macro
+'GSL_FN_FDF_EVAL_F(&FDF,x)' and the derivative f'(x) can be evaluated
+using the macro 'GSL_FN_FDF_EVAL_DF(&FDF,x)'.  Both the function y =
+f(x) and its derivative dy = f'(x) can be evaluated at the same time
+using the macro 'GSL_FN_FDF_EVAL_F_DF(&FDF,x,y,dy)'.  The macro stores
+f(x) in its Y argument and f'(x) in its DY argument--both of these
+should be pointers to 'double'.
 
-     #include <stdlib.h>
-     #include <stdio.h>
-     #include <gsl/gsl_vector.h>
-     #include <gsl/gsl_multiroots.h>
+
+File: gsl-ref.info,  Node: Search Bounds and Guesses,  Next: Root Finding Iteration,  Prev: Providing the function to solve,  Up: One dimensional Root-Finding
 
-     struct rparams
-       {
-         double a;
-         double b;
-       };
+34.5 Search Bounds and Guesses
+==============================
 
-     int
-     rosenbrock_f (const gsl_vector * x, void *params,
-                   gsl_vector * f)
-     {
-       double a = ((struct rparams *) params)->a;
-       double b = ((struct rparams *) params)->b;
+You provide either search bounds or an initial guess; this section
+explains how search bounds and guesses work and how function arguments
+control them.
 
-       const double x0 = gsl_vector_get (x, 0);
-       const double x1 = gsl_vector_get (x, 1);
+   A guess is simply an x value which is iterated until it is within the
+desired precision of a root.  It takes the form of a 'double'.
 
-       const double y0 = a * (1 - x0);
-       const double y1 = b * (x1 - x0 * x0);
+   Search bounds are the endpoints of an interval which is iterated
+until the length of the interval is smaller than the requested
+precision.  The interval is defined by two values, the lower limit and
+the upper limit.  Whether the endpoints are intended to be included in
+the interval or not depends on the context in which the interval is
+used.
 
-       gsl_vector_set (f, 0, y0);
-       gsl_vector_set (f, 1, y1);
+
+File: gsl-ref.info,  Node: Root Finding Iteration,  Next: Search Stopping Parameters,  Prev: Search Bounds and Guesses,  Up: One dimensional Root-Finding
 
-       return GSL_SUCCESS;
-     }
+34.6 Iteration
+==============
 
-The main program begins by creating the function object 'f', with the
-arguments '(x,y)' and parameters '(a,b)'.  The solver 's' is initialized
-to use this function, with the 'hybrids' method.
+The following functions drive the iteration of each algorithm.  Each
+function performs one iteration to update the state of any solver of the
+corresponding type.  The same functions work for all solvers so that
+different methods can be substituted at runtime without modifications to
+the code.
 
-     int
-     main (void)
-     {
-       const gsl_multiroot_fsolver_type *T;
-       gsl_multiroot_fsolver *s;
+ -- Function: int gsl_root_fsolver_iterate (gsl_root_fsolver * S)
+ -- Function: int gsl_root_fdfsolver_iterate (gsl_root_fdfsolver * S)
+     These functions perform a single iteration of the solver S.  If the
+     iteration encounters an unexpected problem then an error code will
+     be returned,
 
-       int status;
-       size_t i, iter = 0;
+     'GSL_EBADFUNC'
+          the iteration encountered a singular point where the function
+          or its derivative evaluated to 'Inf' or 'NaN'.
 
-       const size_t n = 2;
-       struct rparams p = {1.0, 10.0};
-       gsl_multiroot_function f = {&rosenbrock_f, n, &p};
+     'GSL_EZERODIV'
+          the derivative of the function vanished at the iteration
+          point, preventing the algorithm from continuing without a
+          division by zero.
+
+   The solver maintains a current best estimate of the root at all
+times.  The bracketing solvers also keep track of the current best
+interval bounding the root.  This information can be accessed with the
+following auxiliary functions,
 
-       double x_init[2] = {-10.0, -5.0};
-       gsl_vector *x = gsl_vector_alloc (n);
+ -- Function: double gsl_root_fsolver_root (const gsl_root_fsolver * S)
+ -- Function: double gsl_root_fdfsolver_root (const gsl_root_fdfsolver *
+          S)
+     These functions return the current estimate of the root for the
+     solver S.
 
-       gsl_vector_set (x, 0, x_init[0]);
-       gsl_vector_set (x, 1, x_init[1]);
+ -- Function: double gsl_root_fsolver_x_lower (const gsl_root_fsolver *
+          S)
+ -- Function: double gsl_root_fsolver_x_upper (const gsl_root_fsolver *
+          S)
+     These functions return the current bracketing interval for the
+     solver S.
 
-       T = gsl_multiroot_fsolver_hybrids;
-       s = gsl_multiroot_fsolver_alloc (T, 2);
-       gsl_multiroot_fsolver_set (s, &f, x);
+
+File: gsl-ref.info,  Node: Search Stopping Parameters,  Next: Root Bracketing Algorithms,  Prev: Root Finding Iteration,  Up: One dimensional Root-Finding
 
-       print_state (iter, s);
+34.7 Search Stopping Parameters
+===============================
 
-       do
-         {
-           iter++;
-           status = gsl_multiroot_fsolver_iterate (s);
+A root finding procedure should stop when one of the following
+conditions is true:
 
-           print_state (iter, s);
+   * A root has been found to within the user-specified precision.
 
-           if (status)   /* check if solver is stuck */
-             break;
+   * A user-specified maximum number of iterations has been reached.
 
-           status =
-             gsl_multiroot_test_residual (s->f, 1e-7);
-         }
-       while (status == GSL_CONTINUE && iter < 1000);
+   * An error has occurred.
 
-       printf ("status = %s\n", gsl_strerror (status));
+The handling of these conditions is under user control.  The functions
+below allow the user to test the precision of the current result in
+several standard ways.
 
-       gsl_multiroot_fsolver_free (s);
-       gsl_vector_free (x);
-       return 0;
-     }
+ -- Function: int gsl_root_test_interval (double X_LOWER, double
+          X_UPPER, double EPSABS, double EPSREL)
+     This function tests for the convergence of the interval [X_LOWER,
+     X_UPPER] with absolute error EPSABS and relative error EPSREL.  The
+     test returns 'GSL_SUCCESS' if the following condition is achieved,
 
-Note that it is important to check the return status of each solver
-step, in case the algorithm becomes stuck.  If an error condition is
-detected, indicating that the algorithm cannot proceed, then the error
-can be reported to the user, a new starting point chosen or a different
-algorithm used.
+          |a - b| < epsabs + epsrel min(|a|,|b|)
 
-   The intermediate state of the solution is displayed by the following
-function.  The solver state contains the vector 's->x' which is the
-current position, and the vector 's->f' with corresponding function
-values.
+     when the interval x = [a,b] does not include the origin.  If the
+     interval includes the origin then \min(|a|,|b|) is replaced by zero
+     (which is the minimum value of |x| over the interval).  This
+     ensures that the relative error is accurately estimated for roots
+     close to the origin.
 
-     int
-     print_state (size_t iter, gsl_multiroot_fsolver * s)
-     {
-       printf ("iter = %3u x = % .3f % .3f "
-               "f(x) = % .3e % .3e\n",
-               iter,
-               gsl_vector_get (s->x, 0),
-               gsl_vector_get (s->x, 1),
-               gsl_vector_get (s->f, 0),
-               gsl_vector_get (s->f, 1));
-     }
+     This condition on the interval also implies that any estimate of
+     the root r in the interval satisfies the same condition with
+     respect to the true root r^*,
 
-Here are the results of running the program.  The algorithm is started
-at (-10,-5) far from the solution.  Since the solution is hidden in a
-narrow valley the earliest steps follow the gradient of the function
-downhill, in an attempt to reduce the large value of the residual.  Once
-the root has been approximately located, on iteration 8, the Newton
-behavior takes over and convergence is very rapid.
+          |r - r^*| < epsabs + epsrel r^*
 
-     iter =  0 x = -10.000  -5.000  f(x) = 1.100e+01 -1.050e+03
-     iter =  1 x = -10.000  -5.000  f(x) = 1.100e+01 -1.050e+03
-     iter =  2 x =  -3.976  24.827  f(x) = 4.976e+00  9.020e+01
-     iter =  3 x =  -3.976  24.827  f(x) = 4.976e+00  9.020e+01
-     iter =  4 x =  -3.976  24.827  f(x) = 4.976e+00  9.020e+01
-     iter =  5 x =  -1.274  -5.680  f(x) = 2.274e+00 -7.302e+01
-     iter =  6 x =  -1.274  -5.680  f(x) = 2.274e+00 -7.302e+01
-     iter =  7 x =   0.249   0.298  f(x) = 7.511e-01  2.359e+00
-     iter =  8 x =   0.249   0.298  f(x) = 7.511e-01  2.359e+00
-     iter =  9 x =   1.000   0.878  f(x) = 1.268e-10 -1.218e+00
-     iter = 10 x =   1.000   0.989  f(x) = 1.124e-11 -1.080e-01
-     iter = 11 x =   1.000   1.000  f(x) = 0.000e+00  0.000e+00
-     status = success
+     assuming that the true root r^* is contained within the interval.
 
-Note that the algorithm does not update the location on every iteration.
-Some iterations are used to adjust the trust-region parameter, after
-trying a step which was found to be divergent, or to recompute the
-Jacobian, when poor convergence behavior is detected.
+ -- Function: int gsl_root_test_delta (double X1, double X0, double
+          EPSABS, double EPSREL)
 
-   The next example program adds derivative information, in order to
-accelerate the solution.  There are two derivative functions
-'rosenbrock_df' and 'rosenbrock_fdf'.  The latter computes both the
-function and its derivative simultaneously.  This allows the
-optimization of any common terms.  For simplicity we substitute calls to
-the separate 'f' and 'df' functions at this point in the code below.
+     This function tests for the convergence of the sequence ..., X0, X1
+     with absolute error EPSABS and relative error EPSREL.  The test
+     returns 'GSL_SUCCESS' if the following condition is achieved,
 
-     int
-     rosenbrock_df (const gsl_vector * x, void *params,
-                    gsl_matrix * J)
-     {
-       const double a = ((struct rparams *) params)->a;
-       const double b = ((struct rparams *) params)->b;
+          |x_1 - x_0| < epsabs + epsrel |x_1|
 
-       const double x0 = gsl_vector_get (x, 0);
+     and returns 'GSL_CONTINUE' otherwise.
 
-       const double df00 = -a;
-       const double df01 = 0;
-       const double df10 = -2 * b  * x0;
-       const double df11 = b;
+ -- Function: int gsl_root_test_residual (double F, double EPSABS)
+     This function tests the residual value F against the absolute error
+     bound EPSABS.  The test returns 'GSL_SUCCESS' if the following
+     condition is achieved,
 
-       gsl_matrix_set (J, 0, 0, df00);
-       gsl_matrix_set (J, 0, 1, df01);
-       gsl_matrix_set (J, 1, 0, df10);
-       gsl_matrix_set (J, 1, 1, df11);
+          |f| < epsabs
 
-       return GSL_SUCCESS;
-     }
+     and returns 'GSL_CONTINUE' otherwise.  This criterion is suitable
+     for situations where the precise location of the root, x, is
+     unimportant provided a value can be found where the residual,
+     |f(x)|, is small enough.
 
-     int
-     rosenbrock_fdf (const gsl_vector * x, void *params,
-                     gsl_vector * f, gsl_matrix * J)
-     {
-       rosenbrock_f (x, params, f);
-       rosenbrock_df (x, params, J);
+
+File: gsl-ref.info,  Node: Root Bracketing Algorithms,  Next: Root Finding Algorithms using Derivatives,  Prev: Search Stopping Parameters,  Up: One dimensional Root-Finding
 
-       return GSL_SUCCESS;
-     }
+34.8 Root Bracketing Algorithms
+===============================
 
-The main program now makes calls to the corresponding 'fdfsolver'
-versions of the functions,
+The root bracketing algorithms described in this section require an
+initial interval which is guaranteed to contain a root--if a and b are
+the endpoints of the interval then f(a) must differ in sign from f(b).
+This ensures that the function crosses zero at least once in the
+interval.  If a valid initial interval is used then these algorithm
+cannot fail, provided the function is well-behaved.
+
+   Note that a bracketing algorithm cannot find roots of even degree,
+since these do not cross the x-axis.
+
+ -- Solver: gsl_root_fsolver_bisection
+
+     The "bisection algorithm" is the simplest method of bracketing the
+     roots of a function.  It is the slowest algorithm provided by the
+     library, with linear convergence.
+
+     On each iteration, the interval is bisected and the value of the
+     function at the midpoint is calculated.  The sign of this value is
+     used to determine which half of the interval does not contain a
+     root.  That half is discarded to give a new, smaller interval
+     containing the root.  This procedure can be continued indefinitely
+     until the interval is sufficiently small.
+
+     At any time the current estimate of the root is taken as the
+     midpoint of the interval.
+
+ -- Solver: gsl_root_fsolver_falsepos
+
+     The "false position algorithm" is a method of finding roots based
+     on linear interpolation.  Its convergence is linear, but it is
+     usually faster than bisection.
+
+     On each iteration a line is drawn between the endpoints (a,f(a))
+     and (b,f(b)) and the point where this line crosses the x-axis taken
+     as a "midpoint".  The value of the function at this point is
+     calculated and its sign is used to determine which side of the
+     interval does not contain a root.  That side is discarded to give a
+     new, smaller interval containing the root.  This procedure can be
+     continued indefinitely until the interval is sufficiently small.
+
+     The best estimate of the root is taken from the linear
+     interpolation of the interval on the current iteration.
+
+ -- Solver: gsl_root_fsolver_brent
+
+     The "Brent-Dekker method" (referred to here as "Brent's method")
+     combines an interpolation strategy with the bisection algorithm.
+     This produces a fast algorithm which is still robust.
+
+     On each iteration Brent's method approximates the function using an
+     interpolating curve.  On the first iteration this is a linear
+     interpolation of the two endpoints.  For subsequent iterations the
+     algorithm uses an inverse quadratic fit to the last three points,
+     for higher accuracy.  The intercept of the interpolating curve with
+     the x-axis is taken as a guess for the root.  If it lies within the
+     bounds of the current interval then the interpolating point is
+     accepted, and used to generate a smaller interval.  If the
+     interpolating point is not accepted then the algorithm falls back
+     to an ordinary bisection step.
 
-     int
-     main (void)
-     {
-       const gsl_multiroot_fdfsolver_type *T;
-       gsl_multiroot_fdfsolver *s;
+     The best estimate of the root is taken from the most recent
+     interpolation or bisection.
 
-       int status;
-       size_t i, iter = 0;
+
+File: gsl-ref.info,  Node: Root Finding Algorithms using Derivatives,  Next: Root Finding Examples,  Prev: Root Bracketing Algorithms,  Up: One dimensional Root-Finding
 
-       const size_t n = 2;
-       struct rparams p = {1.0, 10.0};
-       gsl_multiroot_function_fdf f = {&rosenbrock_f,
-                                       &rosenbrock_df,
-                                       &rosenbrock_fdf,
-                                       n, &p};
+34.9 Root Finding Algorithms using Derivatives
+==============================================
 
-       double x_init[2] = {-10.0, -5.0};
-       gsl_vector *x = gsl_vector_alloc (n);
+The root polishing algorithms described in this section require an
+initial guess for the location of the root.  There is no absolute
+guarantee of convergence--the function must be suitable for this
+technique and the initial guess must be sufficiently close to the root
+for it to work.  When these conditions are satisfied then convergence is
+quadratic.
 
-       gsl_vector_set (x, 0, x_init[0]);
-       gsl_vector_set (x, 1, x_init[1]);
+   These algorithms make use of both the function and its derivative.
 
-       T = gsl_multiroot_fdfsolver_gnewton;
-       s = gsl_multiroot_fdfsolver_alloc (T, n);
-       gsl_multiroot_fdfsolver_set (s, &f, x);
+ -- Derivative Solver: gsl_root_fdfsolver_newton
 
-       print_state (iter, s);
+     Newton's Method is the standard root-polishing algorithm.  The
+     algorithm begins with an initial guess for the location of the
+     root.  On each iteration, a line tangent to the function f is drawn
+     at that position.  The point where this line crosses the x-axis
+     becomes the new guess.  The iteration is defined by the following
+     sequence,
 
-       do
-         {
-           iter++;
+          x_{i+1} = x_i - f(x_i)/f'(x_i)
 
-           status = gsl_multiroot_fdfsolver_iterate (s);
+     Newton's method converges quadratically for single roots, and
+     linearly for multiple roots.
 
-           print_state (iter, s);
+ -- Derivative Solver: gsl_root_fdfsolver_secant
 
-           if (status)
-             break;
+     The "secant method" is a simplified version of Newton's method
+     which does not require the computation of the derivative on every
+     step.
 
-           status = gsl_multiroot_test_residual (s->f, 1e-7);
-         }
-       while (status == GSL_CONTINUE && iter < 1000);
+     On its first iteration the algorithm begins with Newton's method,
+     using the derivative to compute a first step,
 
-       printf ("status = %s\n", gsl_strerror (status));
+          x_1 = x_0 - f(x_0)/f'(x_0)
 
-       gsl_multiroot_fdfsolver_free (s);
-       gsl_vector_free (x);
-       return 0;
-     }
+     Subsequent iterations avoid the evaluation of the derivative by
+     replacing it with a numerical estimate, the slope of the line
+     through the previous two points,
 
-The addition of derivative information to the 'hybrids' solver does not
-make any significant difference to its behavior, since it able to
-approximate the Jacobian numerically with sufficient accuracy.  To
-illustrate the behavior of a different derivative solver we switch to
-'gnewton'.  This is a traditional Newton solver with the constraint that
-it scales back its step if the full step would lead "uphill".  Here is
-the output for the 'gnewton' algorithm,
+          x_{i+1} = x_i f(x_i) / f'_{est} where
+           f'_{est} = (f(x_i) - f(x_{i-1})/(x_i - x_{i-1})
 
-     iter = 0 x = -10.000  -5.000 f(x) =  1.100e+01 -1.050e+03
-     iter = 1 x =  -4.231 -65.317 f(x) =  5.231e+00 -8.321e+02
-     iter = 2 x =   1.000 -26.358 f(x) = -8.882e-16 -2.736e+02
-     iter = 3 x =   1.000   1.000 f(x) = -2.220e-16 -4.441e-15
-     status = success
+     When the derivative does not change significantly in the vicinity
+     of the root the secant method gives a useful saving.
+     Asymptotically the secant method is faster than Newton's method
+     whenever the cost of evaluating the derivative is more than 0.44
+     times the cost of evaluating the function itself.  As with all
+     methods of computing a numerical derivative the estimate can suffer
+     from cancellation errors if the separation of the points becomes
+     too small.
 
-The convergence is much more rapid, but takes a wide excursion out to
-the point (-4.23,-65.3).  This could cause the algorithm to go astray in
-a realistic application.  The hybrid algorithm follows the downhill path
-to the solution more reliably.
+     On single roots, the method has a convergence of order (1 + \sqrt
+     5)/2 (approximately 1.62).  It converges linearly for multiple
+     roots.
 
-
-File: gsl-ref.info,  Node: References and Further Reading for Multidimensional Root Finding,  Prev: Example programs for Multidimensional Root finding,  Up: Multidimensional Root-Finding
+ -- Derivative Solver: gsl_root_fdfsolver_steffenson
 
-35.9 References and Further Reading
-===================================
+     The "Steffenson Method"(1) provides the fastest convergence of all
+     the routines.  It combines the basic Newton algorithm with an
+     Aitken "delta-squared" acceleration.  If the Newton iterates are
+     x_i then the acceleration procedure generates a new sequence R_i,
 
-The original version of the Hybrid method is described in the following
-articles by Powell,
+          R_i = x_i - (x_{i+1} - x_i)^2 / (x_{i+2} - 2 x_{i+1} + x_{i})
 
-     M.J.D. Powell, "A Hybrid Method for Nonlinear Equations" (Chap 6, p
-     87-114) and "A Fortran Subroutine for Solving systems of Nonlinear
-     Algebraic Equations" (Chap 7, p 115-161), in 'Numerical Methods for
-     Nonlinear Algebraic Equations', P. Rabinowitz, editor.  Gordon and
-     Breach, 1970.
+     which converges faster than the original sequence under reasonable
+     conditions.  The new sequence requires three terms before it can
+     produce its first value so the method returns accelerated values on
+     the second and subsequent iterations.  On the first iteration it
+     returns the ordinary Newton estimate.  The Newton iterate is also
+     returned if the denominator of the acceleration term ever becomes
+     zero.
 
-The following papers are also relevant to the algorithms described in
-this section,
+     As with all acceleration procedures this method can become unstable
+     if the function is not well-behaved.
 
-     J.J. More', M.Y. Cosnard, "Numerical Solution of Nonlinear
-     Equations", 'ACM Transactions on Mathematical Software', Vol 5, No
-     1, (1979), p 64-85
+   ---------- Footnotes ----------
 
-     C.G. Broyden, "A Class of Methods for Solving Nonlinear
-     Simultaneous Equations", 'Mathematics of Computation', Vol 19
-     (1965), p 577-593
+   (1) J.F. Steffensen (1873-1961).  The spelling used in the name of
+the function is slightly incorrect, but has been preserved to avoid
+incompatibility.
 
-     J.J. More', B.S. Garbow, K.E. Hillstrom, "Testing Unconstrained
-     Optimization Software", ACM Transactions on Mathematical Software,
-     Vol 7, No 1 (1981), p 17-41
+
+File: gsl-ref.info,  Node: Root Finding Examples,  Next: Root Finding References and Further Reading,  Prev: Root Finding Algorithms using Derivatives,  Up: One dimensional Root-Finding
+
+34.10 Examples
+==============
+
+For any root finding algorithm we need to prepare the function to be
+solved.  For this example we will use the general quadratic equation
+described earlier.  We first need a header file ('demo_fn.h') to define
+the function parameters,
+
+     struct quadratic_params
+       {
+         double a, b, c;
+       };
+
+     double quadratic (double x, void *params);
+     double quadratic_deriv (double x, void *params);
+     void quadratic_fdf (double x, void *params,
+                         double *y, double *dy);
+
+We place the function definitions in a separate file ('demo_fn.c'),
+
+     double
+     quadratic (double x, void *params)
+     {
+       struct quadratic_params *p
+         = (struct quadratic_params *) params;
+
+       double a = p->a;
+       double b = p->b;
+       double c = p->c;
+
+       return (a * x + b) * x + c;
+     }
+
+     double
+     quadratic_deriv (double x, void *params)
+     {
+       struct quadratic_params *p
+         = (struct quadratic_params *) params;
+
+       double a = p->a;
+       double b = p->b;
+
+       return 2.0 * a * x + b;
+     }
+
+     void
+     quadratic_fdf (double x, void *params,
+                    double *y, double *dy)
+     {
+       struct quadratic_params *p
+         = (struct quadratic_params *) params;
+
+       double a = p->a;
+       double b = p->b;
+       double c = p->c;
+
+       *y = (a * x + b) * x + c;
+       *dy = 2.0 * a * x + b;
+     }
+
+The first program uses the function solver 'gsl_root_fsolver_brent' for
+Brent's method and the general quadratic defined above to solve the
+following equation,
+
+     x^2 - 5 = 0
+
+with solution x = \sqrt 5 = 2.236068...
+
+     #include <stdio.h>
+     #include <gsl/gsl_errno.h>
+     #include <gsl/gsl_math.h>
+     #include <gsl/gsl_roots.h>
+
+     #include "demo_fn.h"
+     #include "demo_fn.c"
+
+     int
+     main (void)
+     {
+       int status;
+       int iter = 0, max_iter = 100;
+       const gsl_root_fsolver_type *T;
+       gsl_root_fsolver *s;
+       double r = 0, r_expected = sqrt (5.0);
+       double x_lo = 0.0, x_hi = 5.0;
+       gsl_function F;
+       struct quadratic_params params = {1.0, 0.0, -5.0};
+
+       F.function = &quadratic;
+       F.params = &params;
+
+       T = gsl_root_fsolver_brent;
+       s = gsl_root_fsolver_alloc (T);
+       gsl_root_fsolver_set (s, &F, x_lo, x_hi);
+
+       printf ("using %s method\n",
+               gsl_root_fsolver_name (s));
+
+       printf ("%5s [%9s, %9s] %9s %10s %9s\n",
+               "iter", "lower", "upper", "root",
+               "err", "err(est)");
+
+       do
+         {
+           iter++;
+           status = gsl_root_fsolver_iterate (s);
+           r = gsl_root_fsolver_root (s);
+           x_lo = gsl_root_fsolver_x_lower (s);
+           x_hi = gsl_root_fsolver_x_upper (s);
+           status = gsl_root_test_interval (x_lo, x_hi,
+                                            0, 0.001);
+
+           if (status == GSL_SUCCESS)
+             printf ("Converged:\n");
+
+           printf ("%5d [%.7f, %.7f] %.7f %+.7f %.7f\n",
+                   iter, x_lo, x_hi,
+                   r, r - r_expected,
+                   x_hi - x_lo);
+         }
+       while (status == GSL_CONTINUE && iter < max_iter);
+
+       gsl_root_fsolver_free (s);
+
+       return status;
+     }
+
+Here are the results of the iterations,
+
+     $ ./a.out
+     using brent method
+      iter [    lower,     upper]      root        err  err(est)
+         1 [1.0000000, 5.0000000] 1.0000000 -1.2360680 4.0000000
+         2 [1.0000000, 3.0000000] 3.0000000 +0.7639320 2.0000000
+         3 [2.0000000, 3.0000000] 2.0000000 -0.2360680 1.0000000
+         4 [2.2000000, 3.0000000] 2.2000000 -0.0360680 0.8000000
+         5 [2.2000000, 2.2366300] 2.2366300 +0.0005621 0.0366300
+     Converged:
+         6 [2.2360634, 2.2366300] 2.2360634 -0.0000046 0.0005666
+
+If the program is modified to use the bisection solver instead of
+Brent's method, by changing 'gsl_root_fsolver_brent' to
+'gsl_root_fsolver_bisection' the slower convergence of the Bisection
+method can be observed,
+
+     $ ./a.out
+     using bisection method
+      iter [    lower,     upper]      root        err  err(est)
+         1 [0.0000000, 2.5000000] 1.2500000 -0.9860680 2.5000000
+         2 [1.2500000, 2.5000000] 1.8750000 -0.3610680 1.2500000
+         3 [1.8750000, 2.5000000] 2.1875000 -0.0485680 0.6250000
+         4 [2.1875000, 2.5000000] 2.3437500 +0.1076820 0.3125000
+         5 [2.1875000, 2.3437500] 2.2656250 +0.0295570 0.1562500
+         6 [2.1875000, 2.2656250] 2.2265625 -0.0095055 0.0781250
+         7 [2.2265625, 2.2656250] 2.2460938 +0.0100258 0.0390625
+         8 [2.2265625, 2.2460938] 2.2363281 +0.0002601 0.0195312
+         9 [2.2265625, 2.2363281] 2.2314453 -0.0046227 0.0097656
+        10 [2.2314453, 2.2363281] 2.2338867 -0.0021813 0.0048828
+        11 [2.2338867, 2.2363281] 2.2351074 -0.0009606 0.0024414
+     Converged:
+        12 [2.2351074, 2.2363281] 2.2357178 -0.0003502 0.0012207
+
+   The next program solves the same function using a derivative solver
+instead.
+
+     #include <stdio.h>
+     #include <gsl/gsl_errno.h>
+     #include <gsl/gsl_math.h>
+     #include <gsl/gsl_roots.h>
+
+     #include "demo_fn.h"
+     #include "demo_fn.c"
+
+     int
+     main (void)
+     {
+       int status;
+       int iter = 0, max_iter = 100;
+       const gsl_root_fdfsolver_type *T;
+       gsl_root_fdfsolver *s;
+       double x0, x = 5.0, r_expected = sqrt (5.0);
+       gsl_function_fdf FDF;
+       struct quadratic_params params = {1.0, 0.0, -5.0};
+
+       FDF.f = &quadratic;
+       FDF.df = &quadratic_deriv;
+       FDF.fdf = &quadratic_fdf;
+       FDF.params = &params;
+
+       T = gsl_root_fdfsolver_newton;
+       s = gsl_root_fdfsolver_alloc (T);
+       gsl_root_fdfsolver_set (s, &FDF, x);
+
+       printf ("using %s method\n",
+               gsl_root_fdfsolver_name (s));
+
+       printf ("%-5s %10s %10s %10s\n",
+               "iter", "root", "err", "err(est)");
+       do
+         {
+           iter++;
+           status = gsl_root_fdfsolver_iterate (s);
+           x0 = x;
+           x = gsl_root_fdfsolver_root (s);
+           status = gsl_root_test_delta (x, x0, 0, 1e-3);
+
+           if (status == GSL_SUCCESS)
+             printf ("Converged:\n");
+
+           printf ("%5d %10.7f %+10.7f %10.7f\n",
+                   iter, x, x - r_expected, x - x0);
+         }
+       while (status == GSL_CONTINUE && iter < max_iter);
+
+       gsl_root_fdfsolver_free (s);
+       return status;
+     }
+
+Here are the results for Newton's method,
+
+     $ ./a.out
+     using newton method
+     iter        root        err   err(est)
+         1  3.0000000 +0.7639320 -2.0000000
+         2  2.3333333 +0.0972654 -0.6666667
+         3  2.2380952 +0.0020273 -0.0952381
+     Converged:
+         4  2.2360689 +0.0000009 -0.0020263
+
+Note that the error can be estimated more accurately by taking the
+difference between the current iterate and next iterate rather than the
+previous iterate.  The other derivative solvers can be investigated by
+changing 'gsl_root_fdfsolver_newton' to 'gsl_root_fdfsolver_secant' or
+'gsl_root_fdfsolver_steffenson'.
 
 
-File: gsl-ref.info,  Node: Multidimensional Minimization,  Next: Least-Squares Fitting,  Prev: Multidimensional Root-Finding,  Up: Top
+File: gsl-ref.info,  Node: Root Finding References and Further Reading,  Prev: Root Finding Examples,  Up: One dimensional Root-Finding
 
-36 Multidimensional Minimization
-********************************
+34.11 References and Further Reading
+====================================
+
+For information on the Brent-Dekker algorithm see the following two
+papers,
+
+     R. P. Brent, "An algorithm with guaranteed convergence for finding
+     a zero of a function", 'Computer Journal', 14 (1971) 422-425
+
+     J. C. P. Bus and T. J. Dekker, "Two Efficient Algorithms with
+     Guaranteed Convergence for Finding a Zero of a Function", 'ACM
+     Transactions of Mathematical Software', Vol. 1 No. 4 (1975) 330-345
+
+
+File: gsl-ref.info,  Node: One dimensional Minimization,  Next: Multidimensional Root-Finding,  Prev: One dimensional Root-Finding,  Up: Top
+
+35 One dimensional Minimization
+*******************************
 
 This chapter describes routines for finding minima of arbitrary
-multidimensional functions.  The library provides low level components
+one-dimensional functions.  The library provides low level components
 for a variety of iterative minimizers and convergence tests.  These can
-be combined by the user to achieve the desired solution, while providing
-full access to the intermediate steps of the algorithms.  Each class of
+be combined by the user to achieve the desired solution, with full
+access to the intermediate steps of the algorithms.  Each class of
 methods uses the same framework, so that you can switch between
 minimizers at runtime without needing to recompile your program.  Each
 instance of a minimizer keeps track of its own state, allowing the
-minimizers to be used in multi-threaded programs.  The minimization
-algorithms can be used to maximize a function by inverting its sign.
+minimizers to be used in multi-threaded programs.
 
-   The header file 'gsl_multimin.h' contains prototypes for the
-minimization functions and related declarations.
+   The header file 'gsl_min.h' contains prototypes for the minimization
+functions and related declarations.  To use the minimization algorithms
+to find the maximum of a function simply invert its sign.
 
 * Menu:
 
-* Multimin Overview::           
-* Multimin Caveats::            
-* Initializing the Multidimensional Minimizer::  
-* Providing a function to minimize::  
-* Multimin Iteration::          
-* Multimin Stopping Criteria::  
-* Multimin Algorithms with Derivatives::  
-* Multimin Algorithms without Derivatives::  
-* Multimin Examples::           
-* Multimin References and Further Reading::  
+* Minimization Overview::       
+* Minimization Caveats::        
+* Initializing the Minimizer::  
+* Providing the function to minimize::  
+* Minimization Iteration::      
+* Minimization Stopping Parameters::  
+* Minimization Algorithms::     
+* Minimization Examples::       
+* Minimization References and Further Reading::  
 
 
-File: gsl-ref.info,  Node: Multimin Overview,  Next: Multimin Caveats,  Up: Multidimensional Minimization
+File: gsl-ref.info,  Node: Minimization Overview,  Next: Minimization Caveats,  Up: One dimensional Minimization
 
-36.1 Overview
+35.1 Overview
 =============
 
-The problem of multidimensional minimization requires finding a point x
-such that the scalar function,
-
-     f(x_1, ..., x_n)
-
-takes a value which is lower than at any neighboring point.  For smooth
-functions the gradient g = \nabla f vanishes at the minimum.  In general
-there are no bracketing methods available for the minimization of
-n-dimensional functions.  The algorithms proceed from an initial guess
-using a search algorithm which attempts to move in a downhill direction.
-
-   Algorithms making use of the gradient of the function perform a
-one-dimensional line minimisation along this direction until the lowest
-point is found to a suitable tolerance.  The search direction is then
-updated with local information from the function and its derivatives,
-and the whole process repeated until the true n-dimensional minimum is
-found.
-
-   Algorithms which do not require the gradient of the function use
-different strategies.  For example, the Nelder-Mead Simplex algorithm
-maintains n+1 trial parameter vectors as the vertices of a n-dimensional
-simplex.  On each iteration it tries to improve the worst vertex of the
-simplex by geometrical transformations.  The iterations are continued
-until the overall size of the simplex has decreased sufficiently.
-
-   Both types of algorithms use a standard framework.  The user provides
-a high-level driver for the algorithms, and the library provides the
-individual functions necessary for each of the steps.  There are three
-main phases of the iteration.  The steps are,
+The minimization algorithms begin with a bounded region known to contain
+a minimum.  The region is described by a lower bound a and an upper
+bound b, with an estimate of the location of the minimum x.
+
+The value of the function at x must be less than the value of the
+function at the ends of the interval,
+
+     f(a) > f(x) < f(b)
+
+This condition guarantees that a minimum is contained somewhere within
+the interval.  On each iteration a new point x' is selected using one of
+the available algorithms.  If the new point is a better estimate of the
+minimum, i.e. where f(x') < f(x), then the current estimate of the
+minimum x is updated.  The new point also allows the size of the bounded
+interval to be reduced, by choosing the most compact set of points which
+satisfies the constraint f(a) > f(x) < f(b).  The interval is reduced
+until it encloses the true minimum to a desired tolerance.  This
+provides a best estimate of the location of the minimum and a rigorous
+error estimate.
+
+   Several bracketing algorithms are available within a single
+framework.  The user provides a high-level driver for the algorithm, and
+the library provides the individual functions necessary for each of the
+steps.  There are three main phases of the iteration.  The steps are,
 
    * initialize minimizer state, S, for algorithm T
 
@@ -950,9498 +1453,5588 @@
 
    * test S for convergence, and repeat iteration if necessary
 
-Each iteration step consists either of an improvement to the
-line-minimisation in the current direction or an update to the search
-direction itself.  The state for the minimizers is held in a
-'gsl_multimin_fdfminimizer' struct or a 'gsl_multimin_fminimizer'
-struct.
+The state for the minimizers is held in a 'gsl_min_fminimizer' struct.
+The updating procedure uses only function evaluations (not derivatives).
 
 
-File: gsl-ref.info,  Node: Multimin Caveats,  Next: Initializing the Multidimensional Minimizer,  Prev: Multimin Overview,  Up: Multidimensional Minimization
+File: gsl-ref.info,  Node: Minimization Caveats,  Next: Initializing the Minimizer,  Prev: Minimization Overview,  Up: One dimensional Minimization
 
-36.2 Caveats
+35.2 Caveats
 ============
 
-Note that the minimization algorithms can only search for one local
-minimum at a time.  When there are several local minima in the search
-area, the first minimum to be found will be returned; however it is
-difficult to predict which of the minima this will be.  In most cases,
-no error will be reported if you try to find a local minimum in an area
-where there is more than one.
-
-   It is also important to note that the minimization algorithms find
-local minima; there is no way to determine whether a minimum is a global
-minimum of the function in question.
+Note that minimization functions can only search for one minimum at a
+time.  When there are several minima in the search area, the first
+minimum to be found will be returned; however it is difficult to predict
+which of the minima this will be.  _In most cases, no error will be
+reported if you try to find a minimum in an area where there is more
+than one._
+
+   With all minimization algorithms it can be difficult to determine the
+location of the minimum to full numerical precision.  The behavior of
+the function in the region of the minimum x^* can be approximated by a
+Taylor expansion,
+
+     y = f(x^*) + (1/2) f''(x^*) (x - x^*)^2
+
+and the second term of this expansion can be lost when added to the
+first term at finite precision.  This magnifies the error in locating
+x^*, making it proportional to \sqrt \epsilon (where \epsilon is the
+relative accuracy of the floating point numbers).  For functions with
+higher order minima, such as x^4, the magnification of the error is
+correspondingly worse.  The best that can be achieved is to converge to
+the limit of numerical accuracy in the function values, rather than the
+location of the minimum itself.
 
 
-File: gsl-ref.info,  Node: Initializing the Multidimensional Minimizer,  Next: Providing a function to minimize,  Prev: Multimin Caveats,  Up: Multidimensional Minimization
-
-36.3 Initializing the Multidimensional Minimizer
-================================================
+File: gsl-ref.info,  Node: Initializing the Minimizer,  Next: Providing the function to minimize,  Prev: Minimization Caveats,  Up: One dimensional Minimization
 
-The following function initializes a multidimensional minimizer.  The
-minimizer itself depends only on the dimension of the problem and the
-algorithm and can be reused for different problems.
+35.3 Initializing the Minimizer
+===============================
 
- -- Function: gsl_multimin_fdfminimizer *
-          gsl_multimin_fdfminimizer_alloc (const
-          gsl_multimin_fdfminimizer_type * T, size_t N)
- -- Function: gsl_multimin_fminimizer * gsl_multimin_fminimizer_alloc
-          (const gsl_multimin_fminimizer_type * T, size_t N)
+ -- Function: gsl_min_fminimizer * gsl_min_fminimizer_alloc (const
+          gsl_min_fminimizer_type * T)
      This function returns a pointer to a newly allocated instance of a
-     minimizer of type T for an N-dimension function.  If there is
-     insufficient memory to create the minimizer then the function
-     returns a null pointer and the error handler is invoked with an
-     error code of 'GSL_ENOMEM'.
+     minimizer of type T.  For example, the following code creates an
+     instance of a golden section minimizer,
 
- -- Function: int gsl_multimin_fdfminimizer_set
-          (gsl_multimin_fdfminimizer * S, gsl_multimin_function_fdf *
-          FDF, const gsl_vector * X, double STEP_SIZE, double TOL)
- -- Function: int gsl_multimin_fminimizer_set (gsl_multimin_fminimizer *
-          S, gsl_multimin_function * F, const gsl_vector * X, const
-          gsl_vector * STEP_SIZE)
-     The function 'gsl_multimin_fdfminimizer_set' initializes the
-     minimizer S to minimize the function FDF starting from the initial
-     point X.  The size of the first trial step is given by STEP_SIZE.
-     The accuracy of the line minimization is specified by TOL.  The
-     precise meaning of this parameter depends on the method used.
-     Typically the line minimization is considered successful if the
-     gradient of the function g is orthogonal to the current search
-     direction p to a relative accuracy of TOL, where dot(p,g) < tol |p|
-     |g|.  A TOL value of 0.1 is suitable for most purposes, since line
-     minimization only needs to be carried out approximately.  Note that
-     setting TOL to zero will force the use of "exact" line-searches,
-     which are extremely expensive.
+          const gsl_min_fminimizer_type * T
+            = gsl_min_fminimizer_goldensection;
+          gsl_min_fminimizer * s
+            = gsl_min_fminimizer_alloc (T);
 
-     The function 'gsl_multimin_fminimizer_set' initializes the
-     minimizer S to minimize the function F, starting from the initial
-     point X.  The size of the initial trial steps is given in vector
-     STEP_SIZE.  The precise meaning of this parameter depends on the
-     method used.
+     If there is insufficient memory to create the minimizer then the
+     function returns a null pointer and the error handler is invoked
+     with an error code of 'GSL_ENOMEM'.
 
- -- Function: void gsl_multimin_fdfminimizer_free
-          (gsl_multimin_fdfminimizer * S)
- -- Function: void gsl_multimin_fminimizer_free (gsl_multimin_fminimizer
-          * S)
+ -- Function: int gsl_min_fminimizer_set (gsl_min_fminimizer * S,
+          gsl_function * F, double X_MINIMUM, double X_LOWER, double
+          X_UPPER)
+     This function sets, or resets, an existing minimizer S to use the
+     function F and the initial search interval [X_LOWER, X_UPPER], with
+     a guess for the location of the minimum X_MINIMUM.
+
+     If the interval given does not contain a minimum, then the function
+     returns an error code of 'GSL_EINVAL'.
+
+ -- Function: int gsl_min_fminimizer_set_with_values (gsl_min_fminimizer
+          * S, gsl_function * F, double X_MINIMUM, double F_MINIMUM,
+          double X_LOWER, double F_LOWER, double X_UPPER, double
+          F_UPPER)
+     This function is equivalent to 'gsl_min_fminimizer_set' but uses
+     the values F_MINIMUM, F_LOWER and F_UPPER instead of computing
+     'f(x_minimum)', 'f(x_lower)' and 'f(x_upper)'.
+
+ -- Function: void gsl_min_fminimizer_free (gsl_min_fminimizer * S)
      This function frees all the memory associated with the minimizer S.
 
- -- Function: const char * gsl_multimin_fdfminimizer_name (const
-          gsl_multimin_fdfminimizer * S)
- -- Function: const char * gsl_multimin_fminimizer_name (const
-          gsl_multimin_fminimizer * S)
+ -- Function: const char * gsl_min_fminimizer_name (const
+          gsl_min_fminimizer * S)
      This function returns a pointer to the name of the minimizer.  For
      example,
 
           printf ("s is a '%s' minimizer\n",
-                  gsl_multimin_fdfminimizer_name (s));
+                  gsl_min_fminimizer_name (s));
 
-     would print something like 's is a 'conjugate_pr' minimizer'.
+     would print something like 's is a 'brent' minimizer'.
 
 
-File: gsl-ref.info,  Node: Providing a function to minimize,  Next: Multimin Iteration,  Prev: Initializing the Multidimensional Minimizer,  Up: Multidimensional Minimization
+File: gsl-ref.info,  Node: Providing the function to minimize,  Next: Minimization Iteration,  Prev: Initializing the Minimizer,  Up: One dimensional Minimization
 
-36.4 Providing a function to minimize
-=====================================
+35.4 Providing the function to minimize
+=======================================
 
-You must provide a parametric function of n variables for the minimizers
-to operate on.  You may also need to provide a routine which calculates
-the gradient of the function and a third routine which calculates both
-the function value and the gradient together.  In order to allow for
-general parameters the functions are defined by the following data
-types:
+You must provide a continuous function of one variable for the
+minimizers to operate on.  In order to allow for general parameters the
+functions are defined by a 'gsl_function' data type (*note Providing the
+function to solve::).
 
- -- Data Type: gsl_multimin_function_fdf
-     This data type defines a general function of n variables with
-     parameters and the corresponding gradient vector of derivatives,
+
+File: gsl-ref.info,  Node: Minimization Iteration,  Next: Minimization Stopping Parameters,  Prev: Providing the function to minimize,  Up: One dimensional Minimization
 
-     'double (* f) (const gsl_vector * X, void * PARAMS)'
-          this function should return the result f(x,params) for
-          argument X and parameters PARAMS.  If the function cannot be
-          computed, an error value of 'GSL_NAN' should be returned.
+35.5 Iteration
+==============
 
-     'void (* df) (const gsl_vector * X, void * PARAMS, gsl_vector * G)'
-          this function should store the N-dimensional gradient g_i = d
-          f(x,params) / d x_i in the vector G for argument X and
-          parameters PARAMS, returning an appropriate error code if the
-          function cannot be computed.
+The following functions drive the iteration of each algorithm.  Each
+function performs one iteration to update the state of any minimizer of
+the corresponding type.  The same functions work for all minimizers so
+that different methods can be substituted at runtime without
+modifications to the code.
 
-     'void (* fdf) (const gsl_vector * X, void * PARAMS, double * f, gsl_vector * G)'
-          This function should set the values of the F and G as above,
-          for arguments X and parameters PARAMS.  This function provides
-          an optimization of the separate functions for f(x) and
-          g(x)--it is always faster to compute the function and its
-          derivative at the same time.
+ -- Function: int gsl_min_fminimizer_iterate (gsl_min_fminimizer * S)
+     This function performs a single iteration of the minimizer S.  If
+     the iteration encounters an unexpected problem then an error code
+     will be returned,
 
-     'size_t n'
-          the dimension of the system, i.e.  the number of components of
-          the vectors X.
+     'GSL_EBADFUNC'
+          the iteration encountered a singular point where the function
+          evaluated to 'Inf' or 'NaN'.
 
-     'void * params'
-          a pointer to the parameters of the function.
- -- Data Type: gsl_multimin_function
-     This data type defines a general function of n variables with
-     parameters,
+     'GSL_FAILURE'
+          the algorithm could not improve the current best approximation
+          or bounding interval.
+
+   The minimizer maintains a current best estimate of the position of
+the minimum at all times, and the current interval bounding the minimum.
+This information can be accessed with the following auxiliary functions,
+
+ -- Function: double gsl_min_fminimizer_x_minimum (const
+          gsl_min_fminimizer * S)
+     This function returns the current estimate of the position of the
+     minimum for the minimizer S.
+
+ -- Function: double gsl_min_fminimizer_x_upper (const
+          gsl_min_fminimizer * S)
+ -- Function: double gsl_min_fminimizer_x_lower (const
+          gsl_min_fminimizer * S)
+     These functions return the current upper and lower bound of the
+     interval for the minimizer S.
+
+ -- Function: double gsl_min_fminimizer_f_minimum (const
+          gsl_min_fminimizer * S)
+ -- Function: double gsl_min_fminimizer_f_upper (const
+          gsl_min_fminimizer * S)
+ -- Function: double gsl_min_fminimizer_f_lower (const
+          gsl_min_fminimizer * S)
+     These functions return the value of the function at the current
+     estimate of the minimum and at the upper and lower bounds of the
+     interval for the minimizer S.
 
-     'double (* f) (const gsl_vector * X, void * PARAMS)'
-          this function should return the result f(x,params) for
-          argument X and parameters PARAMS.  If the function cannot be
-          computed, an error value of 'GSL_NAN' should be returned.
+
+File: gsl-ref.info,  Node: Minimization Stopping Parameters,  Next: Minimization Algorithms,  Prev: Minimization Iteration,  Up: One dimensional Minimization
 
-     'size_t n'
-          the dimension of the system, i.e.  the number of components of
-          the vectors X.
+35.6 Stopping Parameters
+========================
 
-     'void * params'
-          a pointer to the parameters of the function.
+A minimization procedure should stop when one of the following
+conditions is true:
 
-The following example function defines a simple two-dimensional
-paraboloid with five parameters,
+   * A minimum has been found to within the user-specified precision.
 
-     /* Paraboloid centered on (p[0],p[1]), with
-        scale factors (p[2],p[3]) and minimum p[4] */
+   * A user-specified maximum number of iterations has been reached.
 
-     double
-     my_f (const gsl_vector *v, void *params)
-     {
-       double x, y;
-       double *p = (double *)params;
+   * An error has occurred.
 
-       x = gsl_vector_get(v, 0);
-       y = gsl_vector_get(v, 1);
+The handling of these conditions is under user control.  The function
+below allows the user to test the precision of the current result.
 
-       return p[2] * (x - p[0]) * (x - p[0]) +
-                p[3] * (y - p[1]) * (y - p[1]) + p[4];
-     }
+ -- Function: int gsl_min_test_interval (double X_LOWER, double X_UPPER,
+          double EPSABS, double EPSREL)
+     This function tests for the convergence of the interval [X_LOWER,
+     X_UPPER] with absolute error EPSABS and relative error EPSREL.  The
+     test returns 'GSL_SUCCESS' if the following condition is achieved,
 
-     /* The gradient of f, df = (df/dx, df/dy). */
-     void
-     my_df (const gsl_vector *v, void *params,
-            gsl_vector *df)
-     {
-       double x, y;
-       double *p = (double *)params;
+          |a - b| < epsabs + epsrel min(|a|,|b|)
 
-       x = gsl_vector_get(v, 0);
-       y = gsl_vector_get(v, 1);
+     when the interval x = [a,b] does not include the origin.  If the
+     interval includes the origin then \min(|a|,|b|) is replaced by zero
+     (which is the minimum value of |x| over the interval).  This
+     ensures that the relative error is accurately estimated for minima
+     close to the origin.
 
-       gsl_vector_set(df, 0, 2.0 * p[2] * (x - p[0]));
-       gsl_vector_set(df, 1, 2.0 * p[3] * (y - p[1]));
-     }
+     This condition on the interval also implies that any estimate of
+     the minimum x_m in the interval satisfies the same condition with
+     respect to the true minimum x_m^*,
 
-     /* Compute both f and df together. */
-     void
-     my_fdf (const gsl_vector *x, void *params,
-             double *f, gsl_vector *df)
-     {
-       *f = my_f(x, params);
-       my_df(x, params, df);
-     }
+          |x_m - x_m^*| < epsabs + epsrel x_m^*
 
-The function can be initialized using the following code,
+     assuming that the true minimum x_m^* is contained within the
+     interval.
 
-     gsl_multimin_function_fdf my_func;
+
+File: gsl-ref.info,  Node: Minimization Algorithms,  Next: Minimization Examples,  Prev: Minimization Stopping Parameters,  Up: One dimensional Minimization
 
-     /* Paraboloid center at (1,2), scale factors (10, 20),
-        minimum value 30 */
-     double p[5] = { 1.0, 2.0, 10.0, 20.0, 30.0 };
+35.7 Minimization Algorithms
+============================
 
-     my_func.n = 2;  /* number of function components */
-     my_func.f = &my_f;
-     my_func.df = &my_df;
-     my_func.fdf = &my_fdf;
-     my_func.params = (void *)p;
+The minimization algorithms described in this section require an initial
+interval which is guaranteed to contain a minimum--if a and b are the
+endpoints of the interval and x is an estimate of the minimum then f(a)
+> f(x) < f(b).  This ensures that the function has at least one minimum
+somewhere in the interval.  If a valid initial interval is used then
+these algorithm cannot fail, provided the function is well-behaved.
+
+ -- Minimizer: gsl_min_fminimizer_goldensection
+
+     The "golden section algorithm" is the simplest method of bracketing
+     the minimum of a function.  It is the slowest algorithm provided by
+     the library, with linear convergence.
+
+     On each iteration, the algorithm first compares the subintervals
+     from the endpoints to the current minimum.  The larger subinterval
+     is divided in a golden section (using the famous ratio (3-\sqrt
+     5)/2 = 0.3819660...) and the value of the function at this new
+     point is calculated.  The new value is used with the constraint
+     f(a') > f(x') < f(b') to a select new interval containing the
+     minimum, by discarding the least useful point.  This procedure can
+     be continued indefinitely until the interval is sufficiently small.
+     Choosing the golden section as the bisection ratio can be shown to
+     provide the fastest convergence for this type of algorithm.
+
+ -- Minimizer: gsl_min_fminimizer_brent
+
+     The "Brent minimization algorithm" combines a parabolic
+     interpolation with the golden section algorithm.  This produces a
+     fast algorithm which is still robust.
+
+     The outline of the algorithm can be summarized as follows: on each
+     iteration Brent's method approximates the function using an
+     interpolating parabola through three existing points.  The minimum
+     of the parabola is taken as a guess for the minimum.  If it lies
+     within the bounds of the current interval then the interpolating
+     point is accepted, and used to generate a smaller interval.  If the
+     interpolating point is not accepted then the algorithm falls back
+     to an ordinary golden section step.  The full details of Brent's
+     method include some additional checks to improve convergence.
+
+ -- Minimizer: gsl_min_fminimizer_quad_golden
+     This is a variant of Brent's algorithm which uses the safeguarded
+     step-length algorithm of Gill and Murray.
 
 
-File: gsl-ref.info,  Node: Multimin Iteration,  Next: Multimin Stopping Criteria,  Prev: Providing a function to minimize,  Up: Multidimensional Minimization
+File: gsl-ref.info,  Node: Minimization Examples,  Next: Minimization References and Further Reading,  Prev: Minimization Algorithms,  Up: One dimensional Minimization
 
-36.5 Iteration
-==============
+35.8 Examples
+=============
 
-The following function drives the iteration of each algorithm.  The
-function performs one iteration to update the state of the minimizer.
-The same function works for all minimizers so that different methods can
-be substituted at runtime without modifications to the code.
+The following program uses the Brent algorithm to find the minimum of
+the function f(x) = \cos(x) + 1, which occurs at x = \pi.  The starting
+interval is (0,6), with an initial guess for the minimum of 2.
 
- -- Function: int gsl_multimin_fdfminimizer_iterate
-          (gsl_multimin_fdfminimizer * S)
- -- Function: int gsl_multimin_fminimizer_iterate
-          (gsl_multimin_fminimizer * S)
-     These functions perform a single iteration of the minimizer S.  If
-     the iteration encounters an unexpected problem then an error code
-     will be returned.  The error code 'GSL_ENOPROG' signifies that the
-     minimizer is unable to improve on its current estimate, either due
-     to numerical difficulty or because a genuine local minimum has been
-     reached.
+     #include <stdio.h>
+     #include <gsl/gsl_errno.h>
+     #include <gsl/gsl_math.h>
+     #include <gsl/gsl_min.h>
 
-The minimizer maintains a current best estimate of the minimum at all
-times.  This information can be accessed with the following auxiliary
-functions,
+     double fn1 (double x, void * params)
+     {
+       (void)(params); /* avoid unused parameter warning */
+       return cos(x) + 1.0;
+     }
 
- -- Function: gsl_vector * gsl_multimin_fdfminimizer_x (const
-          gsl_multimin_fdfminimizer * S)
- -- Function: gsl_vector * gsl_multimin_fminimizer_x (const
-          gsl_multimin_fminimizer * S)
- -- Function: double gsl_multimin_fdfminimizer_minimum (const
-          gsl_multimin_fdfminimizer * S)
- -- Function: double gsl_multimin_fminimizer_minimum (const
-          gsl_multimin_fminimizer * S)
- -- Function: gsl_vector * gsl_multimin_fdfminimizer_gradient (const
-          gsl_multimin_fdfminimizer * S)
- -- Function: double gsl_multimin_fminimizer_size (const
-          gsl_multimin_fminimizer * S)
-     These functions return the current best estimate of the location of
-     the minimum, the value of the function at that point, its gradient,
-     and minimizer specific characteristic size for the minimizer S.
+     int
+     main (void)
+     {
+       int status;
+       int iter = 0, max_iter = 100;
+       const gsl_min_fminimizer_type *T;
+       gsl_min_fminimizer *s;
+       double m = 2.0, m_expected = M_PI;
+       double a = 0.0, b = 6.0;
+       gsl_function F;
+
+       F.function = &fn1;
+       F.params = 0;
+
+       T = gsl_min_fminimizer_brent;
+       s = gsl_min_fminimizer_alloc (T);
+       gsl_min_fminimizer_set (s, &F, m, a, b);
+
+       printf ("using %s method\n",
+               gsl_min_fminimizer_name (s));
+
+       printf ("%5s [%9s, %9s] %9s %10s %9s\n",
+               "iter", "lower", "upper", "min",
+               "err", "err(est)");
+
+       printf ("%5d [%.7f, %.7f] %.7f %+.7f %.7f\n",
+               iter, a, b,
+               m, m - m_expected, b - a);
 
- -- Function: int gsl_multimin_fdfminimizer_restart
-          (gsl_multimin_fdfminimizer * S)
-     This function resets the minimizer S to use the current point as a
-     new starting point.
+       do
+         {
+           iter++;
+           status = gsl_min_fminimizer_iterate (s);
 
-
-File: gsl-ref.info,  Node: Multimin Stopping Criteria,  Next: Multimin Algorithms with Derivatives,  Prev: Multimin Iteration,  Up: Multidimensional Minimization
+           m = gsl_min_fminimizer_x_minimum (s);
+           a = gsl_min_fminimizer_x_lower (s);
+           b = gsl_min_fminimizer_x_upper (s);
 
-36.6 Stopping Criteria
-======================
+           status
+             = gsl_min_test_interval (a, b, 0.001, 0.0);
 
-A minimization procedure should stop when one of the following
-conditions is true:
+           if (status == GSL_SUCCESS)
+             printf ("Converged:\n");
 
-   * A minimum has been found to within the user-specified precision.
+           printf ("%5d [%.7f, %.7f] "
+                   "%.7f %+.7f %.7f\n",
+                   iter, a, b,
+                   m, m - m_expected, b - a);
+         }
+       while (status == GSL_CONTINUE && iter < max_iter);
 
-   * A user-specified maximum number of iterations has been reached.
+       gsl_min_fminimizer_free (s);
 
-   * An error has occurred.
+       return status;
+     }
 
-The handling of these conditions is under user control.  The functions
-below allow the user to test the precision of the current result.
+Here are the results of the minimization procedure.
 
- -- Function: int gsl_multimin_test_gradient (const gsl_vector * G,
-          double EPSABS)
-     This function tests the norm of the gradient G against the absolute
-     tolerance EPSABS.  The gradient of a multidimensional function goes
-     to zero at a minimum.  The test returns 'GSL_SUCCESS' if the
-     following condition is achieved,
+     $ ./a.out
+     using brent method
+      iter [    lower,     upper]       min        err  err(est)
+         0 [0.0000000, 6.0000000] 2.0000000 -1.1415927 6.0000000
+         1 [2.0000000, 6.0000000] 3.5278640 +0.3862713 4.0000000
+         2 [2.0000000, 3.5278640] 3.1748217 +0.0332290 1.5278640
+         3 [2.0000000, 3.1748217] 3.1264576 -0.0151351 1.1748217
+         4 [3.1264576, 3.1748217] 3.1414743 -0.0001183 0.0483641
+         5 [3.1414743, 3.1748217] 3.1415930 +0.0000004 0.0333474
+     Converged:
+         6 [3.1414743, 3.1415930] 3.1415927 +0.0000000 0.0001187
 
-          |g| < epsabs
+
+File: gsl-ref.info,  Node: Minimization References and Further Reading,  Prev: Minimization Examples,  Up: One dimensional Minimization
 
-     and returns 'GSL_CONTINUE' otherwise.  A suitable choice of EPSABS
-     can be made from the desired accuracy in the function for small
-     variations in x.  The relationship between these quantities is
-     given by \delta f = g \delta x.
+35.9 References and Further Reading
+===================================
 
- -- Function: int gsl_multimin_test_size (const double SIZE, double
-          EPSABS)
-     This function tests the minimizer specific characteristic size (if
-     applicable to the used minimizer) against absolute tolerance
-     EPSABS.  The test returns 'GSL_SUCCESS' if the size is smaller than
-     tolerance, otherwise 'GSL_CONTINUE' is returned.
+Further information on Brent's algorithm is available in the following
+book,
 
-
-File: gsl-ref.info,  Node: Multimin Algorithms with Derivatives,  Next: Multimin Algorithms without Derivatives,  Prev: Multimin Stopping Criteria,  Up: Multidimensional Minimization
+     Richard Brent, 'Algorithms for minimization without derivatives',
+     Prentice-Hall (1973), republished by Dover in paperback (2002),
+     ISBN 0-486-41998-3.
 
-36.7 Algorithms with Derivatives
-================================
+
+File: gsl-ref.info,  Node: Multidimensional Root-Finding,  Next: Multidimensional Minimization,  Prev: One dimensional Minimization,  Up: Top
 
-There are several minimization methods available.  The best choice of
-algorithm depends on the problem.  The algorithms described in this
-section use the value of the function and its gradient at each
-evaluation point.
+36 Multidimensional Root-Finding
+********************************
 
- -- Minimizer: gsl_multimin_fdfminimizer_conjugate_fr
-     This is the Fletcher-Reeves conjugate gradient algorithm.  The
-     conjugate gradient algorithm proceeds as a succession of line
-     minimizations.  The sequence of search directions is used to build
-     up an approximation to the curvature of the function in the
-     neighborhood of the minimum.
+This chapter describes functions for multidimensional root-finding
+(solving nonlinear systems with n equations in n unknowns).  The library
+provides low level components for a variety of iterative solvers and
+convergence tests.  These can be combined by the user to achieve the
+desired solution, with full access to the intermediate steps of the
+iteration.  Each class of methods uses the same framework, so that you
+can switch between solvers at runtime without needing to recompile your
+program.  Each instance of a solver keeps track of its own state,
+allowing the solvers to be used in multi-threaded programs.  The solvers
+are based on the original Fortran library MINPACK.
 
-     An initial search direction P is chosen using the gradient, and
-     line minimization is carried out in that direction.  The accuracy
-     of the line minimization is specified by the parameter TOL.  The
-     minimum along this line occurs when the function gradient G and the
-     search direction P are orthogonal.  The line minimization
-     terminates when dot(p,g) < tol |p| |g|.  The search direction is
-     updated using the Fletcher-Reeves formula p' = g' - \beta g where
-     \beta=-|g'|^2/|g|^2, and the line minimization is then repeated for
-     the new search direction.
+   The header file 'gsl_multiroots.h' contains prototypes for the
+multidimensional root finding functions and related declarations.
 
- -- Minimizer: gsl_multimin_fdfminimizer_conjugate_pr
-     This is the Polak-Ribiere conjugate gradient algorithm.  It is
-     similar to the Fletcher-Reeves method, differing only in the choice
-     of the coefficient \beta.  Both methods work well when the
-     evaluation point is close enough to the minimum of the objective
-     function that it is well approximated by a quadratic hypersurface.
+* Menu:
 
- -- Minimizer: gsl_multimin_fdfminimizer_vector_bfgs2
- -- Minimizer: gsl_multimin_fdfminimizer_vector_bfgs
-     These methods use the vector Broyden-Fletcher-Goldfarb-Shanno
-     (BFGS) algorithm.  This is a quasi-Newton method which builds up an
-     approximation to the second derivatives of the function f using the
-     difference between successive gradient vectors.  By combining the
-     first and second derivatives the algorithm is able to take
-     Newton-type steps towards the function minimum, assuming quadratic
-     behavior in that region.
+* Overview of Multidimensional Root Finding::  
+* Initializing the Multidimensional Solver::  
+* Providing the multidimensional system of equations to solve::  
+* Iteration of the multidimensional solver::  
+* Search Stopping Parameters for the multidimensional solver::  
+* Algorithms using Derivatives::  
+* Algorithms without Derivatives::  
+* Example programs for Multidimensional Root finding::  
+* References and Further Reading for Multidimensional Root Finding::  
 
-     The 'bfgs2' version of this minimizer is the most efficient version
-     available, and is a faithful implementation of the line
-     minimization scheme described in Fletcher's 'Practical Methods of
-     Optimization', Algorithms 2.6.2 and 2.6.4.  It supersedes the
-     original 'bfgs' routine and requires substantially fewer function
-     and gradient evaluations.  The user-supplied tolerance TOL
-     corresponds to the parameter \sigma used by Fletcher.  A value of
-     0.1 is recommended for typical use (larger values correspond to
-     less accurate line searches).
+
+File: gsl-ref.info,  Node: Overview of Multidimensional Root Finding,  Next: Initializing the Multidimensional Solver,  Up: Multidimensional Root-Finding
 
- -- Minimizer: gsl_multimin_fdfminimizer_steepest_descent
-     The steepest descent algorithm follows the downhill gradient of the
-     function at each step.  When a downhill step is successful the
-     step-size is increased by a factor of two.  If the downhill step
-     leads to a higher function value then the algorithm backtracks and
-     the step size is decreased using the parameter TOL.  A suitable
-     value of TOL for most applications is 0.1.  The steepest descent
-     method is inefficient and is included only for demonstration
-     purposes.
+36.1 Overview
+=============
 
-
-File: gsl-ref.info,  Node: Multimin Algorithms without Derivatives,  Next: Multimin Examples,  Prev: Multimin Algorithms with Derivatives,  Up: Multidimensional Minimization
+The problem of multidimensional root finding requires the simultaneous
+solution of n equations, f_i, in n variables, x_i,
 
-36.8 Algorithms without Derivatives
-===================================
+     f_i (x_1, ..., x_n) = 0    for i = 1 ... n.
 
-The algorithms described in this section use only the value of the
-function at each evaluation point.
+In general there are no bracketing methods available for n dimensional
+systems, and no way of knowing whether any solutions exist.  All
+algorithms proceed from an initial guess using a variant of the Newton
+iteration,
 
- -- Minimizer: gsl_multimin_fminimizer_nmsimplex2
- -- Minimizer: gsl_multimin_fminimizer_nmsimplex
-     These methods use the Simplex algorithm of Nelder and Mead.
-     Starting from the initial vector X = p_0, the algorithm constructs
-     an additional n vectors p_i using the step size vector s =
-     STEP_SIZE as follows:
+     x -> x' = x - J^{-1} f(x)
 
-          p_0 = (x_0, x_1, ... , x_n)
-          p_1 = (x_0 + s_0, x_1, ... , x_n)
-          p_2 = (x_0, x_1 + s_1, ... , x_n)
-          ... = ...
-          p_n = (x_0, x_1, ... , x_n + s_n)
+where x, f are vector quantities and J is the Jacobian matrix J_{ij} = d
+f_i / d x_j.  Additional strategies can be used to enlarge the region of
+convergence.  These include requiring a decrease in the norm |f| on each
+step proposed by Newton's method, or taking steepest-descent steps in
+the direction of the negative gradient of |f|.
 
-     These vectors form the n+1 vertices of a simplex in n dimensions.
-     On each iteration the algorithm uses simple geometrical
-     transformations to update the vector corresponding to the highest
-     function value.  The geometric transformations are reflection,
-     reflection followed by expansion, contraction and multiple
-     contraction.  Using these transformations the simplex moves through
-     the space towards the minimum, where it contracts itself.
+   Several root-finding algorithms are available within a single
+framework.  The user provides a high-level driver for the algorithms,
+and the library provides the individual functions necessary for each of
+the steps.  There are three main phases of the iteration.  The steps
+are,
 
-     After each iteration, the best vertex is returned.  Note, that due
-     to the nature of the algorithm not every step improves the current
-     best parameter vector.  Usually several iterations are required.
+   * initialize solver state, S, for algorithm T
 
-     The minimizer-specific characteristic size is calculated as the
-     average distance from the geometrical center of the simplex to all
-     its vertices.  This size can be used as a stopping criteria, as the
-     simplex contracts itself near the minimum.  The size is returned by
-     the function 'gsl_multimin_fminimizer_size'.
+   * update S using the iteration T
 
-     The 'nmsimplex2' version of this minimiser is a new O(N) operations
-     implementation of the earlier O(N^2) operations 'nmsimplex'
-     minimiser.  It uses the same underlying algorithm, but the simplex
-     updates are computed more efficiently for high-dimensional
-     problems.  In addition, the size of simplex is calculated as the
-     RMS distance of each vertex from the center rather than the mean
-     distance, allowing a linear update of this quantity on each step.
-     The memory usage is O(N^2) for both algorithms.
+   * test S for convergence, and repeat iteration if necessary
 
- -- Minimizer: gsl_multimin_fminimizer_nmsimplex2rand
-     This method is a variant of 'nmsimplex2' which initialises the
-     simplex around the starting point X using a randomly-oriented set
-     of basis vectors instead of the fixed coordinate axes.  The final
-     dimensions of the simplex are scaled along the coordinate axes by
-     the vector STEP_SIZE.  The randomisation uses a simple
-     deterministic generator so that repeated calls to
-     'gsl_multimin_fminimizer_set' for a given solver object will vary
-     the orientation in a well-defined way.
+The evaluation of the Jacobian matrix can be problematic, either because
+programming the derivatives is intractable or because computation of the
+n^2 terms of the matrix becomes too expensive.  For these reasons the
+algorithms provided by the library are divided into two classes
+according to whether the derivatives are available or not.
+
+   The state for solvers with an analytic Jacobian matrix is held in a
+'gsl_multiroot_fdfsolver' struct.  The updating procedure requires both
+the function and its derivatives to be supplied by the user.
+
+   The state for solvers which do not use an analytic Jacobian matrix is
+held in a 'gsl_multiroot_fsolver' struct.  The updating procedure uses
+only function evaluations (not derivatives).  The algorithms estimate
+the matrix J or J^{-1} by approximate methods.
 
 
-File: gsl-ref.info,  Node: Multimin Examples,  Next: Multimin References and Further Reading,  Prev: Multimin Algorithms without Derivatives,  Up: Multidimensional Minimization
+File: gsl-ref.info,  Node: Initializing the Multidimensional Solver,  Next: Providing the multidimensional system of equations to solve,  Prev: Overview of Multidimensional Root Finding,  Up: Multidimensional Root-Finding
 
-36.9 Examples
-=============
+36.2 Initializing the Solver
+============================
 
-This example program finds the minimum of the paraboloid function
-defined earlier.  The location of the minimum is offset from the origin
-in x and y, and the function value at the minimum is non-zero.  The main
-program is given below, it requires the example function given earlier
-in this chapter.
+The following functions initialize a multidimensional solver, either
+with or without derivatives.  The solver itself depends only on the
+dimension of the problem and the algorithm and can be reused for
+different problems.
 
-     int
-     main (void)
-     {
-       size_t iter = 0;
-       int status;
+ -- Function: gsl_multiroot_fsolver * gsl_multiroot_fsolver_alloc (const
+          gsl_multiroot_fsolver_type * T, size_t N)
+     This function returns a pointer to a newly allocated instance of a
+     solver of type T for a system of N dimensions.  For example, the
+     following code creates an instance of a hybrid solver, to solve a
+     3-dimensional system of equations.
 
-       const gsl_multimin_fdfminimizer_type *T;
-       gsl_multimin_fdfminimizer *s;
+          const gsl_multiroot_fsolver_type * T
+              = gsl_multiroot_fsolver_hybrid;
+          gsl_multiroot_fsolver * s
+              = gsl_multiroot_fsolver_alloc (T, 3);
 
-       /* Position of the minimum (1,2), scale factors
-          10,20, height 30. */
-       double par[5] = { 1.0, 2.0, 10.0, 20.0, 30.0 };
+     If there is insufficient memory to create the solver then the
+     function returns a null pointer and the error handler is invoked
+     with an error code of 'GSL_ENOMEM'.
 
-       gsl_vector *x;
-       gsl_multimin_function_fdf my_func;
+ -- Function: gsl_multiroot_fdfsolver * gsl_multiroot_fdfsolver_alloc
+          (const gsl_multiroot_fdfsolver_type * T, size_t N)
+     This function returns a pointer to a newly allocated instance of a
+     derivative solver of type T for a system of N dimensions.  For
+     example, the following code creates an instance of a Newton-Raphson
+     solver, for a 2-dimensional system of equations.
 
-       my_func.n = 2;
-       my_func.f = my_f;
-       my_func.df = my_df;
-       my_func.fdf = my_fdf;
-       my_func.params = par;
+          const gsl_multiroot_fdfsolver_type * T
+              = gsl_multiroot_fdfsolver_newton;
+          gsl_multiroot_fdfsolver * s =
+              gsl_multiroot_fdfsolver_alloc (T, 2);
 
-       /* Starting point, x = (5,7) */
-       x = gsl_vector_alloc (2);
-       gsl_vector_set (x, 0, 5.0);
-       gsl_vector_set (x, 1, 7.0);
+     If there is insufficient memory to create the solver then the
+     function returns a null pointer and the error handler is invoked
+     with an error code of 'GSL_ENOMEM'.
 
-       T = gsl_multimin_fdfminimizer_conjugate_fr;
-       s = gsl_multimin_fdfminimizer_alloc (T, 2);
+ -- Function: int gsl_multiroot_fsolver_set (gsl_multiroot_fsolver * S,
+          gsl_multiroot_function * F, const gsl_vector * X)
+ -- Function: int gsl_multiroot_fdfsolver_set (gsl_multiroot_fdfsolver *
+          S, gsl_multiroot_function_fdf * FDF, const gsl_vector * X)
+     These functions set, or reset, an existing solver S to use the
+     function F or function and derivative FDF, and the initial guess X.
+     Note that the initial position is copied from X, this argument is
+     not modified by subsequent iterations.
 
-       gsl_multimin_fdfminimizer_set (s, &my_func, x, 0.01, 1e-4);
+ -- Function: void gsl_multiroot_fsolver_free (gsl_multiroot_fsolver *
+          S)
+ -- Function: void gsl_multiroot_fdfsolver_free (gsl_multiroot_fdfsolver
+          * S)
+     These functions free all the memory associated with the solver S.
 
-       do
-         {
-           iter++;
-           status = gsl_multimin_fdfminimizer_iterate (s);
+ -- Function: const char * gsl_multiroot_fsolver_name (const
+          gsl_multiroot_fsolver * S)
+ -- Function: const char * gsl_multiroot_fdfsolver_name (const
+          gsl_multiroot_fdfsolver * S)
+     These functions return a pointer to the name of the solver.  For
+     example,
 
-           if (status)
-             break;
+          printf ("s is a '%s' solver\n",
+                  gsl_multiroot_fdfsolver_name (s));
 
-           status = gsl_multimin_test_gradient (s->gradient, 1e-3);
+     would print something like 's is a 'newton' solver'.
 
-           if (status == GSL_SUCCESS)
-             printf ("Minimum found at:\n");
+
+File: gsl-ref.info,  Node: Providing the multidimensional system of equations to solve,  Next: Iteration of the multidimensional solver,  Prev: Initializing the Multidimensional Solver,  Up: Multidimensional Root-Finding
 
-           printf ("%5d %.5f %.5f %10.5f\n", iter,
-                   gsl_vector_get (s->x, 0),
-                   gsl_vector_get (s->x, 1),
-                   s->f);
+36.3 Providing the function to solve
+====================================
 
-         }
-       while (status == GSL_CONTINUE && iter < 100);
+You must provide n functions of n variables for the root finders to
+operate on.  In order to allow for general parameters the functions are
+defined by the following data types:
 
-       gsl_multimin_fdfminimizer_free (s);
-       gsl_vector_free (x);
+ -- Data Type: gsl_multiroot_function
+     This data type defines a general system of functions with
+     parameters.
 
-       return 0;
-     }
+     'int (* f) (const gsl_vector * X, void * PARAMS, gsl_vector * F)'
+          this function should store the vector result f(x,params) in F
+          for argument X and parameters PARAMS, returning an appropriate
+          error code if the function cannot be computed.
 
-The initial step-size is chosen as 0.01, a conservative estimate in this
-case, and the line minimization parameter is set at 0.0001.  The program
-terminates when the norm of the gradient has been reduced below 0.001.
-The output of the program is shown below,
+     'size_t n'
+          the dimension of the system, i.e.  the number of components of
+          the vectors X and F.
 
-              x       y         f
-         1 4.99629 6.99072  687.84780
-         2 4.98886 6.97215  683.55456
-         3 4.97400 6.93501  675.01278
-         4 4.94429 6.86073  658.10798
-         5 4.88487 6.71217  625.01340
-         6 4.76602 6.41506  561.68440
-         7 4.52833 5.82083  446.46694
-         8 4.05295 4.63238  261.79422
-         9 3.10219 2.25548   75.49762
-        10 2.85185 1.62963   67.03704
-        11 2.19088 1.76182   45.31640
-        12 0.86892 2.02622   30.18555
-     Minimum found at:
-        13 1.00000 2.00000   30.00000
+     'void * params'
+          a pointer to the parameters of the function.
 
-Note that the algorithm gradually increases the step size as it
-successfully moves downhill, as can be seen by plotting the successive
-points.
+Here is an example using Powell's test function,
 
-The conjugate gradient algorithm finds the minimum on its second
-direction because the function is purely quadratic.  Additional
-iterations would be needed for a more complicated function.
+     f_1(x) = A x_0 x_1 - 1,
+     f_2(x) = exp(-x_0) + exp(-x_1) - (1 + 1/A)
 
-   Here is another example using the Nelder-Mead Simplex algorithm to
-minimize the same example object function, as above.
+with A = 10^4.  The following code defines a 'gsl_multiroot_function'
+system 'F' which you could pass to a solver:
+
+     struct powell_params { double A; };
 
      int
-     main(void)
-     {
-       double par[5] = {1.0, 2.0, 10.0, 20.0, 30.0};
+     powell (gsl_vector * x, void * p, gsl_vector * f) {
+        struct powell_params * params
+          = (struct powell_params *)p;
+        const double A = (params->A);
+        const double x0 = gsl_vector_get(x,0);
+        const double x1 = gsl_vector_get(x,1);
 
-       const gsl_multimin_fminimizer_type *T =
-         gsl_multimin_fminimizer_nmsimplex2;
-       gsl_multimin_fminimizer *s = NULL;
-       gsl_vector *ss, *x;
-       gsl_multimin_function minex_func;
+        gsl_vector_set (f, 0, A * x0 * x1 - 1);
+        gsl_vector_set (f, 1, (exp(-x0) + exp(-x1)
+                               - (1.0 + 1.0/A)));
+        return GSL_SUCCESS
+     }
 
-       size_t iter = 0;
-       int status;
-       double size;
+     gsl_multiroot_function F;
+     struct powell_params params = { 10000.0 };
 
-       /* Starting point */
-       x = gsl_vector_alloc (2);
-       gsl_vector_set (x, 0, 5.0);
-       gsl_vector_set (x, 1, 7.0);
+     F.f = &powell;
+     F.n = 2;
+     F.params = &params;
 
-       /* Set initial step sizes to 1 */
-       ss = gsl_vector_alloc (2);
-       gsl_vector_set_all (ss, 1.0);
+ -- Data Type: gsl_multiroot_function_fdf
+     This data type defines a general system of functions with
+     parameters and the corresponding Jacobian matrix of derivatives,
 
-       /* Initialize method and iterate */
-       minex_func.n = 2;
-       minex_func.f = my_f;
-       minex_func.params = par;
-
-       s = gsl_multimin_fminimizer_alloc (T, 2);
-       gsl_multimin_fminimizer_set (s, &minex_func, x, ss);
-
-       do
-         {
-           iter++;
-           status = gsl_multimin_fminimizer_iterate(s);
+     'int (* f) (const gsl_vector * X, void * PARAMS, gsl_vector * F)'
+          this function should store the vector result f(x,params) in F
+          for argument X and parameters PARAMS, returning an appropriate
+          error code if the function cannot be computed.
 
-           if (status)
-             break;
+     'int (* df) (const gsl_vector * X, void * PARAMS, gsl_matrix * J)'
+          this function should store the N-by-N matrix result J_ij = d
+          f_i(x,params) / d x_j in J for argument X and parameters
+          PARAMS, returning an appropriate error code if the function
+          cannot be computed.
 
-           size = gsl_multimin_fminimizer_size (s);
-           status = gsl_multimin_test_size (size, 1e-2);
+     'int (* fdf) (const gsl_vector * X, void * PARAMS, gsl_vector * F, gsl_matrix * J)'
+          This function should set the values of the F and J as above,
+          for arguments X and parameters PARAMS.  This function provides
+          an optimization of the separate functions for f(x) and
+          J(x)--it is always faster to compute the function and its
+          derivative at the same time.
 
-           if (status == GSL_SUCCESS)
-             {
-               printf ("converged to minimum at\n");
-             }
+     'size_t n'
+          the dimension of the system, i.e.  the number of components of
+          the vectors X and F.
 
-           printf ("%5d %10.3e %10.3e f() = %7.3f size = %.3f\n",
-                   iter,
-                   gsl_vector_get (s->x, 0),
-                   gsl_vector_get (s->x, 1),
-                   s->fval, size);
-         }
-       while (status == GSL_CONTINUE && iter < 100);
+     'void * params'
+          a pointer to the parameters of the function.
 
-       gsl_vector_free(x);
-       gsl_vector_free(ss);
-       gsl_multimin_fminimizer_free (s);
+The example of Powell's test function defined above can be extended to
+include analytic derivatives using the following code,
 
-       return status;
+     int
+     powell_df (gsl_vector * x, void * p, gsl_matrix * J)
+     {
+        struct powell_params * params
+          = (struct powell_params *)p;
+        const double A = (params->A);
+        const double x0 = gsl_vector_get(x,0);
+        const double x1 = gsl_vector_get(x,1);
+        gsl_matrix_set (J, 0, 0, A * x1);
+        gsl_matrix_set (J, 0, 1, A * x0);
+        gsl_matrix_set (J, 1, 0, -exp(-x0));
+        gsl_matrix_set (J, 1, 1, -exp(-x1));
+        return GSL_SUCCESS
      }
 
-The minimum search stops when the Simplex size drops to 0.01.  The
-output is shown below.
+     int
+     powell_fdf (gsl_vector * x, void * p,
+                 gsl_matrix * f, gsl_matrix * J) {
+        struct powell_params * params
+          = (struct powell_params *)p;
+        const double A = (params->A);
+        const double x0 = gsl_vector_get(x,0);
+        const double x1 = gsl_vector_get(x,1);
 
-         1  6.500e+00  5.000e+00 f() = 512.500 size = 1.130
-         2  5.250e+00  4.000e+00 f() = 290.625 size = 1.409
-         3  5.250e+00  4.000e+00 f() = 290.625 size = 1.409
-         4  5.500e+00  1.000e+00 f() = 252.500 size = 1.409
-         5  2.625e+00  3.500e+00 f() = 101.406 size = 1.847
-         6  2.625e+00  3.500e+00 f() = 101.406 size = 1.847
-         7  0.000e+00  3.000e+00 f() =  60.000 size = 1.847
-         8  2.094e+00  1.875e+00 f() =  42.275 size = 1.321
-         9  2.578e-01  1.906e+00 f() =  35.684 size = 1.069
-        10  5.879e-01  2.445e+00 f() =  35.664 size = 0.841
-        11  1.258e+00  2.025e+00 f() =  30.680 size = 0.476
-        12  1.258e+00  2.025e+00 f() =  30.680 size = 0.367
-        13  1.093e+00  1.849e+00 f() =  30.539 size = 0.300
-        14  8.830e-01  2.004e+00 f() =  30.137 size = 0.172
-        15  8.830e-01  2.004e+00 f() =  30.137 size = 0.126
-        16  9.582e-01  2.060e+00 f() =  30.090 size = 0.106
-        17  1.022e+00  2.004e+00 f() =  30.005 size = 0.063
-        18  1.022e+00  2.004e+00 f() =  30.005 size = 0.043
-        19  1.022e+00  2.004e+00 f() =  30.005 size = 0.043
-        20  1.022e+00  2.004e+00 f() =  30.005 size = 0.027
-        21  1.022e+00  2.004e+00 f() =  30.005 size = 0.022
-        22  9.920e-01  1.997e+00 f() =  30.001 size = 0.016
-        23  9.920e-01  1.997e+00 f() =  30.001 size = 0.013
-     converged to minimum at
-        24  9.920e-01  1.997e+00 f() =  30.001 size = 0.008
+        const double u0 = exp(-x0);
+        const double u1 = exp(-x1);
 
-The simplex size first increases, while the simplex moves towards the
-minimum.  After a while the size begins to decrease as the simplex
-contracts around the minimum.
+        gsl_vector_set (f, 0, A * x0 * x1 - 1);
+        gsl_vector_set (f, 1, u0 + u1 - (1 + 1/A));
 
-
-File: gsl-ref.info,  Node: Multimin References and Further Reading,  Prev: Multimin Examples,  Up: Multidimensional Minimization
+        gsl_matrix_set (J, 0, 0, A * x1);
+        gsl_matrix_set (J, 0, 1, A * x0);
+        gsl_matrix_set (J, 1, 0, -u0);
+        gsl_matrix_set (J, 1, 1, -u1);
+        return GSL_SUCCESS
+     }
 
-36.10 References and Further Reading
-====================================
+     gsl_multiroot_function_fdf FDF;
 
-The conjugate gradient and BFGS methods are described in detail in the
-following book,
+     FDF.f = &powell_f;
+     FDF.df = &powell_df;
+     FDF.fdf = &powell_fdf;
+     FDF.n = 2;
+     FDF.params = 0;
 
-     R. Fletcher, 'Practical Methods of Optimization (Second Edition)'
-     Wiley (1987), ISBN 0471915475.
+Note that the function 'powell_fdf' is able to reuse existing terms from
+the function when calculating the Jacobian, thus saving time.
 
-   A brief description of multidimensional minimization algorithms and
-more recent references can be found in,
+
+File: gsl-ref.info,  Node: Iteration of the multidimensional solver,  Next: Search Stopping Parameters for the multidimensional solver,  Prev: Providing the multidimensional system of equations to solve,  Up: Multidimensional Root-Finding
 
-     C.W. Ueberhuber, 'Numerical Computation (Volume 2)', Chapter 14,
-     Section 4.4 "Minimization Methods", p. 325-335, Springer (1997),
-     ISBN 3-540-62057-5.
+36.4 Iteration
+==============
 
-The simplex algorithm is described in the following paper,
+The following functions drive the iteration of each algorithm.  Each
+function performs one iteration to update the state of any solver of the
+corresponding type.  The same functions work for all solvers so that
+different methods can be substituted at runtime without modifications to
+the code.
 
-     J.A. Nelder and R. Mead, 'A simplex method for function
-     minimization', Computer Journal vol. 7 (1965), 308-313.
+ -- Function: int gsl_multiroot_fsolver_iterate (gsl_multiroot_fsolver *
+          S)
+ -- Function: int gsl_multiroot_fdfsolver_iterate
+          (gsl_multiroot_fdfsolver * S)
+     These functions perform a single iteration of the solver S.  If the
+     iteration encounters an unexpected problem then an error code will
+     be returned,
 
-
-File: gsl-ref.info,  Node: Least-Squares Fitting,  Next: Nonlinear Least-Squares Fitting,  Prev: Multidimensional Minimization,  Up: Top
+     'GSL_EBADFUNC'
+          the iteration encountered a singular point where the function
+          or its derivative evaluated to 'Inf' or 'NaN'.
 
-37 Least-Squares Fitting
-************************
+     'GSL_ENOPROG'
+          the iteration is not making any progress, preventing the
+          algorithm from continuing.
 
-This chapter describes routines for performing least squares fits to
-experimental data using linear combinations of functions.  The data may
-be weighted or unweighted, i.e.  with known or unknown errors.  For
-weighted data the functions compute the best fit parameters and their
-associated covariance matrix.  For unweighted data the covariance matrix
-is estimated from the scatter of the points, giving a
-variance-covariance matrix.
+   The solver maintains a current best estimate of the root 's->x' and
+its function value 's->f' at all times.  This information can be
+accessed with the following auxiliary functions,
 
-   The functions are divided into separate versions for simple one- or
-two-parameter regression and multiple-parameter fits.  The functions are
-declared in the header file 'gsl_fit.h'.
+ -- Function: gsl_vector * gsl_multiroot_fsolver_root (const
+          gsl_multiroot_fsolver * S)
+ -- Function: gsl_vector * gsl_multiroot_fdfsolver_root (const
+          gsl_multiroot_fdfsolver * S)
+     These functions return the current estimate of the root for the
+     solver S, given by 's->x'.
 
-* Menu:
+ -- Function: gsl_vector * gsl_multiroot_fsolver_f (const
+          gsl_multiroot_fsolver * S)
+ -- Function: gsl_vector * gsl_multiroot_fdfsolver_f (const
+          gsl_multiroot_fdfsolver * S)
+     These functions return the function value f(x) at the current
+     estimate of the root for the solver S, given by 's->f'.
 
-* Fitting Overview::            
-* Linear regression::           
-* Linear fitting without a constant term::
-* Multi-parameter fitting::
-* Robust linear regression::
-* Troubleshooting::
-* Fitting Examples::            
-* Fitting References and Further Reading::  
+ -- Function: gsl_vector * gsl_multiroot_fsolver_dx (const
+          gsl_multiroot_fsolver * S)
+ -- Function: gsl_vector * gsl_multiroot_fdfsolver_dx (const
+          gsl_multiroot_fdfsolver * S)
+     These functions return the last step dx taken by the solver S,
+     given by 's->dx'.
 
 
-File: gsl-ref.info,  Node: Fitting Overview,  Next: Linear regression,  Up: Least-Squares Fitting
+File: gsl-ref.info,  Node: Search Stopping Parameters for the multidimensional solver,  Next: Algorithms using Derivatives,  Prev: Iteration of the multidimensional solver,  Up: Multidimensional Root-Finding
 
-37.1 Overview
-=============
+36.5 Search Stopping Parameters
+===============================
 
-Least-squares fits are found by minimizing \chi^2 (chi-squared), the
-weighted sum of squared residuals over n experimental datapoints (x_i,
-y_i) for the model Y(c,x),
+A root finding procedure should stop when one of the following
+conditions is true:
 
-     \chi^2 = \sum_i w_i (y_i - Y(c, x_i))^2
+   * A multidimensional root has been found to within the user-specified
+     precision.
 
-The p parameters of the model are c = {c_0, c_1, ...}.  The weight
-factors w_i are given by w_i = 1/\sigma_i^2, where \sigma_i is the
-experimental error on the data-point y_i.  The errors are assumed to be
-Gaussian and uncorrelated.  For unweighted data the chi-squared sum is
-computed without any weight factors.
+   * A user-specified maximum number of iterations has been reached.
 
-   The fitting routines return the best-fit parameters c and their p
-\times p covariance matrix.  The covariance matrix measures the
-statistical errors on the best-fit parameters resulting from the errors
-on the data, \sigma_i, and is defined as C_{ab} = <\delta c_a \delta
-c_b> where < > denotes an average over the Gaussian error distributions
-of the underlying datapoints.
+   * An error has occurred.
 
-   The covariance matrix is calculated by error propagation from the
-data errors \sigma_i.  The change in a fitted parameter \delta c_a
-caused by a small change in the data \delta y_i is given by
+The handling of these conditions is under user control.  The functions
+below allow the user to test the precision of the current result in
+several standard ways.
 
-     \delta c_a = \sum_i (dc_a/dy_i) \delta y_i
+ -- Function: int gsl_multiroot_test_delta (const gsl_vector * DX, const
+          gsl_vector * X, double EPSABS, double EPSREL)
 
-allowing the covariance matrix to be written in terms of the errors on
-the data,
+     This function tests for the convergence of the sequence by
+     comparing the last step DX with the absolute error EPSABS and
+     relative error EPSREL to the current position X.  The test returns
+     'GSL_SUCCESS' if the following condition is achieved,
 
-     C_{ab} = \sum_{i,j} (dc_a/dy_i) (dc_b/dy_j) <\delta y_i \delta y_j>
+          |dx_i| < epsabs + epsrel |x_i|
 
-For uncorrelated data the fluctuations of the underlying datapoints
-satisfy <\delta y_i \delta y_j> = \sigma_i^2 \delta_{ij}, giving a
-corresponding parameter covariance matrix of
+     for each component of X and returns 'GSL_CONTINUE' otherwise.
 
-     C_{ab} = \sum_i (1/w_i) (dc_a/dy_i) (dc_b/dy_i)
+ -- Function: int gsl_multiroot_test_residual (const gsl_vector * F,
+          double EPSABS)
+     This function tests the residual value F against the absolute error
+     bound EPSABS.  The test returns 'GSL_SUCCESS' if the following
+     condition is achieved,
 
-When computing the covariance matrix for unweighted data, i.e.  data
-with unknown errors, the weight factors w_i in this sum are replaced by
-the single estimate w = 1/\sigma^2, where \sigma^2 is the computed
-variance of the residuals about the best-fit model, \sigma^2 = \sum (y_i
-- Y(c,x_i))^2 / (n-p).  This is referred to as the "variance-covariance
-matrix".
+          \sum_i |f_i| < epsabs
 
-   The standard deviations of the best-fit parameters are given by the
-square root of the corresponding diagonal elements of the covariance
-matrix, \sigma_{c_a} = \sqrt{C_{aa}}.  The correlation coefficient of
-the fit parameters c_a and c_b is given by \rho_{ab} = C_{ab} /
-\sqrt{C_{aa} C_{bb}}.
+     and returns 'GSL_CONTINUE' otherwise.  This criterion is suitable
+     for situations where the precise location of the root, x, is
+     unimportant provided a value can be found where the residual is
+     small enough.
 
 
-File: gsl-ref.info,  Node: Linear regression,  Next: Linear fitting without a constant term,  Prev: Fitting Overview,  Up: Least-Squares Fitting
+File: gsl-ref.info,  Node: Algorithms using Derivatives,  Next: Algorithms without Derivatives,  Prev: Search Stopping Parameters for the multidimensional solver,  Up: Multidimensional Root-Finding
 
-37.2 Linear regression
-======================
+36.6 Algorithms using Derivatives
+=================================
 
-The functions described in this section can be used to perform
-least-squares fits to a straight line model, Y(c,x) = c_0 + c_1 x.
+The root finding algorithms described in this section make use of both
+the function and its derivative.  They require an initial guess for the
+location of the root, but there is no absolute guarantee of
+convergence--the function must be suitable for this technique and the
+initial guess must be sufficiently close to the root for it to work.
+When the conditions are satisfied then convergence is quadratic.
 
- -- Function: int gsl_fit_linear (const double * X, const size_t
-          XSTRIDE, const double * Y, const size_t YSTRIDE, size_t N,
-          double * C0, double * C1, double * COV00, double * COV01,
-          double * COV11, double * SUMSQ)
-     This function computes the best-fit linear regression coefficients
-     (C0,C1) of the model Y = c_0 + c_1 X for the dataset (X, Y), two
-     vectors of length N with strides XSTRIDE and YSTRIDE.  The errors
-     on Y are assumed unknown so the variance-covariance matrix for the
-     parameters (C0, C1) is estimated from the scatter of the points
-     around the best-fit line and returned via the parameters (COV00,
-     COV01, COV11).  The sum of squares of the residuals from the
-     best-fit line is returned in SUMSQ.  Note: the correlation
-     coefficient of the data can be computed using
-     'gsl_stats_correlation' (*note Correlation::), it does not depend
-     on the fit.
+ -- Derivative Solver: gsl_multiroot_fdfsolver_hybridsj
+     This is a modified version of Powell's Hybrid method as implemented
+     in the HYBRJ algorithm in MINPACK.  Minpack was written by Jorge J.
+     More', Burton S. Garbow and Kenneth E. Hillstrom.  The Hybrid
+     algorithm retains the fast convergence of Newton's method but will
+     also reduce the residual when Newton's method is unreliable.
 
- -- Function: int gsl_fit_wlinear (const double * X, const size_t
-          XSTRIDE, const double * W, const size_t WSTRIDE, const double
-          * Y, const size_t YSTRIDE, size_t N, double * C0, double * C1,
-          double * COV00, double * COV01, double * COV11, double *
-          CHISQ)
-     This function computes the best-fit linear regression coefficients
-     (C0,C1) of the model Y = c_0 + c_1 X for the weighted dataset (X,
-     Y), two vectors of length N with strides XSTRIDE and YSTRIDE.  The
-     vector W, of length N and stride WSTRIDE, specifies the weight of
-     each datapoint.  The weight is the reciprocal of the variance for
-     each datapoint in Y.
+     The algorithm uses a generalized trust region to keep each step
+     under control.  In order to be accepted a proposed new position x'
+     must satisfy the condition |D (x' - x)| < \delta, where D is a
+     diagonal scaling matrix and \delta is the size of the trust region.
+     The components of D are computed internally, using the column norms
+     of the Jacobian to estimate the sensitivity of the residual to each
+     component of x.  This improves the behavior of the algorithm for
+     badly scaled functions.
 
-     The covariance matrix for the parameters (C0, C1) is computed using
-     the weights and returned via the parameters (COV00, COV01, COV11).
-     The weighted sum of squares of the residuals from the best-fit
-     line, \chi^2, is returned in CHISQ.
+     On each iteration the algorithm first determines the standard
+     Newton step by solving the system J dx = - f.  If this step falls
+     inside the trust region it is used as a trial step in the next
+     stage.  If not, the algorithm uses the linear combination of the
+     Newton and gradient directions which is predicted to minimize the
+     norm of the function while staying inside the trust region,
 
- -- Function: int gsl_fit_linear_est (double X, double C0, double C1,
-          double COV00, double COV01, double COV11, double * Y, double *
-          Y_ERR)
-     This function uses the best-fit linear regression coefficients C0,
-     C1 and their covariance COV00, COV01, COV11 to compute the fitted
-     function Y and its standard deviation Y_ERR for the model Y = c_0 +
-     c_1 X at the point X.
+          dx = - \alpha J^{-1} f(x) - \beta \nabla |f(x)|^2.
 
-
-File: gsl-ref.info,  Node: Linear fitting without a constant term,  Next: Multi-parameter fitting,  Prev: Linear regression,  Up: Least-Squares Fitting
+     This combination of Newton and gradient directions is referred to
+     as a "dogleg step".
 
-37.3 Linear fitting without a constant term
-===========================================
+     The proposed step is now tested by evaluating the function at the
+     resulting point, x'.  If the step reduces the norm of the function
+     sufficiently then it is accepted and size of the trust region is
+     increased.  If the proposed step fails to improve the solution then
+     the size of the trust region is decreased and another trial step is
+     computed.
 
-The functions described in this section can be used to perform
-least-squares fits to a straight line model without a constant term, Y =
-c_1 X.
+     The speed of the algorithm is increased by computing the changes to
+     the Jacobian approximately, using a rank-1 update.  If two
+     successive attempts fail to reduce the residual then the full
+     Jacobian is recomputed.  The algorithm also monitors the progress
+     of the solution and returns an error if several steps fail to make
+     any improvement,
 
- -- Function: int gsl_fit_mul (const double * X, const size_t XSTRIDE,
-          const double * Y, const size_t YSTRIDE, size_t N, double * C1,
-          double * COV11, double * SUMSQ)
-     This function computes the best-fit linear regression coefficient
-     C1 of the model Y = c_1 X for the datasets (X, Y), two vectors of
-     length N with strides XSTRIDE and YSTRIDE.  The errors on Y are
-     assumed unknown so the variance of the parameter C1 is estimated
-     from the scatter of the points around the best-fit line and
-     returned via the parameter COV11.  The sum of squares of the
-     residuals from the best-fit line is returned in SUMSQ.
+     'GSL_ENOPROG'
+          the iteration is not making any progress, preventing the
+          algorithm from continuing.
 
- -- Function: int gsl_fit_wmul (const double * X, const size_t XSTRIDE,
-          const double * W, const size_t WSTRIDE, const double * Y,
-          const size_t YSTRIDE, size_t N, double * C1, double * COV11,
-          double * SUMSQ)
-     This function computes the best-fit linear regression coefficient
-     C1 of the model Y = c_1 X for the weighted datasets (X, Y), two
-     vectors of length N with strides XSTRIDE and YSTRIDE.  The vector
-     W, of length N and stride WSTRIDE, specifies the weight of each
-     datapoint.  The weight is the reciprocal of the variance for each
-     datapoint in Y.
+     'GSL_ENOPROGJ'
+          re-evaluations of the Jacobian indicate that the iteration is
+          not making any progress, preventing the algorithm from
+          continuing.
 
-     The variance of the parameter C1 is computed using the weights and
-     returned via the parameter COV11.  The weighted sum of squares of
-     the residuals from the best-fit line, \chi^2, is returned in CHISQ.
+ -- Derivative Solver: gsl_multiroot_fdfsolver_hybridj
+     This algorithm is an unscaled version of 'hybridsj'.  The steps are
+     controlled by a spherical trust region |x' - x| < \delta, instead
+     of a generalized region.  This can be useful if the generalized
+     region estimated by 'hybridsj' is inappropriate.
 
- -- Function: int gsl_fit_mul_est (double X, double C1, double COV11,
-          double * Y, double * Y_ERR)
-     This function uses the best-fit linear regression coefficient C1
-     and its covariance COV11 to compute the fitted function Y and its
-     standard deviation Y_ERR for the model Y = c_1 X at the point X.
+ -- Derivative Solver: gsl_multiroot_fdfsolver_newton
 
-
-File: gsl-ref.info,  Node: Multi-parameter fitting,  Next: Robust linear regression,  Prev: Linear fitting without a constant term,  Up: Least-Squares Fitting
+     Newton's Method is the standard root-polishing algorithm.  The
+     algorithm begins with an initial guess for the location of the
+     solution.  On each iteration a linear approximation to the function
+     F is used to estimate the step which will zero all the components
+     of the residual.  The iteration is defined by the following
+     sequence,
 
-37.4 Multi-parameter fitting
-============================
+          x -> x' = x - J^{-1} f(x)
 
-The functions described in this section perform least-squares fits to a
-general linear model, y = X c where y is a vector of n observations, X
-is an n by p matrix of predictor variables, and the elements of the
-vector c are the p unknown best-fit parameters which are to be
-estimated.  The chi-squared value is given by \chi^2 = \sum_i w_i (y_i -
-\sum_j X_{ij} c_j)^2.
+     where the Jacobian matrix J is computed from the derivative
+     functions provided by F.  The step dx is obtained by solving the
+     linear system,
 
-   This formulation can be used for fits to any number of functions
-and/or variables by preparing the n-by-p matrix X appropriately.  For
-example, to fit to a p-th order polynomial in X, use the following
-matrix,
+          J dx = - f(x)
 
-     X_{ij} = x_i^j
+     using LU decomposition.  If the Jacobian matrix is singular, an
+     error code of 'GSL_EDOM' is returned.
 
-where the index i runs over the observations and the index j runs from 0
-to p-1.
+ -- Derivative Solver: gsl_multiroot_fdfsolver_gnewton
+     This is a modified version of Newton's method which attempts to
+     improve global convergence by requiring every step to reduce the
+     Euclidean norm of the residual, |f(x)|.  If the Newton step leads
+     to an increase in the norm then a reduced step of relative size,
 
-   To fit to a set of p sinusoidal functions with fixed frequencies
-\omega_1, \omega_2, ..., \omega_p, use,
+          t = (\sqrt(1 + 6 r) - 1) / (3 r)
 
-     X_{ij} = sin(\omega_j x_i)
+     is proposed, with r being the ratio of norms |f(x')|^2/|f(x)|^2.
+     This procedure is repeated until a suitable step size is found.
 
-To fit to p independent variables x_1, x_2, ..., x_p, use,
+
+File: gsl-ref.info,  Node: Algorithms without Derivatives,  Next: Example programs for Multidimensional Root finding,  Prev: Algorithms using Derivatives,  Up: Multidimensional Root-Finding
 
-     X_{ij} = x_j(i)
+36.7 Algorithms without Derivatives
+===================================
 
-where x_j(i) is the i-th value of the predictor variable x_j.
+The algorithms described in this section do not require any derivative
+information to be supplied by the user.  Any derivatives needed are
+approximated by finite differences.  Note that if the
+finite-differencing step size chosen by these routines is inappropriate,
+an explicit user-supplied numerical derivative can always be used with
+the algorithms described in the previous section.
 
-   The functions described in this section are declared in the header
-file 'gsl_multifit.h'.
+ -- Solver: gsl_multiroot_fsolver_hybrids
+     This is a version of the Hybrid algorithm which replaces calls to
+     the Jacobian function by its finite difference approximation.  The
+     finite difference approximation is computed using
+     'gsl_multiroots_fdjac' with a relative step size of
+     'GSL_SQRT_DBL_EPSILON'.  Note that this step size will not be
+     suitable for all problems.
 
-   The solution of the general linear least-squares system requires an
-additional working space for intermediate results, such as the singular
-value decomposition of the matrix X.
+ -- Solver: gsl_multiroot_fsolver_hybrid
+     This is a finite difference version of the Hybrid algorithm without
+     internal scaling.
 
- -- Function: gsl_multifit_linear_workspace * gsl_multifit_linear_alloc
-          (size_t N, size_t P)
-     This function allocates a workspace for fitting a model to N
-     observations using P parameters.
+ -- Solver: gsl_multiroot_fsolver_dnewton
 
- -- Function: void gsl_multifit_linear_free
-          (gsl_multifit_linear_workspace * WORK)
-     This function frees the memory associated with the workspace W.
+     The "discrete Newton algorithm" is the simplest method of solving a
+     multidimensional system.  It uses the Newton iteration
 
- -- Function: int gsl_multifit_linear (const gsl_matrix * X, const
-          gsl_vector * Y, gsl_vector * C, gsl_matrix * COV, double *
-          CHISQ, gsl_multifit_linear_workspace * WORK)
-     This function computes the best-fit parameters C of the model y = X
-     c for the observations Y and the matrix of predictor variables X,
-     using the preallocated workspace provided in WORK.  The p-by-p
-     variance-covariance matrix of the model parameters COV is set to
-     \sigma^2 (X^T X)^{-1}, where \sigma is the standard deviation of
-     the fit residuals.  The sum of squares of the residuals from the
-     best-fit, \chi^2, is returned in CHISQ.  If the coefficient of
-     determination is desired, it can be computed from the expression
-     R^2 = 1 - \chi^2 / TSS, where the total sum of squares (TSS) of the
-     observations Y may be computed from 'gsl_stats_tss'.
+          x -> x - J^{-1} f(x)
 
-     The best-fit is found by singular value decomposition of the matrix
-     X using the modified Golub-Reinsch SVD algorithm, with column
-     scaling to improve the accuracy of the singular values.  Any
-     components which have zero singular value (to machine precision)
-     are discarded from the fit.
+     where the Jacobian matrix J is approximated by taking finite
+     differences of the function F.  The approximation scheme used by
+     this implementation is,
 
- -- Function: int gsl_multifit_wlinear (const gsl_matrix * X, const
-          gsl_vector * W, const gsl_vector * Y, gsl_vector * C,
-          gsl_matrix * COV, double * CHISQ,
-          gsl_multifit_linear_workspace * WORK)
-     This function computes the best-fit parameters C of the weighted
-     model y = X c for the observations Y with weights W and the matrix
-     of predictor variables X, using the preallocated workspace provided
-     in WORK.  The p-by-p covariance matrix of the model parameters COV
-     is computed as (X^T W X)^{-1}.  The weighted sum of squares of the
-     residuals from the best-fit, \chi^2, is returned in CHISQ.  If the
-     coefficient of determination is desired, it can be computed from
-     the expression R^2 = 1 - \chi^2 / WTSS, where the weighted total
-     sum of squares (WTSS) of the observations Y may be computed from
-     'gsl_stats_wtss'.
+          J_{ij} = (f_i(x + \delta_j) - f_i(x)) /  \delta_j
 
- -- Function: int gsl_multifit_linear_svd (const gsl_matrix * X, const
-          gsl_vector * Y, double TOL, size_t * RANK, gsl_vector * C,
-          gsl_matrix * COV, double * CHISQ,
-          gsl_multifit_linear_workspace * WORK)
- -- Function: int gsl_multifit_wlinear_svd (const gsl_matrix * X, const
-          gsl_vector * W, const gsl_vector * Y, double TOL, size_t *
-          RANK, gsl_vector * C, gsl_matrix * COV, double * CHISQ,
-          gsl_multifit_linear_workspace * WORK)
-     In these functions components of the fit are discarded if the ratio
-     of singular values s_i/s_0 falls below the user-specified tolerance
-     TOL, and the effective rank is returned in RANK.
+     where \delta_j is a step of size \sqrt\epsilon |x_j| with \epsilon
+     being the machine precision (\epsilon \approx 2.22 \times 10^-16).
+     The order of convergence of Newton's algorithm is quadratic, but
+     the finite differences require n^2 function evaluations on each
+     iteration.  The algorithm may become unstable if the finite
+     differences are not a good approximation to the true derivatives.
 
- -- Function: int gsl_multifit_linear_usvd (const gsl_matrix * X, const
-          gsl_vector * Y, double TOL, size_t * RANK, gsl_vector * C,
-          gsl_matrix * COV, double * CHISQ,
-          gsl_multifit_linear_workspace * WORK)
- -- Function: int gsl_multifit_wlinear_usvd (const gsl_matrix * X, const
-          gsl_vector * W, const gsl_vector * Y, double TOL, size_t *
-          RANK, gsl_vector * C, gsl_matrix * COV, double * CHISQ,
-          gsl_multifit_linear_workspace * WORK)
-     These functions compute the fit using an SVD without column
-     scaling.
+ -- Solver: gsl_multiroot_fsolver_broyden
 
- -- Function: int gsl_multifit_linear_est (const gsl_vector * X, const
-          gsl_vector * C, const gsl_matrix * COV, double * Y, double *
-          Y_ERR)
-     This function uses the best-fit multilinear regression coefficients
-     C and their covariance matrix COV to compute the fitted function
-     value Y and its standard deviation Y_ERR for the model y = x.c at
-     the point X.
+     The "Broyden algorithm" is a version of the discrete Newton
+     algorithm which attempts to avoids the expensive update of the
+     Jacobian matrix on each iteration.  The changes to the Jacobian are
+     also approximated, using a rank-1 update,
 
- -- Function: int gsl_multifit_linear_residuals (const gsl_matrix * X,
-          const gsl_vector * Y, const gsl_vector * C, gsl_vector * R)
-     This function computes the vector of residuals r = y - X c for the
-     observations Y, coefficients C and matrix of predictor variables X.
+          J^{-1} \to J^{-1} - (J^{-1} df - dx) dx^T J^{-1} / dx^T J^{-1} df
 
-
-File: gsl-ref.info,  Node: Robust linear regression,  Next: Troubleshooting,  Prev: Multi-parameter fitting,  Up: Least-Squares Fitting
+     where the vectors dx and df are the changes in x and f.  On the
+     first iteration the inverse Jacobian is estimated using finite
+     differences, as in the discrete Newton algorithm.
 
-37.5 Robust linear regression
-=============================
+     This approximation gives a fast update but is unreliable if the
+     changes are not small, and the estimate of the inverse Jacobian
+     becomes worse as time passes.  The algorithm has a tendency to
+     become unstable unless it starts close to the root.  The Jacobian
+     is refreshed if this instability is detected (consult the source
+     for details).
 
-Ordinary least squares (OLS) models are often heavily influenced by the
-presence of outliers.  Outliers are data points which do not follow the
-general trend of the other observations, although there is strictly no
-precise definition of an outlier.  Robust linear regression refers to
-regression algorithms which are robust to outliers.  The most common
-type of robust regression is M-estimation.  The general M-estimator
-minimizes the objective function
+     This algorithm is included only for demonstration purposes, and is
+     not recommended for serious use.
 
-     \sum_i \rho(e_i) = \sum_i \rho (y_i - Y(c, x_i))
+
+File: gsl-ref.info,  Node: Example programs for Multidimensional Root finding,  Next: References and Further Reading for Multidimensional Root Finding,  Prev: Algorithms without Derivatives,  Up: Multidimensional Root-Finding
 
-   where e_i = y_i - Y(c, x_i) is the residual of the ith data point,
-and \rho(e_i) is a function which should have the following properties:
-     \rho(e) \ge 0
-     \rho(0) = 0
-     \rho(-e) = \rho(e)
-     \rho(e_1) > \rho(e_2) for |e_1| > |e_2|
-The special case of ordinary least squares is given by \rho(e_i) =
-e_i^2.  Letting \psi = \rho' be the derivative of \rho, differentiating
-the objective function with respect to the coefficients c and setting
-the partial derivatives to zero produces the system of equations
+36.8 Examples
+=============
 
-     \sum_i \psi(e_i) X_i = 0
+The multidimensional solvers are used in a similar way to the
+one-dimensional root finding algorithms.  This first example
+demonstrates the 'hybrids' scaled-hybrid algorithm, which does not
+require derivatives.  The program solves the Rosenbrock system of
+equations,
 
-   where X_i is a vector containing row i of the design matrix X.  Next,
-we define a weight function w(e) = \psi(e)/e, and let w_i = w(e_i):
+     f_1 (x, y) = a (1 - x)
+     f_2 (x, y) = b (y - x^2)
 
-     \sum_i w_i e_i X_i = 0
+with a = 1, b = 10.  The solution of this system lies at (x,y) = (1,1)
+in a narrow valley.
 
-   This system of equations is equivalent to solving a weighted ordinary
-least squares problem, minimizing \chi^2 = \sum_i w_i e_i^2.  The
-weights however, depend on the residuals e_i, which depend on the
-coefficients c, which depend on the weights.  Therefore, an iterative
-solution is used, called Iteratively Reweighted Least Squares (IRLS).
-  1. Compute initial estimates of the coefficients c^{(0)} using
-     ordinary least squares
+   The first stage of the program is to define the system of equations,
 
-  2. For iteration k, form the residuals e_i^{(k)} = (y_i - X_i
-     c^{(k-1)})/(t \sigma^{(k)} \sqrt{1 - h_i}), where t is a tuning
-     constant depending on the choice of \psi, and h_i are the
-     statistical leverages (diagonal elements of the matrix X (X^T
-     X)^{-1} X^T).  Including t and h_i in the residual calculation has
-     been shown to improve the convergence of the method.  The residual
-     standard deviation is approximated as \sigma^{(k)} = MAD / 0.6745,
-     where MAD is the Median-Absolute-Deviation of the n-p largest
-     residuals from the previous iteration.
+     #include <stdlib.h>
+     #include <stdio.h>
+     #include <gsl/gsl_vector.h>
+     #include <gsl/gsl_multiroots.h>
 
-  3. Compute new weights w_i^{(k)} = \psi(e_i^{(k)})/e_i^{(k)}.
+     struct rparams
+       {
+         double a;
+         double b;
+       };
 
-  4. Compute new coefficients c^{(k)} by solving the weighted least
-     squares problem with weights w_i^{(k)}.
+     int
+     rosenbrock_f (const gsl_vector * x, void *params,
+                   gsl_vector * f)
+     {
+       double a = ((struct rparams *) params)->a;
+       double b = ((struct rparams *) params)->b;
 
-  5. Steps 2 through 4 are iterated until the coefficients converge or
-     until some maximum iteration limit is reached.  Coefficients are
-     tested for convergence using the critera:
+       const double x0 = gsl_vector_get (x, 0);
+       const double x1 = gsl_vector_get (x, 1);
 
-          |c_i^(k) - c_i^(k-1)| \le \epsilon \times max(|c_i^(k)|, |c_i^(k-1)|)
+       const double y0 = a * (1 - x0);
+       const double y1 = b * (x1 - x0 * x0);
 
-     for all 0 \le i < p where \epsilon is a small tolerance factor.
-The key to this method lies in selecting the function \psi(e_i) to
-assign smaller weights to large residuals, and larger weights to smaller
-residuals.  As the iteration proceeds, outliers are assigned smaller and
-smaller weights, eventually having very little or no effect on the
-fitted model.
+       gsl_vector_set (f, 0, y0);
+       gsl_vector_set (f, 1, y1);
 
- -- Function: gsl_multifit_robust_workspace * gsl_multifit_robust_alloc
-          (const gsl_multifit_robust_type * T, const size_t N, const
-          size_t P)
-     This function allocates a workspace for fitting a model to N
-     observations using P parameters.  The type T specifies the function
-     \psi and can be selected from the following choices.
-      -- Robust type: gsl_multifit_robust_default
-          This specifies the 'gsl_multifit_robust_bisquare' type (see
-          below) and is a good general purpose choice for robust
-          regression.
+       return GSL_SUCCESS;
+     }
 
-      -- Robust type: gsl_multifit_robust_bisquare
-          This is Tukey's biweight (bisquare) function and is a good
-          general purpose choice for robust regression.  The weight
-          function is given by
+The main program begins by creating the function object 'f', with the
+arguments '(x,y)' and parameters '(a,b)'.  The solver 's' is initialized
+to use this function, with the 'hybrids' method.
 
-               w(e) = (1 - e^2)^2
+     int
+     main (void)
+     {
+       const gsl_multiroot_fsolver_type *T;
+       gsl_multiroot_fsolver *s;
 
-          and the default tuning constant is t = 4.685.
+       int status;
+       size_t i, iter = 0;
 
-      -- Robust type: gsl_multifit_robust_cauchy
-          This is Cauchy's function, also known as the Lorentzian
-          function.  This function does not guarantee a unique solution,
-          meaning different choices of the coefficient vector C could
-          minimize the objective function.  Therefore this option should
-          be used with care.  The weight function is given by
+       const size_t n = 2;
+       struct rparams p = {1.0, 10.0};
+       gsl_multiroot_function f = {&rosenbrock_f, n, &p};
 
-               w(e) = 1 / (1 + e^2)
+       double x_init[2] = {-10.0, -5.0};
+       gsl_vector *x = gsl_vector_alloc (n);
 
-          and the default tuning constant is t = 2.385.
+       gsl_vector_set (x, 0, x_init[0]);
+       gsl_vector_set (x, 1, x_init[1]);
 
-      -- Robust type: gsl_multifit_robust_fair
-          This is the fair \rho function, which guarantees a unique
-          solution and has continuous derivatives to three orders.  The
-          weight function is given by
+       T = gsl_multiroot_fsolver_hybrids;
+       s = gsl_multiroot_fsolver_alloc (T, 2);
+       gsl_multiroot_fsolver_set (s, &f, x);
 
-               w(e) = 1 / (1 + |e|)
+       print_state (iter, s);
 
-          and the default tuning constant is t = 1.400.
+       do
+         {
+           iter++;
+           status = gsl_multiroot_fsolver_iterate (s);
 
-      -- Robust type: gsl_multifit_robust_huber
-          This specifies Huber's \rho function, which is a parabola in
-          the vicinity of zero and increases linearly for a given
-          threshold |e| > t.  This function is also considered an
-          excellent general purpose robust estimator, however,
-          occasional difficulties can be encountered due to the
-          discontinuous first derivative of the \psi function.  The
-          weight function is given by
+           print_state (iter, s);
 
-               w(e) = 1/max(1,|e|)
+           if (status)   /* check if solver is stuck */
+             break;
 
-          and the default tuning constant is t = 1.345.
+           status =
+             gsl_multiroot_test_residual (s->f, 1e-7);
+         }
+       while (status == GSL_CONTINUE && iter < 1000);
 
-      -- Robust type: gsl_multifit_robust_ols
-          This specifies the ordinary least squares solution, which can
-          be useful for quickly checking the difference between the
-          various robust and OLS solutions.  The weight function is
-          given by
+       printf ("status = %s\n", gsl_strerror (status));
 
-               w(e) = 1
+       gsl_multiroot_fsolver_free (s);
+       gsl_vector_free (x);
+       return 0;
+     }
 
-          and the default tuning constant is t = 1.
+Note that it is important to check the return status of each solver
+step, in case the algorithm becomes stuck.  If an error condition is
+detected, indicating that the algorithm cannot proceed, then the error
+can be reported to the user, a new starting point chosen or a different
+algorithm used.
 
-      -- Robust type: gsl_multifit_robust_welsch
-          This specifies the Welsch function which can perform well in
-          cases where the residuals have an exponential distribution.
-          The weight function is given by
+   The intermediate state of the solution is displayed by the following
+function.  The solver state contains the vector 's->x' which is the
+current position, and the vector 's->f' with corresponding function
+values.
 
-               w(e) = \exp(-e^2)
+     int
+     print_state (size_t iter, gsl_multiroot_fsolver * s)
+     {
+       printf ("iter = %3u x = % .3f % .3f "
+               "f(x) = % .3e % .3e\n",
+               iter,
+               gsl_vector_get (s->x, 0),
+               gsl_vector_get (s->x, 1),
+               gsl_vector_get (s->f, 0),
+               gsl_vector_get (s->f, 1));
+     }
 
-          and the default tuning constant is t = 2.985.
+Here are the results of running the program.  The algorithm is started
+at (-10,-5) far from the solution.  Since the solution is hidden in a
+narrow valley the earliest steps follow the gradient of the function
+downhill, in an attempt to reduce the large value of the residual.  Once
+the root has been approximately located, on iteration 8, the Newton
+behavior takes over and convergence is very rapid.
 
- -- Function: void gsl_multifit_robust_free
-          (gsl_multifit_robust_workspace * W)
-     This function frees the memory associated with the workspace W.
+     iter =  0 x = -10.000  -5.000  f(x) = 1.100e+01 -1.050e+03
+     iter =  1 x = -10.000  -5.000  f(x) = 1.100e+01 -1.050e+03
+     iter =  2 x =  -3.976  24.827  f(x) = 4.976e+00  9.020e+01
+     iter =  3 x =  -3.976  24.827  f(x) = 4.976e+00  9.020e+01
+     iter =  4 x =  -3.976  24.827  f(x) = 4.976e+00  9.020e+01
+     iter =  5 x =  -1.274  -5.680  f(x) = 2.274e+00 -7.302e+01
+     iter =  6 x =  -1.274  -5.680  f(x) = 2.274e+00 -7.302e+01
+     iter =  7 x =   0.249   0.298  f(x) = 7.511e-01  2.359e+00
+     iter =  8 x =   0.249   0.298  f(x) = 7.511e-01  2.359e+00
+     iter =  9 x =   1.000   0.878  f(x) = 1.268e-10 -1.218e+00
+     iter = 10 x =   1.000   0.989  f(x) = 1.124e-11 -1.080e-01
+     iter = 11 x =   1.000   1.000  f(x) = 0.000e+00  0.000e+00
+     status = success
 
- -- Function: const char * gsl_multifit_robust_name (const
-          gsl_multifit_robust_workspace * W)
-     This function returns the name of the robust type T specified to
-     'gsl_multifit_robust_alloc'.
+Note that the algorithm does not update the location on every iteration.
+Some iterations are used to adjust the trust-region parameter, after
+trying a step which was found to be divergent, or to recompute the
+Jacobian, when poor convergence behavior is detected.
 
- -- Function: int gsl_multifit_robust_tune (const double TUNE,
-          gsl_multifit_robust_workspace * W)
-     This function sets the tuning constant t used to adjust the
-     residuals at each iteration to TUNE.  Decreasing the tuning
-     constant increases the downweight assigned to large residuals,
-     while increasing the tuning constant decreases the downweight
-     assigned to large residuals.
+   The next example program adds derivative information, in order to
+accelerate the solution.  There are two derivative functions
+'rosenbrock_df' and 'rosenbrock_fdf'.  The latter computes both the
+function and its derivative simultaneously.  This allows the
+optimization of any common terms.  For simplicity we substitute calls to
+the separate 'f' and 'df' functions at this point in the code below.
 
- -- Function: int gsl_multifit_robust (const gsl_matrix * X, const
-          gsl_vector * Y, gsl_vector * C, gsl_matrix * COV,
-          gsl_multifit_robust_workspace * W)
-     This function computes the best-fit parameters C of the model y = X
-     c for the observations Y and the matrix of predictor variables X,
-     attemping to reduce the influence of outliers using the algorithm
-     outlined above.  The p-by-p variance-covariance matrix of the model
-     parameters COV is estimated as \sigma^2 (X^T X)^{-1}, where \sigma
-     is an approximation of the residual standard deviation using the
-     theory of robust regression.  Special care must be taken when
-     estimating \sigma and other statistics such as R^2, and so these
-     are computed internally and are available by calling the function
-     'gsl_multifit_robust_statistics'.
+     int
+     rosenbrock_df (const gsl_vector * x, void *params,
+                    gsl_matrix * J)
+     {
+       const double a = ((struct rparams *) params)->a;
+       const double b = ((struct rparams *) params)->b;
 
- -- Function: int gsl_multifit_robust_est (const gsl_vector * X, const
-          gsl_vector * C, const gsl_matrix * COV, double * Y, double *
-          Y_ERR)
-     This function uses the best-fit robust regression coefficients C
-     and their covariance matrix COV to compute the fitted function
-     value Y and its standard deviation Y_ERR for the model y = x.c at
-     the point X.
+       const double x0 = gsl_vector_get (x, 0);
 
- -- Function: gsl_multifit_robust_stats gsl_multifit_robust_statistics
-          (const gsl_multifit_robust_workspace * W)
-     This function returns a structure containing relevant statistics
-     from a robust regression.  The function 'gsl_multifit_robust' must
-     be called first to perform the regression and calculate these
-     statistics.  The returned 'gsl_multifit_robust_stats' structure
-     contains the following fields.
-          double 'sigma_ols' This contains the standard deviation of the
-          residuals as computed from ordinary least squares (OLS).
+       const double df00 = -a;
+       const double df01 = 0;
+       const double df10 = -2 * b  * x0;
+       const double df11 = b;
 
-          double 'sigma_mad' This contains an estimate of the standard
-          deviation of the final residuals using the
-          Median-Absolute-Deviation statistic
+       gsl_matrix_set (J, 0, 0, df00);
+       gsl_matrix_set (J, 0, 1, df01);
+       gsl_matrix_set (J, 1, 0, df10);
+       gsl_matrix_set (J, 1, 1, df11);
 
-          double 'sigma_rob' This contains an estimate of the standard
-          deviation of the final residuals from the theory of robust
-          regression (see Street et al, 1988).
+       return GSL_SUCCESS;
+     }
 
-          double 'sigma' This contains an estimate of the standard
-          deviation of the final residuals by attemping to reconcile
-          'sigma_rob' and 'sigma_ols' in a reasonable way.
+     int
+     rosenbrock_fdf (const gsl_vector * x, void *params,
+                     gsl_vector * f, gsl_matrix * J)
+     {
+       rosenbrock_f (x, params, f);
+       rosenbrock_df (x, params, J);
 
-          double 'Rsq' This contains the R^2 coefficient of
-          determination statistic using the estimate 'sigma'.
+       return GSL_SUCCESS;
+     }
 
-          double 'adj_Rsq' This contains the adjusted R^2 coefficient of
-          determination statistic using the estimate 'sigma'.
+The main program now makes calls to the corresponding 'fdfsolver'
+versions of the functions,
 
-          double 'rmse' This contains the root mean squared error of the
-          final residuals
+     int
+     main (void)
+     {
+       const gsl_multiroot_fdfsolver_type *T;
+       gsl_multiroot_fdfsolver *s;
 
-          double 'sse' This contains the residual sum of squares taking
-          into account the robust covariance matrix.
+       int status;
+       size_t i, iter = 0;
 
-          size_t 'dof' This contains the number of degrees of freedom n
-          - p
+       const size_t n = 2;
+       struct rparams p = {1.0, 10.0};
+       gsl_multiroot_function_fdf f = {&rosenbrock_f,
+                                       &rosenbrock_df,
+                                       &rosenbrock_fdf,
+                                       n, &p};
 
-          size_t 'numit' Upon successful convergence, this contains the
-          number of iterations performed
+       double x_init[2] = {-10.0, -5.0};
+       gsl_vector *x = gsl_vector_alloc (n);
 
-          gsl_vector * 'weights' This contains the final weight vector
-          of length N
+       gsl_vector_set (x, 0, x_init[0]);
+       gsl_vector_set (x, 1, x_init[1]);
 
-          gsl_vector * 'r' This contains the final residual vector of
-          length N, r = y - X c
+       T = gsl_multiroot_fdfsolver_gnewton;
+       s = gsl_multiroot_fdfsolver_alloc (T, n);
+       gsl_multiroot_fdfsolver_set (s, &f, x);
 
-
-File: gsl-ref.info,  Node: Troubleshooting,  Next: Fitting Examples,  Prev: Robust linear regression,  Up: Least-Squares Fitting
+       print_state (iter, s);
 
-37.6 Troubleshooting
-====================
+       do
+         {
+           iter++;
 
-When using models based on polynomials, care should be taken when
-constructing the design matrix X.  If the x values are large, then the
-matrix X could be ill-conditioned since its columns are powers of x,
-leading to unstable least-squares solutions.  In this case it can often
-help to center and scale the x values using the mean and standard
-deviation:
+           status = gsl_multiroot_fdfsolver_iterate (s);
 
-     x' = (x - mu)/sigma
+           print_state (iter, s);
 
-and then construct the X matrix using the transformed values x'.
+           if (status)
+             break;
 
-
-File: gsl-ref.info,  Node: Fitting Examples,  Next: Fitting References and Further Reading,  Prev: Troubleshooting,  Up: Least-Squares Fitting
+           status = gsl_multiroot_test_residual (s->f, 1e-7);
+         }
+       while (status == GSL_CONTINUE && iter < 1000);
 
-37.7 Examples
-=============
+       printf ("status = %s\n", gsl_strerror (status));
 
-The following program computes a least squares straight-line fit to a
-simple dataset, and outputs the best-fit line and its associated one
-standard-deviation error bars.
+       gsl_multiroot_fdfsolver_free (s);
+       gsl_vector_free (x);
+       return 0;
+     }
 
-     #include <stdio.h>
-     #include <gsl/gsl_fit.h>
+The addition of derivative information to the 'hybrids' solver does not
+make any significant difference to its behavior, since it able to
+approximate the Jacobian numerically with sufficient accuracy.  To
+illustrate the behavior of a different derivative solver we switch to
+'gnewton'.  This is a traditional Newton solver with the constraint that
+it scales back its step if the full step would lead "uphill".  Here is
+the output for the 'gnewton' algorithm,
 
-     int
-     main (void)
-     {
-       int i, n = 4;
-       double x[4] = { 1970, 1980, 1990, 2000 };
-       double y[4] = {   12,   11,   14,   13 };
-       double w[4] = {  0.1,  0.2,  0.3,  0.4 };
+     iter = 0 x = -10.000  -5.000 f(x) =  1.100e+01 -1.050e+03
+     iter = 1 x =  -4.231 -65.317 f(x) =  5.231e+00 -8.321e+02
+     iter = 2 x =   1.000 -26.358 f(x) = -8.882e-16 -2.736e+02
+     iter = 3 x =   1.000   1.000 f(x) = -2.220e-16 -4.441e-15
+     status = success
 
-       double c0, c1, cov00, cov01, cov11, chisq;
+The convergence is much more rapid, but takes a wide excursion out to
+the point (-4.23,-65.3).  This could cause the algorithm to go astray in
+a realistic application.  The hybrid algorithm follows the downhill path
+to the solution more reliably.
 
-       gsl_fit_wlinear (x, 1, w, 1, y, 1, n,
-                        &c0, &c1, &cov00, &cov01, &cov11,
-                        &chisq);
+
+File: gsl-ref.info,  Node: References and Further Reading for Multidimensional Root Finding,  Prev: Example programs for Multidimensional Root finding,  Up: Multidimensional Root-Finding
 
-       printf ("# best fit: Y = %g + %g X\n", c0, c1);
-       printf ("# covariance matrix:\n");
-       printf ("# [ %g, %g\n#   %g, %g]\n",
-               cov00, cov01, cov01, cov11);
-       printf ("# chisq = %g\n", chisq);
+36.9 References and Further Reading
+===================================
 
-       for (i = 0; i < n; i++)
-         printf ("data: %g %g %g\n",
-                        x[i], y[i], 1/sqrt(w[i]));
+The original version of the Hybrid method is described in the following
+articles by Powell,
 
-       printf ("\n");
+     M.J.D. Powell, "A Hybrid Method for Nonlinear Equations" (Chap 6, p
+     87-114) and "A Fortran Subroutine for Solving systems of Nonlinear
+     Algebraic Equations" (Chap 7, p 115-161), in 'Numerical Methods for
+     Nonlinear Algebraic Equations', P. Rabinowitz, editor.  Gordon and
+     Breach, 1970.
 
-       for (i = -30; i < 130; i++)
-         {
-           double xf = x[0] + (i/100.0) * (x[n-1] - x[0]);
-           double yf, yf_err;
+The following papers are also relevant to the algorithms described in
+this section,
 
-           gsl_fit_linear_est (xf,
-                               c0, c1,
-                               cov00, cov01, cov11,
-                               &yf, &yf_err);
+     J.J. More', M.Y. Cosnard, "Numerical Solution of Nonlinear
+     Equations", 'ACM Transactions on Mathematical Software', Vol 5, No
+     1, (1979), p 64-85
 
-           printf ("fit: %g %g\n", xf, yf);
-           printf ("hi : %g %g\n", xf, yf + yf_err);
-           printf ("lo : %g %g\n", xf, yf - yf_err);
-         }
-       return 0;
-     }
+     C.G. Broyden, "A Class of Methods for Solving Nonlinear
+     Simultaneous Equations", 'Mathematics of Computation', Vol 19
+     (1965), p 577-593
 
-The following commands extract the data from the output of the program
-and display it using the GNU plotutils 'graph' utility,
+     J.J. More', B.S. Garbow, K.E. Hillstrom, "Testing Unconstrained
+     Optimization Software", ACM Transactions on Mathematical Software,
+     Vol 7, No 1 (1981), p 17-41
 
-     $ ./demo > tmp
-     $ more tmp
-     # best fit: Y = -106.6 + 0.06 X
-     # covariance matrix:
-     # [ 39602, -19.9
-     #   -19.9, 0.01]
-     # chisq = 0.8
+
+File: gsl-ref.info,  Node: Multidimensional Minimization,  Next: Least-Squares Fitting,  Prev: Multidimensional Root-Finding,  Up: Top
 
-     $ for n in data fit hi lo ;
-        do
-          grep "^$n" tmp | cut -d: -f2 > $n ;
-        done
-     $ graph -T X -X x -Y y -y 0 20 -m 0 -S 2 -Ie data
-          -S 0 -I a -m 1 fit -m 2 hi -m 2 lo
+37 Multidimensional Minimization
+********************************
 
-   The next program performs a quadratic fit y = c_0 + c_1 x + c_2 x^2
-to a weighted dataset using the generalised linear fitting function
-'gsl_multifit_wlinear'.  The model matrix X for a quadratic fit is given
-by,
+This chapter describes routines for finding minima of arbitrary
+multidimensional functions.  The library provides low level components
+for a variety of iterative minimizers and convergence tests.  These can
+be combined by the user to achieve the desired solution, while providing
+full access to the intermediate steps of the algorithms.  Each class of
+methods uses the same framework, so that you can switch between
+minimizers at runtime without needing to recompile your program.  Each
+instance of a minimizer keeps track of its own state, allowing the
+minimizers to be used in multi-threaded programs.  The minimization
+algorithms can be used to maximize a function by inverting its sign.
 
-     X = [ 1   , x_0  , x_0^2 ;
-           1   , x_1  , x_1^2 ;
-           1   , x_2  , x_2^2 ;
-           ... , ...  , ...   ]
+   The header file 'gsl_multimin.h' contains prototypes for the
+minimization functions and related declarations.
 
-where the column of ones corresponds to the constant term c_0.  The two
-remaining columns corresponds to the terms c_1 x and c_2 x^2.
+* Menu:
 
-   The program reads N lines of data in the format (X, Y, ERR) where ERR
-is the error (standard deviation) in the value Y.
+* Multimin Overview::           
+* Multimin Caveats::            
+* Initializing the Multidimensional Minimizer::  
+* Providing a function to minimize::  
+* Multimin Iteration::          
+* Multimin Stopping Criteria::  
+* Multimin Algorithms with Derivatives::  
+* Multimin Algorithms without Derivatives::  
+* Multimin Examples::           
+* Multimin References and Further Reading::  
 
-     #include <stdio.h>
-     #include <gsl/gsl_multifit.h>
+
+File: gsl-ref.info,  Node: Multimin Overview,  Next: Multimin Caveats,  Up: Multidimensional Minimization
 
-     int
-     main (int argc, char **argv)
-     {
-       int i, n;
-       double xi, yi, ei, chisq;
-       gsl_matrix *X, *cov;
-       gsl_vector *y, *w, *c;
+37.1 Overview
+=============
 
-       if (argc != 2)
-         {
-           fprintf (stderr,"usage: fit n < data\n");
-           exit (-1);
-         }
+The problem of multidimensional minimization requires finding a point x
+such that the scalar function,
 
-       n = atoi (argv[1]);
+     f(x_1, ..., x_n)
 
-       X = gsl_matrix_alloc (n, 3);
-       y = gsl_vector_alloc (n);
-       w = gsl_vector_alloc (n);
+takes a value which is lower than at any neighboring point.  For smooth
+functions the gradient g = \nabla f vanishes at the minimum.  In general
+there are no bracketing methods available for the minimization of
+n-dimensional functions.  The algorithms proceed from an initial guess
+using a search algorithm which attempts to move in a downhill direction.
 
-       c = gsl_vector_alloc (3);
-       cov = gsl_matrix_alloc (3, 3);
+   Algorithms making use of the gradient of the function perform a
+one-dimensional line minimisation along this direction until the lowest
+point is found to a suitable tolerance.  The search direction is then
+updated with local information from the function and its derivatives,
+and the whole process repeated until the true n-dimensional minimum is
+found.
 
-       for (i = 0; i < n; i++)
-         {
-           int count = fscanf (stdin, "%lg %lg %lg",
-                               &xi, &yi, &ei);
+   Algorithms which do not require the gradient of the function use
+different strategies.  For example, the Nelder-Mead Simplex algorithm
+maintains n+1 trial parameter vectors as the vertices of a n-dimensional
+simplex.  On each iteration it tries to improve the worst vertex of the
+simplex by geometrical transformations.  The iterations are continued
+until the overall size of the simplex has decreased sufficiently.
 
-           if (count != 3)
-             {
-               fprintf (stderr, "error reading file\n");
-               exit (-1);
-             }
+   Both types of algorithms use a standard framework.  The user provides
+a high-level driver for the algorithms, and the library provides the
+individual functions necessary for each of the steps.  There are three
+main phases of the iteration.  The steps are,
 
-           printf ("%g %g +/- %g\n", xi, yi, ei);
+   * initialize minimizer state, S, for algorithm T
 
-           gsl_matrix_set (X, i, 0, 1.0);
-           gsl_matrix_set (X, i, 1, xi);
-           gsl_matrix_set (X, i, 2, xi*xi);
+   * update S using the iteration T
 
-           gsl_vector_set (y, i, yi);
-           gsl_vector_set (w, i, 1.0/(ei*ei));
-         }
+   * test S for convergence, and repeat iteration if necessary
 
-       {
-         gsl_multifit_linear_workspace * work
-           = gsl_multifit_linear_alloc (n, 3);
-         gsl_multifit_wlinear (X, w, y, c, cov,
-                               &chisq, work);
-         gsl_multifit_linear_free (work);
-       }
+Each iteration step consists either of an improvement to the
+line-minimisation in the current direction or an update to the search
+direction itself.  The state for the minimizers is held in a
+'gsl_multimin_fdfminimizer' struct or a 'gsl_multimin_fminimizer'
+struct.
 
-     #define C(i) (gsl_vector_get(c,(i)))
-     #define COV(i,j) (gsl_matrix_get(cov,(i),(j)))
+
+File: gsl-ref.info,  Node: Multimin Caveats,  Next: Initializing the Multidimensional Minimizer,  Prev: Multimin Overview,  Up: Multidimensional Minimization
 
-       {
-         printf ("# best fit: Y = %g + %g X + %g X^2\n",
-                 C(0), C(1), C(2));
+37.2 Caveats
+============
 
-         printf ("# covariance matrix:\n");
-         printf ("[ %+.5e, %+.5e, %+.5e  \n",
-                    COV(0,0), COV(0,1), COV(0,2));
-         printf ("  %+.5e, %+.5e, %+.5e  \n",
-                    COV(1,0), COV(1,1), COV(1,2));
-         printf ("  %+.5e, %+.5e, %+.5e ]\n",
-                    COV(2,0), COV(2,1), COV(2,2));
-         printf ("# chisq = %g\n", chisq);
-       }
+Note that the minimization algorithms can only search for one local
+minimum at a time.  When there are several local minima in the search
+area, the first minimum to be found will be returned; however it is
+difficult to predict which of the minima this will be.  In most cases,
+no error will be reported if you try to find a local minimum in an area
+where there is more than one.
 
-       gsl_matrix_free (X);
-       gsl_vector_free (y);
-       gsl_vector_free (w);
-       gsl_vector_free (c);
-       gsl_matrix_free (cov);
+   It is also important to note that the minimization algorithms find
+local minima; there is no way to determine whether a minimum is a global
+minimum of the function in question.
 
-       return 0;
-     }
+
+File: gsl-ref.info,  Node: Initializing the Multidimensional Minimizer,  Next: Providing a function to minimize,  Prev: Multimin Caveats,  Up: Multidimensional Minimization
 
-A suitable set of data for fitting can be generated using the following
-program.  It outputs a set of points with gaussian errors from the curve
-y = e^x in the region 0 < x < 2.
+37.3 Initializing the Multidimensional Minimizer
+================================================
 
-     #include <stdio.h>
-     #include <math.h>
-     #include <gsl/gsl_randist.h>
+The following function initializes a multidimensional minimizer.  The
+minimizer itself depends only on the dimension of the problem and the
+algorithm and can be reused for different problems.
 
-     int
-     main (void)
-     {
-       double x;
-       const gsl_rng_type * T;
-       gsl_rng * r;
+ -- Function: gsl_multimin_fdfminimizer *
+          gsl_multimin_fdfminimizer_alloc (const
+          gsl_multimin_fdfminimizer_type * T, size_t N)
+ -- Function: gsl_multimin_fminimizer * gsl_multimin_fminimizer_alloc
+          (const gsl_multimin_fminimizer_type * T, size_t N)
+     This function returns a pointer to a newly allocated instance of a
+     minimizer of type T for an N-dimension function.  If there is
+     insufficient memory to create the minimizer then the function
+     returns a null pointer and the error handler is invoked with an
+     error code of 'GSL_ENOMEM'.
 
-       gsl_rng_env_setup ();
+ -- Function: int gsl_multimin_fdfminimizer_set
+          (gsl_multimin_fdfminimizer * S, gsl_multimin_function_fdf *
+          FDF, const gsl_vector * X, double STEP_SIZE, double TOL)
+ -- Function: int gsl_multimin_fminimizer_set (gsl_multimin_fminimizer *
+          S, gsl_multimin_function * F, const gsl_vector * X, const
+          gsl_vector * STEP_SIZE)
+     The function 'gsl_multimin_fdfminimizer_set' initializes the
+     minimizer S to minimize the function FDF starting from the initial
+     point X.  The size of the first trial step is given by STEP_SIZE.
+     The accuracy of the line minimization is specified by TOL.  The
+     precise meaning of this parameter depends on the method used.
+     Typically the line minimization is considered successful if the
+     gradient of the function g is orthogonal to the current search
+     direction p to a relative accuracy of TOL, where dot(p,g) < tol |p|
+     |g|.  A TOL value of 0.1 is suitable for most purposes, since line
+     minimization only needs to be carried out approximately.  Note that
+     setting TOL to zero will force the use of "exact" line-searches,
+     which are extremely expensive.
 
-       T = gsl_rng_default;
-       r = gsl_rng_alloc (T);
+     The function 'gsl_multimin_fminimizer_set' initializes the
+     minimizer S to minimize the function F, starting from the initial
+     point X.  The size of the initial trial steps is given in vector
+     STEP_SIZE.  The precise meaning of this parameter depends on the
+     method used.
 
-       for (x = 0.1; x < 2; x+= 0.1)
-         {
-           double y0 = exp (x);
-           double sigma = 0.1 * y0;
-           double dy = gsl_ran_gaussian (r, sigma);
+ -- Function: void gsl_multimin_fdfminimizer_free
+          (gsl_multimin_fdfminimizer * S)
+ -- Function: void gsl_multimin_fminimizer_free (gsl_multimin_fminimizer
+          * S)
+     This function frees all the memory associated with the minimizer S.
 
-           printf ("%g %g %g\n", x, y0 + dy, sigma);
-         }
+ -- Function: const char * gsl_multimin_fdfminimizer_name (const
+          gsl_multimin_fdfminimizer * S)
+ -- Function: const char * gsl_multimin_fminimizer_name (const
+          gsl_multimin_fminimizer * S)
+     This function returns a pointer to the name of the minimizer.  For
+     example,
 
-       gsl_rng_free(r);
+          printf ("s is a '%s' minimizer\n",
+                  gsl_multimin_fdfminimizer_name (s));
 
-       return 0;
-     }
+     would print something like 's is a 'conjugate_pr' minimizer'.
 
-The data can be prepared by running the resulting executable program,
+
+File: gsl-ref.info,  Node: Providing a function to minimize,  Next: Multimin Iteration,  Prev: Initializing the Multidimensional Minimizer,  Up: Multidimensional Minimization
 
-     $ GSL_RNG_TYPE=mt19937_1999 ./generate > exp.dat
-     $ more exp.dat
-     0.1 0.97935 0.110517
-     0.2 1.3359 0.12214
-     0.3 1.52573 0.134986
-     0.4 1.60318 0.149182
-     0.5 1.81731 0.164872
-     0.6 1.92475 0.182212
-     ....
+37.4 Providing a function to minimize
+=====================================
 
-To fit the data use the previous program, with the number of data points
-given as the first argument.  In this case there are 19 data points.
+You must provide a parametric function of n variables for the minimizers
+to operate on.  You may also need to provide a routine which calculates
+the gradient of the function and a third routine which calculates both
+the function value and the gradient together.  In order to allow for
+general parameters the functions are defined by the following data
+types:
 
-     $ ./fit 19 < exp.dat
-     0.1 0.97935 +/- 0.110517
-     0.2 1.3359 +/- 0.12214
-     ...
-     # best fit: Y = 1.02318 + 0.956201 X + 0.876796 X^2
-     # covariance matrix:
-     [ +1.25612e-02, -3.64387e-02, +1.94389e-02
-       -3.64387e-02, +1.42339e-01, -8.48761e-02
-       +1.94389e-02, -8.48761e-02, +5.60243e-02 ]
-     # chisq = 23.0987
+ -- Data Type: gsl_multimin_function_fdf
+     This data type defines a general function of n variables with
+     parameters and the corresponding gradient vector of derivatives,
 
-The parameters of the quadratic fit match the coefficients of the
-expansion of e^x, taking into account the errors on the parameters and
-the O(x^3) difference between the exponential and quadratic functions
-for the larger values of x.  The errors on the parameters are given by
-the square-root of the corresponding diagonal elements of the covariance
-matrix.  The chi-squared per degree of freedom is 1.4, indicating a
-reasonable fit to the data.
+     'double (* f) (const gsl_vector * X, void * PARAMS)'
+          this function should return the result f(x,params) for
+          argument X and parameters PARAMS.  If the function cannot be
+          computed, an error value of 'GSL_NAN' should be returned.
 
-   The next program demonstrates the advantage of robust least squares
-on a dataset with outliers.  The program generates linear (x,y) data
-pairs on the line y = 1.45 x + 3.88, adds some random noise, and inserts
-3 outliers into the dataset.  Both the robust and ordinary least squares
-(OLS) coefficients are computed for comparison.
+     'void (* df) (const gsl_vector * X, void * PARAMS, gsl_vector * G)'
+          this function should store the N-dimensional gradient g_i = d
+          f(x,params) / d x_i in the vector G for argument X and
+          parameters PARAMS, returning an appropriate error code if the
+          function cannot be computed.
 
-     #include <stdio.h>
-     #include <gsl/gsl_multifit.h>
-     #include <gsl/gsl_randist.h>
+     'void (* fdf) (const gsl_vector * X, void * PARAMS, double * f, gsl_vector * G)'
+          This function should set the values of the F and G as above,
+          for arguments X and parameters PARAMS.  This function provides
+          an optimization of the separate functions for f(x) and
+          g(x)--it is always faster to compute the function and its
+          derivative at the same time.
 
-     int
-     dofit(const gsl_multifit_robust_type *T,
-           const gsl_matrix *X, const gsl_vector *y,
-           gsl_vector *c, gsl_matrix *cov)
+     'size_t n'
+          the dimension of the system, i.e.  the number of components of
+          the vectors X.
+
+     'void * params'
+          a pointer to the parameters of the function.
+ -- Data Type: gsl_multimin_function
+     This data type defines a general function of n variables with
+     parameters,
+
+     'double (* f) (const gsl_vector * X, void * PARAMS)'
+          this function should return the result f(x,params) for
+          argument X and parameters PARAMS.  If the function cannot be
+          computed, an error value of 'GSL_NAN' should be returned.
+
+     'size_t n'
+          the dimension of the system, i.e.  the number of components of
+          the vectors X.
+
+     'void * params'
+          a pointer to the parameters of the function.
+
+The following example function defines a simple two-dimensional
+paraboloid with five parameters,
+
+     /* Paraboloid centered on (p[0],p[1]), with
+        scale factors (p[2],p[3]) and minimum p[4] */
+
+     double
+     my_f (const gsl_vector *v, void *params)
      {
-       int s;
-       gsl_multifit_robust_workspace * work
-         = gsl_multifit_robust_alloc (T, X->size1, X->size2);
+       double x, y;
+       double *p = (double *)params;
 
-       s = gsl_multifit_robust (X, y, c, cov, work);
-       gsl_multifit_robust_free (work);
+       x = gsl_vector_get(v, 0);
+       y = gsl_vector_get(v, 1);
 
-       return s;
+       return p[2] * (x - p[0]) * (x - p[0]) +
+                p[3] * (y - p[1]) * (y - p[1]) + p[4];
+     }
+
+     /* The gradient of f, df = (df/dx, df/dy). */
+     void
+     my_df (const gsl_vector *v, void *params,
+            gsl_vector *df)
+     {
+       double x, y;
+       double *p = (double *)params;
+
+       x = gsl_vector_get(v, 0);
+       y = gsl_vector_get(v, 1);
+
+       gsl_vector_set(df, 0, 2.0 * p[2] * (x - p[0]));
+       gsl_vector_set(df, 1, 2.0 * p[3] * (y - p[1]));
+     }
+
+     /* Compute both f and df together. */
+     void
+     my_fdf (const gsl_vector *x, void *params,
+             double *f, gsl_vector *df)
+     {
+       *f = my_f(x, params);
+       my_df(x, params, df);
      }
 
-     int
-     main (int argc, char **argv)
-     {
-       int i;
-       size_t n;
-       const size_t p = 2; /* linear fit */
-       gsl_matrix *X, *cov;
-       gsl_vector *x, *y, *c, *c_ols;
-       const double a = 1.45; /* slope */
-       const double b = 3.88; /* intercept */
-       gsl_rng *r;
+The function can be initialized using the following code,
+
+     gsl_multimin_function_fdf my_func;
+
+     /* Paraboloid center at (1,2), scale factors (10, 20),
+        minimum value 30 */
+     double p[5] = { 1.0, 2.0, 10.0, 20.0, 30.0 };
+
+     my_func.n = 2;  /* number of function components */
+     my_func.f = &my_f;
+     my_func.df = &my_df;
+     my_func.fdf = &my_fdf;
+     my_func.params = (void *)p;
+
+
+File: gsl-ref.info,  Node: Multimin Iteration,  Next: Multimin Stopping Criteria,  Prev: Providing a function to minimize,  Up: Multidimensional Minimization
+
+37.5 Iteration
+==============
+
+The following function drives the iteration of each algorithm.  The
+function performs one iteration to update the state of the minimizer.
+The same function works for all minimizers so that different methods can
+be substituted at runtime without modifications to the code.
+
+ -- Function: int gsl_multimin_fdfminimizer_iterate
+          (gsl_multimin_fdfminimizer * S)
+ -- Function: int gsl_multimin_fminimizer_iterate
+          (gsl_multimin_fminimizer * S)
+     These functions perform a single iteration of the minimizer S.  If
+     the iteration encounters an unexpected problem then an error code
+     will be returned.  The error code 'GSL_ENOPROG' signifies that the
+     minimizer is unable to improve on its current estimate, either due
+     to numerical difficulty or because a genuine local minimum has been
+     reached.
+
+The minimizer maintains a current best estimate of the minimum at all
+times.  This information can be accessed with the following auxiliary
+functions,
+
+ -- Function: gsl_vector * gsl_multimin_fdfminimizer_x (const
+          gsl_multimin_fdfminimizer * S)
+ -- Function: gsl_vector * gsl_multimin_fminimizer_x (const
+          gsl_multimin_fminimizer * S)
+ -- Function: double gsl_multimin_fdfminimizer_minimum (const
+          gsl_multimin_fdfminimizer * S)
+ -- Function: double gsl_multimin_fminimizer_minimum (const
+          gsl_multimin_fminimizer * S)
+ -- Function: gsl_vector * gsl_multimin_fdfminimizer_gradient (const
+          gsl_multimin_fdfminimizer * S)
+ -- Function: gsl_vector * gsl_multimin_fdfminimizer_dx (const
+          gsl_multimin_fdfminimizer * S)
+ -- Function: double gsl_multimin_fminimizer_size (const
+          gsl_multimin_fminimizer * S)
+     These functions return the current best estimate of the location of
+     the minimum, the value of the function at that point, its gradient,
+     the last step increment of the estimate, and minimizer specific
+     characteristic size for the minimizer S.
+
+ -- Function: int gsl_multimin_fdfminimizer_restart
+          (gsl_multimin_fdfminimizer * S)
+     This function resets the minimizer S to use the current point as a
+     new starting point.
+
+
+File: gsl-ref.info,  Node: Multimin Stopping Criteria,  Next: Multimin Algorithms with Derivatives,  Prev: Multimin Iteration,  Up: Multidimensional Minimization
+
+37.6 Stopping Criteria
+======================
+
+A minimization procedure should stop when one of the following
+conditions is true:
+
+   * A minimum has been found to within the user-specified precision.
+
+   * A user-specified maximum number of iterations has been reached.
+
+   * An error has occurred.
+
+The handling of these conditions is under user control.  The functions
+below allow the user to test the precision of the current result.
+
+ -- Function: int gsl_multimin_test_gradient (const gsl_vector * G,
+          double EPSABS)
+     This function tests the norm of the gradient G against the absolute
+     tolerance EPSABS.  The gradient of a multidimensional function goes
+     to zero at a minimum.  The test returns 'GSL_SUCCESS' if the
+     following condition is achieved,
+
+          |g| < epsabs
+
+     and returns 'GSL_CONTINUE' otherwise.  A suitable choice of EPSABS
+     can be made from the desired accuracy in the function for small
+     variations in x.  The relationship between these quantities is
+     given by \delta f = g \delta x.
+
+ -- Function: int gsl_multimin_test_size (const double SIZE, double
+          EPSABS)
+     This function tests the minimizer specific characteristic size (if
+     applicable to the used minimizer) against absolute tolerance
+     EPSABS.  The test returns 'GSL_SUCCESS' if the size is smaller than
+     tolerance, otherwise 'GSL_CONTINUE' is returned.
+
+
+File: gsl-ref.info,  Node: Multimin Algorithms with Derivatives,  Next: Multimin Algorithms without Derivatives,  Prev: Multimin Stopping Criteria,  Up: Multidimensional Minimization
+
+37.7 Algorithms with Derivatives
+================================
+
+There are several minimization methods available.  The best choice of
+algorithm depends on the problem.  The algorithms described in this
+section use the value of the function and its gradient at each
+evaluation point.
+
+ -- Minimizer: gsl_multimin_fdfminimizer_conjugate_fr
+     This is the Fletcher-Reeves conjugate gradient algorithm.  The
+     conjugate gradient algorithm proceeds as a succession of line
+     minimizations.  The sequence of search directions is used to build
+     up an approximation to the curvature of the function in the
+     neighborhood of the minimum.
 
-       if (argc != 2)
-         {
-           fprintf (stderr,"usage: robfit n\n");
-           exit (-1);
-         }
+     An initial search direction P is chosen using the gradient, and
+     line minimization is carried out in that direction.  The accuracy
+     of the line minimization is specified by the parameter TOL.  The
+     minimum along this line occurs when the function gradient G and the
+     search direction P are orthogonal.  The line minimization
+     terminates when dot(p,g) < tol |p| |g|.  The search direction is
+     updated using the Fletcher-Reeves formula p' = g' - \beta g where
+     \beta=-|g'|^2/|g|^2, and the line minimization is then repeated for
+     the new search direction.
 
-       n = atoi (argv[1]);
+ -- Minimizer: gsl_multimin_fdfminimizer_conjugate_pr
+     This is the Polak-Ribiere conjugate gradient algorithm.  It is
+     similar to the Fletcher-Reeves method, differing only in the choice
+     of the coefficient \beta.  Both methods work well when the
+     evaluation point is close enough to the minimum of the objective
+     function that it is well approximated by a quadratic hypersurface.
 
-       X = gsl_matrix_alloc (n, p);
-       x = gsl_vector_alloc (n);
-       y = gsl_vector_alloc (n);
+ -- Minimizer: gsl_multimin_fdfminimizer_vector_bfgs2
+ -- Minimizer: gsl_multimin_fdfminimizer_vector_bfgs
+     These methods use the vector Broyden-Fletcher-Goldfarb-Shanno
+     (BFGS) algorithm.  This is a quasi-Newton method which builds up an
+     approximation to the second derivatives of the function f using the
+     difference between successive gradient vectors.  By combining the
+     first and second derivatives the algorithm is able to take
+     Newton-type steps towards the function minimum, assuming quadratic
+     behavior in that region.
 
-       c = gsl_vector_alloc (p);
-       c_ols = gsl_vector_alloc (p);
-       cov = gsl_matrix_alloc (p, p);
+     The 'bfgs2' version of this minimizer is the most efficient version
+     available, and is a faithful implementation of the line
+     minimization scheme described in Fletcher's 'Practical Methods of
+     Optimization', Algorithms 2.6.2 and 2.6.4.  It supersedes the
+     original 'bfgs' routine and requires substantially fewer function
+     and gradient evaluations.  The user-supplied tolerance TOL
+     corresponds to the parameter \sigma used by Fletcher.  A value of
+     0.1 is recommended for typical use (larger values correspond to
+     less accurate line searches).
 
-       r = gsl_rng_alloc(gsl_rng_default);
+ -- Minimizer: gsl_multimin_fdfminimizer_steepest_descent
+     The steepest descent algorithm follows the downhill gradient of the
+     function at each step.  When a downhill step is successful the
+     step-size is increased by a factor of two.  If the downhill step
+     leads to a higher function value then the algorithm backtracks and
+     the step size is decreased using the parameter TOL.  A suitable
+     value of TOL for most applications is 0.1.  The steepest descent
+     method is inefficient and is included only for demonstration
+     purposes.
 
-       /* generate linear dataset */
-       for (i = 0; i < n - 3; i++)
-         {
-           double dx = 10.0 / (n - 1.0);
-           double ei = gsl_rng_uniform(r);
-           double xi = -5.0 + i * dx;
-           double yi = a * xi + b;
+
+File: gsl-ref.info,  Node: Multimin Algorithms without Derivatives,  Next: Multimin Examples,  Prev: Multimin Algorithms with Derivatives,  Up: Multidimensional Minimization
 
-           gsl_vector_set (x, i, xi);
-           gsl_vector_set (y, i, yi + ei);
-         }
+37.8 Algorithms without Derivatives
+===================================
 
-       /* add a few outliers */
-       gsl_vector_set(x, n - 3, 4.7);
-       gsl_vector_set(y, n - 3, -8.3);
+The algorithms described in this section use only the value of the
+function at each evaluation point.
 
-       gsl_vector_set(x, n - 2, 3.5);
-       gsl_vector_set(y, n - 2, -6.7);
+ -- Minimizer: gsl_multimin_fminimizer_nmsimplex2
+ -- Minimizer: gsl_multimin_fminimizer_nmsimplex
+     These methods use the Simplex algorithm of Nelder and Mead.
+     Starting from the initial vector X = p_0, the algorithm constructs
+     an additional n vectors p_i using the step size vector s =
+     STEP_SIZE as follows:
 
-       gsl_vector_set(x, n - 1, 4.1);
-       gsl_vector_set(y, n - 1, -6.0);
+          p_0 = (x_0, x_1, ... , x_n)
+          p_1 = (x_0 + s_0, x_1, ... , x_n)
+          p_2 = (x_0, x_1 + s_1, ... , x_n)
+          ... = ...
+          p_n = (x_0, x_1, ... , x_n + s_n)
 
-       /* construct design matrix X for linear fit */
-       for (i = 0; i < n; ++i)
-         {
-           double xi = gsl_vector_get(x, i);
+     These vectors form the n+1 vertices of a simplex in n dimensions.
+     On each iteration the algorithm uses simple geometrical
+     transformations to update the vector corresponding to the highest
+     function value.  The geometric transformations are reflection,
+     reflection followed by expansion, contraction and multiple
+     contraction.  Using these transformations the simplex moves through
+     the space towards the minimum, where it contracts itself.
 
-           gsl_matrix_set (X, i, 0, 1.0);
-           gsl_matrix_set (X, i, 1, xi);
-         }
+     After each iteration, the best vertex is returned.  Note, that due
+     to the nature of the algorithm not every step improves the current
+     best parameter vector.  Usually several iterations are required.
 
-       /* perform robust and OLS fit */
-       dofit(gsl_multifit_robust_ols, X, y, c_ols, cov);
-       dofit(gsl_multifit_robust_bisquare, X, y, c, cov);
+     The minimizer-specific characteristic size is calculated as the
+     average distance from the geometrical center of the simplex to all
+     its vertices.  This size can be used as a stopping criteria, as the
+     simplex contracts itself near the minimum.  The size is returned by
+     the function 'gsl_multimin_fminimizer_size'.
 
-       /* output data and model */
-       for (i = 0; i < n; ++i)
-         {
-           double xi = gsl_vector_get(x, i);
-           double yi = gsl_vector_get(y, i);
-           gsl_vector_view v = gsl_matrix_row(X, i);
-           double y_ols, y_rob, y_err;
+     The 'nmsimplex2' version of this minimiser is a new O(N) operations
+     implementation of the earlier O(N^2) operations 'nmsimplex'
+     minimiser.  It uses the same underlying algorithm, but the simplex
+     updates are computed more efficiently for high-dimensional
+     problems.  In addition, the size of simplex is calculated as the
+     RMS distance of each vertex from the center rather than the mean
+     distance, allowing a linear update of this quantity on each step.
+     The memory usage is O(N^2) for both algorithms.
 
-           gsl_multifit_robust_est(&v.vector, c, cov, &y_rob, &y_err);
-           gsl_multifit_robust_est(&v.vector, c_ols, cov, &y_ols, &y_err);
+ -- Minimizer: gsl_multimin_fminimizer_nmsimplex2rand
+     This method is a variant of 'nmsimplex2' which initialises the
+     simplex around the starting point X using a randomly-oriented set
+     of basis vectors instead of the fixed coordinate axes.  The final
+     dimensions of the simplex are scaled along the coordinate axes by
+     the vector STEP_SIZE.  The randomisation uses a simple
+     deterministic generator so that repeated calls to
+     'gsl_multimin_fminimizer_set' for a given solver object will vary
+     the orientation in a well-defined way.
 
-           printf("%g %g %g %g\n", xi, yi, y_rob, y_ols);
-         }
+
+File: gsl-ref.info,  Node: Multimin Examples,  Next: Multimin References and Further Reading,  Prev: Multimin Algorithms without Derivatives,  Up: Multidimensional Minimization
 
-     #define C(i) (gsl_vector_get(c,(i)))
-     #define COV(i,j) (gsl_matrix_get(cov,(i),(j)))
+37.9 Examples
+=============
 
-       {
-         printf ("# best fit: Y = %g + %g X\n",
-                 C(0), C(1));
+This example program finds the minimum of the paraboloid function
+defined earlier.  The location of the minimum is offset from the origin
+in x and y, and the function value at the minimum is non-zero.  The main
+program is given below, it requires the example function given earlier
+in this chapter.
 
-         printf ("# covariance matrix:\n");
-         printf ("# [ %+.5e, %+.5e\n",
-                    COV(0,0), COV(0,1));
-         printf ("#   %+.5e, %+.5e\n",
-                    COV(1,0), COV(1,1));
-       }
+     int
+     main (void)
+     {
+       size_t iter = 0;
+       int status;
 
-       gsl_matrix_free (X);
-       gsl_vector_free (x);
-       gsl_vector_free (y);
-       gsl_vector_free (c);
-       gsl_vector_free (c_ols);
-       gsl_matrix_free (cov);
-       gsl_rng_free(r);
+       const gsl_multimin_fdfminimizer_type *T;
+       gsl_multimin_fdfminimizer *s;
 
-       return 0;
-     }
+       /* Position of the minimum (1,2), scale factors
+          10,20, height 30. */
+       double par[5] = { 1.0, 2.0, 10.0, 20.0, 30.0 };
 
-   The output from the program is shown in the following plot.
+       gsl_vector *x;
+       gsl_multimin_function_fdf my_func;
 
-
-File: gsl-ref.info,  Node: Fitting References and Further Reading,  Prev: Fitting Examples,  Up: Least-Squares Fitting
+       my_func.n = 2;
+       my_func.f = my_f;
+       my_func.df = my_df;
+       my_func.fdf = my_fdf;
+       my_func.params = par;
 
-37.8 References and Further Reading
-===================================
+       /* Starting point, x = (5,7) */
+       x = gsl_vector_alloc (2);
+       gsl_vector_set (x, 0, 5.0);
+       gsl_vector_set (x, 1, 7.0);
 
-A summary of formulas and techniques for least squares fitting can be
-found in the "Statistics" chapter of the Annual Review of Particle
-Physics prepared by the Particle Data Group,
+       T = gsl_multimin_fdfminimizer_conjugate_fr;
+       s = gsl_multimin_fdfminimizer_alloc (T, 2);
 
-     'Review of Particle Properties', R.M. Barnett et al., Physical
-     Review D54, 1 (1996) <http://pdg.lbl.gov/>
+       gsl_multimin_fdfminimizer_set (s, &my_func, x, 0.01, 1e-4);
 
-The Review of Particle Physics is available online at the website given
-above.
+       do
+         {
+           iter++;
+           status = gsl_multimin_fdfminimizer_iterate (s);
 
-   The tests used to prepare these routines are based on the NIST
-Statistical Reference Datasets.  The datasets and their documentation
-are available from NIST at the following website,
+           if (status)
+             break;
 
-           <http://www.nist.gov/itl/div898/strd/index.html>.
+           status = gsl_multimin_test_gradient (s->gradient, 1e-3);
 
-The GSL implementation of robust linear regression closely follows the
-publications
+           if (status == GSL_SUCCESS)
+             printf ("Minimum found at:\n");
 
-     DuMouchel, W. and F. O'Brien (1989), "Integrating a robust option
-     into a multiple regression computing environment," Computer Science
-     and Statistics: Proceedings of the 21st Symposium on the Interface,
-     American Statistical Association
+           printf ("%5d %.5f %.5f %10.5f\n", iter,
+                   gsl_vector_get (s->x, 0),
+                   gsl_vector_get (s->x, 1),
+                   s->f);
 
-     Street, J.O., R.J. Carroll, and D. Ruppert (1988), "A note on
-     computing robust regression estimates via iteratively reweighted
-     least squares," The American Statistician, v.  42, pp.  152-154.
+         }
+       while (status == GSL_CONTINUE && iter < 100);
 
-
-File: gsl-ref.info,  Node: Nonlinear Least-Squares Fitting,  Next: Basis Splines,  Prev: Least-Squares Fitting,  Up: Top
+       gsl_multimin_fdfminimizer_free (s);
+       gsl_vector_free (x);
 
-38 Nonlinear Least-Squares Fitting
-**********************************
+       return 0;
+     }
 
-This chapter describes functions for multidimensional nonlinear
-least-squares fitting.  The library provides low level components for a
-variety of iterative solvers and convergence tests.  These can be
-combined by the user to achieve the desired solution, with full access
-to the intermediate steps of the iteration.  Each class of methods uses
-the same framework, so that you can switch between solvers at runtime
-without needing to recompile your program.  Each instance of a solver
-keeps track of its own state, allowing the solvers to be used in
-multi-threaded programs.
+The initial step-size is chosen as 0.01, a conservative estimate in this
+case, and the line minimization parameter is set at 0.0001.  The program
+terminates when the norm of the gradient has been reduced below 0.001.
+The output of the program is shown below,
 
-   The header file 'gsl_multifit_nlin.h' contains prototypes for the
-multidimensional nonlinear fitting functions and related declarations.
+              x       y         f
+         1 4.99629 6.99072  687.84780
+         2 4.98886 6.97215  683.55456
+         3 4.97400 6.93501  675.01278
+         4 4.94429 6.86073  658.10798
+         5 4.88487 6.71217  625.01340
+         6 4.76602 6.41506  561.68440
+         7 4.52833 5.82083  446.46694
+         8 4.05295 4.63238  261.79422
+         9 3.10219 2.25548   75.49762
+        10 2.85185 1.62963   67.03704
+        11 2.19088 1.76182   45.31640
+        12 0.86892 2.02622   30.18555
+     Minimum found at:
+        13 1.00000 2.00000   30.00000
 
-* Menu:
+Note that the algorithm gradually increases the step size as it
+successfully moves downhill, as can be seen by plotting the successive
+points.
 
-* Overview of Nonlinear Least-Squares Fitting::  
-* Initializing the Nonlinear Least-Squares Solver::  
-* Providing the Function to be Minimized::  
-* Finite Difference Jacobian::  
-* Iteration of the Minimization Algorithm::  
-* Search Stopping Parameters for Minimization Algorithms::  
-* High Level Driver::
-* Minimization Algorithms using Derivatives::  
-* Minimization Algorithms without Derivatives::  
-* Computing the covariance matrix of best fit parameters::  
-* Example programs for Nonlinear Least-Squares Fitting::  
-* References and Further Reading for Nonlinear Least-Squares Fitting::  
+The conjugate gradient algorithm finds the minimum on its second
+direction because the function is purely quadratic.  Additional
+iterations would be needed for a more complicated function.
 
-
-File: gsl-ref.info,  Node: Overview of Nonlinear Least-Squares Fitting,  Next: Initializing the Nonlinear Least-Squares Solver,  Up: Nonlinear Least-Squares Fitting
+   Here is another example using the Nelder-Mead Simplex algorithm to
+minimize the same example object function, as above.
 
-38.1 Overview
-=============
+     int
+     main(void)
+     {
+       double par[5] = {1.0, 2.0, 10.0, 20.0, 30.0};
 
-The problem of multidimensional nonlinear least-squares fitting requires
-the minimization of the squared residuals of n functions, f_i, in p
-parameters, x_i,
+       const gsl_multimin_fminimizer_type *T =
+         gsl_multimin_fminimizer_nmsimplex2;
+       gsl_multimin_fminimizer *s = NULL;
+       gsl_vector *ss, *x;
+       gsl_multimin_function minex_func;
 
-     \Phi(x) = (1/2) || F(x) ||^2
-             = (1/2) \sum_{i=1}^{n} f_i(x_1, ..., x_p)^2
+       size_t iter = 0;
+       int status;
+       double size;
+
+       /* Starting point */
+       x = gsl_vector_alloc (2);
+       gsl_vector_set (x, 0, 5.0);
+       gsl_vector_set (x, 1, 7.0);
 
-All algorithms proceed from an initial guess using the linearization,
+       /* Set initial step sizes to 1 */
+       ss = gsl_vector_alloc (2);
+       gsl_vector_set_all (ss, 1.0);
 
-     \psi(p) = || F(x+p) || ~=~ || F(x) + J p ||
+       /* Initialize method and iterate */
+       minex_func.n = 2;
+       minex_func.f = my_f;
+       minex_func.params = par;
 
-where x is the initial point, p is the proposed step and J is the
-Jacobian matrix J_{ij} = d f_i / d x_j.  Additional strategies are used
-to enlarge the region of convergence.  These include requiring a
-decrease in the norm ||F|| on each step or using a trust region to avoid
-steps which fall outside the linear regime.
+       s = gsl_multimin_fminimizer_alloc (T, 2);
+       gsl_multimin_fminimizer_set (s, &minex_func, x, ss);
 
-   To perform a weighted least-squares fit of a nonlinear model Y(x,t)
-to data (t_i, y_i) with independent Gaussian errors \sigma_i, use
-function components of the following form,
+       do
+         {
+           iter++;
+           status = gsl_multimin_fminimizer_iterate(s);
 
-     f_i = (Y(x, t_i) - y_i) / \sigma_i
+           if (status)
+             break;
 
-Note that the model parameters are denoted by x in this chapter since
-the non-linear least-squares algorithms are described geometrically
-(i.e.  finding the minimum of a surface).  The independent variable of
-any data to be fitted is denoted by t.
+           size = gsl_multimin_fminimizer_size (s);
+           status = gsl_multimin_test_size (size, 1e-2);
 
-   With the definition above the Jacobian is J_{ij} =(1 / \sigma_i) d
-Y_i / d x_j, where Y_i = Y(x,t_i).
+           if (status == GSL_SUCCESS)
+             {
+               printf ("converged to minimum at\n");
+             }
 
-
-File: gsl-ref.info,  Node: Initializing the Nonlinear Least-Squares Solver,  Next: Providing the Function to be Minimized,  Prev: Overview of Nonlinear Least-Squares Fitting,  Up: Nonlinear Least-Squares Fitting
+           printf ("%5d %10.3e %10.3e f() = %7.3f size = %.3f\n",
+                   iter,
+                   gsl_vector_get (s->x, 0),
+                   gsl_vector_get (s->x, 1),
+                   s->fval, size);
+         }
+       while (status == GSL_CONTINUE && iter < 100);
 
-38.2 Initializing the Solver
-============================
+       gsl_vector_free(x);
+       gsl_vector_free(ss);
+       gsl_multimin_fminimizer_free (s);
 
- -- Function: gsl_multifit_fsolver * gsl_multifit_fsolver_alloc (const
-          gsl_multifit_fsolver_type * T, size_t N, size_t P)
-     This function returns a pointer to a newly allocated instance of a
-     solver of type T for N observations and P parameters.  The number
-     of observations N must be greater than or equal to parameters P.
+       return status;
+     }
 
-     If there is insufficient memory to create the solver then the
-     function returns a null pointer and the error handler is invoked
-     with an error code of 'GSL_ENOMEM'.
+The minimum search stops when the Simplex size drops to 0.01.  The
+output is shown below.
 
- -- Function: gsl_multifit_fdfsolver * gsl_multifit_fdfsolver_alloc
-          (const gsl_multifit_fdfsolver_type * T, size_t N, size_t P)
-     This function returns a pointer to a newly allocated instance of a
-     derivative solver of type T for N observations and P parameters.
-     For example, the following code creates an instance of a
-     Levenberg-Marquardt solver for 100 data points and 3 parameters,
+         1  6.500e+00  5.000e+00 f() = 512.500 size = 1.130
+         2  5.250e+00  4.000e+00 f() = 290.625 size = 1.409
+         3  5.250e+00  4.000e+00 f() = 290.625 size = 1.409
+         4  5.500e+00  1.000e+00 f() = 252.500 size = 1.409
+         5  2.625e+00  3.500e+00 f() = 101.406 size = 1.847
+         6  2.625e+00  3.500e+00 f() = 101.406 size = 1.847
+         7  0.000e+00  3.000e+00 f() =  60.000 size = 1.847
+         8  2.094e+00  1.875e+00 f() =  42.275 size = 1.321
+         9  2.578e-01  1.906e+00 f() =  35.684 size = 1.069
+        10  5.879e-01  2.445e+00 f() =  35.664 size = 0.841
+        11  1.258e+00  2.025e+00 f() =  30.680 size = 0.476
+        12  1.258e+00  2.025e+00 f() =  30.680 size = 0.367
+        13  1.093e+00  1.849e+00 f() =  30.539 size = 0.300
+        14  8.830e-01  2.004e+00 f() =  30.137 size = 0.172
+        15  8.830e-01  2.004e+00 f() =  30.137 size = 0.126
+        16  9.582e-01  2.060e+00 f() =  30.090 size = 0.106
+        17  1.022e+00  2.004e+00 f() =  30.005 size = 0.063
+        18  1.022e+00  2.004e+00 f() =  30.005 size = 0.043
+        19  1.022e+00  2.004e+00 f() =  30.005 size = 0.043
+        20  1.022e+00  2.004e+00 f() =  30.005 size = 0.027
+        21  1.022e+00  2.004e+00 f() =  30.005 size = 0.022
+        22  9.920e-01  1.997e+00 f() =  30.001 size = 0.016
+        23  9.920e-01  1.997e+00 f() =  30.001 size = 0.013
+     converged to minimum at
+        24  9.920e-01  1.997e+00 f() =  30.001 size = 0.008
 
-          const gsl_multifit_fdfsolver_type * T
-              = gsl_multifit_fdfsolver_lmder;
-          gsl_multifit_fdfsolver * s
-              = gsl_multifit_fdfsolver_alloc (T, 100, 3);
+The simplex size first increases, while the simplex moves towards the
+minimum.  After a while the size begins to decrease as the simplex
+contracts around the minimum.
 
-     The number of observations N must be greater than or equal to
-     parameters P.
+
+File: gsl-ref.info,  Node: Multimin References and Further Reading,  Prev: Multimin Examples,  Up: Multidimensional Minimization
 
-     If there is insufficient memory to create the solver then the
-     function returns a null pointer and the error handler is invoked
-     with an error code of 'GSL_ENOMEM'.
+37.10 References and Further Reading
+====================================
 
- -- Function: int gsl_multifit_fsolver_set (gsl_multifit_fsolver * S,
-          gsl_multifit_function * F, const gsl_vector * X)
-     This function initializes, or reinitializes, an existing solver S
-     to use the function F and the initial guess X.
+The conjugate gradient and BFGS methods are described in detail in the
+following book,
 
- -- Function: int gsl_multifit_fdfsolver_set (gsl_multifit_fdfsolver *
-          S, gsl_multifit_function_fdf * FDF, const gsl_vector * X)
-     This function initializes, or reinitializes, an existing solver S
-     to use the function and derivative FDF and the initial guess X.
+     R. Fletcher, 'Practical Methods of Optimization (Second Edition)'
+     Wiley (1987), ISBN 0471915475.
 
- -- Function: void gsl_multifit_fsolver_free (gsl_multifit_fsolver * S)
- -- Function: void gsl_multifit_fdfsolver_free (gsl_multifit_fdfsolver *
-          S)
-     These functions free all the memory associated with the solver S.
+   A brief description of multidimensional minimization algorithms and
+more recent references can be found in,
 
- -- Function: const char * gsl_multifit_fsolver_name (const
-          gsl_multifit_fsolver * S)
- -- Function: const char * gsl_multifit_fdfsolver_name (const
-          gsl_multifit_fdfsolver * S)
-     These functions return a pointer to the name of the solver.  For
-     example,
+     C.W. Ueberhuber, 'Numerical Computation (Volume 2)', Chapter 14,
+     Section 4.4 "Minimization Methods", p. 325-335, Springer (1997),
+     ISBN 3-540-62057-5.
 
-          printf ("s is a '%s' solver\n",
-                  gsl_multifit_fdfsolver_name (s));
+The simplex algorithm is described in the following paper,
 
-     would print something like 's is a 'lmder' solver'.
+     J.A. Nelder and R. Mead, 'A simplex method for function
+     minimization', Computer Journal vol. 7 (1965), 308-313.
 
 
-File: gsl-ref.info,  Node: Providing the Function to be Minimized,  Next: Finite Difference Jacobian,  Prev: Initializing the Nonlinear Least-Squares Solver,  Up: Nonlinear Least-Squares Fitting
+File: gsl-ref.info,  Node: Least-Squares Fitting,  Next: Nonlinear Least-Squares Fitting,  Prev: Multidimensional Minimization,  Up: Top
 
-38.3 Providing the Function to be Minimized
-===========================================
+38 Least-Squares Fitting
+************************
 
-You must provide n functions of p variables for the minimization
-algorithms to operate on.  In order to allow for arbitrary parameters
-the functions are defined by the following data types:
+This chapter describes routines for performing least squares fits to
+experimental data using linear combinations of functions.  The data may
+be weighted or unweighted, i.e.  with known or unknown errors.  For
+weighted data the functions compute the best fit parameters and their
+associated covariance matrix.  For unweighted data the covariance matrix
+is estimated from the scatter of the points, giving a
+variance-covariance matrix.
 
- -- Data Type: gsl_multifit_function
-     This data type defines a general system of functions with arbitrary
-     parameters.
+   The functions are divided into separate versions for simple one- or
+two-parameter regression and multiple-parameter fits.
 
-     'int (* f) (const gsl_vector * X, void * PARAMS, gsl_vector * F)'
-          this function should store the vector result f(x,params) in F
-          for argument X and arbitrary parameters PARAMS, returning an
-          appropriate error code if the function cannot be computed.
+* Menu:
 
-     'size_t n'
-          the number of functions, i.e.  the number of components of the
-          vector F.
+* Fitting Overview::            
+* Linear regression::           
+* Multi-parameter regression::
+* Regularized regression::
+* Robust linear regression::
+* Large Dense Linear Systems::
+* Troubleshooting::
+* Fitting Examples::
+* Fitting References and Further Reading::  
 
-     'size_t p'
-          the number of independent variables, i.e.  the number of
-          components of the vector X.
+
+File: gsl-ref.info,  Node: Fitting Overview,  Next: Linear regression,  Up: Least-Squares Fitting
 
-     'void * params'
-          a pointer to the arbitrary parameters of the function.
+38.1 Overview
+=============
 
- -- Data Type: gsl_multifit_function_fdf
-     This data type defines a general system of functions with arbitrary
-     parameters and the corresponding Jacobian matrix of derivatives,
+Least-squares fits are found by minimizing \chi^2 (chi-squared), the
+weighted sum of squared residuals over n experimental datapoints (x_i,
+y_i) for the model Y(c,x),
 
-     'int (* f) (const gsl_vector * X, void * PARAMS, gsl_vector * F)'
-          this function should store the vector result f(x,params) in F
-          for argument X and arbitrary parameters PARAMS, returning an
-          appropriate error code if the function cannot be computed.
+     \chi^2 = \sum_i w_i (y_i - Y(c, x_i))^2
 
-     'int (* df) (const gsl_vector * X, void * PARAMS, gsl_matrix * J)'
-          this function should store the N-by-P matrix result J_ij = d
-          f_i(x,params) / d x_j in J for argument X and arbitrary
-          parameters PARAMS, returning an appropriate error code if the
-          function cannot be computed.  If an analytic Jacobian is
-          unavailable, or too expensive to compute, this function
-          pointer may be set to NULL, in which case the Jacobian will be
-          internally computed using finite difference approximations of
-          the function F.
+The p parameters of the model are c = {c_0, c_1, ...}.  The weight
+factors w_i are given by w_i = 1/\sigma_i^2, where \sigma_i is the
+experimental error on the data-point y_i.  The errors are assumed to be
+Gaussian and uncorrelated.  For unweighted data the chi-squared sum is
+computed without any weight factors.
 
-     'int (* fdf) (const gsl_vector * X, void * PARAMS, gsl_vector * F, gsl_matrix * J)'
-          This function should set the values of the F and J as above,
-          for arguments X and arbitrary parameters PARAMS.  This
-          function provides an optimization of the separate functions
-          for f(x) and J(x)--it is always faster to compute the function
-          and its derivative at the same time.  If an analytic Jacobian
-          is unavailable, or too expensive to compute, this function
-          pointer may be set to NULL, in which case the Jacobian will be
-          internally computed using finite difference approximations of
-          the function F.
+   The fitting routines return the best-fit parameters c and their p
+\times p covariance matrix.  The covariance matrix measures the
+statistical errors on the best-fit parameters resulting from the errors
+on the data, \sigma_i, and is defined as C_{ab} = <\delta c_a \delta
+c_b> where < > denotes an average over the Gaussian error distributions
+of the underlying datapoints.
 
-     'size_t n'
-          the number of functions, i.e.  the number of components of the
-          vector F.
+   The covariance matrix is calculated by error propagation from the
+data errors \sigma_i.  The change in a fitted parameter \delta c_a
+caused by a small change in the data \delta y_i is given by
 
-     'size_t p'
-          the number of independent variables, i.e.  the number of
-          components of the vector X.
+     \delta c_a = \sum_i (dc_a/dy_i) \delta y_i
 
-     'void * params'
-          a pointer to the arbitrary parameters of the function.
+allowing the covariance matrix to be written in terms of the errors on
+the data,
 
-   Note that when fitting a non-linear model against experimental data,
-the data is passed to the functions above using the PARAMS argument and
-the trial best-fit parameters through the X argument.
+     C_{ab} = \sum_{i,j} (dc_a/dy_i) (dc_b/dy_j) <\delta y_i \delta y_j>
 
-
-File: gsl-ref.info,  Node: Finite Difference Jacobian,  Next: Iteration of the Minimization Algorithm,  Prev: Providing the Function to be Minimized,  Up: Nonlinear Least-Squares Fitting
+For uncorrelated data the fluctuations of the underlying datapoints
+satisfy <\delta y_i \delta y_j> = \sigma_i^2 \delta_{ij}, giving a
+corresponding parameter covariance matrix of
 
-38.4 Finite Difference Jacobian
-===============================
+     C_{ab} = \sum_i (1/w_i) (dc_a/dy_i) (dc_b/dy_i)
+
+When computing the covariance matrix for unweighted data, i.e.  data
+with unknown errors, the weight factors w_i in this sum are replaced by
+the single estimate w = 1/\sigma^2, where \sigma^2 is the computed
+variance of the residuals about the best-fit model, \sigma^2 = \sum (y_i
+- Y(c,x_i))^2 / (n-p).  This is referred to as the "variance-covariance
+matrix".
 
-For the algorithms which require a Jacobian matrix of derivatives of the
-fit functions, there are times when an analytic Jacobian may be
-unavailable or too expensive to compute.  Therefore GSL supports
-approximating the Jacobian numerically using finite differences of the
-fit functions.  This is typically done by setting the relevant function
-pointers of the 'gsl_multifit_function_fdf' data type to NULL, however
-the following functions allow the user to access the approximate
-Jacobian directly if needed.
-
- -- Function: int gsl_multifit_fdfsolver_dif_df (const gsl_vector * X,
-          gsl_multifit_function_fdf * FDF, const gsl_vector * F,
-          gsl_matrix * J)
-     This function takes as input the current position X with the
-     function values computed at the current position F, along with FDF
-     which specifies the fit function and parameters and approximates
-     the N-by-P Jacobian J using forward finite differences: J_ij = d
-     f_i(x,params) / d x_j = (f_i(x^*,params) - f_i(x,params)) / d x_j.
-     where x^* has the jth element perturbed by \Delta x_j and \Delta
-     x_j = \epsilon |x_j|, where \epsilon is the square root of the
-     machine precision 'GSL_DBL_EPSILON'.
-
- -- Function: int gsl_multifit_fdfsolver_dif_fdf (const gsl_vector * X,
-          gsl_multifit_function_fdf * FDF, gsl_vector * F, gsl_matrix *
-          J)
-     This function computes the vector of function values F and the
-     approximate Jacobian J at the position vector X using the system
-     described in FDF.  See 'gsl_multifit_fdfsolver_dif_df' for a
-     description of how the Jacobian is computed.
+   The standard deviations of the best-fit parameters are given by the
+square root of the corresponding diagonal elements of the covariance
+matrix, \sigma_{c_a} = \sqrt{C_{aa}}.  The correlation coefficient of
+the fit parameters c_a and c_b is given by \rho_{ab} = C_{ab} /
+\sqrt{C_{aa} C_{bb}}.
 
 
-File: gsl-ref.info,  Node: Iteration of the Minimization Algorithm,  Next: Search Stopping Parameters for Minimization Algorithms,  Prev: Finite Difference Jacobian,  Up: Nonlinear Least-Squares Fitting
-
-38.5 Iteration
-==============
+File: gsl-ref.info,  Node: Linear regression,  Next: Multi-parameter regression,  Prev: Fitting Overview,  Up: Least-Squares Fitting
 
-The following functions drive the iteration of each algorithm.  Each
-function performs one iteration to update the state of any solver of the
-corresponding type.  The same functions work for all solvers so that
-different methods can be substituted at runtime without modifications to
-the code.
+38.2 Linear regression
+======================
 
- -- Function: int gsl_multifit_fsolver_iterate (gsl_multifit_fsolver *
-          S)
- -- Function: int gsl_multifit_fdfsolver_iterate (gsl_multifit_fdfsolver
-          * S)
-     These functions perform a single iteration of the solver S.  If the
-     iteration encounters an unexpected problem then an error code will
-     be returned.  The solver maintains a current estimate of the
-     best-fit parameters at all times.
+The functions in this section are used to fit simple one or two
+parameter linear regression models.  The functions are declared in the
+header file 'gsl_fit.h'.
 
-   The solver struct S contains the following entries, which can be used
-to track the progress of the solution:
+* Menu:
 
-'gsl_vector * x'
-     The current position.
+* Linear regression with a constant term::
+* Linear regression without a constant term::
 
-'gsl_vector * f'
-     The function value at the current position.
+
+File: gsl-ref.info,  Node: Linear regression with a constant term,  Next: Linear regression without a constant term,  Up: Linear regression
 
-'gsl_vector * dx'
-     The difference between the current position and the previous
-     position, i.e.  the last step, taken as a vector.
+38.2.1 Linear regression with a constant term
+---------------------------------------------
 
-'gsl_matrix * J'
-     The Jacobian matrix at the current position (for the
-     'gsl_multifit_fdfsolver' struct only)
+The functions described in this section can be used to perform
+least-squares fits to a straight line model, Y(c,x) = c_0 + c_1 x.
+
+ -- Function: int gsl_fit_linear (const double * X, const size_t
+          XSTRIDE, const double * Y, const size_t YSTRIDE, size_t N,
+          double * C0, double * C1, double * COV00, double * COV01,
+          double * COV11, double * SUMSQ)
+     This function computes the best-fit linear regression coefficients
+     (C0,C1) of the model Y = c_0 + c_1 X for the dataset (X, Y), two
+     vectors of length N with strides XSTRIDE and YSTRIDE.  The errors
+     on Y are assumed unknown so the variance-covariance matrix for the
+     parameters (C0, C1) is estimated from the scatter of the points
+     around the best-fit line and returned via the parameters (COV00,
+     COV01, COV11).  The sum of squares of the residuals from the
+     best-fit line is returned in SUMSQ.  Note: the correlation
+     coefficient of the data can be computed using
+     'gsl_stats_correlation' (*note Correlation::), it does not depend
+     on the fit.
+
+ -- Function: int gsl_fit_wlinear (const double * X, const size_t
+          XSTRIDE, const double * W, const size_t WSTRIDE, const double
+          * Y, const size_t YSTRIDE, size_t N, double * C0, double * C1,
+          double * COV00, double * COV01, double * COV11, double *
+          CHISQ)
+     This function computes the best-fit linear regression coefficients
+     (C0,C1) of the model Y = c_0 + c_1 X for the weighted dataset (X,
+     Y), two vectors of length N with strides XSTRIDE and YSTRIDE.  The
+     vector W, of length N and stride WSTRIDE, specifies the weight of
+     each datapoint.  The weight is the reciprocal of the variance for
+     each datapoint in Y.
 
-   The best-fit information also can be accessed with the following
-auxiliary functions,
+     The covariance matrix for the parameters (C0, C1) is computed using
+     the weights and returned via the parameters (COV00, COV01, COV11).
+     The weighted sum of squares of the residuals from the best-fit
+     line, \chi^2, is returned in CHISQ.
 
- -- Function: gsl_vector * gsl_multifit_fsolver_position (const
-          gsl_multifit_fsolver * S)
- -- Function: gsl_vector * gsl_multifit_fdfsolver_position (const
-          gsl_multifit_fdfsolver * S)
-     These functions return the current position (i.e.  best-fit
-     parameters) 's->x' of the solver S.
+ -- Function: int gsl_fit_linear_est (double X, double C0, double C1,
+          double COV00, double COV01, double COV11, double * Y, double *
+          Y_ERR)
+     This function uses the best-fit linear regression coefficients C0,
+     C1 and their covariance COV00, COV01, COV11 to compute the fitted
+     function Y and its standard deviation Y_ERR for the model Y = c_0 +
+     c_1 X at the point X.
 
 
-File: gsl-ref.info,  Node: Search Stopping Parameters for Minimization Algorithms,  Next: High Level Driver,  Prev: Iteration of the Minimization Algorithm,  Up: Nonlinear Least-Squares Fitting
+File: gsl-ref.info,  Node: Linear regression without a constant term,  Prev: Linear regression with a constant term,  Up: Linear regression
 
-38.6 Search Stopping Parameters
-===============================
+38.2.2 Linear regression without a constant term
+------------------------------------------------
 
-A minimization procedure should stop when one of the following
-conditions is true:
+The functions described in this section can be used to perform
+least-squares fits to a straight line model without a constant term, Y =
+c_1 X.
 
-   * A minimum has been found to within the user-specified precision.
+ -- Function: int gsl_fit_mul (const double * X, const size_t XSTRIDE,
+          const double * Y, const size_t YSTRIDE, size_t N, double * C1,
+          double * COV11, double * SUMSQ)
+     This function computes the best-fit linear regression coefficient
+     C1 of the model Y = c_1 X for the datasets (X, Y), two vectors of
+     length N with strides XSTRIDE and YSTRIDE.  The errors on Y are
+     assumed unknown so the variance of the parameter C1 is estimated
+     from the scatter of the points around the best-fit line and
+     returned via the parameter COV11.  The sum of squares of the
+     residuals from the best-fit line is returned in SUMSQ.
 
-   * A user-specified maximum number of iterations has been reached.
+ -- Function: int gsl_fit_wmul (const double * X, const size_t XSTRIDE,
+          const double * W, const size_t WSTRIDE, const double * Y,
+          const size_t YSTRIDE, size_t N, double * C1, double * COV11,
+          double * SUMSQ)
+     This function computes the best-fit linear regression coefficient
+     C1 of the model Y = c_1 X for the weighted datasets (X, Y), two
+     vectors of length N with strides XSTRIDE and YSTRIDE.  The vector
+     W, of length N and stride WSTRIDE, specifies the weight of each
+     datapoint.  The weight is the reciprocal of the variance for each
+     datapoint in Y.
 
-   * An error has occurred.
+     The variance of the parameter C1 is computed using the weights and
+     returned via the parameter COV11.  The weighted sum of squares of
+     the residuals from the best-fit line, \chi^2, is returned in CHISQ.
 
-The handling of these conditions is under user control.  The functions
-below allow the user to test the current estimate of the best-fit
-parameters in several standard ways.
+ -- Function: int gsl_fit_mul_est (double X, double C1, double COV11,
+          double * Y, double * Y_ERR)
+     This function uses the best-fit linear regression coefficient C1
+     and its covariance COV11 to compute the fitted function Y and its
+     standard deviation Y_ERR for the model Y = c_1 X at the point X.
 
- -- Function: int gsl_multifit_test_delta (const gsl_vector * DX, const
-          gsl_vector * X, double EPSABS, double EPSREL)
+
+File: gsl-ref.info,  Node: Multi-parameter regression,  Next: Regularized regression,  Prev: Linear regression,  Up: Least-Squares Fitting
 
-     This function tests for the convergence of the sequence by
-     comparing the last step DX with the absolute error EPSABS and
-     relative error EPSREL to the current position X.  The test returns
-     'GSL_SUCCESS' if the following condition is achieved,
+38.3 Multi-parameter regression
+===============================
 
-          |dx_i| < epsabs + epsrel |x_i|
+This section describes routines which perform least squares fits to a
+linear model by minimizing the cost function
+     \chi^2 = \sum_i w_i (y_i - \sum_j X_ij c_j)^2 = || y - Xc ||_W^2
+   where y is a vector of n observations, X is an n-by-p matrix of
+predictor variables, c is a vector of the p unknown best-fit parameters
+to be estimated, and ||r||_W^2 = r^T W r.  The matrix W =
+diag(w_1,w_2,...,w_n) defines the weights or uncertainties of the
+observation vector.
 
-     for each component of X and returns 'GSL_CONTINUE' otherwise.
+   This formulation can be used for fits to any number of functions
+and/or variables by preparing the n-by-p matrix X appropriately.  For
+example, to fit to a p-th order polynomial in X, use the following
+matrix,
 
- -- Function: int gsl_multifit_test_gradient (const gsl_vector * G,
-          double EPSABS)
-     This function tests the residual gradient G against the absolute
-     error bound EPSABS.  Mathematically, the gradient should be exactly
-     zero at the minimum.  The test returns 'GSL_SUCCESS' if the
-     following condition is achieved,
+     X_{ij} = x_i^j
 
-          \sum_i |g_i| < epsabs
+where the index i runs over the observations and the index j runs from 0
+to p-1.
 
-     and returns 'GSL_CONTINUE' otherwise.  This criterion is suitable
-     for situations where the precise location of the minimum, x, is
-     unimportant provided a value can be found where the gradient is
-     small enough.
+   To fit to a set of p sinusoidal functions with fixed frequencies
+\omega_1, \omega_2, ..., \omega_p, use,
 
- -- Function: int gsl_multifit_gradient (const gsl_matrix * J, const
-          gsl_vector * F, gsl_vector * G)
-     This function computes the gradient G of \Phi(x) = (1/2) ||F(x)||^2
-     from the Jacobian matrix J and the function values F, using the
-     formula g = J^T f.
+     X_{ij} = sin(\omega_j x_i)
 
-
-File: gsl-ref.info,  Node: High Level Driver,  Next: Minimization Algorithms using Derivatives,  Prev: Search Stopping Parameters for Minimization Algorithms,  Up: Nonlinear Least-Squares Fitting
+To fit to p independent variables x_1, x_2, ..., x_p, use,
 
-38.7 High Level Driver
-======================
+     X_{ij} = x_j(i)
 
-These routines provide a high level wrapper that combine the iteration
-and convergence testing for easy use.
+where x_j(i) is the i-th value of the predictor variable x_j.
 
- -- Function: int gsl_multifit_fsolver_driver (gsl_multifit_fsolver * S,
-          const size_t MAXITER, const double EPSABS, const double
-          EPSREL)
- -- Function: int gsl_multifit_fdfsolver_driver (gsl_multifit_fdfsolver
-          * S, const size_t MAXITER, const double EPSABS, const double
-          EPSREL)
-     These functions iterate the solver S for a maximum of MAXITER
-     iterations.  After each iteration, the system is tested for
-     convergence using 'gsl_multifit_test_delta' with the error
-     tolerances EPSABS and EPSREL.
+   The solution of the general linear least-squares system requires an
+additional working space for intermediate results, such as the singular
+value decomposition of the matrix X.
 
-
-File: gsl-ref.info,  Node: Minimization Algorithms using Derivatives,  Next: Minimization Algorithms without Derivatives,  Prev: High Level Driver,  Up: Nonlinear Least-Squares Fitting
+   These functions are declared in the header file 'gsl_multifit.h'.
 
-38.8 Minimization Algorithms using Derivatives
-==============================================
+ -- Function: gsl_multifit_linear_workspace * gsl_multifit_linear_alloc
+          (const size_t N, const size_t P)
+     This function allocates a workspace for fitting a model to a
+     maximum of N observations using a maximum of P parameters.  The
+     user may later supply a smaller least squares system if desired.
+     The size of the workspace is O(np + p^2).
 
-The minimization algorithms described in this section make use of both
-the function and its derivative.  They require an initial guess for the
-location of the minimum.  There is no absolute guarantee of
-convergence--the function must be suitable for this technique and the
-initial guess must be sufficiently close to the minimum for it to work.
+ -- Function: void gsl_multifit_linear_free
+          (gsl_multifit_linear_workspace * WORK)
+     This function frees the memory associated with the workspace W.
 
- -- Derivative Solver: gsl_multifit_fdfsolver_lmsder
-     This is a robust and efficient version of the Levenberg-Marquardt
-     algorithm as implemented in the scaled LMDER routine in MINPACK.
-     Minpack was written by Jorge J. More', Burton S. Garbow and Kenneth
-     E. Hillstrom.
+ -- Function: int gsl_multifit_linear_svd (const gsl_matrix * X,
+          gsl_multifit_linear_workspace * WORK)
+     This function performs a singular value decomposition of the matrix
+     X and stores the SVD factors internally in WORK.
 
-     The algorithm uses a generalized trust region to keep each step
-     under control.  In order to be accepted a proposed new position x'
-     must satisfy the condition |D (x' - x)| < \delta, where D is a
-     diagonal scaling matrix and \delta is the size of the trust region.
-     The components of D are computed internally, using the column norms
-     of the Jacobian to estimate the sensitivity of the residual to each
-     component of x.  This improves the behavior of the algorithm for
-     badly scaled functions.
+ -- Function: int gsl_multifit_linear_bsvd (const gsl_matrix * X,
+          gsl_multifit_linear_workspace * WORK)
+     This function performs a singular value decomposition of the matrix
+     X and stores the SVD factors internally in WORK.  The matrix X is
+     first balanced by applying column scaling factors to improve the
+     accuracy of the singular values.
 
-     On each iteration the algorithm attempts to minimize the linear
-     system |F + J p| subject to the constraint |D p| < \Delta.  The
-     solution to this constrained linear system is found using the
-     Levenberg-Marquardt method.
+ -- Function: int gsl_multifit_linear (const gsl_matrix * X, const
+          gsl_vector * Y, gsl_vector * C, gsl_matrix * COV, double *
+          CHISQ, gsl_multifit_linear_workspace * WORK)
+     This function computes the best-fit parameters C of the model y = X
+     c for the observations Y and the matrix of predictor variables X,
+     using the preallocated workspace provided in WORK.  The p-by-p
+     variance-covariance matrix of the model parameters COV is set to
+     \sigma^2 (X^T X)^{-1}, where \sigma is the standard deviation of
+     the fit residuals.  The sum of squares of the residuals from the
+     best-fit, \chi^2, is returned in CHISQ.  If the coefficient of
+     determination is desired, it can be computed from the expression
+     R^2 = 1 - \chi^2 / TSS, where the total sum of squares (TSS) of the
+     observations Y may be computed from 'gsl_stats_tss'.
 
-     The proposed step is now tested by evaluating the function at the
-     resulting point, x'.  If the step reduces the norm of the function
-     sufficiently, and follows the predicted behavior of the function
-     within the trust region, then it is accepted and the size of the
-     trust region is increased.  If the proposed step fails to improve
-     the solution, or differs significantly from the expected behavior
-     within the trust region, then the size of the trust region is
-     decreased and another trial step is computed.
-
-     The algorithm also monitors the progress of the solution and
-     returns an error if the changes in the solution are smaller than
-     the machine precision.  The possible error codes are,
-
-     'GSL_ETOLF'
-          the decrease in the function falls below machine precision
-
-     'GSL_ETOLX'
-          the change in the position vector falls below machine
-          precision
-
-     'GSL_ETOLG'
-          the norm of the gradient, relative to the norm of the
-          function, falls below machine precision
+     The best-fit is found by singular value decomposition of the matrix
+     X using the modified Golub-Reinsch SVD algorithm, with column
+     scaling to improve the accuracy of the singular values.  Any
+     components which have zero singular value (to machine precision)
+     are discarded from the fit.
 
-     'GSL_ENOPROG'
-          the routine has made 10 or more attempts to find a suitable
-          trial step without success (but subsequent calls can be made
-          to continue the search).(1)
-
-     These error codes indicate that further iterations will be unlikely
-     to change the solution from its current value.
-
- -- Derivative Solver: gsl_multifit_fdfsolver_lmder
-     This is an unscaled version of the LMDER algorithm.  The elements
-     of the diagonal scaling matrix D are set to 1.  This algorithm may
-     be useful in circumstances where the scaled version of LMDER
-     converges too slowly, or the function is already scaled
-     appropriately.
+ -- Function: int gsl_multifit_linear_tsvd (const gsl_matrix * X, const
+          gsl_vector * Y, const double TOL, gsl_vector * C, gsl_matrix *
+          COV, double * CHISQ, size_t * RANK,
+          gsl_multifit_linear_workspace * WORK)
+     This function computes the best-fit parameters C of the model y = X
+     c for the observations Y and the matrix of predictor variables X,
+     using a truncated SVD expansion.  Singular values which satisfy s_i
+     \le tol \times s_0 are discarded from the fit, where s_0 is the
+     largest singular value.  The p-by-p variance-covariance matrix of
+     the model parameters COV is set to \sigma^2 (X^T X)^{-1}, where
+     \sigma is the standard deviation of the fit residuals.  The sum of
+     squares of the residuals from the best-fit, \chi^2, is returned in
+     CHISQ.  The effective rank (number of singular values used in
+     solution) is returned in RANK.  If the coefficient of determination
+     is desired, it can be computed from the expression R^2 = 1 - \chi^2
+     / TSS, where the total sum of squares (TSS) of the observations Y
+     may be computed from 'gsl_stats_tss'.
 
-   ---------- Footnotes ----------
+ -- Function: int gsl_multifit_wlinear (const gsl_matrix * X, const
+          gsl_vector * W, const gsl_vector * Y, gsl_vector * C,
+          gsl_matrix * COV, double * CHISQ,
+          gsl_multifit_linear_workspace * WORK)
+     This function computes the best-fit parameters C of the weighted
+     model y = X c for the observations Y with weights W and the matrix
+     of predictor variables X, using the preallocated workspace provided
+     in WORK.  The p-by-p covariance matrix of the model parameters COV
+     is computed as (X^T W X)^{-1}.  The weighted sum of squares of the
+     residuals from the best-fit, \chi^2, is returned in CHISQ.  If the
+     coefficient of determination is desired, it can be computed from
+     the expression R^2 = 1 - \chi^2 / WTSS, where the weighted total
+     sum of squares (WTSS) of the observations Y may be computed from
+     'gsl_stats_wtss'.
 
-   (1) The return code 'GSL_CONTINUE' was used for this case in versions
-prior to 1.14.
+ -- Function: int gsl_multifit_wlinear_tsvd (const gsl_matrix * X, const
+          gsl_vector * W, const gsl_vector * Y, const double TOL,
+          gsl_vector * C, gsl_matrix * COV, double * CHISQ, size_t *
+          RANK, gsl_multifit_linear_workspace * WORK)
+     This function computes the best-fit parameters C of the weighted
+     model y = X c for the observations Y with weights W and the matrix
+     of predictor variables X, using a truncated SVD expansion.
+     Singular values which satisfy s_i \le tol \times s_0 are discarded
+     from the fit, where s_0 is the largest singular value.  The p-by-p
+     covariance matrix of the model parameters COV is computed as (X^T W
+     X)^{-1}.  The weighted sum of squares of the residuals from the
+     best-fit, \chi^2, is returned in CHISQ.  The effective rank of the
+     system (number of singular values used in the solution) is returned
+     in RANK.  If the coefficient of determination is desired, it can be
+     computed from the expression R^2 = 1 - \chi^2 / WTSS, where the
+     weighted total sum of squares (WTSS) of the observations Y may be
+     computed from 'gsl_stats_wtss'.
 
-
-File: gsl-ref.info,  Node: Minimization Algorithms without Derivatives,  Next: Computing the covariance matrix of best fit parameters,  Prev: Minimization Algorithms using Derivatives,  Up: Nonlinear Least-Squares Fitting
+ -- Function: int gsl_multifit_linear_est (const gsl_vector * X, const
+          gsl_vector * C, const gsl_matrix * COV, double * Y, double *
+          Y_ERR)
+     This function uses the best-fit multilinear regression coefficients
+     C and their covariance matrix COV to compute the fitted function
+     value Y and its standard deviation Y_ERR for the model y = x.c at
+     the point X.
 
-38.9 Minimization Algorithms without Derivatives
-================================================
+ -- Function: int gsl_multifit_linear_residuals (const gsl_matrix * X,
+          const gsl_vector * Y, const gsl_vector * C, gsl_vector * R)
+     This function computes the vector of residuals r = y - X c for the
+     observations Y, coefficients C and matrix of predictor variables X.
 
-There are no algorithms implemented in this section at the moment.
+ -- Function: size_t gsl_multifit_linear_rank (const double TOL, const
+          gsl_multifit_linear_workspace * WORK)
+     This function returns the rank of the matrix X which must first
+     have its singular value decomposition computed.  The rank is
+     computed by counting the number of singular values \sigma_j which
+     satisfy \sigma_j > tol \times \sigma_0, where \sigma_0 is the
+     largest singular value.
 
 
-File: gsl-ref.info,  Node: Computing the covariance matrix of best fit parameters,  Next: Example programs for Nonlinear Least-Squares Fitting,  Prev: Minimization Algorithms without Derivatives,  Up: Nonlinear Least-Squares Fitting
-
-38.10 Computing the covariance matrix of best fit parameters
-============================================================
+File: gsl-ref.info,  Node: Regularized regression,  Next: Robust linear regression,  Prev: Multi-parameter regression,  Up: Least-Squares Fitting
 
- -- Function: int gsl_multifit_covar (const gsl_matrix * J, double
-          EPSREL, gsl_matrix * COVAR)
-     This function uses the Jacobian matrix J to compute the covariance
-     matrix of the best-fit parameters, COVAR.  The parameter EPSREL is
-     used to remove linear-dependent columns when J is rank deficient.
+38.4 Regularized regression
+===========================
 
-     The covariance matrix is given by,
+Ordinary weighted least squares models seek a solution vector c which
+minimizes the residual
+     \chi^2 = || y - Xc ||_W^2
+   where y is the n-by-1 observation vector, X is the n-by-p design
+matrix, c is the p-by-1 solution vector, W = diag(w_1,...,w_n) is the
+data weighting matrix, and ||r||_W^2 = r^T W r.  In cases where the
+least squares matrix X is ill-conditioned, small perturbations (ie:
+noise) in the observation vector could lead to widely different solution
+vectors c.  One way of dealing with ill-conditioned matrices is to use a
+"truncated SVD" in which small singular values, below some given
+tolerance, are discarded from the solution.  The truncated SVD method is
+available using the functions 'gsl_multifit_linear_tsvd' and
+'gsl_multifit_wlinear_tsvd'.  Another way to help solve ill-posed
+problems is to include a regularization term in the least squares
+minimization
+     \chi^2 = || y - Xc ||_W^2 + \lambda^2 || L c ||^2
+   for a suitably chosen regularization parameter \lambda and matrix L.
+This type of regularization is known as Tikhonov, or ridge, regression.
+In some applications, L is chosen as the identity matrix, giving
+preference to solution vectors c with smaller norms.  Including this
+regularization term leads to the explicit "normal equations" solution
+     c = ( X^T W X + \lambda^2 L^T L )^-1 X^T W y
+   which reduces to the ordinary least squares solution when L = 0.  In
+practice, it is often advantageous to transform a regularized least
+squares system into the form
+     \chi^2 = || y~ - X~ c~ ||^2 + \lambda^2 || c~ ||^2
+   This is known as the Tikhonov "standard form" and has the normal
+equations solution \tilde{c} = \left( \tilde{X}^T \tilde{X} + \lambda^2
+I \right)^{-1} \tilde{X}^T \tilde{y}.  For an m-by-p matrix L which is
+full rank and has m >= p (ie: L is square or has more rows than
+columns), we can calculate the "thin" QR decomposition of L, and note
+that ||L c|| = ||R c|| since the Q factor will not change the norm.
+Since R is p-by-p, we can then use the transformation
+     X~ = sqrt(W) X R^-1
+     y~ = sqrt(W) y
+     c~ = R c
+   to achieve the standard form.  For a rectangular matrix L with m < p,
+a more sophisticated approach is needed (see Hansen 1998, chapter 2.3).
+In practice, the normal equations solution above is not desirable due to
+numerical instabilities, and so the system is solved using the singular
+value decomposition of the matrix \tilde{X}.  The matrix L is often
+chosen as the identity matrix, or as a first or second finite difference
+operator, to ensure a smoothly varying coefficient vector c, or as a
+diagonal matrix to selectively damp each model parameter differently.
+If L \ne I, the user must first convert the least squares problem to
+standard form using 'gsl_multifit_linear_stdform1' or
+'gsl_multifit_linear_stdform2', solve the system, and then backtransform
+the solution vector to recover the solution of the original problem (see
+'gsl_multifit_linear_genform1' and 'gsl_multifit_linear_genform2').
+
+   In many regularization problems, care must be taken when choosing the
+regularization parameter \lambda.  Since both the residual norm ||y - X
+c|| and solution norm ||L c|| are being minimized, the parameter \lambda
+represents a tradeoff between minimizing either the residuals or the
+solution vector.  A common tool for visualizing the comprimise between
+the minimization of these two quantities is known as the L-curve.  The
+L-curve is a log-log plot of the residual norm ||y - X c|| on the
+horizontal axis and the solution norm ||L c|| on the vertical axis.
+This curve nearly always as an L shaped appearance, with a distinct
+corner separating the horizontal and vertical sections of the curve.
+The regularization parameter corresponding to this corner is often
+chosen as the optimal value.  GSL provides routines to calculate the
+L-curve for all relevant regularization parameters as well as locating
+the corner.
+
+   Another method of choosing the regularization parameter is known as
+Generalized Cross Validation (GCV). This method is based on the idea
+that if an arbitrary element y_i is left out of the right hand side, the
+resulting regularized solution should predict this element accurately.
+This leads to choosing the parameter \lambda which minimizes the GCV
+function
+
+     G(\lambda) = (||y - X c_{\lambda}||^2) / Tr(I_n - X X^I)^2
+
+   where X_{\lambda}^I is the matrix which relates the solution
+c_{\lambda} to the right hand side y, ie: c_{\lambda} = X_{\lambda}^I y.
+GSL provides routines to compute the GCV curve and its minimum.
+
+For most applications, the steps required to solve a regularized least
+squares problem are as follows:
+
+  1. Construct the least squares system (X, y, W, L)
+
+  2. Transform the system to standard form (\tilde{X},\tilde{y}).  This
+     step can be skipped if L = I_p and W = I_n.
+
+  3. Calculate the SVD of \tilde{X}.
+
+  4. Determine an appropriate regularization parameter \lambda (using
+     for example L-curve or GCV analysis).
+
+  5. Solve the standard form system using the chosen \lambda and the SVD
+     of \tilde{X}.
+
+  6. Backtransform the standard form solution \tilde{c} to recover the
+     original solution vector c.
+
+ -- Function: int gsl_multifit_linear_stdform1 (const gsl_vector * L,
+          const gsl_matrix * X, const gsl_vector * Y, gsl_matrix * XS,
+          gsl_vector * YS, gsl_multifit_linear_workspace * WORK)
+ -- Function: int gsl_multifit_linear_wstdform1 (const gsl_vector * L,
+          const gsl_matrix * X, const gsl_vector * W, const gsl_vector *
+          Y, gsl_matrix * XS, gsl_vector * YS,
+          gsl_multifit_linear_workspace * WORK)
+     These functions define a regularization matrix L =
+     diag(l_0,l_1,...,l_{p-1}).  The diagonal matrix element l_i is
+     provided by the ith element of the input vector L.  The n-by-p
+     least squares matrix X and vector Y of length n are then converted
+     to standard form as described above and the parameters
+     (\tilde{X},\tilde{y}) are stored in XS and YS on output.  XS and YS
+     have the same dimensions as X and Y.  Optional data weights may be
+     supplied in the vector W of length n.  In order to apply this
+     transformation, L^{-1} must exist and so none of the l_i may be
+     zero.  After the standard form system has been solved, use
+     'gsl_multifit_linear_genform1' to recover the original solution
+     vector.  It is allowed to have X = XS and Y = YS for an in-place
+     transform.  In order to perform a weighted regularized fit with L =
+     I, the user may call 'gsl_multifit_linear_applyW' to convert to
+     standard form.
+
+ -- Function: int gsl_multifit_linear_L_decomp (gsl_matrix * L,
+          gsl_vector * TAU)
+     This function factors the m-by-p regularization matrix L into a
+     form needed for the later transformation to standard form.  L may
+     have any number of rows m.  If m \ge p the QR decomposition of L is
+     computed and stored in L on output.  If m < p, the QR decomposition
+     of L^T is computed and stored in L on output.  On output, the
+     Householder scalars are stored in the vector TAU of size MIN(m,p).
+     These outputs will be used by 'gsl_multifit_linear_wstdform2' to
+     complete the transformation to standard form.
+
+ -- Function: int gsl_multifit_linear_stdform2 (const gsl_matrix * LQR,
+          const gsl_vector * LTAU, const gsl_matrix * X, const
+          gsl_vector * Y, gsl_matrix * XS, gsl_vector * YS, gsl_matrix *
+          M, gsl_multifit_linear_workspace * WORK)
+ -- Function: int gsl_multifit_linear_wstdform2 (const gsl_matrix * LQR,
+          const gsl_vector * LTAU, const gsl_matrix * X, const
+          gsl_vector * W, const gsl_vector * Y, gsl_matrix * XS,
+          gsl_vector * YS, gsl_matrix * M, gsl_multifit_linear_workspace
+          * WORK)
+     These functions convert the least squares system (X,Y,W,L) to
+     standard form (\tilde{X},\tilde{y}) which are stored in XS and YS
+     respectively.  The m-by-p regularization matrix L is specified by
+     the inputs LQR and LTAU, which are outputs from
+     'gsl_multifit_linear_L_decomp'.  The dimensions of the standard
+     form parameters (\tilde{X},\tilde{y}) depend on whether m is larger
+     or less than p.  For m \ge p, XS is n-by-p, YS is n-by-1, and M is
+     not used.  For m < p, XS is (n - p + m)-by-m, YS is (n - p +
+     m)-by-1, and M is additional n-by-p workspace, which is required to
+     recover the original solution vector after the system has been
+     solved (see 'gsl_multifit_linear_genform2').  Optional data weights
+     may be supplied in the vector W of length n, where W = diag(w).
+
+ -- Function: int gsl_multifit_linear_solve (const double LAMBDA, const
+          gsl_matrix * XS, const gsl_vector * YS, gsl_vector * CS,
+          double * RNORM, double * SNORM, gsl_multifit_linear_workspace
+          * WORK)
+     This function computes the regularized best-fit parameters
+     \tilde{c} which minimize the cost function \chi^2 = || \tilde{y} -
+     \tilde{X} \tilde{c} ||^2 + \lambda^2 || \tilde{c} ||^2 which is in
+     standard form.  The least squares system must therefore be
+     converted to standard form prior to calling this function.  The
+     observation vector \tilde{y} is provided in YS and the matrix of
+     predictor variables \tilde{X} in XS.  The solution vector \tilde{c}
+     is returned in CS, which has length min(m,p).  The SVD of XS must
+     be computed prior to calling this function, using
+     'gsl_multifit_linear_svd'.  The regularization parameter \lambda is
+     provided in LAMBDA.  The residual norm || \tilde{y} - \tilde{X}
+     \tilde{c} || = ||y - X c||_W is returned in RNORM.  The solution
+     norm || \tilde{c} || = ||L c|| is returned in SNORM.
 
-          covar = (J^T J)^{-1}
+ -- Function: int gsl_multifit_linear_genform1 (const gsl_vector * L,
+          const gsl_vector * CS, gsl_vector * C,
+          gsl_multifit_linear_workspace * WORK)
+     After a regularized system has been solved with L =
+     diag(\l_0,\l_1,...,\l_{p-1}), this function backtransforms the
+     standard form solution vector CS to recover the solution vector of
+     the original problem C.  The diagonal matrix elements l_i are
+     provided in the vector L.  It is allowed to have C = CS for an
+     in-place transform.
+
+ -- Function: int gsl_multifit_linear_genform2 (const gsl_matrix * LQR,
+          const gsl_vector * LTAU, const gsl_matrix * X, const
+          gsl_vector * Y, const gsl_vector * CS, const gsl_matrix * M,
+          gsl_vector * C, gsl_multifit_linear_workspace * WORK)
+ -- Function: int gsl_multifit_linear_wgenform2 (const gsl_matrix * LQR,
+          const gsl_vector * LTAU, const gsl_matrix * X, const
+          gsl_vector * W, const gsl_vector * Y, const gsl_vector * CS,
+          const gsl_matrix * M, gsl_vector * C,
+          gsl_multifit_linear_workspace * WORK)
+     After a regularized system has been solved with a general
+     rectangular matrix L, specified by (LQR,LTAU), this function
+     backtransforms the standard form solution CS to recover the
+     solution vector of the original problem, which is stored in C, of
+     length p.  The original least squares matrix and observation vector
+     are provided in X and Y respectively.  M is the matrix computed by
+     'gsl_multifit_linear_stdform2'.  For weighted fits, the weight
+     vector W must also be supplied.
+
+ -- Function: int gsl_multifit_linear_applyW (const gsl_matrix * X,
+          const gsl_vector * W, const gsl_vector * Y, gsl_matrix * WX,
+          gsl_vector * WY)
+     For weighted least squares systems with L = I, this function may be
+     used to convert the system to standard form by applying the weight
+     matrix W = diag(W) to the least squares matrix X and observation
+     vector Y.  On output, WX is equal to W^{1/2} X and WY is equal to
+     W^{1/2} y.  It is allowed for WX = X and WY = Y for an in-place
+     transform.
 
-     and is computed by QR decomposition of J with column-pivoting.  Any
-     columns of R which satisfy
+ -- Function: int gsl_multifit_linear_lcurve (const gsl_vector * Y,
+          gsl_vector * REG_PARAM, gsl_vector * RHO, gsl_vector * ETA,
+          gsl_multifit_linear_workspace * WORK)
+     This function computes the L-curve for a least squares system using
+     the right hand side vector Y and the SVD decomposition of the least
+     squares matrix X, which must be provided to
+     'gsl_multifit_linear_svd' prior to calling this function.  The
+     output vectors REG_PARAM, RHO, and ETA must all be the same size,
+     and will contain the regularization parameters \lambda_i, residual
+     norms ||y - X c_i||, and solution norms || L c_i || which compose
+     the L-curve, where c_i is the regularized solution vector
+     corresponding to \lambda_i.  The user may determine the number of
+     points on the L-curve by adjusting the size of these input arrays.
+     The regularization parameters \lambda_i are estimated from the
+     singular values of X, and chosen to represent the most relevant
+     portion of the L-curve.
+
+ -- Function: int gsl_multifit_linear_lcorner (const gsl_vector * RHO,
+          const gsl_vector * ETA, size_t * IDX)
+     This function attempts to locate the corner of the L-curve (||y - X
+     c||, ||L c||) defined by the RHO and ETA input arrays respectively.
+     The corner is defined as the point of maximum curvature of the
+     L-curve in log-log scale.  The RHO and ETA arrays can be outputs of
+     'gsl_multifit_linear_lcurve'.  The algorithm used simply fits a
+     circle to 3 consecutive points on the L-curve and uses the circle's
+     radius to determine the curvature at the middle point.  Therefore,
+     the input array sizes must be \ge 3.  With more points provided for
+     the L-curve, a better estimate of the curvature can be obtained.
+     The array index corresponding to maximum curvature (ie: the corner)
+     is returned in IDX.  If the input arrays contain colinear points,
+     this function could fail and return 'GSL_EINVAL'.
+
+ -- Function: int gsl_multifit_linear_lcorner2 (const gsl_vector *
+          REG_PARAM, const gsl_vector * ETA, size_t * IDX)
+     This function attempts to locate the corner of an alternate L-curve
+     (\lambda^2, ||L c||^2) studied by Rezghi and Hosseini, 2009.  This
+     alternate L-curve can provide better estimates of the
+     regularization parameter for smooth solution vectors.  The
+     regularization parameters \lambda and solution norms ||L c|| are
+     provided in the REG_PARAM and ETA input arrays respectively.  The
+     corner is defined as the point of maximum curvature of this
+     alternate L-curve in linear scale.  The REG_PARAM and ETA arrays
+     can be outputs of 'gsl_multifit_linear_lcurve'.  The algorithm used
+     simply fits a circle to 3 consecutive points on the L-curve and
+     uses the circle's radius to determine the curvature at the middle
+     point.  Therefore, the input array sizes must be \ge 3.  With more
+     points provided for the L-curve, a better estimate of the curvature
+     can be obtained.  The array index corresponding to maximum
+     curvature (ie: the corner) is returned in IDX.  If the input arrays
+     contain colinear points, this function could fail and return
+     'GSL_EINVAL'.
 
-          |R_{kk}| <= epsrel |R_{11}|
+ -- Function: int gsl_multifit_linear_gcv_init(const gsl_vector * Y,
+          gsl_vector * REG_PARAM, gsl_vector * UTY, double * DELTA0,
+          gsl_multifit_linear_workspace * WORK)
+     This function performs some initialization in preparation for
+     computing the GCV curve and its minimum.  The right hand side
+     vector is provided in Y.  On output, REG_PARAM is set to a vector
+     of regularization parameters in decreasing order and may be of any
+     size.  The vector UTY of size p is set to U^T y.  The parameter
+     DELTA0 is needed for subsequent steps of the GCV calculation.
+
+ -- Function: int gsl_multifit_linear_gcv_curve(const gsl_vector *
+          REG_PARAM, const gsl_vector * UTY, const double DELTA0,
+          gsl_vector * G, gsl_multifit_linear_workspace * WORK)
+     This funtion calculates the GCV curve G(\lambda) and stores it in G
+     on output, which must be the same size as REG_PARAM.  The inputs
+     REG_PARAM, UTY and DELTA0 are computed in
+     'gsl_multifit_linear_gcv_init'.
+
+ -- Function: int gsl_multifit_linear_gcv_min(const gsl_vector *
+          REG_PARAM, const gsl_vector * UTY, const gsl_vector * G, const
+          double DELTA0, double * LAMBDA, gsl_multifit_linear_workspace
+          * WORK)
+     This function computes the value of the regularization parameter
+     which minimizes the GCV curve G(\lambda) and stores it in LAMBDA.
+     The input G is calculated by 'gsl_multifit_linear_gcv_curve' and
+     the inputs REG_PARAM, UTY and DELTA0 are computed by
+     'gsl_multifit_linear_gcv_init'.
 
-     are considered linearly-dependent and are excluded from the
-     covariance matrix (the corresponding rows and columns of the
-     covariance matrix are set to zero).
+ -- Function: double gsl_multifit_linear_gcv_calc(const double LAMBDA,
+          const gsl_vector * UTY, const double DELTA0,
+          gsl_multifit_linear_workspace * WORK)
+     This function returns the value of the GCV curve G(\lambda)
+     corresponding to the input LAMBDA.
 
-     If the minimisation uses the weighted least-squares function f_i =
-     (Y(x, t_i) - y_i) / \sigma_i then the covariance matrix above gives
-     the statistical error on the best-fit parameters resulting from the
-     Gaussian errors \sigma_i on the underlying data y_i.  This can be
-     verified from the relation \delta f = J \delta c and the fact that
-     the fluctuations in f from the data y_i are normalised by \sigma_i
-     and so satisfy <\delta f \delta f^T> = I.
+ -- Function: int gsl_multifit_linear_gcv(const gsl_vector * Y,
+          gsl_vector * REG_PARAM, gsl_vector * G, double * LAMBDA,
+          double * G_LAMBDA, gsl_multifit_linear_workspace * WORK)
+     This function combines the steps 'gcv_init', 'gcv_curve', and
+     'gcv_min' defined above into a single function.  The input Y is the
+     right hand side vector.  On output, REG_PARAM and G, which must be
+     the same size, are set to vectors of \lambda and G(\lambda) values
+     respectively.  The output LAMBDA is set to the optimal value of
+     \lambda which minimizes the GCV curve.  The minimum value of the
+     GCV curve is returned in G_LAMBDA.
+
+ -- Function: int gsl_multifit_linear_Lk (const size_t P, const size_t
+          K, gsl_matrix * L)
+     This function computes the discrete approximation to the derivative
+     operator L_k of order K on a regular grid of P points and stores it
+     in L.  The dimensions of L are (p-k)-by-p.
 
-     For an unweighted least-squares function f_i = (Y(x, t_i) - y_i)
-     the covariance matrix above should be multiplied by the variance of
-     the residuals about the best-fit \sigma^2 = \sum (y_i - Y(x,t_i))^2
-     / (n-p) to give the variance-covariance matrix \sigma^2 C.  This
-     estimates the statistical error on the best-fit parameters from the
-     scatter of the underlying data.
+ -- Function: int gsl_multifit_linear_Lsobolev (const size_t P, const
+          size_t KMAX, const gsl_vector * ALPHA, gsl_matrix * L,
+          gsl_multifit_linear_workspace * WORK)
+     This function computes the regularization matrix L corresponding to
+     the weighted Sobolov norm ||L c||^2 = \sum_k \alpha_k^2 ||L_k c||^2
+     where L_k approximates the derivative operator of order k.  This
+     regularization norm can be useful in applications where it is
+     necessary to smooth several derivatives of the solution.  P is the
+     number of model parameters, KMAX is the highest derivative to
+     include in the summation above, and ALPHA is the vector of weights
+     of size KMAX + 1, where ALPHA[k] = \alpha_k is the weight assigned
+     to the derivative of order k.  The output matrix L is size P-by-P
+     and upper triangular.
 
-     For more information about covariance matrices see *note Fitting
-     Overview::.
+ -- Function: double gsl_multifit_linear_rcond (const
+          gsl_multifit_linear_workspace * WORK)
+     This function returns the reciprocal condition number of the least
+     squares matrix X, defined as the ratio of the smallest and largest
+     singular values, rcond = \sigma_{min}/\sigma_{max}.  The routine
+     'gsl_multifit_linear_svd' must first be called to compute the SVD
+     of X.
 
 
-File: gsl-ref.info,  Node: Example programs for Nonlinear Least-Squares Fitting,  Next: References and Further Reading for Nonlinear Least-Squares Fitting,  Prev: Computing the covariance matrix of best fit parameters,  Up: Nonlinear Least-Squares Fitting
-
-38.11 Examples
-==============
+File: gsl-ref.info,  Node: Robust linear regression,  Next: Large Dense Linear Systems,  Prev: Regularized regression,  Up: Least-Squares Fitting
 
-The following example program fits a weighted exponential model with
-background to experimental data, Y = A \exp(-\lambda t) + b.  The first
-part of the program sets up the functions 'expb_f' and 'expb_df' to
-calculate the model and its Jacobian.  The appropriate fitting function
-is given by,
-
-     f_i = ((A \exp(-\lambda t_i) + b) - y_i)/\sigma_i
+38.5 Robust linear regression
+=============================
 
-where we have chosen t_i = i.  The Jacobian matrix J is the derivative
-of these functions with respect to the three parameters (A, \lambda, b).
-It is given by,
+Ordinary least squares (OLS) models are often heavily influenced by the
+presence of outliers.  Outliers are data points which do not follow the
+general trend of the other observations, although there is strictly no
+precise definition of an outlier.  Robust linear regression refers to
+regression algorithms which are robust to outliers.  The most common
+type of robust regression is M-estimation.  The general M-estimator
+minimizes the objective function
 
-     J_{ij} = d f_i / d x_j
+     \sum_i \rho(e_i) = \sum_i \rho (y_i - Y(c, x_i))
 
-where x_0 = A, x_1 = \lambda and x_2 = b.
+   where e_i = y_i - Y(c, x_i) is the residual of the ith data point,
+and \rho(e_i) is a function which should have the following properties:
+     \rho(e) \ge 0
+     \rho(0) = 0
+     \rho(-e) = \rho(e)
+     \rho(e_1) > \rho(e_2) for |e_1| > |e_2|
+The special case of ordinary least squares is given by \rho(e_i) =
+e_i^2.  Letting \psi = \rho' be the derivative of \rho, differentiating
+the objective function with respect to the coefficients c and setting
+the partial derivatives to zero produces the system of equations
 
-     /* expfit.c -- model functions for exponential + background */
+     \sum_i \psi(e_i) X_i = 0
 
-     struct data {
-       size_t n;
-       double * y;
-       double * sigma;
-     };
+   where X_i is a vector containing row i of the design matrix X.  Next,
+we define a weight function w(e) = \psi(e)/e, and let w_i = w(e_i):
 
-     int
-     expb_f (const gsl_vector * x, void *data,
-             gsl_vector * f)
-     {
-       size_t n = ((struct data *)data)->n;
-       double *y = ((struct data *)data)->y;
-       double *sigma = ((struct data *) data)->sigma;
+     \sum_i w_i e_i X_i = 0
 
-       double A = gsl_vector_get (x, 0);
-       double lambda = gsl_vector_get (x, 1);
-       double b = gsl_vector_get (x, 2);
+   This system of equations is equivalent to solving a weighted ordinary
+least squares problem, minimizing \chi^2 = \sum_i w_i e_i^2.  The
+weights however, depend on the residuals e_i, which depend on the
+coefficients c, which depend on the weights.  Therefore, an iterative
+solution is used, called Iteratively Reweighted Least Squares (IRLS).
+  1. Compute initial estimates of the coefficients c^{(0)} using
+     ordinary least squares
 
-       size_t i;
+  2. For iteration k, form the residuals e_i^{(k)} = (y_i - X_i
+     c^{(k-1)})/(t \sigma^{(k)} \sqrt{1 - h_i}), where t is a tuning
+     constant depending on the choice of \psi, and h_i are the
+     statistical leverages (diagonal elements of the matrix X (X^T
+     X)^{-1} X^T).  Including t and h_i in the residual calculation has
+     been shown to improve the convergence of the method.  The residual
+     standard deviation is approximated as \sigma^{(k)} = MAD / 0.6745,
+     where MAD is the Median-Absolute-Deviation of the n-p largest
+     residuals from the previous iteration.
 
-       for (i = 0; i < n; i++)
-         {
-           /* Model Yi = A * exp(-lambda * i) + b */
-           double t = i;
-           double Yi = A * exp (-lambda * t) + b;
-           gsl_vector_set (f, i, (Yi - y[i])/sigma[i]);
-         }
+  3. Compute new weights w_i^{(k)} = \psi(e_i^{(k)})/e_i^{(k)}.
 
-       return GSL_SUCCESS;
-     }
+  4. Compute new coefficients c^{(k)} by solving the weighted least
+     squares problem with weights w_i^{(k)}.
 
-     int
-     expb_df (const gsl_vector * x, void *data,
-              gsl_matrix * J)
-     {
-       size_t n = ((struct data *)data)->n;
-       double *sigma = ((struct data *) data)->sigma;
+  5. Steps 2 through 4 are iterated until the coefficients converge or
+     until some maximum iteration limit is reached.  Coefficients are
+     tested for convergence using the critera:
 
-       double A = gsl_vector_get (x, 0);
-       double lambda = gsl_vector_get (x, 1);
+          |c_i^(k) - c_i^(k-1)| \le \epsilon \times max(|c_i^(k)|, |c_i^(k-1)|)
 
-       size_t i;
+     for all 0 \le i < p where \epsilon is a small tolerance factor.
+The key to this method lies in selecting the function \psi(e_i) to
+assign smaller weights to large residuals, and larger weights to smaller
+residuals.  As the iteration proceeds, outliers are assigned smaller and
+smaller weights, eventually having very little or no effect on the
+fitted model.
 
-       for (i = 0; i < n; i++)
-         {
-           /* Jacobian matrix J(i,j) = dfi / dxj, */
-           /* where fi = (Yi - yi)/sigma[i],      */
-           /*       Yi = A * exp(-lambda * i) + b  */
-           /* and the xj are the parameters (A,lambda,b) */
-           double t = i;
-           double s = sigma[i];
-           double e = exp(-lambda * t);
-           gsl_matrix_set (J, i, 0, e/s);
-           gsl_matrix_set (J, i, 1, -t * A * e/s);
-           gsl_matrix_set (J, i, 2, 1/s);
-         }
-       return GSL_SUCCESS;
-     }
+ -- Function: gsl_multifit_robust_workspace * gsl_multifit_robust_alloc
+          (const gsl_multifit_robust_type * T, const size_t N, const
+          size_t P)
+     This function allocates a workspace for fitting a model to N
+     observations using P parameters.  The size of the workspace is O(np
+     + p^2).  The type T specifies the function \psi and can be selected
+     from the following choices.
+      -- Robust type: gsl_multifit_robust_default
+          This specifies the 'gsl_multifit_robust_bisquare' type (see
+          below) and is a good general purpose choice for robust
+          regression.
 
-     int
-     expb_fdf (const gsl_vector * x, void *data,
-               gsl_vector * f, gsl_matrix * J)
-     {
-       expb_f (x, data, f);
-       expb_df (x, data, J);
+      -- Robust type: gsl_multifit_robust_bisquare
+          This is Tukey's biweight (bisquare) function and is a good
+          general purpose choice for robust regression.  The weight
+          function is given by
 
-       return GSL_SUCCESS;
-     }
+               w(e) = (1 - e^2)^2
 
-The main part of the program sets up a Levenberg-Marquardt solver and
-some simulated random data.  The data uses the known parameters
-(1.0,5.0,0.1) combined with Gaussian noise (standard deviation = 0.1)
-over a range of 40 timesteps.  The initial guess for the parameters is
-chosen as (0.0, 1.0, 0.0).
+          and the default tuning constant is t = 4.685.
 
-     #include <stdlib.h>
-     #include <stdio.h>
-     #include <gsl/gsl_rng.h>
-     #include <gsl/gsl_randist.h>
-     #include <gsl/gsl_vector.h>
-     #include <gsl/gsl_blas.h>
-     #include <gsl/gsl_multifit_nlin.h>
+      -- Robust type: gsl_multifit_robust_cauchy
+          This is Cauchy's function, also known as the Lorentzian
+          function.  This function does not guarantee a unique solution,
+          meaning different choices of the coefficient vector C could
+          minimize the objective function.  Therefore this option should
+          be used with care.  The weight function is given by
 
-     #include "expfit.c"
+               w(e) = 1 / (1 + e^2)
 
-     #define N 40
+          and the default tuning constant is t = 2.385.
 
-     void print_state (size_t iter, gsl_multifit_fdfsolver * s);
+      -- Robust type: gsl_multifit_robust_fair
+          This is the fair \rho function, which guarantees a unique
+          solution and has continuous derivatives to three orders.  The
+          weight function is given by
 
-     int
-     main (void)
-     {
-       const gsl_multifit_fdfsolver_type *T;
-       gsl_multifit_fdfsolver *s;
-       int status;
-       unsigned int i, iter = 0;
-       const size_t n = N;
-       const size_t p = 3;
+               w(e) = 1 / (1 + |e|)
 
-       gsl_matrix *covar = gsl_matrix_alloc (p, p);
-       double y[N], sigma[N];
-       struct data d = { n, y, sigma};
-       gsl_multifit_function_fdf f;
-       double x_init[3] = { 1.0, 0.0, 0.0 };
-       gsl_vector_view x = gsl_vector_view_array (x_init, p);
-       const gsl_rng_type * type;
-       gsl_rng * r;
+          and the default tuning constant is t = 1.400.
 
-       gsl_rng_env_setup();
+      -- Robust type: gsl_multifit_robust_huber
+          This specifies Huber's \rho function, which is a parabola in
+          the vicinity of zero and increases linearly for a given
+          threshold |e| > t.  This function is also considered an
+          excellent general purpose robust estimator, however,
+          occasional difficulties can be encountered due to the
+          discontinuous first derivative of the \psi function.  The
+          weight function is given by
 
-       type = gsl_rng_default;
-       r = gsl_rng_alloc (type);
+               w(e) = 1/max(1,|e|)
 
-       f.f = &expb_f;
-       f.df = &expb_df;
-       f.fdf = &expb_fdf;
-       f.n = n;
-       f.p = p;
-       f.params = &d;
+          and the default tuning constant is t = 1.345.
 
-       /* This is the data to be fitted */
+      -- Robust type: gsl_multifit_robust_ols
+          This specifies the ordinary least squares solution, which can
+          be useful for quickly checking the difference between the
+          various robust and OLS solutions.  The weight function is
+          given by
 
-       for (i = 0; i < n; i++)
-         {
-           double t = i;
-           y[i] = 1.0 + 5 * exp (-0.1 * t)
-                      + gsl_ran_gaussian (r, 0.1);
-           sigma[i] = 0.1;
-           printf ("data: %u %g %g\n", i, y[i], sigma[i]);
-         };
+               w(e) = 1
 
-       T = gsl_multifit_fdfsolver_lmsder;
-       s = gsl_multifit_fdfsolver_alloc (T, n, p);
-       gsl_multifit_fdfsolver_set (s, &f, &x.vector);
+          and the default tuning constant is t = 1.
 
-       print_state (iter, s);
+      -- Robust type: gsl_multifit_robust_welsch
+          This specifies the Welsch function which can perform well in
+          cases where the residuals have an exponential distribution.
+          The weight function is given by
 
-       do
-         {
-           iter++;
-           status = gsl_multifit_fdfsolver_iterate (s);
+               w(e) = \exp(-e^2)
 
-           printf ("status = %s\n", gsl_strerror (status));
+          and the default tuning constant is t = 2.985.
 
-           print_state (iter, s);
+ -- Function: void gsl_multifit_robust_free
+          (gsl_multifit_robust_workspace * W)
+     This function frees the memory associated with the workspace W.
 
-           if (status)
-             break;
+ -- Function: const char * gsl_multifit_robust_name (const
+          gsl_multifit_robust_workspace * W)
+     This function returns the name of the robust type T specified to
+     'gsl_multifit_robust_alloc'.
 
-           status = gsl_multifit_test_delta (s->dx, s->x,
-                                             1e-4, 1e-4);
-         }
-       while (status == GSL_CONTINUE && iter < 500);
+ -- Function: int gsl_multifit_robust_tune (const double TUNE,
+          gsl_multifit_robust_workspace * W)
+     This function sets the tuning constant t used to adjust the
+     residuals at each iteration to TUNE.  Decreasing the tuning
+     constant increases the downweight assigned to large residuals,
+     while increasing the tuning constant decreases the downweight
+     assigned to large residuals.
 
-       gsl_multifit_covar (s->J, 0.0, covar);
+ -- Function: int gsl_multifit_robust_maxiter (const size_t MAXITER,
+          gsl_multifit_robust_workspace * W)
+     This function sets the maximum number of iterations in the
+     iteratively reweighted least squares algorithm to MAXITER.  By
+     default, this value is set to 100 by 'gsl_multifit_robust_alloc'.
+
+ -- Function: int gsl_multifit_robust_weights (const gsl_vector * R,
+          gsl_vector * WTS, gsl_multifit_robust_workspace * W)
+     This function assigns weights to the vector WTS using the residual
+     vector R and previously specified weighting function.  The output
+     weights are given by wts_i = w(r_i / (t \sigma)), where the
+     weighting functions w are detailed in 'gsl_multifit_robust_alloc'.
+     \sigma is an estimate of the residual standard deviation based on
+     the Median-Absolute-Deviation and t is the tuning constant.  This
+     function is useful if the user wishes to implement their own robust
+     regression rather than using the supplied 'gsl_multifit_robust'
+     routine below.
 
-     #define FIT(i) gsl_vector_get(s->x, i)
-     #define ERR(i) sqrt(gsl_matrix_get(covar,i,i))
+ -- Function: int gsl_multifit_robust (const gsl_matrix * X, const
+          gsl_vector * Y, gsl_vector * C, gsl_matrix * COV,
+          gsl_multifit_robust_workspace * W)
+     This function computes the best-fit parameters C of the model y = X
+     c for the observations Y and the matrix of predictor variables X,
+     attemping to reduce the influence of outliers using the algorithm
+     outlined above.  The p-by-p variance-covariance matrix of the model
+     parameters COV is estimated as \sigma^2 (X^T X)^{-1}, where \sigma
+     is an approximation of the residual standard deviation using the
+     theory of robust regression.  Special care must be taken when
+     estimating \sigma and other statistics such as R^2, and so these
+     are computed internally and are available by calling the function
+     'gsl_multifit_robust_statistics'.
 
-       {
-         double chi = gsl_blas_dnrm2(s->f);
-         double dof = n - p;
-         double c = GSL_MAX_DBL(1, chi / sqrt(dof));
+     If the coefficients do not converge within the maximum iteration
+     limit, the function returns 'GSL_EMAXITER'.  In this case, the
+     current estimates of the coefficients and covariance matrix are
+     returned in C and COV and the internal fit statistics are computed
+     with these estimates.
 
-         printf("chisq/dof = %g\n",  pow(chi, 2.0) / dof);
+ -- Function: int gsl_multifit_robust_est (const gsl_vector * X, const
+          gsl_vector * C, const gsl_matrix * COV, double * Y, double *
+          Y_ERR)
+     This function uses the best-fit robust regression coefficients C
+     and their covariance matrix COV to compute the fitted function
+     value Y and its standard deviation Y_ERR for the model y = x.c at
+     the point X.
 
-         printf ("A      = %.5f +/- %.5f\n", FIT(0), c*ERR(0));
-         printf ("lambda = %.5f +/- %.5f\n", FIT(1), c*ERR(1));
-         printf ("b      = %.5f +/- %.5f\n", FIT(2), c*ERR(2));
-       }
+ -- Function: int gsl_multifit_robust_residuals (const gsl_matrix * X,
+          const gsl_vector * Y, const gsl_vector * C, gsl_vector * R,
+          gsl_multifit_robust_workspace * W)
+     This function computes the vector of studentized residuals r_i =
+     {y_i - (X c)_i \over \sigma \sqrt{1 - h_i}} for the observations Y,
+     coefficients C and matrix of predictor variables X.  The routine
+     'gsl_multifit_robust' must first be called to compute the
+     statisical leverages h_i of the matrix X and residual standard
+     deviation estimate \sigma.
 
-       printf ("status = %s\n", gsl_strerror (status));
+ -- Function: gsl_multifit_robust_stats gsl_multifit_robust_statistics
+          (const gsl_multifit_robust_workspace * W)
+     This function returns a structure containing relevant statistics
+     from a robust regression.  The function 'gsl_multifit_robust' must
+     be called first to perform the regression and calculate these
+     statistics.  The returned 'gsl_multifit_robust_stats' structure
+     contains the following fields.
+          double 'sigma_ols' This contains the standard deviation of the
+          residuals as computed from ordinary least squares (OLS).
 
-       gsl_multifit_fdfsolver_free (s);
-       gsl_matrix_free (covar);
-       gsl_rng_free (r);
-       return 0;
-     }
+          double 'sigma_mad' This contains an estimate of the standard
+          deviation of the final residuals using the
+          Median-Absolute-Deviation statistic
 
-     void
-     print_state (size_t iter, gsl_multifit_fdfsolver * s)
-     {
-       printf ("iter: %3u x = % 15.8f % 15.8f % 15.8f "
-               "|f(x)| = %g\n",
-               iter,
-               gsl_vector_get (s->x, 0),
-               gsl_vector_get (s->x, 1),
-               gsl_vector_get (s->x, 2),
-               gsl_blas_dnrm2 (s->f));
-     }
+          double 'sigma_rob' This contains an estimate of the standard
+          deviation of the final residuals from the theory of robust
+          regression (see Street et al, 1988).
 
-The iteration terminates when the change in x is smaller than 0.0001, as
-both an absolute and relative change.  Here are the results of running
-the program:
-
-     iter: 0 x=1.00000000 0.00000000 0.00000000 |f(x)|=117.349
-     status=success
-     iter: 1 x=1.64659312 0.01814772 0.64659312 |f(x)|=76.4578
-     status=success
-     iter: 2 x=2.85876037 0.08092095 1.44796363 |f(x)|=37.6838
-     status=success
-     iter: 3 x=4.94899512 0.11942928 1.09457665 |f(x)|=9.58079
-     status=success
-     iter: 4 x=5.02175572 0.10287787 1.03388354 |f(x)|=5.63049
-     status=success
-     iter: 5 x=5.04520433 0.10405523 1.01941607 |f(x)|=5.44398
-     status=success
-     iter: 6 x=5.04535782 0.10404906 1.01924871 |f(x)|=5.44397
-     chisq/dof = 0.800996
-     A      = 5.04536 +/- 0.06028
-     lambda = 0.10405 +/- 0.00316
-     b      = 1.01925 +/- 0.03782
-     status = success
+          double 'sigma' This contains an estimate of the standard
+          deviation of the final residuals by attemping to reconcile
+          'sigma_rob' and 'sigma_ols' in a reasonable way.
 
-The approximate values of the parameters are found correctly, and the
-chi-squared value indicates a good fit (the chi-squared per degree of
-freedom is approximately 1).  In this case the errors on the parameters
-can be estimated from the square roots of the diagonal elements of the
-covariance matrix.
+          double 'Rsq' This contains the R^2 coefficient of
+          determination statistic using the estimate 'sigma'.
 
-   If the chi-squared value shows a poor fit (i.e.  chi^2/dof >> 1) then
-the error estimates obtained from the covariance matrix will be too
-small.  In the example program the error estimates are multiplied by
-\sqrt{\chi^2/dof} in this case, a common way of increasing the errors
-for a poor fit.  Note that a poor fit will result from the use an
-inappropriate model, and the scaled error estimates may then be outside
-the range of validity for Gaussian errors.
+          double 'adj_Rsq' This contains the adjusted R^2 coefficient of
+          determination statistic using the estimate 'sigma'.
 
-
-File: gsl-ref.info,  Node: References and Further Reading for Nonlinear Least-Squares Fitting,  Prev: Example programs for Nonlinear Least-Squares Fitting,  Up: Nonlinear Least-Squares Fitting
+          double 'rmse' This contains the root mean squared error of the
+          final residuals
 
-38.12 References and Further Reading
-====================================
+          double 'sse' This contains the residual sum of squares taking
+          into account the robust covariance matrix.
 
-The MINPACK algorithm is described in the following article,
+          size_t 'dof' This contains the number of degrees of freedom n
+          - p
 
-     J.J. More', 'The Levenberg-Marquardt Algorithm: Implementation and
-     Theory', Lecture Notes in Mathematics, v630 (1978), ed G. Watson.
+          size_t 'numit' Upon successful convergence, this contains the
+          number of iterations performed
 
-The following paper is also relevant to the algorithms described in this
-section,
+          gsl_vector * 'weights' This contains the final weight vector
+          of length N
 
-     J.J. More', B.S. Garbow, K.E. Hillstrom, "Testing Unconstrained
-     Optimization Software", ACM Transactions on Mathematical Software,
-     Vol 7, No 1 (1981), p 17-41.
+          gsl_vector * 'r' This contains the final residual vector of
+          length N, r = y - X c
 
 
-File: gsl-ref.info,  Node: Basis Splines,  Next: Physical Constants,  Prev: Nonlinear Least-Squares Fitting,  Up: Top
+File: gsl-ref.info,  Node: Large Dense Linear Systems,  Next: Troubleshooting,  Prev: Robust linear regression,  Up: Least-Squares Fitting
 
-39 Basis Splines
-****************
-
-This chapter describes functions for the computation of smoothing basis
-splines (B-splines).  A smoothing spline differs from an interpolating
-spline in that the resulting curve is not required to pass through each
-datapoint.  *Note Interpolation::, for information about interpolating
-splines.
+38.6 Large dense linear systems
+===============================
 
-   The header file 'gsl_bspline.h' contains the prototypes for the
-bspline functions and related declarations.
+This module is concerned with solving large dense least squares systems
+X c = y where the n-by-p matrix X has n >> p (ie: many more rows than
+columns).  This type of matrix is called a "tall skinny" matrix, and for
+some applications, it may not be possible to fit the entire matrix in
+memory at once to use the standard SVD approach.  Therefore, the
+algorithms in this module are designed to allow the user to construct
+smaller blocks of the matrix X and accumulate those blocks into the
+larger system one at a time.  The algorithms in this module never need
+to store the entire matrix X in memory.  The large linear least squares
+routines support data weights and Tikhonov regularization, and are
+designed to minimize the residual
+     \chi^2 = || y - Xc ||_W^2 + \lambda^2 || L c ||^2
+   where y is the n-by-1 observation vector, X is the n-by-p design
+matrix, c is the p-by-1 solution vector, W = diag(w_1,...,w_n) is the
+data weighting matrix, L is an m-by-p regularization matrix, \lambda is
+a regularization parameter, and ||r||_W^2 = r^T W r.  In the discussion
+which follows, we will assume that the system has been converted into
+Tikhonov standard form,
+     \chi^2 = || y~ - X~ c~ ||^2 + \lambda^2 || c~ ||^2
+   and we will drop the tilde characters from the various parameters.
+For a discussion of the transformation to standard form *note
+Regularized regression::.
+
+   The basic idea is to partition the matrix X and observation vector y
+as
+     [ X_1 ] c = [ y_1 ]
+     [ X_2 ]     [ y_2 ]
+     [ X_3 ]     [ y_3 ]
+     [ ... ]     [ ... ]
+     [ X_k ]     [ y_k ]
+   into k blocks, where each block (X_i,y_i) may have any number of
+rows, but each X_i has p columns.  The sections below describe the
+methods available for solving this partitioned system.  The functions
+are declared in the header file 'gsl_multilarge.h'.
 
 * Menu:
 
-* Overview of B-splines::
-* Initializing the B-splines solver::
-* Constructing the knots vector::
-* Evaluation of B-spline basis functions::
-* Evaluation of B-spline basis function derivatives::
-* Working with the Greville abscissae::
-* Example programs for B-splines::
-* References and Further Reading::
-
-
-File: gsl-ref.info,  Node: Overview of B-splines,  Next: Initializing the B-splines solver,  Up: Basis Splines
-
-39.1 Overview
-=============
-
-B-splines are commonly used as basis functions to fit smoothing curves
-to large data sets.  To do this, the abscissa axis is broken up into
-some number of intervals, where the endpoints of each interval are
-called "breakpoints".  These breakpoints are then converted to "knots"
-by imposing various continuity and smoothness conditions at each
-interface.  Given a nondecreasing knot vector t = {t_0, t_1, ...,
-t_{n+k-1}}, the n basis splines of order k are defined by
-
-     B_(i,1)(x) = (1, t_i <= x < t_(i+1)
-                  (0, else
-     B_(i,k)(x) = [(x - t_i)/(t_(i+k-1) - t_i)] B_(i,k-1)(x)
-                   + [(t_(i+k) - x)/(t_(i+k) - t_(i+1))] B_(i+1,k-1)(x)
-
-for i = 0, ..., n-1.  The common case of cubic B-splines is given by k =
-4.  The above recurrence relation can be evaluated in a numerically
-stable way by the de Boor algorithm.
-
-   If we define appropriate knots on an interval [a,b] then the B-spline
-basis functions form a complete set on that interval.  Therefore we can
-expand a smoothing function as
-
-     f(x) = \sum_i c_i B_(i,k)(x)
-
-given enough (x_j, f(x_j)) data pairs.  The coefficients c_i can be
-readily obtained from a least-squares fit.
-
-
-File: gsl-ref.info,  Node: Initializing the B-splines solver,  Next: Constructing the knots vector,  Prev: Overview of B-splines,  Up: Basis Splines
-
-39.2 Initializing the B-splines solver
-======================================
-
-The computation of B-spline functions requires a preallocated workspace
-of type 'gsl_bspline_workspace'.  If B-spline derivatives are also
-required, an additional 'gsl_bspline_deriv_workspace' is needed.
-
- -- Function: gsl_bspline_workspace * gsl_bspline_alloc (const size_t K,
-          const size_t NBREAK)
-     This function allocates a workspace for computing B-splines of
-     order K.  The number of breakpoints is given by NBREAK.  This leads
-     to n = nbreak + k - 2 basis functions.  Cubic B-splines are
-     specified by k = 4.  The size of the workspace is O(5k + nbreak).
+* Large Dense Linear Systems Normal Equations::
+* Large Dense Linear Systems TSQR::
+* Large Dense Linear Systems Solution Steps::
+* Large Dense Linear Systems Routines::
+
+
+File: gsl-ref.info,  Node: Large Dense Linear Systems Normal Equations,  Next: Large Dense Linear Systems TSQR,  Up: Large Dense Linear Systems
+
+38.6.1 Normal Equations Approach
+--------------------------------
+
+The normal equations approach to the large linear least squares problem
+described above is popular due to its speed and simplicity.  Since the
+normal equations solution to the problem is given by
+     c = ( X^T X + \lambda^2 I )^-1 X^T y
+   only the p-by-p matrix X^T X and p-by-1 vector X^T y need to be
+stored.  Using the partition scheme described above, these are given by
+     X^T X = \sum_i X_i^T X_i
+     X^T y = \sum_i X_i^T y_i
+   Since the matrix X^T X is symmetric, only half of it needs to be
+calculated.  Once all of the blocks (X_i,y_i) have been accumulated into
+the final X^T X and X^T y, the system can be solved with a Cholesky
+factorization of the X^T X matrix.  If the Cholesky factorization fails
+(occasionally due to numerical rounding errors), a QR decomposition is
+then used.  In both cases, the X^T X matrix is first transformed via a
+diagonal scaling transformation to attempt to reduce its condition
+number as much as possible to recover a more accurate solution vector.
+The normal equations approach is the fastest method for solving the
+large least squares problem, and is accurate for well-conditioned
+matrices X.  However, for ill-conditioned matrices, as is often the case
+for large systems, this method can suffer from numerical instabilities
+(see Trefethen and Bau, 1997).  The number of operations for this method
+is O(np^2 + {1 \over 3}p^3).
+
+
+File: gsl-ref.info,  Node: Large Dense Linear Systems TSQR,  Next: Large Dense Linear Systems Solution Steps,  Prev: Large Dense Linear Systems Normal Equations,  Up: Large Dense Linear Systems
+
+38.6.2 Tall Skinny QR (TSQR) Approach
+-------------------------------------
+
+An algorithm which has better numerical stability for ill-conditioned
+problems is known as the Tall Skinny QR (TSQR) method.  This method is
+based on computing the thin QR decomposition of the least squares matrix
+X = Q R, where Q is an n-by-p matrix with orthogonal columns, and R is a
+p-by-p upper triangular matrix.  Once these factors are calculated, the
+residual becomes
+     \chi^2 = || Q^T y - R c ||^2 + \lambda^2 || c ||^2
+   which can be written as the matrix equation
+     [ R ; \lambda I ] c = [ Q^T b ; 0 ]
+   The matrix on the left hand side is now a much smaller 2p-by-p matrix
+which can be solved with a standard SVD approach.  The Q matrix is just
+as large as the original matrix X, however it does not need to be
+explicitly constructed.  The TSQR algorithm computes only the p-by-p
+matrix R and the p-by-1 vector Q^T y, and updates these quantities as
+new blocks are added to the system.  Each time a new block of rows
+(X_i,y_i) is added, the algorithm performs a QR decomposition of the
+matrix
+     [ R_(i-1) ; X_i ]
+   where R_{i-1} is the upper triangular R factor for the matrix
+     [ X_1 ; ... ; X_(i-1) ]
+   This QR decomposition is done efficiently taking into account the
+sparse structure of R_{i-1}.  See Demmel et al, 2008 for more details on
+how this is accomplished.  The number of operations for this method is
+O(2np^2 - {2 \over 3}p^3).
+
+
+File: gsl-ref.info,  Node: Large Dense Linear Systems Solution Steps,  Next: Large Dense Linear Systems Routines,  Prev: Large Dense Linear Systems TSQR,  Up: Large Dense Linear Systems
+
+38.6.3 Large Dense Linear Systems Solution Steps
+------------------------------------------------
+
+The typical steps required to solve large regularized linear least
+squares problems are as follows:
+
+  1. Choose the regularization matrix L.
+
+  2. Construct a block of rows of the least squares matrix, right hand
+     side vector, and weight vector (X_i, y_i, w_i).
+
+  3. Transform the block to standard form (\tilde{X_i},\tilde{y_i}).
+     This step can be skipped if L = I and W = I.
+
+  4. Accumulate the standard form block (\tilde{X_i},\tilde{y_i}) into
+     the system.
+
+  5. Repeat steps 2-4 until the entire matrix and right hand side vector
+     have been accumulated.
+
+  6. Determine an appropriate regularization parameter \lambda (using
+     for example L-curve analysis).
+
+  7. Solve the standard form system using the chosen \lambda.
+
+  8. Backtransform the standard form solution \tilde{c} to recover the
+     original solution vector c.
+
+
+File: gsl-ref.info,  Node: Large Dense Linear Systems Routines,  Prev: Large Dense Linear Systems Solution Steps,  Up: Large Dense Linear Systems
+
+38.6.4 Large Dense Linear Least Squares Routines
+------------------------------------------------
+
+ -- Function: gsl_multilarge_linear_workspace *
+          gsl_multilarge_linear_alloc (const gsl_multilarge_linear_type
+          * T, const size_t P)
+     This function allocates a workspace for solving large linear least
+     squares systems.  The least squares matrix X has P columns, but may
+     have any number of rows.  The parameter T specifies the method to
+     be used for solving the large least squares system and may be
+     selected from the following choices
+
+      -- Multilarge type: gsl_multilarge_linear_normal
+          This specifies the normal equations approach for solving the
+          least squares system.  This method is suitable in cases where
+          performance is critical and it is known that the least squares
+          matrix X is well conditioned.  The size of this workspace is
+          O(p^2).
+
+      -- Multilarge type: gsl_multilarge_linear_tsqr
+          This specifies the sequential Tall Skinny QR (TSQR) approach
+          for solving the least squares system.  This method is a good
+          general purpose choice for large systems, but requires about
+          twice as many operations as the normal equations method for n
+          >> p.  The size of this workspace is O(p^2).
 
- -- Function: void gsl_bspline_free (gsl_bspline_workspace * W)
+ -- Function: void gsl_multilarge_linear_free
+          (gsl_multilarge_linear_workspace * W)
      This function frees the memory associated with the workspace W.
 
- -- Function: gsl_bspline_deriv_workspace * gsl_bspline_deriv_alloc
-          (const size_t K)
-     This function allocates a workspace for computing the derivatives
-     of a B-spline basis function of order K.  The size of the workspace
-     is O(2k^2).
-
- -- Function: void gsl_bspline_deriv_free (gsl_bspline_deriv_workspace *
-          W)
-     This function frees the memory associated with the derivative
-     workspace W.
+ -- Function: const char * gsl_multilarge_linear_name
+          (gsl_multilarge_linear_workspace * W)
+     This function returns a string pointer to the name of the
+     multilarge solver.
+
+ -- Function: int gsl_multilarge_linear_reset
+          (gsl_multilarge_linear_workspace * W)
+     This function resets the workspace W so it can begin to accumulate
+     a new least squares system.
+
+ -- Function: int gsl_multilarge_linear_stdform1 (const gsl_vector * L,
+          const gsl_matrix * X, const gsl_vector * Y, gsl_matrix * XS,
+          gsl_vector * YS, gsl_multilarge_linear_workspace * WORK)
+ -- Function: int gsl_multilarge_linear_wstdform1 (const gsl_vector * L,
+          const gsl_matrix * X, const gsl_vector * W, const gsl_vector *
+          Y, gsl_matrix * XS, gsl_vector * YS,
+          gsl_multilarge_linear_workspace * WORK)
+     These functions define a regularization matrix L =
+     diag(l_0,l_1,...,l_{p-1}).  The diagonal matrix element l_i is
+     provided by the ith element of the input vector L.  The block (X,Y)
+     is converted to standard form and the parameters
+     (\tilde{X},\tilde{y}) are stored in XS and YS on output.  XS and YS
+     have the same dimensions as X and Y.  Optional data weights may be
+     supplied in the vector W.  In order to apply this transformation,
+     L^{-1} must exist and so none of the l_i may be zero.  After the
+     standard form system has been solved, use
+     'gsl_multilarge_linear_genform1' to recover the original solution
+     vector.  It is allowed to have X = XS and Y = YS for an in-place
+     transform.
+
+ -- Function: int gsl_multilarge_linear_L_decomp (gsl_matrix * L,
+          gsl_vector * TAU)
+     This function calculates the QR decomposition of the m-by-p
+     regularization matrix L.  L must have m \ge p.  On output, the
+     Householder scalars are stored in the vector TAU of size p.  These
+     outputs will be used by 'gsl_multilarge_linear_wstdform2' to
+     complete the transformation to standard form.
+
+ -- Function: int gsl_multilarge_linear_stdform2 (const gsl_matrix *
+          LQR, const gsl_vector * LTAU, const gsl_matrix * X, const
+          gsl_vector * Y, gsl_matrix * XS, gsl_vector * YS,
+          gsl_multilarge_linear_workspace * WORK)
+ -- Function: int gsl_multilarge_linear_wstdform2 (const gsl_matrix *
+          LQR, const gsl_vector * LTAU, const gsl_matrix * X, const
+          gsl_vector * W, const gsl_vector * Y, gsl_matrix * XS,
+          gsl_vector * YS, gsl_multilarge_linear_workspace * WORK)
+     These functions convert a block of rows (X,Y,W) to standard form
+     (\tilde{X},\tilde{y}) which are stored in XS and YS respectively.
+     X, Y, and W must all have the same number of rows.  The m-by-p
+     regularization matrix L is specified by the inputs LQR and LTAU,
+     which are outputs from 'gsl_multilarge_linear_L_decomp'.  XS and YS
+     have the same dimensions as X and Y.  After the standard form
+     system has been solved, use 'gsl_multilarge_linear_genform2' to
+     recover the original solution vector.  Optional data weights may be
+     supplied in the vector W, where W = diag(w).
+
+ -- Function: int gsl_multilarge_linear_accumulate (gsl_matrix * X,
+          gsl_vector * Y, gsl_multilarge_linear_workspace * W)
+     This function accumulates the standard form block (X,y) into the
+     current least squares system.  X and Y have the same number of
+     rows, which can be arbitrary.  X must have p columns.  For the TSQR
+     method, X and Y are destroyed on output.  For the normal equations
+     method, they are both unchanged.
+
+ -- Function: int gsl_multilarge_linear_solve (const double LAMBDA,
+          gsl_vector * C, double * RNORM, double * SNORM,
+          gsl_multilarge_linear_workspace * W)
+     After all blocks (X_i,y_i) have been accumulated into the large
+     least squares system, this function will compute the solution
+     vector which is stored in C on output.  The regularization
+     parameter \lambda is provided in LAMBDA.  On output, RNORM contains
+     the residual norm ||y - X c||_W and SNORM contains the solution
+     norm ||L c||.
+
+ -- Function: int gsl_multilarge_linear_genform1 (const gsl_vector * L,
+          const gsl_vector * CS, gsl_vector * C,
+          gsl_multilarge_linear_workspace * WORK)
+     After a regularized system has been solved with L =
+     diag(\l_0,\l_1,...,\l_{p-1}), this function backtransforms the
+     standard form solution vector CS to recover the solution vector of
+     the original problem C.  The diagonal matrix elements l_i are
+     provided in the vector L.  It is allowed to have C = CS for an
+     in-place transform.
+
+ -- Function: int gsl_multilarge_linear_genform2 (const gsl_matrix *
+          LQR, const gsl_vector * LTAU, const gsl_vector * CS,
+          gsl_vector * C, gsl_multilarge_linear_workspace * WORK)
+     After a regularized system has been solved with a regularization
+     matrix L, specified by (LQR,LTAU), this function backtransforms the
+     standard form solution CS to recover the solution vector of the
+     original problem, which is stored in C, of length p.
+
+ -- Function: int gsl_multilarge_linear_lcurve (gsl_vector * REG_PARAM,
+          gsl_vector * RHO, gsl_vector * ETA,
+          gsl_multilarge_linear_workspace * WORK)
+     This function computes the L-curve for a large least squares system
+     after it has been fully accumulated into the workspace WORK.  The
+     output vectors REG_PARAM, RHO, and ETA must all be the same size,
+     and will contain the regularization parameters \lambda_i, residual
+     norms ||y - X c_i||, and solution norms || L c_i || which compose
+     the L-curve, where c_i is the regularized solution vector
+     corresponding to \lambda_i.  The user may determine the number of
+     points on the L-curve by adjusting the size of these input arrays.
+     For the TSQR method, the regularization parameters \lambda_i are
+     estimated from the singular values of the triangular R factor.  For
+     the normal equations method, they are estimated from the
+     eigenvalues of the X^T X matrix.
+
+ -- Function: int gsl_multilarge_linear_rcond (double * RCOND,
+          gsl_multilarge_linear_workspace * WORK)
+     This function computes the reciprocal condition number, stored in
+     RCOND, of the least squares matrix after it has been accumulated
+     into the workspace WORK.  For the TSQR algorithm, this is
+     accomplished by calculating the SVD of the R factor, which has the
+     same singular values as the matrix X.  For the normal equations
+     method, this is done by computing the eigenvalues of X^T X, which
+     could be inaccurate for ill-conditioned matrices X.
 
 
-File: gsl-ref.info,  Node: Constructing the knots vector,  Next: Evaluation of B-spline basis functions,  Prev: Initializing the B-splines solver,  Up: Basis Splines
-
-39.3 Constructing the knots vector
-==================================
+File: gsl-ref.info,  Node: Troubleshooting,  Next: Fitting Examples,  Prev: Large Dense Linear Systems,  Up: Least-Squares Fitting
 
- -- Function: int gsl_bspline_knots (const gsl_vector * BREAKPTS,
-          gsl_bspline_workspace * W)
-     This function computes the knots associated with the given
-     breakpoints and stores them internally in 'w->knots'.
-
- -- Function: int gsl_bspline_knots_uniform (const double A, const
-          double B, gsl_bspline_workspace * W)
-     This function assumes uniformly spaced breakpoints on [a,b] and
-     constructs the corresponding knot vector using the previously
-     specified NBREAK parameter.  The knots are stored in 'w->knots'.
+38.7 Troubleshooting
+====================
 
-
-File: gsl-ref.info,  Node: Evaluation of B-spline basis functions,  Next: Evaluation of B-spline basis function derivatives,  Prev: Constructing the knots vector,  Up: Basis Splines
+When using models based on polynomials, care should be taken when
+constructing the design matrix X.  If the x values are large, then the
+matrix X could be ill-conditioned since its columns are powers of x,
+leading to unstable least-squares solutions.  In this case it can often
+help to center and scale the x values using the mean and standard
+deviation:
 
-39.4 Evaluation of B-splines
-============================
+     x' = (x - mu)/sigma
 
- -- Function: int gsl_bspline_eval (const double X, gsl_vector * B,
-          gsl_bspline_workspace * W)
-     This function evaluates all B-spline basis functions at the
-     position X and stores them in the vector B, so that the i-th
-     element is B_i(x).  The vector B must be of length n = nbreak + k -
-     2.  This value may also be obtained by calling
-     'gsl_bspline_ncoeffs'.  Computing all the basis functions at once
-     is more efficient than computing them individually, due to the
-     nature of the defining recurrence relation.
-
- -- Function: int gsl_bspline_eval_nonzero (const double X, gsl_vector *
-          BK, size_t * ISTART, size_t * IEND, gsl_bspline_workspace * W)
-     This function evaluates all potentially nonzero B-spline basis
-     functions at the position X and stores them in the vector BK, so
-     that the i-th element is B_(istart+i)(x).  The last element of BK
-     is B_(iend)(x).  The vector BK must be of length k.  By returning
-     only the nonzero basis functions, this function allows quantities
-     involving linear combinations of the B_i(x) to be computed without
-     unnecessary terms (such linear combinations occur, for example,
-     when evaluating an interpolated function).
-
- -- Function: size_t gsl_bspline_ncoeffs (gsl_bspline_workspace * W)
-     This function returns the number of B-spline coefficients given by
-     n = nbreak + k - 2.
+and then construct the X matrix using the transformed values x'.
 
 
-File: gsl-ref.info,  Node: Evaluation of B-spline basis function derivatives,  Next: Working with the Greville abscissae,  Prev: Evaluation of B-spline basis functions,  Up: Basis Splines
+File: gsl-ref.info,  Node: Fitting Examples,  Next: Fitting References and Further Reading,  Prev: Troubleshooting,  Up: Least-Squares Fitting
 
-39.5 Evaluation of B-spline derivatives
-=======================================
+38.8 Examples
+=============
 
- -- Function: int gsl_bspline_deriv_eval (const double X, const size_t
-          NDERIV, gsl_matrix * DB, gsl_bspline_workspace * W,
-          gsl_bspline_deriv_workspace * DW)
-     This function evaluates all B-spline basis function derivatives of
-     orders 0 through nderiv (inclusive) at the position X and stores
-     them in the matrix DB.  The (i,j)-th element of DB is
-     d^jB_i(x)/dx^j.  The matrix DB must be of size n = nbreak + k - 2
-     by nderiv + 1.  The value n may also be obtained by calling
-     'gsl_bspline_ncoeffs'.  Note that function evaluations are included
-     as the zeroth order derivatives in DB.  Computing all the basis
-     function derivatives at once is more efficient than computing them
-     individually, due to the nature of the defining recurrence
-     relation.
-
- -- Function: int gsl_bspline_deriv_eval_nonzero (const double X, const
-          size_t NDERIV, gsl_matrix * DB, size_t * ISTART, size_t *
-          IEND, gsl_bspline_workspace * W, gsl_bspline_deriv_workspace *
-          DW)
-     This function evaluates all potentially nonzero B-spline basis
-     function derivatives of orders 0 through nderiv (inclusive) at the
-     position X and stores them in the matrix DB.  The (i,j)-th element
-     of DB is d^j/dx^j B_(istart+i)(x).  The last row of DB contains
-     d^j/dx^j B_(iend)(x).  The matrix DB must be of size k by at least
-     nderiv + 1.  Note that function evaluations are included as the
-     zeroth order derivatives in DB.  By returning only the nonzero
-     basis functions, this function allows quantities involving linear
-     combinations of the B_i(x) and their derivatives to be computed
-     without unnecessary terms.
-
-
-File: gsl-ref.info,  Node: Working with the Greville abscissae,  Next: Example programs for B-splines,  Prev: Evaluation of B-spline basis function derivatives,  Up: Basis Splines
-
-39.6 Working with the Greville abscissae
-========================================
-
-The Greville abscissae are defined to be the mean location of k-1
-consecutive knots in the knot vector for each basis spline function of
-order k.  With the first and last knots in the 'gsl_bspline_workspace'
-knot vector excluded, there are 'gsl_bspline_ncoeffs' Greville abscissae
-for any given B-spline basis.  These values are often used in B-spline
-collocation applications and may also be called Marsden-Schoenberg
-points.
+The example programs in this section demonstrate the various linear
+regression methods.
+
+* Menu:
 
- -- Function: double gsl_bspline_greville_abscissa (size_t I,
-          gsl_bspline_workspace *W);
-     Returns the location of the i-th Greville abscissa for the given
-     B-spline basis.  For the ill-defined case when k=1, the
-     implementation chooses to return breakpoint interval midpoints.
+* Fitting linear regression example::
+* Fitting multi-parameter linear regression example::
+* Fitting regularized linear regression example 1::
+* Fitting regularized linear regression example 2::
+* Fitting robust linear regression example::
+* Fitting large linear systems example::
 
 
-File: gsl-ref.info,  Node: Example programs for B-splines,  Next: References and Further Reading,  Prev: Working with the Greville abscissae,  Up: Basis Splines
+File: gsl-ref.info,  Node: Fitting linear regression example,  Next: Fitting multi-parameter linear regression example,  Up: Fitting Examples
 
-39.7 Examples
-=============
+38.8.1 Simple Linear Regression Example
+---------------------------------------
 
-The following program computes a linear least squares fit to data using
-cubic B-spline basis functions with uniform breakpoints.  The data is
-generated from the curve y(x) = \cos{(x)} \exp{(-x/10)} on the interval
-[0, 15] with Gaussian noise added.
+The following program computes a least squares straight-line fit to a
+simple dataset, and outputs the best-fit line and its associated one
+standard-deviation error bars.
 
      #include <stdio.h>
-     #include <stdlib.h>
-     #include <math.h>
-     #include <gsl/gsl_bspline.h>
-     #include <gsl/gsl_multifit.h>
-     #include <gsl/gsl_rng.h>
-     #include <gsl/gsl_randist.h>
-     #include <gsl/gsl_statistics.h>
-
-     /* number of data points to fit */
-     #define N        200
-
-     /* number of fit coefficients */
-     #define NCOEFFS  12
-
-     /* nbreak = ncoeffs + 2 - k = ncoeffs - 2 since k = 4 */
-     #define NBREAK   (NCOEFFS - 2)
+     #include <gsl/gsl_fit.h>
 
      int
      main (void)
      {
-       const size_t n = N;
-       const size_t ncoeffs = NCOEFFS;
-       const size_t nbreak = NBREAK;
-       size_t i, j;
-       gsl_bspline_workspace *bw;
-       gsl_vector *B;
-       double dy;
-       gsl_rng *r;
-       gsl_vector *c, *w;
-       gsl_vector *x, *y;
-       gsl_matrix *X, *cov;
-       gsl_multifit_linear_workspace *mw;
-       double chisq, Rsq, dof, tss;
-
-       gsl_rng_env_setup();
-       r = gsl_rng_alloc(gsl_rng_default);
+       int i, n = 4;
+       double x[4] = { 1970, 1980, 1990, 2000 };
+       double y[4] = {   12,   11,   14,   13 };
+       double w[4] = {  0.1,  0.2,  0.3,  0.4 };
 
-       /* allocate a cubic bspline workspace (k = 4) */
-       bw = gsl_bspline_alloc(4, nbreak);
-       B = gsl_vector_alloc(ncoeffs);
-
-       x = gsl_vector_alloc(n);
-       y = gsl_vector_alloc(n);
-       X = gsl_matrix_alloc(n, ncoeffs);
-       c = gsl_vector_alloc(ncoeffs);
-       w = gsl_vector_alloc(n);
-       cov = gsl_matrix_alloc(ncoeffs, ncoeffs);
-       mw = gsl_multifit_linear_alloc(n, ncoeffs);
+       double c0, c1, cov00, cov01, cov11, chisq;
 
-       printf("#m=0,S=0\n");
-       /* this is the data to be fitted */
-       for (i = 0; i < n; ++i)
-         {
-           double sigma;
-           double xi = (15.0 / (N - 1)) * i;
-           double yi = cos(xi) * exp(-0.1 * xi);
-
-           sigma = 0.1 * yi;
-           dy = gsl_ran_gaussian(r, sigma);
-           yi += dy;
+       gsl_fit_wlinear (x, 1, w, 1, y, 1, n,
+                        &c0, &c1, &cov00, &cov01, &cov11,
+                        &chisq);
 
-           gsl_vector_set(x, i, xi);
-           gsl_vector_set(y, i, yi);
-           gsl_vector_set(w, i, 1.0 / (sigma * sigma));
+       printf ("# best fit: Y = %g + %g X\n", c0, c1);
+       printf ("# covariance matrix:\n");
+       printf ("# [ %g, %g\n#   %g, %g]\n",
+               cov00, cov01, cov01, cov11);
+       printf ("# chisq = %g\n", chisq);
 
-           printf("%f %f\n", xi, yi);
-         }
+       for (i = 0; i < n; i++)
+         printf ("data: %g %g %g\n",
+                        x[i], y[i], 1/sqrt(w[i]));
 
-       /* use uniform breakpoints on [0, 15] */
-       gsl_bspline_knots_uniform(0.0, 15.0, bw);
+       printf ("\n");
 
-       /* construct the fit matrix X */
-       for (i = 0; i < n; ++i)
+       for (i = -30; i < 130; i++)
          {
-           double xi = gsl_vector_get(x, i);
+           double xf = x[0] + (i/100.0) * (x[n-1] - x[0]);
+           double yf, yf_err;
 
-           /* compute B_j(xi) for all j */
-           gsl_bspline_eval(xi, B, bw);
+           gsl_fit_linear_est (xf,
+                               c0, c1,
+                               cov00, cov01, cov11,
+                               &yf, &yf_err);
 
-           /* fill in row i of X */
-           for (j = 0; j < ncoeffs; ++j)
-             {
-               double Bj = gsl_vector_get(B, j);
-               gsl_matrix_set(X, i, j, Bj);
-             }
+           printf ("fit: %g %g\n", xf, yf);
+           printf ("hi : %g %g\n", xf, yf + yf_err);
+           printf ("lo : %g %g\n", xf, yf - yf_err);
          }
-
-       /* do the fit */
-       gsl_multifit_wlinear(X, w, y, c, cov, &chisq, mw);
-
-       dof = n - ncoeffs;
-       tss = gsl_stats_wtss(w->data, 1, y->data, 1, y->size);
-       Rsq = 1.0 - chisq / tss;
-
-       fprintf(stderr, "chisq/dof = %e, Rsq = %f\n",
-                        chisq / dof, Rsq);
-
-       /* output the smoothed curve */
-       {
-         double xi, yi, yerr;
-
-         printf("#m=1,S=0\n");
-         for (xi = 0.0; xi < 15.0; xi += 0.1)
-           {
-             gsl_bspline_eval(xi, B, bw);
-             gsl_multifit_linear_est(B, c, cov, &yi, &yerr);
-             printf("%f %f\n", xi, yi);
-           }
-       }
-
-       gsl_rng_free(r);
-       gsl_bspline_free(bw);
-       gsl_vector_free(B);
-       gsl_vector_free(x);
-       gsl_vector_free(y);
-       gsl_matrix_free(X);
-       gsl_vector_free(c);
-       gsl_vector_free(w);
-       gsl_matrix_free(cov);
-       gsl_multifit_linear_free(mw);
-
        return 0;
-     } /* main() */
-
-   The output can be plotted with GNU 'graph'.
-
-     $ ./a.out > bspline.dat
-     chisq/dof = 1.118217e+00, Rsq = 0.989771
-     $ graph -T ps -X x -Y y -x 0 15 -y -1 1.3 < bspline.dat > bspline.ps
-
-
-File: gsl-ref.info,  Node: References and Further Reading,  Prev: Example programs for B-splines,  Up: Basis Splines
-
-39.8 References and Further Reading
-===================================
-
-Further information on the algorithms described in this section can be
-found in the following book,
-
-     C. de Boor, 'A Practical Guide to Splines' (1978), Springer-Verlag,
-     ISBN 0-387-90356-9.
-
-   Further information of Greville abscissae and B-spline collocation
-can be found in the following paper,
-
-     Richard W. Johnson, Higher order B-spline collocation at the
-     Greville abscissae.  'Applied Numerical Mathematics'.  vol. 52,
-     2005, 63-75.
-
-A large collection of B-spline routines is available in the PPPACK
-library available at <http://www.netlib.org/pppack>, which is also part
-of SLATEC.
-
-
-File: gsl-ref.info,  Node: Physical Constants,  Next: IEEE floating-point arithmetic,  Prev: Basis Splines,  Up: Top
-
-40 Physical Constants
-*********************
-
-This chapter describes macros for the values of physical constants, such
-as the speed of light, c, and gravitational constant, G.  The values are
-available in different unit systems, including the standard MKSA system
-(meters, kilograms, seconds, amperes) and the CGSM system (centimeters,
-grams, seconds, gauss), which is commonly used in Astronomy.
-
-   The definitions of constants in the MKSA system are available in the
-file 'gsl_const_mksa.h'.  The constants in the CGSM system are defined
-in 'gsl_const_cgsm.h'.  Dimensionless constants, such as the fine
-structure constant, which are pure numbers are defined in
-'gsl_const_num.h'.
+     }
 
-* Menu:
+The following commands extract the data from the output of the program
+and display it using the GNU plotutils 'graph' utility,
 
-* Fundamental Constants::       
-* Astronomy and Astrophysics::  
-* Atomic and Nuclear Physics::  
-* Measurement of Time::         
-* Imperial Units ::             
-* Speed and Nautical Units::    
-* Printers Units::              
-* Volume Area and Length::      
-* Mass and Weight ::            
-* Thermal Energy and Power::    
-* Pressure::                    
-* Viscosity::                   
-* Light and Illumination::      
-* Radioactivity::               
-* Force and Energy::            
-* Prefixes::                    
-* Physical Constant Examples::  
-* Physical Constant References and Further Reading::  
+     $ ./demo > tmp
+     $ more tmp
+     # best fit: Y = -106.6 + 0.06 X
+     # covariance matrix:
+     # [ 39602, -19.9
+     #   -19.9, 0.01]
+     # chisq = 0.8
 
-   The full list of constants is described briefly below.  Consult the
-header files themselves for the values of the constants used in the
-library.
+     $ for n in data fit hi lo ;
+        do
+          grep "^$n" tmp | cut -d: -f2 > $n ;
+        done
+     $ graph -T X -X x -Y y -y 0 20 -m 0 -S 2 -Ie data
+          -S 0 -I a -m 1 fit -m 2 hi -m 2 lo
 
 
-File: gsl-ref.info,  Node: Fundamental Constants,  Next: Astronomy and Astrophysics,  Up: Physical Constants
-
-40.1 Fundamental Constants
-==========================
-
-'GSL_CONST_MKSA_SPEED_OF_LIGHT'
-     The speed of light in vacuum, c.
-
-'GSL_CONST_MKSA_VACUUM_PERMEABILITY'
-     The permeability of free space, \mu_0.  This constant is defined in
-     the MKSA system only.
+File: gsl-ref.info,  Node: Fitting multi-parameter linear regression example,  Next: Fitting regularized linear regression example 1,  Prev: Fitting linear regression example,  Up: Fitting Examples
 
-'GSL_CONST_MKSA_VACUUM_PERMITTIVITY'
-     The permittivity of free space, \epsilon_0.  This constant is
-     defined in the MKSA system only.
+38.8.2 Multi-parameter Linear Regression Example
+------------------------------------------------
 
-'GSL_CONST_MKSA_PLANCKS_CONSTANT_H'
-     Planck's constant, h.
-
-'GSL_CONST_MKSA_PLANCKS_CONSTANT_HBAR'
-     Planck's constant divided by 2\pi, \hbar.
-
-'GSL_CONST_NUM_AVOGADRO'
-     Avogadro's number, N_a.
+The following program performs a quadratic fit y = c_0 + c_1 x + c_2 x^2
+to a weighted dataset using the generalised linear fitting function
+'gsl_multifit_wlinear'.  The model matrix X for a quadratic fit is given
+by,
 
-'GSL_CONST_MKSA_FARADAY'
-     The molar charge of 1 Faraday.
+     X = [ 1   , x_0  , x_0^2 ;
+           1   , x_1  , x_1^2 ;
+           1   , x_2  , x_2^2 ;
+           ... , ...  , ...   ]
 
-'GSL_CONST_MKSA_BOLTZMANN'
-     The Boltzmann constant, k.
+where the column of ones corresponds to the constant term c_0.  The two
+remaining columns corresponds to the terms c_1 x and c_2 x^2.
 
-'GSL_CONST_MKSA_MOLAR_GAS'
-     The molar gas constant, R_0.
+   The program reads N lines of data in the format (X, Y, ERR) where ERR
+is the error (standard deviation) in the value Y.
 
-'GSL_CONST_MKSA_STANDARD_GAS_VOLUME'
-     The standard gas volume, V_0.
+     #include <stdio.h>
+     #include <gsl/gsl_multifit.h>
 
-'GSL_CONST_MKSA_STEFAN_BOLTZMANN_CONSTANT'
-     The Stefan-Boltzmann radiation constant, \sigma.
+     int
+     main (int argc, char **argv)
+     {
+       int i, n;
+       double xi, yi, ei, chisq;
+       gsl_matrix *X, *cov;
+       gsl_vector *y, *w, *c;
 
-'GSL_CONST_MKSA_GAUSS'
-     The magnetic field of 1 Gauss.
+       if (argc != 2)
+         {
+           fprintf (stderr,"usage: fit n < data\n");
+           exit (-1);
+         }
 
-
-File: gsl-ref.info,  Node: Astronomy and Astrophysics,  Next: Atomic and Nuclear Physics,  Prev: Fundamental Constants,  Up: Physical Constants
+       n = atoi (argv[1]);
 
-40.2 Astronomy and Astrophysics
-===============================
+       X = gsl_matrix_alloc (n, 3);
+       y = gsl_vector_alloc (n);
+       w = gsl_vector_alloc (n);
 
-'GSL_CONST_MKSA_ASTRONOMICAL_UNIT'
-     The length of 1 astronomical unit (mean earth-sun distance), au.
+       c = gsl_vector_alloc (3);
+       cov = gsl_matrix_alloc (3, 3);
 
-'GSL_CONST_MKSA_GRAVITATIONAL_CONSTANT'
-     The gravitational constant, G.
+       for (i = 0; i < n; i++)
+         {
+           int count = fscanf (stdin, "%lg %lg %lg",
+                               &xi, &yi, &ei);
 
-'GSL_CONST_MKSA_LIGHT_YEAR'
-     The distance of 1 light-year, ly.
+           if (count != 3)
+             {
+               fprintf (stderr, "error reading file\n");
+               exit (-1);
+             }
 
-'GSL_CONST_MKSA_PARSEC'
-     The distance of 1 parsec, pc.
+           printf ("%g %g +/- %g\n", xi, yi, ei);
 
-'GSL_CONST_MKSA_GRAV_ACCEL'
-     The standard gravitational acceleration on Earth, g.
+           gsl_matrix_set (X, i, 0, 1.0);
+           gsl_matrix_set (X, i, 1, xi);
+           gsl_matrix_set (X, i, 2, xi*xi);
 
-'GSL_CONST_MKSA_SOLAR_MASS'
-     The mass of the Sun.
+           gsl_vector_set (y, i, yi);
+           gsl_vector_set (w, i, 1.0/(ei*ei));
+         }
 
-
-File: gsl-ref.info,  Node: Atomic and Nuclear Physics,  Next: Measurement of Time,  Prev: Astronomy and Astrophysics,  Up: Physical Constants
+       {
+         gsl_multifit_linear_workspace * work
+           = gsl_multifit_linear_alloc (n, 3);
+         gsl_multifit_wlinear (X, w, y, c, cov,
+                               &chisq, work);
+         gsl_multifit_linear_free (work);
+       }
 
-40.3 Atomic and Nuclear Physics
-===============================
+     #define C(i) (gsl_vector_get(c,(i)))
+     #define COV(i,j) (gsl_matrix_get(cov,(i),(j)))
 
-'GSL_CONST_MKSA_ELECTRON_CHARGE'
-     The charge of the electron, e.
+       {
+         printf ("# best fit: Y = %g + %g X + %g X^2\n",
+                 C(0), C(1), C(2));
 
-'GSL_CONST_MKSA_ELECTRON_VOLT'
-     The energy of 1 electron volt, eV.
+         printf ("# covariance matrix:\n");
+         printf ("[ %+.5e, %+.5e, %+.5e  \n",
+                    COV(0,0), COV(0,1), COV(0,2));
+         printf ("  %+.5e, %+.5e, %+.5e  \n",
+                    COV(1,0), COV(1,1), COV(1,2));
+         printf ("  %+.5e, %+.5e, %+.5e ]\n",
+                    COV(2,0), COV(2,1), COV(2,2));
+         printf ("# chisq = %g\n", chisq);
+       }
 
-'GSL_CONST_MKSA_UNIFIED_ATOMIC_MASS'
-     The unified atomic mass, amu.
+       gsl_matrix_free (X);
+       gsl_vector_free (y);
+       gsl_vector_free (w);
+       gsl_vector_free (c);
+       gsl_matrix_free (cov);
 
-'GSL_CONST_MKSA_MASS_ELECTRON'
-     The mass of the electron, m_e.
+       return 0;
+     }
 
-'GSL_CONST_MKSA_MASS_MUON'
-     The mass of the muon, m_\mu.
+A suitable set of data for fitting can be generated using the following
+program.  It outputs a set of points with gaussian errors from the curve
+y = e^x in the region 0 < x < 2.
 
-'GSL_CONST_MKSA_MASS_PROTON'
-     The mass of the proton, m_p.
+     #include <stdio.h>
+     #include <math.h>
+     #include <gsl/gsl_randist.h>
 
-'GSL_CONST_MKSA_MASS_NEUTRON'
-     The mass of the neutron, m_n.
+     int
+     main (void)
+     {
+       double x;
+       const gsl_rng_type * T;
+       gsl_rng * r;
 
-'GSL_CONST_NUM_FINE_STRUCTURE'
-     The electromagnetic fine structure constant \alpha.
+       gsl_rng_env_setup ();
 
-'GSL_CONST_MKSA_RYDBERG'
-     The Rydberg constant, Ry, in units of energy.  This is related to
-     the Rydberg inverse wavelength R_\infty by Ry = h c R_\infty.
+       T = gsl_rng_default;
+       r = gsl_rng_alloc (T);
 
-'GSL_CONST_MKSA_BOHR_RADIUS'
-     The Bohr radius, a_0.
+       for (x = 0.1; x < 2; x+= 0.1)
+         {
+           double y0 = exp (x);
+           double sigma = 0.1 * y0;
+           double dy = gsl_ran_gaussian (r, sigma);
 
-'GSL_CONST_MKSA_ANGSTROM'
-     The length of 1 angstrom.
+           printf ("%g %g %g\n", x, y0 + dy, sigma);
+         }
 
-'GSL_CONST_MKSA_BARN'
-     The area of 1 barn.
+       gsl_rng_free(r);
 
-'GSL_CONST_MKSA_BOHR_MAGNETON'
-     The Bohr Magneton, \mu_B.
+       return 0;
+     }
 
-'GSL_CONST_MKSA_NUCLEAR_MAGNETON'
-     The Nuclear Magneton, \mu_N.
+The data can be prepared by running the resulting executable program,
 
-'GSL_CONST_MKSA_ELECTRON_MAGNETIC_MOMENT'
-     The absolute value of the magnetic moment of the electron, \mu_e.
-     The physical magnetic moment of the electron is negative.
+     $ GSL_RNG_TYPE=mt19937_1999 ./generate > exp.dat
+     $ more exp.dat
+     0.1 0.97935 0.110517
+     0.2 1.3359 0.12214
+     0.3 1.52573 0.134986
+     0.4 1.60318 0.149182
+     0.5 1.81731 0.164872
+     0.6 1.92475 0.182212
+     ....
 
-'GSL_CONST_MKSA_PROTON_MAGNETIC_MOMENT'
-     The magnetic moment of the proton, \mu_p.
+To fit the data use the previous program, with the number of data points
+given as the first argument.  In this case there are 19 data points.
 
-'GSL_CONST_MKSA_THOMSON_CROSS_SECTION'
-     The Thomson cross section, \sigma_T.
+     $ ./fit 19 < exp.dat
+     0.1 0.97935 +/- 0.110517
+     0.2 1.3359 +/- 0.12214
+     ...
+     # best fit: Y = 1.02318 + 0.956201 X + 0.876796 X^2
+     # covariance matrix:
+     [ +1.25612e-02, -3.64387e-02, +1.94389e-02
+       -3.64387e-02, +1.42339e-01, -8.48761e-02
+       +1.94389e-02, -8.48761e-02, +5.60243e-02 ]
+     # chisq = 23.0987
 
-'GSL_CONST_MKSA_DEBYE'
-     The electric dipole moment of 1 Debye, D.
+The parameters of the quadratic fit match the coefficients of the
+expansion of e^x, taking into account the errors on the parameters and
+the O(x^3) difference between the exponential and quadratic functions
+for the larger values of x.  The errors on the parameters are given by
+the square-root of the corresponding diagonal elements of the covariance
+matrix.  The chi-squared per degree of freedom is 1.4, indicating a
+reasonable fit to the data.
 
 
-File: gsl-ref.info,  Node: Measurement of Time,  Next: Imperial Units,  Prev: Atomic and Nuclear Physics,  Up: Physical Constants
-
-40.4 Measurement of Time
-========================
-
-'GSL_CONST_MKSA_MINUTE'
-     The number of seconds in 1 minute.
+File: gsl-ref.info,  Node: Fitting regularized linear regression example 1,  Next: Fitting regularized linear regression example 2,  Prev: Fitting multi-parameter linear regression example,  Up: Fitting Examples
 
-'GSL_CONST_MKSA_HOUR'
-     The number of seconds in 1 hour.
+38.8.3 Regularized Linear Regression Example 1
+----------------------------------------------
 
-'GSL_CONST_MKSA_DAY'
-     The number of seconds in 1 day.
+The next program demonstrates the difference between ordinary and
+regularized least squares when the design matrix is near-singular.  In
+this program, we generate two random normally distributed variables u
+and v, with v = u + noise so that u and v are nearly colinear.  We then
+set a third dependent variable y = u + v + noise and solve for the
+coefficients c_1,c_2 of the model Y(c_1,c_2) = c_1 u + c_2 v.  Since u
+\approx v, the design matrix X is nearly singular, leading to unstable
+ordinary least squares solutions.
+
+Here is the program output:
+     matrix condition number = 1.025113e+04
+     === Unregularized fit ===
+     best fit: y = -43.6588 u + 45.6636 v
+     residual norm = 31.6248
+     solution norm = 63.1764
+     chisq/dof = 1.00213
+     === Regularized fit (L-curve) ===
+     optimal lambda: 4.51103
+     best fit: y = 1.00113 u + 1.0032 v
+     residual norm = 31.6547
+     solution norm = 1.41728
+     chisq/dof = 1.04499
+     === Regularized fit (GCV) ===
+     optimal lambda: 0.0232029
+     best fit: y = -19.8367 u + 21.8417 v
+     residual norm = 31.6332
+     solution norm = 29.5051
+     chisq/dof = 1.00314
+
+We see that the ordinary least squares solution is completely wrong,
+while the L-curve regularized method with the optimal \lambda = 4.51103
+finds the correct solution c_1 \approx c_2 \approx 1.  The GCV
+regularized method finds a regularization parameter \lambda = 0.0232029
+which is too small to give an accurate solution, although it performs
+better than OLS. The L-curve and its computed corner, as well as the GCV
+curve and its minimum are plotted below.
 
-'GSL_CONST_MKSA_WEEK'
-     The number of seconds in 1 week.
+The program is given below.
+     #include <gsl/gsl_math.h>
+     #include <gsl/gsl_vector.h>
+     #include <gsl/gsl_matrix.h>
+     #include <gsl/gsl_rng.h>
+     #include <gsl/gsl_randist.h>
+     #include <gsl/gsl_multifit.h>
 
-
-File: gsl-ref.info,  Node: Imperial Units,  Next: Speed and Nautical Units,  Prev: Measurement of Time,  Up: Physical Constants
+     int
+     main()
+     {
+       const size_t n = 1000; /* number of observations */
+       const size_t p = 2;    /* number of model parameters */
+       size_t i;
+       gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+       gsl_matrix *X = gsl_matrix_alloc(n, p);
+       gsl_vector *y = gsl_vector_alloc(n);
 
-40.5 Imperial Units
-===================
+       for (i = 0; i < n; ++i)
+         {
+           /* generate first random variable u */
+           double ui = 5.0 * gsl_ran_gaussian(r, 1.0);
 
-'GSL_CONST_MKSA_INCH'
-     The length of 1 inch.
+           /* set v = u + noise */
+           double vi = ui + gsl_ran_gaussian(r, 0.001);
 
-'GSL_CONST_MKSA_FOOT'
-     The length of 1 foot.
+           /* set y = u + v + noise */
+           double yi = ui + vi + gsl_ran_gaussian(r, 1.0);
 
-'GSL_CONST_MKSA_YARD'
-     The length of 1 yard.
+           /* since u =~ v, the matrix X is ill-conditioned */
+           gsl_matrix_set(X, i, 0, ui);
+           gsl_matrix_set(X, i, 1, vi);
 
-'GSL_CONST_MKSA_MILE'
-     The length of 1 mile.
+           /* rhs vector */
+           gsl_vector_set(y, i, yi);
+         }
 
-'GSL_CONST_MKSA_MIL'
-     The length of 1 mil (1/1000th of an inch).
+       {
+         const size_t npoints = 200;                   /* number of points on L-curve and GCV curve */
+         gsl_multifit_linear_workspace *w =
+           gsl_multifit_linear_alloc(n, p);
+         gsl_vector *c = gsl_vector_alloc(p);          /* OLS solution */
+         gsl_vector *c_lcurve = gsl_vector_alloc(p);   /* regularized solution (L-curve) */
+         gsl_vector *c_gcv = gsl_vector_alloc(p);      /* regularized solution (GCV) */
+         gsl_vector *reg_param = gsl_vector_alloc(npoints);
+         gsl_vector *rho = gsl_vector_alloc(npoints);  /* residual norms */
+         gsl_vector *eta = gsl_vector_alloc(npoints);  /* solution norms */
+         gsl_vector *G = gsl_vector_alloc(npoints);    /* GCV function values */
+         double lambda_l;                              /* optimal regularization parameter (L-curve) */
+         double lambda_gcv;                            /* optimal regularization parameter (GCV) */
+         double G_gcv;                                 /* G(lambda_gcv) */
+         size_t reg_idx;                               /* index of optimal lambda */
+         double rcond;                                 /* reciprocal condition number of X */
+         double chisq, rnorm, snorm;
+
+         /* compute SVD of X */
+         gsl_multifit_linear_svd(X, w);
+
+         rcond = gsl_multifit_linear_rcond(w);
+         fprintf(stderr, "matrix condition number = %e\n", 1.0 / rcond);
+
+         /* unregularized (standard) least squares fit, lambda = 0 */
+         gsl_multifit_linear_solve(0.0, X, y, c, &rnorm, &snorm, w);
+         chisq = pow(rnorm, 2.0);
+
+         fprintf(stderr, "=== Unregularized fit ===\n");
+         fprintf(stderr, "best fit: y = %g u + %g v\n",
+           gsl_vector_get(c, 0), gsl_vector_get(c, 1));
+         fprintf(stderr, "residual norm = %g\n", rnorm);
+         fprintf(stderr, "solution norm = %g\n", snorm);
+         fprintf(stderr, "chisq/dof = %g\n", chisq / (n - p));
+
+         /* calculate L-curve and find its corner */
+         gsl_multifit_linear_lcurve(y, reg_param, rho, eta, w);
+         gsl_multifit_linear_lcorner(rho, eta, &reg_idx);
+
+         /* store optimal regularization parameter */
+         lambda_l = gsl_vector_get(reg_param, reg_idx);
+
+         /* regularize with lambda_l */
+         gsl_multifit_linear_solve(lambda_l, X, y, c_lcurve, &rnorm, &snorm, w);
+         chisq = pow(rnorm, 2.0) + pow(lambda_l * snorm, 2.0);
+
+         fprintf(stderr, "=== Regularized fit (L-curve) ===\n");
+         fprintf(stderr, "optimal lambda: %g\n", lambda_l);
+         fprintf(stderr, "best fit: y = %g u + %g v\n",
+                 gsl_vector_get(c_lcurve, 0), gsl_vector_get(c_lcurve, 1));
+         fprintf(stderr, "residual norm = %g\n", rnorm);
+         fprintf(stderr, "solution norm = %g\n", snorm);
+         fprintf(stderr, "chisq/dof = %g\n", chisq / (n - p));
+
+         /* calculate GCV curve and find its minimum */
+         gsl_multifit_linear_gcv(y, reg_param, G, &lambda_gcv, &G_gcv, w);
+
+         /* regularize with lambda_gcv */
+         gsl_multifit_linear_solve(lambda_gcv, X, y, c_gcv, &rnorm, &snorm, w);
+         chisq = pow(rnorm, 2.0) + pow(lambda_gcv * snorm, 2.0);
+
+         fprintf(stderr, "=== Regularized fit (GCV) ===\n");
+         fprintf(stderr, "optimal lambda: %g\n", lambda_gcv);
+         fprintf(stderr, "best fit: y = %g u + %g v\n",
+                 gsl_vector_get(c_gcv, 0), gsl_vector_get(c_gcv, 1));
+         fprintf(stderr, "residual norm = %g\n", rnorm);
+         fprintf(stderr, "solution norm = %g\n", snorm);
+         fprintf(stderr, "chisq/dof = %g\n", chisq / (n - p));
 
-
-File: gsl-ref.info,  Node: Speed and Nautical Units,  Next: Printers Units,  Prev: Imperial Units,  Up: Physical Constants
+         /* output L-curve and GCV curve */
+         for (i = 0; i < npoints; ++i)
+           {
+             printf("%e %e %e %e\n",
+                    gsl_vector_get(reg_param, i),
+                    gsl_vector_get(rho, i),
+                    gsl_vector_get(eta, i),
+                    gsl_vector_get(G, i));
+           }
 
-40.6 Speed and Nautical Units
-=============================
+         /* output L-curve corner point */
+         printf("\n\n%f %f\n",
+                gsl_vector_get(rho, reg_idx),
+                gsl_vector_get(eta, reg_idx));
+
+         /* output GCV curve corner minimum */
+         printf("\n\n%e %e\n",
+                lambda_gcv,
+                G_gcv);
+
+         gsl_multifit_linear_free(w);
+         gsl_vector_free(c);
+         gsl_vector_free(c_lcurve);
+         gsl_vector_free(reg_param);
+         gsl_vector_free(rho);
+         gsl_vector_free(eta);
+         gsl_vector_free(G);
+       }
 
-'GSL_CONST_MKSA_KILOMETERS_PER_HOUR'
-     The speed of 1 kilometer per hour.
+       gsl_rng_free(r);
+       gsl_matrix_free(X);
+       gsl_vector_free(y);
 
-'GSL_CONST_MKSA_MILES_PER_HOUR'
-     The speed of 1 mile per hour.
+       return 0;
+     }
 
-'GSL_CONST_MKSA_NAUTICAL_MILE'
-     The length of 1 nautical mile.
+
+File: gsl-ref.info,  Node: Fitting regularized linear regression example 2,  Next: Fitting robust linear regression example,  Prev: Fitting regularized linear regression example 1,  Up: Fitting Examples
 
-'GSL_CONST_MKSA_FATHOM'
-     The length of 1 fathom.
+38.8.4 Regularized Linear Regression Example 2
+----------------------------------------------
 
-'GSL_CONST_MKSA_KNOT'
-     The speed of 1 knot.
+The following example program minimizes the cost function
 
-
-File: gsl-ref.info,  Node: Printers Units,  Next: Volume Area and Length,  Prev: Speed and Nautical Units,  Up: Physical Constants
+     ||y - X c||^2 + \lambda^2 ||x||^2
 
-40.7 Printers Units
-===================
+where X is the 10-by-8 Hilbert matrix whose entries are given by
+
+     X_{ij} = 1 / (i + j - 1)
+
+and the right hand side vector is given by y =
+[1,-1,1,-1,1,-1,1,-1,1,-1]^T.  Solutions are computed for \lambda = 0
+(unregularized) as well as for optimal parameters \lambda chosen by
+analyzing the L-curve and GCV curve.
+
+Here is the program output:
+     matrix condition number = 3.565872e+09
+     === Unregularized fit ===
+     residual norm = 2.15376
+     solution norm = 2.92217e+09
+     chisq/dof = 2.31934
+     === Regularized fit (L-curve) ===
+     optimal lambda: 7.11407e-07
+     residual norm = 2.60386
+     solution norm = 424507
+     chisq/dof = 3.43565
+     === Regularized fit (GCV) ===
+     optimal lambda: 1.72278
+     residual norm = 3.1375
+     solution norm = 0.139357
+     chisq/dof = 4.95076
+
+Here we see the unregularized solution results in a large solution norm
+due to the ill-conditioned matrix.  The L-curve solution finds a small
+value of \lambda = 7.11e-7 which still results in a badly conditioned
+system and a large solution norm.  The GCV method finds a parameter
+\lambda = 1.72 which results in a well-conditioned system and small
+solution norm.
 
-'GSL_CONST_MKSA_POINT'
-     The length of 1 printer's point (1/72 inch).
+The L-curve and its computed corner, as well as the GCV curve and its
+minimum are plotted below.
 
-'GSL_CONST_MKSA_TEXPOINT'
-     The length of 1 TeX point (1/72.27 inch).
+The program is given below.
+     #include <gsl/gsl_math.h>
+     #include <gsl/gsl_vector.h>
+     #include <gsl/gsl_matrix.h>
+     #include <gsl/gsl_multifit.h>
+     #include <gsl/gsl_blas.h>
 
-
-File: gsl-ref.info,  Node: Volume Area and Length,  Next: Mass and Weight,  Prev: Printers Units,  Up: Physical Constants
+     static int
+     hilbert_matrix(gsl_matrix * m)
+     {
+       const size_t N = m->size1;
+       const size_t M = m->size2;
+       size_t i, j;
 
-40.8 Volume, Area and Length
-============================
+       for (i = 0; i < N; i++)
+         {
+           for (j = 0; j < M; j++)
+             {
+               gsl_matrix_set(m, i, j, 1.0/(i+j+1.0));
+             }
+         }
 
-'GSL_CONST_MKSA_MICRON'
-     The length of 1 micron.
+       return GSL_SUCCESS;
+     }
 
-'GSL_CONST_MKSA_HECTARE'
-     The area of 1 hectare.
+     int
+     main()
+     {
+       const size_t n = 10; /* number of observations */
+       const size_t p = 8;  /* number of model parameters */
+       size_t i;
+       gsl_matrix *X = gsl_matrix_alloc(n, p);
+       gsl_vector *y = gsl_vector_alloc(n);
 
-'GSL_CONST_MKSA_ACRE'
-     The area of 1 acre.
+       /* construct Hilbert matrix and rhs vector */
+       hilbert_matrix(X);
 
-'GSL_CONST_MKSA_LITER'
-     The volume of 1 liter.
+       {
+         double val = 1.0;
+         for (i = 0; i < n; ++i)
+           {
+             gsl_vector_set(y, i, val);
+             val *= -1.0;
+           }
+       }
 
-'GSL_CONST_MKSA_US_GALLON'
-     The volume of 1 US gallon.
+       {
+         const size_t npoints = 200;                   /* number of points on L-curve and GCV curve */
+         gsl_multifit_linear_workspace *w =
+           gsl_multifit_linear_alloc(n, p);
+         gsl_vector *c = gsl_vector_alloc(p);          /* OLS solution */
+         gsl_vector *c_lcurve = gsl_vector_alloc(p);   /* regularized solution (L-curve) */
+         gsl_vector *c_gcv = gsl_vector_alloc(p);      /* regularized solution (GCV) */
+         gsl_vector *reg_param = gsl_vector_alloc(npoints);
+         gsl_vector *rho = gsl_vector_alloc(npoints);  /* residual norms */
+         gsl_vector *eta = gsl_vector_alloc(npoints);  /* solution norms */
+         gsl_vector *G = gsl_vector_alloc(npoints);    /* GCV function values */
+         double lambda_l;                              /* optimal regularization parameter (L-curve) */
+         double lambda_gcv;                            /* optimal regularization parameter (GCV) */
+         double G_gcv;                                 /* G(lambda_gcv) */
+         size_t reg_idx;                               /* index of optimal lambda */
+         double rcond;                                 /* reciprocal condition number of X */
+         double chisq, rnorm, snorm;
+
+         /* compute SVD of X */
+         gsl_multifit_linear_svd(X, w);
+
+         rcond = gsl_multifit_linear_rcond(w);
+         fprintf(stderr, "matrix condition number = %e\n", 1.0 / rcond);
+
+         /* unregularized (standard) least squares fit, lambda = 0 */
+         gsl_multifit_linear_solve(0.0, X, y, c, &rnorm, &snorm, w);
+         chisq = pow(rnorm, 2.0);
+
+         fprintf(stderr, "=== Unregularized fit ===\n");
+         fprintf(stderr, "residual norm = %g\n", rnorm);
+         fprintf(stderr, "solution norm = %g\n", snorm);
+         fprintf(stderr, "chisq/dof = %g\n", chisq / (n - p));
+
+         /* calculate L-curve and find its corner */
+         gsl_multifit_linear_lcurve(y, reg_param, rho, eta, w);
+         gsl_multifit_linear_lcorner(rho, eta, &reg_idx);
+
+         /* store optimal regularization parameter */
+         lambda_l = gsl_vector_get(reg_param, reg_idx);
+
+         /* regularize with lambda_l */
+         gsl_multifit_linear_solve(lambda_l, X, y, c_lcurve, &rnorm, &snorm, w);
+         chisq = pow(rnorm, 2.0) + pow(lambda_l * snorm, 2.0);
+
+         fprintf(stderr, "=== Regularized fit (L-curve) ===\n");
+         fprintf(stderr, "optimal lambda: %g\n", lambda_l);
+         fprintf(stderr, "residual norm = %g\n", rnorm);
+         fprintf(stderr, "solution norm = %g\n", snorm);
+         fprintf(stderr, "chisq/dof = %g\n", chisq / (n - p));
+
+         /* calculate GCV curve and find its minimum */
+         gsl_multifit_linear_gcv(y, reg_param, G, &lambda_gcv, &G_gcv, w);
+
+         /* regularize with lambda_gcv */
+         gsl_multifit_linear_solve(lambda_gcv, X, y, c_gcv, &rnorm, &snorm, w);
+         chisq = pow(rnorm, 2.0) + pow(lambda_gcv * snorm, 2.0);
+
+         fprintf(stderr, "=== Regularized fit (GCV) ===\n");
+         fprintf(stderr, "optimal lambda: %g\n", lambda_gcv);
+         fprintf(stderr, "residual norm = %g\n", rnorm);
+         fprintf(stderr, "solution norm = %g\n", snorm);
+         fprintf(stderr, "chisq/dof = %g\n", chisq / (n - p));
 
-'GSL_CONST_MKSA_CANADIAN_GALLON'
-     The volume of 1 Canadian gallon.
+         /* output L-curve and GCV curve */
+         for (i = 0; i < npoints; ++i)
+           {
+             printf("%e %e %e %e\n",
+                    gsl_vector_get(reg_param, i),
+                    gsl_vector_get(rho, i),
+                    gsl_vector_get(eta, i),
+                    gsl_vector_get(G, i));
+           }
 
-'GSL_CONST_MKSA_UK_GALLON'
-     The volume of 1 UK gallon.
+         /* output L-curve corner point */
+         printf("\n\n%f %f\n",
+                gsl_vector_get(rho, reg_idx),
+                gsl_vector_get(eta, reg_idx));
+
+         /* output GCV curve corner minimum */
+         printf("\n\n%e %e\n",
+                lambda_gcv,
+                G_gcv);
+
+         gsl_multifit_linear_free(w);
+         gsl_vector_free(c);
+         gsl_vector_free(c_lcurve);
+         gsl_vector_free(reg_param);
+         gsl_vector_free(rho);
+         gsl_vector_free(eta);
+         gsl_vector_free(G);
+       }
 
-'GSL_CONST_MKSA_QUART'
-     The volume of 1 quart.
+       gsl_matrix_free(X);
+       gsl_vector_free(y);
 
-'GSL_CONST_MKSA_PINT'
-     The volume of 1 pint.
+       return 0;
+     }
 
 
-File: gsl-ref.info,  Node: Mass and Weight,  Next: Thermal Energy and Power,  Prev: Volume Area and Length,  Up: Physical Constants
-
-40.9 Mass and Weight
-====================
-
-'GSL_CONST_MKSA_POUND_MASS'
-     The mass of 1 pound.
+File: gsl-ref.info,  Node: Fitting robust linear regression example,  Next: Fitting large linear systems example,  Prev: Fitting regularized linear regression example 2,  Up: Fitting Examples
 
-'GSL_CONST_MKSA_OUNCE_MASS'
-     The mass of 1 ounce.
+38.8.5 Robust Linear Regression Example
+---------------------------------------
 
-'GSL_CONST_MKSA_TON'
-     The mass of 1 ton.
+The next program demonstrates the advantage of robust least squares on a
+dataset with outliers.  The program generates linear (x,y) data pairs on
+the line y = 1.45 x + 3.88, adds some random noise, and inserts 3
+outliers into the dataset.  Both the robust and ordinary least squares
+(OLS) coefficients are computed for comparison.
 
-'GSL_CONST_MKSA_METRIC_TON'
-     The mass of 1 metric ton (1000 kg).
+     #include <stdio.h>
+     #include <gsl/gsl_multifit.h>
+     #include <gsl/gsl_randist.h>
 
-'GSL_CONST_MKSA_UK_TON'
-     The mass of 1 UK ton.
+     int
+     dofit(const gsl_multifit_robust_type *T,
+           const gsl_matrix *X, const gsl_vector *y,
+           gsl_vector *c, gsl_matrix *cov)
+     {
+       int s;
+       gsl_multifit_robust_workspace * work
+         = gsl_multifit_robust_alloc (T, X->size1, X->size2);
 
-'GSL_CONST_MKSA_TROY_OUNCE'
-     The mass of 1 troy ounce.
+       s = gsl_multifit_robust (X, y, c, cov, work);
+       gsl_multifit_robust_free (work);
 
-'GSL_CONST_MKSA_CARAT'
-     The mass of 1 carat.
+       return s;
+     }
 
-'GSL_CONST_MKSA_GRAM_FORCE'
-     The force of 1 gram weight.
+     int
+     main (int argc, char **argv)
+     {
+       size_t i;
+       size_t n;
+       const size_t p = 2; /* linear fit */
+       gsl_matrix *X, *cov;
+       gsl_vector *x, *y, *c, *c_ols;
+       const double a = 1.45; /* slope */
+       const double b = 3.88; /* intercept */
+       gsl_rng *r;
 
-'GSL_CONST_MKSA_POUND_FORCE'
-     The force of 1 pound weight.
+       if (argc != 2)
+         {
+           fprintf (stderr,"usage: robfit n\n");
+           exit (-1);
+         }
 
-'GSL_CONST_MKSA_KILOPOUND_FORCE'
-     The force of 1 kilopound weight.
+       n = atoi (argv[1]);
 
-'GSL_CONST_MKSA_POUNDAL'
-     The force of 1 poundal.
+       X = gsl_matrix_alloc (n, p);
+       x = gsl_vector_alloc (n);
+       y = gsl_vector_alloc (n);
 
-
-File: gsl-ref.info,  Node: Thermal Energy and Power,  Next: Pressure,  Prev: Mass and Weight,  Up: Physical Constants
+       c = gsl_vector_alloc (p);
+       c_ols = gsl_vector_alloc (p);
+       cov = gsl_matrix_alloc (p, p);
 
-40.10 Thermal Energy and Power
-==============================
+       r = gsl_rng_alloc(gsl_rng_default);
 
-'GSL_CONST_MKSA_CALORIE'
-     The energy of 1 calorie.
+       /* generate linear dataset */
+       for (i = 0; i < n - 3; i++)
+         {
+           double dx = 10.0 / (n - 1.0);
+           double ei = gsl_rng_uniform(r);
+           double xi = -5.0 + i * dx;
+           double yi = a * xi + b;
 
-'GSL_CONST_MKSA_BTU'
-     The energy of 1 British Thermal Unit, btu.
+           gsl_vector_set (x, i, xi);
+           gsl_vector_set (y, i, yi + ei);
+         }
 
-'GSL_CONST_MKSA_THERM'
-     The energy of 1 Therm.
+       /* add a few outliers */
+       gsl_vector_set(x, n - 3, 4.7);
+       gsl_vector_set(y, n - 3, -8.3);
 
-'GSL_CONST_MKSA_HORSEPOWER'
-     The power of 1 horsepower.
+       gsl_vector_set(x, n - 2, 3.5);
+       gsl_vector_set(y, n - 2, -6.7);
 
-
-File: gsl-ref.info,  Node: Pressure,  Next: Viscosity,  Prev: Thermal Energy and Power,  Up: Physical Constants
+       gsl_vector_set(x, n - 1, 4.1);
+       gsl_vector_set(y, n - 1, -6.0);
 
-40.11 Pressure
-==============
+       /* construct design matrix X for linear fit */
+       for (i = 0; i < n; ++i)
+         {
+           double xi = gsl_vector_get(x, i);
 
-'GSL_CONST_MKSA_BAR'
-     The pressure of 1 bar.
+           gsl_matrix_set (X, i, 0, 1.0);
+           gsl_matrix_set (X, i, 1, xi);
+         }
 
-'GSL_CONST_MKSA_STD_ATMOSPHERE'
-     The pressure of 1 standard atmosphere.
+       /* perform robust and OLS fit */
+       dofit(gsl_multifit_robust_ols, X, y, c_ols, cov);
+       dofit(gsl_multifit_robust_bisquare, X, y, c, cov);
 
-'GSL_CONST_MKSA_TORR'
-     The pressure of 1 torr.
+       /* output data and model */
+       for (i = 0; i < n; ++i)
+         {
+           double xi = gsl_vector_get(x, i);
+           double yi = gsl_vector_get(y, i);
+           gsl_vector_view v = gsl_matrix_row(X, i);
+           double y_ols, y_rob, y_err;
 
-'GSL_CONST_MKSA_METER_OF_MERCURY'
-     The pressure of 1 meter of mercury.
+           gsl_multifit_robust_est(&v.vector, c, cov, &y_rob, &y_err);
+           gsl_multifit_robust_est(&v.vector, c_ols, cov, &y_ols, &y_err);
 
-'GSL_CONST_MKSA_INCH_OF_MERCURY'
-     The pressure of 1 inch of mercury.
+           printf("%g %g %g %g\n", xi, yi, y_rob, y_ols);
+         }
 
-'GSL_CONST_MKSA_INCH_OF_WATER'
-     The pressure of 1 inch of water.
+     #define C(i) (gsl_vector_get(c,(i)))
+     #define COV(i,j) (gsl_matrix_get(cov,(i),(j)))
 
-'GSL_CONST_MKSA_PSI'
-     The pressure of 1 pound per square inch.
+       {
+         printf ("# best fit: Y = %g + %g X\n",
+                 C(0), C(1));
 
-
-File: gsl-ref.info,  Node: Viscosity,  Next: Light and Illumination,  Prev: Pressure,  Up: Physical Constants
+         printf ("# covariance matrix:\n");
+         printf ("# [ %+.5e, %+.5e\n",
+                    COV(0,0), COV(0,1));
+         printf ("#   %+.5e, %+.5e\n",
+                    COV(1,0), COV(1,1));
+       }
 
-40.12 Viscosity
-===============
+       gsl_matrix_free (X);
+       gsl_vector_free (x);
+       gsl_vector_free (y);
+       gsl_vector_free (c);
+       gsl_vector_free (c_ols);
+       gsl_matrix_free (cov);
+       gsl_rng_free(r);
 
-'GSL_CONST_MKSA_POISE'
-     The dynamic viscosity of 1 poise.
+       return 0;
+     }
 
-'GSL_CONST_MKSA_STOKES'
-     The kinematic viscosity of 1 stokes.
+   The output from the program is shown in the following plot.
 
 
-File: gsl-ref.info,  Node: Light and Illumination,  Next: Radioactivity,  Prev: Viscosity,  Up: Physical Constants
-
-40.13 Light and Illumination
-============================
+File: gsl-ref.info,  Node: Fitting large linear systems example,  Prev: Fitting robust linear regression example,  Up: Fitting Examples
 
-'GSL_CONST_MKSA_STILB'
-     The luminance of 1 stilb.
+38.8.6 Large Dense Linear Regression Example
+--------------------------------------------
 
-'GSL_CONST_MKSA_LUMEN'
-     The luminous flux of 1 lumen.
+The following program demostrates the large dense linear least squares
+solvers.  This example is adapted from Trefethen and Bau, and fits the
+function f(t) = \exp{(\sin^3{(10t)}}) on the interval [0,1] with a
+degree 15 polynomial.  The program generates n = 50000 equally spaced
+points t_i on this interval, calculates the function value and adds
+random noise to determine the observation value y_i.  The entries of the
+least squares matrix are X_{ij} = t_i^j, representing a polynomial fit.
+The matrix is highly ill-conditioned, with a condition number of about
+1.4 \cdot 10^{11}.  The program accumulates the matrix into the least
+squares system in 5 blocks, each with 10000 rows.  This way the full
+matrix X is never stored in memory.  We solve the system with both the
+normal equations and TSQR methods.  The results are shown in the plot
+below.  In the top left plot, we see the unregularized normal equations
+solution has larger error than TSQR due to the ill-conditioning of the
+matrix.  In the bottom left plot, we show the L-curve, which exhibits
+multiple corners.  In the top right panel, we plot a regularized
+solution using \lambda = 10^{-6}.  The TSQR and normal solutions now
+agree, however they are unable to provide a good fit due to the damping.
+This indicates that for some ill-conditioned problems, regularizing the
+normal equations does not improve the solution.  This is further
+illustrated in the bottom right panel, where we plot the L-curve
+calculated from the normal equations.  The curve agrees with the TSQR
+curve for larger damping parameters, but for small \lambda, the normal
+equations approach cannot provide accurate solution vectors leading to
+numerical inaccuracies in the left portion of the curve.
 
-'GSL_CONST_MKSA_LUX'
-     The illuminance of 1 lux.
-
-'GSL_CONST_MKSA_PHOT'
-     The illuminance of 1 phot.
-
-'GSL_CONST_MKSA_FOOTCANDLE'
-     The illuminance of 1 footcandle.
-
-'GSL_CONST_MKSA_LAMBERT'
-     The luminance of 1 lambert.
+     #include <gsl/gsl_math.h>
+     #include <gsl/gsl_vector.h>
+     #include <gsl/gsl_matrix.h>
+     #include <gsl/gsl_rng.h>
+     #include <gsl/gsl_randist.h>
+     #include <gsl/gsl_multifit.h>
+     #include <gsl/gsl_multilarge.h>
+     #include <gsl/gsl_blas.h>
 
-'GSL_CONST_MKSA_FOOTLAMBERT'
-     The luminance of 1 footlambert.
+     /* function to be fitted */
+     double
+     func(const double t)
+     {
+       double x = sin(10.0 * t);
+       return exp(x*x*x);
+     }
 
-
-File: gsl-ref.info,  Node: Radioactivity,  Next: Force and Energy,  Prev: Light and Illumination,  Up: Physical Constants
+     /* construct a row of the least squares matrix */
+     int
+     build_row(const double t, gsl_vector *row)
+     {
+       const size_t p = row->size;
+       double Xj = 1.0;
+       size_t j;
 
-40.14 Radioactivity
-===================
+       for (j = 0; j < p; ++j)
+         {
+           gsl_vector_set(row, j, Xj);
+           Xj *= t;
+         }
 
-'GSL_CONST_MKSA_CURIE'
-     The activity of 1 curie.
+       return 0;
+     }
 
-'GSL_CONST_MKSA_ROENTGEN'
-     The exposure of 1 roentgen.
+     int
+     solve_system(const int print_data, const gsl_multilarge_linear_type * T,
+                  const double lambda, const size_t n, const size_t p,
+                  gsl_vector * c)
+     {
+       const size_t nblock = 5;         /* number of blocks to accumulate */
+       const size_t nrows = n / nblock; /* number of rows per block */
+       gsl_multilarge_linear_workspace * w =
+         gsl_multilarge_linear_alloc(T, p);
+       gsl_matrix *X = gsl_matrix_alloc(nrows, p);
+       gsl_vector *y = gsl_vector_alloc(nrows);
+       gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+       const size_t nlcurve = 200;
+       gsl_vector *reg_param = gsl_vector_alloc(nlcurve);
+       gsl_vector *rho = gsl_vector_alloc(nlcurve);
+       gsl_vector *eta = gsl_vector_alloc(nlcurve);
+       size_t rowidx = 0;
+       double rnorm, snorm, rcond;
+       double t = 0.0;
+       double dt = 1.0 / (n - 1.0);
 
-'GSL_CONST_MKSA_RAD'
-     The absorbed dose of 1 rad.
+       while (rowidx < n)
+         {
+           size_t nleft = n - rowidx;         /* number of rows left to accumulate */
+           size_t nr = GSL_MIN(nrows, nleft); /* number of rows in this block */
+           gsl_matrix_view Xv = gsl_matrix_submatrix(X, 0, 0, nr, p);
+           gsl_vector_view yv = gsl_vector_subvector(y, 0, nr);
+           size_t i;
 
-
-File: gsl-ref.info,  Node: Force and Energy,  Next: Prefixes,  Prev: Radioactivity,  Up: Physical Constants
+           /* build (X,y) block with 'nr' rows */
+           for (i = 0; i < nr; ++i)
+             {
+               gsl_vector_view row = gsl_matrix_row(&Xv.matrix, i);
+               double fi = func(t);
+               double ei = gsl_ran_gaussian (r, 0.1 * fi); /* noise */
+               double yi = fi + ei;
 
-40.15 Force and Energy
-======================
+               /* construct this row of LS matrix */
+               build_row(t, &row.vector);
 
-'GSL_CONST_MKSA_NEWTON'
-     The SI unit of force, 1 Newton.
+               /* set right hand side value with added noise */
+               gsl_vector_set(&yv.vector, i, yi);
 
-'GSL_CONST_MKSA_DYNE'
-     The force of 1 Dyne = 10^-5 Newton.
+               if (print_data && (i % 100 == 0))
+                 printf("%f %f\n", t, yi);
 
-'GSL_CONST_MKSA_JOULE'
-     The SI unit of energy, 1 Joule.
+               t += dt;
+             }
 
-'GSL_CONST_MKSA_ERG'
-     The energy 1 erg = 10^-7 Joule.
+           /* accumulate (X,y) block into LS system */
+           gsl_multilarge_linear_accumulate(&Xv.matrix, &yv.vector, w);
 
-
-File: gsl-ref.info,  Node: Prefixes,  Next: Physical Constant Examples,  Prev: Force and Energy,  Up: Physical Constants
+           rowidx += nr;
+         }
 
-40.16 Prefixes
-==============
+       if (print_data)
+         printf("\n\n");
 
-These constants are dimensionless scaling factors.
+       /* compute L-curve */
+       gsl_multilarge_linear_lcurve(reg_param, rho, eta, w);
 
-'GSL_CONST_NUM_YOTTA'
-     10^24
+       /* solve large LS system and store solution in c */
+       gsl_multilarge_linear_solve(lambda, c, &rnorm, &snorm, w);
 
-'GSL_CONST_NUM_ZETTA'
-     10^21
+       /* compute reciprocal condition number */
+       gsl_multilarge_linear_rcond(&rcond, w);
 
-'GSL_CONST_NUM_EXA'
-     10^18
+       fprintf(stderr, "=== Method %s ===\n", gsl_multilarge_linear_name(w));
+       fprintf(stderr, "condition number = %e\n", 1.0 / rcond);
+       fprintf(stderr, "residual norm    = %e\n", rnorm);
+       fprintf(stderr, "solution norm    = %e\n", snorm);
 
-'GSL_CONST_NUM_PETA'
-     10^15
+       /* output L-curve */
+       {
+         size_t i;
+         for (i = 0; i < nlcurve; ++i)
+           {
+             printf("%.12e %.12e %.12e\n",
+                    gsl_vector_get(reg_param, i),
+                    gsl_vector_get(rho, i),
+                    gsl_vector_get(eta, i));
+           }
+         printf("\n\n");
+       }
 
-'GSL_CONST_NUM_TERA'
-     10^12
+       gsl_matrix_free(X);
+       gsl_vector_free(y);
+       gsl_multilarge_linear_free(w);
+       gsl_rng_free(r);
+       gsl_vector_free(reg_param);
+       gsl_vector_free(rho);
+       gsl_vector_free(eta);
 
-'GSL_CONST_NUM_GIGA'
-     10^9
+       return 0;
+     }
 
-'GSL_CONST_NUM_MEGA'
-     10^6
+     int
+     main(int argc, char *argv[])
+     {
+       const size_t n = 50000;   /* number of observations */
+       const size_t p = 16;      /* polynomial order + 1 */
+       double lambda = 0.0;      /* regularization parameter */
+       gsl_vector *c_tsqr = gsl_vector_alloc(p);
+       gsl_vector *c_normal = gsl_vector_alloc(p);
+
+       if (argc > 1)
+         lambda = atof(argv[1]);
 
-'GSL_CONST_NUM_KILO'
-     10^3
+       /* solve system with TSQR method */
+       solve_system(1, gsl_multilarge_linear_tsqr, lambda, n, p, c_tsqr);
 
-'GSL_CONST_NUM_MILLI'
-     10^-3
+       /* solve system with Normal equations method */
+       solve_system(0, gsl_multilarge_linear_normal, lambda, n, p, c_normal);
 
-'GSL_CONST_NUM_MICRO'
-     10^-6
+       /* output solutions */
+       {
+         gsl_vector *v = gsl_vector_alloc(p);
+         double t;
 
-'GSL_CONST_NUM_NANO'
-     10^-9
+         for (t = 0.0; t <= 1.0; t += 0.01)
+           {
+             double f_exact = func(t);
+             double f_tsqr, f_normal;
 
-'GSL_CONST_NUM_PICO'
-     10^-12
+             build_row(t, v);
+             gsl_blas_ddot(v, c_tsqr, &f_tsqr);
+             gsl_blas_ddot(v, c_normal, &f_normal);
 
-'GSL_CONST_NUM_FEMTO'
-     10^-15
+             printf("%f %e %e %e\n", t, f_exact, f_tsqr, f_normal);
+           }
 
-'GSL_CONST_NUM_ATTO'
-     10^-18
+         gsl_vector_free(v);
+       }
 
-'GSL_CONST_NUM_ZEPTO'
-     10^-21
+       gsl_vector_free(c_tsqr);
+       gsl_vector_free(c_normal);
 
-'GSL_CONST_NUM_YOCTO'
-     10^-24
+       return 0;
+     }
 
 
-File: gsl-ref.info,  Node: Physical Constant Examples,  Next: Physical Constant References and Further Reading,  Prev: Prefixes,  Up: Physical Constants
-
-40.17 Examples
-==============
-
-The following program demonstrates the use of the physical constants in
-a calculation.  In this case, the goal is to calculate the range of
-light-travel times from Earth to Mars.
-
-   The required data is the average distance of each planet from the Sun
-in astronomical units (the eccentricities and inclinations of the orbits
-will be neglected for the purposes of this calculation).  The average
-radius of the orbit of Mars is 1.52 astronomical units, and for the
-orbit of Earth it is 1 astronomical unit (by definition).  These values
-are combined with the MKSA values of the constants for the speed of
-light and the length of an astronomical unit to produce a result for the
-shortest and longest light-travel times in seconds.  The figures are
-converted into minutes before being displayed.
+File: gsl-ref.info,  Node: Fitting References and Further Reading,  Prev: Fitting Examples,  Up: Least-Squares Fitting
 
-     #include <stdio.h>
-     #include <gsl/gsl_const_mksa.h>
+38.9 References and Further Reading
+===================================
 
-     int
-     main (void)
-     {
-       double c  = GSL_CONST_MKSA_SPEED_OF_LIGHT;
-       double au = GSL_CONST_MKSA_ASTRONOMICAL_UNIT;
-       double minutes = GSL_CONST_MKSA_MINUTE;
-
-       /* distance stored in meters */
-       double r_earth = 1.00 * au;
-       double r_mars  = 1.52 * au;
-
-       double t_min, t_max;
-
-       t_min = (r_mars - r_earth) / c;
-       t_max = (r_mars + r_earth) / c;
-
-       printf ("light travel time from Earth to Mars:\n");
-       printf ("minimum = %.1f minutes\n", t_min / minutes);
-       printf ("maximum = %.1f minutes\n", t_max / minutes);
+A summary of formulas and techniques for least squares fitting can be
+found in the "Statistics" chapter of the Annual Review of Particle
+Physics prepared by the Particle Data Group,
 
-       return 0;
-     }
+     'Review of Particle Properties', R.M. Barnett et al., Physical
+     Review D54, 1 (1996) <http://pdg.lbl.gov/>
 
-Here is the output from the program,
+The Review of Particle Physics is available online at the website given
+above.
 
-     light travel time from Earth to Mars:
-     minimum = 4.3 minutes
-     maximum = 21.0 minutes
+   The tests used to prepare these routines are based on the NIST
+Statistical Reference Datasets.  The datasets and their documentation
+are available from NIST at the following website,
 
-
-File: gsl-ref.info,  Node: Physical Constant References and Further Reading,  Prev: Physical Constant Examples,  Up: Physical Constants
+           <http://www.nist.gov/itl/div898/strd/index.html>.
 
-40.18 References and Further Reading
-====================================
+More information on Tikhonov regularization can be found in
 
-The authoritative sources for physical constants are the 2006 CODATA
-recommended values, published in the article below.  Further information
-on the values of physical constants is also available from the NIST
-website.
-
-     P.J. Mohr, B.N. Taylor, D.B. Newell, "CODATA Recommended Values of
-     the Fundamental Physical Constants: 2006", Reviews of Modern
-     Physics, 80(2), pp.  633-730 (2008).
-     <http://www.physics.nist.gov/cuu/Constants/index.html>
-     <http://physics.nist.gov/Pubs/SP811/appenB9.html>
-
-
-File: gsl-ref.info,  Node: IEEE floating-point arithmetic,  Next: Debugging Numerical Programs,  Prev: Physical Constants,  Up: Top
-
-41 IEEE floating-point arithmetic
-*********************************
-
-This chapter describes functions for examining the representation of
-floating point numbers and controlling the floating point environment of
-your program.  The functions described in this chapter are declared in
-the header file 'gsl_ieee_utils.h'.
+     Hansen, P. C. (1998), Rank-Deficient and Discrete Ill-Posed
+     Problems: Numerical Aspects of Linear Inversion.  SIAM Monogr.  on
+     Mathematical Modeling and Computation, Society for Industrial and
+     Applied Mathematics
+
+     M. Rezghi and S. M. Hosseini (2009), A new variant of L-curve for
+     Tikhonov regularization, Journal of Computational and Applied
+     Mathematics, Volume 231, Issue 2, pages 914-924.
 
-* Menu:
+The GSL implementation of robust linear regression closely follows the
+publications
 
-* Representation of floating point numbers::  
-* Setting up your IEEE environment::  
-* IEEE References and Further Reading::  
+     DuMouchel, W. and F. O'Brien (1989), "Integrating a robust option
+     into a multiple regression computing environment," Computer Science
+     and Statistics: Proceedings of the 21st Symposium on the Interface,
+     American Statistical Association
 
-
-File: gsl-ref.info,  Node: Representation of floating point numbers,  Next: Setting up your IEEE environment,  Up: IEEE floating-point arithmetic
+     Street, J.O., R.J. Carroll, and D. Ruppert (1988), "A note on
+     computing robust regression estimates via iteratively reweighted
+     least squares," The American Statistician, v.  42, pp.  152-154.
 
-41.1 Representation of floating point numbers
-=============================================
+More information about the normal equations and TSQR approach for
+solving large linear least squares systems can be found in the
+publications
 
-The IEEE Standard for Binary Floating-Point Arithmetic defines binary
-formats for single and double precision numbers.  Each number is
-composed of three parts: a "sign bit" (s), an "exponent" (E) and a
-"fraction" (f).  The numerical value of the combination (s,E,f) is given
-by the following formula,
+     Trefethen, L. N. and Bau, D. (1997), "Numerical Linear Algebra",
+     SIAM.
 
-     (-1)^s (1.fffff...) 2^E
+     Demmel, J., Grigori, L., Hoemmen, M. F., and Langou, J.
+     "Communication-optimal parallel and sequential QR and LU
+     factorizations", UCB Technical Report No.  UCB/EECS-2008-89, 2008.
 
-The sign bit is either zero or one.  The exponent ranges from a minimum
-value E_min to a maximum value E_max depending on the precision.  The
-exponent is converted to an unsigned number e, known as the "biased
-exponent", for storage by adding a "bias" parameter, e = E + bias.  The
-sequence fffff... represents the digits of the binary fraction f.  The
-binary digits are stored in "normalized form", by adjusting the exponent
-to give a leading digit of 1.  Since the leading digit is always 1 for
-normalized numbers it is assumed implicitly and does not have to be
-stored.  Numbers smaller than 2^(E_min) are be stored in "denormalized
-form" with a leading zero,
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares Fitting,  Next: Basis Splines,  Prev: Least-Squares Fitting,  Up: Top
 
-     (-1)^s (0.fffff...) 2^(E_min)
+39 Nonlinear Least-Squares Fitting
+**********************************
 
-This allows gradual underflow down to 2^(E_min - p) for p bits of
-precision.  A zero is encoded with the special exponent of 2^(E_min - 1)
-and infinities with the exponent of 2^(E_max + 1).
+This chapter describes functions for multidimensional nonlinear
+least-squares fitting.  There are generally two classes of algorithms
+for solving nonlinear least squares problems, which fall under line
+search methods and trust region methods.  GSL currently implements only
+trust region methods and provides the user with full access to
+intermediate steps of the iteration.  The user also has the ability to
+tune a number of parameters which affect low-level aspects of the
+algorithm which can help to accelerate convergence for the specific
+problem at hand.  GSL provides two separate interfaces for nonlinear
+least squares fitting.  The first is designed for small to moderate
+sized problems, and the second is designed for very large problems,
+which may or may not have significant sparse structure.
+
+   The header file 'gsl_multifit_nlinear.h' contains prototypes for the
+multidimensional nonlinear fitting functions and related declarations
+relating to the small to moderate sized systems.
+
+   The header file 'gsl_multilarge_nlinear.h' contains prototypes for
+the multidimensional nonlinear fitting functions and related
+declarations relating to large systems.
 
-The format for single precision numbers uses 32 bits divided in the
-following way,
+* Menu:
 
-     seeeeeeeefffffffffffffffffffffff
+* Nonlinear Least-Squares Overview::
+* Nonlinear Least-Squares TRS Overview::
+* Nonlinear Least-Squares Weighted Overview::
+* Nonlinear Least-Squares Tunable Parameters::
+* Nonlinear Least-Squares Initialization::
+* Nonlinear Least-Squares Function Definition::
+* Nonlinear Least-Squares Iteration::
+* Nonlinear Least-Squares Testing for Convergence::
+* Nonlinear Least-Squares High Level Driver::
+* Nonlinear Least-Squares Covariance Matrix::
+* Nonlinear Least-Squares Troubleshooting::
+* Nonlinear Least-Squares Examples::
+* Nonlinear Least-Squares References and Further Reading::
 
-     s = sign bit, 1 bit
-     e = exponent, 8 bits  (E_min=-126, E_max=127, bias=127)
-     f = fraction, 23 bits
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares Overview,  Next: Nonlinear Least-Squares TRS Overview,  Up: Nonlinear Least-Squares Fitting
 
-The format for double precision numbers uses 64 bits divided in the
-following way,
+39.1 Overview
+=============
 
-     seeeeeeeeeeeffffffffffffffffffffffffffffffffffffffffffffffffffff
+The problem of multidimensional nonlinear least-squares fitting requires
+the minimization of the squared residuals of n functions, f_i, in p
+parameters, x_i,
 
-     s = sign bit, 1 bit
-     e = exponent, 11 bits  (E_min=-1022, E_max=1023, bias=1023)
-     f = fraction, 52 bits
+     \Phi(x) = (1/2) || f(x) ||^2
+             = (1/2) \sum_{i=1}^{n} f_i(x_1, ..., x_p)^2
 
-It is often useful to be able to investigate the behavior of a
-calculation at the bit-level and the library provides functions for
-printing the IEEE representations in a human-readable form.
+In trust region methods, the objective (or cost) function \Phi(x) is
+approximated by a model function m_k(\delta) in the vicinity of some
+point x_k.  The model function is often simply a second order Taylor
+series expansion around the point x_k, ie:
+
+     \Phi(x_k + \delta) ~=~ m_k(\delta) = \Phi(x_k) + g_k^T \delta + 1/2 \delta^T B_k \delta
+
+   where g_k = \nabla \Phi(x_k) = J^T f is the gradient vector at the
+point x_k, B_k = \nabla^2 \Phi(x_k) is the Hessian matrix at x_k, or
+some approximation to it, and J is the n-by-p Jacobian matrix J_{ij} = d
+f_i / d x_j.  In order to find the next step \delta, we minimize the
+model function m_k(\delta), but search for solutions only within a
+region where we trust that m_k(\delta) is a good approximation to the
+objective function \Phi(x_k + \delta).  In other words, we seek a
+solution of the trust region subproblem (TRS)
+
+     \min_(\delta \in R^p) m_k(\delta), s.t. || D_k \delta || <= \Delta_k
+
+   where \Delta_k > 0 is the trust region radius and D_k is a scaling
+matrix.  If D_k = I, then the trust region is a ball of radius \Delta_k
+centered at x_k.  In some applications, the parameter vector x may have
+widely different scales.  For example, one parameter might be a
+temperature on the order of 10^3 K, while another might be a length on
+the order of 10^{-6} m.  In such cases, a spherical trust region may not
+be the best choice, since if \Phi changes rapidly along directions with
+one scale, and more slowly along directions with a different scale, the
+model function m_k may be a poor approximation to \Phi along the rapidly
+changing directions.  In such problems, it may be best to use an
+elliptical trust region, by setting D_k to a diagonal matrix whose
+entries are designed so that the scaled step D_k \delta has entries of
+approximately the same order of magnitude.
+
+   The trust region subproblem above normally amounts to solving a
+linear least squares system (or multiple systems) for the step \delta.
+Once \delta is computed, it is checked whether or not it reduces the
+objective function \Phi(x).  A useful statistic for this is to look at
+the ratio
+
+     \rho_k = ( \Phi(x_k) - \Phi(x_k + \delta_k) / ( m_k(0) - m_k(\delta_k) )
+
+   where the numerator is the actual reduction of the objective function
+due to the step \delta_k, and the denominator is the predicted reduction
+due to the model m_k.  If \rho_k is negative, it means that the step
+\delta_k increased the objective function and so it is rejected.  If
+\rho_k is positive, then we have found a step which reduced the
+objective function and it is accepted.  Furthermore, if \rho_k is close
+to 1, then this indicates that the model function is a good
+approximation to the objective function in the trust region, and so on
+the next iteration the trust region is enlarged in order to take more
+ambitious steps.  When a step is rejected, the trust region is made
+smaller and the TRS is solved again.  An outline for the general trust
+region method used by GSL can now be given.
+
+Trust Region Algorithm
+
+  1. Initialize: given x_0, construct m_0(\delta), D_0 and \Delta_0 > 0
+
+  2. For k = 0, 1, 2, ...
+
+       a. If converged, then stop
+
+       b. Solve TRS for trial step \delta_k
+
+       c. Evaluate trial step by computing \rho_k
+
+            1. if step is accepted, set x_{k+1} = x_k + \delta_k and
+               increase radius, \Delta_{k+1} = \alpha \Delta_k
+            2. if step is rejected, set x_{k+1} = x_k and decrease
+               radius, \Delta_{k+1} = {\Delta_k \over \beta}; goto 2(b)
+
+       d. Construct m_{k+1}(\delta) and D_{k+1}
+
+GSL offers the user a number of different algorithms for solving the
+trust region subproblem in 2(b), as well as different choices of scaling
+matrices D_k and different methods of updating the trust region radius
+\Delta_k.  Therefore, while reasonable default methods are provided, the
+user has a lot of control to fine-tune the various steps of the
+algorithm for their specific problem.
 
- -- Function: void gsl_ieee_fprintf_float (FILE * STREAM, const float *
-          X)
- -- Function: void gsl_ieee_fprintf_double (FILE * STREAM, const double
-          * X)
-     These functions output a formatted version of the IEEE
-     floating-point number pointed to by X to the stream STREAM.  A
-     pointer is used to pass the number indirectly, to avoid any
-     undesired promotion from 'float' to 'double'.  The output takes one
-     of the following forms,
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares TRS Overview,  Next: Nonlinear Least-Squares Weighted Overview,  Prev: Nonlinear Least-Squares Overview,  Up: Nonlinear Least-Squares Fitting
 
-     'NaN'
-          the Not-a-Number symbol
+39.2 Solving the Trust Region Subproblem (TRS)
+==============================================
 
-     'Inf, -Inf'
-          positive or negative infinity
+* Menu:
 
-     '1.fffff...*2^E, -1.fffff...*2^E'
-          a normalized floating point number
+* Nonlinear Least-Squares TRS Levenberg-Marquardt::
+* Nonlinear Least-Squares TRS Levenberg-Marquardt with Geodesic Acceleration::
+* Nonlinear Least-Squares TRS Dogleg::
+* Nonlinear Least-Squares TRS Double Dogleg::
+* Nonlinear Least-Squares TRS 2D Subspace::
+* Nonlinear Least-Squares TRS Steihaug-Toint Conjugate Gradient::
+
+Below we describe the methods available for solving the trust region
+subproblem.  The methods available provide either exact or approximate
+solutions to the trust region subproblem.  In all algorithms below, the
+Hessian matrix B_k is approximated as B_k \approx J_k^T J_k, where J_k =
+J(x_k).  In all methods, the solution of the TRS involves solving a
+linear least squares system involving the Jacobian matrix.  For small to
+moderate sized problems ('gsl_multifit_nlinear' interface), this is
+accomplished by factoring the full Jacobian matrix, which is provided by
+the user, with the Cholesky, QR, or SVD decompositions.  For large
+systems ('gsl_multilarge_nlinear' interface), the user has two choices.
+One is to solve the system iteratively, without needing to store the
+full Jacobian matrix in memory.  With this method, the user must provide
+a routine to calculate the matrix-vector products J u or J^T u for a
+given vector u.  This iterative method is particularly useful for
+systems where the Jacobian has sparse structure, since forming
+matrix-vector products can be done cheaply.  The second option for large
+systems involves forming the normal equations matrix J^T J and then
+factoring it using a Cholesky decomposition.  The normal equations
+matrix is p-by-p, typically much smaller than the full n-by-p Jacobian,
+and can usually be stored in memory even if the full Jacobian matrix
+cannot.  This option is useful for large, dense systems, or if the
+iterative method has difficulty converging.
+
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares TRS Levenberg-Marquardt,  Next: Nonlinear Least-Squares TRS Levenberg-Marquardt with Geodesic Acceleration,  Up: Nonlinear Least-Squares TRS Overview
+
+39.2.1 Levenberg-Marquardt
+--------------------------
+
+There is a theorem which states that if \delta_k is a solution to the
+trust region subproblem given above, then there exists \mu_k \ge 0 such
+that
+
+     ( B_k + \mu_k D_k^T D_k ) \delta_k = -g_k
+
+   with \mu_k (\Delta_k - ||D_k \delta_k||) = 0.  This forms the basis
+of the Levenberg-Marquardt algorithm, which controls the trust region
+size by adjusting the parameter \mu_k rather than the radius \Delta_k
+directly.  For each radius \Delta_k, there is a unique parameter \mu_k
+which solves the TRS, and they have an inverse relationship, so that
+large values of \mu_k correspond to smaller trust regions, while small
+values of \mu_k correspond to larger trust regions.
+
+With the approximation B_k \approx J_k^T J_k, on each iteration, in
+order to calculate the step \delta_k, the following linear least squares
+problem is solved:
+
+     [J_k; sqrt(mu_k) D_k] \delta_k = - [f_k; 0]
+
+If the step \delta_k is accepted, then \mu_k is decreased on the next
+iteration in order to take a larger step, otherwise it is increased to
+take a smaller step.  The Levenberg-Marquardt algorithm provides an
+exact solution of the trust region subproblem, but typically has a
+higher computational cost per iteration than the approximate methods
+discussed below, since it may need to solve the least squares system
+above several times for different values of \mu_k.
+
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares TRS Levenberg-Marquardt with Geodesic Acceleration,  Next: Nonlinear Least-Squares TRS Dogleg,  Prev: Nonlinear Least-Squares TRS Levenberg-Marquardt,  Up: Nonlinear Least-Squares TRS Overview
+
+39.2.2 Levenberg-Marquardt with Geodesic Acceleration
+-----------------------------------------------------
+
+This method applies a so-called geodesic acceleration correction to the
+standard Levenberg-Marquardt step \delta_k (Transtrum et al, 2011).  By
+interpreting \delta_k as a first order step along a geodesic in the
+model parameter space (ie: a velocity \delta_k = v_k), the geodesic
+acceleration a_k is a second order correction along the geodesic which
+is determined by solving the linear least squares system
+
+     [J_k; sqrt(mu_k) D_k] a_k = - [f_vv(x_k); 0]
+
+where f_{vv} is the second directional derivative of the residual vector
+in the velocity direction v, f_{vv}(x) = D_v^2 f = \sum_{\alpha\beta}
+v_{\alpha} v_{\beta} \partial_{\alpha} \partial_{\beta} f(x), where
+\alpha and \beta are summed over the p parameters.  The new total step
+is then \delta_k' = v_k + {1 \over 2}a_k.  The second order correction
+a_k can be calculated with a modest additional cost, and has been shown
+to dramatically reduce the number of iterations (and expensive Jacobian
+evaluations) required to reach convergence on a variety of different
+problems.  In order to utilize the geodesic acceleration, the user must
+supply a function which provides the second directional derivative
+vector f_{vv}(x), or alternatively the library can use a finite
+difference method to estimate this vector with one additional function
+evaluation of f(x + h v) where h is a tunable step size (see the 'h_fvv'
+parameter description).
+
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares TRS Dogleg,  Next: Nonlinear Least-Squares TRS Double Dogleg,  Prev: Nonlinear Least-Squares TRS Levenberg-Marquardt with Geodesic Acceleration,  Up: Nonlinear Least-Squares TRS Overview
+
+39.2.3 Dogleg
+-------------
+
+This is Powell's dogleg method, which finds an approximate solution to
+the trust region subproblem, by restricting its search to a piecewise
+linear "dogleg" path, composed of the origin, the Cauchy point which
+represents the model minimizer along the steepest descent direction, and
+the Gauss-Newton point, which is the overall minimizer of the
+unconstrained model.  The Gauss-Newton step is calculated by solving
+
+     J_k \delta_gn = -f_k
+
+   which is the main computational task for each iteration, but only
+needs to be performed once per iteration.  If the Gauss-Newton point is
+inside the trust region, it is selected as the step.  If it is outside,
+the method then calculates the Cauchy point, which is located along the
+gradient direction.  If the Cauchy point is also outside the trust
+region, the method assumes that it is still far from the minimum and so
+proceeds along the gradient direction, truncating the step at the trust
+region boundary.  If the Cauchy point is inside the trust region, with
+the Gauss-Newton point outside, the method uses a dogleg step, which is
+a linear combination of the gradient direction and the Gauss-Newton
+direction, stopping at the trust region boundary.
+
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares TRS Double Dogleg,  Next: Nonlinear Least-Squares TRS 2D Subspace,  Prev: Nonlinear Least-Squares TRS Dogleg,  Up: Nonlinear Least-Squares TRS Overview
+
+39.2.4 Double Dogleg
+--------------------
+
+This method is an improvement over the classical dogleg algorithm, which
+attempts to include information about the Gauss-Newton step while the
+iteration is still far from the minimum.  When the Cauchy point is
+inside the trust region and the Gauss-Newton point is outside, the
+method computes a scaled Gauss-Newton point and then takes a dogleg step
+between the Cauchy point and the scaled Gauss-Newton point.  The scaling
+is calculated to ensure that the reduction in the model m_k is about the
+same as the reduction provided by the Cauchy point.
+
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares TRS 2D Subspace,  Next: Nonlinear Least-Squares TRS Steihaug-Toint Conjugate Gradient,  Prev: Nonlinear Least-Squares TRS Double Dogleg,  Up: Nonlinear Least-Squares TRS Overview
+
+39.2.5 Two Dimensional Subspace
+-------------------------------
+
+The dogleg methods restrict the search for the TRS solution to a 1D
+curve defined by the Cauchy and Gauss-Newton points.  An improvement to
+this is to search for a solution using the full two dimensional subspace
+spanned by the Cauchy and Gauss-Newton directions.  The dogleg path is
+of course inside this subspace, and so this method solves the TRS at
+least as accurately as the dogleg methods.  Since this method searches a
+larger subspace for a solution, it can converge more quickly than dogleg
+on some problems.  Because the subspace is only two dimensional, this
+method is very efficient and the main computation per iteration is to
+determine the Gauss-Newton point.
+
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares TRS Steihaug-Toint Conjugate Gradient,  Prev: Nonlinear Least-Squares TRS 2D Subspace,  Up: Nonlinear Least-Squares TRS Overview
+
+39.2.6 Steihaug-Toint Conjugate Gradient
+----------------------------------------
+
+One difficulty of the dogleg methods is calculating the Gauss-Newton
+step when the Jacobian matrix is singular.  The Steihaug-Toint method
+also computes a generalized dogleg step, but avoids solving for the
+Gauss-Newton step directly, instead using an iterative conjugate
+gradient algorithm.  This method performs well at points where the
+Jacobian is singular, and is also suitable for large-scale problems
+where factoring the Jacobian matrix could be prohibitively expensive.
 
-     '0.fffff...*2^E, -0.fffff...*2^E'
-          a denormalized floating point number
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares Weighted Overview,  Next: Nonlinear Least-Squares Tunable Parameters,  Prev: Nonlinear Least-Squares TRS Overview,  Up: Nonlinear Least-Squares Fitting
 
-     '0, -0'
-          positive or negative zero
+39.3 Weighted Nonlinear Least-Squares
+=====================================
 
-     The output can be used directly in GNU Emacs Calc mode by preceding
-     it with '2#' to indicate binary.
+Weighted nonlinear least-squares fitting minimizes the function
 
- -- Function: void gsl_ieee_printf_float (const float * X)
- -- Function: void gsl_ieee_printf_double (const double * X)
-     These functions output a formatted version of the IEEE
-     floating-point number pointed to by X to the stream 'stdout'.
+     \Phi(x) = (1/2) || f(x) ||_W^2
+             = (1/2) \sum_{i=1}^{n} f_i(x_1, ..., x_p)^2
 
-The following program demonstrates the use of the functions by printing
-the single and double precision representations of the fraction 1/3.
-For comparison the representation of the value promoted from single to
-double precision is also printed.
+   where W = diag(w_1,w_2,...,w_n) is the weighting matrix, and
+||f||_W^2 = f^T W f.  The weights w_i are commonly defined as w_i =
+1/\sigma_i^2, where \sigma_i is the error in the ith measurement.  A
+simple change of variables \tilde{f} = W^{1 \over 2} f yields \Phi(x) =
+{1 \over 2} ||\tilde{f}||^2, which is in the same form as the unweighted
+case.  The user can either perform this transform directly on their
+function residuals and Jacobian, or use the 'gsl_multifit_nlinear_winit'
+interface which automatically performs the correct scaling.  To manually
+perform this transformation, the residuals and Jacobian should be
+modified according to
+
+     f~_i = f_i / \sigma_i
+     J~_ij = 1 / \sigma_i df_i/dx_j
+
+For large systems, the user must perform their own weighting.
+
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares Tunable Parameters,  Next: Nonlinear Least-Squares Initialization,  Prev: Nonlinear Least-Squares Weighted Overview,  Up: Nonlinear Least-Squares Fitting
+
+39.4 Tunable Parameters
+=======================
+
+The user can tune nearly all aspects of the iteration at allocation
+time.  For the 'gsl_multifit_nlinear' interface, the user may modify the
+'gsl_multifit_nlinear_parameters' structure, which is defined as
+follows:
 
-     #include <stdio.h>
-     #include <gsl/gsl_ieee_utils.h>
+     typedef struct
+     {
+       const gsl_multifit_nlinear_trs *trs;        /* trust region subproblem method */
+       const gsl_multifit_nlinear_scale *scale;    /* scaling method */
+       const gsl_multifit_nlinear_solver *solver;  /* solver method */
+       gsl_multifit_nlinear_fdtype fdtype;         /* finite difference method */
+       double factor_up;                           /* factor for increasing trust radius */
+       double factor_down;                         /* factor for decreasing trust radius */
+       double avmax;                               /* max allowed |a|/|v| */
+       double h_df;                                /* step size for finite difference Jacobian */
+       double h_fvv;                               /* step size for finite difference fvv */
+     } gsl_multifit_nlinear_parameters;
+
+For the 'gsl_multilarge_nlinear' interface, the user may modify the
+'gsl_multilarge_nlinear_parameters' structure, which is defined as
+follows:
 
-     int
-     main (void)
+     typedef struct
      {
-       float f = 1.0/3.0;
-       double d = 1.0/3.0;
+       const gsl_multilarge_nlinear_trs *trs;       /* trust region subproblem method */
+       const gsl_multilarge_nlinear_scale *scale;   /* scaling method */
+       const gsl_multilarge_nlinear_solver *solver; /* solver method */
+       gsl_multilarge_nlinear_fdtype fdtype;        /* finite difference method */
+       double factor_up;                            /* factor for increasing trust radius */
+       double factor_down;                          /* factor for decreasing trust radius */
+       double avmax;                                /* max allowed |a|/|v| */
+       double h_df;                                 /* step size for finite difference Jacobian */
+       double h_fvv;                                /* step size for finite difference fvv */
+       size_t max_iter;                             /* maximum iterations for trs method */
+       double tol;                                  /* tolerance for solving trs */
+     } gsl_multilarge_nlinear_parameters;
+
+Each of these parameters is discussed in further detail below.
+
+ -- Parameter: const gsl_multifit_nlinear_trs * trs
+ -- Parameter: const gsl_multilarge_nlinear_trs * trs
+
+     This parameter determines the method used to solve the trust region
+     subproblem, and may be selected from the following choices,
+
+      -- Default: gsl_multifit_nlinear_trs_lm
+      -- Default: gsl_multilarge_nlinear_trs_lm
+          This selects the Levenberg-Marquardt algorithm.
+
+      -- Option: gsl_multifit_nlinear_trs_lmaccel
+      -- Option: gsl_multilarge_nlinear_trs_lmaccel
+          This selects the Levenberg-Marquardt algorithm with geodesic
+          acceleration.
+
+      -- Option: gsl_multifit_nlinear_trs_dogleg
+      -- Option: gsl_multilarge_nlinear_trs_dogleg
+          This selects the dogleg algorithm.
+
+      -- Option: gsl_multifit_nlinear_trs_ddogleg
+      -- Option: gsl_multilarge_nlinear_trs_ddogleg
+          This selects the double dogleg algorithm.
+
+      -- Option: gsl_multifit_nlinear_trs_subspace2D
+      -- Option: gsl_multilarge_nlinear_trs_subspace2D
+          This selects the 2D subspace algorithm.
+
+      -- Option: gsl_multilarge_nlinear_trs_cgst
+          This selects the Steihaug-Toint conjugate gradient algorithm.
+          This method is available only for large systems.
+
+ -- Parameter: const gsl_multifit_nlinear_scale * scale
+ -- Parameter: const gsl_multilarge_nlinear_scale * scale
+
+     This parameter determines the diagonal scaling matrix D and may be
+     selected from the following choices,
+
+      -- Default: gsl_multifit_nlinear_scale_more
+      -- Default: gsl_multilarge_nlinear_scale_more
+          This damping strategy was suggested by More', and corresponds
+          to D^T D = max(diag(J^T J)), in other words the maximum
+          elements of diag(J^T J) encountered thus far in the iteration.
+          This choice of D makes the problem scale-invariant, so that if
+          the model parameters x_i are each scaled by an arbitrary
+          constant, \tilde{x}_i = a_i x_i, then the sequence of iterates
+          produced by the algorithm would be unchanged.  This method can
+          work very well in cases where the model parameters have widely
+          different scales (ie: if some parameters are measured in
+          nanometers, while others are measured in degrees Kelvin).
+          This strategy has been proven effective on a large class of
+          problems and so it is the library default, but it may not be
+          the best choice for all problems.
+
+      -- Option: gsl_multifit_nlinear_scale_levenberg
+      -- Option: gsl_multilarge_nlinear_scale_levenberg
+          This damping strategy was originally suggested by Levenberg,
+          and corresponds to D^T D = I.  This method has also proven
+          effective on a large class of problems, but is not
+          scale-invariant.  However, some authors (e.g.  Transtrum and
+          Sethna 2012) argue that this choice is better for problems
+          which are susceptible to parameter evaporation (ie: parameters
+          go to infinity)
+
+      -- Option: gsl_multifit_nlinear_scale_marquardt
+      -- Option: gsl_multilarge_nlinear_scale_marquardt
+          This damping strategy was suggested by Marquardt, and
+          corresponds to D^T D = diag(J^T J).  This method is
+          scale-invariant, but it is generally considered inferior to
+          both the Levenberg and More' strategies, though may work well
+          on certain classes of problems.
+
+ -- Parameter: const gsl_multifit_nlinear_solver * solver
+ -- Parameter: const gsl_multilarge_nlinear_solver * solver
+
+     Solving the trust region subproblem on each iteration almost always
+     requires the solution of the following linear least squares system
+
+          [J; sqrt(mu) D] \delta = - [f; 0]
+
+     The SOLVER parameter determines how the system is solved and can be
+     selected from the following choices:
+
+      -- Default: gsl_multifit_nlinear_solver_qr
+          This method solves the system using a rank revealing QR
+          decomposition of the Jacobian J.  This method will produce
+          reliable solutions in cases where the Jacobian is rank
+          deficient or near-singular but does require about twice as
+          many operations as the Cholesky method discussed below.
+
+      -- Option: gsl_multifit_nlinear_solver_cholesky
+      -- Default: gsl_multilarge_nlinear_solver_cholesky
+          This method solves the alternate normal equations problem
+
+               ( J^T J + \mu D^T D ) \delta = -J^T f
+
+          by using a Cholesky decomposition of the matrix J^T J + \mu
+          D^T D.  This method is faster than the QR approach, however it
+          is susceptible to numerical instabilities if the Jacobian
+          matrix is rank deficient or near-singular.  In these cases, an
+          attempt is made to reduce the condition number of the matrix
+          using Jacobi preconditioning, but for highly ill-conditioned
+          problems the QR approach is better.  If it is known that the
+          Jacobian matrix is well conditioned, this method is accurate
+          and will perform faster than the QR approach.
+
+      -- Option: gsl_multifit_nlinear_solver_svd
+          This method solves the system using a singular value
+          decomposition of the Jacobian J.  This method will produce the
+          most reliable solutions for ill-conditioned Jacobians but is
+          also the slowest solver method.
+
+ -- Parameter: gsl_multifit_nlinear_fdtype fdtype
+
+     This parameter specifies whether to use forward or centered
+     differences when approximating the Jacobian.  This is only used
+     when an analytic Jacobian is not provided to the solver.  This
+     parameter may be set to one of the following choices.
+
+      -- Default: GSL_MULTIFIT_NLINEAR_FWDIFF
+          This specifies a forward finite difference to approximate the
+          Jacobian matrix.  The Jacobian matrix will be calculated as
+
+               J_ij = 1 / \Delta_j ( f_i(x + \Delta_j e_j) - f_i(x) )
+
+          where \Delta_j = h |x_j| and e_j is the standard jth Cartesian
+          unit basis vector so that x + \Delta_j e_j represents a small
+          (forward) perturbation of the jth parameter by an amount
+          \Delta_j.  The perturbation \Delta_j is proportional to the
+          current value |x_j| which helps to calculate an accurate
+          Jacobian when the various parameters have different scale
+          sizes.  The value of h is specified by the 'h_df' parameter.
+          The accuracy of this method is O(h), and evaluating this
+          matrix requires an additional p function evaluations.
+
+      -- Option: GSL_MULTIFIT_NLINEAR_CTRDIFF
+          This specifies a centered finite difference to approximate the
+          Jacobian matrix.  The Jacobian matrix will be calculated as
+
+               J_ij = 1 / \Delta_j ( f_i(x + 1/2 \Delta_j e_j) - f_i(x - 1/2 \Delta_j e_j) )
+
+          See above for a description of \Delta_j.  The accuracy of this
+          method is O(h^2), but evaluating this matrix requires an
+          additional 2p function evaluations.
+
+ -- Parameter: double factor_up
+
+     When a step is accepted, the trust region radius will be increased
+     by this factor.  The default value is 3.
+
+ -- Parameter: double factor_down
+
+     When a step is rejected, the trust region radius will be decreased
+     by this factor.  The default value is 2.
+
+ -- Parameter: double avmax
+
+     When using geodesic acceleration to solve a nonlinear least squares
+     problem, an important parameter to monitor is the ratio of the
+     acceleration term to the velocity term,
+
+          |a| / |v|
+
+     If this ratio is small, it means the acceleration correction is
+     contributing very little to the step.  This could be because the
+     problem is not "nonlinear" enough to benefit from the acceleration.
+     If the ratio is large (> 1) it means that the acceleration is
+     larger than the velocity, which shouldn't happen since the step
+     represents a truncated series and so the second order term a should
+     be smaller than the first order term v to guarantee convergence.
+     Therefore any steps with a ratio larger than the parameter AVMAX
+     are rejected.  AVMAX is set to 0.75 by default.  For problems which
+     experience difficulty converging, this threshold could be lowered.
+
+ -- Parameter: double h_df
+
+     This parameter specifies the step size for approximating the
+     Jacobian matrix with finite differences.  It is set to
+     \sqrt{\epsilon} by default, where \epsilon is 'GSL_DBL_EPSILON'.
+
+ -- Parameter: double h_fvv
+
+     When using geodesic acceleration, the user must either supply a
+     function to calculate f_{vv}(x) or the library can estimate this
+     second directional derivative using a finite difference method.
+     When using finite differences, the library must calculate f(x + h
+     v) where h represents a small step in the velocity direction.  The
+     parameter H_FVV defines this step size and is set to 0.02 by
+     default.
 
-       double fd = f; /* promote from float to double */
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares Initialization,  Next: Nonlinear Least-Squares Function Definition,  Prev: Nonlinear Least-Squares Tunable Parameters,  Up: Nonlinear Least-Squares Fitting
 
-       printf (" f="); gsl_ieee_printf_float(&f);
-       printf ("\n");
+39.5 Initializing the Solver
+============================
 
-       printf ("fd="); gsl_ieee_printf_double(&fd);
-       printf ("\n");
+ -- Function: gsl_multifit_nlinear_workspace *
+          gsl_multifit_nlinear_alloc (const gsl_multifit_nlinear_type *
+          T, const gsl_multifit_nlinear_parameters * PARAMS, const
+          size_t N, const size_t P)
+ -- Function: gsl_multilarge_nlinear_workspace *
+          gsl_multilarge_nlinear_alloc (const
+          gsl_multilarge_nlinear_type * T, const
+          gsl_multilarge_nlinear_parameters * PARAMS, const size_t N,
+          const size_t P)
+     These functions return a pointer to a newly allocated instance of a
+     derivative solver of type T for N observations and P parameters.
+     The PARAMS input specifies a tunable set of parameters which will
+     affect important details in each iteration of the trust region
+     subproblem algorithm.  It is recommended to start with the
+     suggested default parameters (see
+     'gsl_multifit_nlinear_default_parameters' and
+     'gsl_multilarge_nlinear_default_parameters') and then tune the
+     parameters once the code is working correctly.  See *note Nonlinear
+     Least-Squares Tunable Parameters:: for descriptions of the various
+     parameters.  For example, the following code creates an instance of
+     a Levenberg-Marquardt solver for 100 data points and 3 parameters,
+     using suggested defaults:
+
+          const gsl_multifit_nlinear_type * T
+              = gsl_multifit_nlinear_lm;
+          gsl_multifit_nlinear_parameters params
+              = gsl_multifit_nlinear_default_parameters();
+          gsl_multifit_nlinear_workspace * w
+              = gsl_multifit_nlinear_alloc (T, &params, 100, 3);
 
-       printf (" d="); gsl_ieee_printf_double(&d);
-       printf ("\n");
+     The number of observations N must be greater than or equal to
+     parameters P.
 
-       return 0;
-     }
+     If there is insufficient memory to create the solver then the
+     function returns a null pointer and the error handler is invoked
+     with an error code of 'GSL_ENOMEM'.
 
-The binary representation of 1/3 is 0.01010101... .  The output below
-shows that the IEEE format normalizes this fraction to give a leading
-digit of 1,
+ -- Function: gsl_multifit_nlinear_parameters
+          gsl_multifit_nlinear_default_parameters (void)
+ -- Function: gsl_multilarge_nlinear_parameters
+          gsl_multilarge_nlinear_default_parameters (void)
+     These functions return a set of recommended default parameters for
+     use in solving nonlinear least squares problems.  The user can tune
+     each parameter to improve the performance on their particular
+     problem, see *note Nonlinear Least-Squares Tunable Parameters::.
+
+ -- Function: int gsl_multifit_nlinear_init (const gsl_vector * X,
+          gsl_multifit_nlinear_fdf * FDF, gsl_multifit_nlinear_workspace
+          * W)
+ -- Function: int gsl_multifit_nlinear_winit (const gsl_vector * X,
+          const gsl_vector * WTS, gsl_multifit_nlinear_fdf * FDF,
+          gsl_multifit_nlinear_workspace * W)
+ -- Function: int gsl_multilarge_nlinear_init (const gsl_vector * X,
+          gsl_multilarge_nlinear_fdf * FDF,
+          gsl_multilarge_nlinear_workspace * W)
+ -- Function: int gsl_multilarge_nlinear_winit (const gsl_vector * X,
+          const gsl_vector * WTS, gsl_multilarge_nlinear_fdf * FDF,
+          gsl_multilarge_nlinear_workspace * W)
+     These functions initialize, or reinitialize, an existing workspace
+     W to use the system FDF and the initial guess X.  See *note
+     Nonlinear Least-Squares Function Definition:: for a description of
+     the FDF structure.
+
+     Optionally, a weight vector WTS can be given to perform a weighted
+     nonlinear regression.  Here, the weighting matrix is W =
+     diag(w_1,w_2,...,w_n).
+
+ -- Function: void gsl_multifit_nlinear_free
+          (gsl_multifit_nlinear_workspace * W)
+ -- Function: void gsl_multilarge_nlinear_free
+          (gsl_multilarge_nlinear_workspace * W)
+     These functions free all the memory associated with the workspace
+     W.
+
+ -- Function: const char * gsl_multifit_nlinear_name (const
+          gsl_multifit_nlinear_workspace * W)
+ -- Function: const char * gsl_multilarge_nlinear_name (const
+          gsl_multilarge_nlinear_workspace * W)
+     These functions return a pointer to the name of the solver.  For
+     example,
 
-      f= 1.01010101010101010101011*2^-2
-     fd= 1.0101010101010101010101100000000000000000000000000000*2^-2
-      d= 1.0101010101010101010101010101010101010101010101010101*2^-2
+          printf ("w is a '%s' solver\n",
+                  gsl_multifit_nlinear_name (w));
 
-The output also shows that a single-precision number is promoted to
-double-precision by adding zeros in the binary representation.
+     would print something like 'w is a 'trust-region' solver'.
 
-
-File: gsl-ref.info,  Node: Setting up your IEEE environment,  Next: IEEE References and Further Reading,  Prev: Representation of floating point numbers,  Up: IEEE floating-point arithmetic
+ -- Function: const char * gsl_multifit_nlinear_trs_name (const
+          gsl_multifit_nlinear_workspace * W)
+ -- Function: const char * gsl_multilarge_nlinear_trs_name (const
+          gsl_multilarge_nlinear_workspace * W)
+     These functions return a pointer to the name of the trust region
+     subproblem method.  For example,
 
-41.2 Setting up your IEEE environment
-=====================================
+          printf ("w is a '%s' solver\n",
+                  gsl_multifit_nlinear_trs_name (w));
 
-The IEEE standard defines several "modes" for controlling the behavior
-of floating point operations.  These modes specify the important
-properties of computer arithmetic: the direction used for rounding (e.g.
-whether numbers should be rounded up, down or to the nearest number),
-the rounding precision and how the program should handle arithmetic
-exceptions, such as division by zero.
-
-   Many of these features can now be controlled via standard functions
-such as 'fpsetround', which should be used whenever they are available.
-Unfortunately in the past there has been no universal API for
-controlling their behavior--each system has had its own low-level way of
-accessing them.  To help you write portable programs GSL allows you to
-specify modes in a platform-independent way using the environment
-variable 'GSL_IEEE_MODE'.  The library then takes care of all the
-necessary machine-specific initializations for you when you call the
-function 'gsl_ieee_env_setup'.
-
- -- Function: void gsl_ieee_env_setup ()
-     This function reads the environment variable 'GSL_IEEE_MODE' and
-     attempts to set up the corresponding specified IEEE modes.  The
-     environment variable should be a list of keywords, separated by
-     commas, like this,
-
-          'GSL_IEEE_MODE' = "KEYWORD,KEYWORD,..."
-
-     where KEYWORD is one of the following mode-names,
-
-          'single-precision'
-          'double-precision'
-          'extended-precision'
-          'round-to-nearest'
-          'round-down'
-          'round-up'
-          'round-to-zero'
-          'mask-all'
-          'mask-invalid'
-          'mask-denormalized'
-          'mask-division-by-zero'
-          'mask-overflow'
-          'mask-underflow'
-          'trap-inexact'
-          'trap-common'
-
-     If 'GSL_IEEE_MODE' is empty or undefined then the function returns
-     immediately and no attempt is made to change the system's IEEE
-     mode.  When the modes from 'GSL_IEEE_MODE' are turned on the
-     function prints a short message showing the new settings to remind
-     you that the results of the program will be affected.
-
-     If the requested modes are not supported by the platform being used
-     then the function calls the error handler and returns an error code
-     of 'GSL_EUNSUP'.
-
-     When options are specified using this method, the resulting mode is
-     based on a default setting of the highest available precision
-     (double precision or extended precision, depending on the platform)
-     in round-to-nearest mode, with all exceptions enabled apart from
-     the INEXACT exception.  The INEXACT exception is generated whenever
-     rounding occurs, so it must generally be disabled in typical
-     scientific calculations.  All other floating-point exceptions are
-     enabled by default, including underflows and the use of
-     denormalized numbers, for safety.  They can be disabled with the
-     individual 'mask-' settings or together using 'mask-all'.
-
-     The following adjusted combination of modes is convenient for many
-     purposes,
-
-          GSL_IEEE_MODE="double-precision,"\
-                          "mask-underflow,"\
-                            "mask-denormalized"
-
-     This choice ignores any errors relating to small numbers (either
-     denormalized, or underflowing to zero) but traps overflows,
-     division by zero and invalid operations.
-
-     Note that on the x86 series of processors this function sets both
-     the original x87 mode and the newer MXCSR mode, which controls SSE
-     floating-point operations.  The SSE floating-point units do not
-     have a precision-control bit, and always work in double-precision.
-     The single-precision and extended-precision keywords have no effect
-     in this case.
-
-To demonstrate the effects of different rounding modes consider the
-following program which computes e, the base of natural logarithms, by
-summing a rapidly-decreasing series,
+     would print something like 'w is a 'levenberg-marquardt' solver'.
 
-     e = 1 + 1/2! + 1/3! + 1/4! + ...
-       = 2.71828182846...
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares Function Definition,  Next: Nonlinear Least-Squares Iteration,  Prev: Nonlinear Least-Squares Initialization,  Up: Nonlinear Least-Squares Fitting
 
-     #include <stdio.h>
-     #include <gsl/gsl_math.h>
-     #include <gsl/gsl_ieee_utils.h>
+39.6 Providing the Function to be Minimized
+===========================================
 
-     int
-     main (void)
-     {
-       double x = 1, oldsum = 0, sum = 0;
-       int i = 0;
+The user must provide n functions of p variables for the minimization
+algorithm to operate on.  In order to allow for arbitrary parameters the
+functions are defined by the following data types:
 
-       gsl_ieee_env_setup (); /* read GSL_IEEE_MODE */
+ -- Data Type: gsl_multifit_nlinear_fdf
+     This data type defines a general system of functions with arbitrary
+     parameters, the corresponding Jacobian matrix of derivatives, and
+     optionally the second directional derivative of the functions for
+     geodesic acceleration.
 
-       do
-         {
-           i++;
+     'int (* f) (const gsl_vector * X, void * PARAMS, gsl_vector * F)'
+          This function should store the n components of the vector f(x)
+          in F for argument X and arbitrary parameters PARAMS, returning
+          an appropriate error code if the function cannot be computed.
 
-           oldsum = sum;
-           sum += x;
-           x = x / i;
+     'int (* df) (const gsl_vector * X, void * PARAMS, gsl_matrix * J)'
+          This function should store the N-by-P matrix result J_ij = d
+          f_i(x) / d x_j in J for argument X and arbitrary parameters
+          PARAMS, returning an appropriate error code if the matrix
+          cannot be computed.  If an analytic Jacobian is unavailable,
+          or too expensive to compute, this function pointer may be set
+          to NULL, in which case the Jacobian will be internally
+          computed using finite difference approximations of the
+          function F.
+
+     'int (* fvv) (const gsl_vector * X, const gsl_vector * V, void * PARAMS, gsl_vector * FVV)'
+          When geodesic acceleration is enabled, this function should
+          store the n components of the vector f_{vv}(x) =
+          \sum_{\alpha\beta} v_{\alpha} v_{\beta} {\partial \over
+          \partial x_{\alpha}} {\partial \over \partial x_{\beta}} f(x),
+          representing second directional derivatives of the function to
+          be minimized, into the output FVV.  The parameter vector is
+          provided in X and the velocity vector is provided in V, both
+          of which have p components.  The arbitrary parameters are
+          given in PARAMS.  If analytic expressions for f_{vv}(x) are
+          unavailable or too difficult to compute, this function pointer
+          may be set to NULL, in which case f_{vv}(x) will be computed
+          internally using a finite difference approximation.
 
-           printf ("i=%2d sum=%.18f error=%g\n",
-                   i, sum, sum - M_E);
+     'size_t n'
+          the number of functions, i.e.  the number of components of the
+          vector F.
 
-           if (i > 30)
-              break;
-         }
-       while (sum != oldsum);
+     'size_t p'
+          the number of independent variables, i.e.  the number of
+          components of the vector X.
 
-       return 0;
-     }
+     'void * params'
+          a pointer to the arbitrary parameters of the function.
 
-Here are the results of running the program in 'round-to-nearest' mode.
-This is the IEEE default so it isn't really necessary to specify it
-here,
-
-     $ GSL_IEEE_MODE="round-to-nearest" ./a.out
-     i= 1 sum=1.000000000000000000 error=-1.71828
-     i= 2 sum=2.000000000000000000 error=-0.718282
-     ....
-     i=18 sum=2.718281828459045535 error=4.44089e-16
-     i=19 sum=2.718281828459045535 error=4.44089e-16
+     'size_t nevalf'
+          This does not need to be set by the user.  It counts the
+          number of function evaluations and is initialized by the
+          '_init' function.
+
+     'size_t nevaldf'
+          This does not need to be set by the user.  It counts the
+          number of Jacobian evaluations and is initialized by the
+          '_init' function.
+
+     'size_t nevalfvv'
+          This does not need to be set by the user.  It counts the
+          number of f_{vv}(x) evaluations and is initialized by the
+          '_init' function.
 
-After nineteen terms the sum converges to within 4 \times 10^-16 of the
-correct value.  If we now change the rounding mode to 'round-down' the
-final result is less accurate,
+ -- Data Type: gsl_multilarge_nlinear_fdf
+     This data type defines a general system of functions with arbitrary
+     parameters, a function to compute J u or J^T u for a given vector
+     u, the normal equations matrix J^T J, and optionally the second
+     directional derivative of the functions for geodesic acceleration.
 
-     $ GSL_IEEE_MODE="round-down" ./a.out
-     i= 1 sum=1.000000000000000000 error=-1.71828
-     ....
-     i=19 sum=2.718281828459041094 error=-3.9968e-15
+     'int (* f) (const gsl_vector * X, void * PARAMS, gsl_vector * F)'
+          This function should store the n components of the vector f(x)
+          in F for argument X and arbitrary parameters PARAMS, returning
+          an appropriate error code if the function cannot be computed.
+
+     'int (* df) (CBLAS_TRANSPOSE_t TRANSJ, const gsl_vector * X, const gsl_vector * U, void * PARAMS, gsl_vector * V, gsl_matrix * JTJ)'
+          If TRANSJ is equal to 'CblasNoTrans', then this function
+          should compute the matrix-vector product J u and store the
+          result in V.  If TRANSJ is equal to 'CblasTrans', then this
+          function should compute the matrix-vector product J^T u and
+          store the result in V.  Additionally, the normal equations
+          matrix J^T J should be stored in the lower half of JTJ.  The
+          input matrix JTJ could be set to NULL, for example by
+          iterative methods which do not require this matrix, so the
+          user should check for this prior to constructing the matrix.
+          The input PARAMS contains the arbitrary parameters.
+
+     'int (* fvv) (const gsl_vector * X, const gsl_vector * V, void * PARAMS, gsl_vector * FVV)'
+          When geodesic acceleration is enabled, this function should
+          store the n components of the vector f_{vv}(x) =
+          \sum_{\alpha\beta} v_{\alpha} v_{\beta} {\partial \over
+          \partial x_{\alpha}} {\partial \over \partial x_{\beta}} f(x),
+          representing second directional derivatives of the function to
+          be minimized, into the output FVV.  The parameter vector is
+          provided in X and the velocity vector is provided in V, both
+          of which have p components.  The arbitrary parameters are
+          given in PARAMS.  If analytic expressions for f_{vv}(x) are
+          unavailable or too difficult to compute, this function pointer
+          may be set to NULL, in which case f_{vv}(x) will be computed
+          internally using a finite difference approximation.
 
-The result is about 4 \times 10^-15 below the correct value, an order of
-magnitude worse than the result obtained in the 'round-to-nearest' mode.
+     'size_t n'
+          the number of functions, i.e.  the number of components of the
+          vector F.
 
-   If we change to rounding mode to 'round-up' then the final result is
-higher than the correct value (when we add each term to the sum the
-final result is always rounded up, which increases the sum by at least
-one tick until the added term underflows to zero).  To avoid this
-problem we would need to use a safer converge criterion, such as 'while
-(fabs(sum - oldsum) > epsilon)', with a suitably chosen value of
-epsilon.
-
-   Finally we can see the effect of computing the sum using
-single-precision rounding, in the default 'round-to-nearest' mode.  In
-this case the program thinks it is still using double precision numbers
-but the CPU rounds the result of each floating point operation to
-single-precision accuracy.  This simulates the effect of writing the
-program using single-precision 'float' variables instead of 'double'
-variables.  The iteration stops after about half the number of
-iterations and the final result is much less accurate,
+     'size_t p'
+          the number of independent variables, i.e.  the number of
+          components of the vector X.
 
-     $ GSL_IEEE_MODE="single-precision" ./a.out
-     ....
-     i=12 sum=2.718281984329223633 error=1.5587e-07
+     'void * params'
+          a pointer to the arbitrary parameters of the function.
 
-with an error of O(10^-7), which corresponds to single precision
-accuracy (about 1 part in 10^7).  Continuing the iterations further does
-not decrease the error because all the subsequent results are rounded to
-the same value.
+     'size_t nevalf'
+          This does not need to be set by the user.  It counts the
+          number of function evaluations and is initialized by the
+          '_init' function.
+
+     'size_t nevaldfu'
+          This does not need to be set by the user.  It counts the
+          number of Jacobian matrix-vector evaluations (J u or J^T u)
+          and is initialized by the '_init' function.
+
+     'size_t nevaldf2'
+          This does not need to be set by the user.  It counts the
+          number of J^T J evaluations and is initialized by the '_init'
+          function.
+
+     'size_t nevalfvv'
+          This does not need to be set by the user.  It counts the
+          number of f_{vv}(x) evaluations and is initialized by the
+          '_init' function.
+
+Note that when fitting a non-linear model against experimental data, the
+data is passed to the functions above using the PARAMS argument and the
+trial best-fit parameters through the X argument.
 
 
-File: gsl-ref.info,  Node: IEEE References and Further Reading,  Prev: Setting up your IEEE environment,  Up: IEEE floating-point arithmetic
-
-41.3 References and Further Reading
-===================================
+File: gsl-ref.info,  Node: Nonlinear Least-Squares Iteration,  Next: Nonlinear Least-Squares Testing for Convergence,  Prev: Nonlinear Least-Squares Function Definition,  Up: Nonlinear Least-Squares Fitting
 
-The reference for the IEEE standard is,
-
-     ANSI/IEEE Std 754-1985, IEEE Standard for Binary Floating-Point
-     Arithmetic.
-
-A more pedagogical introduction to the standard can be found in the
-following paper,
+39.7 Iteration
+==============
 
-     David Goldberg: What Every Computer Scientist Should Know About
-     Floating-Point Arithmetic.  'ACM Computing Surveys', Vol. 23, No. 1
-     (March 1991), pages 5-48.
+The following functions drive the iteration of each algorithm.  Each
+function performs one iteration of the trust region method and updates
+the state of the solver.
 
-     Corrigendum: 'ACM Computing Surveys', Vol. 23, No. 3 (September
-     1991), page 413.  and see also the sections by B. A. Wichmann and
-     Charles B. Dunham in Surveyor's Forum: "What Every Computer
-     Scientist Should Know About Floating-Point Arithmetic".  'ACM
-     Computing Surveys', Vol. 24, No. 3 (September 1992), page 319.
+ -- Function: int gsl_multifit_nlinear_iterate
+          (gsl_multifit_nlinear_workspace * W)
+ -- Function: int gsl_multilarge_nlinear_iterate
+          (gsl_multilarge_nlinear_workspace * W)
+     These functions perform a single iteration of the solver W.  If the
+     iteration encounters an unexpected problem then an error code will
+     be returned.  The solver workspace maintains a current estimate of
+     the best-fit parameters at all times.
 
-   A detailed textbook on IEEE arithmetic and its practical use is
-available from SIAM Press,
+The solver workspace W contains the following entries, which can be used
+to track the progress of the solution:
 
-     Michael L. Overton, 'Numerical Computing with IEEE Floating Point
-     Arithmetic', SIAM Press, ISBN 0898715717.
+'gsl_vector * x'
+     The current position, length p.
 
-
-File: gsl-ref.info,  Node: Debugging Numerical Programs,  Next: Contributors to GSL,  Prev: IEEE floating-point arithmetic,  Up: Top
+'gsl_vector * f'
+     The function residual vector at the current position f(x), length
+     n.
 
-Appendix A Debugging Numerical Programs
-***************************************
+'gsl_matrix * J'
+     The Jacobian matrix at the current position J(x), size n-by-p (only
+     for 'gsl_multifit_nlinear' interface).
 
-This chapter describes some tips and tricks for debugging numerical
-programs which use GSL.
+'gsl_vector * dx'
+     The difference between the current position and the previous
+     position, i.e.  the last step \delta, taken as a vector, length p.
 
-* Menu:
+These quantities can be accessed with the following functions,
 
-* Using gdb::                   
-* Examining floating point registers::  
-* Handling floating point exceptions::  
-* GCC warning options for numerical programs::  
-* Debugging References::        
+ -- Function: gsl_vector * gsl_multifit_nlinear_position (const
+          gsl_multifit_nlinear_workspace * W)
+ -- Function: gsl_vector * gsl_multilarge_nlinear_position (const
+          gsl_multilarge_nlinear_workspace * W)
+     These functions return the current position x (i.e.  best-fit
+     parameters) of the solver W.
+
+ -- Function: gsl_vector * gsl_multifit_nlinear_residual (const
+          gsl_multifit_nlinear_workspace * W)
+ -- Function: gsl_vector * gsl_multilarge_nlinear_residual (const
+          gsl_multilarge_nlinear_workspace * W)
+     These functions return the current residual vector f(x) of the
+     solver W.  For weighted systems, the residual vector includes the
+     weighting factor \sqrt{W}.
+
+ -- Function: gsl_matrix * gsl_multifit_nlinear_jac (const
+          gsl_multifit_nlinear_workspace * W)
+     This function returns a pointer to the n-by-p Jacobian matrix for
+     the current iteration of the solver W.  This function is available
+     only for the 'gsl_multifit_nlinear' interface.
+
+ -- Function: size_t gsl_multifit_nlinear_niter (const
+          gsl_multifit_nlinear_workspace * W)
+ -- Function: size_t gsl_multilarge_nlinear_niter (const
+          gsl_multilarge_nlinear_workspace * W)
+     These functions return the number of iterations performed so far.
+     The iteration counter is updated on each call to the '_iterate'
+     functions above, and reset to 0 in the '_init' functions.
+
+ -- Function: int gsl_multifit_nlinear_rcond (double * RCOND, const
+          gsl_multifit_nlinear_workspace * W)
+ -- Function: int gsl_multilarge_nlinear_rcond (double * RCOND, const
+          gsl_multilarge_nlinear_workspace * W)
+     This function estimates the reciprocal condition number of the
+     Jacobian matrix at the current position x and stores it in RCOND.
+     The computed value is only an estimate to give the user a guideline
+     as to the conditioning of their particular problem.  Its
+     calculation is based on which factorization method is used
+     (Cholesky, QR, or SVD).
+
+        * For the Cholesky solver, the matrix J^T J is factored at each
+          iteration.  Therefore this function will estimate the 1-norm
+          condition number rcond^2 = 1/(||J^T J||_1 \cdot ||(J^T
+          J)^{-1}||_1)
+
+        * For the QR solver, J is factored as J = Q R at each iteration.
+          For simplicity, this function calculates the 1-norm
+          conditioning of only the R factor, rcond = 1 / (||R||_1 \cdot
+          ||R^{-1}||_1).  This can be computed efficiently since R is
+          upper triangular.
+
+        * For the SVD solver, in order to efficiently solve the trust
+          region subproblem, the matrix which is factored is J D^{-1},
+          instead of J itself.  The resulting singular values are used
+          to provide the 2-norm reciprocal condition number, as rcond =
+          \sigma_{min} / \sigma_{max}.  Note that when using More'
+          scaling, D \ne I and the resulting RCOND estimate may be
+          significantly different from the true RCOND of J itself.
 
 
-File: gsl-ref.info,  Node: Using gdb,  Next: Examining floating point registers,  Up: Debugging Numerical Programs
+File: gsl-ref.info,  Node: Nonlinear Least-Squares Testing for Convergence,  Next: Nonlinear Least-Squares High Level Driver,  Prev: Nonlinear Least-Squares Iteration,  Up: Nonlinear Least-Squares Fitting
 
-A.1 Using gdb
-=============
+39.8 Testing for Convergence
+============================
 
-Any errors reported by the library are passed to the function
-'gsl_error'.  By running your programs under gdb and setting a
-breakpoint in this function you can automatically catch any library
-errors.  You can add a breakpoint for every session by putting
-
-     break gsl_error
-
-into your '.gdbinit' file in the directory where your program is
-started.
-
-   If the breakpoint catches an error then you can use a backtrace
-('bt') to see the call-tree, and the arguments which possibly caused the
-error.  By moving up into the calling function you can investigate the
-values of variables at that point.  Here is an example from the program
-'fft/test_trap', which contains the following line,
-
-     status = gsl_fft_complex_wavetable_alloc (0, &complex_wavetable);
-
-The function 'gsl_fft_complex_wavetable_alloc' takes the length of an
-FFT as its first argument.  When this line is executed an error will be
-generated because the length of an FFT is not allowed to be zero.
-
-   To debug this problem we start 'gdb', using the file '.gdbinit' to
-define a breakpoint in 'gsl_error',
-
-     $ gdb test_trap
-
-     GDB is free software and you are welcome to distribute copies
-     of it under certain conditions; type "show copying" to see
-     the conditions.  There is absolutely no warranty for GDB;
-     type "show warranty" for details.  GDB 4.16 (i586-debian-linux),
-     Copyright 1996 Free Software Foundation, Inc.
-
-     Breakpoint 1 at 0x8050b1e: file error.c, line 14.
-
-When we run the program this breakpoint catches the error and shows the
-reason for it.
-
-     (gdb) run
-     Starting program: test_trap
-
-     Breakpoint 1, gsl_error (reason=0x8052b0d
-         "length n must be positive integer",
-         file=0x8052b04 "c_init.c", line=108, gsl_errno=1)
-         at error.c:14
-     14        if (gsl_error_handler)
-
-The first argument of 'gsl_error' is always a string describing the
-error.  Now we can look at the backtrace to see what caused the problem,
-
-     (gdb) bt
-     #0  gsl_error (reason=0x8052b0d
-         "length n must be positive integer",
-         file=0x8052b04 "c_init.c", line=108, gsl_errno=1)
-         at error.c:14
-     #1  0x8049376 in gsl_fft_complex_wavetable_alloc (n=0,
-         wavetable=0xbffff778) at c_init.c:108
-     #2  0x8048a00 in main (argc=1, argv=0xbffff9bc)
-         at test_trap.c:94
-     #3  0x80488be in ___crt_dummy__ ()
-
-We can see that the error was generated in the function
-'gsl_fft_complex_wavetable_alloc' when it was called with an argument of
-N=0.  The original call came from line 94 in the file 'test_trap.c'.
-
-   By moving up to the level of the original call we can find the line
-that caused the error,
-
-     (gdb) up
-     #1  0x8049376 in gsl_fft_complex_wavetable_alloc (n=0,
-         wavetable=0xbffff778) at c_init.c:108
-     108   GSL_ERROR ("length n must be positive integer", GSL_EDOM);
-     (gdb) up
-     #2  0x8048a00 in main (argc=1, argv=0xbffff9bc)
-         at test_trap.c:94
-     94    status = gsl_fft_complex_wavetable_alloc (0,
-             &complex_wavetable);
-
-Thus we have found the line that caused the problem.  From this point we
-could also print out the values of other variables such as
-'complex_wavetable'.
-
-
-File: gsl-ref.info,  Node: Examining floating point registers,  Next: Handling floating point exceptions,  Prev: Using gdb,  Up: Debugging Numerical Programs
-
-A.2 Examining floating point registers
-======================================
-
-The contents of floating point registers can be examined using the
-command 'info float' (on supported platforms).
-
-     (gdb) info float
-          st0: 0xc4018b895aa17a945000  Valid Normal -7.838871e+308
-          st1: 0x3ff9ea3f50e4d7275000  Valid Normal 0.0285946
-          st2: 0x3fe790c64ce27dad4800  Valid Normal 6.7415931e-08
-          st3: 0x3ffaa3ef0df6607d7800  Spec  Normal 0.0400229
-          st4: 0x3c028000000000000000  Valid Normal 4.4501477e-308
-          st5: 0x3ffef5412c22219d9000  Zero  Normal 0.9580257
-          st6: 0x3fff8000000000000000  Valid Normal 1
-          st7: 0xc4028b65a1f6d243c800  Valid Normal -1.566206e+309
-        fctrl: 0x0272 53 bit; NEAR; mask DENOR UNDER LOS;
-        fstat: 0xb9ba flags 0001; top 7; excep DENOR OVERF UNDER LOS
-         ftag: 0x3fff
-          fip: 0x08048b5c
-          fcs: 0x051a0023
-       fopoff: 0x08086820
-       fopsel: 0x002b
-
-Individual registers can be examined using the variables $REG, where REG
-is the register name.
-
-     (gdb) p $st1
-     $1 = 0.02859464454261210347719
-
-
-File: gsl-ref.info,  Node: Handling floating point exceptions,  Next: GCC warning options for numerical programs,  Prev: Examining floating point registers,  Up: Debugging Numerical Programs
-
-A.3 Handling floating point exceptions
-======================================
-
-It is possible to stop the program whenever a 'SIGFPE' floating point
-exception occurs.  This can be useful for finding the cause of an
-unexpected infinity or 'NaN'.  The current handler settings can be shown
-with the command 'info signal SIGFPE'.
-
-     (gdb) info signal SIGFPE
-     Signal  Stop  Print  Pass to program Description
-     SIGFPE  Yes   Yes    Yes             Arithmetic exception
-
-Unless the program uses a signal handler the default setting should be
-changed so that SIGFPE is not passed to the program, as this would cause
-it to exit.  The command 'handle SIGFPE stop nopass' prevents this.
-
-     (gdb) handle SIGFPE stop nopass
-     Signal  Stop  Print  Pass to program Description
-     SIGFPE  Yes   Yes    No              Arithmetic exception
-
-Depending on the platform it may be necessary to instruct the kernel to
-generate signals for floating point exceptions.  For programs using GSL
-this can be achieved using the 'GSL_IEEE_MODE' environment variable in
-conjunction with the function 'gsl_ieee_env_setup' as described in *note
-IEEE floating-point arithmetic::.
+A minimization procedure should stop when one of the following
+conditions is true:
 
-     (gdb) set env GSL_IEEE_MODE=double-precision
+   * A minimum has been found to within the user-specified precision.
 
-
-File: gsl-ref.info,  Node: GCC warning options for numerical programs,  Next: Debugging References,  Prev: Handling floating point exceptions,  Up: Debugging Numerical Programs
+   * A user-specified maximum number of iterations has been reached.
 
-A.4 GCC warning options for numerical programs
-==============================================
+   * An error has occurred.
 
-Writing reliable numerical programs in C requires great care.  The
-following GCC warning options are recommended when compiling numerical
-programs:
-
-     gcc -ansi -pedantic -Werror -Wall -W
-       -Wmissing-prototypes -Wstrict-prototypes
-       -Wconversion -Wshadow -Wpointer-arith
-       -Wcast-qual -Wcast-align
-       -Wwrite-strings -Wnested-externs
-       -fshort-enums -fno-common -Dinline= -g -O2
-
-For details of each option consult the manual 'Using and Porting GCC'.
-The following table gives a brief explanation of what types of errors
-these options catch.
-
-'-ansi -pedantic'
-     Use ANSI C, and reject any non-ANSI extensions.  These flags help
-     in writing portable programs that will compile on other systems.
-'-Werror'
-     Consider warnings to be errors, so that compilation stops.  This
-     prevents warnings from scrolling off the top of the screen and
-     being lost.  You won't be able to compile the program until it is
-     completely warning-free.
-'-Wall'
-     This turns on a set of warnings for common programming problems.
-     You need '-Wall', but it is not enough on its own.
-'-O2'
-     Turn on optimization.  The warnings for uninitialized variables in
-     '-Wall' rely on the optimizer to analyze the code.  If there is no
-     optimization then these warnings aren't generated.
-'-W'
-     This turns on some extra warnings not included in '-Wall', such as
-     missing return values and comparisons between signed and unsigned
-     integers.
-'-Wmissing-prototypes -Wstrict-prototypes'
-     Warn if there are any missing or inconsistent prototypes.  Without
-     prototypes it is harder to detect problems with incorrect
-     arguments.
-'-Wconversion'
-     The main use of this option is to warn about conversions from
-     signed to unsigned integers.  For example, 'unsigned int x = -1'.
-     If you need to perform such a conversion you can use an explicit
-     cast.
-'-Wshadow'
-     This warns whenever a local variable shadows another local
-     variable.  If two variables have the same name then it is a
-     potential source of confusion.
-'-Wpointer-arith -Wcast-qual -Wcast-align'
-     These options warn if you try to do pointer arithmetic for types
-     which don't have a size, such as 'void', if you remove a 'const'
-     cast from a pointer, or if you cast a pointer to a type which has a
-     different size, causing an invalid alignment.
-'-Wwrite-strings'
-     This option gives string constants a 'const' qualifier so that it
-     will be a compile-time error to attempt to overwrite them.
-'-fshort-enums'
-     This option makes the type of 'enum' as short as possible.
-     Normally this makes an 'enum' different from an 'int'.
-     Consequently any attempts to assign a pointer-to-int to a
-     pointer-to-enum will generate a cast-alignment warning.
-'-fno-common'
-     This option prevents global variables being simultaneously defined
-     in different object files (you get an error at link time).  Such a
-     variable should be defined in one file and referred to in other
-     files with an 'extern' declaration.
-'-Wnested-externs'
-     This warns if an 'extern' declaration is encountered within a
-     function.
-'-Dinline='
-     The 'inline' keyword is not part of ANSI C. Thus if you want to use
-     '-ansi' with a program which uses inline functions you can use this
-     preprocessor definition to remove the 'inline' keywords.
-'-g'
-     It always makes sense to put debugging symbols in the executable so
-     that you can debug it using 'gdb'.  The only effect of debugging
-     symbols is to increase the size of the file, and you can use the
-     'strip' command to remove them later if necessary.
-
-
-File: gsl-ref.info,  Node: Debugging References,  Prev: GCC warning options for numerical programs,  Up: Debugging Numerical Programs
-
-A.5 References and Further Reading
-==================================
-
-The following books are essential reading for anyone writing and
-debugging numerical programs with GCC and GDB.
-
-     R.M. Stallman, 'Using and Porting GNU CC', Free Software
-     Foundation, ISBN 1882114388
-
-     R.M. Stallman, R.H. Pesch, 'Debugging with GDB: The GNU
-     Source-Level Debugger', Free Software Foundation, ISBN 1882114779
-
-For a tutorial introduction to the GNU C Compiler and related programs,
-see
-
-     B.J. Gough, 'An Introduction to GCC', Network Theory Ltd, ISBN
-     0954161793
-
-
-File: gsl-ref.info,  Node: Contributors to GSL,  Next: Autoconf Macros,  Prev: Debugging Numerical Programs,  Up: Top
-
-Appendix B Contributors to GSL
-******************************
-
-(See the AUTHORS file in the distribution for up-to-date information.)
-
-*Mark Galassi*
-     Conceived GSL (with James Theiler) and wrote the design document.
-     Wrote the simulated annealing package and the relevant chapter in
-     the manual.
-
-*James Theiler*
-     Conceived GSL (with Mark Galassi).  Wrote the random number
-     generators and the relevant chapter in this manual.
-
-*Jim Davies*
-     Wrote the statistical routines and the relevant chapter in this
-     manual.
-
-*Brian Gough*
-     FFTs, numerical integration, random number generators and
-     distributions, root finding, minimization and fitting, polynomial
-     solvers, complex numbers, physical constants, permutations, vector
-     and matrix functions, histograms, statistics, ieee-utils, revised
-     CBLAS Level 2 & 3, matrix decompositions, eigensystems, cumulative
-     distribution functions, testing, documentation and releases.
-
-*Reid Priedhorsky*
-     Wrote and documented the initial version of the root finding
-     routines while at Los Alamos National Laboratory, Mathematical
-     Modeling and Analysis Group.
-
-*Gerard Jungman*
-     Special Functions, Series acceleration, ODEs, BLAS, Linear Algebra,
-     Eigensystems, Hankel Transforms.
-
-*Mike Booth*
-     Wrote the Monte Carlo library.
-
-*Jorma Olavi Ta"htinen*
-     Wrote the initial complex arithmetic functions.
-
-*Thomas Walter*
-     Wrote the initial heapsort routines and Cholesky decomposition.
-
-*Fabrice Rossi*
-     Multidimensional minimization.
-
-*Carlo Perassi*
-     Implementation of the random number generators in Knuth's
-     'Seminumerical Algorithms', 3rd Ed.
-
-*Szymon Jaroszewicz*
-     Wrote the routines for generating combinations.
-
-*Nicolas Darnis*
-     Wrote the cyclic functions and the initial functions for canonical
-     permutations.
-
-*Jason H. Stover*
-     Wrote the major cumulative distribution functions.
-
-*Ivo Alxneit*
-     Wrote the routines for wavelet transforms.
-
-*Tuomo Keskitalo*
-     Improved the implementation of the ODE solvers and wrote the
-     ode-initval2 routines.
-
-*Lowell Johnson*
-     Implementation of the Mathieu functions.
-
-*Patrick Alken*
-     Implementation of nonsymmetric and generalized eigensystems,
-     B-splines, and robust linear regression.
-
-*Rhys Ulerich*
-     Wrote the multiset routines.
-
-*Pavel Holoborodko*
-     Wrote the fixed order Gauss-Legendre quadrature routines.
-
-*Pedro Gonnet*
-     Wrote the CQUAD integration routines.
-
-   Thanks to Nigel Lowry for help in proofreading the manual.
-
-   The non-symmetric eigensystems routines contain code based on the
-LAPACK linear algebra library.  LAPACK is distributed under the
-following license:
-
-
-     Copyright (c) 1992-2006 The University of Tennessee.  All rights
-     reserved.
-
-     Redistribution and use in source and binary forms, with or without
-     modification, are permitted provided that the following conditions
-     are met:
-
-     * Redistributions of source code must retain the above copyright
-     notice, this list of conditions and the following disclaimer.
-
-     * Redistributions in binary form must reproduce the above copyright
-     notice, this list of conditions and the following disclaimer listed
-     in this license in the documentation and/or other materials
-     provided with the distribution.
-
-     * Neither the name of the copyright holders nor the names of its
-     contributors may be used to endorse or promote products derived
-     from this software without specific prior written permission.
-
-     THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-     "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-     LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
-     FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
-     COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
-     INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
-     (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
-     SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
-     HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
-     STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
-     ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
-     OF THE POSSIBILITY OF SUCH DAMAGE.
-
-
-File: gsl-ref.info,  Node: Autoconf Macros,  Next: GSL CBLAS Library,  Prev: Contributors to GSL,  Up: Top
-
-Appendix C Autoconf Macros
-**************************
-
-For applications using 'autoconf' the standard macro 'AC_CHECK_LIB' can
-be used to link with GSL automatically from a 'configure' script.  The
-library itself depends on the presence of a CBLAS and math library as
-well, so these must also be located before linking with the main
-'libgsl' file.  The following commands should be placed in the
-'configure.ac' file to perform these tests,
-
-     AC_CHECK_LIB([m],[cos])
-     AC_CHECK_LIB([gslcblas],[cblas_dgemm])
-     AC_CHECK_LIB([gsl],[gsl_blas_dgemm])
-
-It is important to check for 'libm' and 'libgslcblas' before 'libgsl',
-otherwise the tests will fail.  Assuming the libraries are found the
-output during the configure stage looks like this,
-
-     checking for cos in -lm... yes
-     checking for cblas_dgemm in -lgslcblas... yes
-     checking for gsl_blas_dgemm in -lgsl... yes
-
-If the library is found then the tests will define the macros
-'HAVE_LIBGSL', 'HAVE_LIBGSLCBLAS', 'HAVE_LIBM' and add the options
-'-lgsl -lgslcblas -lm' to the variable 'LIBS'.
-
-   The tests above will find any version of the library.  They are
-suitable for general use, where the versions of the functions are not
-important.  An alternative macro is available in the file 'gsl.m4' to
-test for a specific version of the library.  To use this macro simply
-add the following line to your 'configure.in' file instead of the tests
-above:
-
-     AX_PATH_GSL(GSL_VERSION,
-                [action-if-found],
-                [action-if-not-found])
-
-The argument 'GSL_VERSION' should be the two or three digit MAJOR.MINOR
-or MAJOR.MINOR.MICRO version number of the release you require.  A
-suitable choice for 'action-if-not-found' is,
-
-     AC_MSG_ERROR(could not find required version of GSL)
-
-Then you can add the variables 'GSL_LIBS' and 'GSL_CFLAGS' to your
-Makefile.am files to obtain the correct compiler flags.  'GSL_LIBS' is
-equal to the output of the 'gsl-config --libs' command and 'GSL_CFLAGS'
-is equal to 'gsl-config --cflags' command.  For example,
-
-     libfoo_la_LDFLAGS = -lfoo $(GSL_LIBS) -lgslcblas
-
-Note that the macro 'AX_PATH_GSL' needs to use the C compiler so it
-should appear in the 'configure.in' file before the macro
-'AC_LANG_CPLUSPLUS' for programs that use C++.
-
-   To test for 'inline' the following test should be placed in your
-'configure.in' file,
-
-     AC_C_INLINE
-
-     if test "$ac_cv_c_inline" != no ; then
-       AC_DEFINE(HAVE_INLINE,1)
-       AC_SUBST(HAVE_INLINE)
-     fi
-
-and the macro will then be defined in the compilation flags or by
-including the file 'config.h' before any library headers.
-
-   The following autoconf test will check for 'extern inline',
-
-     dnl Check for "extern inline", using a modified version
-     dnl of the test for AC_C_INLINE from acspecific.mt
-     dnl
-     AC_CACHE_CHECK([for extern inline], ac_cv_c_extern_inline,
-     [ac_cv_c_extern_inline=no
-     AC_TRY_COMPILE([extern $ac_cv_c_inline double foo(double x);
-     extern $ac_cv_c_inline double foo(double x) { return x+1.0; };
-     double foo (double x) { return x + 1.0; };],
-     [  foo(1.0)  ],
-     [ac_cv_c_extern_inline="yes"])
-     ])
-
-     if test "$ac_cv_c_extern_inline" != no ; then
-       AC_DEFINE(HAVE_INLINE,1)
-       AC_SUBST(HAVE_INLINE)
-     fi
-
-   The substitution of portability functions can be made automatically
-if you use 'autoconf'.  For example, to test whether the BSD function
-'hypot' is available you can include the following line in the configure
-file 'configure.in' for your application,
-
-     AC_CHECK_FUNCS(hypot)
-
-and place the following macro definitions in the file 'config.h.in',
-
-     /* Substitute gsl_hypot for missing system hypot */
-
-     #ifndef HAVE_HYPOT
-     #define hypot gsl_hypot
-     #endif
-
-The application source files can then use the include command '#include
-<config.h>' to substitute 'gsl_hypot' for each occurrence of 'hypot'
-when 'hypot' is not available.
-
-
-File: gsl-ref.info,  Node: GSL CBLAS Library,  Next: GNU General Public License,  Prev: Autoconf Macros,  Up: Top
-
-Appendix D GSL CBLAS Library
-****************************
-
-The prototypes for the low-level CBLAS functions are declared in the
-file 'gsl_cblas.h'.  For the definition of the functions consult the
-documentation available from Netlib (*note BLAS References and Further
-Reading::).
+The handling of these conditions is under user control.  The functions
+below allow the user to test the current estimate of the best-fit
+parameters in several standard ways.
 
-* Menu:
+ -- Function: int gsl_multifit_nlinear_test (const double XTOL, const
+          double GTOL, const double FTOL, int * INFO, const
+          gsl_multifit_nlinear_workspace * W)
+ -- Function: int gsl_multilarge_nlinear_test (const double XTOL, const
+          double GTOL, const double FTOL, int * INFO, const
+          gsl_multilarge_nlinear_workspace * W)
+     These functions test for convergence of the minimization method
+     using the following criteria:
+
+        * Testing for a small step size relative to the current
+          parameter vector
+               |\delta_i| <= xtol (|x_i| + xtol)
+          for each 0 <= i < p.  Each element of the step vector \delta
+          is tested individually in case the different parameters have
+          widely different scales.  Adding XTOL to |x_i| helps the test
+          avoid breaking down in situations where the true solution
+          value x_i = 0.  If this test succeeds, INFO is set to 1 and
+          the function returns 'GSL_SUCCESS'.
+
+          A general guideline for selecting the step tolerance is to
+          choose xtol = 10^{-d} where d is the number of accurate
+          decimal digits desired in the solution x.  See Dennis and
+          Schnabel for more information.
+
+        * Testing for a small gradient (g = \nabla \Phi(x) = J^T f)
+          indicating a local function minimum:
+               ||g||_inf <= gtol
+          This expression tests whether the ratio (\nabla \Phi)_i x_i /
+          \Phi is small.  Testing this scaled gradient is a better than
+          \nabla \Phi alone since it is a dimensionless quantity and so
+          independent of the scale of the problem.  The 'max' arguments
+          help ensure the test doesn't break down in regions where x_i
+          or \Phi(x) are close to 0.  If this test succeeds, INFO is set
+          to 2 and the function returns 'GSL_SUCCESS'.
+
+          A general guideline for choosing the gradient tolerance is to
+          set 'gtol = GSL_DBL_EPSILON^(1/3)'.  See Dennis and Schnabel
+          for more information.
 
-* Level 1 CBLAS Functions::     
-* Level 2 CBLAS Functions::     
-* Level 3 CBLAS Functions::     
-* GSL CBLAS Examples::          
+     If none of the tests succeed, INFO is set to 0 and the function
+     returns 'GSL_CONTINUE', indicating further iterations are required.
 
 
-File: gsl-ref.info,  Node: Level 1 CBLAS Functions,  Next: Level 2 CBLAS Functions,  Up: GSL CBLAS Library
-
-D.1 Level 1
-===========
-
- -- Function: float cblas_sdsdot (const int N, const float ALPHA, const
-          float * X, const int INCX, const float * Y, const int INCY)
+File: gsl-ref.info,  Node: Nonlinear Least-Squares High Level Driver,  Next: Nonlinear Least-Squares Covariance Matrix,  Prev: Nonlinear Least-Squares Testing for Convergence,  Up: Nonlinear Least-Squares Fitting
 
- -- Function: double cblas_dsdot (const int N, const float * X, const
-          int INCX, const float * Y, const int INCY)
+39.9 High Level Driver
+======================
 
- -- Function: float cblas_sdot (const int N, const float * X, const int
-          INCX, const float * Y, const int INCY)
+These routines provide a high level wrapper that combines the iteration
+and convergence testing for easy use.
 
- -- Function: double cblas_ddot (const int N, const double * X, const
-          int INCX, const double * Y, const int INCY)
+ -- Function: int gsl_multifit_nlinear_driver (const size_t MAXITER,
+          const double XTOL, const double GTOL, const double FTOL, void
+          (* CALLBACK)(const size_t ITER, void * PARAMS, const
+          gsl_multifit_linear_workspace * W), void * CALLBACK_PARAMS,
+          int * INFO, gsl_multifit_nlinear_workspace * W)
+ -- Function: int gsl_multilarge_nlinear_driver (const size_t MAXITER,
+          const double XTOL, const double GTOL, const double FTOL, void
+          (* CALLBACK)(const size_t ITER, void * PARAMS, const
+          gsl_multilarge_linear_workspace * W), void * CALLBACK_PARAMS,
+          int * INFO, gsl_multilarge_nlinear_workspace * W)
+     These functions iterate the nonlinear least squares solver W for a
+     maximum of MAXITER iterations.  After each iteration, the system is
+     tested for convergence with the error tolerances XTOL, GTOL and
+     FTOL.  Additionally, the user may supply a callback function
+     CALLBACK which is called after each iteration, so that the user may
+     save or print relevant quantities for each iteration.  The
+     parameter CALLBACK_PARAMS is passed to the CALLBACK function.  The
+     parameters CALLBACK and CALLBACK_PARAMS may be set to NULL to
+     disable this feature.  Upon successful convergence, the function
+     returns 'GSL_SUCCESS' and sets INFO to the reason for convergence
+     (see 'gsl_multifit_nlinear_test').  If the function has not
+     converged after MAXITER iterations, 'GSL_EMAXITER' is returned.  In
+     rare cases, during an iteration the algorithm may be unable to find
+     a new acceptable step \delta to take.  In this case, 'GSL_ENOPROG'
+     is returned indicating no further progress can be made.  If your
+     problem is having difficulty converging, see *note Nonlinear
+     Least-Squares Troubleshooting:: for further guidance.
 
- -- Function: void cblas_cdotu_sub (const int N, const void * X, const
-          int INCX, const void * Y, const int INCY, void * DOTU)
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares Covariance Matrix,  Next: Nonlinear Least-Squares Troubleshooting,  Prev: Nonlinear Least-Squares High Level Driver,  Up: Nonlinear Least-Squares Fitting
 
- -- Function: void cblas_cdotc_sub (const int N, const void * X, const
-          int INCX, const void * Y, const int INCY, void * DOTC)
+39.10 Covariance matrix of best fit parameters
+==============================================
 
- -- Function: void cblas_zdotu_sub (const int N, const void * X, const
-          int INCX, const void * Y, const int INCY, void * DOTU)
+ -- Function: int gsl_multifit_nlinear_covar (const gsl_matrix * J,
+          const double EPSREL, gsl_matrix * COVAR)
+ -- Function: int gsl_multilarge_nlinear_covar (gsl_matrix * COVAR,
+          gsl_multilarge_nlinear_workspace * W)
+     This function computes the covariance matrix of best-fit parameters
+     using the Jacobian matrix J and stores it in COVAR.  The parameter
+     EPSREL is used to remove linear-dependent columns when J is rank
+     deficient.
 
- -- Function: void cblas_zdotc_sub (const int N, const void * X, const
-          int INCX, const void * Y, const int INCY, void * DOTC)
+     The covariance matrix is given by,
 
- -- Function: float cblas_snrm2 (const int N, const float * X, const int
-          INCX)
+          covar = (J^T J)^{-1}
 
- -- Function: float cblas_sasum (const int N, const float * X, const int
-          INCX)
+     or in the weighted case,
 
- -- Function: double cblas_dnrm2 (const int N, const double * X, const
-          int INCX)
+          covar = (J^T W J)^{-1}
 
- -- Function: double cblas_dasum (const int N, const double * X, const
-          int INCX)
+     and is computed using the factored form of the Jacobian (Cholesky,
+     QR, or SVD). Any columns of R which satisfy
 
- -- Function: float cblas_scnrm2 (const int N, const void * X, const int
-          INCX)
+          |R_{kk}| <= epsrel |R_{11}|
 
- -- Function: float cblas_scasum (const int N, const void * X, const int
-          INCX)
+     are considered linearly-dependent and are excluded from the
+     covariance matrix (the corresponding rows and columns of the
+     covariance matrix are set to zero).
 
- -- Function: double cblas_dznrm2 (const int N, const void * X, const
-          int INCX)
+     If the minimisation uses the weighted least-squares function f_i =
+     (Y(x, t_i) - y_i) / \sigma_i then the covariance matrix above gives
+     the statistical error on the best-fit parameters resulting from the
+     Gaussian errors \sigma_i on the underlying data y_i.  This can be
+     verified from the relation \delta f = J \delta c and the fact that
+     the fluctuations in f from the data y_i are normalised by \sigma_i
+     and so satisfy <\delta f \delta f^T> = I.
 
- -- Function: double cblas_dzasum (const int N, const void * X, const
-          int INCX)
+     For an unweighted least-squares function f_i = (Y(x, t_i) - y_i)
+     the covariance matrix above should be multiplied by the variance of
+     the residuals about the best-fit \sigma^2 = \sum (y_i - Y(x,t_i))^2
+     / (n-p) to give the variance-covariance matrix \sigma^2 C.  This
+     estimates the statistical error on the best-fit parameters from the
+     scatter of the underlying data.
 
- -- Function: CBLAS_INDEX cblas_isamax (const int N, const float * X,
-          const int INCX)
+     For more information about covariance matrices see *note Fitting
+     Overview::.
 
- -- Function: CBLAS_INDEX cblas_idamax (const int N, const double * X,
-          const int INCX)
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares Troubleshooting,  Next: Nonlinear Least-Squares Examples,  Prev: Nonlinear Least-Squares Covariance Matrix,  Up: Nonlinear Least-Squares Fitting
 
- -- Function: CBLAS_INDEX cblas_icamax (const int N, const void * X,
-          const int INCX)
+39.11 Troubleshooting
+=====================
 
- -- Function: CBLAS_INDEX cblas_izamax (const int N, const void * X,
-          const int INCX)
+When developing a code to solve a nonlinear least squares problem, here
+are a few considerations to keep in mind.
 
- -- Function: void cblas_sswap (const int N, float * X, const int INCX,
-          float * Y, const int INCY)
+  1. The most common difficulty is the accurate implementation of the
+     Jacobian matrix.  If the analytic Jacobian is not properly provided
+     to the solver, this can hinder and many times prevent convergence
+     of the method.  When developing a new nonlinear least squares code,
+     it often helps to compare the program output with the internally
+     computed finite difference Jacobian and the user supplied analytic
+     Jacobian.  If there is a large difference in coefficients, it is
+     likely the analytic Jacobian is incorrectly implemented.
+
+  2. If your code is having difficulty converging, the next thing to
+     check is the starting point provided to the solver.  The methods of
+     this chapter are local methods, meaning if you provide a starting
+     point far away from the true minimum, the method may converge to a
+     local minimum or not converge at all.  Sometimes it is possible to
+     solve a linearized approximation to the nonlinear problem, and use
+     the linear solution as the starting point to the nonlinear problem.
+
+  3. If the various parameters of the coefficient vector x vary widely
+     in magnitude, then the problem is said to be badly scaled.  The
+     methods of this chapter do attempt to automatically rescale the
+     elements of x to have roughly the same order of magnitude, but in
+     extreme cases this could still cause problems for convergence.  In
+     these cases it is recommended for the user to scale their parameter
+     vector x so that each parameter spans roughly the same range, say
+     [-1,1].  The solution vector can be backscaled to recover the
+     original units of the problem.
 
- -- Function: void cblas_scopy (const int N, const float * X, const int
-          INCX, float * Y, const int INCY)
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares Examples,  Next: Nonlinear Least-Squares References and Further Reading,  Prev: Nonlinear Least-Squares Troubleshooting,  Up: Nonlinear Least-Squares Fitting
 
- -- Function: void cblas_saxpy (const int N, const float ALPHA, const
-          float * X, const int INCX, float * Y, const int INCY)
+39.12 Examples
+==============
 
- -- Function: void cblas_dswap (const int N, double * X, const int INCX,
-          double * Y, const int INCY)
+The following example programs demonstrate the nonlinear least squares
+fitting capabilities.
 
- -- Function: void cblas_dcopy (const int N, const double * X, const int
-          INCX, double * Y, const int INCY)
+* Menu:
 
- -- Function: void cblas_daxpy (const int N, const double ALPHA, const
-          double * X, const int INCX, double * Y, const int INCY)
+* Nonlinear Least-Squares Exponential Fit Example::
+* Nonlinear Least-Squares Geodesic Acceleration Example::
+* Nonlinear Least-Squares Comparison Example::
+* Nonlinear Least-Squares Large Example::
 
- -- Function: void cblas_cswap (const int N, void * X, const int INCX,
-          void * Y, const int INCY)
+
+File: gsl-ref.info,  Node: Nonlinear Least-Squares Exponential Fit Example,  Next: Nonlinear Least-Squares Geodesic Acceleration Example,  Up: Nonlinear Least-Squares Examples
 
- -- Function: void cblas_ccopy (const int N, const void * X, const int
-          INCX, void * Y, const int INCY)
+39.12.1 Exponential Fitting Example
+-----------------------------------
 
- -- Function: void cblas_caxpy (const int N, const void * ALPHA, const
-          void * X, const int INCX, void * Y, const int INCY)
+The following example program fits a weighted exponential model with
+background to experimental data, Y = A \exp(-\lambda t) + b.  The first
+part of the program sets up the functions 'expb_f' and 'expb_df' to
+calculate the model and its Jacobian.  The appropriate fitting function
+is given by,
 
- -- Function: void cblas_zswap (const int N, void * X, const int INCX,
-          void * Y, const int INCY)
+     f_i = (A \exp(-\lambda t_i) + b) - y_i
 
- -- Function: void cblas_zcopy (const int N, const void * X, const int
-          INCX, void * Y, const int INCY)
+where we have chosen t_i = i.  The Jacobian matrix J is the derivative
+of these functions with respect to the three parameters (A, \lambda, b).
+It is given by,
 
- -- Function: void cblas_zaxpy (const int N, const void * ALPHA, const
-          void * X, const int INCX, void * Y, const int INCY)
+     J_{ij} = d f_i / d x_j
 
- -- Function: void cblas_srotg (float * A, float * B, float * C, float *
-          S)
+where x_0 = A, x_1 = \lambda and x_2 = b.  The ith row of the Jacobian
+is therefore
 
- -- Function: void cblas_srotmg (float * D1, float * D2, float * B1,
-          const float B2, float * P)
+The main part of the program sets up a Levenberg-Marquardt solver and
+some simulated random data.  The data uses the known parameters
+(5.0,0.1,1.0) combined with Gaussian noise (standard deviation = 0.1)
+over a range of 40 timesteps.  The initial guess for the parameters is
+chosen as (1.0, 1.0, 0.0).  The iteration terminates when the relative
+change in x is smaller than 10^{-8}, or when the magnitude of the
+gradient falls below 10^{-8}.  Here are the results of running the
+program:
+
+     iter  0: A = 1.0000, lambda = 1.0000, b = 0.0000, cond(J) =      inf, |f(x)| = 62.2029
+     iter  1: A = 1.2196, lambda = 0.3663, b = 0.0436, cond(J) =  53.6368, |f(x)| = 59.8062
+     iter  2: A = 1.6062, lambda = 0.1506, b = 0.1054, cond(J) =  23.8178, |f(x)| = 53.9039
+     iter  3: A = 2.4528, lambda = 0.0583, b = 0.2470, cond(J) =  20.0493, |f(x)| = 28.8039
+     iter  4: A = 2.9723, lambda = 0.0494, b = 0.3727, cond(J) =  94.5601, |f(x)| = 15.3252
+     iter  5: A = 3.3473, lambda = 0.0477, b = 0.4410, cond(J) = 229.3627, |f(x)| = 10.7511
+     iter  6: A = 3.6690, lambda = 0.0508, b = 0.4617, cond(J) = 298.3589, |f(x)| = 9.7373
+     iter  7: A = 3.9907, lambda = 0.0580, b = 0.5433, cond(J) = 250.0194, |f(x)| = 8.7661
+     iter  8: A = 4.2353, lambda = 0.0731, b = 0.7989, cond(J) = 154.8571, |f(x)| = 7.4299
+     iter  9: A = 4.6573, lambda = 0.0958, b = 1.0302, cond(J) = 140.2265, |f(x)| = 6.1893
+     iter 10: A = 5.0138, lambda = 0.1060, b = 1.0329, cond(J) = 109.4141, |f(x)| = 5.4961
+     iter 11: A = 5.1505, lambda = 0.1103, b = 1.0497, cond(J) = 100.8762, |f(x)| = 5.4552
+     iter 12: A = 5.1724, lambda = 0.1110, b = 1.0526, cond(J) =  97.3403, |f(x)| = 5.4542
+     iter 13: A = 5.1737, lambda = 0.1110, b = 1.0528, cond(J) =  96.7136, |f(x)| = 5.4542
+     iter 14: A = 5.1738, lambda = 0.1110, b = 1.0528, cond(J) =  96.6678, |f(x)| = 5.4542
+     iter 15: A = 5.1738, lambda = 0.1110, b = 1.0528, cond(J) =  96.6663, |f(x)| = 5.4542
+     iter 16: A = 5.1738, lambda = 0.1110, b = 1.0528, cond(J) =  96.6663, |f(x)| = 5.4542
+     summary from method 'trust-region/levenberg-marquardt'
+     number of iterations: 16
+     function evaluations: 23
+     Jacobian evaluations: 17
+     reason for stopping: small step size
+     initial |f(x)| = 62.202928
+     final   |f(x)| = 5.454180
+     chisq/dof = 0.804002
+     A      = 5.17379 +/- 0.27938
+     lambda = 0.11104 +/- 0.00817
+     b      = 1.05283 +/- 0.05365
+     status = success
 
- -- Function: void cblas_srot (const int N, float * X, const int INCX,
-          float * Y, const int INCY, const float C, const float S)
+The approximate values of the parameters are found correctly, and the
+chi-squared value indicates a good fit (the chi-squared per degree of
+freedom is approximately 1).  In this case the errors on the parameters
+can be estimated from the square roots of the diagonal elements of the
+covariance matrix.  If the chi-squared value shows a poor fit (i.e.
+chi^2/dof >> 1) then the error estimates obtained from the covariance
+matrix will be too small.  In the example program the error estimates
+are multiplied by \sqrt{\chi^2/dof} in this case, a common way of
+increasing the errors for a poor fit.  Note that a poor fit will result
+from the use of an inappropriate model, and the scaled error estimates
+may then be outside the range of validity for Gaussian errors.
+
+Additionally, we see that the condition number of J(x) stays reasonably
+small throughout the iteration.  This indicates we could safely switch
+to the Cholesky solver for speed improvement, although this particular
+system is too small to really benefit.
 
- -- Function: void cblas_srotm (const int N, float * X, const int INCX,
-          float * Y, const int INCY, const float * P)
+     #include <stdlib.h>
+     #include <stdio.h>
+     #include <gsl/gsl_rng.h>
+     #include <gsl/gsl_randist.h>
+     #include <gsl/gsl_matrix.h>
+     #include <gsl/gsl_vector.h>
+     #include <gsl/gsl_blas.h>
+     #include <gsl/gsl_multifit_nlinear.h>
 
- -- Function: void cblas_drotg (double * A, double * B, double * C,
-          double * S)
-
- -- Function: void cblas_drotmg (double * D1, double * D2, double * B1,
-          const double B2, double * P)
-
- -- Function: void cblas_drot (const int N, double * X, const int INCX,
-          double * Y, const int INCY, const double C, const double S)
-
- -- Function: void cblas_drotm (const int N, double * X, const int INCX,
-          double * Y, const int INCY, const double * P)
-
- -- Function: void cblas_sscal (const int N, const float ALPHA, float *
-          X, const int INCX)
-
- -- Function: void cblas_dscal (const int N, const double ALPHA, double
-          * X, const int INCX)
-
- -- Function: void cblas_cscal (const int N, const void * ALPHA, void *
-          X, const int INCX)
-
- -- Function: void cblas_zscal (const int N, const void * ALPHA, void *
-          X, const int INCX)
-
- -- Function: void cblas_csscal (const int N, const float ALPHA, void *
-          X, const int INCX)
-
- -- Function: void cblas_zdscal (const int N, const double ALPHA, void *
-          X, const int INCX)
-
-
-File: gsl-ref.info,  Node: Level 2 CBLAS Functions,  Next: Level 3 CBLAS Functions,  Prev: Level 1 CBLAS Functions,  Up: GSL CBLAS Library
-
-D.2 Level 2
-===========
-
- -- Function: void cblas_sgemv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_TRANSPOSE TRANSA, const int M, const int N, const float
-          ALPHA, const float * A, const int LDA, const float * X, const
-          int INCX, const float BETA, float * Y, const int INCY)
-
- -- Function: void cblas_sgbmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_TRANSPOSE TRANSA, const int M, const int N, const int
-          KL, const int KU, const float ALPHA, const float * A, const
-          int LDA, const float * X, const int INCX, const float BETA,
-          float * Y, const int INCY)
-
- -- Function: void cblas_strmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const float * A, const int LDA,
-          float * X, const int INCX)
-
- -- Function: void cblas_stbmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const int K, const float * A,
-          const int LDA, float * X, const int INCX)
-
- -- Function: void cblas_stpmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const float * AP, float * X,
-          const int INCX)
-
- -- Function: void cblas_strsv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const float * A, const int LDA,
-          float * X, const int INCX)
-
- -- Function: void cblas_stbsv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const int K, const float * A,
-          const int LDA, float * X, const int INCX)
-
- -- Function: void cblas_stpsv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const float * AP, float * X,
-          const int INCX)
-
- -- Function: void cblas_dgemv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_TRANSPOSE TRANSA, const int M, const int N, const double
-          ALPHA, const double * A, const int LDA, const double * X,
-          const int INCX, const double BETA, double * Y, const int INCY)
-
- -- Function: void cblas_dgbmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_TRANSPOSE TRANSA, const int M, const int N, const int
-          KL, const int KU, const double ALPHA, const double * A, const
-          int LDA, const double * X, const int INCX, const double BETA,
-          double * Y, const int INCY)
-
- -- Function: void cblas_dtrmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const double * A, const int LDA,
-          double * X, const int INCX)
-
- -- Function: void cblas_dtbmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const int K, const double * A,
-          const int LDA, double * X, const int INCX)
-
- -- Function: void cblas_dtpmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const double * AP, double * X,
-          const int INCX)
-
- -- Function: void cblas_dtrsv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const double * A, const int LDA,
-          double * X, const int INCX)
-
- -- Function: void cblas_dtbsv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const int K, const double * A,
-          const int LDA, double * X, const int INCX)
-
- -- Function: void cblas_dtpsv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const double * AP, double * X,
-          const int INCX)
-
- -- Function: void cblas_cgemv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_TRANSPOSE TRANSA, const int M, const int N, const void *
-          ALPHA, const void * A, const int LDA, const void * X, const
-          int INCX, const void * BETA, void * Y, const int INCY)
-
- -- Function: void cblas_cgbmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_TRANSPOSE TRANSA, const int M, const int N, const int
-          KL, const int KU, const void * ALPHA, const void * A, const
-          int LDA, const void * X, const int INCX, const void * BETA,
-          void * Y, const int INCY)
-
- -- Function: void cblas_ctrmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const void * A, const int LDA,
-          void * X, const int INCX)
-
- -- Function: void cblas_ctbmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const int K, const void * A,
-          const int LDA, void * X, const int INCX)
-
- -- Function: void cblas_ctpmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const void * AP, void * X, const
-          int INCX)
-
- -- Function: void cblas_ctrsv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const void * A, const int LDA,
-          void * X, const int INCX)
-
- -- Function: void cblas_ctbsv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const int K, const void * A,
-          const int LDA, void * X, const int INCX)
-
- -- Function: void cblas_ctpsv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const void * AP, void * X, const
-          int INCX)
-
- -- Function: void cblas_zgemv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_TRANSPOSE TRANSA, const int M, const int N, const void *
-          ALPHA, const void * A, const int LDA, const void * X, const
-          int INCX, const void * BETA, void * Y, const int INCY)
-
- -- Function: void cblas_zgbmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_TRANSPOSE TRANSA, const int M, const int N, const int
-          KL, const int KU, const void * ALPHA, const void * A, const
-          int LDA, const void * X, const int INCX, const void * BETA,
-          void * Y, const int INCY)
-
- -- Function: void cblas_ztrmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const void * A, const int LDA,
-          void * X, const int INCX)
-
- -- Function: void cblas_ztbmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const int K, const void * A,
-          const int LDA, void * X, const int INCX)
-
- -- Function: void cblas_ztpmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const void * AP, void * X, const
-          int INCX)
-
- -- Function: void cblas_ztrsv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const void * A, const int LDA,
-          void * X, const int INCX)
-
- -- Function: void cblas_ztbsv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const int K, const void * A,
-          const int LDA, void * X, const int INCX)
-
- -- Function: void cblas_ztpsv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANSA, const enum
-          CBLAS_DIAG DIAG, const int N, const void * AP, void * X, const
-          int INCX)
-
- -- Function: void cblas_ssymv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const float ALPHA, const float *
-          A, const int LDA, const float * X, const int INCX, const float
-          BETA, float * Y, const int INCY)
-
- -- Function: void cblas_ssbmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const int K, const float ALPHA,
-          const float * A, const int LDA, const float * X, const int
-          INCX, const float BETA, float * Y, const int INCY)
-
- -- Function: void cblas_sspmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const float ALPHA, const float *
-          AP, const float * X, const int INCX, const float BETA, float *
-          Y, const int INCY)
-
- -- Function: void cblas_sger (const enum CBLAS_ORDER ORDER, const int
-          M, const int N, const float ALPHA, const float * X, const int
-          INCX, const float * Y, const int INCY, float * A, const int
-          LDA)
-
- -- Function: void cblas_ssyr (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const float ALPHA, const float *
-          X, const int INCX, float * A, const int LDA)
-
- -- Function: void cblas_sspr (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const float ALPHA, const float *
-          X, const int INCX, float * AP)
-
- -- Function: void cblas_ssyr2 (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const float ALPHA, const float *
-          X, const int INCX, const float * Y, const int INCY, float * A,
-          const int LDA)
-
- -- Function: void cblas_sspr2 (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const float ALPHA, const float *
-          X, const int INCX, const float * Y, const int INCY, float * A)
-
- -- Function: void cblas_dsymv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const double ALPHA, const double
-          * A, const int LDA, const double * X, const int INCX, const
-          double BETA, double * Y, const int INCY)
-
- -- Function: void cblas_dsbmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const int K, const double ALPHA,
-          const double * A, const int LDA, const double * X, const int
-          INCX, const double BETA, double * Y, const int INCY)
-
- -- Function: void cblas_dspmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const double ALPHA, const double
-          * AP, const double * X, const int INCX, const double BETA,
-          double * Y, const int INCY)
-
- -- Function: void cblas_dger (const enum CBLAS_ORDER ORDER, const int
-          M, const int N, const double ALPHA, const double * X, const
-          int INCX, const double * Y, const int INCY, double * A, const
-          int LDA)
-
- -- Function: void cblas_dsyr (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const double ALPHA, const double
-          * X, const int INCX, double * A, const int LDA)
-
- -- Function: void cblas_dspr (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const double ALPHA, const double
-          * X, const int INCX, double * AP)
-
- -- Function: void cblas_dsyr2 (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const double ALPHA, const double
-          * X, const int INCX, const double * Y, const int INCY, double
-          * A, const int LDA)
-
- -- Function: void cblas_dspr2 (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const double ALPHA, const double
-          * X, const int INCX, const double * Y, const int INCY, double
-          * A)
-
- -- Function: void cblas_chemv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void *
-          A, const int LDA, const void * X, const int INCX, const void *
-          BETA, void * Y, const int INCY)
-
- -- Function: void cblas_chbmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const int K, const void * ALPHA,
-          const void * A, const int LDA, const void * X, const int INCX,
-          const void * BETA, void * Y, const int INCY)
-
- -- Function: void cblas_chpmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void *
-          AP, const void * X, const int INCX, const void * BETA, void *
-          Y, const int INCY)
-
- -- Function: void cblas_cgeru (const enum CBLAS_ORDER ORDER, const int
-          M, const int N, const void * ALPHA, const void * X, const int
-          INCX, const void * Y, const int INCY, void * A, const int LDA)
-
- -- Function: void cblas_cgerc (const enum CBLAS_ORDER ORDER, const int
-          M, const int N, const void * ALPHA, const void * X, const int
-          INCX, const void * Y, const int INCY, void * A, const int LDA)
-
- -- Function: void cblas_cher (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const float ALPHA, const void *
-          X, const int INCX, void * A, const int LDA)
-
- -- Function: void cblas_chpr (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const float ALPHA, const void *
-          X, const int INCX, void * A)
-
- -- Function: void cblas_cher2 (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void *
-          X, const int INCX, const void * Y, const int INCY, void * A,
-          const int LDA)
-
- -- Function: void cblas_chpr2 (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void *
-          X, const int INCX, const void * Y, const int INCY, void * AP)
-
- -- Function: void cblas_zhemv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void *
-          A, const int LDA, const void * X, const int INCX, const void *
-          BETA, void * Y, const int INCY)
-
- -- Function: void cblas_zhbmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const int K, const void * ALPHA,
-          const void * A, const int LDA, const void * X, const int INCX,
-          const void * BETA, void * Y, const int INCY)
-
- -- Function: void cblas_zhpmv (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void *
-          AP, const void * X, const int INCX, const void * BETA, void *
-          Y, const int INCY)
-
- -- Function: void cblas_zgeru (const enum CBLAS_ORDER ORDER, const int
-          M, const int N, const void * ALPHA, const void * X, const int
-          INCX, const void * Y, const int INCY, void * A, const int LDA)
-
- -- Function: void cblas_zgerc (const enum CBLAS_ORDER ORDER, const int
-          M, const int N, const void * ALPHA, const void * X, const int
-          INCX, const void * Y, const int INCY, void * A, const int LDA)
-
- -- Function: void cblas_zher (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const double ALPHA, const void *
-          X, const int INCX, void * A, const int LDA)
-
- -- Function: void cblas_zhpr (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const double ALPHA, const void *
-          X, const int INCX, void * A)
-
- -- Function: void cblas_zher2 (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void *
-          X, const int INCX, const void * Y, const int INCY, void * A,
-          const int LDA)
-
- -- Function: void cblas_zhpr2 (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const int N, const void * ALPHA, const void *
-          X, const int INCX, const void * Y, const int INCY, void * AP)
-
-
-File: gsl-ref.info,  Node: Level 3 CBLAS Functions,  Next: GSL CBLAS Examples,  Prev: Level 2 CBLAS Functions,  Up: GSL CBLAS Library
-
-D.3 Level 3
-===========
-
- -- Function: void cblas_sgemm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_TRANSPOSE TRANSA, const enum CBLAS_TRANSPOSE TRANSB,
-          const int M, const int N, const int K, const float ALPHA,
-          const float * A, const int LDA, const float * B, const int
-          LDB, const float BETA, float * C, const int LDC)
-
- -- Function: void cblas_ssymm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const int M,
-          const int N, const float ALPHA, const float * A, const int
-          LDA, const float * B, const int LDB, const float BETA, float *
-          C, const int LDC)
-
- -- Function: void cblas_ssyrk (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int
-          N, const int K, const float ALPHA, const float * A, const int
-          LDA, const float BETA, float * C, const int LDC)
-
- -- Function: void cblas_ssyr2k (const enum CBLAS_ORDER ORDER, const
-          enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const
-          int N, const int K, const float ALPHA, const float * A, const
-          int LDA, const float * B, const int LDB, const float BETA,
-          float * C, const int LDC)
-
- -- Function: void cblas_strmm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum
-          CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int
-          M, const int N, const float ALPHA, const float * A, const int
-          LDA, float * B, const int LDB)
-
- -- Function: void cblas_strsm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum
-          CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int
-          M, const int N, const float ALPHA, const float * A, const int
-          LDA, float * B, const int LDB)
-
- -- Function: void cblas_dgemm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_TRANSPOSE TRANSA, const enum CBLAS_TRANSPOSE TRANSB,
-          const int M, const int N, const int K, const double ALPHA,
-          const double * A, const int LDA, const double * B, const int
-          LDB, const double BETA, double * C, const int LDC)
-
- -- Function: void cblas_dsymm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const int M,
-          const int N, const double ALPHA, const double * A, const int
-          LDA, const double * B, const int LDB, const double BETA,
-          double * C, const int LDC)
-
- -- Function: void cblas_dsyrk (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int
-          N, const int K, const double ALPHA, const double * A, const
-          int LDA, const double BETA, double * C, const int LDC)
-
- -- Function: void cblas_dsyr2k (const enum CBLAS_ORDER ORDER, const
-          enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const
-          int N, const int K, const double ALPHA, const double * A,
-          const int LDA, const double * B, const int LDB, const double
-          BETA, double * C, const int LDC)
-
- -- Function: void cblas_dtrmm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum
-          CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int
-          M, const int N, const double ALPHA, const double * A, const
-          int LDA, double * B, const int LDB)
-
- -- Function: void cblas_dtrsm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum
-          CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int
-          M, const int N, const double ALPHA, const double * A, const
-          int LDA, double * B, const int LDB)
-
- -- Function: void cblas_cgemm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_TRANSPOSE TRANSA, const enum CBLAS_TRANSPOSE TRANSB,
-          const int M, const int N, const int K, const void * ALPHA,
-          const void * A, const int LDA, const void * B, const int LDB,
-          const void * BETA, void * C, const int LDC)
-
- -- Function: void cblas_csymm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const int M,
-          const int N, const void * ALPHA, const void * A, const int
-          LDA, const void * B, const int LDB, const void * BETA, void *
-          C, const int LDC)
-
- -- Function: void cblas_csyrk (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int
-          N, const int K, const void * ALPHA, const void * A, const int
-          LDA, const void * BETA, void * C, const int LDC)
-
- -- Function: void cblas_csyr2k (const enum CBLAS_ORDER ORDER, const
-          enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const
-          int N, const int K, const void * ALPHA, const void * A, const
-          int LDA, const void * B, const int LDB, const void * BETA,
-          void * C, const int LDC)
-
- -- Function: void cblas_ctrmm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum
-          CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int
-          M, const int N, const void * ALPHA, const void * A, const int
-          LDA, void * B, const int LDB)
-
- -- Function: void cblas_ctrsm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum
-          CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int
-          M, const int N, const void * ALPHA, const void * A, const int
-          LDA, void * B, const int LDB)
-
- -- Function: void cblas_zgemm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_TRANSPOSE TRANSA, const enum CBLAS_TRANSPOSE TRANSB,
-          const int M, const int N, const int K, const void * ALPHA,
-          const void * A, const int LDA, const void * B, const int LDB,
-          const void * BETA, void * C, const int LDC)
-
- -- Function: void cblas_zsymm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const int M,
-          const int N, const void * ALPHA, const void * A, const int
-          LDA, const void * B, const int LDB, const void * BETA, void *
-          C, const int LDC)
-
- -- Function: void cblas_zsyrk (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int
-          N, const int K, const void * ALPHA, const void * A, const int
-          LDA, const void * BETA, void * C, const int LDC)
-
- -- Function: void cblas_zsyr2k (const enum CBLAS_ORDER ORDER, const
-          enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const
-          int N, const int K, const void * ALPHA, const void * A, const
-          int LDA, const void * B, const int LDB, const void * BETA,
-          void * C, const int LDC)
-
- -- Function: void cblas_ztrmm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum
-          CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int
-          M, const int N, const void * ALPHA, const void * A, const int
-          LDA, void * B, const int LDB)
-
- -- Function: void cblas_ztrsm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const enum
-          CBLAS_TRANSPOSE TRANSA, const enum CBLAS_DIAG DIAG, const int
-          M, const int N, const void * ALPHA, const void * A, const int
-          LDA, void * B, const int LDB)
-
- -- Function: void cblas_chemm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const int M,
-          const int N, const void * ALPHA, const void * A, const int
-          LDA, const void * B, const int LDB, const void * BETA, void *
-          C, const int LDC)
-
- -- Function: void cblas_cherk (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int
-          N, const int K, const float ALPHA, const void * A, const int
-          LDA, const float BETA, void * C, const int LDC)
-
- -- Function: void cblas_cher2k (const enum CBLAS_ORDER ORDER, const
-          enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const
-          int N, const int K, const void * ALPHA, const void * A, const
-          int LDA, const void * B, const int LDB, const float BETA, void
-          * C, const int LDC)
-
- -- Function: void cblas_zhemm (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_SIDE SIDE, const enum CBLAS_UPLO UPLO, const int M,
-          const int N, const void * ALPHA, const void * A, const int
-          LDA, const void * B, const int LDB, const void * BETA, void *
-          C, const int LDC)
-
- -- Function: void cblas_zherk (const enum CBLAS_ORDER ORDER, const enum
-          CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const int
-          N, const int K, const double ALPHA, const void * A, const int
-          LDA, const double BETA, void * C, const int LDC)
-
- -- Function: void cblas_zher2k (const enum CBLAS_ORDER ORDER, const
-          enum CBLAS_UPLO UPLO, const enum CBLAS_TRANSPOSE TRANS, const
-          int N, const int K, const void * ALPHA, const void * A, const
-          int LDA, const void * B, const int LDB, const double BETA,
-          void * C, const int LDC)
+     /* number of data points to fit */
+     #define N 40
 
- -- Function: void cblas_xerbla (int P, const char * ROUT, const char *
-          FORM, ...)
+     struct data {
+       size_t n;
+       double * y;
+     };
 
-
-File: gsl-ref.info,  Node: GSL CBLAS Examples,  Prev: Level 3 CBLAS Functions,  Up: GSL CBLAS Library
+     int
+     expb_f (const gsl_vector * x, void *data,
+             gsl_vector * f)
+     {
+       size_t n = ((struct data *)data)->n;
+       double *y = ((struct data *)data)->y;
 
-D.4 Examples
-============
+       double A = gsl_vector_get (x, 0);
+       double lambda = gsl_vector_get (x, 1);
+       double b = gsl_vector_get (x, 2);
 
-The following program computes the product of two matrices using the
-Level-3 BLAS function SGEMM,
+       size_t i;
 
-     [ 0.11 0.12 0.13 ]  [ 1011 1012 ]     [ 367.76 368.12 ]
-     [ 0.21 0.22 0.23 ]  [ 1021 1022 ]  =  [ 674.06 674.72 ]
-                         [ 1031 1032 ]
-
-The matrices are stored in row major order but could be stored in column
-major order if the first argument of the call to 'cblas_sgemm' was
-changed to 'CblasColMajor'.
+       for (i = 0; i < n; i++)
+         {
+           /* Model Yi = A * exp(-lambda * i) + b */
+           double t = i;
+           double Yi = A * exp (-lambda * t) + b;
+           gsl_vector_set (f, i, Yi - y[i]);
+         }
 
-     #include <stdio.h>
-     #include <gsl/gsl_cblas.h>
+       return GSL_SUCCESS;
+     }
 
      int
-     main (void)
+     expb_df (const gsl_vector * x, void *data,
+              gsl_matrix * J)
      {
-       int lda = 3;
-
-       float A[] = { 0.11, 0.12, 0.13,
-                     0.21, 0.22, 0.23 };
-
-       int ldb = 2;
-
-       float B[] = { 1011, 1012,
-                     1021, 1022,
-                     1031, 1032 };
+       size_t n = ((struct data *)data)->n;
 
-       int ldc = 2;
+       double A = gsl_vector_get (x, 0);
+       double lambda = gsl_vector_get (x, 1);
 
-       float C[] = { 0.00, 0.00,
-                     0.00, 0.00 };
+       size_t i;
 
-       /* Compute C = A B */
+       for (i = 0; i < n; i++)
+         {
+           /* Jacobian matrix J(i,j) = dfi / dxj, */
+           /* where fi = (Yi - yi)/sigma[i],      */
+           /*       Yi = A * exp(-lambda * i) + b  */
+           /* and the xj are the parameters (A,lambda,b) */
+           double t = i;
+           double e = exp(-lambda * t);
+           gsl_matrix_set (J, i, 0, e);
+           gsl_matrix_set (J, i, 1, -t * A * e);
+           gsl_matrix_set (J, i, 2, 1.0);
+         }
+       return GSL_SUCCESS;
+     }
 
-       cblas_sgemm (CblasRowMajor,
-                    CblasNoTrans, CblasNoTrans, 2, 2, 3,
-                    1.0, A, lda, B, ldb, 0.0, C, ldc);
+     void
+     callback(const size_t iter, void *params,
+              const gsl_multifit_nlinear_workspace *w)
+     {
+       gsl_vector *f = gsl_multifit_nlinear_residual(w);
+       gsl_vector *x = gsl_multifit_nlinear_position(w);
+       double rcond;
 
-       printf ("[ %g, %g\n", C[0], C[1]);
-       printf ("  %g, %g ]\n", C[2], C[3]);
+       /* compute reciprocal condition number of J(x) */
+       gsl_multifit_nlinear_rcond(&rcond, w);
 
-       return 0;
+       fprintf(stderr, "iter %2zu: A = %.4f, lambda = %.4f, b = %.4f, cond(J) = %8.4f, |f(x)| = %.4f\n",
+               iter,
+               gsl_vector_get(x, 0),
+               gsl_vector_get(x, 1),
+               gsl_vector_get(x, 2),
+               1.0 / rcond,
+               gsl_blas_dnrm2(f));
      }
 
-To compile the program use the following command line,
+     int
+     main (void)
+     {
+       const gsl_multifit_nlinear_type *T = gsl_multifit_nlinear_trust;
+       gsl_multifit_nlinear_workspace *w;
+       gsl_multifit_nlinear_fdf fdf;
+       gsl_multifit_nlinear_parameters fdf_params =
+         gsl_multifit_nlinear_default_parameters();
+       const size_t n = N;
+       const size_t p = 3;
 
-     $ gcc -Wall demo.c -lgslcblas
+       gsl_vector *f;
+       gsl_matrix *J;
+       gsl_matrix *covar = gsl_matrix_alloc (p, p);
+       double y[N], weights[N];
+       struct data d = { n, y };
+       double x_init[3] = { 1.0, 1.0, 0.0 }; /* starting values */
+       gsl_vector_view x = gsl_vector_view_array (x_init, p);
+       gsl_vector_view wts = gsl_vector_view_array(weights, n);
+       gsl_rng * r;
+       double chisq, chisq0;
+       int status, info;
+       size_t i;
 
-There is no need to link with the main library '-lgsl' in this case as
-the CBLAS library is an independent unit.  Here is the output from the
-program,
+       const double xtol = 1e-8;
+       const double gtol = 1e-8;
+       const double ftol = 0.0;
 
-     $ ./a.out
-     [ 367.76, 368.12
-       674.06, 674.72 ]
+       gsl_rng_env_setup();
+       r = gsl_rng_alloc(gsl_rng_default);
 
-
-File: gsl-ref.info,  Node: GNU General Public License,  Next: GNU Free Documentation License,  Prev: GSL CBLAS Library,  Up: Top
+       /* define the function to be minimized */
+       fdf.f = expb_f;
+       fdf.df = expb_df;   /* set to NULL for finite-difference Jacobian */
+       fdf.fvv = NULL;     /* not using geodesic acceleration */
+       fdf.n = n;
+       fdf.p = p;
+       fdf.params = &d;
 
-GNU General Public License
-**************************
+       /* this is the data to be fitted */
+       for (i = 0; i < n; i++)
+         {
+           double t = i;
+           double yi = 1.0 + 5 * exp (-0.1 * t);
+           double si = 0.1 * yi;
+           double dy = gsl_ran_gaussian(r, si);
+
+           weights[i] = 1.0 / (si * si);
+           y[i] = yi + dy;
+           printf ("data: %zu %g %g\n", i, y[i], si);
+         };
 
-                        Version 3, 29 June 2007
-
-     Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
-
-     Everyone is permitted to copy and distribute verbatim copies of this
-     license document, but changing it is not allowed.
-
-Preamble
-========
-
-The GNU General Public License is a free, copyleft license for software
-and other kinds of works.
-
-   The licenses for most software and other practical works are designed
-to take away your freedom to share and change the works.  By contrast,
-the GNU General Public License is intended to guarantee your freedom to
-share and change all versions of a program-to make sure it remains free
-software for all its users.  We, the Free Software Foundation, use the
-GNU General Public License for most of our software; it applies also to
-any other work released this way by its authors.  You can apply it to
-your programs, too.
-
-   When we speak of free software, we are referring to freedom, not
-price.  Our General Public Licenses are designed to make sure that you
-have the freedom to distribute copies of free software (and charge for
-them if you wish), that you receive source code or can get it if you
-want it, that you can change the software or use pieces of it in new
-free programs, and that you know you can do these things.
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-   To protect your rights, we need to prevent others from denying you
-these rights or asking you to surrender the rights.  Therefore, you have
-certain responsibilities if you distribute copies of the software, or if
-you modify it: responsibilities to respect the freedom of others.
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-   For example, if you distribute copies of such a program, whether
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-freedoms that you received.  You must make sure that they, too, receive
-or can get the source code.  And you must show them these terms so they
-know their rights.
-
-   Developers that use the GNU GPL protect your rights with two steps:
-(1) assert copyright on the software, and (2) offer you this License
-giving you legal permission to copy, distribute and/or modify it.
-
-   For the developers' and authors' protection, the GPL clearly explains
-that there is no warranty for this free software.  For both users' and
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-authors of previous versions.
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-   Some devices are designed to deny users access to install or run
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-
-   Finally, every program is threatened constantly by software patents.
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+       /* allocate workspace with default parameters */
+       w = gsl_multifit_nlinear_alloc (T, &fdf_params, n, p);
 
-   The precise terms and conditions for copying, distribution and
-modification follow.
+       /* initialize solver with starting point and weights */
+       gsl_multifit_nlinear_winit (&x.vector, &wts.vector, &fdf, w);
 
-TERMS AND CONDITIONS
-====================
+       /* compute initial cost function */
+       f = gsl_multifit_nlinear_residual(w);
+       gsl_blas_ddot(f, f, &chisq0);
 
-  0. Definitions.
+       /* solve the system with a maximum of 20 iterations */
+       status = gsl_multifit_nlinear_driver(20, xtol, gtol, ftol,
+                                            callback, NULL, &info, w);
 
-     "This License" refers to version 3 of the GNU General Public
-     License.
+       /* compute covariance of best fit parameters */
+       J = gsl_multifit_nlinear_jac(w);
+       gsl_multifit_nlinear_covar (J, 0.0, covar);
 
-     "Copyright" also means copyright-like laws that apply to other
-     kinds of works, such as semiconductor masks.
+       /* compute final cost */
+       gsl_blas_ddot(f, f, &chisq);
 
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+     #define FIT(i) gsl_vector_get(w->x, i)
+     #define ERR(i) sqrt(gsl_matrix_get(covar,i,i))
 
-END OF TERMS AND CONDITIONS
-===========================
+       fprintf(stderr, "summary from method '%s/%s'\n",
+               gsl_multifit_nlinear_name(w),
+               gsl_multifit_nlinear_trs_name(w));
+       fprintf(stderr, "number of iterations: %zu\n",
+               gsl_multifit_nlinear_niter(w));
+       fprintf(stderr, "function evaluations: %zu\n", fdf.nevalf);
+       fprintf(stderr, "Jacobian evaluations: %zu\n", fdf.nevaldf);
+       fprintf(stderr, "reason for stopping: %s\n",
+               (info == 1) ? "small step size" : "small gradient");
+       fprintf(stderr, "initial |f(x)| = %f\n", sqrt(chisq0));
+       fprintf(stderr, "final   |f(x)| = %f\n", sqrt(chisq));
 
-How to Apply These Terms to Your New Programs
-=============================================
+       {
+         double dof = n - p;
+         double c = GSL_MAX_DBL(1, sqrt(chisq / dof));
 
-If you develop a new program, and you want it to be of the greatest
-possible use to the public, the best way to achieve this is to make it
-free software which everyone can redistribute and change under these
-terms.
-
-   To do so, attach the following notices to the program.  It is safest
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-"copyright" line and a pointer to where the full notice is found.
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-     Copyright (C) YEAR NAME OF AUTHOR
-
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-
-   Also add information on how to contact you by electronic and paper
-mail.
-
-   If the program does terminal interaction, make it output a short
-notice like this when it starts in an interactive mode:
-
-     PROGRAM Copyright (C) YEAR NAME OF AUTHOR
-     This program comes with ABSOLUTELY NO WARRANTY; for details type 'show w'.
-     This is free software, and you are welcome to redistribute it
-     under certain conditions; type 'show c' for details.
-
-   The hypothetical commands 'show w' and 'show c' should show the
-appropriate parts of the General Public License.  Of course, your
-program's commands might be different; for a GUI interface, you would
-use an "about box".
-
-   You should also get your employer (if you work as a programmer) or
-school, if any, to sign a "copyright disclaimer" for the program, if
-necessary.  For more information on this, and how to apply and follow
-the GNU GPL, see <http://www.gnu.org/licenses/>.
-
-   The GNU General Public License does not permit incorporating your
-program into proprietary programs.  If your program is a subroutine
-library, you may consider it more useful to permit linking proprietary
-applications with the library.  If this is what you want to do, use the
-GNU Lesser General Public License instead of this License.  But first,
-please read <http://www.gnu.org/philosophy/why-not-lgpl.html>.
-
-
-File: gsl-ref.info,  Node: GNU Free Documentation License,  Next: Function Index,  Prev: GNU General Public License,  Up: Top
-
-GNU Free Documentation License
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-     Document means that it remains a section "Entitled XYZ" according
-     to this definition.
-
-     The Document may include Warranty Disclaimers next to the notice
-     which states that this License applies to the Document.  These
-     Warranty Disclaimers are considered to be included by reference in
-     this License, but only as regards disclaiming warranties: any other
-     implication that these Warranty Disclaimers may have is void and
-     has no effect on the meaning of this License.
-
-  2. VERBATIM COPYING
-
-     You may copy and distribute the Document in any medium, either
-     commercially or noncommercially, provided that this License, the
-     copyright notices, and the license notice saying this License
-     applies to the Document are reproduced in all copies, and that you
-     add no other conditions whatsoever to those of this License.  You
-     may not use technical measures to obstruct or control the reading
-     or further copying of the copies you make or distribute.  However,
-     you may accept compensation in exchange for copies.  If you
-     distribute a large enough number of copies you must also follow the
-     conditions in section 3.
-
-     You may also lend copies, under the same conditions stated above,
-     and you may publicly display copies.
-
-  3. COPYING IN QUANTITY
-
-     If you publish printed copies (or copies in media that commonly
-     have printed covers) of the Document, numbering more than 100, and
-     the Document's license notice requires Cover Texts, you must
-     enclose the copies in covers that carry, clearly and legibly, all
-     these Cover Texts: Front-Cover Texts on the front cover, and
-     Back-Cover Texts on the back cover.  Both covers must also clearly
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-     front cover must present the full title with all words of the title
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-     long as they preserve the title of the Document and satisfy these
-     conditions, can be treated as verbatim copying in other respects.
-
-     If the required texts for either cover are too voluminous to fit
-     legibly, you should put the first ones listed (as many as fit
-     reasonably) on the actual cover, and continue the rest onto
-     adjacent pages.
-
-     If you publish or distribute Opaque copies of the Document
-     numbering more than 100, you must either include a machine-readable
-     Transparent copy along with each Opaque copy, or state in or with
-     each Opaque copy a computer-network location from which the general
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-     reasonably prudent steps, when you begin distribution of Opaque
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-     year after the last time you distribute an Opaque copy (directly or
-     through your agents or retailers) of that edition to the public.
-
-     It is requested, but not required, that you contact the authors of
-     the Document well before redistributing any large number of copies,
-     to give them a chance to provide you with an updated version of the
-     Document.
-
-  4. MODIFICATIONS
-
-     You may copy and distribute a Modified Version of the Document
-     under the conditions of sections 2 and 3 above, provided that you
-     release the Modified Version under precisely this License, with the
-     Modified Version filling the role of the Document, thus licensing
-     distribution and modification of the Modified Version to whoever
-     possesses a copy of it.  In addition, you must do these things in
-     the Modified Version:
-
-       A. Use in the Title Page (and on the covers, if any) a title
-          distinct from that of the Document, and from those of previous
-          versions (which should, if there were any, be listed in the
-          History section of the Document).  You may use the same title
-          as a previous version if the original publisher of that
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-
-       B. List on the Title Page, as authors, one or more persons or
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-          the Modified Version, together with at least five of the
-          principal authors of the Document (all of its principal
-          authors, if it has fewer than five), unless they release you
-          from this requirement.
-
-       C. State on the Title page the name of the publisher of the
-          Modified Version, as the publisher.
-
-       D. Preserve all the copyright notices of the Document.
-
-       E. Add an appropriate copyright notice for your modifications
-          adjacent to the other copyright notices.
-
-       F. Include, immediately after the copyright notices, a license
-          notice giving the public permission to use the Modified
-          Version under the terms of this License, in the form shown in
-          the Addendum below.
-
-       G. Preserve in that license notice the full lists of Invariant
-          Sections and required Cover Texts given in the Document's
-          license notice.
-
-       H. Include an unaltered copy of this License.
-
-       I. Preserve the section Entitled "History", Preserve its Title,
-          and add to it an item stating at least the title, year, new
-          authors, and publisher of the Modified Version as given on the
-          Title Page.  If there is no section Entitled "History" in the
-          Document, create one stating the title, year, authors, and
-          publisher of the Document as given on its Title Page, then add
-          an item describing the Modified Version as stated in the
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-
-       J. Preserve the network location, if any, given in the Document
-          for public access to a Transparent copy of the Document, and
-          likewise the network locations given in the Document for
-          previous versions it was based on.  These may be placed in the
-          "History" section.  You may omit a network location for a work
-          that was published at least four years before the Document
-          itself, or if the original publisher of the version it refers
-          to gives permission.
-
-       K. For any section Entitled "Acknowledgements" or "Dedications",
-          Preserve the Title of the section, and preserve in the section
-          all the substance and tone of each of the contributor
-          acknowledgements and/or dedications given therein.
-
-       L. Preserve all the Invariant Sections of the Document, unaltered
-          in their text and in their titles.  Section numbers or the
-          equivalent are not considered part of the section titles.
-
-       M. Delete any section Entitled "Endorsements".  Such a section
-          may not be included in the Modified Version.
-
-       N. Do not retitle any existing section to be Entitled
-          "Endorsements" or to conflict in title with any Invariant
-          Section.
-
-       O. Preserve any Warranty Disclaimers.
-
-     If the Modified Version includes new front-matter sections or
-     appendices that qualify as Secondary Sections and contain no
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-     some or all of these sections as invariant.  To do this, add their
-     titles to the list of Invariant Sections in the Modified Version's
-     license notice.  These titles must be distinct from any other
-     section titles.
-
-     You may add a section Entitled "Endorsements", provided it contains
-     nothing but endorsements of your Modified Version by various
-     parties--for example, statements of peer review or that the text
-     has been approved by an organization as the authoritative
-     definition of a standard.
-
-     You may add a passage of up to five words as a Front-Cover Text,
-     and a passage of up to 25 words as a Back-Cover Text, to the end of
-     the list of Cover Texts in the Modified Version.  Only one passage
-     of Front-Cover Text and one of Back-Cover Text may be added by (or
-     through arrangements made by) any one entity.  If the Document
-     already includes a cover text for the same cover, previously added
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-     behalf of, you may not add another; but you may replace the old
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-     the old one.
-
-     The author(s) and publisher(s) of the Document do not by this
-     License give permission to use their names for publicity for or to
-     assert or imply endorsement of any Modified Version.
-
-  5. COMBINING DOCUMENTS
-
-     You may combine the Document with other documents released under
-     this License, under the terms defined in section 4 above for
-     modified versions, provided that you include in the combination all
-     of the Invariant Sections of all of the original documents,
-     unmodified, and list them all as Invariant Sections of your
-     combined work in its license notice, and that you preserve all
-     their Warranty Disclaimers.
-
-     The combined work need only contain one copy of this License, and
-     multiple identical Invariant Sections may be replaced with a single
-     copy.  If there are multiple Invariant Sections with the same name
-     but different contents, make the title of each such section unique
-     by adding at the end of it, in parentheses, the name of the
-     original author or publisher of that section if known, or else a
-     unique number.  Make the same adjustment to the section titles in
-     the list of Invariant Sections in the license notice of the
-     combined work.
-
-     In the combination, you must combine any sections Entitled
-     "History" in the various original documents, forming one section
-     Entitled "History"; likewise combine any sections Entitled
-     "Acknowledgements", and any sections Entitled "Dedications".  You
-     must delete all sections Entitled "Endorsements."
-
-  6. COLLECTIONS OF DOCUMENTS
-
-     You may make a collection consisting of the Document and other
-     documents released under this License, and replace the individual
-     copies of this License in the various documents with a single copy
-     that is included in the collection, provided that you follow the
-     rules of this License for verbatim copying of each of the documents
-     in all other respects.
-
-     You may extract a single document from such a collection, and
-     distribute it individually under this License, provided you insert
-     a copy of this License into the extracted document, and follow this
-     License in all other respects regarding verbatim copying of that
-     document.
-
-  7. AGGREGATION WITH INDEPENDENT WORKS
-
-     A compilation of the Document or its derivatives with other
-     separate and independent documents or works, in or on a volume of a
-     storage or distribution medium, is called an "aggregate" if the
-     copyright resulting from the compilation is not used to limit the
-     legal rights of the compilation's users beyond what the individual
-     works permit.  When the Document is included in an aggregate, this
-     License does not apply to the other works in the aggregate which
-     are not themselves derivative works of the Document.
-
-     If the Cover Text requirement of section 3 is applicable to these
-     copies of the Document, then if the Document is less than one half
-     of the entire aggregate, the Document's Cover Texts may be placed
-     on covers that bracket the Document within the aggregate, or the
-     electronic equivalent of covers if the Document is in electronic
-     form.  Otherwise they must appear on printed covers that bracket
-     the whole aggregate.
-
-  8. TRANSLATION
-
-     Translation is considered a kind of modification, so you may
-     distribute translations of the Document under the terms of section
-     4.  Replacing Invariant Sections with translations requires special
-     permission from their copyright holders, but you may include
-     translations of some or all Invariant Sections in addition to the
-     original versions of these Invariant Sections.  You may include a
-     translation of this License, and all the license notices in the
-     Document, and any Warranty Disclaimers, provided that you also
-     include the original English version of this License and the
-     original versions of those notices and disclaimers.  In case of a
-     disagreement between the translation and the original version of
-     this License or a notice or disclaimer, the original version will
-     prevail.
-
-     If a section in the Document is Entitled "Acknowledgements",
-     "Dedications", or "History", the requirement (section 4) to
-     Preserve its Title (section 1) will typically require changing the
-     actual title.
-
-  9. TERMINATION
-
-     You may not copy, modify, sublicense, or distribute the Document
-     except as expressly provided under this License.  Any attempt
-     otherwise to copy, modify, sublicense, or distribute it is void,
-     and will automatically terminate your rights under this License.
-
-     However, if you cease all violation of this License, then your
-     license from a particular copyright holder is reinstated (a)
-     provisionally, unless and until the copyright holder explicitly and
-     finally terminates your license, and (b) permanently, if the
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-     reasonable means prior to 60 days after the cessation.
-
-     Moreover, your license from a particular copyright holder is
-     reinstated permanently if the copyright holder notifies you of the
-     violation by some reasonable means, this is the first time you have
-     received notice of violation of this License (for any work) from
-     that copyright holder, and you cure the violation prior to 30 days
-     after your receipt of the notice.
-
-     Termination of your rights under this section does not terminate
-     the licenses of parties who have received copies or rights from you
-     under this License.  If your rights have been terminated and not
-     permanently reinstated, receipt of a copy of some or all of the
-     same material does not give you any rights to use it.
-
-  10. FUTURE REVISIONS OF THIS LICENSE
-
-     The Free Software Foundation may publish new, revised versions of
-     the GNU Free Documentation License from time to time.  Such new
-     versions will be similar in spirit to the present version, but may
-     differ in detail to address new problems or concerns.  See
-     <http://www.gnu.org/copyleft/>.
-
-     Each version of the License is given a distinguishing version
-     number.  If the Document specifies that a particular numbered
-     version of this License "or any later version" applies to it, you
-     have the option of following the terms and conditions either of
-     that specified version or of any later version that has been
-     published (not as a draft) by the Free Software Foundation.  If the
-     Document does not specify a version number of this License, you may
-     choose any version ever published (not as a draft) by the Free
-     Software Foundation.  If the Document specifies that a proxy can
-     decide which future versions of this License can be used, that
-     proxy's public statement of acceptance of a version permanently
-     authorizes you to choose that version for the Document.
-
-  11. RELICENSING
-
-     "Massive Multiauthor Collaboration Site" (or "MMC Site") means any
-     World Wide Web server that publishes copyrightable works and also
-     provides prominent facilities for anybody to edit those works.  A
-     public wiki that anybody can edit is an example of such a server.
-     A "Massive Multiauthor Collaboration" (or "MMC") contained in the
-     site means any set of copyrightable works thus published on the MMC
-     site.
-
-     "CC-BY-SA" means the Creative Commons Attribution-Share Alike 3.0
-     license published by Creative Commons Corporation, a not-for-profit
-     corporation with a principal place of business in San Francisco,
-     California, as well as future copyleft versions of that license
-     published by that same organization.
-
-     "Incorporate" means to publish or republish a Document, in whole or
-     in part, as part of another Document.
-
-     An MMC is "eligible for relicensing" if it is licensed under this
-     License, and if all works that were first published under this
-     License somewhere other than this MMC, and subsequently
-     incorporated in whole or in part into the MMC, (1) had no cover
-     texts or invariant sections, and (2) were thus incorporated prior
-     to November 1, 2008.
-
-     The operator of an MMC Site may republish an MMC contained in the
-     site under CC-BY-SA on the same site at any time before August 1,
-     2009, provided the MMC is eligible for relicensing.
-
-ADDENDUM: How to use this License for your documents
-====================================================
-
-To use this License in a document you have written, include a copy of
-the License in the document and put the following copyright and license
-notices just after the title page:
-
-       Copyright (C)  YEAR  YOUR NAME.
-       Permission is granted to copy, distribute and/or modify
-       this document under the terms of the GNU Free
-       Documentation License, Version 1.3 or any later version
-       published by the Free Software Foundation; with no
-       Invariant Sections, no Front-Cover Texts, and no
-       Back-Cover Texts.  A copy of the license is included in
-       the section entitled ``GNU Free Documentation License''.
-
-   If you have Invariant Sections, Front-Cover Texts and Back-Cover
-Texts, replace the "with...Texts."  line with this:
-
-       with the Invariant Sections being LIST THEIR
-       TITLES, with the Front-Cover Texts being LIST, and
-       with the Back-Cover Texts being LIST.
-
-   If you have Invariant Sections without Cover Texts, or some other
-combination of the three, merge those two alternatives to suit the
-situation.
-
-   If your document contains nontrivial examples of program code, we
-recommend releasing these examples in parallel under your choice of free
-software license, such as the GNU General Public License, to permit
-their use in free software.
+         fprintf(stderr, "chisq/dof = %g\n", chisq / dof);
 
-
-File: gsl-ref.info,  Node: Function Index,  Next: Variable Index,  Prev: GNU Free Documentation License,  Up: Top
+         fprintf (stderr, "A      = %.5f +/- %.5f\n", FIT(0), c*ERR(0));
+         fprintf (stderr, "lambda = %.5f +/- %.5f\n", FIT(1), c*ERR(1));
+         fprintf (stderr, "b      = %.5f +/- %.5f\n", FIT(2), c*ERR(2));
+       }
 
-Function Index
-**************
+       fprintf (stderr, "status = %s\n", gsl_strerror (status));
 
-[index]
-* Menu:
+       gsl_multifit_nlinear_free (w);
+       gsl_matrix_free (covar);
+       gsl_rng_free (r);
 
-* cblas_caxpy:                           Level 1 CBLAS Functions.
-                                                              (line  90)
-* cblas_ccopy:                           Level 1 CBLAS Functions.
-                                                              (line  87)
-* cblas_cdotc_sub:                       Level 1 CBLAS Functions.
-                                                              (line  21)
-* cblas_cdotu_sub:                       Level 1 CBLAS Functions.
-                                                              (line  18)
-* cblas_cgbmv:                           Level 2 CBLAS Functions.
-                                                              (line  93)
-* cblas_cgemm:                           Level 3 CBLAS Functions.
-                                                              (line  76)
-* cblas_cgemv:                           Level 2 CBLAS Functions.
-                                                              (line  88)
-* cblas_cgerc:                           Level 2 CBLAS Functions.
-                                                              (line 264)
-* cblas_cgeru:                           Level 2 CBLAS Functions.
-                                                              (line 260)
-* cblas_chbmv:                           Level 2 CBLAS Functions.
-                                                              (line 250)
-* cblas_chemm:                           Level 3 CBLAS Functions.
-                                                              (line 146)
-* cblas_chemv:                           Level 2 CBLAS Functions.
-                                                              (line 245)
-* cblas_cher:                            Level 2 CBLAS Functions.
-                                                              (line 268)
-* cblas_cher2:                           Level 2 CBLAS Functions.
-                                                              (line 276)
-* cblas_cher2k:                          Level 3 CBLAS Functions.
-                                                              (line 157)
-* cblas_cherk:                           Level 3 CBLAS Functions.
-                                                              (line 152)
-* cblas_chpmv:                           Level 2 CBLAS Functions.
-                                                              (line 255)
-* cblas_chpr:                            Level 2 CBLAS Functions.
-                                                              (line 272)
-* cblas_chpr2:                           Level 2 CBLAS Functions.
-                                                              (line 281)
-* cblas_cscal:                           Level 1 CBLAS Functions.
-                                                              (line 132)
-* cblas_csscal:                          Level 1 CBLAS Functions.
-                                                              (line 138)
-* cblas_cswap:                           Level 1 CBLAS Functions.
-                                                              (line  84)
-* cblas_csymm:                           Level 3 CBLAS Functions.
-                                                              (line  82)
-* cblas_csyr2k:                          Level 3 CBLAS Functions.
-                                                              (line  93)
-* cblas_csyrk:                           Level 3 CBLAS Functions.
-                                                              (line  88)
-* cblas_ctbmv:                           Level 2 CBLAS Functions.
-                                                              (line 104)
-* cblas_ctbsv:                           Level 2 CBLAS Functions.
-                                                              (line 119)
-* cblas_ctpmv:                           Level 2 CBLAS Functions.
-                                                              (line 109)
-* cblas_ctpsv:                           Level 2 CBLAS Functions.
-                                                              (line 124)
-* cblas_ctrmm:                           Level 3 CBLAS Functions.
-                                                              (line  99)
-* cblas_ctrmv:                           Level 2 CBLAS Functions.
-                                                              (line  99)
-* cblas_ctrsm:                           Level 3 CBLAS Functions.
-                                                              (line 105)
-* cblas_ctrsv:                           Level 2 CBLAS Functions.
-                                                              (line 114)
-* cblas_dasum:                           Level 1 CBLAS Functions.
-                                                              (line  39)
-* cblas_daxpy:                           Level 1 CBLAS Functions.
-                                                              (line  81)
-* cblas_dcopy:                           Level 1 CBLAS Functions.
-                                                              (line  78)
-* cblas_ddot:                            Level 1 CBLAS Functions.
-                                                              (line  15)
-* cblas_dgbmv:                           Level 2 CBLAS Functions.
-                                                              (line  52)
-* cblas_dgemm:                           Level 3 CBLAS Functions.
-                                                              (line  41)
-* cblas_dgemv:                           Level 2 CBLAS Functions.
-                                                              (line  47)
-* cblas_dger:                            Level 2 CBLAS Functions.
-                                                              (line 222)
-* cblas_dnrm2:                           Level 1 CBLAS Functions.
-                                                              (line  36)
-* cblas_drot:                            Level 1 CBLAS Functions.
-                                                              (line 120)
-* cblas_drotg:                           Level 1 CBLAS Functions.
-                                                              (line 114)
-* cblas_drotm:                           Level 1 CBLAS Functions.
-                                                              (line 123)
-* cblas_drotmg:                          Level 1 CBLAS Functions.
-                                                              (line 117)
-* cblas_dsbmv:                           Level 2 CBLAS Functions.
-                                                              (line 212)
-* cblas_dscal:                           Level 1 CBLAS Functions.
-                                                              (line 129)
-* cblas_dsdot:                           Level 1 CBLAS Functions.
-                                                              (line   9)
-* cblas_dspmv:                           Level 2 CBLAS Functions.
-                                                              (line 217)
-* cblas_dspr:                            Level 2 CBLAS Functions.
-                                                              (line 231)
-* cblas_dspr2:                           Level 2 CBLAS Functions.
-                                                              (line 240)
-* cblas_dswap:                           Level 1 CBLAS Functions.
-                                                              (line  75)
-* cblas_dsymm:                           Level 3 CBLAS Functions.
-                                                              (line  47)
-* cblas_dsymv:                           Level 2 CBLAS Functions.
-                                                              (line 207)
-* cblas_dsyr:                            Level 2 CBLAS Functions.
-                                                              (line 227)
-* cblas_dsyr2:                           Level 2 CBLAS Functions.
-                                                              (line 235)
-* cblas_dsyr2k:                          Level 3 CBLAS Functions.
-                                                              (line  58)
-* cblas_dsyrk:                           Level 3 CBLAS Functions.
-                                                              (line  53)
-* cblas_dtbmv:                           Level 2 CBLAS Functions.
-                                                              (line  63)
-* cblas_dtbsv:                           Level 2 CBLAS Functions.
-                                                              (line  78)
-* cblas_dtpmv:                           Level 2 CBLAS Functions.
-                                                              (line  68)
-* cblas_dtpsv:                           Level 2 CBLAS Functions.
-                                                              (line  83)
-* cblas_dtrmm:                           Level 3 CBLAS Functions.
-                                                              (line  64)
-* cblas_dtrmv:                           Level 2 CBLAS Functions.
-                                                              (line  58)
-* cblas_dtrsm:                           Level 3 CBLAS Functions.
-                                                              (line  70)
-* cblas_dtrsv:                           Level 2 CBLAS Functions.
-                                                              (line  73)
-* cblas_dzasum:                          Level 1 CBLAS Functions.
-                                                              (line  51)
-* cblas_dznrm2:                          Level 1 CBLAS Functions.
-                                                              (line  48)
-* cblas_icamax:                          Level 1 CBLAS Functions.
-                                                              (line  60)
-* cblas_idamax:                          Level 1 CBLAS Functions.
-                                                              (line  57)
-* cblas_isamax:                          Level 1 CBLAS Functions.
-                                                              (line  54)
-* cblas_izamax:                          Level 1 CBLAS Functions.
-                                                              (line  63)
-* cblas_sasum:                           Level 1 CBLAS Functions.
-                                                              (line  33)
-* cblas_saxpy:                           Level 1 CBLAS Functions.
-                                                              (line  72)
-* cblas_scasum:                          Level 1 CBLAS Functions.
-                                                              (line  45)
-* cblas_scnrm2:                          Level 1 CBLAS Functions.
-                                                              (line  42)
-* cblas_scopy:                           Level 1 CBLAS Functions.
-                                                              (line  69)
-* cblas_sdot:                            Level 1 CBLAS Functions.
-                                                              (line  12)
-* cblas_sdsdot:                          Level 1 CBLAS Functions.
-                                                              (line   6)
-* cblas_sgbmv:                           Level 2 CBLAS Functions.
-                                                              (line  11)
-* cblas_sgemm:                           Level 3 CBLAS Functions.
-                                                              (line   6)
-* cblas_sgemv:                           Level 2 CBLAS Functions.
-                                                              (line   6)
-* cblas_sger:                            Level 2 CBLAS Functions.
-                                                              (line 185)
-* cblas_snrm2:                           Level 1 CBLAS Functions.
-                                                              (line  30)
-* cblas_srot:                            Level 1 CBLAS Functions.
-                                                              (line 108)
-* cblas_srotg:                           Level 1 CBLAS Functions.
-                                                              (line 102)
-* cblas_srotm:                           Level 1 CBLAS Functions.
-                                                              (line 111)
-* cblas_srotmg:                          Level 1 CBLAS Functions.
-                                                              (line 105)
-* cblas_ssbmv:                           Level 2 CBLAS Functions.
-                                                              (line 175)
-* cblas_sscal:                           Level 1 CBLAS Functions.
-                                                              (line 126)
-* cblas_sspmv:                           Level 2 CBLAS Functions.
-                                                              (line 180)
-* cblas_sspr:                            Level 2 CBLAS Functions.
-                                                              (line 194)
-* cblas_sspr2:                           Level 2 CBLAS Functions.
-                                                              (line 203)
-* cblas_sswap:                           Level 1 CBLAS Functions.
-                                                              (line  66)
-* cblas_ssymm:                           Level 3 CBLAS Functions.
-                                                              (line  12)
-* cblas_ssymv:                           Level 2 CBLAS Functions.
-                                                              (line 170)
-* cblas_ssyr:                            Level 2 CBLAS Functions.
-                                                              (line 190)
-* cblas_ssyr2:                           Level 2 CBLAS Functions.
-                                                              (line 198)
-* cblas_ssyr2k:                          Level 3 CBLAS Functions.
-                                                              (line  23)
-* cblas_ssyrk:                           Level 3 CBLAS Functions.
-                                                              (line  18)
-* cblas_stbmv:                           Level 2 CBLAS Functions.
-                                                              (line  22)
-* cblas_stbsv:                           Level 2 CBLAS Functions.
-                                                              (line  37)
-* cblas_stpmv:                           Level 2 CBLAS Functions.
-                                                              (line  27)
-* cblas_stpsv:                           Level 2 CBLAS Functions.
-                                                              (line  42)
-* cblas_strmm:                           Level 3 CBLAS Functions.
-                                                              (line  29)
-* cblas_strmv:                           Level 2 CBLAS Functions.
-                                                              (line  17)
-* cblas_strsm:                           Level 3 CBLAS Functions.
-                                                              (line  35)
-* cblas_strsv:                           Level 2 CBLAS Functions.
-                                                              (line  32)
-* cblas_xerbla:                          Level 3 CBLAS Functions.
-                                                              (line 180)
-* cblas_zaxpy:                           Level 1 CBLAS Functions.
-                                                              (line  99)
-* cblas_zcopy:                           Level 1 CBLAS Functions.
-                                                              (line  96)
-* cblas_zdotc_sub:                       Level 1 CBLAS Functions.
-                                                              (line  27)
-* cblas_zdotu_sub:                       Level 1 CBLAS Functions.
-                                                              (line  24)
-* cblas_zdscal:                          Level 1 CBLAS Functions.
-                                                              (line 141)
-* cblas_zgbmv:                           Level 2 CBLAS Functions.
-                                                              (line 134)
-* cblas_zgemm:                           Level 3 CBLAS Functions.
-                                                              (line 111)
-* cblas_zgemv:                           Level 2 CBLAS Functions.
-                                                              (line 129)
-* cblas_zgerc:                           Level 2 CBLAS Functions.
-                                                              (line 304)
-* cblas_zgeru:                           Level 2 CBLAS Functions.
-                                                              (line 300)
-* cblas_zhbmv:                           Level 2 CBLAS Functions.
-                                                              (line 290)
-* cblas_zhemm:                           Level 3 CBLAS Functions.
-                                                              (line 163)
-* cblas_zhemv:                           Level 2 CBLAS Functions.
-                                                              (line 285)
-* cblas_zher:                            Level 2 CBLAS Functions.
-                                                              (line 308)
-* cblas_zher2:                           Level 2 CBLAS Functions.
-                                                              (line 316)
-* cblas_zher2k:                          Level 3 CBLAS Functions.
-                                                              (line 174)
-* cblas_zherk:                           Level 3 CBLAS Functions.
-                                                              (line 169)
-* cblas_zhpmv:                           Level 2 CBLAS Functions.
-                                                              (line 295)
-* cblas_zhpr:                            Level 2 CBLAS Functions.
-                                                              (line 312)
-* cblas_zhpr2:                           Level 2 CBLAS Functions.
-                                                              (line 321)
-* cblas_zscal:                           Level 1 CBLAS Functions.
-                                                              (line 135)
-* cblas_zswap:                           Level 1 CBLAS Functions.
-                                                              (line  93)
-* cblas_zsymm:                           Level 3 CBLAS Functions.
-                                                              (line 117)
-* cblas_zsyr2k:                          Level 3 CBLAS Functions.
-                                                              (line 128)
-* cblas_zsyrk:                           Level 3 CBLAS Functions.
-                                                              (line 123)
-* cblas_ztbmv:                           Level 2 CBLAS Functions.
-                                                              (line 145)
-* cblas_ztbsv:                           Level 2 CBLAS Functions.
-                                                              (line 160)
-* cblas_ztpmv:                           Level 2 CBLAS Functions.
-                                                              (line 150)
-* cblas_ztpsv:                           Level 2 CBLAS Functions.
-                                                              (line 165)
-* cblas_ztrmm:                           Level 3 CBLAS Functions.
-                                                              (line 134)
-* cblas_ztrmv:                           Level 2 CBLAS Functions.
-                                                              (line 140)
-* cblas_ztrsm:                           Level 3 CBLAS Functions.
-                                                              (line 140)
-* cblas_ztrsv:                           Level 2 CBLAS Functions.
-                                                              (line 155)
-* gsl_acosh:                             Elementary Functions.
-                                                              (line  32)
-* gsl_asinh:                             Elementary Functions.
-                                                              (line  36)
-* gsl_atanh:                             Elementary Functions.
-                                                              (line  40)
-* gsl_blas_caxpy:                        Level 1 GSL BLAS Interface.
-                                                              (line  92)
-* gsl_blas_ccopy:                        Level 1 GSL BLAS Interface.
-                                                              (line  81)
-* gsl_blas_cdotc:                        Level 1 GSL BLAS Interface.
-                                                              (line  27)
-* gsl_blas_cdotu:                        Level 1 GSL BLAS Interface.
-                                                              (line  20)
-* gsl_blas_cgemm:                        Level 3 GSL BLAS Interface.
-                                                              (line  13)
-* gsl_blas_cgemv:                        Level 2 GSL BLAS Interface.
-                                                              (line  12)
-* gsl_blas_cgerc:                        Level 2 GSL BLAS Interface.
-                                                              (line 106)
-* gsl_blas_cgeru:                        Level 2 GSL BLAS Interface.
-                                                              (line  97)
-* gsl_blas_chemm:                        Level 3 GSL BLAS Interface.
-                                                              (line  47)
-* gsl_blas_chemv:                        Level 2 GSL BLAS Interface.
-                                                              (line  78)
-* gsl_blas_cher:                         Level 2 GSL BLAS Interface.
-                                                              (line 126)
-* gsl_blas_cher2:                        Level 2 GSL BLAS Interface.
-                                                              (line 150)
-* gsl_blas_cher2k:                       Level 3 GSL BLAS Interface.
-                                                              (line 168)
-* gsl_blas_cherk:                        Level 3 GSL BLAS Interface.
-                                                              (line 130)
-* gsl_blas_cscal:                        Level 1 GSL BLAS Interface.
-                                                              (line 101)
-* gsl_blas_csscal:                       Level 1 GSL BLAS Interface.
-                                                              (line 105)
-* gsl_blas_cswap:                        Level 1 GSL BLAS Interface.
-                                                              (line  72)
-* gsl_blas_csymm:                        Level 3 GSL BLAS Interface.
-                                                              (line  32)
-* gsl_blas_csyr2k:                       Level 3 GSL BLAS Interface.
-                                                              (line 151)
-* gsl_blas_csyrk:                        Level 3 GSL BLAS Interface.
-                                                              (line 115)
-* gsl_blas_ctrmm:                        Level 3 GSL BLAS Interface.
-                                                              (line  69)
-* gsl_blas_ctrmv:                        Level 2 GSL BLAS Interface.
-                                                              (line  30)
-* gsl_blas_ctrsm:                        Level 3 GSL BLAS Interface.
-                                                              (line  92)
-* gsl_blas_ctrsv:                        Level 2 GSL BLAS Interface.
-                                                              (line  51)
-* gsl_blas_dasum:                        Level 1 GSL BLAS Interface.
-                                                              (line  46)
-* gsl_blas_daxpy:                        Level 1 GSL BLAS Interface.
-                                                              (line  90)
-* gsl_blas_dcopy:                        Level 1 GSL BLAS Interface.
-                                                              (line  80)
-* gsl_blas_ddot:                         Level 1 GSL BLAS Interface.
-                                                              (line  15)
-* gsl_blas_dgemm:                        Level 3 GSL BLAS Interface.
-                                                              (line  10)
-* gsl_blas_dgemv:                        Level 2 GSL BLAS Interface.
-                                                              (line   9)
-* gsl_blas_dger:                         Level 2 GSL BLAS Interface.
-                                                              (line  95)
-* gsl_blas_dnrm2:                        Level 1 GSL BLAS Interface.
-                                                              (line  35)
-* gsl_blas_drot:                         Level 1 GSL BLAS Interface.
-                                                              (line 126)
-* gsl_blas_drotg:                        Level 1 GSL BLAS Interface.
-                                                              (line 114)
-* gsl_blas_drotm:                        Level 1 GSL BLAS Interface.
-                                                              (line 141)
-* gsl_blas_drotmg:                       Level 1 GSL BLAS Interface.
-                                                              (line 133)
-* gsl_blas_dscal:                        Level 1 GSL BLAS Interface.
-                                                              (line 100)
-* gsl_blas_dsdot:                        Level 1 GSL BLAS Interface.
-                                                              (line  13)
-* gsl_blas_dswap:                        Level 1 GSL BLAS Interface.
-                                                              (line  71)
-* gsl_blas_dsymm:                        Level 3 GSL BLAS Interface.
-                                                              (line  29)
-* gsl_blas_dsymv:                        Level 2 GSL BLAS Interface.
-                                                              (line  68)
-* gsl_blas_dsyr:                         Level 2 GSL BLAS Interface.
-                                                              (line 117)
-* gsl_blas_dsyr2:                        Level 2 GSL BLAS Interface.
-                                                              (line 141)
-* gsl_blas_dsyr2k:                       Level 3 GSL BLAS Interface.
-                                                              (line 148)
-* gsl_blas_dsyrk:                        Level 3 GSL BLAS Interface.
-                                                              (line 112)
-* gsl_blas_dtrmm:                        Level 3 GSL BLAS Interface.
-                                                              (line  66)
-* gsl_blas_dtrmv:                        Level 2 GSL BLAS Interface.
-                                                              (line  27)
-* gsl_blas_dtrsm:                        Level 3 GSL BLAS Interface.
-                                                              (line  89)
-* gsl_blas_dtrsv:                        Level 2 GSL BLAS Interface.
-                                                              (line  48)
-* gsl_blas_dzasum:                       Level 1 GSL BLAS Interface.
-                                                              (line  51)
-* gsl_blas_dznrm2:                       Level 1 GSL BLAS Interface.
-                                                              (line  40)
-* gsl_blas_icamax:                       Level 1 GSL BLAS Interface.
-                                                              (line  58)
-* gsl_blas_idamax:                       Level 1 GSL BLAS Interface.
-                                                              (line  57)
-* gsl_blas_isamax:                       Level 1 GSL BLAS Interface.
-                                                              (line  56)
-* gsl_blas_izamax:                       Level 1 GSL BLAS Interface.
-                                                              (line  60)
-* gsl_blas_sasum:                        Level 1 GSL BLAS Interface.
-                                                              (line  45)
-* gsl_blas_saxpy:                        Level 1 GSL BLAS Interface.
-                                                              (line  88)
-* gsl_blas_scasum:                       Level 1 GSL BLAS Interface.
-                                                              (line  50)
-* gsl_blas_scnrm2:                       Level 1 GSL BLAS Interface.
-                                                              (line  39)
-* gsl_blas_scopy:                        Level 1 GSL BLAS Interface.
-                                                              (line  78)
-* gsl_blas_sdot:                         Level 1 GSL BLAS Interface.
-                                                              (line  11)
-* gsl_blas_sdsdot:                       Level 1 GSL BLAS Interface.
-                                                              (line   6)
-* gsl_blas_sgemm:                        Level 3 GSL BLAS Interface.
-                                                              (line   6)
-* gsl_blas_sgemv:                        Level 2 GSL BLAS Interface.
-                                                              (line   6)
-* gsl_blas_sger:                         Level 2 GSL BLAS Interface.
-                                                              (line  93)
-* gsl_blas_snrm2:                        Level 1 GSL BLAS Interface.
-                                                              (line  34)
-* gsl_blas_srot:                         Level 1 GSL BLAS Interface.
-                                                              (line 124)
-* gsl_blas_srotg:                        Level 1 GSL BLAS Interface.
-                                                              (line 112)
-* gsl_blas_srotm:                        Level 1 GSL BLAS Interface.
-                                                              (line 139)
-* gsl_blas_srotmg:                       Level 1 GSL BLAS Interface.
-                                                              (line 131)
-* gsl_blas_sscal:                        Level 1 GSL BLAS Interface.
-                                                              (line  99)
-* gsl_blas_sswap:                        Level 1 GSL BLAS Interface.
-                                                              (line  69)
-* gsl_blas_ssymm:                        Level 3 GSL BLAS Interface.
-                                                              (line  26)
-* gsl_blas_ssymv:                        Level 2 GSL BLAS Interface.
-                                                              (line  65)
-* gsl_blas_ssyr:                         Level 2 GSL BLAS Interface.
-                                                              (line 115)
-* gsl_blas_ssyr2:                        Level 2 GSL BLAS Interface.
-                                                              (line 138)
-* gsl_blas_ssyr2k:                       Level 3 GSL BLAS Interface.
-                                                              (line 145)
-* gsl_blas_ssyrk:                        Level 3 GSL BLAS Interface.
-                                                              (line 109)
-* gsl_blas_strmm:                        Level 3 GSL BLAS Interface.
-                                                              (line  63)
-* gsl_blas_strmv:                        Level 2 GSL BLAS Interface.
-                                                              (line  24)
-* gsl_blas_strsm:                        Level 3 GSL BLAS Interface.
-                                                              (line  86)
-* gsl_blas_strsv:                        Level 2 GSL BLAS Interface.
-                                                              (line  45)
-* gsl_blas_zaxpy:                        Level 1 GSL BLAS Interface.
-                                                              (line  94)
-* gsl_blas_zcopy:                        Level 1 GSL BLAS Interface.
-                                                              (line  83)
-* gsl_blas_zdotc:                        Level 1 GSL BLAS Interface.
-                                                              (line  29)
-* gsl_blas_zdotu:                        Level 1 GSL BLAS Interface.
-                                                              (line  22)
-* gsl_blas_zdscal:                       Level 1 GSL BLAS Interface.
-                                                              (line 107)
-* gsl_blas_zgemm:                        Level 3 GSL BLAS Interface.
-                                                              (line  17)
-* gsl_blas_zgemv:                        Level 2 GSL BLAS Interface.
-                                                              (line  16)
-* gsl_blas_zgerc:                        Level 2 GSL BLAS Interface.
-                                                              (line 109)
-* gsl_blas_zgeru:                        Level 2 GSL BLAS Interface.
-                                                              (line 100)
-* gsl_blas_zhemm:                        Level 3 GSL BLAS Interface.
-                                                              (line  51)
-* gsl_blas_zhemv:                        Level 2 GSL BLAS Interface.
-                                                              (line  82)
-* gsl_blas_zher:                         Level 2 GSL BLAS Interface.
-                                                              (line 128)
-* gsl_blas_zher2:                        Level 2 GSL BLAS Interface.
-                                                              (line 154)
-* gsl_blas_zher2k:                       Level 3 GSL BLAS Interface.
-                                                              (line 172)
-* gsl_blas_zherk:                        Level 3 GSL BLAS Interface.
-                                                              (line 133)
-* gsl_blas_zscal:                        Level 1 GSL BLAS Interface.
-                                                              (line 103)
-* gsl_blas_zswap:                        Level 1 GSL BLAS Interface.
-                                                              (line  74)
-* gsl_blas_zsymm:                        Level 3 GSL BLAS Interface.
-                                                              (line  36)
-* gsl_blas_zsyr2k:                       Level 3 GSL BLAS Interface.
-                                                              (line 155)
-* gsl_blas_zsyrk:                        Level 3 GSL BLAS Interface.
-                                                              (line 119)
-* gsl_blas_ztrmm:                        Level 3 GSL BLAS Interface.
-                                                              (line  73)
-* gsl_blas_ztrmv:                        Level 2 GSL BLAS Interface.
-                                                              (line  33)
-* gsl_blas_ztrsm:                        Level 3 GSL BLAS Interface.
-                                                              (line  96)
-* gsl_blas_ztrsv:                        Level 2 GSL BLAS Interface.
-                                                              (line  54)
-* gsl_block_alloc:                       Block allocation.    (line  14)
-* gsl_block_calloc:                      Block allocation.    (line  24)
-* gsl_block_fprintf:                     Reading and writing blocks.
-                                                              (line  25)
-* gsl_block_fread:                       Reading and writing blocks.
-                                                              (line  16)
-* gsl_block_free:                        Block allocation.    (line  28)
-* gsl_block_fscanf:                      Reading and writing blocks.
-                                                              (line  33)
-* gsl_block_fwrite:                      Reading and writing blocks.
-                                                              (line   9)
-* gsl_bspline_alloc:                     Initializing the B-splines solver.
-                                                              (line  10)
-* gsl_bspline_deriv_alloc:               Initializing the B-splines solver.
-                                                              (line  20)
-* gsl_bspline_deriv_eval:                Evaluation of B-spline basis function derivatives.
-                                                              (line   6)
-* gsl_bspline_deriv_eval_nonzero:        Evaluation of B-spline basis function derivatives.
-                                                              (line  20)
-* gsl_bspline_deriv_free:                Initializing the B-splines solver.
-                                                              (line  26)
-* gsl_bspline_eval:                      Evaluation of B-spline basis functions.
-                                                              (line   6)
-* gsl_bspline_eval_nonzero:              Evaluation of B-spline basis functions.
-                                                              (line  16)
-* gsl_bspline_free:                      Initializing the B-splines solver.
-                                                              (line  17)
-* gsl_bspline_greville_abscissa:         Working with the Greville abscissae.
-                                                              (line  14)
-* gsl_bspline_knots:                     Constructing the knots vector.
-                                                              (line   6)
-* gsl_bspline_knots_uniform:             Constructing the knots vector.
-                                                              (line  11)
-* gsl_bspline_ncoeffs:                   Evaluation of B-spline basis functions.
-                                                              (line  27)
-* gsl_cdf_beta_P:                        The Beta Distribution.
-                                                              (line  21)
-* gsl_cdf_beta_Pinv:                     The Beta Distribution.
-                                                              (line  23)
-* gsl_cdf_beta_Q:                        The Beta Distribution.
-                                                              (line  22)
-* gsl_cdf_beta_Qinv:                     The Beta Distribution.
-                                                              (line  24)
-* gsl_cdf_binomial_P:                    The Binomial Distribution.
-                                                              (line  24)
-* gsl_cdf_binomial_Q:                    The Binomial Distribution.
-                                                              (line  26)
-* gsl_cdf_cauchy_P:                      The Cauchy Distribution.
-                                                              (line  22)
-* gsl_cdf_cauchy_Pinv:                   The Cauchy Distribution.
-                                                              (line  24)
-* gsl_cdf_cauchy_Q:                      The Cauchy Distribution.
-                                                              (line  23)
-* gsl_cdf_cauchy_Qinv:                   The Cauchy Distribution.
-                                                              (line  25)
-* gsl_cdf_chisq_P:                       The Chi-squared Distribution.
-                                                              (line  29)
-* gsl_cdf_chisq_Pinv:                    The Chi-squared Distribution.
-                                                              (line  31)
-* gsl_cdf_chisq_Q:                       The Chi-squared Distribution.
-                                                              (line  30)
-* gsl_cdf_chisq_Qinv:                    The Chi-squared Distribution.
-                                                              (line  32)
-* gsl_cdf_exponential_P:                 The Exponential Distribution.
-                                                              (line  20)
-* gsl_cdf_exponential_Pinv:              The Exponential Distribution.
-                                                              (line  22)
-* gsl_cdf_exponential_Q:                 The Exponential Distribution.
-                                                              (line  21)
-* gsl_cdf_exponential_Qinv:              The Exponential Distribution.
-                                                              (line  23)
-* gsl_cdf_exppow_P:                      The Exponential Power Distribution.
-                                                              (line  24)
-* gsl_cdf_exppow_Q:                      The Exponential Power Distribution.
-                                                              (line  25)
-* gsl_cdf_fdist_P:                       The F-distribution.  (line  33)
-* gsl_cdf_fdist_Pinv:                    The F-distribution.  (line  35)
-* gsl_cdf_fdist_Q:                       The F-distribution.  (line  34)
-* gsl_cdf_fdist_Qinv:                    The F-distribution.  (line  37)
-* gsl_cdf_flat_P:                        The Flat (Uniform) Distribution.
-                                                              (line  20)
-* gsl_cdf_flat_Pinv:                     The Flat (Uniform) Distribution.
-                                                              (line  22)
-* gsl_cdf_flat_Q:                        The Flat (Uniform) Distribution.
-                                                              (line  21)
-* gsl_cdf_flat_Qinv:                     The Flat (Uniform) Distribution.
-                                                              (line  23)
-* gsl_cdf_gamma_P:                       The Gamma Distribution.
-                                                              (line  33)
-* gsl_cdf_gamma_Pinv:                    The Gamma Distribution.
-                                                              (line  35)
-* gsl_cdf_gamma_Q:                       The Gamma Distribution.
-                                                              (line  34)
-* gsl_cdf_gamma_Qinv:                    The Gamma Distribution.
-                                                              (line  36)
-* gsl_cdf_gaussian_P:                    The Gaussian Distribution.
-                                                              (line  41)
-* gsl_cdf_gaussian_Pinv:                 The Gaussian Distribution.
-                                                              (line  43)
-* gsl_cdf_gaussian_Q:                    The Gaussian Distribution.
-                                                              (line  42)
-* gsl_cdf_gaussian_Qinv:                 The Gaussian Distribution.
-                                                              (line  44)
-* gsl_cdf_geometric_P:                   The Geometric Distribution.
-                                                              (line  25)
-* gsl_cdf_geometric_Q:                   The Geometric Distribution.
-                                                              (line  26)
-* gsl_cdf_gumbel1_P:                     The Type-1 Gumbel Distribution.
-                                                              (line  21)
-* gsl_cdf_gumbel1_Pinv:                  The Type-1 Gumbel Distribution.
-                                                              (line  23)
-* gsl_cdf_gumbel1_Q:                     The Type-1 Gumbel Distribution.
-                                                              (line  22)
-* gsl_cdf_gumbel1_Qinv:                  The Type-1 Gumbel Distribution.
-                                                              (line  24)
-* gsl_cdf_gumbel2_P:                     The Type-2 Gumbel Distribution.
-                                                              (line  21)
-* gsl_cdf_gumbel2_Pinv:                  The Type-2 Gumbel Distribution.
-                                                              (line  23)
-* gsl_cdf_gumbel2_Q:                     The Type-2 Gumbel Distribution.
-                                                              (line  22)
-* gsl_cdf_gumbel2_Qinv:                  The Type-2 Gumbel Distribution.
-                                                              (line  24)
-* gsl_cdf_hypergeometric_P:              The Hypergeometric Distribution.
-                                                              (line  29)
-* gsl_cdf_hypergeometric_Q:              The Hypergeometric Distribution.
-                                                              (line  31)
-* gsl_cdf_laplace_P:                     The Laplace Distribution.
-                                                              (line  19)
-* gsl_cdf_laplace_Pinv:                  The Laplace Distribution.
-                                                              (line  21)
-* gsl_cdf_laplace_Q:                     The Laplace Distribution.
-                                                              (line  20)
-* gsl_cdf_laplace_Qinv:                  The Laplace Distribution.
-                                                              (line  22)
-* gsl_cdf_logistic_P:                    The Logistic Distribution.
-                                                              (line  20)
-* gsl_cdf_logistic_Pinv:                 The Logistic Distribution.
-                                                              (line  22)
-* gsl_cdf_logistic_Q:                    The Logistic Distribution.
-                                                              (line  21)
-* gsl_cdf_logistic_Qinv:                 The Logistic Distribution.
-                                                              (line  23)
-* gsl_cdf_lognormal_P:                   The Lognormal Distribution.
-                                                              (line  22)
-* gsl_cdf_lognormal_Pinv:                The Lognormal Distribution.
-                                                              (line  26)
-* gsl_cdf_lognormal_Q:                   The Lognormal Distribution.
-                                                              (line  24)
-* gsl_cdf_lognormal_Qinv:                The Lognormal Distribution.
-                                                              (line  28)
-* gsl_cdf_negative_binomial_P:           The Negative Binomial Distribution.
-                                                              (line  24)
-* gsl_cdf_negative_binomial_Q:           The Negative Binomial Distribution.
-                                                              (line  26)
-* gsl_cdf_pareto_P:                      The Pareto Distribution.
-                                                              (line  21)
-* gsl_cdf_pareto_Pinv:                   The Pareto Distribution.
-                                                              (line  23)
-* gsl_cdf_pareto_Q:                      The Pareto Distribution.
-                                                              (line  22)
-* gsl_cdf_pareto_Qinv:                   The Pareto Distribution.
-                                                              (line  24)
-* gsl_cdf_pascal_P:                      The Pascal Distribution.
-                                                              (line  23)
-* gsl_cdf_pascal_Q:                      The Pascal Distribution.
-                                                              (line  25)
-* gsl_cdf_poisson_P:                     The Poisson Distribution.
-                                                              (line  21)
-* gsl_cdf_poisson_Q:                     The Poisson Distribution.
-                                                              (line  22)
-* gsl_cdf_rayleigh_P:                    The Rayleigh Distribution.
-                                                              (line  20)
-* gsl_cdf_rayleigh_Pinv:                 The Rayleigh Distribution.
-                                                              (line  22)
-* gsl_cdf_rayleigh_Q:                    The Rayleigh Distribution.
-                                                              (line  21)
-* gsl_cdf_rayleigh_Qinv:                 The Rayleigh Distribution.
-                                                              (line  23)
-* gsl_cdf_tdist_P:                       The t-distribution.  (line  29)
-* gsl_cdf_tdist_Pinv:                    The t-distribution.  (line  31)
-* gsl_cdf_tdist_Q:                       The t-distribution.  (line  30)
-* gsl_cdf_tdist_Qinv:                    The t-distribution.  (line  32)
-* gsl_cdf_ugaussian_P:                   The Gaussian Distribution.
-                                                              (line  49)
-* gsl_cdf_ugaussian_Pinv:                The Gaussian Distribution.
-                                                              (line  51)
-* gsl_cdf_ugaussian_Q:                   The Gaussian Distribution.
-                                                              (line  50)
-* gsl_cdf_ugaussian_Qinv:                The Gaussian Distribution.
-                                                              (line  52)
-* gsl_cdf_weibull_P:                     The Weibull Distribution.
-                                                              (line  21)
-* gsl_cdf_weibull_Pinv:                  The Weibull Distribution.
-                                                              (line  23)
-* gsl_cdf_weibull_Q:                     The Weibull Distribution.
-                                                              (line  22)
-* gsl_cdf_weibull_Qinv:                  The Weibull Distribution.
-                                                              (line  24)
-* gsl_cheb_alloc:                        Creation and Calculation of Chebyshev Series.
-                                                              (line   6)
-* gsl_cheb_calc_deriv:                   Derivatives and Integrals.
-                                                              (line  12)
-* gsl_cheb_calc_integ:                   Derivatives and Integrals.
-                                                              (line  18)
-* gsl_cheb_coeffs:                       Auxiliary Functions for Chebyshev Series.
-                                                              (line  13)
-* gsl_cheb_eval:                         Chebyshev Series Evaluation.
-                                                              (line   6)
-* gsl_cheb_eval_err:                     Chebyshev Series Evaluation.
-                                                              (line  10)
-* gsl_cheb_eval_n:                       Chebyshev Series Evaluation.
-                                                              (line  17)
-* gsl_cheb_eval_n_err:                   Chebyshev Series Evaluation.
-                                                              (line  22)
-* gsl_cheb_free:                         Creation and Calculation of Chebyshev Series.
-                                                              (line  10)
-* gsl_cheb_init:                         Creation and Calculation of Chebyshev Series.
-                                                              (line  13)
-* gsl_cheb_order:                        Auxiliary Functions for Chebyshev Series.
-                                                              (line   9)
-* gsl_cheb_size:                         Auxiliary Functions for Chebyshev Series.
-                                                              (line  12)
-* gsl_combination_alloc:                 Combination allocation.
-                                                              (line   6)
-* gsl_combination_calloc:                Combination allocation.
-                                                              (line  15)
-* gsl_combination_data:                  Combination properties.
-                                                              (line  13)
-* gsl_combination_fprintf:               Reading and writing combinations.
-                                                              (line  27)
-* gsl_combination_fread:                 Reading and writing combinations.
-                                                              (line  17)
-* gsl_combination_free:                  Combination allocation.
-                                                              (line  30)
-* gsl_combination_fscanf:                Reading and writing combinations.
-                                                              (line  36)
-* gsl_combination_fwrite:                Reading and writing combinations.
-                                                              (line   9)
-* gsl_combination_get:                   Accessing combination elements.
-                                                              (line   9)
-* gsl_combination_init_first:            Combination allocation.
-                                                              (line  22)
-* gsl_combination_init_last:             Combination allocation.
-                                                              (line  26)
-* gsl_combination_k:                     Combination properties.
-                                                              (line   9)
-* gsl_combination_memcpy:                Combination allocation.
-                                                              (line  33)
-* gsl_combination_n:                     Combination properties.
-                                                              (line   6)
-* gsl_combination_next:                  Combination functions.
-                                                              (line   6)
-* gsl_combination_prev:                  Combination functions.
-                                                              (line  14)
-* gsl_combination_valid:                 Combination properties.
-                                                              (line  17)
-* gsl_complex_abs:                       Properties of complex numbers.
-                                                              (line  10)
-* gsl_complex_abs2:                      Properties of complex numbers.
-                                                              (line  13)
-* gsl_complex_add:                       Complex arithmetic operators.
-                                                              (line   6)
-* gsl_complex_add_imag:                  Complex arithmetic operators.
-                                                              (line  38)
-* gsl_complex_add_real:                  Complex arithmetic operators.
-                                                              (line  22)
-* gsl_complex_arccos:                    Inverse Complex Trigonometric Functions.
-                                                              (line  19)
-* gsl_complex_arccosh:                   Inverse Complex Hyperbolic Functions.
-                                                              (line  11)
-* gsl_complex_arccosh_real:              Inverse Complex Hyperbolic Functions.
-                                                              (line  18)
-* gsl_complex_arccos_real:               Inverse Complex Trigonometric Functions.
-                                                              (line  24)
-* gsl_complex_arccot:                    Inverse Complex Trigonometric Functions.
-                                                              (line  52)
-* gsl_complex_arccoth:                   Inverse Complex Hyperbolic Functions.
-                                                              (line  39)
-* gsl_complex_arccsc:                    Inverse Complex Trigonometric Functions.
-                                                              (line  44)
-* gsl_complex_arccsch:                   Inverse Complex Hyperbolic Functions.
-                                                              (line  35)
-* gsl_complex_arccsc_real:               Inverse Complex Trigonometric Functions.
-                                                              (line  48)
-* gsl_complex_arcsec:                    Inverse Complex Trigonometric Functions.
-                                                              (line  36)
-* gsl_complex_arcsech:                   Inverse Complex Hyperbolic Functions.
-                                                              (line  31)
-* gsl_complex_arcsec_real:               Inverse Complex Trigonometric Functions.
-                                                              (line  40)
-* gsl_complex_arcsin:                    Inverse Complex Trigonometric Functions.
-                                                              (line   6)
-* gsl_complex_arcsinh:                   Inverse Complex Hyperbolic Functions.
-                                                              (line   6)
-* gsl_complex_arcsin_real:               Inverse Complex Trigonometric Functions.
-                                                              (line  11)
-* gsl_complex_arctan:                    Inverse Complex Trigonometric Functions.
-                                                              (line  31)
-* gsl_complex_arctanh:                   Inverse Complex Hyperbolic Functions.
-                                                              (line  22)
-* gsl_complex_arctanh_real:              Inverse Complex Hyperbolic Functions.
-                                                              (line  27)
-* gsl_complex_arg:                       Properties of complex numbers.
-                                                              (line   6)
-* gsl_complex_conjugate:                 Complex arithmetic operators.
-                                                              (line  54)
-* gsl_complex_cos:                       Complex Trigonometric Functions.
-                                                              (line  10)
-* gsl_complex_cosh:                      Complex Hyperbolic Functions.
-                                                              (line  10)
-* gsl_complex_cot:                       Complex Trigonometric Functions.
-                                                              (line  26)
-* gsl_complex_coth:                      Complex Hyperbolic Functions.
-                                                              (line  26)
-* gsl_complex_csc:                       Complex Trigonometric Functions.
-                                                              (line  22)
-* gsl_complex_csch:                      Complex Hyperbolic Functions.
-                                                              (line  22)
-* gsl_complex_div:                       Complex arithmetic operators.
-                                                              (line  18)
-* gsl_complex_div_imag:                  Complex arithmetic operators.
-                                                              (line  50)
-* gsl_complex_div_real:                  Complex arithmetic operators.
-                                                              (line  34)
-* gsl_complex_exp:                       Elementary Complex Functions.
-                                                              (line  24)
-* gsl_complex_inverse:                   Complex arithmetic operators.
-                                                              (line  58)
-* gsl_complex_log:                       Elementary Complex Functions.
-                                                              (line  28)
-* gsl_complex_log10:                     Elementary Complex Functions.
-                                                              (line  33)
-* gsl_complex_logabs:                    Properties of complex numbers.
-                                                              (line  17)
-* gsl_complex_log_b:                     Elementary Complex Functions.
-                                                              (line  37)
-* gsl_complex_mul:                       Complex arithmetic operators.
-                                                              (line  14)
-* gsl_complex_mul_imag:                  Complex arithmetic operators.
-                                                              (line  46)
-* gsl_complex_mul_real:                  Complex arithmetic operators.
-                                                              (line  30)
-* gsl_complex_negative:                  Complex arithmetic operators.
-                                                              (line  62)
-* gsl_complex_polar:                     Representation of complex numbers.
-                                                              (line  29)
-* gsl_complex_poly_complex_eval:         Polynomial Evaluation.
-                                                              (line  21)
-* gsl_complex_pow:                       Elementary Complex Functions.
-                                                              (line  15)
-* gsl_complex_pow_real:                  Elementary Complex Functions.
-                                                              (line  20)
-* gsl_complex_rect:                      Representation of complex numbers.
-                                                              (line  24)
-* gsl_complex_sec:                       Complex Trigonometric Functions.
-                                                              (line  18)
-* gsl_complex_sech:                      Complex Hyperbolic Functions.
-                                                              (line  18)
-* gsl_complex_sin:                       Complex Trigonometric Functions.
-                                                              (line   6)
-* gsl_complex_sinh:                      Complex Hyperbolic Functions.
-                                                              (line   6)
-* gsl_complex_sqrt:                      Elementary Complex Functions.
-                                                              (line   6)
-* gsl_complex_sqrt_real:                 Elementary Complex Functions.
-                                                              (line  11)
-* gsl_complex_sub:                       Complex arithmetic operators.
-                                                              (line  10)
-* gsl_complex_sub_imag:                  Complex arithmetic operators.
-                                                              (line  42)
-* gsl_complex_sub_real:                  Complex arithmetic operators.
-                                                              (line  26)
-* gsl_complex_tan:                       Complex Trigonometric Functions.
-                                                              (line  14)
-* gsl_complex_tanh:                      Complex Hyperbolic Functions.
-                                                              (line  14)
-* gsl_deriv_backward:                    Numerical Differentiation functions.
-                                                              (line  40)
-* gsl_deriv_central:                     Numerical Differentiation functions.
-                                                              (line   6)
-* gsl_deriv_forward:                     Numerical Differentiation functions.
-                                                              (line  22)
-* gsl_dht_alloc:                         Discrete Hankel Transform Functions.
-                                                              (line   6)
-* gsl_dht_apply:                         Discrete Hankel Transform Functions.
-                                                              (line  22)
-* gsl_dht_free:                          Discrete Hankel Transform Functions.
-                                                              (line  19)
-* gsl_dht_init:                          Discrete Hankel Transform Functions.
-                                                              (line  10)
-* gsl_dht_k_sample:                      Discrete Hankel Transform Functions.
-                                                              (line  36)
-* gsl_dht_new:                           Discrete Hankel Transform Functions.
-                                                              (line  14)
-* gsl_dht_x_sample:                      Discrete Hankel Transform Functions.
-                                                              (line  31)
-* gsl_eigen_gen:                         Real Generalized Nonsymmetric Eigensystems.
-                                                              (line  72)
-* gsl_eigen_genherm:                     Complex Generalized Hermitian-Definite Eigensystems.
-                                                              (line  27)
-* gsl_eigen_genhermv:                    Complex Generalized Hermitian-Definite Eigensystems.
-                                                              (line  45)
-* gsl_eigen_genhermv_alloc:              Complex Generalized Hermitian-Definite Eigensystems.
-                                                              (line  35)
-* gsl_eigen_genhermv_free:               Complex Generalized Hermitian-Definite Eigensystems.
-                                                              (line  41)
-* gsl_eigen_genhermv_sort:               Sorting Eigenvalues and Eigenvectors.
-                                                              (line  45)
-* gsl_eigen_genherm_alloc:               Complex Generalized Hermitian-Definite Eigensystems.
-                                                              (line  17)
-* gsl_eigen_genherm_free:                Complex Generalized Hermitian-Definite Eigensystems.
-                                                              (line  23)
-* gsl_eigen_gensymm:                     Real Generalized Symmetric-Definite Eigensystems.
-                                                              (line  32)
-* gsl_eigen_gensymmv:                    Real Generalized Symmetric-Definite Eigensystems.
-                                                              (line  49)
-* gsl_eigen_gensymmv_alloc:              Real Generalized Symmetric-Definite Eigensystems.
-                                                              (line  39)
-* gsl_eigen_gensymmv_free:               Real Generalized Symmetric-Definite Eigensystems.
-                                                              (line  45)
-* gsl_eigen_gensymmv_sort:               Sorting Eigenvalues and Eigenvectors.
-                                                              (line  38)
-* gsl_eigen_gensymm_alloc:               Real Generalized Symmetric-Definite Eigensystems.
-                                                              (line  22)
-* gsl_eigen_gensymm_free:                Real Generalized Symmetric-Definite Eigensystems.
-                                                              (line  28)
-* gsl_eigen_genv:                        Real Generalized Nonsymmetric Eigensystems.
-                                                              (line 105)
-* gsl_eigen_genv_alloc:                  Real Generalized Nonsymmetric Eigensystems.
-                                                              (line  96)
-* gsl_eigen_genv_free:                   Real Generalized Nonsymmetric Eigensystems.
-                                                              (line 102)
-* gsl_eigen_genv_QZ:                     Real Generalized Nonsymmetric Eigensystems.
-                                                              (line 120)
-* gsl_eigen_genv_sort:                   Sorting Eigenvalues and Eigenvectors.
-                                                              (line  52)
-* gsl_eigen_gen_alloc:                   Real Generalized Nonsymmetric Eigensystems.
-                                                              (line  41)
-* gsl_eigen_gen_free:                    Real Generalized Nonsymmetric Eigensystems.
-                                                              (line  47)
-* gsl_eigen_gen_params:                  Real Generalized Nonsymmetric Eigensystems.
-                                                              (line  50)
-* gsl_eigen_gen_QZ:                      Real Generalized Nonsymmetric Eigensystems.
-                                                              (line  89)
-* gsl_eigen_herm:                        Complex Hermitian Matrices.
-                                                              (line  18)
-* gsl_eigen_hermv:                       Complex Hermitian Matrices.
-                                                              (line  37)
-* gsl_eigen_hermv_alloc:                 Complex Hermitian Matrices.
-                                                              (line  28)
-* gsl_eigen_hermv_free:                  Complex Hermitian Matrices.
-                                                              (line  34)
-* gsl_eigen_hermv_sort:                  Sorting Eigenvalues and Eigenvectors.
-                                                              (line  22)
-* gsl_eigen_herm_alloc:                  Complex Hermitian Matrices.
-                                                              (line   9)
-* gsl_eigen_herm_free:                   Complex Hermitian Matrices.
-                                                              (line  15)
-* gsl_eigen_nonsymm:                     Real Nonsymmetric Matrices.
-                                                              (line  60)
-* gsl_eigen_nonsymmv:                    Real Nonsymmetric Matrices.
-                                                              (line  97)
-* gsl_eigen_nonsymmv_alloc:              Real Nonsymmetric Matrices.
-                                                              (line  78)
-* gsl_eigen_nonsymmv_free:               Real Nonsymmetric Matrices.
-                                                              (line  84)
-* gsl_eigen_nonsymmv_params:             Real Nonsymmetric Matrices.
-                                                              (line  88)
-* gsl_eigen_nonsymmv_sort:               Sorting Eigenvalues and Eigenvectors.
-                                                              (line  29)
-* gsl_eigen_nonsymmv_Z:                  Real Nonsymmetric Matrices.
-                                                              (line 111)
-* gsl_eigen_nonsymm_alloc:               Real Nonsymmetric Matrices.
-                                                              (line  17)
-* gsl_eigen_nonsymm_free:                Real Nonsymmetric Matrices.
-                                                              (line  23)
-* gsl_eigen_nonsymm_params:              Real Nonsymmetric Matrices.
-                                                              (line  27)
-* gsl_eigen_nonsymm_Z:                   Real Nonsymmetric Matrices.
-                                                              (line  72)
-* gsl_eigen_symm:                        Real Symmetric Matrices.
-                                                              (line  21)
-* gsl_eigen_symmv:                       Real Symmetric Matrices.
-                                                              (line  39)
-* gsl_eigen_symmv_alloc:                 Real Symmetric Matrices.
-                                                              (line  30)
-* gsl_eigen_symmv_free:                  Real Symmetric Matrices.
-                                                              (line  36)
-* gsl_eigen_symmv_sort:                  Sorting Eigenvalues and Eigenvectors.
-                                                              (line   6)
-* gsl_eigen_symm_alloc:                  Real Symmetric Matrices.
-                                                              (line  12)
-* gsl_eigen_symm_free:                   Real Symmetric Matrices.
-                                                              (line  18)
-* GSL_ERROR:                             Using GSL error reporting in your own functions.
-                                                              (line  15)
-* GSL_ERROR_VAL:                         Using GSL error reporting in your own functions.
-                                                              (line  36)
-* gsl_expm1:                             Elementary Functions.
-                                                              (line  17)
-* gsl_fcmp:                              Approximate Comparison of Floating Point Numbers.
-                                                              (line  12)
-* gsl_fft_complex_backward:              Mixed-radix FFT routines for complex data.
-                                                              (line 124)
-* gsl_fft_complex_forward:               Mixed-radix FFT routines for complex data.
-                                                              (line 117)
-* gsl_fft_complex_inverse:               Mixed-radix FFT routines for complex data.
-                                                              (line 127)
-* gsl_fft_complex_radix2_backward:       Radix-2 FFT routines for complex data.
-                                                              (line  23)
-* gsl_fft_complex_radix2_dif_backward:   Radix-2 FFT routines for complex data.
-                                                              (line  47)
-* gsl_fft_complex_radix2_dif_forward:    Radix-2 FFT routines for complex data.
-                                                              (line  40)
-* gsl_fft_complex_radix2_dif_inverse:    Radix-2 FFT routines for complex data.
-                                                              (line  50)
-* gsl_fft_complex_radix2_dif_transform:  Radix-2 FFT routines for complex data.
-                                                              (line  43)
-* gsl_fft_complex_radix2_forward:        Radix-2 FFT routines for complex data.
-                                                              (line  16)
-* gsl_fft_complex_radix2_inverse:        Radix-2 FFT routines for complex data.
-                                                              (line  26)
-* gsl_fft_complex_radix2_transform:      Radix-2 FFT routines for complex data.
-                                                              (line  19)
-* gsl_fft_complex_transform:             Mixed-radix FFT routines for complex data.
-                                                              (line 120)
-* gsl_fft_complex_wavetable_alloc:       Mixed-radix FFT routines for complex data.
-                                                              (line  44)
-* gsl_fft_complex_wavetable_free:        Mixed-radix FFT routines for complex data.
-                                                              (line  63)
-* gsl_fft_complex_workspace_alloc:       Mixed-radix FFT routines for complex data.
-                                                              (line 104)
-* gsl_fft_complex_workspace_free:        Mixed-radix FFT routines for complex data.
-                                                              (line 109)
-* gsl_fft_halfcomplex_radix2_backward:   Radix-2 FFT routines for real data.
-                                                              (line  58)
-* gsl_fft_halfcomplex_radix2_inverse:    Radix-2 FFT routines for real data.
-                                                              (line  56)
-* gsl_fft_halfcomplex_radix2_unpack:     Radix-2 FFT routines for real data.
-                                                              (line  66)
-* gsl_fft_halfcomplex_transform:         Mixed-radix FFT routines for real data.
-                                                              (line 122)
-* gsl_fft_halfcomplex_unpack:            Mixed-radix FFT routines for real data.
-                                                              (line 153)
-* gsl_fft_halfcomplex_wavetable_alloc:   Mixed-radix FFT routines for real data.
-                                                              (line  74)
-* gsl_fft_halfcomplex_wavetable_free:    Mixed-radix FFT routines for real data.
-                                                              (line  95)
-* gsl_fft_real_radix2_transform:         Radix-2 FFT routines for real data.
-                                                              (line  13)
-* gsl_fft_real_transform:                Mixed-radix FFT routines for real data.
-                                                              (line 119)
-* gsl_fft_real_unpack:                   Mixed-radix FFT routines for real data.
-                                                              (line 136)
-* gsl_fft_real_wavetable_alloc:          Mixed-radix FFT routines for real data.
-                                                              (line  72)
-* gsl_fft_real_wavetable_free:           Mixed-radix FFT routines for real data.
-                                                              (line  93)
-* gsl_fft_real_workspace_alloc:          Mixed-radix FFT routines for real data.
-                                                              (line 104)
-* gsl_fft_real_workspace_free:           Mixed-radix FFT routines for real data.
-                                                              (line 110)
-* gsl_finite:                            Infinities and Not-a-number.
-                                                              (line  25)
-* gsl_fit_linear:                        Linear regression.   (line   9)
-* gsl_fit_linear_est:                    Linear regression.   (line  42)
-* gsl_fit_mul:                           Linear fitting without a constant term.
-                                                              (line  10)
-* gsl_fit_mul_est:                       Linear fitting without a constant term.
-                                                              (line  36)
-* gsl_fit_wlinear:                       Linear regression.   (line  25)
-* gsl_fit_wmul:                          Linear fitting without a constant term.
-                                                              (line  21)
-* gsl_frexp:                             Elementary Functions.
-                                                              (line  48)
-* gsl_heapsort:                          Sorting objects.     (line  16)
-* gsl_heapsort_index:                    Sorting objects.     (line  58)
-* gsl_histogram2d_accumulate:            Updating and accessing 2D histogram elements.
-                                                              (line  25)
-* gsl_histogram2d_add:                   2D Histogram Operations.
-                                                              (line  11)
-* gsl_histogram2d_alloc:                 2D Histogram allocation.
-                                                              (line  14)
-* gsl_histogram2d_clone:                 Copying 2D Histograms.
-                                                              (line  12)
-* gsl_histogram2d_cov:                   2D Histogram Statistics.
-                                                              (line  52)
-* gsl_histogram2d_div:                   2D Histogram Operations.
-                                                              (line  31)
-* gsl_histogram2d_equal_bins_p:          2D Histogram Operations.
-                                                              (line   6)
-* gsl_histogram2d_find:                  Searching 2D histogram ranges.
-                                                              (line   9)
-* gsl_histogram2d_fprintf:               Reading and writing 2D histograms.
-                                                              (line  27)
-* gsl_histogram2d_fread:                 Reading and writing 2D histograms.
-                                                              (line  17)
-* gsl_histogram2d_free:                  2D Histogram allocation.
-                                                              (line  37)
-* gsl_histogram2d_fscanf:                Reading and writing 2D histograms.
-                                                              (line  64)
-* gsl_histogram2d_fwrite:                Reading and writing 2D histograms.
-                                                              (line   9)
-* gsl_histogram2d_get:                   Updating and accessing 2D histogram elements.
-                                                              (line  31)
-* gsl_histogram2d_get_xrange:            Updating and accessing 2D histogram elements.
-                                                              (line  38)
-* gsl_histogram2d_get_yrange:            Updating and accessing 2D histogram elements.
-                                                              (line  40)
-* gsl_histogram2d_increment:             Updating and accessing 2D histogram elements.
-                                                              (line  12)
-* gsl_histogram2d_max_bin:               2D Histogram Statistics.
-                                                              (line  10)
-* gsl_histogram2d_max_val:               2D Histogram Statistics.
-                                                              (line   6)
-* gsl_histogram2d_memcpy:                Copying 2D Histograms.
-                                                              (line   6)
-* gsl_histogram2d_min_bin:               2D Histogram Statistics.
-                                                              (line  21)
-* gsl_histogram2d_min_val:               2D Histogram Statistics.
-                                                              (line  17)
-* gsl_histogram2d_mul:                   2D Histogram Operations.
-                                                              (line  24)
-* gsl_histogram2d_nx:                    Updating and accessing 2D histogram elements.
-                                                              (line  55)
-* gsl_histogram2d_ny:                    Updating and accessing 2D histogram elements.
-                                                              (line  58)
-* gsl_histogram2d_pdf_alloc:             Resampling from 2D histograms.
-                                                              (line  38)
-* gsl_histogram2d_pdf_free:              Resampling from 2D histograms.
-                                                              (line  54)
-* gsl_histogram2d_pdf_init:              Resampling from 2D histograms.
-                                                              (line  46)
-* gsl_histogram2d_pdf_sample:            Resampling from 2D histograms.
-                                                              (line  58)
-* gsl_histogram2d_reset:                 Updating and accessing 2D histogram elements.
-                                                              (line  64)
-* gsl_histogram2d_scale:                 2D Histogram Operations.
-                                                              (line  38)
-* gsl_histogram2d_set_ranges:            2D Histogram allocation.
-                                                              (line  24)
-* gsl_histogram2d_set_ranges_uniform:    2D Histogram allocation.
-                                                              (line  31)
-* gsl_histogram2d_shift:                 2D Histogram Operations.
-                                                              (line  43)
-* gsl_histogram2d_sub:                   2D Histogram Operations.
-                                                              (line  17)
-* gsl_histogram2d_sum:                   2D Histogram Statistics.
-                                                              (line  58)
-* gsl_histogram2d_xmax:                  Updating and accessing 2D histogram elements.
-                                                              (line  53)
-* gsl_histogram2d_xmean:                 2D Histogram Statistics.
-                                                              (line  28)
-* gsl_histogram2d_xmin:                  Updating and accessing 2D histogram elements.
-                                                              (line  54)
-* gsl_histogram2d_xsigma:                2D Histogram Statistics.
-                                                              (line  40)
-* gsl_histogram2d_ymax:                  Updating and accessing 2D histogram elements.
-                                                              (line  56)
-* gsl_histogram2d_ymean:                 2D Histogram Statistics.
-                                                              (line  34)
-* gsl_histogram2d_ymin:                  Updating and accessing 2D histogram elements.
-                                                              (line  57)
-* gsl_histogram2d_ysigma:                2D Histogram Statistics.
-                                                              (line  46)
-* gsl_histogram_accumulate:              Updating and accessing histogram elements.
-                                                              (line  25)
-* gsl_histogram_add:                     Histogram Operations.
-                                                              (line  11)
-* gsl_histogram_alloc:                   Histogram allocation.
-                                                              (line  14)
-* gsl_histogram_bins:                    Updating and accessing histogram elements.
-                                                              (line  53)
-* gsl_histogram_clone:                   Copying Histograms.  (line  12)
-* gsl_histogram_div:                     Histogram Operations.
-                                                              (line  30)
-* gsl_histogram_equal_bins_p:            Histogram Operations.
-                                                              (line   6)
-* gsl_histogram_find:                    Searching histogram ranges.
-                                                              (line   9)
-* gsl_histogram_fprintf:                 Reading and writing histograms.
-                                                              (line  26)
-* gsl_histogram_fread:                   Reading and writing histograms.
-                                                              (line  17)
-* gsl_histogram_free:                    Histogram allocation.
-                                                              (line  60)
-* gsl_histogram_fscanf:                  Reading and writing histograms.
-                                                              (line  51)
-* gsl_histogram_fwrite:                  Reading and writing histograms.
-                                                              (line   9)
-* gsl_histogram_get:                     Updating and accessing histogram elements.
-                                                              (line  31)
-* gsl_histogram_get_range:               Updating and accessing histogram elements.
-                                                              (line  38)
-* gsl_histogram_increment:               Updating and accessing histogram elements.
-                                                              (line  11)
-* gsl_histogram_max:                     Updating and accessing histogram elements.
-                                                              (line  51)
-* gsl_histogram_max_bin:                 Histogram Statistics.
-                                                              (line  10)
-* gsl_histogram_max_val:                 Histogram Statistics.
-                                                              (line   6)
-* gsl_histogram_mean:                    Histogram Statistics.
-                                                              (line  24)
-* gsl_histogram_memcpy:                  Copying Histograms.  (line   6)
-* gsl_histogram_min:                     Updating and accessing histogram elements.
-                                                              (line  52)
-* gsl_histogram_min_bin:                 Histogram Statistics.
-                                                              (line  19)
-* gsl_histogram_min_val:                 Histogram Statistics.
-                                                              (line  15)
-* gsl_histogram_mul:                     Histogram Operations.
-                                                              (line  23)
-* gsl_histogram_pdf_alloc:               The histogram probability distribution struct.
-                                                              (line  33)
-* gsl_histogram_pdf_free:                The histogram probability distribution struct.
-                                                              (line  47)
-* gsl_histogram_pdf_init:                The histogram probability distribution struct.
-                                                              (line  40)
-* gsl_histogram_pdf_sample:              The histogram probability distribution struct.
-                                                              (line  51)
-* gsl_histogram_reset:                   Updating and accessing histogram elements.
-                                                              (line  59)
-* gsl_histogram_scale:                   Histogram Operations.
-                                                              (line  37)
-* gsl_histogram_set_ranges:              Histogram allocation.
-                                                              (line  23)
-* gsl_histogram_set_ranges_uniform:      Histogram allocation.
-                                                              (line  48)
-* gsl_histogram_shift:                   Histogram Operations.
-                                                              (line  41)
-* gsl_histogram_sigma:                   Histogram Statistics.
-                                                              (line  30)
-* gsl_histogram_sub:                     Histogram Operations.
-                                                              (line  17)
-* gsl_histogram_sum:                     Histogram Statistics.
-                                                              (line  37)
-* gsl_hypot:                             Elementary Functions.
-                                                              (line  22)
-* gsl_hypot3:                            Elementary Functions.
-                                                              (line  27)
-* gsl_ieee_env_setup:                    Setting up your IEEE environment.
-                                                              (line  23)
-* gsl_ieee_fprintf_double:               Representation of floating point numbers.
-                                                              (line  55)
-* gsl_ieee_fprintf_float:                Representation of floating point numbers.
-                                                              (line  53)
-* gsl_ieee_printf_double:                Representation of floating point numbers.
-                                                              (line  82)
-* gsl_ieee_printf_float:                 Representation of floating point numbers.
-                                                              (line  81)
-* GSL_IMAG:                              Representation of complex numbers.
-                                                              (line  35)
-* gsl_integration_cquad:                 CQUAD doubly-adaptive integration.
-                                                              (line  33)
-* gsl_integration_cquad_workspace_alloc: CQUAD doubly-adaptive integration.
-                                                              (line  20)
-* gsl_integration_cquad_workspace_free:  CQUAD doubly-adaptive integration.
-                                                              (line  29)
-* gsl_integration_glfixed:               Fixed order Gauss-Legendre integration.
-                                                              (line  22)
-* gsl_integration_glfixed_point:         Fixed order Gauss-Legendre integration.
-                                                              (line  27)
-* gsl_integration_glfixed_table_alloc:   Fixed order Gauss-Legendre integration.
-                                                              (line  14)
-* gsl_integration_glfixed_table_free:    Fixed order Gauss-Legendre integration.
-                                                              (line  35)
-* gsl_integration_qag:                   QAG adaptive integration.
-                                                              (line  27)
-* gsl_integration_qagi:                  QAGI adaptive integration on infinite intervals.
-                                                              (line   6)
-* gsl_integration_qagil:                 QAGI adaptive integration on infinite intervals.
-                                                              (line  37)
-* gsl_integration_qagiu:                 QAGI adaptive integration on infinite intervals.
-                                                              (line  22)
-* gsl_integration_qagp:                  QAGP adaptive integration with known singular points.
-                                                              (line   6)
-* gsl_integration_qags:                  QAGS adaptive integration with singularities.
-                                                              (line  15)
-* gsl_integration_qawc:                  QAWC adaptive integration for Cauchy principal values.
-                                                              (line   6)
-* gsl_integration_qawf:                  QAWF adaptive integration for Fourier integrals.
-                                                              (line   6)
-* gsl_integration_qawo:                  QAWO adaptive integration for oscillatory functions.
-                                                              (line  53)
-* gsl_integration_qawo_table_alloc:      QAWO adaptive integration for oscillatory functions.
-                                                              (line  11)
-* gsl_integration_qawo_table_free:       QAWO adaptive integration for oscillatory functions.
-                                                              (line  49)
-* gsl_integration_qawo_table_set:        QAWO adaptive integration for oscillatory functions.
-                                                              (line  38)
-* gsl_integration_qawo_table_set_length: QAWO adaptive integration for oscillatory functions.
-                                                              (line  44)
-* gsl_integration_qaws:                  QAWS adaptive integration for singular functions.
-                                                              (line  48)
-* gsl_integration_qaws_table_alloc:      QAWS adaptive integration for singular functions.
-                                                              (line  11)
-* gsl_integration_qaws_table_free:       QAWS adaptive integration for singular functions.
-                                                              (line  43)
-* gsl_integration_qaws_table_set:        QAWS adaptive integration for singular functions.
-                                                              (line  37)
-* gsl_integration_qng:                   QNG non-adaptive Gauss-Kronrod integration.
-                                                              (line  10)
-* gsl_integration_workspace_alloc:       QAG adaptive integration.
-                                                              (line  15)
-* gsl_integration_workspace_free:        QAG adaptive integration.
-                                                              (line  23)
-* gsl_interp_accel_alloc:                Index Look-up and Acceleration.
-                                                              (line  19)
-* gsl_interp_accel_find:                 Index Look-up and Acceleration.
-                                                              (line  25)
-* gsl_interp_accel_free:                 Index Look-up and Acceleration.
-                                                              (line  39)
-* gsl_interp_accel_reset:                Index Look-up and Acceleration.
-                                                              (line  34)
-* gsl_interp_akima:                      Interpolation Types. (line  34)
-* gsl_interp_akima_periodic:             Interpolation Types. (line  38)
-* gsl_interp_alloc:                      Interpolation Functions.
-                                                              (line   9)
-* gsl_interp_bsearch:                    Index Look-up and Acceleration.
-                                                              (line  12)
-* gsl_interp_cspline:                    Interpolation Types. (line  19)
-* gsl_interp_cspline_periodic:           Interpolation Types. (line  25)
-* gsl_interp_eval:                       Evaluation of Interpolating Functions.
-                                                              (line   6)
-* gsl_interp_eval_deriv:                 Evaluation of Interpolating Functions.
-                                                              (line  17)
-* gsl_interp_eval_deriv2:                Evaluation of Interpolating Functions.
-                                                              (line  27)
-* gsl_interp_eval_deriv2_e:              Evaluation of Interpolating Functions.
-                                                              (line  30)
-* gsl_interp_eval_deriv_e:               Evaluation of Interpolating Functions.
-                                                              (line  20)
-* gsl_interp_eval_e:                     Evaluation of Interpolating Functions.
-                                                              (line   9)
-* gsl_interp_eval_integ:                 Evaluation of Interpolating Functions.
-                                                              (line  37)
-* gsl_interp_eval_integ_e:               Evaluation of Interpolating Functions.
-                                                              (line  40)
-* gsl_interp_free:                       Interpolation Functions.
-                                                              (line  24)
-* gsl_interp_init:                       Interpolation Functions.
-                                                              (line  14)
-* gsl_interp_linear:                     Interpolation Types. (line   8)
-* gsl_interp_min_size:                   Interpolation Types. (line  55)
-* gsl_interp_name:                       Interpolation Types. (line  44)
-* gsl_interp_polynomial:                 Interpolation Types. (line  12)
-* gsl_interp_type_min_size:              Interpolation Types. (line  57)
-* gsl_isinf:                             Infinities and Not-a-number.
-                                                              (line  21)
-* gsl_isnan:                             Infinities and Not-a-number.
-                                                              (line  18)
-* GSL_IS_EVEN:                           Testing for Odd and Even Numbers.
-                                                              (line  10)
-* GSL_IS_ODD:                            Testing for Odd and Even Numbers.
-                                                              (line   6)
-* gsl_ldexp:                             Elementary Functions.
-                                                              (line  44)
-* gsl_linalg_balance_matrix:             Balancing.           (line  17)
-* gsl_linalg_bidiag_decomp:              Bidiagonalization.   (line  15)
-* gsl_linalg_bidiag_unpack:              Bidiagonalization.   (line  26)
-* gsl_linalg_bidiag_unpack2:             Bidiagonalization.   (line  35)
-* gsl_linalg_bidiag_unpack_B:            Bidiagonalization.   (line  42)
-* gsl_linalg_cholesky_decomp:            Cholesky Decomposition.
-                                                              (line  19)
-* gsl_linalg_cholesky_invert:            Cholesky Decomposition.
-                                                              (line  56)
-* gsl_linalg_cholesky_solve:             Cholesky Decomposition.
-                                                              (line  36)
-* gsl_linalg_cholesky_svx:               Cholesky Decomposition.
-                                                              (line  46)
-* gsl_linalg_complex_cholesky_decomp:    Cholesky Decomposition.
-                                                              (line  20)
-* gsl_linalg_complex_cholesky_invert:    Cholesky Decomposition.
-                                                              (line  57)
-* gsl_linalg_complex_cholesky_solve:     Cholesky Decomposition.
-                                                              (line  38)
-* gsl_linalg_complex_cholesky_svx:       Cholesky Decomposition.
-                                                              (line  48)
-* gsl_linalg_complex_householder_hm:     Householder Transformations.
-                                                              (line  27)
-* gsl_linalg_complex_householder_hv:     Householder Transformations.
-                                                              (line  43)
-* gsl_linalg_complex_householder_mh:     Householder Transformations.
-                                                              (line  35)
-* gsl_linalg_complex_householder_transform: Householder Transformations.
-                                                              (line  18)
-* gsl_linalg_complex_LU_decomp:          LU Decomposition.    (line  20)
-* gsl_linalg_complex_LU_det:             LU Decomposition.    (line  83)
-* gsl_linalg_complex_LU_invert:          LU Decomposition.    (line  71)
-* gsl_linalg_complex_LU_lndet:           LU Decomposition.    (line  91)
-* gsl_linalg_complex_LU_refine:          LU Decomposition.    (line  60)
-* gsl_linalg_complex_LU_sgndet:          LU Decomposition.    (line  99)
-* gsl_linalg_complex_LU_solve:           LU Decomposition.    (line  41)
-* gsl_linalg_complex_LU_svx:             LU Decomposition.    (line  50)
-* gsl_linalg_hermtd_decomp:              Tridiagonal Decomposition of Hermitian Matrices.
-                                                              (line  14)
-* gsl_linalg_hermtd_unpack:              Tridiagonal Decomposition of Hermitian Matrices.
-                                                              (line  26)
-* gsl_linalg_hermtd_unpack_T:            Tridiagonal Decomposition of Hermitian Matrices.
-                                                              (line  34)
-* gsl_linalg_hessenberg_decomp:          Hessenberg Decomposition of Real Matrices.
-                                                              (line  16)
-* gsl_linalg_hessenberg_set_zero:        Hessenberg Decomposition of Real Matrices.
-                                                              (line  42)
-* gsl_linalg_hessenberg_unpack:          Hessenberg Decomposition of Real Matrices.
-                                                              (line  27)
-* gsl_linalg_hessenberg_unpack_accum:    Hessenberg Decomposition of Real Matrices.
-                                                              (line  33)
-* gsl_linalg_hesstri_decomp:             Hessenberg-Triangular Decomposition of Real Matrices.
-                                                              (line  17)
-* gsl_linalg_HH_solve:                   Householder solver for linear systems.
-                                                              (line   6)
-* gsl_linalg_HH_svx:                     Householder solver for linear systems.
-                                                              (line  13)
-* gsl_linalg_householder_hm:             Householder Transformations.
-                                                              (line  25)
-* gsl_linalg_householder_hv:             Householder Transformations.
-                                                              (line  41)
-* gsl_linalg_householder_mh:             Householder Transformations.
-                                                              (line  33)
-* gsl_linalg_householder_transform:      Householder Transformations.
-                                                              (line  17)
-* gsl_linalg_LU_decomp:                  LU Decomposition.    (line  18)
-* gsl_linalg_LU_det:                     LU Decomposition.    (line  82)
-* gsl_linalg_LU_invert:                  LU Decomposition.    (line  69)
-* gsl_linalg_LU_lndet:                   LU Decomposition.    (line  90)
-* gsl_linalg_LU_refine:                  LU Decomposition.    (line  57)
-* gsl_linalg_LU_sgndet:                  LU Decomposition.    (line  98)
-* gsl_linalg_LU_solve:                   LU Decomposition.    (line  39)
-* gsl_linalg_LU_svx:                     LU Decomposition.    (line  48)
-* gsl_linalg_QRPT_decomp:                QR Decomposition with Column Pivoting.
-                                                              (line  18)
-* gsl_linalg_QRPT_decomp2:               QR Decomposition with Column Pivoting.
-                                                              (line  39)
-* gsl_linalg_QRPT_QRsolve:               QR Decomposition with Column Pivoting.
-                                                              (line  60)
-* gsl_linalg_QRPT_Rsolve:                QR Decomposition with Column Pivoting.
-                                                              (line  76)
-* gsl_linalg_QRPT_Rsvx:                  QR Decomposition with Column Pivoting.
-                                                              (line  81)
-* gsl_linalg_QRPT_solve:                 QR Decomposition with Column Pivoting.
-                                                              (line  46)
-* gsl_linalg_QRPT_svx:                   QR Decomposition with Column Pivoting.
-                                                              (line  53)
-* gsl_linalg_QRPT_update:                QR Decomposition with Column Pivoting.
-                                                              (line  67)
-* gsl_linalg_QR_decomp:                  QR Decomposition.    (line  19)
-* gsl_linalg_QR_lssolve:                 QR Decomposition.    (line  50)
-* gsl_linalg_QR_QRsolve:                 QR Decomposition.    (line 102)
-* gsl_linalg_QR_QTmat:                   QR Decomposition.    (line  76)
-* gsl_linalg_QR_QTvec:                   QR Decomposition.    (line  61)
-* gsl_linalg_QR_Qvec:                    QR Decomposition.    (line  69)
-* gsl_linalg_QR_Rsolve:                  QR Decomposition.    (line  84)
-* gsl_linalg_QR_Rsvx:                    QR Decomposition.    (line  90)
-* gsl_linalg_QR_solve:                   QR Decomposition.    (line  35)
-* gsl_linalg_QR_svx:                     QR Decomposition.    (line  42)
-* gsl_linalg_QR_unpack:                  QR Decomposition.    (line  97)
-* gsl_linalg_QR_update:                  QR Decomposition.    (line 108)
-* gsl_linalg_R_solve:                    QR Decomposition.    (line 115)
-* gsl_linalg_R_svx:                      QR Decomposition.    (line 120)
-* gsl_linalg_solve_cyc_tridiag:          Tridiagonal Systems. (line  39)
-* gsl_linalg_solve_symm_cyc_tridiag:     Tridiagonal Systems. (line  53)
-* gsl_linalg_solve_symm_tridiag:         Tridiagonal Systems. (line  26)
-* gsl_linalg_solve_tridiag:              Tridiagonal Systems. (line  13)
-* gsl_linalg_SV_decomp:                  Singular Value Decomposition.
-                                                              (line  37)
-* gsl_linalg_SV_decomp_jacobi:           Singular Value Decomposition.
-                                                              (line  56)
-* gsl_linalg_SV_decomp_mod:              Singular Value Decomposition.
-                                                              (line  50)
-* gsl_linalg_SV_leverage:                Singular Value Decomposition.
-                                                              (line  79)
-* gsl_linalg_SV_solve:                   Singular Value Decomposition.
-                                                              (line  63)
-* gsl_linalg_symmtd_decomp:              Tridiagonal Decomposition of Real Symmetric Matrices.
-                                                              (line  13)
-* gsl_linalg_symmtd_unpack:              Tridiagonal Decomposition of Real Symmetric Matrices.
-                                                              (line  24)
-* gsl_linalg_symmtd_unpack_T:            Tridiagonal Decomposition of Real Symmetric Matrices.
-                                                              (line  32)
-* gsl_log1p:                             Elementary Functions.
-                                                              (line  12)
-* gsl_matrix_add:                        Matrix operations.   (line   8)
-* gsl_matrix_add_constant:               Matrix operations.   (line  38)
-* gsl_matrix_alloc:                      Matrix allocation.   (line  14)
-* gsl_matrix_calloc:                     Matrix allocation.   (line  21)
-* gsl_matrix_column:                     Creating row and column views.
-                                                              (line  24)
-* gsl_matrix_const_column:               Creating row and column views.
-                                                              (line  26)
-* gsl_matrix_const_diagonal:             Creating row and column views.
-                                                              (line  63)
-* gsl_matrix_const_ptr:                  Accessing matrix elements.
-                                                              (line  36)
-* gsl_matrix_const_row:                  Creating row and column views.
-                                                              (line  14)
-* gsl_matrix_const_subcolumn:            Creating row and column views.
-                                                              (line  51)
-* gsl_matrix_const_subdiagonal:          Creating row and column views.
-                                                              (line  76)
-* gsl_matrix_const_submatrix:            Matrix views.        (line  20)
-* gsl_matrix_const_subrow:               Creating row and column views.
-                                                              (line  38)
-* gsl_matrix_const_superdiagonal:        Creating row and column views.
-                                                              (line  88)
-* gsl_matrix_const_view_array:           Matrix views.        (line  51)
-* gsl_matrix_const_view_array_with_tda:  Matrix views.        (line  75)
-* gsl_matrix_const_view_vector:          Matrix views.        (line 101)
-* gsl_matrix_const_view_vector_with_tda: Matrix views.        (line 125)
-* gsl_matrix_diagonal:                   Creating row and column views.
-                                                              (line  62)
-* gsl_matrix_div_elements:               Matrix operations.   (line  27)
-* gsl_matrix_equal:                      Matrix properties.   (line  20)
-* gsl_matrix_fprintf:                    Reading and writing matrices.
-                                                              (line  26)
-* gsl_matrix_fread:                      Reading and writing matrices.
-                                                              (line  17)
-* gsl_matrix_free:                       Matrix allocation.   (line  25)
-* gsl_matrix_fscanf:                     Reading and writing matrices.
-                                                              (line  34)
-* gsl_matrix_fwrite:                     Reading and writing matrices.
-                                                              (line   9)
-* gsl_matrix_get:                        Accessing matrix elements.
-                                                              (line  20)
-* gsl_matrix_get_col:                    Copying rows and columns.
-                                                              (line  19)
-* gsl_matrix_get_row:                    Copying rows and columns.
-                                                              (line  13)
-* gsl_matrix_isneg:                      Matrix properties.   (line  12)
-* gsl_matrix_isnonneg:                   Matrix properties.   (line  13)
-* gsl_matrix_isnull:                     Matrix properties.   (line  10)
-* gsl_matrix_ispos:                      Matrix properties.   (line  11)
-* gsl_matrix_max:                        Finding maximum and minimum elements of matrices.
-                                                              (line   8)
-* gsl_matrix_max_index:                  Finding maximum and minimum elements of matrices.
-                                                              (line  19)
-* gsl_matrix_memcpy:                     Copying matrices.    (line   6)
-* gsl_matrix_min:                        Finding maximum and minimum elements of matrices.
-                                                              (line  11)
-* gsl_matrix_minmax:                     Finding maximum and minimum elements of matrices.
-                                                              (line  14)
-* gsl_matrix_minmax_index:               Finding maximum and minimum elements of matrices.
-                                                              (line  33)
-* gsl_matrix_min_index:                  Finding maximum and minimum elements of matrices.
-                                                              (line  26)
-* gsl_matrix_mul_elements:               Matrix operations.   (line  20)
-* gsl_matrix_ptr:                        Accessing matrix elements.
-                                                              (line  34)
-* gsl_matrix_row:                        Creating row and column views.
-                                                              (line  13)
-* gsl_matrix_scale:                      Matrix operations.   (line  34)
-* gsl_matrix_set:                        Accessing matrix elements.
-                                                              (line  27)
-* gsl_matrix_set_all:                    Initializing matrix elements.
-                                                              (line   6)
-* gsl_matrix_set_col:                    Copying rows and columns.
-                                                              (line  31)
-* gsl_matrix_set_identity:               Initializing matrix elements.
-                                                              (line  12)
-* gsl_matrix_set_row:                    Copying rows and columns.
-                                                              (line  25)
-* gsl_matrix_set_zero:                   Initializing matrix elements.
-                                                              (line   9)
-* gsl_matrix_sub:                        Matrix operations.   (line  14)
-* gsl_matrix_subcolumn:                  Creating row and column views.
-                                                              (line  49)
-* gsl_matrix_subdiagonal:                Creating row and column views.
-                                                              (line  74)
-* gsl_matrix_submatrix:                  Matrix views.        (line  18)
-* gsl_matrix_subrow:                     Creating row and column views.
-                                                              (line  36)
-* gsl_matrix_superdiagonal:              Creating row and column views.
-                                                              (line  86)
-* gsl_matrix_swap:                       Copying matrices.    (line  11)
-* gsl_matrix_swap_columns:               Exchanging rows and columns.
-                                                              (line  14)
-* gsl_matrix_swap_rowcol:                Exchanging rows and columns.
-                                                              (line  19)
-* gsl_matrix_swap_rows:                  Exchanging rows and columns.
-                                                              (line   9)
-* gsl_matrix_transpose:                  Exchanging rows and columns.
-                                                              (line  32)
-* gsl_matrix_transpose_memcpy:           Exchanging rows and columns.
-                                                              (line  25)
-* gsl_matrix_view_array:                 Matrix views.        (line  49)
-* gsl_matrix_view_array_with_tda:        Matrix views.        (line  73)
-* gsl_matrix_view_vector:                Matrix views.        (line  99)
-* gsl_matrix_view_vector_with_tda:       Matrix views.        (line 123)
-* GSL_MAX:                               Maximum and Minimum functions.
-                                                              (line  10)
-* GSL_MAX_DBL:                           Maximum and Minimum functions.
-                                                              (line  18)
-* GSL_MAX_INT:                           Maximum and Minimum functions.
-                                                              (line  32)
-* GSL_MAX_LDBL:                          Maximum and Minimum functions.
-                                                              (line  39)
-* GSL_MIN:                               Maximum and Minimum functions.
-                                                              (line  14)
-* GSL_MIN_DBL:                           Maximum and Minimum functions.
-                                                              (line  25)
-* gsl_min_fminimizer_alloc:              Initializing the Minimizer.
-                                                              (line   6)
-* gsl_min_fminimizer_brent:              Minimization Algorithms.
-                                                              (line  30)
-* gsl_min_fminimizer_free:               Initializing the Minimizer.
-                                                              (line  39)
-* gsl_min_fminimizer_f_lower:            Minimization Iteration.
-                                                              (line  45)
-* gsl_min_fminimizer_f_minimum:          Minimization Iteration.
-                                                              (line  41)
-* gsl_min_fminimizer_f_upper:            Minimization Iteration.
-                                                              (line  43)
-* gsl_min_fminimizer_goldensection:      Minimization Algorithms.
-                                                              (line  13)
-* gsl_min_fminimizer_iterate:            Minimization Iteration.
-                                                              (line  12)
-* gsl_min_fminimizer_name:               Initializing the Minimizer.
-                                                              (line  42)
-* gsl_min_fminimizer_quad_golden:        Minimization Algorithms.
-                                                              (line  46)
-* gsl_min_fminimizer_set:                Initializing the Minimizer.
-                                                              (line  21)
-* gsl_min_fminimizer_set_with_values:    Initializing the Minimizer.
-                                                              (line  31)
-* gsl_min_fminimizer_x_lower:            Minimization Iteration.
-                                                              (line  36)
-* gsl_min_fminimizer_x_minimum:          Minimization Iteration.
-                                                              (line  29)
-* gsl_min_fminimizer_x_upper:            Minimization Iteration.
-                                                              (line  34)
-* GSL_MIN_INT:                           Maximum and Minimum functions.
-                                                              (line  33)
-* GSL_MIN_LDBL:                          Maximum and Minimum functions.
-                                                              (line  41)
-* gsl_min_test_interval:                 Minimization Stopping Parameters.
-                                                              (line  18)
-* gsl_monte_miser_alloc:                 MISER.               (line  45)
-* gsl_monte_miser_free:                  MISER.               (line  68)
-* gsl_monte_miser_init:                  MISER.               (line  50)
-* gsl_monte_miser_integrate:             MISER.               (line  55)
-* gsl_monte_miser_params_get:            MISER.               (line  75)
-* gsl_monte_miser_params_set:            MISER.               (line  80)
-* gsl_monte_plain_alloc:                 PLAIN Monte Carlo.   (line  29)
-* gsl_monte_plain_free:                  PLAIN Monte Carlo.   (line  51)
-* gsl_monte_plain_init:                  PLAIN Monte Carlo.   (line  33)
-* gsl_monte_plain_integrate:             PLAIN Monte Carlo.   (line  38)
-* gsl_monte_vegas_alloc:                 VEGAS.               (line  50)
-* gsl_monte_vegas_chisq:                 VEGAS.               (line 113)
-* gsl_monte_vegas_free:                  VEGAS.               (line  77)
-* gsl_monte_vegas_init:                  VEGAS.               (line  55)
-* gsl_monte_vegas_integrate:             VEGAS.               (line  60)
-* gsl_monte_vegas_params_get:            VEGAS.               (line 131)
-* gsl_monte_vegas_params_set:            VEGAS.               (line 136)
-* gsl_monte_vegas_runval:                VEGAS.               (line 122)
-* gsl_multifit_covar:                    Computing the covariance matrix of best fit parameters.
-                                                              (line   6)
-* gsl_multifit_fdfsolver_alloc:          Initializing the Nonlinear Least-Squares Solver.
-                                                              (line  16)
-* gsl_multifit_fdfsolver_dif_df:         Finite Difference Jacobian.
-                                                              (line  15)
-* gsl_multifit_fdfsolver_dif_fdf:        Finite Difference Jacobian.
-                                                              (line  27)
-* gsl_multifit_fdfsolver_driver:         High Level Driver.   (line  12)
-* gsl_multifit_fdfsolver_free:           Initializing the Nonlinear Least-Squares Solver.
-                                                              (line  46)
-* gsl_multifit_fdfsolver_iterate:        Iteration of the Minimization Algorithm.
-                                                              (line  14)
-* gsl_multifit_fdfsolver_lmder:          Minimization Algorithms using Derivatives.
-                                                              (line  64)
-* gsl_multifit_fdfsolver_lmsder:         Minimization Algorithms using Derivatives.
-                                                              (line  12)
-* gsl_multifit_fdfsolver_name:           Initializing the Nonlinear Least-Squares Solver.
-                                                              (line  52)
-* gsl_multifit_fdfsolver_position:       Iteration of the Minimization Algorithm.
-                                                              (line  43)
-* gsl_multifit_fdfsolver_set:            Initializing the Nonlinear Least-Squares Solver.
-                                                              (line  40)
-* gsl_multifit_fsolver_alloc:            Initializing the Nonlinear Least-Squares Solver.
-                                                              (line   6)
-* gsl_multifit_fsolver_driver:           High Level Driver.   (line   9)
-* gsl_multifit_fsolver_free:             Initializing the Nonlinear Least-Squares Solver.
-                                                              (line  45)
-* gsl_multifit_fsolver_iterate:          Iteration of the Minimization Algorithm.
-                                                              (line  12)
-* gsl_multifit_fsolver_name:             Initializing the Nonlinear Least-Squares Solver.
-                                                              (line  50)
-* gsl_multifit_fsolver_position:         Iteration of the Minimization Algorithm.
-                                                              (line  41)
-* gsl_multifit_fsolver_set:              Initializing the Nonlinear Least-Squares Solver.
-                                                              (line  35)
-* gsl_multifit_gradient:                 Search Stopping Parameters for Minimization Algorithms.
-                                                              (line  45)
-* gsl_multifit_linear:                   Multi-parameter fitting.
-                                                              (line  50)
-* gsl_multifit_linear_alloc:             Multi-parameter fitting.
-                                                              (line  41)
-* gsl_multifit_linear_est:               Multi-parameter fitting.
-                                                              (line 108)
-* gsl_multifit_linear_free:              Multi-parameter fitting.
-                                                              (line  46)
-* gsl_multifit_linear_residuals:         Multi-parameter fitting.
-                                                              (line 116)
-* gsl_multifit_linear_svd:               Multi-parameter fitting.
-                                                              (line  85)
-* gsl_multifit_linear_usvd:              Multi-parameter fitting.
-                                                              (line  97)
-* gsl_multifit_robust:                   Robust linear regression.
-                                                              (line 159)
-* gsl_multifit_robust_alloc:             Robust linear regression.
-                                                              (line  70)
-* gsl_multifit_robust_bisquare:          Robust linear regression.
-                                                              (line  81)
-* gsl_multifit_robust_cauchy:            Robust linear regression.
-                                                              (line  90)
-* gsl_multifit_robust_default:           Robust linear regression.
-                                                              (line  76)
-* gsl_multifit_robust_est:               Robust linear regression.
-                                                              (line 173)
-* gsl_multifit_robust_fair:              Robust linear regression.
-                                                              (line 101)
-* gsl_multifit_robust_free:              Robust linear regression.
-                                                              (line 142)
-* gsl_multifit_robust_huber:             Robust linear regression.
-                                                              (line 110)
-* gsl_multifit_robust_name:              Robust linear regression.
-                                                              (line 146)
-* gsl_multifit_robust_ols:               Robust linear regression.
-                                                              (line 123)
-* gsl_multifit_robust_statistics:        Robust linear regression.
-                                                              (line 181)
-* gsl_multifit_robust_tune:              Robust linear regression.
-                                                              (line 151)
-* gsl_multifit_robust_welsch:            Robust linear regression.
-                                                              (line 133)
-* gsl_multifit_test_delta:               Search Stopping Parameters for Minimization Algorithms.
-                                                              (line  19)
-* gsl_multifit_test_gradient:            Search Stopping Parameters for Minimization Algorithms.
-                                                              (line  31)
-* gsl_multifit_wlinear:                  Multi-parameter fitting.
-                                                              (line  70)
-* gsl_multifit_wlinear_svd:              Multi-parameter fitting.
-                                                              (line  89)
-* gsl_multifit_wlinear_usvd:             Multi-parameter fitting.
-                                                              (line 101)
-* gsl_multimin_fdfminimizer_alloc:       Initializing the Multidimensional Minimizer.
-                                                              (line  10)
-* gsl_multimin_fdfminimizer_conjugate_fr: Multimin Algorithms with Derivatives.
-                                                              (line  11)
-* gsl_multimin_fdfminimizer_conjugate_pr: Multimin Algorithms with Derivatives.
-                                                              (line  28)
-* gsl_multimin_fdfminimizer_free:        Initializing the Multidimensional Minimizer.
-                                                              (line  46)
-* gsl_multimin_fdfminimizer_gradient:    Multimin Iteration.  (line  34)
-* gsl_multimin_fdfminimizer_iterate:     Multimin Iteration.  (line  11)
-* gsl_multimin_fdfminimizer_minimum:     Multimin Iteration.  (line  30)
-* gsl_multimin_fdfminimizer_name:        Initializing the Multidimensional Minimizer.
-                                                              (line  52)
-* gsl_multimin_fdfminimizer_restart:     Multimin Iteration.  (line  42)
-* gsl_multimin_fdfminimizer_set:         Initializing the Multidimensional Minimizer.
-                                                              (line  21)
-* gsl_multimin_fdfminimizer_steepest_descent: Multimin Algorithms with Derivatives.
-                                                              (line  55)
-* gsl_multimin_fdfminimizer_vector_bfgs: Multimin Algorithms with Derivatives.
-                                                              (line  36)
-* gsl_multimin_fdfminimizer_vector_bfgs2: Multimin Algorithms with Derivatives.
-                                                              (line  35)
-* gsl_multimin_fdfminimizer_x:           Multimin Iteration.  (line  26)
-* gsl_multimin_fminimizer_alloc:         Initializing the Multidimensional Minimizer.
-                                                              (line  13)
-* gsl_multimin_fminimizer_free:          Initializing the Multidimensional Minimizer.
-                                                              (line  48)
-* gsl_multimin_fminimizer_iterate:       Multimin Iteration.  (line  13)
-* gsl_multimin_fminimizer_minimum:       Multimin Iteration.  (line  32)
-* gsl_multimin_fminimizer_name:          Initializing the Multidimensional Minimizer.
-                                                              (line  54)
-* gsl_multimin_fminimizer_nmsimplex:     Multimin Algorithms without Derivatives.
-                                                              (line  10)
-* gsl_multimin_fminimizer_nmsimplex2:    Multimin Algorithms without Derivatives.
-                                                              (line   9)
-* gsl_multimin_fminimizer_nmsimplex2rand: Multimin Algorithms without Derivatives.
-                                                              (line  49)
-* gsl_multimin_fminimizer_set:           Initializing the Multidimensional Minimizer.
-                                                              (line  24)
-* gsl_multimin_fminimizer_size:          Multimin Iteration.  (line  36)
-* gsl_multimin_fminimizer_x:             Multimin Iteration.  (line  28)
-* gsl_multimin_test_gradient:            Multimin Stopping Criteria.
-                                                              (line  18)
-* gsl_multimin_test_size:                Multimin Stopping Criteria.
-                                                              (line  32)
-* gsl_multiroot_fdfsolver_alloc:         Initializing the Multidimensional Solver.
-                                                              (line  27)
-* gsl_multiroot_fdfsolver_dx:            Iteration of the multidimensional solver.
-                                                              (line  48)
-* gsl_multiroot_fdfsolver_f:             Iteration of the multidimensional solver.
-                                                              (line  41)
-* gsl_multiroot_fdfsolver_free:          Initializing the Multidimensional Solver.
-                                                              (line  54)
-* gsl_multiroot_fdfsolver_gnewton:       Algorithms using Derivatives.
-                                                              (line  90)
-* gsl_multiroot_fdfsolver_hybridj:       Algorithms using Derivatives.
-                                                              (line  64)
-* gsl_multiroot_fdfsolver_hybridsj:      Algorithms using Derivatives.
-                                                              (line  13)
-* gsl_multiroot_fdfsolver_iterate:       Iteration of the multidimensional solver.
-                                                              (line  14)
-* gsl_multiroot_fdfsolver_name:          Initializing the Multidimensional Solver.
-                                                              (line  60)
-* gsl_multiroot_fdfsolver_newton:        Algorithms using Derivatives.
-                                                              (line  70)
-* gsl_multiroot_fdfsolver_root:          Iteration of the multidimensional solver.
-                                                              (line  34)
-* gsl_multiroot_fdfsolver_set:           Initializing the Multidimensional Solver.
-                                                              (line  45)
-* gsl_multiroot_fsolver_alloc:           Initializing the Multidimensional Solver.
-                                                              (line  11)
-* gsl_multiroot_fsolver_broyden:         Algorithms without Derivatives.
-                                                              (line  45)
-* gsl_multiroot_fsolver_dnewton:         Algorithms without Derivatives.
-                                                              (line  25)
-* gsl_multiroot_fsolver_dx:              Iteration of the multidimensional solver.
-                                                              (line  46)
-* gsl_multiroot_fsolver_f:               Iteration of the multidimensional solver.
-                                                              (line  39)
-* gsl_multiroot_fsolver_free:            Initializing the Multidimensional Solver.
-                                                              (line  52)
-* gsl_multiroot_fsolver_hybrid:          Algorithms without Derivatives.
-                                                              (line  21)
-* gsl_multiroot_fsolver_hybrids:         Algorithms without Derivatives.
-                                                              (line  13)
-* gsl_multiroot_fsolver_iterate:         Iteration of the multidimensional solver.
-                                                              (line  12)
-* gsl_multiroot_fsolver_name:            Initializing the Multidimensional Solver.
-                                                              (line  58)
-* gsl_multiroot_fsolver_root:            Iteration of the multidimensional solver.
-                                                              (line  32)
-* gsl_multiroot_fsolver_set:             Initializing the Multidimensional Solver.
-                                                              (line  43)
-* gsl_multiroot_test_delta:              Search Stopping Parameters for the multidimensional solver.
-                                                              (line  20)
-* gsl_multiroot_test_residual:           Search Stopping Parameters for the multidimensional solver.
-                                                              (line  32)
-* gsl_multiset_alloc:                    Multiset allocation. (line   6)
-* gsl_multiset_calloc:                   Multiset allocation. (line  14)
-* gsl_multiset_data:                     Multiset properties. (line  12)
-* gsl_multiset_fprintf:                  Reading and writing multisets.
-                                                              (line  26)
-* gsl_multiset_fread:                    Reading and writing multisets.
-                                                              (line  17)
-* gsl_multiset_free:                     Multiset allocation. (line  28)
-* gsl_multiset_fscanf:                   Reading and writing multisets.
-                                                              (line  35)
-* gsl_multiset_fwrite:                   Reading and writing multisets.
-                                                              (line   9)
-* gsl_multiset_get:                      Accessing multiset elements.
-                                                              (line   8)
-* gsl_multiset_init_first:               Multiset allocation. (line  20)
-* gsl_multiset_init_last:                Multiset allocation. (line  24)
-* gsl_multiset_k:                        Multiset properties. (line   9)
-* gsl_multiset_memcpy:                   Multiset allocation. (line  31)
-* gsl_multiset_n:                        Multiset properties. (line   6)
-* gsl_multiset_next:                     Multiset functions.  (line   6)
-* gsl_multiset_prev:                     Multiset functions.  (line  14)
-* gsl_multiset_valid:                    Multiset properties. (line  16)
-* gsl_ntuple_bookdata:                   Writing ntuples.     (line  10)
-* gsl_ntuple_close:                      Closing an ntuple file.
-                                                              (line   6)
-* gsl_ntuple_create:                     Creating ntuples.    (line   6)
-* gsl_ntuple_open:                       Opening an existing ntuple file.
-                                                              (line   6)
-* gsl_ntuple_project:                    Histogramming ntuple values.
-                                                              (line  35)
-* gsl_ntuple_read:                       Reading ntuples.     (line   6)
-* gsl_ntuple_write:                      Writing ntuples.     (line   6)
-* gsl_odeiv2_control_alloc:              Adaptive Step-size Control.
-                                                              (line  73)
-* gsl_odeiv2_control_errlevel:           Adaptive Step-size Control.
-                                                              (line 115)
-* gsl_odeiv2_control_free:               Adaptive Step-size Control.
-                                                              (line  86)
-* gsl_odeiv2_control_hadjust:            Adaptive Step-size Control.
-                                                              (line  90)
-* gsl_odeiv2_control_init:               Adaptive Step-size Control.
-                                                              (line  80)
-* gsl_odeiv2_control_name:               Adaptive Step-size Control.
-                                                              (line 105)
-* gsl_odeiv2_control_scaled_new:         Adaptive Step-size Control.
-                                                              (line  60)
-* gsl_odeiv2_control_set_driver:         Adaptive Step-size Control.
-                                                              (line 122)
-* gsl_odeiv2_control_standard_new:       Adaptive Step-size Control.
-                                                              (line  10)
-* gsl_odeiv2_control_yp_new:             Adaptive Step-size Control.
-                                                              (line  52)
-* gsl_odeiv2_control_y_new:              Adaptive Step-size Control.
-                                                              (line  44)
-* gsl_odeiv2_driver_alloc_scaled_new:    Driver.              (line  19)
-* gsl_odeiv2_driver_alloc_standard_new:  Driver.              (line  15)
-* gsl_odeiv2_driver_alloc_yp_new:        Driver.              (line  12)
-* gsl_odeiv2_driver_alloc_y_new:         Driver.              (line   9)
-* gsl_odeiv2_driver_apply:               Driver.              (line  46)
-* gsl_odeiv2_driver_apply_fixed_step:    Driver.              (line  61)
-* gsl_odeiv2_driver_free:                Driver.              (line  78)
-* gsl_odeiv2_driver_reset:               Driver.              (line  69)
-* gsl_odeiv2_driver_reset_hstart:        Driver.              (line  72)
-* gsl_odeiv2_driver_set_hmax:            Driver.              (line  36)
-* gsl_odeiv2_driver_set_hmin:            Driver.              (line  31)
-* gsl_odeiv2_driver_set_nmax:            Driver.              (line  41)
-* gsl_odeiv2_evolve_alloc:               Evolution.           (line  10)
-* gsl_odeiv2_evolve_apply:               Evolution.           (line  14)
-* gsl_odeiv2_evolve_apply_fixed_step:    Evolution.           (line  52)
-* gsl_odeiv2_evolve_free:                Evolution.           (line  68)
-* gsl_odeiv2_evolve_reset:               Evolution.           (line  63)
-* gsl_odeiv2_evolve_set_driver:          Evolution.           (line  72)
-* gsl_odeiv2_step_alloc:                 Stepping Functions.  (line  10)
-* gsl_odeiv2_step_apply:                 Stepping Functions.  (line  51)
-* gsl_odeiv2_step_bsimp:                 Stepping Functions.  (line 122)
-* gsl_odeiv2_step_free:                  Stepping Functions.  (line  23)
-* gsl_odeiv2_step_msadams:               Stepping Functions.  (line 127)
-* gsl_odeiv2_step_msbdf:                 Stepping Functions.  (line 135)
-* gsl_odeiv2_step_name:                  Stepping Functions.  (line  27)
-* gsl_odeiv2_step_order:                 Stepping Functions.  (line  37)
-* gsl_odeiv2_step_reset:                 Stepping Functions.  (line  18)
-* gsl_odeiv2_step_rk1imp:                Stepping Functions.  (line 104)
-* gsl_odeiv2_step_rk2:                   Stepping Functions.  (line  86)
-* gsl_odeiv2_step_rk2imp:                Stepping Functions.  (line 110)
-* gsl_odeiv2_step_rk4:                   Stepping Functions.  (line  89)
-* gsl_odeiv2_step_rk4imp:                Stepping Functions.  (line 116)
-* gsl_odeiv2_step_rk8pd:                 Stepping Functions.  (line 101)
-* gsl_odeiv2_step_rkck:                  Stepping Functions.  (line  98)
-* gsl_odeiv2_step_rkf45:                 Stepping Functions.  (line  94)
-* gsl_odeiv2_step_set_driver:            Stepping Functions.  (line  43)
-* gsl_permutation_alloc:                 Permutation allocation.
-                                                              (line   6)
-* gsl_permutation_calloc:                Permutation allocation.
-                                                              (line  14)
-* gsl_permutation_canonical_cycles:      Permutations in cyclic form.
-                                                              (line  67)
-* gsl_permutation_canonical_to_linear:   Permutations in cyclic form.
-                                                              (line  49)
-* gsl_permutation_data:                  Permutation properties.
-                                                              (line   9)
-* gsl_permutation_fprintf:               Reading and writing permutations.
-                                                              (line  27)
-* gsl_permutation_fread:                 Reading and writing permutations.
-                                                              (line  17)
-* gsl_permutation_free:                  Permutation allocation.
-                                                              (line  23)
-* gsl_permutation_fscanf:                Reading and writing permutations.
-                                                              (line  36)
-* gsl_permutation_fwrite:                Reading and writing permutations.
-                                                              (line   9)
-* gsl_permutation_get:                   Accessing permutation elements.
-                                                              (line   9)
-* gsl_permutation_init:                  Permutation allocation.
-                                                              (line  19)
-* gsl_permutation_inverse:               Permutation functions.
-                                                              (line   9)
-* gsl_permutation_inversions:            Permutations in cyclic form.
-                                                              (line  54)
-* gsl_permutation_linear_cycles:         Permutations in cyclic form.
-                                                              (line  62)
-* gsl_permutation_linear_to_canonical:   Permutations in cyclic form.
-                                                              (line  44)
-* gsl_permutation_memcpy:                Permutation allocation.
-                                                              (line  26)
-* gsl_permutation_mul:                   Applying Permutations.
-                                                              (line  35)
-* gsl_permutation_next:                  Permutation functions.
-                                                              (line  14)
-* gsl_permutation_prev:                  Permutation functions.
-                                                              (line  22)
-* gsl_permutation_reverse:               Permutation functions.
-                                                              (line   6)
-* gsl_permutation_size:                  Permutation properties.
-                                                              (line   6)
-* gsl_permutation_swap:                  Accessing permutation elements.
-                                                              (line  16)
-* gsl_permutation_valid:                 Permutation properties.
-                                                              (line  13)
-* gsl_permute:                           Applying Permutations.
-                                                              (line   6)
-* gsl_permute_inverse:                   Applying Permutations.
-                                                              (line  11)
-* gsl_permute_vector:                    Applying Permutations.
-                                                              (line  16)
-* gsl_permute_vector_inverse:            Applying Permutations.
-                                                              (line  25)
-* gsl_poly_complex_eval:                 Polynomial Evaluation.
-                                                              (line  16)
-* gsl_poly_complex_solve:                General Polynomial Equations.
-                                                              (line  25)
-* gsl_poly_complex_solve_cubic:          Cubic Equations.     (line  24)
-* gsl_poly_complex_solve_quadratic:      Quadratic Equations. (line  28)
-* gsl_poly_complex_workspace_alloc:      General Polynomial Equations.
-                                                              (line  11)
-* gsl_poly_complex_workspace_free:       General Polynomial Equations.
-                                                              (line  21)
-* gsl_poly_dd_eval:                      Divided Difference Representation of Polynomials.
-                                                              (line  38)
-* gsl_poly_dd_hermite_init:              Divided Difference Representation of Polynomials.
-                                                              (line  54)
-* gsl_poly_dd_init:                      Divided Difference Representation of Polynomials.
-                                                              (line  30)
-* gsl_poly_dd_taylor:                    Divided Difference Representation of Polynomials.
-                                                              (line  45)
-* gsl_poly_eval:                         Polynomial Evaluation.
-                                                              (line  11)
-* gsl_poly_eval_derivs:                  Polynomial Evaluation.
-                                                              (line  26)
-* gsl_poly_solve_cubic:                  Cubic Equations.     (line   6)
-* gsl_poly_solve_quadratic:              Quadratic Equations. (line   6)
-* gsl_pow_2:                             Small integer powers.
-                                                              (line  19)
-* gsl_pow_3:                             Small integer powers.
-                                                              (line  20)
-* gsl_pow_4:                             Small integer powers.
-                                                              (line  21)
-* gsl_pow_5:                             Small integer powers.
-                                                              (line  22)
-* gsl_pow_6:                             Small integer powers.
-                                                              (line  23)
-* gsl_pow_7:                             Small integer powers.
-                                                              (line  24)
-* gsl_pow_8:                             Small integer powers.
-                                                              (line  25)
-* gsl_pow_9:                             Small integer powers.
-                                                              (line  26)
-* gsl_pow_int:                           Small integer powers.
-                                                              (line  11)
-* gsl_pow_uint:                          Small integer powers.
-                                                              (line  12)
-* gsl_qrng_alloc:                        Quasi-random number generator initialization.
-                                                              (line   6)
-* gsl_qrng_clone:                        Saving and resorting quasi-random number generator state.
-                                                              (line  12)
-* gsl_qrng_free:                         Quasi-random number generator initialization.
-                                                              (line  14)
-* gsl_qrng_get:                          Sampling from a quasi-random number generator.
-                                                              (line   6)
-* gsl_qrng_halton:                       Quasi-random number generator algorithms.
-                                                              (line  18)
-* gsl_qrng_init:                         Quasi-random number generator initialization.
-                                                              (line  17)
-* gsl_qrng_memcpy:                       Saving and resorting quasi-random number generator state.
-                                                              (line   6)
-* gsl_qrng_name:                         Auxiliary quasi-random number generator functions.
-                                                              (line   6)
-* gsl_qrng_niederreiter_2:               Quasi-random number generator algorithms.
-                                                              (line   8)
-* gsl_qrng_reversehalton:                Quasi-random number generator algorithms.
-                                                              (line  19)
-* gsl_qrng_size:                         Auxiliary quasi-random number generator functions.
-                                                              (line   9)
-* gsl_qrng_sobol:                        Quasi-random number generator algorithms.
-                                                              (line  13)
-* gsl_qrng_state:                        Auxiliary quasi-random number generator functions.
-                                                              (line  10)
-* gsl_ran_bernoulli:                     The Bernoulli Distribution.
-                                                              (line   6)
-* gsl_ran_bernoulli_pdf:                 The Bernoulli Distribution.
-                                                              (line  15)
-* gsl_ran_beta:                          The Beta Distribution.
-                                                              (line   6)
-* gsl_ran_beta_pdf:                      The Beta Distribution.
-                                                              (line  15)
-* gsl_ran_binomial:                      The Binomial Distribution.
-                                                              (line   6)
-* gsl_ran_binomial_pdf:                  The Binomial Distribution.
-                                                              (line  17)
-* gsl_ran_bivariate_gaussian:            The Bivariate Gaussian Distribution.
-                                                              (line   6)
-* gsl_ran_bivariate_gaussian_pdf:        The Bivariate Gaussian Distribution.
-                                                              (line  18)
-* gsl_ran_cauchy:                        The Cauchy Distribution.
-                                                              (line   6)
-* gsl_ran_cauchy_pdf:                    The Cauchy Distribution.
-                                                              (line  16)
-* gsl_ran_chisq:                         The Chi-squared Distribution.
-                                                              (line  14)
-* gsl_ran_chisq_pdf:                     The Chi-squared Distribution.
-                                                              (line  23)
-* gsl_ran_choose:                        Shuffling and Sampling.
-                                                              (line  33)
-* gsl_ran_dirichlet:                     The Dirichlet Distribution.
-                                                              (line   6)
-* gsl_ran_dirichlet_lnpdf:               The Dirichlet Distribution.
-                                                              (line  30)
-* gsl_ran_dirichlet_pdf:                 The Dirichlet Distribution.
-                                                              (line  24)
-* gsl_ran_dir_2d:                        Spherical Vector Distributions.
-                                                              (line  10)
-* gsl_ran_dir_2d_trig_method:            Spherical Vector Distributions.
-                                                              (line  12)
-* gsl_ran_dir_3d:                        Spherical Vector Distributions.
-                                                              (line  31)
-* gsl_ran_dir_nd:                        Spherical Vector Distributions.
-                                                              (line  40)
-* gsl_ran_discrete:                      General Discrete Distributions.
-                                                              (line  59)
-* gsl_ran_discrete_free:                 General Discrete Distributions.
-                                                              (line  72)
-* gsl_ran_discrete_pdf:                  General Discrete Distributions.
-                                                              (line  64)
-* gsl_ran_discrete_preproc:              General Discrete Distributions.
-                                                              (line  49)
-* gsl_ran_exponential:                   The Exponential Distribution.
-                                                              (line   6)
-* gsl_ran_exponential_pdf:               The Exponential Distribution.
-                                                              (line  14)
-* gsl_ran_exppow:                        The Exponential Power Distribution.
-                                                              (line   6)
-* gsl_ran_exppow_pdf:                    The Exponential Power Distribution.
-                                                              (line  18)
-* gsl_ran_fdist:                         The F-distribution.  (line  13)
-* gsl_ran_fdist_pdf:                     The F-distribution.  (line  26)
-* gsl_ran_flat:                          The Flat (Uniform) Distribution.
-                                                              (line   6)
-* gsl_ran_flat_pdf:                      The Flat (Uniform) Distribution.
-                                                              (line  15)
-* gsl_ran_gamma:                         The Gamma Distribution.
-                                                              (line   6)
-* gsl_ran_gamma_knuth:                   The Gamma Distribution.
-                                                              (line  22)
-* gsl_ran_gamma_pdf:                     The Gamma Distribution.
-                                                              (line  27)
-* gsl_ran_gaussian:                      The Gaussian Distribution.
-                                                              (line   6)
-* gsl_ran_gaussian_pdf:                  The Gaussian Distribution.
-                                                              (line  19)
-* gsl_ran_gaussian_ratio_method:         The Gaussian Distribution.
-                                                              (line  27)
-* gsl_ran_gaussian_tail:                 The Gaussian Tail Distribution.
-                                                              (line   6)
-* gsl_ran_gaussian_tail_pdf:             The Gaussian Tail Distribution.
-                                                              (line  23)
-* gsl_ran_gaussian_ziggurat:             The Gaussian Distribution.
-                                                              (line  25)
-* gsl_ran_geometric:                     The Geometric Distribution.
-                                                              (line   6)
-* gsl_ran_geometric_pdf:                 The Geometric Distribution.
-                                                              (line  19)
-* gsl_ran_gumbel1:                       The Type-1 Gumbel Distribution.
-                                                              (line   6)
-* gsl_ran_gumbel1_pdf:                   The Type-1 Gumbel Distribution.
-                                                              (line  15)
-* gsl_ran_gumbel2:                       The Type-2 Gumbel Distribution.
-                                                              (line   6)
-* gsl_ran_gumbel2_pdf:                   The Type-2 Gumbel Distribution.
-                                                              (line  15)
-* gsl_ran_hypergeometric:                The Hypergeometric Distribution.
-                                                              (line   6)
-* gsl_ran_hypergeometric_pdf:            The Hypergeometric Distribution.
-                                                              (line  22)
-* gsl_ran_landau:                        The Landau Distribution.
-                                                              (line   6)
-* gsl_ran_landau_pdf:                    The Landau Distribution.
-                                                              (line  17)
-* gsl_ran_laplace:                       The Laplace Distribution.
-                                                              (line   6)
-* gsl_ran_laplace_pdf:                   The Laplace Distribution.
-                                                              (line  14)
-* gsl_ran_levy:                          The Levy alpha-Stable Distributions.
-                                                              (line   6)
-* gsl_ran_levy_skew:                     The Levy skew alpha-Stable Distribution.
-                                                              (line   6)
-* gsl_ran_logarithmic:                   The Logarithmic Distribution.
-                                                              (line   6)
-* gsl_ran_logarithmic_pdf:               The Logarithmic Distribution.
-                                                              (line  16)
-* gsl_ran_logistic:                      The Logistic Distribution.
-                                                              (line   6)
-* gsl_ran_logistic_pdf:                  The Logistic Distribution.
-                                                              (line  14)
-* gsl_ran_lognormal:                     The Lognormal Distribution.
-                                                              (line   6)
-* gsl_ran_lognormal_pdf:                 The Lognormal Distribution.
-                                                              (line  15)
-* gsl_ran_multinomial:                   The Multinomial Distribution.
-                                                              (line   6)
-* gsl_ran_multinomial_lnpdf:             The Multinomial Distribution.
-                                                              (line  34)
-* gsl_ran_multinomial_pdf:               The Multinomial Distribution.
-                                                              (line  28)
-* gsl_ran_negative_binomial:             The Negative Binomial Distribution.
-                                                              (line   6)
-* gsl_ran_negative_binomial_pdf:         The Negative Binomial Distribution.
-                                                              (line  17)
-* gsl_ran_pareto:                        The Pareto Distribution.
-                                                              (line   6)
-* gsl_ran_pareto_pdf:                    The Pareto Distribution.
-                                                              (line  15)
-* gsl_ran_pascal:                        The Pascal Distribution.
-                                                              (line   6)
-* gsl_ran_pascal_pdf:                    The Pascal Distribution.
-                                                              (line  16)
-* gsl_ran_poisson:                       The Poisson Distribution.
-                                                              (line   6)
-* gsl_ran_poisson_pdf:                   The Poisson Distribution.
-                                                              (line  16)
-* gsl_ran_rayleigh:                      The Rayleigh Distribution.
-                                                              (line   6)
-* gsl_ran_rayleigh_pdf:                  The Rayleigh Distribution.
-                                                              (line  14)
-* gsl_ran_rayleigh_tail:                 The Rayleigh Tail Distribution.
-                                                              (line   6)
-* gsl_ran_rayleigh_tail_pdf:             The Rayleigh Tail Distribution.
-                                                              (line  16)
-* gsl_ran_sample:                        Shuffling and Sampling.
-                                                              (line  59)
-* gsl_ran_shuffle:                       Shuffling and Sampling.
-                                                              (line  13)
-* gsl_ran_tdist:                         The t-distribution.  (line  14)
-* gsl_ran_tdist_pdf:                     The t-distribution.  (line  23)
-* gsl_ran_ugaussian:                     The Gaussian Distribution.
-                                                              (line  34)
-* gsl_ran_ugaussian_pdf:                 The Gaussian Distribution.
-                                                              (line  35)
-* gsl_ran_ugaussian_ratio_method:        The Gaussian Distribution.
-                                                              (line  36)
-* gsl_ran_ugaussian_tail:                The Gaussian Tail Distribution.
-                                                              (line  30)
-* gsl_ran_ugaussian_tail_pdf:            The Gaussian Tail Distribution.
-                                                              (line  32)
-* gsl_ran_weibull:                       The Weibull Distribution.
-                                                              (line   6)
-* gsl_ran_weibull_pdf:                   The Weibull Distribution.
-                                                              (line  15)
-* GSL_REAL:                              Representation of complex numbers.
-                                                              (line  34)
-* gsl_rng_alloc:                         Random number generator initialization.
-                                                              (line   6)
-* gsl_rng_borosh13:                      Other random number generators.
-                                                              (line 174)
-* gsl_rng_clone:                         Copying random number generator state.
-                                                              (line  16)
-* gsl_rng_cmrg:                          Random number generator algorithms.
-                                                              (line  98)
-* gsl_rng_coveyou:                       Other random number generators.
-                                                              (line 201)
-* gsl_rng_env_setup:                     Random number environment variables.
-                                                              (line  11)
-* gsl_rng_fishman18:                     Other random number generators.
-                                                              (line 175)
-* gsl_rng_fishman20:                     Other random number generators.
-                                                              (line 176)
-* gsl_rng_fishman2x:                     Other random number generators.
-                                                              (line 191)
-* gsl_rng_fread:                         Reading and writing random number generator state.
-                                                              (line  17)
-* gsl_rng_free:                          Random number generator initialization.
-                                                              (line  45)
-* gsl_rng_fwrite:                        Reading and writing random number generator state.
-                                                              (line   9)
-* gsl_rng_get:                           Sampling from a random number generator.
-                                                              (line  11)
-* gsl_rng_gfsr4:                         Random number generator algorithms.
-                                                              (line 173)
-* gsl_rng_knuthran:                      Other random number generators.
-                                                              (line 167)
-* gsl_rng_knuthran2:                     Other random number generators.
-                                                              (line 157)
-* gsl_rng_knuthran2002:                  Other random number generators.
-                                                              (line 166)
-* gsl_rng_lecuyer21:                     Other random number generators.
-                                                              (line 177)
-* gsl_rng_max:                           Auxiliary random number generator functions.
-                                                              (line  19)
-* gsl_rng_memcpy:                        Copying random number generator state.
-                                                              (line  11)
-* gsl_rng_min:                           Auxiliary random number generator functions.
-                                                              (line  23)
-* gsl_rng_minstd:                        Other random number generators.
-                                                              (line 113)
-* gsl_rng_mrg:                           Random number generator algorithms.
-                                                              (line 120)
-* gsl_rng_mt19937:                       Random number generator algorithms.
-                                                              (line  19)
-* gsl_rng_name:                          Auxiliary random number generator functions.
-                                                              (line  10)
-* gsl_rng_r250:                          Other random number generators.
-                                                              (line  59)
-* gsl_rng_rand:                          Unix random number generators.
-                                                              (line  17)
-* gsl_rng_rand48:                        Unix random number generators.
-                                                              (line  57)
-* gsl_rng_random_bsd:                    Unix random number generators.
-                                                              (line  26)
-* gsl_rng_random_glibc2:                 Unix random number generators.
-                                                              (line  28)
-* gsl_rng_random_libc5:                  Unix random number generators.
-                                                              (line  27)
-* gsl_rng_randu:                         Other random number generators.
-                                                              (line 104)
-* gsl_rng_ranf:                          Other random number generators.
-                                                              (line  22)
-* gsl_rng_ranlux:                        Random number generator algorithms.
-                                                              (line  71)
-* gsl_rng_ranlux389:                     Random number generator algorithms.
-                                                              (line  72)
-* gsl_rng_ranlxd1:                       Random number generator algorithms.
-                                                              (line  64)
-* gsl_rng_ranlxd2:                       Random number generator algorithms.
-                                                              (line  65)
-* gsl_rng_ranlxs0:                       Random number generator algorithms.
-                                                              (line  44)
-* gsl_rng_ranlxs1:                       Random number generator algorithms.
-                                                              (line  45)
-* gsl_rng_ranlxs2:                       Random number generator algorithms.
-                                                              (line  46)
-* gsl_rng_ranmar:                        Other random number generators.
-                                                              (line  53)
-* gsl_rng_set:                           Random number generator initialization.
-                                                              (line  25)
-* gsl_rng_size:                          Auxiliary random number generator functions.
-                                                              (line  30)
-* gsl_rng_slatec:                        Other random number generators.
-                                                              (line 140)
-* gsl_rng_state:                         Auxiliary random number generator functions.
-                                                              (line  29)
-* gsl_rng_taus:                          Random number generator algorithms.
-                                                              (line 137)
-* gsl_rng_taus2:                         Random number generator algorithms.
-                                                              (line 138)
-* gsl_rng_transputer:                    Other random number generators.
-                                                              (line  95)
-* gsl_rng_tt800:                         Other random number generators.
-                                                              (line  74)
-* gsl_rng_types_setup:                   Auxiliary random number generator functions.
-                                                              (line  40)
-* gsl_rng_uni:                           Other random number generators.
-                                                              (line 133)
-* gsl_rng_uni32:                         Other random number generators.
-                                                              (line 134)
-* gsl_rng_uniform:                       Sampling from a random number generator.
-                                                              (line  18)
-* gsl_rng_uniform_int:                   Sampling from a random number generator.
-                                                              (line  36)
-* gsl_rng_uniform_pos:                   Sampling from a random number generator.
-                                                              (line  28)
-* gsl_rng_vax:                           Other random number generators.
-                                                              (line  86)
-* gsl_rng_waterman14:                    Other random number generators.
-                                                              (line 178)
-* gsl_rng_zuf:                           Other random number generators.
-                                                              (line 144)
-* gsl_root_fdfsolver_alloc:              Initializing the Solver.
-                                                              (line  21)
-* gsl_root_fdfsolver_free:               Initializing the Solver.
-                                                              (line  48)
-* gsl_root_fdfsolver_iterate:            Root Finding Iteration.
-                                                              (line  13)
-* gsl_root_fdfsolver_name:               Initializing the Solver.
-                                                              (line  53)
-* gsl_root_fdfsolver_newton:             Root Finding Algorithms using Derivatives.
-                                                              (line  15)
-* gsl_root_fdfsolver_root:               Root Finding Iteration.
-                                                              (line  33)
-* gsl_root_fdfsolver_secant:             Root Finding Algorithms using Derivatives.
-                                                              (line  29)
-* gsl_root_fdfsolver_set:                Initializing the Solver.
-                                                              (line  42)
-* gsl_root_fdfsolver_steffenson:         Root Finding Algorithms using Derivatives.
-                                                              (line  60)
-* gsl_root_fsolver_alloc:                Initializing the Solver.
-                                                              (line   6)
-* gsl_root_fsolver_bisection:            Root Bracketing Algorithms.
-                                                              (line  16)
-* gsl_root_fsolver_brent:                Root Bracketing Algorithms.
-                                                              (line  49)
-* gsl_root_fsolver_falsepos:             Root Bracketing Algorithms.
-                                                              (line  32)
-* gsl_root_fsolver_free:                 Initializing the Solver.
-                                                              (line  47)
-* gsl_root_fsolver_iterate:              Root Finding Iteration.
-                                                              (line  12)
-* gsl_root_fsolver_name:                 Initializing the Solver.
-                                                              (line  51)
-* gsl_root_fsolver_root:                 Root Finding Iteration.
-                                                              (line  32)
-* gsl_root_fsolver_set:                  Initializing the Solver.
-                                                              (line  36)
-* gsl_root_fsolver_x_lower:              Root Finding Iteration.
-                                                              (line  38)
-* gsl_root_fsolver_x_upper:              Root Finding Iteration.
-                                                              (line  40)
-* gsl_root_test_delta:                   Search Stopping Parameters.
-                                                              (line  41)
-* gsl_root_test_interval:                Search Stopping Parameters.
-                                                              (line  19)
-* gsl_root_test_residual:                Search Stopping Parameters.
-                                                              (line  52)
-* GSL_SET_COMPLEX:                       Representation of complex numbers.
-                                                              (line  39)
-* gsl_set_error_handler:                 Error Handlers.      (line  43)
-* gsl_set_error_handler_off:             Error Handlers.      (line  69)
-* GSL_SET_IMAG:                          Representation of complex numbers.
-                                                              (line  49)
-* GSL_SET_REAL:                          Representation of complex numbers.
-                                                              (line  48)
-* gsl_sf_airy_Ai:                        Airy Functions.      (line   6)
-* gsl_sf_airy_Ai_deriv:                  Derivatives of Airy Functions.
-                                                              (line   6)
-* gsl_sf_airy_Ai_deriv_e:                Derivatives of Airy Functions.
-                                                              (line   7)
-* gsl_sf_airy_Ai_deriv_scaled:           Derivatives of Airy Functions.
-                                                              (line  18)
-* gsl_sf_airy_Ai_deriv_scaled_e:         Derivatives of Airy Functions.
-                                                              (line  20)
-* gsl_sf_airy_Ai_e:                      Airy Functions.      (line   7)
-* gsl_sf_airy_Ai_scaled:                 Airy Functions.      (line  18)
-* gsl_sf_airy_Ai_scaled_e:               Airy Functions.      (line  19)
-* gsl_sf_airy_Bi:                        Airy Functions.      (line  12)
-* gsl_sf_airy_Bi_deriv:                  Derivatives of Airy Functions.
-                                                              (line  12)
-* gsl_sf_airy_Bi_deriv_e:                Derivatives of Airy Functions.
-                                                              (line  13)
-* gsl_sf_airy_Bi_deriv_scaled:           Derivatives of Airy Functions.
-                                                              (line  26)
-* gsl_sf_airy_Bi_deriv_scaled_e:         Derivatives of Airy Functions.
-                                                              (line  28)
-* gsl_sf_airy_Bi_e:                      Airy Functions.      (line  13)
-* gsl_sf_airy_Bi_scaled:                 Airy Functions.      (line  25)
-* gsl_sf_airy_Bi_scaled_e:               Airy Functions.      (line  26)
-* gsl_sf_airy_zero_Ai:                   Zeros of Airy Functions.
-                                                              (line   6)
-* gsl_sf_airy_zero_Ai_deriv:             Zeros of Derivatives of Airy Functions.
-                                                              (line   6)
-* gsl_sf_airy_zero_Ai_deriv_e:           Zeros of Derivatives of Airy Functions.
-                                                              (line   7)
-* gsl_sf_airy_zero_Ai_e:                 Zeros of Airy Functions.
-                                                              (line   7)
-* gsl_sf_airy_zero_Bi:                   Zeros of Airy Functions.
-                                                              (line  12)
-* gsl_sf_airy_zero_Bi_deriv:             Zeros of Derivatives of Airy Functions.
-                                                              (line  12)
-* gsl_sf_airy_zero_Bi_deriv_e:           Zeros of Derivatives of Airy Functions.
-                                                              (line  13)
-* gsl_sf_airy_zero_Bi_e:                 Zeros of Airy Functions.
-                                                              (line  13)
-* gsl_sf_angle_restrict_pos:             Restriction Functions.
-                                                              (line  15)
-* gsl_sf_angle_restrict_pos_e:           Restriction Functions.
-                                                              (line  16)
-* gsl_sf_angle_restrict_symm:            Restriction Functions.
-                                                              (line   6)
-* gsl_sf_angle_restrict_symm_e:          Restriction Functions.
-                                                              (line   7)
-* gsl_sf_atanint:                        Arctangent Integral. (line   6)
-* gsl_sf_atanint_e:                      Arctangent Integral. (line   7)
-* gsl_sf_bessel_I0:                      Regular Modified Cylindrical Bessel Functions.
-                                                              (line   6)
-* gsl_sf_bessel_I0_e:                    Regular Modified Cylindrical Bessel Functions.
-                                                              (line   7)
-* gsl_sf_bessel_I0_scaled:               Regular Modified Cylindrical Bessel Functions.
-                                                              (line  31)
-* gsl_sf_bessel_i0_scaled:               Regular Modified Spherical Bessel Functions.
-                                                              (line  10)
-* gsl_sf_bessel_I0_scaled_e:             Regular Modified Cylindrical Bessel Functions.
-                                                              (line  32)
-* gsl_sf_bessel_i0_scaled_e:             Regular Modified Spherical Bessel Functions.
-                                                              (line  11)
-* gsl_sf_bessel_I1:                      Regular Modified Cylindrical Bessel Functions.
-                                                              (line  11)
-* gsl_sf_bessel_I1_e:                    Regular Modified Cylindrical Bessel Functions.
-                                                              (line  12)
-* gsl_sf_bessel_I1_scaled:               Regular Modified Cylindrical Bessel Functions.
-                                                              (line  37)
-* gsl_sf_bessel_i1_scaled:               Regular Modified Spherical Bessel Functions.
-                                                              (line  16)
-* gsl_sf_bessel_I1_scaled_e:             Regular Modified Cylindrical Bessel Functions.
-                                                              (line  38)
-* gsl_sf_bessel_i1_scaled_e:             Regular Modified Spherical Bessel Functions.
-                                                              (line  17)
-* gsl_sf_bessel_i2_scaled:               Regular Modified Spherical Bessel Functions.
-                                                              (line  22)
-* gsl_sf_bessel_i2_scaled_e:             Regular Modified Spherical Bessel Functions.
-                                                              (line  23)
-* gsl_sf_bessel_il_scaled:               Regular Modified Spherical Bessel Functions.
-                                                              (line  28)
-* gsl_sf_bessel_il_scaled_array:         Regular Modified Spherical Bessel Functions.
-                                                              (line  34)
-* gsl_sf_bessel_il_scaled_e:             Regular Modified Spherical Bessel Functions.
-                                                              (line  29)
-* gsl_sf_bessel_In:                      Regular Modified Cylindrical Bessel Functions.
-                                                              (line  16)
-* gsl_sf_bessel_Inu:                     Regular Modified Bessel Functions - Fractional Order.
-                                                              (line   6)
-* gsl_sf_bessel_Inu_e:                   Regular Modified Bessel Functions - Fractional Order.
-                                                              (line   7)
-* gsl_sf_bessel_Inu_scaled:              Regular Modified Bessel Functions - Fractional Order.
-                                                              (line  12)
-* gsl_sf_bessel_Inu_scaled_e:            Regular Modified Bessel Functions - Fractional Order.
-                                                              (line  13)
-* gsl_sf_bessel_In_array:                Regular Modified Cylindrical Bessel Functions.
-                                                              (line  22)
-* gsl_sf_bessel_In_e:                    Regular Modified Cylindrical Bessel Functions.
-                                                              (line  17)
-* gsl_sf_bessel_In_scaled:               Regular Modified Cylindrical Bessel Functions.
-                                                              (line  43)
-* gsl_sf_bessel_In_scaled_array:         Regular Modified Cylindrical Bessel Functions.
-                                                              (line  49)
-* gsl_sf_bessel_In_scaled_e:             Regular Modified Cylindrical Bessel Functions.
-                                                              (line  44)
-* gsl_sf_bessel_J0:                      Regular Cylindrical Bessel Functions.
-                                                              (line   6)
-* gsl_sf_bessel_j0:                      Regular Spherical Bessel Functions.
-                                                              (line   6)
-* gsl_sf_bessel_J0_e:                    Regular Cylindrical Bessel Functions.
-                                                              (line   7)
-* gsl_sf_bessel_j0_e:                    Regular Spherical Bessel Functions.
-                                                              (line   7)
-* gsl_sf_bessel_J1:                      Regular Cylindrical Bessel Functions.
-                                                              (line  11)
-* gsl_sf_bessel_j1:                      Regular Spherical Bessel Functions.
-                                                              (line  11)
-* gsl_sf_bessel_J1_e:                    Regular Cylindrical Bessel Functions.
-                                                              (line  12)
-* gsl_sf_bessel_j1_e:                    Regular Spherical Bessel Functions.
-                                                              (line  12)
-* gsl_sf_bessel_j2:                      Regular Spherical Bessel Functions.
-                                                              (line  16)
-* gsl_sf_bessel_j2_e:                    Regular Spherical Bessel Functions.
-                                                              (line  17)
-* gsl_sf_bessel_jl:                      Regular Spherical Bessel Functions.
-                                                              (line  21)
-* gsl_sf_bessel_jl_array:                Regular Spherical Bessel Functions.
-                                                              (line  27)
-* gsl_sf_bessel_jl_e:                    Regular Spherical Bessel Functions.
-                                                              (line  22)
-* gsl_sf_bessel_jl_steed_array:          Regular Spherical Bessel Functions.
-                                                              (line  35)
-* gsl_sf_bessel_Jn:                      Regular Cylindrical Bessel Functions.
-                                                              (line  16)
-* gsl_sf_bessel_Jnu:                     Regular Bessel Function - Fractional Order.
-                                                              (line   6)
-* gsl_sf_bessel_Jnu_e:                   Regular Bessel Function - Fractional Order.
-                                                              (line   7)
-* gsl_sf_bessel_Jn_array:                Regular Cylindrical Bessel Functions.
-                                                              (line  22)
-* gsl_sf_bessel_Jn_e:                    Regular Cylindrical Bessel Functions.
-                                                              (line  17)
-* gsl_sf_bessel_K0:                      Irregular Modified Cylindrical Bessel Functions.
-                                                              (line   6)
-* gsl_sf_bessel_K0_e:                    Irregular Modified Cylindrical Bessel Functions.
-                                                              (line   7)
-* gsl_sf_bessel_K0_scaled:               Irregular Modified Cylindrical Bessel Functions.
-                                                              (line  32)
-* gsl_sf_bessel_k0_scaled:               Irregular Modified Spherical Bessel Functions.
-                                                              (line  10)
-* gsl_sf_bessel_K0_scaled_e:             Irregular Modified Cylindrical Bessel Functions.
-                                                              (line  33)
-* gsl_sf_bessel_k0_scaled_e:             Irregular Modified Spherical Bessel Functions.
-                                                              (line  11)
-* gsl_sf_bessel_K1:                      Irregular Modified Cylindrical Bessel Functions.
-                                                              (line  11)
-* gsl_sf_bessel_K1_e:                    Irregular Modified Cylindrical Bessel Functions.
-                                                              (line  12)
-* gsl_sf_bessel_K1_scaled:               Irregular Modified Cylindrical Bessel Functions.
-                                                              (line  38)
-* gsl_sf_bessel_k1_scaled:               Irregular Modified Spherical Bessel Functions.
-                                                              (line  16)
-* gsl_sf_bessel_K1_scaled_e:             Irregular Modified Cylindrical Bessel Functions.
-                                                              (line  39)
-* gsl_sf_bessel_k1_scaled_e:             Irregular Modified Spherical Bessel Functions.
-                                                              (line  17)
-* gsl_sf_bessel_k2_scaled:               Irregular Modified Spherical Bessel Functions.
-                                                              (line  22)
-* gsl_sf_bessel_k2_scaled_e:             Irregular Modified Spherical Bessel Functions.
-                                                              (line  23)
-* gsl_sf_bessel_kl_scaled:               Irregular Modified Spherical Bessel Functions.
-                                                              (line  28)
-* gsl_sf_bessel_kl_scaled_array:         Irregular Modified Spherical Bessel Functions.
-                                                              (line  34)
-* gsl_sf_bessel_kl_scaled_e:             Irregular Modified Spherical Bessel Functions.
-                                                              (line  29)
-* gsl_sf_bessel_Kn:                      Irregular Modified Cylindrical Bessel Functions.
-                                                              (line  16)
-* gsl_sf_bessel_Knu:                     Irregular Modified Bessel Functions - Fractional Order.
-                                                              (line   6)
-* gsl_sf_bessel_Knu_e:                   Irregular Modified Bessel Functions - Fractional Order.
-                                                              (line   7)
-* gsl_sf_bessel_Knu_scaled:              Irregular Modified Bessel Functions - Fractional Order.
-                                                              (line  19)
-* gsl_sf_bessel_Knu_scaled_e:            Irregular Modified Bessel Functions - Fractional Order.
-                                                              (line  20)
-* gsl_sf_bessel_Kn_array:                Irregular Modified Cylindrical Bessel Functions.
-                                                              (line  22)
-* gsl_sf_bessel_Kn_e:                    Irregular Modified Cylindrical Bessel Functions.
-                                                              (line  17)
-* gsl_sf_bessel_Kn_scaled:               Irregular Modified Cylindrical Bessel Functions.
-                                                              (line  44)
-* gsl_sf_bessel_Kn_scaled_array:         Irregular Modified Cylindrical Bessel Functions.
-                                                              (line  50)
-* gsl_sf_bessel_Kn_scaled_e:             Irregular Modified Cylindrical Bessel Functions.
-                                                              (line  45)
-* gsl_sf_bessel_lnKnu:                   Irregular Modified Bessel Functions - Fractional Order.
-                                                              (line  12)
-* gsl_sf_bessel_lnKnu_e:                 Irregular Modified Bessel Functions - Fractional Order.
-                                                              (line  13)
-* gsl_sf_bessel_sequence_Jnu_e:          Regular Bessel Function - Fractional Order.
-                                                              (line  12)
-* gsl_sf_bessel_Y0:                      Irregular Cylindrical Bessel Functions.
-                                                              (line   6)
-* gsl_sf_bessel_y0:                      Irregular Spherical Bessel Functions.
-                                                              (line   6)
-* gsl_sf_bessel_Y0_e:                    Irregular Cylindrical Bessel Functions.
-                                                              (line   7)
-* gsl_sf_bessel_y0_e:                    Irregular Spherical Bessel Functions.
-                                                              (line   7)
-* gsl_sf_bessel_Y1:                      Irregular Cylindrical Bessel Functions.
-                                                              (line  11)
-* gsl_sf_bessel_y1:                      Irregular Spherical Bessel Functions.
-                                                              (line  11)
-* gsl_sf_bessel_Y1_e:                    Irregular Cylindrical Bessel Functions.
-                                                              (line  12)
-* gsl_sf_bessel_y1_e:                    Irregular Spherical Bessel Functions.
-                                                              (line  12)
-* gsl_sf_bessel_y2:                      Irregular Spherical Bessel Functions.
-                                                              (line  16)
-* gsl_sf_bessel_y2_e:                    Irregular Spherical Bessel Functions.
-                                                              (line  17)
-* gsl_sf_bessel_yl:                      Irregular Spherical Bessel Functions.
-                                                              (line  21)
-* gsl_sf_bessel_yl_array:                Irregular Spherical Bessel Functions.
-                                                              (line  27)
-* gsl_sf_bessel_yl_e:                    Irregular Spherical Bessel Functions.
-                                                              (line  22)
-* gsl_sf_bessel_Yn:                      Irregular Cylindrical Bessel Functions.
-                                                              (line  16)
-* gsl_sf_bessel_Ynu:                     Irregular Bessel Functions - Fractional Order.
-                                                              (line   6)
-* gsl_sf_bessel_Ynu_e:                   Irregular Bessel Functions - Fractional Order.
-                                                              (line   7)
-* gsl_sf_bessel_Yn_array:                Irregular Cylindrical Bessel Functions.
-                                                              (line  22)
-* gsl_sf_bessel_Yn_e:                    Irregular Cylindrical Bessel Functions.
-                                                              (line  17)
-* gsl_sf_bessel_zero_J0:                 Zeros of Regular Bessel Functions.
-                                                              (line   6)
-* gsl_sf_bessel_zero_J0_e:               Zeros of Regular Bessel Functions.
-                                                              (line   7)
-* gsl_sf_bessel_zero_J1:                 Zeros of Regular Bessel Functions.
-                                                              (line  12)
-* gsl_sf_bessel_zero_J1_e:               Zeros of Regular Bessel Functions.
-                                                              (line  13)
-* gsl_sf_bessel_zero_Jnu:                Zeros of Regular Bessel Functions.
-                                                              (line  18)
-* gsl_sf_bessel_zero_Jnu_e:              Zeros of Regular Bessel Functions.
-                                                              (line  19)
-* gsl_sf_beta:                           Beta Functions.      (line   6)
-* gsl_sf_beta_e:                         Beta Functions.      (line   7)
-* gsl_sf_beta_inc:                       Incomplete Beta Function.
-                                                              (line   6)
-* gsl_sf_beta_inc_e:                     Incomplete Beta Function.
-                                                              (line   7)
-* gsl_sf_Chi:                            Hyperbolic Integrals.
-                                                              (line  11)
-* gsl_sf_Chi_e:                          Hyperbolic Integrals.
-                                                              (line  12)
-* gsl_sf_choose:                         Factorials.          (line  38)
-* gsl_sf_choose_e:                       Factorials.          (line  39)
-* gsl_sf_Ci:                             Trigonometric Integrals.
-                                                              (line  11)
-* gsl_sf_Ci_e:                           Trigonometric Integrals.
-                                                              (line  12)
-* gsl_sf_clausen:                        Clausen Functions.   (line  14)
-* gsl_sf_clausen_e:                      Clausen Functions.   (line  15)
-* gsl_sf_complex_cos_e:                  Trigonometric Functions for Complex Arguments.
-                                                              (line  11)
-* gsl_sf_complex_dilog_e:                Complex Argument.    (line   6)
-* gsl_sf_complex_logsin_e:               Trigonometric Functions for Complex Arguments.
-                                                              (line  16)
-* gsl_sf_complex_log_e:                  Logarithm and Related Functions.
-                                                              (line  19)
-* gsl_sf_complex_sin_e:                  Trigonometric Functions for Complex Arguments.
-                                                              (line   6)
-* gsl_sf_conicalP_0:                     Conical Functions.   (line  22)
-* gsl_sf_conicalP_0_e:                   Conical Functions.   (line  23)
-* gsl_sf_conicalP_1:                     Conical Functions.   (line  28)
-* gsl_sf_conicalP_1_e:                   Conical Functions.   (line  29)
-* gsl_sf_conicalP_cyl_reg:               Conical Functions.   (line  41)
-* gsl_sf_conicalP_cyl_reg_e:             Conical Functions.   (line  43)
-* gsl_sf_conicalP_half:                  Conical Functions.   (line  10)
-* gsl_sf_conicalP_half_e:                Conical Functions.   (line  11)
-* gsl_sf_conicalP_mhalf:                 Conical Functions.   (line  16)
-* gsl_sf_conicalP_mhalf_e:               Conical Functions.   (line  17)
-* gsl_sf_conicalP_sph_reg:               Conical Functions.   (line  34)
-* gsl_sf_conicalP_sph_reg_e:             Conical Functions.   (line  36)
-* gsl_sf_cos:                            Circular Trigonometric Functions.
-                                                              (line  10)
-* gsl_sf_cos_e:                          Circular Trigonometric Functions.
-                                                              (line  11)
-* gsl_sf_cos_err_e:                      Trigonometric Functions With Error Estimates.
-                                                              (line  13)
-* gsl_sf_coulomb_CL_array:               Coulomb Wave Function Normalization Constant.
-                                                              (line  14)
-* gsl_sf_coulomb_CL_e:                   Coulomb Wave Function Normalization Constant.
-                                                              (line   9)
-* gsl_sf_coulomb_wave_FGp_array:         Coulomb Wave Functions.
-                                                              (line  47)
-* gsl_sf_coulomb_wave_FG_array:          Coulomb Wave Functions.
-                                                              (line  39)
-* gsl_sf_coulomb_wave_FG_e:              Coulomb Wave Functions.
-                                                              (line  19)
-* gsl_sf_coulomb_wave_F_array:           Coulomb Wave Functions.
-                                                              (line  33)
-* gsl_sf_coulomb_wave_sphF_array:        Coulomb Wave Functions.
-                                                              (line  57)
-* gsl_sf_coupling_3j:                    3-j Symbols.         (line   6)
-* gsl_sf_coupling_3j_e:                  3-j Symbols.         (line   8)
-* gsl_sf_coupling_6j:                    6-j Symbols.         (line   6)
-* gsl_sf_coupling_6j_e:                  6-j Symbols.         (line   8)
-* gsl_sf_coupling_9j:                    9-j Symbols.         (line   6)
-* gsl_sf_coupling_9j_e:                  9-j Symbols.         (line   9)
-* gsl_sf_dawson:                         Dawson Function.     (line  11)
-* gsl_sf_dawson_e:                       Dawson Function.     (line  12)
-* gsl_sf_debye_1:                        Debye Functions.     (line  13)
-* gsl_sf_debye_1_e:                      Debye Functions.     (line  14)
-* gsl_sf_debye_2:                        Debye Functions.     (line  18)
-* gsl_sf_debye_2_e:                      Debye Functions.     (line  19)
-* gsl_sf_debye_3:                        Debye Functions.     (line  23)
-* gsl_sf_debye_3_e:                      Debye Functions.     (line  24)
-* gsl_sf_debye_4:                        Debye Functions.     (line  28)
-* gsl_sf_debye_4_e:                      Debye Functions.     (line  29)
-* gsl_sf_debye_5:                        Debye Functions.     (line  33)
-* gsl_sf_debye_5_e:                      Debye Functions.     (line  34)
-* gsl_sf_debye_6:                        Debye Functions.     (line  38)
-* gsl_sf_debye_6_e:                      Debye Functions.     (line  39)
-* gsl_sf_dilog:                          Real Argument.       (line   6)
-* gsl_sf_dilog_e:                        Real Argument.       (line   7)
-* gsl_sf_doublefact:                     Factorials.          (line  18)
-* gsl_sf_doublefact_e:                   Factorials.          (line  19)
-* gsl_sf_ellint_D:                       Legendre Form of Incomplete Elliptic Integrals.
-                                                              (line  34)
-* gsl_sf_ellint_D_e:                     Legendre Form of Incomplete Elliptic Integrals.
-                                                              (line  36)
-* gsl_sf_ellint_E:                       Legendre Form of Incomplete Elliptic Integrals.
-                                                              (line  15)
-* gsl_sf_ellint_Ecomp:                   Legendre Form of Complete Elliptic Integrals.
-                                                              (line  13)
-* gsl_sf_ellint_Ecomp_e:                 Legendre Form of Complete Elliptic Integrals.
-                                                              (line  14)
-* gsl_sf_ellint_E_e:                     Legendre Form of Incomplete Elliptic Integrals.
-                                                              (line  17)
-* gsl_sf_ellint_F:                       Legendre Form of Incomplete Elliptic Integrals.
-                                                              (line   6)
-* gsl_sf_ellint_F_e:                     Legendre Form of Incomplete Elliptic Integrals.
-                                                              (line   8)
-* gsl_sf_ellint_Kcomp:                   Legendre Form of Complete Elliptic Integrals.
-                                                              (line   6)
-* gsl_sf_ellint_Kcomp_e:                 Legendre Form of Complete Elliptic Integrals.
-                                                              (line   7)
-* gsl_sf_ellint_P:                       Legendre Form of Incomplete Elliptic Integrals.
-                                                              (line  24)
-* gsl_sf_ellint_Pcomp:                   Legendre Form of Complete Elliptic Integrals.
-                                                              (line  20)
-* gsl_sf_ellint_Pcomp_e:                 Legendre Form of Complete Elliptic Integrals.
-                                                              (line  22)
-* gsl_sf_ellint_P_e:                     Legendre Form of Incomplete Elliptic Integrals.
-                                                              (line  26)
-* gsl_sf_ellint_RC:                      Carlson Forms.       (line   6)
-* gsl_sf_ellint_RC_e:                    Carlson Forms.       (line   8)
-* gsl_sf_ellint_RD:                      Carlson Forms.       (line  13)
-* gsl_sf_ellint_RD_e:                    Carlson Forms.       (line  15)
-* gsl_sf_ellint_RF:                      Carlson Forms.       (line  20)
-* gsl_sf_ellint_RF_e:                    Carlson Forms.       (line  22)
-* gsl_sf_ellint_RJ:                      Carlson Forms.       (line  27)
-* gsl_sf_ellint_RJ_e:                    Carlson Forms.       (line  29)
-* gsl_sf_elljac_e:                       Elliptic Functions (Jacobi).
-                                                              (line  10)
-* gsl_sf_erf:                            Error Function.      (line   6)
-* gsl_sf_erfc:                           Complementary Error Function.
-                                                              (line   6)
-* gsl_sf_erfc_e:                         Complementary Error Function.
-                                                              (line   7)
-* gsl_sf_erf_e:                          Error Function.      (line   7)
-* gsl_sf_erf_Q:                          Probability functions.
-                                                              (line  14)
-* gsl_sf_erf_Q_e:                        Probability functions.
-                                                              (line  15)
-* gsl_sf_erf_Z:                          Probability functions.
-                                                              (line   9)
-* gsl_sf_erf_Z_e:                        Probability functions.
-                                                              (line  10)
-* gsl_sf_eta:                            Eta Function.        (line  12)
-* gsl_sf_eta_e:                          Eta Function.        (line  13)
-* gsl_sf_eta_int:                        Eta Function.        (line   8)
-* gsl_sf_eta_int_e:                      Eta Function.        (line   9)
-* gsl_sf_exp:                            Exponential Function.
-                                                              (line   6)
-* gsl_sf_expint_3:                       Ei_3(x).             (line   6)
-* gsl_sf_expint_3_e:                     Ei_3(x).             (line   7)
-* gsl_sf_expint_E1:                      Exponential Integral.
-                                                              (line   6)
-* gsl_sf_expint_E1_e:                    Exponential Integral.
-                                                              (line   7)
-* gsl_sf_expint_E2:                      Exponential Integral.
-                                                              (line  12)
-* gsl_sf_expint_E2_e:                    Exponential Integral.
-                                                              (line  13)
-* gsl_sf_expint_Ei:                      Ei(x).               (line   6)
-* gsl_sf_expint_Ei_e:                    Ei(x).               (line   7)
-* gsl_sf_expint_En:                      Exponential Integral.
-                                                              (line  19)
-* gsl_sf_expint_En_e:                    Exponential Integral.
-                                                              (line  20)
-* gsl_sf_expm1:                          Relative Exponential Functions.
-                                                              (line   6)
-* gsl_sf_expm1_e:                        Relative Exponential Functions.
-                                                              (line   7)
-* gsl_sf_exprel:                         Relative Exponential Functions.
-                                                              (line  11)
-* gsl_sf_exprel_2:                       Relative Exponential Functions.
-                                                              (line  18)
-* gsl_sf_exprel_2_e:                     Relative Exponential Functions.
-                                                              (line  19)
-* gsl_sf_exprel_e:                       Relative Exponential Functions.
-                                                              (line  12)
-* gsl_sf_exprel_n:                       Relative Exponential Functions.
-                                                              (line  25)
-* gsl_sf_exprel_n_e:                     Relative Exponential Functions.
-                                                              (line  26)
-* gsl_sf_exp_e:                          Exponential Function.
-                                                              (line   7)
-* gsl_sf_exp_e10_e:                      Exponential Function.
-                                                              (line  11)
-* gsl_sf_exp_err_e:                      Exponentiation With Error Estimate.
-                                                              (line   6)
-* gsl_sf_exp_err_e10_e:                  Exponentiation With Error Estimate.
-                                                              (line  10)
-* gsl_sf_exp_mult:                       Exponential Function.
-                                                              (line  18)
-* gsl_sf_exp_mult_e:                     Exponential Function.
-                                                              (line  19)
-* gsl_sf_exp_mult_e10_e:                 Exponential Function.
-                                                              (line  24)
-* gsl_sf_exp_mult_err_e:                 Exponentiation With Error Estimate.
-                                                              (line  16)
-* gsl_sf_exp_mult_err_e10_e:             Exponentiation With Error Estimate.
-                                                              (line  21)
-* gsl_sf_fact:                           Factorials.          (line  11)
-* gsl_sf_fact_e:                         Factorials.          (line  12)
-* gsl_sf_fermi_dirac_0:                  Complete Fermi-Dirac Integrals.
-                                                              (line  19)
-* gsl_sf_fermi_dirac_0_e:                Complete Fermi-Dirac Integrals.
-                                                              (line  20)
-* gsl_sf_fermi_dirac_1:                  Complete Fermi-Dirac Integrals.
-                                                              (line  25)
-* gsl_sf_fermi_dirac_1_e:                Complete Fermi-Dirac Integrals.
-                                                              (line  26)
-* gsl_sf_fermi_dirac_2:                  Complete Fermi-Dirac Integrals.
-                                                              (line  31)
-* gsl_sf_fermi_dirac_2_e:                Complete Fermi-Dirac Integrals.
-                                                              (line  32)
-* gsl_sf_fermi_dirac_3half:              Complete Fermi-Dirac Integrals.
-                                                              (line  56)
-* gsl_sf_fermi_dirac_3half_e:            Complete Fermi-Dirac Integrals.
-                                                              (line  57)
-* gsl_sf_fermi_dirac_half:               Complete Fermi-Dirac Integrals.
-                                                              (line  50)
-* gsl_sf_fermi_dirac_half_e:             Complete Fermi-Dirac Integrals.
-                                                              (line  51)
-* gsl_sf_fermi_dirac_inc_0:              Incomplete Fermi-Dirac Integrals.
-                                                              (line  10)
-* gsl_sf_fermi_dirac_inc_0_e:            Incomplete Fermi-Dirac Integrals.
-                                                              (line  11)
-* gsl_sf_fermi_dirac_int:                Complete Fermi-Dirac Integrals.
-                                                              (line  37)
-* gsl_sf_fermi_dirac_int_e:              Complete Fermi-Dirac Integrals.
-                                                              (line  38)
-* gsl_sf_fermi_dirac_m1:                 Complete Fermi-Dirac Integrals.
-                                                              (line  12)
-* gsl_sf_fermi_dirac_m1_e:               Complete Fermi-Dirac Integrals.
-                                                              (line  13)
-* gsl_sf_fermi_dirac_mhalf:              Complete Fermi-Dirac Integrals.
-                                                              (line  44)
-* gsl_sf_fermi_dirac_mhalf_e:            Complete Fermi-Dirac Integrals.
-                                                              (line  45)
-* gsl_sf_gamma:                          Gamma Functions.     (line  14)
-* gsl_sf_gammainv:                       Gamma Functions.     (line  49)
-* gsl_sf_gammainv_e:                     Gamma Functions.     (line  50)
-* gsl_sf_gammastar:                      Gamma Functions.     (line  40)
-* gsl_sf_gammastar_e:                    Gamma Functions.     (line  41)
-* gsl_sf_gamma_e:                        Gamma Functions.     (line  15)
-* gsl_sf_gamma_inc:                      Incomplete Gamma Functions.
-                                                              (line   6)
-* gsl_sf_gamma_inc_e:                    Incomplete Gamma Functions.
-                                                              (line   7)
-* gsl_sf_gamma_inc_P:                    Incomplete Gamma Functions.
-                                                              (line  20)
-* gsl_sf_gamma_inc_P_e:                  Incomplete Gamma Functions.
-                                                              (line  21)
-* gsl_sf_gamma_inc_Q:                    Incomplete Gamma Functions.
-                                                              (line  13)
-* gsl_sf_gamma_inc_Q_e:                  Incomplete Gamma Functions.
-                                                              (line  14)
-* gsl_sf_gegenpoly_1:                    Gegenbauer Functions.
-                                                              (line  11)
-* gsl_sf_gegenpoly_1_e:                  Gegenbauer Functions.
-                                                              (line  14)
-* gsl_sf_gegenpoly_2:                    Gegenbauer Functions.
-                                                              (line  12)
-* gsl_sf_gegenpoly_2_e:                  Gegenbauer Functions.
-                                                              (line  16)
-* gsl_sf_gegenpoly_3:                    Gegenbauer Functions.
-                                                              (line  13)
-* gsl_sf_gegenpoly_3_e:                  Gegenbauer Functions.
-                                                              (line  18)
-* gsl_sf_gegenpoly_array:                Gegenbauer Functions.
-                                                              (line  30)
-* gsl_sf_gegenpoly_n:                    Gegenbauer Functions.
-                                                              (line  23)
-* gsl_sf_gegenpoly_n_e:                  Gegenbauer Functions.
-                                                              (line  24)
-* gsl_sf_hazard:                         Probability functions.
-                                                              (line  27)
-* gsl_sf_hazard_e:                       Probability functions.
-                                                              (line  28)
-* gsl_sf_hydrogenicR:                    Normalized Hydrogenic Bound States.
-                                                              (line  12)
-* gsl_sf_hydrogenicR_1:                  Normalized Hydrogenic Bound States.
-                                                              (line   6)
-* gsl_sf_hydrogenicR_1_e:                Normalized Hydrogenic Bound States.
-                                                              (line   7)
-* gsl_sf_hydrogenicR_e:                  Normalized Hydrogenic Bound States.
-                                                              (line  14)
-* gsl_sf_hyperg_0F1:                     Hypergeometric Functions.
-                                                              (line  10)
-* gsl_sf_hyperg_0F1_e:                   Hypergeometric Functions.
-                                                              (line  11)
-* gsl_sf_hyperg_1F1:                     Hypergeometric Functions.
-                                                              (line  21)
-* gsl_sf_hyperg_1F1_e:                   Hypergeometric Functions.
-                                                              (line  22)
-* gsl_sf_hyperg_1F1_int:                 Hypergeometric Functions.
-                                                              (line  15)
-* gsl_sf_hyperg_1F1_int_e:               Hypergeometric Functions.
-                                                              (line  16)
-* gsl_sf_hyperg_2F0:                     Hypergeometric Functions.
-                                                              (line  85)
-* gsl_sf_hyperg_2F0_e:                   Hypergeometric Functions.
-                                                              (line  86)
-* gsl_sf_hyperg_2F1:                     Hypergeometric Functions.
-                                                              (line  51)
-* gsl_sf_hyperg_2F1_conj:                Hypergeometric Functions.
-                                                              (line  63)
-* gsl_sf_hyperg_2F1_conj_e:              Hypergeometric Functions.
-                                                              (line  65)
-* gsl_sf_hyperg_2F1_conj_renorm:         Hypergeometric Functions.
-                                                              (line  77)
-* gsl_sf_hyperg_2F1_conj_renorm_e:       Hypergeometric Functions.
-                                                              (line  79)
-* gsl_sf_hyperg_2F1_e:                   Hypergeometric Functions.
-                                                              (line  53)
-* gsl_sf_hyperg_2F1_renorm:              Hypergeometric Functions.
-                                                              (line  70)
-* gsl_sf_hyperg_2F1_renorm_e:            Hypergeometric Functions.
-                                                              (line  72)
-* gsl_sf_hyperg_U:                       Hypergeometric Functions.
-                                                              (line  39)
-* gsl_sf_hyperg_U_e:                     Hypergeometric Functions.
-                                                              (line  40)
-* gsl_sf_hyperg_U_e10_e:                 Hypergeometric Functions.
-                                                              (line  45)
-* gsl_sf_hyperg_U_int:                   Hypergeometric Functions.
-                                                              (line  27)
-* gsl_sf_hyperg_U_int_e:                 Hypergeometric Functions.
-                                                              (line  28)
-* gsl_sf_hyperg_U_int_e10_e:             Hypergeometric Functions.
-                                                              (line  33)
-* gsl_sf_hypot:                          Circular Trigonometric Functions.
-                                                              (line  14)
-* gsl_sf_hypot_e:                        Circular Trigonometric Functions.
-                                                              (line  15)
-* gsl_sf_hzeta:                          Hurwitz Zeta Function.
-                                                              (line   9)
-* gsl_sf_hzeta_e:                        Hurwitz Zeta Function.
-                                                              (line  10)
-* gsl_sf_laguerre_1:                     Laguerre Functions.  (line  16)
-* gsl_sf_laguerre_1_e:                   Laguerre Functions.  (line  19)
-* gsl_sf_laguerre_2:                     Laguerre Functions.  (line  17)
-* gsl_sf_laguerre_2_e:                   Laguerre Functions.  (line  21)
-* gsl_sf_laguerre_3:                     Laguerre Functions.  (line  18)
-* gsl_sf_laguerre_3_e:                   Laguerre Functions.  (line  23)
-* gsl_sf_laguerre_n:                     Laguerre Functions.  (line  28)
-* gsl_sf_laguerre_n_e:                   Laguerre Functions.  (line  30)
-* gsl_sf_lambert_W0:                     Lambert W Functions. (line  13)
-* gsl_sf_lambert_W0_e:                   Lambert W Functions. (line  14)
-* gsl_sf_lambert_Wm1:                    Lambert W Functions. (line  18)
-* gsl_sf_lambert_Wm1_e:                  Lambert W Functions. (line  19)
-* gsl_sf_legendre_array_size:            Associated Legendre Polynomials and Spherical Harmonics.
-                                                              (line  47)
-* gsl_sf_legendre_H3d:                   Radial Functions for Hyperbolic Space.
-                                                              (line  30)
-* gsl_sf_legendre_H3d_0:                 Radial Functions for Hyperbolic Space.
-                                                              (line  11)
-* gsl_sf_legendre_H3d_0_e:               Radial Functions for Hyperbolic Space.
-                                                              (line  12)
-* gsl_sf_legendre_H3d_1:                 Radial Functions for Hyperbolic Space.
-                                                              (line  20)
-* gsl_sf_legendre_H3d_1_e:               Radial Functions for Hyperbolic Space.
-                                                              (line  21)
-* gsl_sf_legendre_H3d_array:             Radial Functions for Hyperbolic Space.
-                                                              (line  39)
-* gsl_sf_legendre_H3d_e:                 Radial Functions for Hyperbolic Space.
-                                                              (line  32)
-* gsl_sf_legendre_P1:                    Legendre Polynomials.
-                                                              (line   6)
-* gsl_sf_legendre_P1_e:                  Legendre Polynomials.
-                                                              (line   9)
-* gsl_sf_legendre_P2:                    Legendre Polynomials.
-                                                              (line   7)
-* gsl_sf_legendre_P2_e:                  Legendre Polynomials.
-                                                              (line  11)
-* gsl_sf_legendre_P3:                    Legendre Polynomials.
-                                                              (line   8)
-* gsl_sf_legendre_P3_e:                  Legendre Polynomials.
-                                                              (line  13)
-* gsl_sf_legendre_Pl:                    Legendre Polynomials.
-                                                              (line  18)
-* gsl_sf_legendre_Plm:                   Associated Legendre Polynomials and Spherical Harmonics.
-                                                              (line  17)
-* gsl_sf_legendre_Plm_array:             Associated Legendre Polynomials and Spherical Harmonics.
-                                                              (line  23)
-* gsl_sf_legendre_Plm_deriv_array:       Associated Legendre Polynomials and Spherical Harmonics.
-                                                              (line  25)
-* gsl_sf_legendre_Plm_e:                 Associated Legendre Polynomials and Spherical Harmonics.
-                                                              (line  18)
-* gsl_sf_legendre_Pl_array:              Legendre Polynomials.
-                                                              (line  24)
-* gsl_sf_legendre_Pl_deriv_array:        Legendre Polynomials.
-                                                              (line  26)
-* gsl_sf_legendre_Pl_e:                  Legendre Polynomials.
-                                                              (line  19)
-* gsl_sf_legendre_Q0:                    Legendre Polynomials.
-                                                              (line  32)
-* gsl_sf_legendre_Q0_e:                  Legendre Polynomials.
-                                                              (line  33)
-* gsl_sf_legendre_Q1:                    Legendre Polynomials.
-                                                              (line  38)
-* gsl_sf_legendre_Q1_e:                  Legendre Polynomials.
-                                                              (line  39)
-* gsl_sf_legendre_Ql:                    Legendre Polynomials.
-                                                              (line  44)
-* gsl_sf_legendre_Ql_e:                  Legendre Polynomials.
-                                                              (line  45)
-* gsl_sf_legendre_sphPlm:                Associated Legendre Polynomials and Spherical Harmonics.
-                                                              (line  30)
-* gsl_sf_legendre_sphPlm_array:          Associated Legendre Polynomials and Spherical Harmonics.
-                                                              (line  39)
-* gsl_sf_legendre_sphPlm_deriv_array:    Associated Legendre Polynomials and Spherical Harmonics.
-                                                              (line  41)
-* gsl_sf_legendre_sphPlm_e:              Associated Legendre Polynomials and Spherical Harmonics.
-                                                              (line  31)
-* gsl_sf_lnbeta:                         Beta Functions.      (line  13)
-* gsl_sf_lnbeta_e:                       Beta Functions.      (line  14)
-* gsl_sf_lnchoose:                       Factorials.          (line  44)
-* gsl_sf_lnchoose_e:                     Factorials.          (line  45)
-* gsl_sf_lncosh:                         Hyperbolic Trigonometric Functions.
-                                                              (line  10)
-* gsl_sf_lncosh_e:                       Hyperbolic Trigonometric Functions.
-                                                              (line  11)
-* gsl_sf_lndoublefact:                   Factorials.          (line  32)
-* gsl_sf_lndoublefact_e:                 Factorials.          (line  33)
-* gsl_sf_lnfact:                         Factorials.          (line  25)
-* gsl_sf_lnfact_e:                       Factorials.          (line  26)
-* gsl_sf_lngamma:                        Gamma Functions.     (line  22)
-* gsl_sf_lngamma_complex_e:              Gamma Functions.     (line  54)
-* gsl_sf_lngamma_e:                      Gamma Functions.     (line  23)
-* gsl_sf_lngamma_sgn_e:                  Gamma Functions.     (line  30)
-* gsl_sf_lnpoch:                         Pochhammer Symbol.   (line  14)
-* gsl_sf_lnpoch_e:                       Pochhammer Symbol.   (line  15)
-* gsl_sf_lnpoch_sgn_e:                   Pochhammer Symbol.   (line  20)
-* gsl_sf_lnsinh:                         Hyperbolic Trigonometric Functions.
-                                                              (line   6)
-* gsl_sf_lnsinh_e:                       Hyperbolic Trigonometric Functions.
-                                                              (line   7)
-* gsl_sf_log:                            Logarithm and Related Functions.
-                                                              (line  10)
-* gsl_sf_log_1plusx:                     Logarithm and Related Functions.
-                                                              (line  25)
-* gsl_sf_log_1plusx_e:                   Logarithm and Related Functions.
-                                                              (line  26)
-* gsl_sf_log_1plusx_mx:                  Logarithm and Related Functions.
-                                                              (line  30)
-* gsl_sf_log_1plusx_mx_e:                Logarithm and Related Functions.
-                                                              (line  31)
-* gsl_sf_log_abs:                        Logarithm and Related Functions.
-                                                              (line  14)
-* gsl_sf_log_abs_e:                      Logarithm and Related Functions.
-                                                              (line  15)
-* gsl_sf_log_e:                          Logarithm and Related Functions.
-                                                              (line  11)
-* gsl_sf_log_erfc:                       Log Complementary Error Function.
-                                                              (line   6)
-* gsl_sf_log_erfc_e:                     Log Complementary Error Function.
-                                                              (line   7)
-* gsl_sf_mathieu_a:                      Mathieu Function Characteristic Values.
-                                                              (line   6)
-* gsl_sf_mathieu_alloc:                  Mathieu Function Workspace.
-                                                              (line  10)
-* gsl_sf_mathieu_a_array:                Mathieu Function Characteristic Values.
-                                                              (line  13)
-* gsl_sf_mathieu_b:                      Mathieu Function Characteristic Values.
-                                                              (line   8)
-* gsl_sf_mathieu_b_array:                Mathieu Function Characteristic Values.
-                                                              (line  16)
-* gsl_sf_mathieu_ce:                     Angular Mathieu Functions.
-                                                              (line   6)
-* gsl_sf_mathieu_ce_array:               Angular Mathieu Functions.
-                                                              (line  13)
-* gsl_sf_mathieu_free:                   Mathieu Function Workspace.
-                                                              (line  17)
-* gsl_sf_mathieu_Mc:                     Radial Mathieu Functions.
-                                                              (line   6)
-* gsl_sf_mathieu_Mc_array:               Radial Mathieu Functions.
-                                                              (line  17)
-* gsl_sf_mathieu_Ms:                     Radial Mathieu Functions.
-                                                              (line   8)
-* gsl_sf_mathieu_Ms_array:               Radial Mathieu Functions.
-                                                              (line  20)
-* gsl_sf_mathieu_se:                     Angular Mathieu Functions.
-                                                              (line   8)
-* gsl_sf_mathieu_se_array:               Angular Mathieu Functions.
-                                                              (line  16)
-* gsl_sf_multiply_e:                     Elementary Operations.
-                                                              (line  10)
-* gsl_sf_multiply_err_e:                 Elementary Operations.
-                                                              (line  15)
-* gsl_sf_poch:                           Pochhammer Symbol.   (line   6)
-* gsl_sf_pochrel:                        Pochhammer Symbol.   (line  27)
-* gsl_sf_pochrel_e:                      Pochhammer Symbol.   (line  28)
-* gsl_sf_poch_e:                         Pochhammer Symbol.   (line   7)
-* gsl_sf_polar_to_rect:                  Conversion Functions.
-                                                              (line   6)
-* gsl_sf_pow_int:                        Power Function.      (line  10)
-* gsl_sf_pow_int_e:                      Power Function.      (line  11)
-* gsl_sf_psi:                            Digamma Function.    (line  11)
-* gsl_sf_psi_1:                          Trigamma Function.   (line  11)
-* gsl_sf_psi_1piy:                       Digamma Function.    (line  16)
-* gsl_sf_psi_1piy_e:                     Digamma Function.    (line  17)
-* gsl_sf_psi_1_e:                        Trigamma Function.   (line  12)
-* gsl_sf_psi_1_int:                      Trigamma Function.   (line   6)
-* gsl_sf_psi_1_int_e:                    Trigamma Function.   (line   7)
-* gsl_sf_psi_e:                          Digamma Function.    (line  12)
-* gsl_sf_psi_int:                        Digamma Function.    (line   6)
-* gsl_sf_psi_int_e:                      Digamma Function.    (line   7)
-* gsl_sf_psi_n:                          Polygamma Function.  (line   6)
-* gsl_sf_psi_n_e:                        Polygamma Function.  (line   7)
-* gsl_sf_rect_to_polar:                  Conversion Functions.
-                                                              (line  12)
-* gsl_sf_Shi:                            Hyperbolic Integrals.
-                                                              (line   6)
-* gsl_sf_Shi_e:                          Hyperbolic Integrals.
-                                                              (line   7)
-* gsl_sf_Si:                             Trigonometric Integrals.
-                                                              (line   6)
-* gsl_sf_sin:                            Circular Trigonometric Functions.
-                                                              (line   6)
-* gsl_sf_sinc:                           Circular Trigonometric Functions.
-                                                              (line  20)
-* gsl_sf_sinc_e:                         Circular Trigonometric Functions.
-                                                              (line  21)
-* gsl_sf_sin_e:                          Circular Trigonometric Functions.
-                                                              (line   7)
-* gsl_sf_sin_err_e:                      Trigonometric Functions With Error Estimates.
-                                                              (line   6)
-* gsl_sf_Si_e:                           Trigonometric Integrals.
-                                                              (line   7)
-* gsl_sf_synchrotron_1:                  Synchrotron Functions.
-                                                              (line   9)
-* gsl_sf_synchrotron_1_e:                Synchrotron Functions.
-                                                              (line  10)
-* gsl_sf_synchrotron_2:                  Synchrotron Functions.
-                                                              (line  15)
-* gsl_sf_synchrotron_2_e:                Synchrotron Functions.
-                                                              (line  16)
-* gsl_sf_taylorcoeff:                    Factorials.          (line  50)
-* gsl_sf_taylorcoeff_e:                  Factorials.          (line  51)
-* gsl_sf_transport_2:                    Transport Functions. (line  10)
-* gsl_sf_transport_2_e:                  Transport Functions. (line  11)
-* gsl_sf_transport_3:                    Transport Functions. (line  15)
-* gsl_sf_transport_3_e:                  Transport Functions. (line  16)
-* gsl_sf_transport_4:                    Transport Functions. (line  20)
-* gsl_sf_transport_4_e:                  Transport Functions. (line  21)
-* gsl_sf_transport_5:                    Transport Functions. (line  25)
-* gsl_sf_transport_5_e:                  Transport Functions. (line  26)
-* gsl_sf_zeta:                           Riemann Zeta Function.
-                                                              (line  14)
-* gsl_sf_zetam1:                         Riemann Zeta Function Minus One.
-                                                              (line  14)
-* gsl_sf_zetam1_e:                       Riemann Zeta Function Minus One.
-                                                              (line  15)
-* gsl_sf_zetam1_int:                     Riemann Zeta Function Minus One.
-                                                              (line  10)
-* gsl_sf_zetam1_int_e:                   Riemann Zeta Function Minus One.
-                                                              (line  11)
-* gsl_sf_zeta_e:                         Riemann Zeta Function.
-                                                              (line  15)
-* gsl_sf_zeta_int:                       Riemann Zeta Function.
-                                                              (line   9)
-* gsl_sf_zeta_int_e:                     Riemann Zeta Function.
-                                                              (line  10)
-* GSL_SIGN:                              Testing the Sign of Numbers.
-                                                              (line   6)
-* gsl_siman_solve:                       Simulated Annealing functions.
-                                                              (line   6)
-* gsl_sort:                              Sorting vectors.     (line  23)
-* gsl_sort2:                             Sorting vectors.     (line  28)
-* gsl_sort_index:                        Sorting vectors.     (line  44)
-* gsl_sort_largest:                      Selecting the k smallest or largest elements.
-                                                              (line  23)
-* gsl_sort_largest_index:                Selecting the k smallest or largest elements.
-                                                              (line  49)
-* gsl_sort_smallest:                     Selecting the k smallest or largest elements.
-                                                              (line  16)
-* gsl_sort_smallest_index:               Selecting the k smallest or largest elements.
-                                                              (line  41)
-* gsl_sort_vector:                       Sorting vectors.     (line  35)
-* gsl_sort_vector2:                      Sorting vectors.     (line  39)
-* gsl_sort_vector_index:                 Sorting vectors.     (line  54)
-* gsl_sort_vector_largest:               Selecting the k smallest or largest elements.
-                                                              (line  32)
-* gsl_sort_vector_largest_index:         Selecting the k smallest or largest elements.
-                                                              (line  59)
-* gsl_sort_vector_smallest:              Selecting the k smallest or largest elements.
-                                                              (line  30)
-* gsl_sort_vector_smallest_index:        Selecting the k smallest or largest elements.
-                                                              (line  57)
-* gsl_spline_alloc:                      Higher-level Interface.
-                                                              (line  13)
-* gsl_spline_eval:                       Higher-level Interface.
-                                                              (line  26)
-* gsl_spline_eval_deriv:                 Higher-level Interface.
-                                                              (line  31)
-* gsl_spline_eval_deriv2:                Higher-level Interface.
-                                                              (line  36)
-* gsl_spline_eval_deriv2_e:              Higher-level Interface.
-                                                              (line  38)
-* gsl_spline_eval_deriv_e:               Higher-level Interface.
-                                                              (line  33)
-* gsl_spline_eval_e:                     Higher-level Interface.
-                                                              (line  28)
-* gsl_spline_eval_integ:                 Higher-level Interface.
-                                                              (line  41)
-* gsl_spline_eval_integ_e:               Higher-level Interface.
-                                                              (line  43)
-* gsl_spline_free:                       Higher-level Interface.
-                                                              (line  19)
-* gsl_spline_init:                       Higher-level Interface.
-                                                              (line  16)
-* gsl_spline_min_size:                   Higher-level Interface.
-                                                              (line  23)
-* gsl_spline_name:                       Higher-level Interface.
-                                                              (line  21)
-* gsl_stats_absdev:                      Absolute deviation.  (line   6)
-* gsl_stats_absdev_m:                    Absolute deviation.  (line  19)
-* gsl_stats_correlation:                 Correlation.         (line   6)
-* gsl_stats_covariance:                  Covariance.          (line   6)
-* gsl_stats_covariance_m:                Covariance.          (line  14)
-* gsl_stats_kurtosis:                    Higher moments (skewness and kurtosis).
-                                                              (line  29)
-* gsl_stats_kurtosis_m_sd:               Higher moments (skewness and kurtosis).
-                                                              (line  40)
-* gsl_stats_lag1_autocorrelation:        Autocorrelation.     (line   6)
-* gsl_stats_lag1_autocorrelation_m:      Autocorrelation.     (line  15)
-* gsl_stats_max:                         Maximum and Minimum values.
-                                                              (line  12)
-* gsl_stats_max_index:                   Maximum and Minimum values.
-                                                              (line  37)
-* gsl_stats_mean:                        Mean and standard deviation and variance.
-                                                              (line   6)
-* gsl_stats_median_from_sorted_data:     Median and Percentiles.
-                                                              (line  10)
-* gsl_stats_min:                         Maximum and Minimum values.
-                                                              (line  22)
-* gsl_stats_minmax:                      Maximum and Minimum values.
-                                                              (line  32)
-* gsl_stats_minmax_index:                Maximum and Minimum values.
-                                                              (line  53)
-* gsl_stats_min_index:                   Maximum and Minimum values.
-                                                              (line  45)
-* gsl_stats_quantile_from_sorted_data:   Median and Percentiles.
-                                                              (line  25)
-* gsl_stats_sd:                          Mean and standard deviation and variance.
-                                                              (line  44)
-* gsl_stats_sd_m:                        Mean and standard deviation and variance.
-                                                              (line  46)
-* gsl_stats_sd_with_fixed_mean:          Mean and standard deviation and variance.
-                                                              (line  73)
-* gsl_stats_skew:                        Higher moments (skewness and kurtosis).
-                                                              (line   6)
-* gsl_stats_skew_m_sd:                   Higher moments (skewness and kurtosis).
-                                                              (line  19)
-* gsl_stats_spearman:                    Correlation.         (line  18)
-* gsl_stats_tss:                         Mean and standard deviation and variance.
-                                                              (line  52)
-* gsl_stats_tss_m:                       Mean and standard deviation and variance.
-                                                              (line  54)
-* gsl_stats_variance:                    Mean and standard deviation and variance.
-                                                              (line  18)
-* gsl_stats_variance_m:                  Mean and standard deviation and variance.
-                                                              (line  36)
-* gsl_stats_variance_with_fixed_mean:    Mean and standard deviation and variance.
-                                                              (line  63)
-* gsl_stats_wabsdev:                     Weighted Samples.    (line  83)
-* gsl_stats_wabsdev_m:                   Weighted Samples.    (line  91)
-* gsl_stats_wkurtosis:                   Weighted Samples.    (line 110)
-* gsl_stats_wkurtosis_m_sd:              Weighted Samples.    (line 116)
-* gsl_stats_wmean:                       Weighted Samples.    (line  14)
-* gsl_stats_wsd:                         Weighted Samples.    (line  42)
-* gsl_stats_wsd_m:                       Weighted Samples.    (line  48)
-* gsl_stats_wsd_with_fixed_mean:         Weighted Samples.    (line  64)
-* gsl_stats_wskew:                       Weighted Samples.    (line  97)
-* gsl_stats_wskew_m_sd:                  Weighted Samples.    (line 103)
-* gsl_stats_wtss:                        Weighted Samples.    (line  71)
-* gsl_stats_wtss_m:                      Weighted Samples.    (line  73)
-* gsl_stats_wvariance:                   Weighted Samples.    (line  22)
-* gsl_stats_wvariance_m:                 Weighted Samples.    (line  36)
-* gsl_stats_wvariance_with_fixed_mean:   Weighted Samples.    (line  53)
-* gsl_strerror:                          Error Codes.         (line  37)
-* gsl_sum_levin_utrunc_accel:            Acceleration functions without error estimation.
-                                                              (line  32)
-* gsl_sum_levin_utrunc_alloc:            Acceleration functions without error estimation.
-                                                              (line  22)
-* gsl_sum_levin_utrunc_free:             Acceleration functions without error estimation.
-                                                              (line  28)
-* gsl_sum_levin_u_accel:                 Acceleration functions.
-                                                              (line  31)
-* gsl_sum_levin_u_alloc:                 Acceleration functions.
-                                                              (line  23)
-* gsl_sum_levin_u_free:                  Acceleration functions.
-                                                              (line  28)
-* gsl_vector_add:                        Vector operations.   (line   6)
-* gsl_vector_add_constant:               Vector operations.   (line  32)
-* gsl_vector_alloc:                      Vector allocation.   (line  14)
-* gsl_vector_calloc:                     Vector allocation.   (line  21)
-* gsl_vector_complex_const_imag:         Vector views.        (line 108)
-* gsl_vector_complex_const_real:         Vector views.        (line  97)
-* gsl_vector_complex_imag:               Vector views.        (line 106)
-* gsl_vector_complex_real:               Vector views.        (line  95)
-* gsl_vector_const_ptr:                  Accessing vector elements.
-                                                              (line  52)
-* gsl_vector_const_subvector:            Vector views.        (line  29)
-* gsl_vector_const_subvector_with_stride: Vector views.       (line  59)
-* gsl_vector_const_view_array:           Vector views.        (line 119)
-* gsl_vector_const_view_array_with_stride: Vector views.      (line 142)
-* gsl_vector_div:                        Vector operations.   (line  23)
-* gsl_vector_equal:                      Vector properties.   (line  18)
-* gsl_vector_fprintf:                    Reading and writing vectors.
-                                                              (line  26)
-* gsl_vector_fread:                      Reading and writing vectors.
-                                                              (line  17)
-* gsl_vector_free:                       Vector allocation.   (line  25)
-* gsl_vector_fscanf:                     Reading and writing vectors.
-                                                              (line  34)
-* gsl_vector_fwrite:                     Reading and writing vectors.
-                                                              (line   9)
-* gsl_vector_get:                        Accessing vector elements.
-                                                              (line  39)
-* gsl_vector_isneg:                      Vector properties.   (line  12)
-* gsl_vector_isnonneg:                   Vector properties.   (line  13)
-* gsl_vector_isnull:                     Vector properties.   (line  10)
-* gsl_vector_ispos:                      Vector properties.   (line  11)
-* gsl_vector_max:                        Finding maximum and minimum elements of vectors.
-                                                              (line   8)
-* gsl_vector_max_index:                  Finding maximum and minimum elements of vectors.
-                                                              (line  19)
-* gsl_vector_memcpy:                     Copying vectors.     (line  12)
-* gsl_vector_min:                        Finding maximum and minimum elements of vectors.
-                                                              (line  11)
-* gsl_vector_minmax:                     Finding maximum and minimum elements of vectors.
-                                                              (line  14)
-* gsl_vector_minmax_index:               Finding maximum and minimum elements of vectors.
-                                                              (line  29)
-* gsl_vector_min_index:                  Finding maximum and minimum elements of vectors.
-                                                              (line  24)
-* gsl_vector_mul:                        Vector operations.   (line  17)
-* gsl_vector_ptr:                        Accessing vector elements.
-                                                              (line  51)
-* gsl_vector_reverse:                    Exchanging elements. (line  14)
-* gsl_vector_scale:                      Vector operations.   (line  28)
-* gsl_vector_set:                        Accessing vector elements.
-                                                              (line  45)
-* gsl_vector_set_all:                    Initializing vector elements.
-                                                              (line   6)
-* gsl_vector_set_basis:                  Initializing vector elements.
-                                                              (line  12)
-* gsl_vector_set_zero:                   Initializing vector elements.
-                                                              (line   9)
-* gsl_vector_sub:                        Vector operations.   (line  11)
-* gsl_vector_subvector:                  Vector views.        (line  27)
-* gsl_vector_subvector_with_stride:      Vector views.        (line  57)
-* gsl_vector_swap:                       Copying vectors.     (line  17)
-* gsl_vector_swap_elements:              Exchanging elements. (line   9)
-* gsl_vector_view_array:                 Vector views.        (line 117)
-* gsl_vector_view_array_with_stride:     Vector views.        (line 140)
-* gsl_wavelet2d_nstransform:             DWT in two dimension.
-                                                              (line  64)
-* gsl_wavelet2d_nstransform_forward:     DWT in two dimension.
-                                                              (line  67)
-* gsl_wavelet2d_nstransform_inverse:     DWT in two dimension.
-                                                              (line  70)
-* gsl_wavelet2d_nstransform_matrix:      DWT in two dimension.
-                                                              (line  76)
-* gsl_wavelet2d_nstransform_matrix_forward: DWT in two dimension.
-                                                              (line  79)
-* gsl_wavelet2d_nstransform_matrix_inverse: DWT in two dimension.
-                                                              (line  81)
-* gsl_wavelet2d_transform:               DWT in two dimension.
-                                                              (line  29)
-* gsl_wavelet2d_transform_forward:       DWT in two dimension.
-                                                              (line  32)
-* gsl_wavelet2d_transform_inverse:       DWT in two dimension.
-                                                              (line  35)
-* gsl_wavelet2d_transform_matrix:        DWT in two dimension.
-                                                              (line  54)
-* gsl_wavelet2d_transform_matrix_forward: DWT in two dimension.
-                                                              (line  57)
-* gsl_wavelet2d_transform_matrix_inverse: DWT in two dimension.
-                                                              (line  59)
-* gsl_wavelet_alloc:                     DWT Initialization.  (line   9)
-* gsl_wavelet_bspline:                   DWT Initialization.  (line  29)
-* gsl_wavelet_bspline_centered:          DWT Initialization.  (line  30)
-* gsl_wavelet_daubechies:                DWT Initialization.  (line  18)
-* gsl_wavelet_daubechies_centered:       DWT Initialization.  (line  19)
-* gsl_wavelet_free:                      DWT Initialization.  (line  44)
-* gsl_wavelet_haar:                      DWT Initialization.  (line  24)
-* gsl_wavelet_haar_centered:             DWT Initialization.  (line  25)
-* gsl_wavelet_name:                      DWT Initialization.  (line  40)
-* gsl_wavelet_transform:                 DWT in one dimension.
-                                                              (line   6)
-* gsl_wavelet_transform_forward:         DWT in one dimension.
-                                                              (line   9)
-* gsl_wavelet_transform_inverse:         DWT in one dimension.
-                                                              (line  12)
-* gsl_wavelet_workspace_alloc:           DWT Initialization.  (line  51)
-* gsl_wavelet_workspace_free:            DWT Initialization.  (line  61)
+       return 0;
+     }
 
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diff -Nru gsl-doc-1.16/doc/gsl-ref.texi gsl-doc-2.3/doc/gsl-ref.texi
--- gsl-doc-1.16/doc/gsl-ref.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/gsl-ref.texi	2016-08-29 15:35:25.000000000 +0000
@@ -125,13 +125,19 @@
 @set GSL @i{GNU Scientific Library}
 
 @copying
-Copyright @copyright{} 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 The GSL Team.
+Copyright @copyright{} 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 The GSL Team.
 
 Permission is granted to copy, distribute and/or modify this document
 under the terms of the GNU Free Documentation License, Version 1.3 or
-any later version published by the Free Software Foundation; with no
-Invariant Sections and no cover texts.  A copy of the license is
-included in the section entitled ``GNU Free Documentation License''.
+any later version published by the Free Software Foundation; with the
+Invariant Sections being ``GNU General Public License'' and ``Free Software
+Needs Free Documentation'', the Front-Cover text being ``A GNU Manual'',
+and with the Back-Cover Text being (a) (see below). A copy of the
+license is included in the section entitled ``GNU Free Documentation
+License''.
+
+(a) The Back-Cover Text is: ``You have the freedom to copy and modify this
+GNU Manual.''
 @end copying
 
 @titlepage
@@ -251,6 +257,7 @@
 * Quasi-Random Sequences::      
 * Random Number Distributions::  
 * Statistics::                  
+* Running Statistics::                  
 * Histograms::                  
 * N-tuples::                    
 * Monte Carlo Integration::     
@@ -268,7 +275,10 @@
 * Multidimensional Minimization::  
 * Least-Squares Fitting::       
 * Nonlinear Least-Squares Fitting::  
-* Basis Splines::               
+* Basis Splines::
+* Sparse Matrices::
+* Sparse BLAS Support::
+* Sparse Linear Algebra::
 * Physical Constants::          
 * IEEE floating-point arithmetic::  
 * Debugging Numerical Programs::  
@@ -365,11 +375,15 @@
 @chapter Random Number Distributions
 @include randist.texi
 
-@node Statistics, Histograms, Random Number Distributions, Top
+@node Statistics, Running Statistics, Random Number Distributions, Top
 @chapter Statistics
 @include statistics.texi
 
-@node Histograms, N-tuples, Statistics, Top
+@node Running Statistics, Histograms, Statistics, Top
+@chapter Running Statistics
+@include rstat.texi
+
+@node Histograms, N-tuples, Running Statistics, Top
 @chapter Histograms
 @include histogram.texi
 
@@ -435,13 +449,25 @@
 
 @node Nonlinear Least-Squares Fitting, Basis Splines, Least-Squares Fitting, Top
 @chapter Nonlinear Least-Squares Fitting
-@include multifit.texi
+@include multifit-nlinear.texi
 
-@node Basis Splines, Physical Constants, Nonlinear Least-Squares Fitting, Top
+@node Basis Splines, Sparse Matrices, Nonlinear Least-Squares Fitting, Top
 @chapter Basis Splines
 @include bspline.texi
 
-@node  Physical Constants, IEEE floating-point arithmetic, Basis Splines, Top
+@node Sparse Matrices, Sparse BLAS Support, Basis Splines, Top
+@chapter Sparse Matrices
+@include spmatrix.texi
+
+@node Sparse BLAS Support, Sparse Linear Algebra, Sparse Matrices, Top
+@chapter Sparse BLAS Support
+@include spblas.texi
+
+@node Sparse Linear Algebra, Physical Constants, Sparse BLAS Support, Top
+@chapter Sparse Linear Algebra
+@include splinalg.texi
+
+@node Physical Constants, IEEE floating-point arithmetic, Sparse Linear Algebra, Top
 @chapter Physical Constants
 @include const.texi
 
@@ -529,7 +555,7 @@
 
 @item Patrick Alken
 Implementation of nonsymmetric and generalized eigensystems, B-splines,
-and robust linear regression.
+robust linear regression, and sparse matrices.
 
 @item Rhys Ulerich 
 Wrote the multiset routines.
diff -Nru gsl-doc-1.16/doc/ieee754.texi gsl-doc-2.3/doc/ieee754.texi
--- gsl-doc-1.16/doc/ieee754.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/ieee754.texi	2015-11-03 16:21:55.000000000 +0000
@@ -232,7 +232,7 @@
 function @code{gsl_ieee_env_setup}.
 
 @deftypefun void gsl_ieee_env_setup ()
-@vrindex @env{GSL_IEEE_MODE}
+@vindex @env{GSL_IEEE_MODE}
 This function reads the environment variable @code{GSL_IEEE_MODE} and
 attempts to set up the corresponding specified IEEE modes.  The
 environment variable should be a list of keywords, separated by
diff -Nru gsl-doc-1.16/doc/integration.texi gsl-doc-2.3/doc/integration.texi
--- gsl-doc-1.16/doc/integration.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/integration.texi	2015-11-09 05:23:40.000000000 +0000
@@ -227,7 +227,7 @@
 estimates.
 
 @deftypefun {gsl_integration_workspace *} gsl_integration_workspace_alloc (size_t @var{n}) 
-@tpindex gsl_integration_workspace
+@tindex gsl_integration_workspace
 This function allocates a workspace sufficient to hold @var{n} double
 precision intervals, their integration results and error estimates.
 One workspace may be used multiple times as all necessary reinitialization
@@ -462,7 +462,7 @@
 Chebyshev moments.
 
 @deftypefun {gsl_integration_qaws_table *} gsl_integration_qaws_table_alloc (double @var{alpha}, double @var{beta}, int @var{mu}, int @var{nu})
-@tpindex gsl_integration_qaws_table
+@tindex gsl_integration_qaws_table
 This function allocates space for a @code{gsl_integration_qaws_table}
 struct describing a singular weight function
 @math{W(x)} with the parameters @math{(\alpha, \beta, \mu, \nu)},
@@ -571,7 +571,7 @@
 which must be pre-computed with calls to the functions below.
 
 @deftypefun {gsl_integration_qawo_table *} gsl_integration_qawo_table_alloc (double @var{omega}, double @var{L}, enum gsl_integration_qawo_enum @var{sine}, size_t @var{n})
-@tpindex gsl_integration_qawo_table
+@tindex gsl_integration_qawo_table
 This function allocates space for a @code{gsl_integration_qawo_table}
 struct and its associated workspace describing a sine or cosine weight
 function @math{W(x)} with the parameters @math{(\omega, L)},
@@ -802,7 +802,7 @@
 rules is too large or a rule of maximum degree has been reached.
      
 @deftypefun {gsl_integration_cquad_workspace *} gsl_integration_cquad_workspace_alloc (size_t @var{n}) 
-@tpindex gsl_integration_cquad_workspace
+@tindex gsl_integration_cquad_workspace
 This function allocates a workspace sufficient to hold the data for
 @var{n} intervals. The number @var{n} is not the maximum number of
 intervals that will be evaluated. If the workspace is full, intervals
@@ -853,7 +853,7 @@
 absolute or relative error bounds.
 
 @deftypefun {gsl_integration_glfixed_table *} gsl_integration_glfixed_table_alloc (size_t @var{n})
-@tpindex gsl_integration_glfixed_table
+@tindex gsl_integration_glfixed_table
 This function determines the Gauss-Legendre abscissae and weights necessary for
 an @math{n}-point fixed order integration scheme.  If possible, high precision
 precomputed coefficients are used.  If precomputed weights are not available,
@@ -874,7 +874,7 @@
 @end deftypefun
 
 @deftypefun void gsl_integration_glfixed_table_free ({gsl_integration_glfixed_table *} @var{t})
-@tpindex gsl_integration_glfixed_table
+@tindex gsl_integration_glfixed_table
 This function frees the memory associated with the table @var{t}.
 @end deftypefun
 
@@ -932,7 +932,7 @@
 
 @example
 $ ./a.out 
-@verbatiminclude examples/integration.out
+@verbatiminclude examples/integration.txt
 @end example
 
 @noindent
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+++ gsl-doc-2.3/doc/interp2d.eps	2015-11-03 16:21:55.000000000 +0000
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diff -Nru gsl-doc-1.16/doc/interp_compare.eps gsl-doc-2.3/doc/interp_compare.eps
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+++ gsl-doc-2.3/doc/interp_compare.eps	2015-11-03 16:21:55.000000000 +0000
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diff -Nru gsl-doc-1.16/doc/interp.texi gsl-doc-2.3/doc/interp.texi
--- gsl-doc-1.16/doc/interp.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/interp.texi	2016-07-02 23:02:41.000000000 +0000
@@ -2,12 +2,13 @@
 @cindex spline
 
 This chapter describes functions for performing interpolation.  The
-library provides a variety of interpolation methods, including Cubic
-splines and Akima splines.  The interpolation types are interchangeable,
+library provides a variety of interpolation methods, including Cubic,
+Akima, and Steffen splines.  The interpolation types are interchangeable,
 allowing different methods to be used without recompiling.
 Interpolations can be defined for both normal and periodic boundary
 conditions.  Additional functions are available for computing
-derivatives and integrals of interpolating functions.
+derivatives and integrals of interpolating functions. Routines
+are provided for interpolating both one and two dimensional datasets.
 
 These interpolation methods produce curves that pass through each
 datapoint.  To interpolate noisy data with a smoothing curve see
@@ -17,18 +18,25 @@
 @file{gsl_interp.h} and @file{gsl_spline.h}.
 
 @menu
-* Introduction to Interpolation::  
-* Interpolation Functions::     
-* Interpolation Types::         
-* Index Look-up and Acceleration::  
-* Evaluation of Interpolating Functions::  
-* Higher-level Interface::      
-* Interpolation Example programs::  
-* Interpolation References and Further Reading::  
+* 1D Introduction to Interpolation::  
+* 1D Interpolation Functions::     
+* 1D Interpolation Types::         
+* 1D Index Look-up and Acceleration::  
+* 1D Evaluation of Interpolating Functions::  
+* 1D Higher-level Interface::      
+* 1D Interpolation Example programs::  
+* 1D Interpolation References and Further Reading::  
+* 2D Introduction to Interpolation::  
+* 2D Interpolation Functions::     
+* 2D Interpolation Grids::     
+* 2D Interpolation Types::         
+* 2D Evaluation of Interpolating Functions::  
+* 2D Higher-level Interface::      
+* 2D Interpolation Example programs::  
 @end menu
 
-@node Introduction to Interpolation
-@section Introduction
+@node 1D Introduction to Interpolation
+@section Introduction to 1D Interpolation
 
 Given a set of data points @math{(x_1, y_1) \dots (x_n, y_n)} the
 routines described in this section compute a continuous interpolating
@@ -36,14 +44,14 @@
 is piecewise smooth, and its behavior at the end-points is determined by
 the type of interpolation used.
 
-@node Interpolation Functions
-@section Interpolation Functions
+@node 1D Interpolation Functions
+@section 1D Interpolation Functions
 
 The interpolation function for a given dataset is stored in a
 @code{gsl_interp} object.  These are created by the following functions.
 
 @deftypefun {gsl_interp *} gsl_interp_alloc (const gsl_interp_type * @var{T}, size_t @var{size})
-@tpindex gsl_interp
+@tindex gsl_interp
 This function returns a pointer to a newly allocated interpolation
 object of type @var{T} for @var{size} data-points.
 @end deftypefun
@@ -62,10 +70,10 @@
 This function frees the interpolation object @var{interp}.
 @end deftypefun
 
-@node Interpolation Types
-@section Interpolation Types
-@tpindex gsl_interp_type
-The interpolation library provides six interpolation types:
+@node 1D Interpolation Types
+@section 1D Interpolation Types
+@tindex gsl_interp_type
+The interpolation library provides the following interpolation types:
 
 @deffn {Interpolation Type} gsl_interp_linear
 @cindex linear interpolation
@@ -112,6 +120,17 @@
 uses the non-rounded corner algorithm of Wodicka.
 @end deffn
 
+@deffn {Interpolation Type} gsl_interp_steffen
+Steffen's method guarantees the monotonicity of the interpolating function
+between the given data points. Therefore, minima and maxima can only occur
+exactly at the data points, and there can never be spurious oscillations
+between data points. The interpolated function is piecewise cubic
+in each interval. The resulting curve and its first derivative
+are guaranteed to be continuous, but the second derivative may be
+discontinuous.
+@end deffn
+
+@noindent
 The following related functions are available:
 
 @deftypefun {const char *} gsl_interp_name (const gsl_interp * @var{interp})
@@ -140,8 +159,8 @@
 
 
 
-@node Index Look-up and Acceleration
-@section Index Look-up and Acceleration
+@node 1D Index Look-up and Acceleration
+@section 1D Index Look-up and Acceleration
 
 The state of searches can be stored in a @code{gsl_interp_accel} object,
 which is a kind of iterator for interpolation lookups.  It caches the
@@ -156,7 +175,7 @@
 @end deftypefun
 
 @deftypefun {gsl_interp_accel *} gsl_interp_accel_alloc (void)
-@tpindex gsl_interp_accel
+@tindex gsl_interp_accel
 This function returns a pointer to an accelerator object, which is a
 kind of iterator for interpolation lookups.  It tracks the state of
 lookups, thus allowing for application of various acceleration
@@ -181,8 +200,8 @@
 This function frees the accelerator object @var{acc}.
 @end deftypefun
 
-@node Evaluation of Interpolating Functions
-@section Evaluation of Interpolating Functions
+@node 1D Evaluation of Interpolating Functions
+@section 1D Evaluation of Interpolating Functions
 
 @deftypefun  double gsl_interp_eval (const gsl_interp * @var{interp}, const double @var{xa}[], const double @var{ya}[], double @var{x}, gsl_interp_accel * @var{acc})
 @deftypefunx int gsl_interp_eval_e (const gsl_interp * @var{interp}, const double @var{xa}[], const double @var{ya}[], double @var{x}, gsl_interp_accel * @var{acc}, double * @var{y})
@@ -218,8 +237,8 @@
 the accelerator @var{acc}.
 @end deftypefun
 
-@node Higher-level Interface
-@section Higher-level Interface
+@node 1D Higher-level Interface
+@section 1D Higher-level Interface
 
 The functions described in the previous sections required the user to
 supply pointers to the @math{x} and @math{y} arrays on each call.  The
@@ -230,7 +249,7 @@
 defined in the header file @file{gsl_spline.h}.
 
 @deftypefun {gsl_spline *} gsl_spline_alloc (const gsl_interp_type * @var{T}, size_t @var{size})
-@tpindex gsl_spline
+@tindex gsl_spline
 @end deftypefun
 
 @deftypefun int gsl_spline_init (gsl_spline * @var{spline}, const double @var{xa}[], const double @var{ya}[], size_t @var{size})
@@ -261,8 +280,8 @@
 @deftypefunx int gsl_spline_eval_integ_e (const gsl_spline * @var{spline}, double @var{a}, double @var{b}, gsl_interp_accel * @var{acc}, double * @var{result})
 @end deftypefun
 
-@node Interpolation Example programs
-@section Examples
+@node 1D Interpolation Example programs
+@section Examples of 1D Interpolation
 
 The following program demonstrates the use of the interpolation and
 spline functions.  It computes a cubic spline interpolation of the
@@ -319,20 +338,316 @@
 slope of the fitted curve is the same at the beginning and end of the
 data, and the second derivative is also.
 
-@node Interpolation References and Further Reading
+The next program illustrates the difference between the cubic spline,
+Akima, and Steffen interpolation types on a difficult dataset.
+
+@example
+@verbatiminclude examples/interp_compare.c
+@end example
+
+@iftex
+@sp 1
+@center @image{interp_compare,6in}
+@end iftex
+
+@noindent
+The cubic method exhibits a local maxima between the 6th and 7th data points
+and continues oscillating for the rest of the data. Akima also shows a
+local maxima but recovers and follows the data well after the 7th grid point.
+Steffen preserves monotonicity in all intervals and does not exhibit oscillations,
+at the expense of having a discontinuous second derivative.
+
+@node 1D Interpolation References and Further Reading
 @section References and Further Reading
 
 Descriptions of the interpolation algorithms and further references can
-be found in the following books:
+be found in the following publications:
 
 @itemize @w{}
 @item C.W. Ueberhuber,
 @cite{Numerical Computation (Volume 1), Chapter 9 ``Interpolation''},
 Springer (1997), ISBN 3-540-62058-3.
 
-@item D.M. Young, R.T. Gregory
+@item D.M. Young, R.T. Gregory,
 @cite{A Survey of Numerical Mathematics (Volume 1), Chapter 6.8},
 Dover (1988), ISBN 0-486-65691-8.
+
+@item M. Steffen,
+@cite{A simple method for monotonic interpolation in one dimension},
+Astron. Astrophys. 239, 443-450, 1990.
 @end itemize
 
+@node 2D Introduction to Interpolation
+@section Introduction to 2D Interpolation
+
+Given a set of @math{x} coordinates @math{x_1,...,x_m} and a set of
+@math{y} coordinates @math{y_1,...,y_n}, each in increasing order,
+plus a set of function values @math{z_{ij}}
+for each grid point @math{(x_i,y_j)}, the routines described in this
+section compute a continuous interpolation function @math{z(x,y)} such
+that @math{z(x_i,y_j) = z_{ij}}.
+
+@node 2D Interpolation Functions
+@section 2D Interpolation Functions
+
+The interpolation function for a given dataset is stored in a
+@code{gsl_interp2d} object. These are created by the following functions.
+
+@deftypefun {gsl_interp2d *} gsl_interp2d_alloc (const gsl_interp2d_type * @var{T}, const size_t @var{xsize}, const size_t @var{ysize})
+@tindex gsl_interp
+This function returns a pointer to a newly allocated interpolation
+object of type @var{T} for @var{xsize} grid points in the @math{x}
+direction and @var{ysize} grid points in the @math{y} direction.
+@end deftypefun
+
+@deftypefun int gsl_interp2d_init (gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const size_t @var{xsize}, const size_t @var{ysize})
+This function initializes the interpolation object @var{interp} for the
+data (@var{xa},@var{ya},@var{za}) where @var{xa} and @var{ya} are arrays of
+the @math{x} and @math{y} grid points of size @var{xsize} and @var{ysize}
+respectively, and @var{za} is an array of function values of size
+@var{xsize}*@var{ysize}.  The interpolation object (@code{gsl_interp2d}) does
+not save the data arrays @var{xa}, @var{ya}, and @var{za} and only stores the
+static state computed from the data. The @var{xa} and @var{ya} data arrays
+are always assumed to be strictly ordered, with increasing @math{x,y} values; 
+the behavior for other arrangements is not defined.
+@end deftypefun
+
+@deftypefun void gsl_interp2d_free (gsl_interp2d * @var{interp})
+This function frees the interpolation object @var{interp}.
+@end deftypefun
+
+@node 2D Interpolation Grids
+@section 2D Interpolation Grids
+
+The 2D interpolation routines access the function values @math{z_{ij}}
+with the following ordering:
+@tex
+\beforedisplay
+$$
+z_{ij} = za[j*xsize + i]
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+z_ij = za[j*xsize + i]
+@end example
+
+@end ifinfo
+with @math{i = 0,...,xsize-1} and @math{j = 0,...,ysize-1}. However,
+for ease of use, the following functions are provided to add and retrieve
+elements from the function grid without requiring knowledge of the
+internal ordering.
+
+@deftypefun int gsl_interp2d_set (const gsl_interp2d * @var{interp}, double @var{za}[], const size_t @var{i}, const size_t @var{j}, const double @var{z})
+This function sets the value @math{z_{ij}} for grid point
+(@var{i},@var{j}) of the array @var{za} to @var{z}.
+@end deftypefun
+
+@deftypefun double gsl_interp2d_get (const gsl_interp2d * @var{interp}, const double @var{za}[], const size_t @var{i}, const size_t @var{j})
+This function returns the value @math{z_{ij}} for grid point
+(@var{i},@var{j}) stored in the array @var{za}.
+@end deftypefun
+
+@deftypefun size_t gsl_interp2d_idx (const gsl_interp2d * @var{interp}, const size_t @var{i}, const size_t @var{j})
+This function returns the index corresponding to the grid point
+(@var{i},@var{j}). The index is given by @math{j*xsize + i}.
+@end deftypefun
+
+@node 2D Interpolation Types
+@section 2D Interpolation Types
+@tindex gsl_interp2d_type
+The interpolation library provides the following 2D interpolation types:
+
+@deffn {Interpolation Type} gsl_interp2d_bilinear
+@cindex bilinear interpolation
+Bilinear interpolation.  This interpolation method does not require any
+additional memory.
+@end deffn
+
+@deffn {Interpolation Type} gsl_interp2d_bicubic
+@cindex bicubic interpolation
+Bicubic interpolation.
+@end deffn
+
+@deftypefun {const char *} gsl_interp2d_name (const gsl_interp2d * @var{interp})
+This function returns the name of the interpolation type used by @var{interp}.
+For example,
+
+@example
+printf ("interp uses '%s' interpolation.\n", 
+        gsl_interp2d_name (interp));
+@end example
+
 @noindent
+would print something like,
+
+@example
+interp uses 'bilinear' interpolation.
+@end example
+@end deftypefun
+
+@deftypefun {unsigned int} gsl_interp2d_min_size (const gsl_interp2d * @var{interp})
+@deftypefunx {unsigned int} gsl_interp2d_type_min_size (const gsl_interp2d_type * @var{T})
+These functions return the minimum number of points required by the
+interpolation object @var{interp} or interpolation type @var{T}.  For
+example, bicubic interpolation requires a minimum of 4 points.
+@end deftypefun
+
+@node 2D Evaluation of Interpolating Functions
+@section 2D Evaluation of Interpolating Functions
+
+@deftypefun double gsl_interp2d_eval (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_interp2d_eval_e (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{z})
+These functions return the interpolated value of @var{z} for a given
+point (@var{x},@var{y}), using the interpolation object @var{interp}, data
+arrays @var{xa}, @var{ya}, and @var{za} and the accelerators @var{xacc}
+and @var{yacc}.  When @var{x} is outside the range of @var{xa} or @var{y}
+is outside the range of @var{ya}, the error code
+@code{GSL_EDOM} is returned.
+@end deftypefun
+
+@deftypefun double gsl_interp2d_eval_extrap (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_interp2d_eval_extrap_e (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{z})
+These functions return the interpolated value of @var{z} for a given
+point (@var{x},@var{y}), using the interpolation object @var{interp}, data
+arrays @var{xa}, @var{ya}, and @var{za} and the accelerators @var{xacc}
+and @var{yacc}. The functions perform no bounds checking, so
+when @var{x} is outside the range of @var{xa} or @var{y}
+is outside the range of @var{ya}, extrapolation is performed.
+@end deftypefun
+
+@deftypefun double gsl_interp2d_eval_deriv_x (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_interp2d_eval_deriv_x_e (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{d})
+These functions return the interpolated value @var{d}
+@math{= \partial z / \partial x} for a given point (@var{x},@var{y}),
+using the interpolation object @var{interp}, data
+arrays @var{xa}, @var{ya}, and @var{za} and the accelerators @var{xacc}
+and @var{yacc}.  When @var{x} is outside the range of @var{xa} or @var{y}
+is outside the range of @var{ya}, the error code
+@code{GSL_EDOM} is returned.
+@end deftypefun
+
+@deftypefun double gsl_interp2d_eval_deriv_y (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_interp2d_eval_deriv_y_e (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{d})
+These functions return the interpolated value @var{d}
+@math{= \partial z / \partial y} for a given point (@var{x},@var{y}),
+using the interpolation object @var{interp}, data
+arrays @var{xa}, @var{ya}, and @var{za} and the accelerators @var{xacc}
+and @var{yacc}.  When @var{x} is outside the range of @var{xa} or @var{y}
+is outside the range of @var{ya}, the error code
+@code{GSL_EDOM} is returned.
+@end deftypefun
+
+@deftypefun double gsl_interp2d_eval_deriv_xx (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_interp2d_eval_deriv_xx_e (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{d})
+These functions return the interpolated value @var{d}
+@math{= \partial^2 z / \partial x^2} for a given point (@var{x},@var{y}),
+using the interpolation object @var{interp}, data
+arrays @var{xa}, @var{ya}, and @var{za} and the accelerators @var{xacc}
+and @var{yacc}.  When @var{x} is outside the range of @var{xa} or @var{y}
+is outside the range of @var{ya}, the error code
+@code{GSL_EDOM} is returned.
+@end deftypefun
+
+@deftypefun double gsl_interp2d_eval_deriv_yy (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_interp2d_eval_deriv_yy_e (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{d})
+These functions return the interpolated value @var{d}
+@math{= \partial^2 z / \partial y^2} for a given point (@var{x},@var{y}),
+using the interpolation object @var{interp}, data
+arrays @var{xa}, @var{ya}, and @var{za} and the accelerators @var{xacc}
+and @var{yacc}.  When @var{x} is outside the range of @var{xa} or @var{y}
+is outside the range of @var{ya}, the error code
+@code{GSL_EDOM} is returned.
+@end deftypefun
+
+@deftypefun double gsl_interp2d_eval_deriv_xy (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_interp2d_eval_deriv_xy_e (const gsl_interp2d * @var{interp}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{d})
+These functions return the interpolated value @var{d}
+@math{= \partial^2 z / \partial x \partial y} for a given point (@var{x},@var{y}),
+using the interpolation object @var{interp}, data
+arrays @var{xa}, @var{ya}, and @var{za} and the accelerators @var{xacc}
+and @var{yacc}.  When @var{x} is outside the range of @var{xa} or @var{y}
+is outside the range of @var{ya}, the error code
+@code{GSL_EDOM} is returned.
+@end deftypefun
+
+@node 2D Higher-level Interface
+@section 2D Higher-level Interface
+
+The functions described in the previous sections required the user to
+supply pointers to the @math{x}, @math{y}, and @math{z} arrays on each call.
+The following functions are equivalent to the corresponding
+@code{gsl_interp2d} functions but maintain a copy of this data in the
+@code{gsl_spline2d} object.  This removes the need to pass @var{xa},
+@var{ya}, and @var{za} as arguments on each evaluation. These functions are
+defined in the header file @file{gsl_spline2d.h}.
+
+@deftypefun {gsl_spline2d *} gsl_spline2d_alloc (const gsl_interp2d_type * @var{T}, size_t @var{xsize}, size_t @var{ysize})
+@tindex gsl_spline2d
+@end deftypefun
+
+@deftypefun int gsl_spline2d_init (gsl_spline2d * @var{spline}, const double @var{xa}[], const double @var{ya}[], const double @var{za}[], size_t @var{xsize}, size_t @var{ysize})
+@end deftypefun
+
+@deftypefun void gsl_spline2d_free (gsl_spline2d * @var{spline})
+@end deftypefun
+
+@deftypefun {const char *} gsl_spline2d_name (const gsl_spline2d * @var{spline})
+@end deftypefun
+
+@deftypefun {unsigned int} gsl_spline2d_min_size (const gsl_spline2d * @var{spline})
+@end deftypefun
+
+@deftypefun double gsl_spline2d_eval (const gsl_spline2d * @var{spline}, const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_spline2d_eval_e (const gsl_spline2d * @var{spline}, const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{z})
+@end deftypefun
+
+@deftypefun double gsl_spline2d_eval_deriv_x (const gsl_spline2d * @var{spline}, const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_spline2d_eval_deriv_x_e (const gsl_spline2d * @var{spline}, const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{d})
+@end deftypefun
+
+@deftypefun double gsl_spline2d_eval_deriv_y (const gsl_spline2d * @var{spline}, const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_spline2d_eval_deriv_y_e (const gsl_spline2d * @var{spline}, const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{d})
+@end deftypefun
+
+@deftypefun double gsl_spline2d_eval_deriv_xx (const gsl_spline2d * @var{spline}, const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_spline2d_eval_deriv_xx_e (const gsl_spline2d * @var{spline}, const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{d})
+@end deftypefun
+
+@deftypefun double gsl_spline2d_eval_deriv_yy (const gsl_spline2d * @var{spline}, const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_spline2d_eval_deriv_yy_e (const gsl_spline2d * @var{spline}, const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{d})
+@end deftypefun
+
+@deftypefun double gsl_spline2d_eval_deriv_xy (const gsl_spline2d * @var{spline}, const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc})
+@deftypefunx int gsl_spline2d_eval_deriv_xy_e (const gsl_spline2d * @var{spline}, const double @var{x}, const double @var{y}, gsl_interp_accel * @var{xacc}, gsl_interp_accel * @var{yacc}, double * @var{d})
+@end deftypefun
+
+@deftypefun int gsl_spline2d_set (const gsl_spline2d * @var{spline}, double @var{za}[], const size_t @var{i}, const size_t @var{j}, const double @var{z})
+@end deftypefun
+
+@deftypefun double gsl_spline2d_get (const gsl_spline2d * @var{spline}, const double @var{za}[], const size_t @var{i}, const size_t @var{j})
+This function returns the value @math{z_{ij}} for grid point
+(@var{i},@var{j}) stored in the array @var{za}.
+@end deftypefun
+
+@node 2D Interpolation Example programs
+@section 2D Interpolation Example programs
+
+The following example performs bilinear interpolation on the unit
+square, using @math{z} values of @math{(0,1,0.5,1)} going clockwise
+around the square.
+
+@example
+@verbatiminclude examples/interp2d.c
+@end example
+
+@noindent
+The results of the interpolation are shown in the following plot,
+where the corners are labeled with their fixed @math{z} values.
+
+@iftex
+@sp 1
+@center @image{interp2d,6in}
+@end iftex
diff -Nru gsl-doc-1.16/doc/linalg.texi gsl-doc-2.3/doc/linalg.texi
--- gsl-doc-1.16/doc/linalg.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/linalg.texi	2016-11-29 21:55:39.000000000 +0000
@@ -16,17 +16,22 @@
 @menu
 * LU Decomposition::            
 * QR Decomposition::            
-* QR Decomposition with Column Pivoting::  
+* QR Decomposition with Column Pivoting::
+* Complete Orthogonal Decomposition::
 * Singular Value Decomposition::  
 * Cholesky Decomposition::      
+* Pivoted Cholesky Decomposition::      
+* Modified Cholesky Decomposition::      
 * Tridiagonal Decomposition of Real Symmetric Matrices::  
 * Tridiagonal Decomposition of Hermitian Matrices::  
 * Hessenberg Decomposition of Real Matrices::
 * Hessenberg-Triangular Decomposition of Real Matrices::
 * Bidiagonalization::           
+* Givens Rotations::  
 * Householder Transformations::  
 * Householder solver for linear systems::  
-* Tridiagonal Systems::         
+* Tridiagonal Systems::
+* Triangular Systems::
 * Balancing::
 * Linear Algebra Examples::     
 * Linear Algebra References and Further Reading::  
@@ -36,7 +41,7 @@
 @section LU Decomposition
 @cindex LU decomposition
 
-A general square matrix @math{A} has an @math{LU} decomposition into
+A general @math{N}-by-@math{N} square matrix @math{A} has an @math{LU} decomposition into
 upper and lower triangular matrices,
 @tex
 \beforedisplay
@@ -70,8 +75,9 @@
 unity, and are not stored.
 
 The permutation matrix @math{P} is encoded in the permutation
-@var{p}. The @math{j}-th column of the matrix @math{P} is given by the
-@math{k}-th column of the identity matrix, where @math{k = p_j} the
+@var{p} on output. The @math{j}-th column of the matrix @math{P}
+is given by the @math{k}-th column of the identity matrix, where
+@math{k = p_j} the
 @math{j}-th element of the permutation vector. The sign of the
 permutation is given by @var{signum}. It has the value @math{(-1)^n},
 where @math{n} is the number of interchanges in the permutation.
@@ -100,12 +106,11 @@
 @cindex refinement of solutions in linear systems
 @cindex iterative refinement of solutions in linear systems
 @cindex linear systems, refinement of solutions
-@deftypefun int gsl_linalg_LU_refine (const gsl_matrix * @var{A}, const gsl_matrix * @var{LU}, const gsl_permutation * @var{p}, const gsl_vector * @var{b}, gsl_vector * @var{x}, gsl_vector * @var{residual})
-@deftypefunx int gsl_linalg_complex_LU_refine (const gsl_matrix_complex * @var{A}, const gsl_matrix_complex * @var{LU}, const gsl_permutation * @var{p}, const gsl_vector_complex * @var{b}, gsl_vector_complex * @var{x}, gsl_vector_complex * @var{residual})
+@deftypefun int gsl_linalg_LU_refine (const gsl_matrix * @var{A}, const gsl_matrix * @var{LU}, const gsl_permutation * @var{p}, const gsl_vector * @var{b}, gsl_vector * @var{x}, gsl_vector * @var{work})
+@deftypefunx int gsl_linalg_complex_LU_refine (const gsl_matrix_complex * @var{A}, const gsl_matrix_complex * @var{LU}, const gsl_permutation * @var{p}, const gsl_vector_complex * @var{b}, gsl_vector_complex * @var{x}, gsl_vector_complex * @var{work})
 These functions apply an iterative improvement to @var{x}, the solution
 of @math{A x = b}, from the precomputed @math{LU} decomposition of @math{A} into
-(@var{LU},@var{p}). The initial residual @math{r = A x - b} is also
-computed and stored in @var{residual}.
+(@var{LU},@var{p}). Additional workspace of length @var{N} is required in @var{work}.
 @end deftypefun
 
 @cindex inverse of a matrix, by LU decomposition
@@ -297,8 +302,8 @@
 @section QR Decomposition with Column Pivoting
 @cindex QR decomposition with column pivoting
 
-The @math{QR} decomposition can be extended to the rank deficient case
-by introducing a column permutation @math{P},
+The @math{QR} decomposition of an @math{M}-by-@math{N} matrix @math{A}
+can be extended to the rank deficient case by introducing a column permutation @math{P},
 @tex
 \beforedisplay
 $$
@@ -320,7 +325,58 @@
 b} into the triangular system @math{R y = Q^T b, x = P y}, which can be
 solved by back-substitution and permutation.  We denote the @math{QR}
 decomposition with column pivoting by @math{QRP^T} since @math{A = Q R
-P^T}.
+P^T}. When @math{A} is rank deficient with @math{r = {\rm rank}(A)}, the matrix
+@math{R} can be partitioned as
+@tex
+\beforedisplay
+$$
+R = \left(
+\matrix{
+R_{11} & R_{12} \cr
+0 & R_{22} \cr
+}
+\right) \approx
+\left(
+\matrix{
+R_{11} & R_{12} \cr
+0 & 0 \cr
+}
+\right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+R = [ R11 R12; 0 R22 ] =~ [ R11 R12; 0 0 ]
+@end example
+
+@end ifinfo
+where @math{R_{11}} is @math{r}-by-@math{r} and nonsingular. In this case,
+a ``basic'' least squares solution for the overdetermined system @math{A x = b}
+can be obtained as
+@tex
+\beforedisplay
+$$
+x = P \left(
+\matrix{
+R_{11}^{-1} c_1 \cr
+0 \cr
+}
+\right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+x = P [ R11^-1 c1 ; 0 ]
+@end example
+
+@end ifinfo
+where @math{c_1} consists of the first @math{r} elements of @math{Q^T b}.
+This basic solution is not guaranteed to be the minimum norm solution unless
+@math{R_{12} = 0} (see @ref{Complete Orthogonal Decomposition}).
 
 @deftypefun int gsl_linalg_QRPT_decomp (gsl_matrix * @var{A}, gsl_vector * @var{tau}, gsl_permutation * @var{p}, int * @var{signum}, gsl_vector * @var{norm})
 This function factorizes the @math{M}-by-@math{N} matrix @var{A} into
@@ -364,6 +420,30 @@
 right-hand side @math{b}, which is replaced by the solution on output.
 @end deftypefun
 
+@deftypefun int gsl_linalg_QRPT_lssolve (const gsl_matrix * @var{QR}, const gsl_vector * @var{tau}, const gsl_permutation * @var{p}, const gsl_vector * @var{b}, gsl_vector * @var{x}, gsl_vector * @var{residual})
+This function finds the least squares solution to the overdetermined
+system @math{A x = b} where the matrix @var{A} has more rows than
+columns and is assumed to have full rank. The least squares solution minimizes
+the Euclidean norm of the residual, @math{||b - A x||}. The routine requires as input 
+the @math{QR} decomposition of @math{A} into (@var{QR}, @var{tau}, @var{p}) given by
+@code{gsl_linalg_QRPT_decomp}.  The solution is returned in @var{x}.  The
+residual is computed as a by-product and stored in @var{residual}. For rank
+deficient matrices, @code{gsl_linalg_QRPT_lssolve2} should be used instead.
+@end deftypefun
+
+@deftypefun int gsl_linalg_QRPT_lssolve2 (const gsl_matrix * @var{QR}, const gsl_vector * @var{tau}, const gsl_permutation * @var{p}, const gsl_vector * @var{b}, const size_t @var{rank}, gsl_vector * @var{x}, gsl_vector * @var{residual})
+This function finds the least squares solution to the overdetermined
+system @math{A x = b} where the matrix @var{A} has more rows than
+columns and has rank given by the input @var{rank}. If the user does not
+know the rank of @math{A}, the routine @code{gsl_linalg_QRPT_rank} can be
+called to estimate it. The least squares solution is
+the so-called ``basic'' solution discussed above and may not be the minimum
+norm solution. The routine requires as input 
+the @math{QR} decomposition of @math{A} into (@var{QR}, @var{tau}, @var{p}) given by
+@code{gsl_linalg_QRPT_decomp}.  The solution is returned in @var{x}.  The
+residual is computed as a by-product and stored in @var{residual}.
+@end deftypefun
+
 @deftypefun int gsl_linalg_QRPT_QRsolve (const gsl_matrix * @var{Q}, const gsl_matrix * @var{R}, const gsl_permutation * @var{p}, const gsl_vector * @var{b}, gsl_vector * @var{x})
 This function solves the square system @math{R P^T x = Q^T b} for
 @var{x}. It can be used when the @math{QR} decomposition of a matrix is
@@ -390,6 +470,115 @@
 replaced by the solution on output.
 @end deftypefun
 
+@deftypefun size_t gsl_linalg_QRPT_rank (const gsl_matrix * @var{QR}, const double @var{tol})
+This function estimates the rank of the triangular matrix @math{R} contained in @var{QR}.
+The algorithm simply counts the number of diagonal elements of @math{R} whose absolute value
+is greater than the specified tolerance @var{tol}. If the input @var{tol} is negative,
+a default value of @math{20 (M + N) eps(max(|diag(R)|))} is used.
+@end deftypefun
+
+@deftypefun int gsl_linalg_QRPT_rcond (const gsl_matrix * @var{QR}, double * @var{rcond}, gsl_vector * @var{work})
+This function estimates the reciprocal condition number (using the 1-norm) of the @math{R} factor,
+stored in the upper triangle of @var{QR}. The reciprocal condition number estimate, defined as
+@math{1 / (||R||_1 \cdot ||R^{-1}||_1)}, is stored in @var{rcond}.
+Additional workspace of size @math{3 N} is required in @var{work}.
+@end deftypefun
+
+@node Complete Orthogonal Decomposition
+@section Complete Orthogonal Decomposition
+
+The complete orthogonal decomposition of a @math{M}-by-@math{N} matrix
+@math{A} is a generalization of the QR decomposition with column pivoting, given by
+@tex
+\beforedisplay
+$$
+A P = Q
+\left(
+\matrix{
+R_{11} & 0 \cr
+0 & 0 \cr
+}
+\right) Z
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+A P = Q [ R11 0 ] Z
+        [  0  0 ]
+@end example
+
+@end ifinfo
+@noindent
+where @math{P} is a @math{N}-by-@math{N} permutation matrix,
+@math{Q} is @math{M}-by-@math{M} orthogonal, @math{R_{11}} is
+@math{r}-by-@math{r} upper triangular, with @math{r = {\rm rank}(A)},
+and @math{Z} is @math{N}-by-@math{N} orthogonal. If @math{A}
+has full rank, then @math{R_{11} = R}, @math{Z = I} and this reduces to the
+QR decomposition with column pivoting. The advantage of using
+the complete orthogonal decomposition for rank deficient matrices
+is the ability to compute the minimum norm solution to the linear
+least squares problem @math{Ax = b}, which is given by
+@tex
+\beforedisplay
+$$
+x = P Z^T
+\left(
+\matrix{
+R_{11}^{-1} c_1 \cr
+0 \cr
+}
+\right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+x = P Z^T [ R11^-1 c1 ]
+          [    0      ]
+@end example
+
+@end ifinfo
+and the vector @math{c_1} is the first @math{r} elements of @math{Q^T b}.
+
+@deftypefun int gsl_linalg_COD_decomp (gsl_matrix * @var{A}, gsl_vector * @var{tau_Q}, gsl_vector * @var{tau_Z}, gsl_permutation * @var{p}, size_t * @var{rank}, gsl_vector * @var{work})
+@deftypefunx int gsl_linalg_COD_decomp_e (gsl_matrix * @var{A}, gsl_vector * @var{tau_Q}, gsl_vector * @var{tau_Z}, gsl_permutation * @var{p}, double @var{tol}, size_t * @var{rank}, gsl_vector * @var{work})
+These functions factor the @math{M}-by-@math{N} matrix @var{A} into the decomposition @math{A = Q R Z P^T}. The rank of @var{A}
+is computed as the number of diagonal elements of @math{R} greater than the tolerance @var{tol} and output in @var{rank}.
+If @var{tol} is not specified, a default value is used (see @code{gsl_linalg_QRPT_rank}). On output, the permutation
+matrix @math{P} is stored in @var{p}. The matrix @math{R_{11}} is stored in the upper @var{rank}-by-@var{rank} block of @var{A}.
+The matrices @math{Q} and @math{Z} are encoded in packed storage in @var{A} on output. The vectors @var{tau_Q} and @var{tau_Z}
+contain the Householder scalars corresponding to the matrices @math{Q} and @math{Z} respectively and must be
+of length @math{k = \min(M,N)}. The vector @var{work} is additional workspace of length @math{N}.
+@end deftypefun
+
+@deftypefun int gsl_linalg_COD_lssolve (const gsl_matrix * @var{QRZ}, const gsl_vector * @var{tau_Q}, const gsl_vector * @var{tau_Z}, const gsl_permutation * @var{p}, const size_t @var{rank}, const gsl_vector * @var{b}, gsl_vector * @var{x}, gsl_vector * @var{residual})
+This function finds the least squares solution to the overdetermined
+system @math{A x = b} where the matrix @var{A} has more rows than
+columns.  The least squares solution minimizes the Euclidean norm of the
+residual, @math{||b - A x||}.  The routine requires as input 
+the @math{QRZ} decomposition of @math{A} into (@var{QRZ}, @var{tau_Q}, @var{tau_Z}, @var{p}, @var{rank})
+given by @code{gsl_linalg_COD_decomp}.  The solution is returned in @var{x}.  The
+residual is computed as a by-product and stored in @var{residual}.
+@end deftypefun
+
+@deftypefun int gsl_linalg_COD_unpack (const gsl_matrix * @var{QRZ}, const gsl_vector * @var{tau_Q}, const gsl_vector * @var{tau_Z}, const size_t @var{rank}, gsl_matrix * @var{Q}, gsl_matrix * @var{R}, gsl_matrix * @var{Z})
+This function unpacks the encoded @math{QRZ} decomposition
+(@var{QRZ}, @var{tau_Q}, @var{tau_Z}, @var{rank}) into the matrices
+@var{Q}, @var{R}, and @var{Z}, where @var{Q} is @math{M}-by-@math{M},
+@var{R} is @math{M}-by-@math{N}, and @var{Z} is @math{N}-by-@math{N}.
+@end deftypefun
+
+@deftypefun int gsl_linalg_COD_matZ (const gsl_matrix * @var{QRZ}, const gsl_vector * @var{tau_Z}, const size_t @var{rank}, gsl_matrix * @var{A}, gsl_vector * @var{work})
+This function multiplies the input matrix @var{A} on the right by @var{Z},
+@math{A' = A Z} using the encoded @math{QRZ} decomposition
+(@var{QRZ}, @var{tau_Z}, @var{rank}). @var{A} must have @math{N} columns but may
+have any number of rows. Additional workspace of length @math{M} is provided
+in @var{work}.
+@end deftypefun
+
 @node Singular Value Decomposition
 @section Singular Value Decomposition
 @cindex SVD
@@ -529,16 +718,38 @@
 (@math{L y = b}, @math{L^T x = y}), which can be solved by forward and
 back-substitution.
 
-@deftypefun int gsl_linalg_cholesky_decomp (gsl_matrix * @var{A})
+If the matrix @math{A} is near singular, it is sometimes possible to reduce
+the condition number and recover a more accurate solution vector @math{x}
+by scaling as
+@tex
+\beforedisplay
+$$
+\left( S A S \right) \left( S^{-1} x \right) = S b
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+( S A S ) ( S^(-1) x ) = S b
+@end example
+
+@end ifinfo
+where @math{S} is a diagonal matrix whose elements are given by
+@math{S_{ii} = 1/\sqrt{A_{ii}}}. This scaling is also known as
+Jacobi preconditioning. There are routines below to solve
+both the scaled and unscaled systems.
+
+@deftypefun int gsl_linalg_cholesky_decomp1 (gsl_matrix * @var{A})
 @deftypefunx int gsl_linalg_complex_cholesky_decomp (gsl_matrix_complex * @var{A})
 These functions factorize the symmetric, positive-definite square matrix
 @var{A} into the Cholesky decomposition @math{A = L L^T} (or
 @c{$A = L L^{\dagger}$}
 @math{A = L L^H}
-for the complex case). On input, the values from the diagonal and lower-triangular part of the matrix @var{A} are used (the upper triangular part is ignored).  On output the diagonal and lower triangular part of the input
-matrix @var{A} contain the matrix @math{L}, while the upper triangular part
-of the input matrix is overwritten with @math{L^T} (the diagonal terms being
-identical for both @math{L} and @math{L^T}).  If the matrix is not
+for the complex case). On input, the values from the diagonal and lower-triangular
+part of the matrix @var{A} are used (the upper triangular part is ignored).  On output
+the diagonal and lower triangular part of the input matrix @var{A} contain the matrix
+@math{L}, while the upper triangular part is unmodified.  If the matrix is not
 positive-definite then the decomposition will fail, returning the
 error code @code{GSL_EDOM}.  
 
@@ -546,6 +757,10 @@
 handler first to avoid triggering an error.
 @end deftypefun
 
+@deftypefun int gsl_linalg_cholesky_decomp (gsl_matrix * @var{A})
+This function is now deprecated and is provided only for backward compatibility.
+@end deftypefun
+
 @deftypefun int gsl_linalg_cholesky_solve (const gsl_matrix * @var{cholesky}, const gsl_vector * @var{b}, gsl_vector * @var{x})
 @deftypefunx int gsl_linalg_complex_cholesky_solve (const gsl_matrix_complex * @var{cholesky}, const gsl_vector_complex * @var{b}, gsl_vector_complex * @var{x})
 These functions solve the system @math{A x = b} using the Cholesky
@@ -574,6 +789,233 @@
 stored in-place in @var{cholesky}.
 @end deftypefun
 
+@deftypefun int gsl_linalg_cholesky_decomp2 (gsl_matrix * @var{A}, gsl_vector * @var{S})
+This function calculates a diagonal scaling transformation @math{S} for
+the symmetric, positive-definite square matrix @var{A}, and then
+computes the Cholesky decomposition @math{S A S = L L^T}.
+On input, the values from the diagonal and lower-triangular part of the matrix @var{A} are
+used (the upper triangular part is ignored).  On output the diagonal and lower triangular part
+of the input matrix @var{A} contain the matrix @math{L}, while the upper triangular part
+of the input matrix is overwritten with @math{L^T} (the diagonal terms being
+identical for both @math{L} and @math{L^T}).  If the matrix is not
+positive-definite then the decomposition will fail, returning the
+error code @code{GSL_EDOM}. The diagonal scale factors are stored in @var{S}
+on output.
+
+When testing whether a matrix is positive-definite, disable the error
+handler first to avoid triggering an error.
+@end deftypefun
+
+@deftypefun int gsl_linalg_cholesky_solve2 (const gsl_matrix * @var{cholesky}, const gsl_vector * @var{S}, const gsl_vector * @var{b}, gsl_vector * @var{x})
+This function solves the system @math{(S A S) (S^{-1} x) = S b} using the Cholesky
+decomposition of @math{S A S} held in the matrix @var{cholesky} which must
+have been previously computed by @code{gsl_linalg_cholesky_decomp2}.
+@end deftypefun
+
+@deftypefun int gsl_linalg_cholesky_svx2 (const gsl_matrix * @var{cholesky}, const gsl_vector * @var{S}, gsl_vector * @var{x})
+This function solves the system @math{(S A S) (S^{-1} x) = S b} in-place using the
+Cholesky decomposition of @math{S A S} held in the matrix @var{cholesky}
+which must have been previously computed by
+@code{gsl_linalg_cholesky_decomp2}.  On input @var{x} should
+contain the right-hand side @math{b}, which is replaced by the
+solution on output.
+@end deftypefun
+
+@deftypefun int gsl_linalg_cholesky_scale (const gsl_matrix * @var{A}, gsl_vector * @var{S})
+This function calculates a diagonal scaling transformation of the
+symmetric, positive definite matrix @var{A}, such that
+@math{S A S} has a condition number within a factor of @math{N}
+of the matrix of smallest possible condition number over all
+possible diagonal scalings. On output, @var{S} contains the
+scale factors, given by @math{S_i = 1/\sqrt{A_{ii}}}.
+For any @math{A_{ii} \le 0}, the corresponding scale factor @math{S_i}
+is set to @math{1}.
+@end deftypefun
+
+@deftypefun int gsl_linalg_cholesky_scale_apply (gsl_matrix * @var{A}, const gsl_vector * @var{S})
+This function applies the scaling transformation @var{S} to the matrix @var{A}. On output,
+@var{A} is replaced by @math{S A S}.
+@end deftypefun
+
+@deftypefun int gsl_linalg_cholesky_rcond (const gsl_matrix * @var{cholesky}, double * @var{rcond}, gsl_vector * @var{work})
+This function estimates the reciprocal condition number (using the 1-norm) of the symmetric positive
+definite matrix @math{A}, using its Cholesky decomposition provided in @var{cholesky}.
+The reciprocal condition number estimate, defined as @math{1 / (||A||_1 \cdot ||A^{-1}||_1)}, is stored
+in @var{rcond}.  Additional workspace of size @math{3 N} is required in @var{work}.
+@end deftypefun
+
+@node Pivoted Cholesky Decomposition
+@section Pivoted Cholesky Decomposition
+@cindex Cholesky decomposition, pivoted
+@cindex Pivoted Cholesky Decomposition
+
+A symmetric, positive definite square matrix @math{A} has an alternate
+Cholesky decomposition into a product of a lower unit triangular matrix @math{L},
+a diagonal matrix @math{D} and @math{L^T}, given by @math{L D L^T}. This is
+equivalent to the Cholesky formulation discussed above, with
+the standard Cholesky lower triangular factor given by @math{L D^{1 \over 2}}.
+For ill-conditioned matrices, it can help to use a pivoting strategy to
+prevent the entries of @math{D} and @math{L} from growing too large, and also
+ensure @math{D_1 \ge D_2 \ge \cdots \ge D_n > 0}, where @math{D_i} are
+the diagonal entries of @math{D}. The final decomposition is given by
+@tex
+\beforedisplay
+$$
+P A P^T = L D L^T
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+P A P^T = L D L^T
+@end example
+
+@end ifinfo
+where @math{P} is a permutation matrix.
+
+@deftypefun int gsl_linalg_pcholesky_decomp (gsl_matrix * @var{A}, gsl_permutation * @var{p})
+This function factors the symmetric, positive-definite square matrix
+@var{A} into the Pivoted Cholesky decomposition @math{P A P^T = L D L^T}.
+On input, the values from the diagonal and lower-triangular part of the matrix @var{A} are
+used to construct the factorization. On output the diagonal of the input matrix @var{A} stores
+the diagonal elements of @math{D}, and the lower triangular portion of @var{A}
+contains the matrix @math{L}. Since @math{L} has ones on its diagonal these
+do not need to be explicitely stored. The upper triangular portion of @var{A} is
+unmodified. The permutation matrix @math{P} is stored in @var{p} on output.
+@end deftypefun
+
+@deftypefun int gsl_linalg_pcholesky_solve (const gsl_matrix * @var{LDLT}, const gsl_permutation * @var{p}, const gsl_vector * @var{b}, gsl_vector * @var{x})
+This function solves the system @math{A x = b} using the Pivoted Cholesky
+decomposition of @math{A} held in the matrix @var{LDLT} and permutation
+@var{p} which must have been previously computed by @code{gsl_linalg_pcholesky_decomp}.
+@end deftypefun
+
+@deftypefun int gsl_linalg_pcholesky_svx (const gsl_matrix * @var{LDLT}, const gsl_permutation * @var{p}, gsl_vector * @var{x})
+This function solves the system @math{A x = b} in-place using the Pivoted Cholesky
+decomposition of @math{A} held in the matrix @var{LDLT} and permutation
+@var{p} which must have been previously computed by @code{gsl_linalg_pcholesky_decomp}.
+On input, @var{x} contains the right hand side vector @math{b} which is
+replaced by the solution vector on output.
+@end deftypefun
+
+@deftypefun int gsl_linalg_pcholesky_decomp2 (gsl_matrix * @var{A}, gsl_permutation * @var{p}, gsl_vector * @var{S})
+This function computes the pivoted Cholesky factorization of the matrix
+@math{S A S}, where the input matrix @var{A} is symmetric and positive
+definite, and the diagonal scaling matrix @var{S} is computed to reduce the
+condition number of @var{A} as much as possible. See
+@ref{Cholesky Decomposition} for more information on the matrix @var{S}.
+The Pivoted Cholesky decomposition satisfies @math{P S A S P^T = L D L^T}.
+On input, the values from the diagonal and lower-triangular part of the matrix @var{A} are
+used to construct the factorization.  On output the diagonal of the input matrix @var{A} stores the diagonal
+elements of @math{D}, and the lower triangular portion of @var{A}
+contains the matrix @math{L}. Since @math{L} has ones on its diagonal these
+do not need to be explicitely stored. The upper triangular portion of @var{A}
+is unmodified. The permutation matrix @math{P} is stored in @var{p} on output.
+The diagonal scaling transformation is stored in @var{S} on output.
+@end deftypefun
+
+@deftypefun int gsl_linalg_pcholesky_solve2 (const gsl_matrix * @var{LDLT}, const gsl_permutation * @var{p}, const gsl_vector * @var{S}, const gsl_vector * @var{b}, gsl_vector * @var{x})
+This function solves the system @math{(S A S) (S^{-1} x) = S b} using the Pivoted Cholesky
+decomposition of @math{S A S} held in the matrix @var{LDLT}, permutation
+@var{p}, and vector @var{S}, which must have been previously computed by
+@code{gsl_linalg_pcholesky_decomp2}.
+@end deftypefun
+
+@deftypefun int gsl_linalg_pcholesky_svx2 (const gsl_matrix * @var{LDLT}, const gsl_permutation * @var{p}, const gsl_vector * @var{S}, gsl_vector * @var{x})
+This function solves the system @math{(S A S) (S^{-1} x) = S b} in-place using the Pivoted Cholesky
+decomposition of @math{S A S} held in the matrix @var{LDLT}, permutation
+@var{p} and vector @var{S}, which must have been previously computed by
+@code{gsl_linalg_pcholesky_decomp2}.
+On input, @var{x} contains the right hand side vector @math{b} which is
+replaced by the solution vector on output.
+@end deftypefun
+
+@deftypefun int gsl_linalg_pcholesky_invert (const gsl_matrix * @var{LDLT}, const gsl_permutation * @var{p}, gsl_matrix * @var{Ainv})
+This function computes the inverse of the matrix @math{A}, using the Pivoted
+Cholesky decomposition stored in @var{LDLT} and @var{p}. On output, the
+matrix @var{Ainv} contains @math{A^{-1}}.
+@end deftypefun
+
+@deftypefun int gsl_linalg_pcholesky_rcond (const gsl_matrix * @var{LDLT}, const gsl_permutation * @var{p}, double * @var{rcond}, gsl_vector * @var{work})
+This function estimates the reciprocal condition number (using the 1-norm) of the symmetric positive
+definite matrix @math{A}, using its pivoted Cholesky decomposition provided in @var{LDLT}.
+The reciprocal condition number estimate, defined as @math{1 / (||A||_1 \cdot ||A^{-1}||_1)}, is stored
+in @var{rcond}.  Additional workspace of size @math{3 N} is required in @var{work}.
+@end deftypefun
+
+@node Modified Cholesky Decomposition
+@section Modified Cholesky Decomposition
+@cindex Cholesky decomposition, modified
+@cindex Modified Cholesky Decomposition
+
+The modified Cholesky decomposition is suitable for solving systems
+@math{A x = b} where @math{A} is a symmetric indefinite matrix. Such
+matrices arise in nonlinear optimization algorithms. The standard
+Cholesky decomposition requires a positive definite matrix and would
+fail in this case. Instead of resorting to a method like QR or SVD,
+which do not take into account the symmetry of the matrix, we can
+instead introduce a small perturbation to the matrix @math{A} to
+make it positive definite, and then use a Cholesky decomposition on
+the perturbed matrix. The resulting decomposition satisfies
+@tex
+\beforedisplay
+$$
+P (A + E) P^T = L D L^T
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+P (A + E) P^T = L D L^T
+@end example
+
+@end ifinfo
+where @math{P} is a permutation matrix, @math{E} is a diagonal
+perturbation matrix, @math{L} is unit lower triangular, and
+@math{D} is diagonal. If @math{A} is sufficiently positive
+definite, then the perturbation matrix @math{E} will be zero
+and this method is equivalent to the pivoted Cholesky algorithm.
+For indefinite matrices, the perturbation matrix @math{E} is
+computed to ensure that @math{A + E} is positive definite and
+well conditioned.
+
+@deftypefun int gsl_linalg_mcholesky_decomp (gsl_matrix * @var{A}, gsl_permutation * @var{p}, gsl_vector * @var{E})
+This function factors the symmetric, indefinite square matrix
+@var{A} into the Modified Cholesky decomposition @math{P (A + E) P^T = L D L^T}.
+On input, the values from the diagonal and lower-triangular part of the matrix @var{A} are
+used to construct the factorization. On output the diagonal of the input matrix @var{A} stores the diagonal
+elements of @math{D}, and the lower triangular portion of @var{A}
+contains the matrix @math{L}. Since @math{L} has ones on its diagonal these
+do not need to be explicitely stored. The upper triangular portion of @var{A}
+is unmodified. The permutation matrix @math{P} is
+stored in @var{p} on output. The diagonal perturbation matrix is stored in
+@var{E} on output. The parameter @var{E} may be set to NULL if it is not
+required.
+@end deftypefun
+
+@deftypefun int gsl_linalg_mcholesky_solve (const gsl_matrix * @var{LDLT}, const gsl_permutation * @var{p}, const gsl_vector * @var{b}, gsl_vector * @var{x})
+This function solves the perturbed system @math{(A + E) x = b} using the Cholesky
+decomposition of @math{A + E} held in the matrix @var{LDLT} and permutation
+@var{p} which must have been previously computed by @code{gsl_linalg_mcholesky_decomp}.
+@end deftypefun
+
+@deftypefun int gsl_linalg_mcholesky_svx (const gsl_matrix * @var{LDLT}, const gsl_permutation * @var{p}, gsl_vector * @var{x})
+This function solves the perturbed system @math{(A + E) x = b} in-place using the Cholesky
+decomposition of @math{A + E} held in the matrix @var{LDLT} and permutation
+@var{p} which must have been previously computed by @code{gsl_linalg_mcholesky_decomp}.
+On input, @var{x} contains the right hand side vector @math{b} which is
+replaced by the solution vector on output.
+@end deftypefun
+
+@deftypefun int gsl_linalg_mcholesky_rcond (const gsl_matrix * @var{LDLT}, const gsl_permutation * @var{p}, double * @var{rcond}, gsl_vector * @var{work})
+This function estimates the reciprocal condition number (using the 1-norm) of the perturbed matrix
+@math{A + E}, using its pivoted Cholesky decomposition provided in @var{LDLT}.
+The reciprocal condition number estimate, defined as @math{1 / (||A + E||_1 \cdot ||(A + E)^{-1}||_1)}, is stored
+in @var{rcond}.  Additional workspace of size @math{3 N} is required in @var{work}.
+@end deftypefun
+
 @node Tridiagonal Decomposition of Real Symmetric Matrices
 @section Tridiagonal Decomposition of Real Symmetric Matrices
 @cindex  tridiagonal decomposition
@@ -831,6 +1273,84 @@
 the diagonal vector @var{diag} and superdiagonal vector @var{superdiag}.
 @end deftypefun
 
+@node Givens Rotations
+@section Givens Rotations
+@cindex Givens rotation
+
+A Givens rotation is a rotation in the plane acting on two elements
+of a given vector. It can be represented in matrix form as
+@tex
+\beforedisplay
+$$
+G(i,j,\theta) =
+\left(
+\matrix{
+1 & \ldots & 0 & \ldots & 0 & \ldots & 0 \cr
+\vdots & \ddots & \vdots &  & \vdots & & \vdots \cr
+0 & \ldots & \cos{\theta} & \ldots & -\sin{\theta} & \ldots & 0 \cr
+\vdots &  & \vdots & \ddots & \vdots & & \vdots \cr
+0 & \ldots & \sin{\theta} & \ldots & \cos{\theta} & \ldots & 0 \cr
+\vdots &  & \vdots &  & \vdots & \ddots & \vdots \cr
+0 & \ldots & 0 & \ldots & 0 & \ldots & 1 \cr
+}
+\right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+@end example
+@end ifinfo
+where the @math{\cos{\theta}} and @math{\sin{\theta}} appear at
+the intersection of the @math{i}th and @math{j}th rows and columns.
+When acting on a vector @math{x}, @math{G(i,j,\theta) x} performs
+a rotation of the @math{(i,j)} elements of @math{x}. Givens
+rotations are typically used to introduce zeros in
+vectors, such as during the QR decomposition of a matrix. In this
+case, it is typically desired to find @math{c} and @math{s} such that
+@tex
+\beforedisplay
+$$
+\left(
+\matrix{
+c & -s \cr
+s & c
+}
+\right)
+\left(
+\matrix{
+a \cr
+b
+}
+\right) =
+\left(
+\matrix{
+r \cr
+0
+}
+\right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+@end example
+@end ifinfo
+with @math{r = \sqrt{a^2 + b^2}}.
+
+@deftypefun void gsl_linalg_givens (const double @var{a}, const double @var{b}, double * @var{c}, double * @var{s})
+This function computes @math{c = \cos{\theta}} and @math{s = \sin{\theta}}
+so that the Givens matrix @math{G(\theta)} acting on the
+vector @math{(a,b)} produces @math{(r, 0)}, with @math{r = \sqrt{a^2 + b^2}}.
+@end deftypefun
+
+@deftypefun void gsl_linalg_givens_gv (gsl_vector * @var{v}, const size_t @var{i}, const size_t @var{j}, const double @var{c}, const double @var{s})
+This function applies the Givens rotation defined by
+@math{c = \cos{\theta}} and @math{s = \sin{\theta}} to the @var{i}
+and @var{j} elements of @var{v}. On output,
+@math{(v(i),v(j)) \leftarrow G(\theta) (v(i),v(j))}.
+@end deftypefun
+
 @node Householder Transformations
 @section Householder Transformations
 @cindex Householder matrix
@@ -856,16 +1376,21 @@
 @end ifinfo
 @noindent
 where @math{v} is a vector (called the @dfn{Householder vector}) and
-@math{\tau = 2/(v^T v)}.  The functions described in this section use the
+@math{\tau = 2/(v^T v)}. The functions described in this section use the
 rank-1 structure of the Householder matrix to create and apply
 Householder transformations efficiently.
 
-@deftypefun double gsl_linalg_householder_transform (gsl_vector * @var{v})
-@deftypefunx gsl_complex gsl_linalg_complex_householder_transform (gsl_vector_complex * @var{v})
+@deftypefun double gsl_linalg_householder_transform (gsl_vector * @var{w})
+@deftypefunx gsl_complex gsl_linalg_complex_householder_transform (gsl_vector_complex * @var{w})
 This function prepares a Householder transformation @math{P = I - \tau v
-v^T} which can be used to zero all the elements of the input vector except
-the first.  On output the transformation is stored in the vector @var{v}
-and the scalar @math{\tau} is returned.
+v^T} which can be used to zero all the elements of the input vector @var{w}
+except the first. On output the Householder vector @var{v} is stored in
+@var{w} and the scalar @math{\tau} is returned. The householder vector
+@var{v} is normalized so that @var{v}[0] = 1, however this 1 is not
+stored in the output vector. Instead, @var{w}[0] is set to
+the first element of the transformed vector, so that if
+@math{u = P w}, @var{w}[0] = @math{u}[0] on output and the remainder
+of @math{u} is zero.
 @end deftypefun
 
 @deftypefun int gsl_linalg_householder_hm (double @var{tau}, const gsl_vector * @var{v}, gsl_matrix * @var{A})
@@ -1038,6 +1563,29 @@
 @end ifinfo
 @end deftypefun
 
+@node Triangular Systems
+@section Triangular Systems
+@cindex triangular systems
+
+@deftypefun int gsl_linalg_tri_upper_invert (gsl_matrix * @var{T})
+@deftypefunx int gsl_linalg_tri_lower_invert (gsl_matrix * @var{T})
+@deftypefunx int gsl_linalg_tri_upper_unit_invert (gsl_matrix * @var{T})
+@deftypefunx int gsl_linalg_tri_lower_unit_invert (gsl_matrix * @var{T})
+These functions calculate the in-place inverse of the triangular matrix @var{T}. When
+the @code{upper} prefix is specified, then the upper triangle of @var{T} is used, and when
+the @code{lower} prefix is specified, the lower triangle is used. If the @code{unit}
+prefix is specified, then the diagonal elements of the matrix @var{T} are taken as
+unity and are not referenced. Otherwise the diagonal elements are used in the inversion.
+@end deftypefun
+
+@deftypefun int gsl_linalg_tri_upper_rcond (const gsl_matrix * @var{T}, double * @var{rcond}, gsl_vector * @var{work})
+@deftypefunx int gsl_linalg_tri_lower_rcond (const gsl_matrix * @var{T}, double * @var{rcond}, gsl_vector * @var{work})
+These functions estimate the reciprocal condition number, in the 1-norm, of the upper or lower
+@math{N}-by-@math{N} triangular matrix @var{T}. The reciprocal condition number
+is stored in @var{rcond} on output, and is defined by @math{1 / (||T||_1 \cdot ||T^{-1}||_1)}.
+Additional workspace of size @math{3 N} is required in @var{work}.
+@end deftypefun
+
 @node Balancing
 @section Balancing
 @cindex balancing matrices
@@ -1121,7 +1669,7 @@
 Here is the output from the program,
 
 @example
-@verbatiminclude examples/linalglu.out
+@verbatiminclude examples/linalglu.txt
 @end example
 
 @noindent
@@ -1207,5 +1755,13 @@
 @code{lawnspdf} directories.
 @end itemize
 
+@noindent
+The algorithm for estimating a matrix condition number is described in
+the following paper,
 
-
+@itemize @w{}
+@item
+N. J. Higham, "FORTRAN codes for estimating the one-norm of
+a real or complex matrix, with applications to condition estimation",
+ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
+@end itemize
diff -Nru gsl-doc-1.16/doc/Makefile.am gsl-doc-2.3/doc/Makefile.am
--- gsl-doc-1.16/doc/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/Makefile.am	2016-10-27 11:20:46.000000000 +0000
@@ -1,18 +1,16 @@
 ## Process this file with automake to produce Makefile.in
 
+SUBDIRS = . examples
+
 info_TEXINFOS = gsl-ref.texi
 noinst_TEXINFOS = gsl-design.texi
-gsl_ref_TEXINFOS = err.texi cblas.texi blas.texi min.texi fft.texi rng.texi randist.texi roots.texi statistics.texi specfunc.texi specfunc-airy.texi specfunc-bessel.texi specfunc-clausen.texi specfunc-coulomb.texi specfunc-coupling.texi specfunc-dawson.texi specfunc-debye.texi specfunc-dilog.texi specfunc-elementary.texi specfunc-ellint.texi specfunc-elljac.texi specfunc-erf.texi specfunc-exp.texi specfunc-expint.texi specfunc-fermi-dirac.texi specfunc-gamma.texi specfunc-gegenbauer.texi specfunc-hyperg.texi specfunc-lambert.texi specfunc-laguerre.texi specfunc-legendre.texi specfunc-log.texi specfunc-mathieu.texi specfunc-pow-int.texi specfunc-psi.texi specfunc-synchrotron.texi specfunc-transport.texi specfunc-trig.texi specfunc-zeta.texi siman.texi vectors.texi debug.texi histogram.texi ode-initval.texi integration.texi ieee754.texi montecarlo.texi sum.texi intro.texi usage.texi dwt.texi dht.texi interp.texi poly.texi linalg.texi eigen.texi multiroots.texi sort.texi permutation.texi combination.texi multiset.texi complex.texi math.texi fitting.texi multifit.texi const.texi ntuple.texi diff.texi qrng.texi cheb.texi multimin.texi gpl.texi fdl.texi autoconf.texi bspline.texi
+gsl_ref_TEXINFOS = err.texi cblas.texi blas.texi min.texi fft.texi rng.texi randist.texi roots.texi rstat.texi statistics.texi specfunc.texi specfunc-airy.texi specfunc-bessel.texi specfunc-clausen.texi specfunc-coulomb.texi specfunc-coupling.texi specfunc-dawson.texi specfunc-debye.texi specfunc-dilog.texi specfunc-elementary.texi specfunc-ellint.texi specfunc-elljac.texi specfunc-erf.texi specfunc-exp.texi specfunc-expint.texi specfunc-fermi-dirac.texi specfunc-gamma.texi specfunc-gegenbauer.texi specfunc-hyperg.texi specfunc-lambert.texi specfunc-laguerre.texi specfunc-legendre.texi specfunc-log.texi specfunc-mathieu.texi specfunc-pow-int.texi specfunc-psi.texi specfunc-synchrotron.texi specfunc-transport.texi specfunc-trig.texi specfunc-zeta.texi siman.texi vectors.texi debug.texi histogram.texi ode-initval.texi integration.texi ieee754.texi montecarlo.texi sum.texi intro.texi usage.texi dwt.texi dht.texi interp.texi poly.texi linalg.texi eigen.texi multiroots.texi sort.texi permutation.texi combination.texi multiset.texi complex.texi math.texi fitting.texi multifit-nlinear.texi const.texi ntuple.texi diff.texi qrng.texi cheb.texi multimin.texi gpl.texi fdl.texi autoconf.texi bspline.texi spblas.texi spmatrix.texi splinalg.texi
 
 man_MANS = gsl.3 gsl-config.1 gsl-randist.1 gsl-histogram.1
 
-figures = multimin.eps siman-test.eps siman-energy.eps 12-cities.eps initial-route.eps final-route.eps fft-complex-radix2-f.eps fft-complex-radix2-t.eps fft-complex-radix2.eps fft-real-mixedradix.eps roots-bisection.eps roots-false-position.eps roots-newtons-method.eps roots-secant-method.eps histogram.eps histogram2d.eps min-interval.eps fit-wlinear.eps fit-wlinear2.eps fit-exp.eps ntuple.eps qrng.eps cheb.eps vdp.eps interp2.eps rand-beta.tex rand-binomial.tex rand-cauchy.tex rand-chisq.tex rand-erlang.tex rand-exponential.tex rand-fdist.tex rand-flat.tex rand-gamma.tex rand-gaussian.tex rand-geometric.tex rand-laplace.tex rand-logarithmic.tex rand-logistic.tex rand-lognormal.tex rand-pareto.tex rand-poisson.tex rand-hypergeometric.tex rand-nbinomial.tex rand-pascal.tex rand-bivariate-gaussian.tex rand-rayleigh.tex rand-rayleigh-tail.tex rand-tdist.tex rand-weibull.tex random-walk.tex randplots.gnp rand-exppow.tex rand-levy.tex rand-levyskew.tex rand-gumbel.tex rand-bernoulli.tex rand-gaussian-tail.tex rand-gumbel1.tex rand-gumbel2.tex landau.dat rand-landau.tex dwt-orig.eps dwt-samp.eps interpp2.eps bspline.eps robust.eps
-
-examples_src = examples/blas.c examples/block.c examples/cblas.c examples/cdf.c examples/cheb.c examples/combination.c examples/multiset.c examples/const.c examples/demo_fn.c examples/diff.c examples/eigen.c examples/fft.c examples/fftmr.c examples/fftreal.c examples/fitting.c examples/fitting2.c examples/fitting3.c examples/histogram.c examples/histogram2d.c examples/ieee.c examples/ieeeround.c examples/integration.c examples/interp.c examples/intro.c examples/linalglu.c examples/matrix.c examples/matrixw.c examples/min.c examples/monte.c examples/ntupler.c examples/ntuplew.c examples/ode-initval.c examples/odefixed.c examples/permseq.c examples/permshuffle.c examples/polyroots.c examples/qrng.c examples/randpoisson.c examples/randwalk.c examples/rng.c examples/rngunif.c examples/robfit.c examples/rootnewt.c examples/roots.c examples/siman.c examples/sortsmall.c examples/specfun.c examples/specfun_e.c examples/stat.c examples/statsort.c examples/sum.c examples/vector.c examples/vectorr.c examples/vectorview.c examples/vectorw.c examples/demo_fn.h examples/dwt.c examples/expfit.c examples/nlfit.c examples/interpp.c examples/eigen_nonsymm.c examples/bspline.c examples/multimin.c examples/multiminfn.c examples/nmsimplex.c examples/ode-initval-low-level.c
-
-examples_out = examples/blas.out examples/block.out examples/cblas.out examples/cdf.out examples/combination.out examples/multiset.out examples/const.out examples/diff.out examples/integration.out examples/intro.out examples/linalglu.out examples/min.out examples/polyroots.out examples/randpoisson.2.out examples/randpoisson.out examples/rng.out examples/rngunif.2.out examples/rngunif.out examples/sortsmall.out examples/specfun.out examples/specfun_e.out examples/stat.out examples/statsort.out examples/sum.out examples/vectorview.out examples/ecg.dat examples/dwt.dat examples/multimin.out examples/nmsimplex.out
+figures = multimin.eps siman-test.eps siman-energy.eps 12-cities.eps initial-route.eps final-route.eps fft-complex-radix2-f.eps fft-complex-radix2-t.eps fft-complex-radix2.eps fft-real-mixedradix.eps roots-bisection.eps roots-false-position.eps roots-newtons-method.eps roots-secant-method.eps histogram.eps histogram2d.eps min-interval.eps fit-wlinear.eps fit-wlinear2.eps fit-exp.eps ntuple.eps qrng.eps cheb.eps vdp.eps interp2.eps interp2d.eps nlfit2.eps nlfit3.eps rand-beta.tex rand-binomial.tex rand-cauchy.tex rand-chisq.tex rand-erlang.tex rand-exponential.tex rand-fdist.tex rand-flat.tex rand-gamma.tex rand-gaussian.tex rand-geometric.tex rand-laplace.tex rand-logarithmic.tex rand-logistic.tex rand-lognormal.tex rand-pareto.tex rand-poisson.tex rand-hypergeometric.tex rand-nbinomial.tex rand-pascal.tex rand-bivariate-gaussian.tex rand-rayleigh.tex rand-rayleigh-tail.tex rand-tdist.tex rand-weibull.tex random-walk.tex randplots.gnp rand-exppow.tex rand-levy.tex rand-levyskew.tex rand-gumbel.tex rand-bernoulli.tex rand-gaussian-tail.tex rand-gumbel1.tex rand-gumbel2.tex landau.dat rand-landau.tex dwt-orig.eps dwt-samp.eps interpp2.eps bspline.eps robust.eps sparse_poisson.eps interp_compare.eps regularized.eps regularized2.eps multilarge.eps
 
-noinst_DATA = $(examples_src) $(examples_out) $(figures)
+noinst_DATA = $(figures)
 
 EXTRA_DIST = $(man_MANS) $(noinst_DATA) gsl-design.texi fftalgorithms.tex fftalgorithms.bib algorithm.sty algorithmic.sty calc.sty statnotes.tex
 
diff -Nru gsl-doc-1.16/doc/Makefile.in gsl-doc-2.3/doc/Makefile.in
--- gsl-doc-1.16/doc/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/doc/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -145,6 +145,14 @@
 MAKEINFOHTML = $(MAKEINFO) --html
 AM_MAKEINFOHTMLFLAGS = $(AM_MAKEINFOFLAGS)
 DVIPS = dvips
+RECURSIVE_TARGETS = all-recursive check-recursive cscopelist-recursive \
+	ctags-recursive dvi-recursive html-recursive info-recursive \
+	install-data-recursive install-dvi-recursive \
+	install-exec-recursive install-html-recursive \
+	install-info-recursive install-pdf-recursive \
+	install-ps-recursive install-recursive installcheck-recursive \
+	installdirs-recursive pdf-recursive ps-recursive \
+	tags-recursive uninstall-recursive
 am__can_run_installinfo = \
   case $$AM_UPDATE_INFO_DIR in \
     n|no|NO) false;; \
@@ -184,12 +192,65 @@
 NROFF = nroff
 MANS = $(man_MANS)
 DATA = $(noinst_DATA)
+RECURSIVE_CLEAN_TARGETS = mostlyclean-recursive clean-recursive	\
+  distclean-recursive maintainer-clean-recursive
+am__recursive_targets = \
+  $(RECURSIVE_TARGETS) \
+  $(RECURSIVE_CLEAN_TARGETS) \
+  $(am__extra_recursive_targets)
+AM_RECURSIVE_TARGETS = $(am__recursive_targets:-recursive=) TAGS CTAGS \
+	distdir
 am__tagged_files = $(HEADERS) $(SOURCES) $(TAGS_FILES) $(LISP)
+# Read a list of newline-separated strings from the standard input,
+# and print each of them once, without duplicates.  Input order is
+# *not* preserved.
+am__uniquify_input = $(AWK) '\
+  BEGIN { nonempty = 0; } \
+  { items[$$0] = 1; nonempty = 1; } \
+  END { if (nonempty) { for (i in items) print i; }; } \
+'
+# Make sure the list of sources is unique.  This is necessary because,
+# e.g., the same source file might be shared among _SOURCES variables
+# for different programs/libraries.
+am__define_uniq_tagged_files = \
+  list='$(am__tagged_files)'; \
+  unique=`for i in $$list; do \
+    if test -f "$$i"; then echo $$i; else echo $(srcdir)/$$i; fi; \
+  done | $(am__uniquify_input)`
+ETAGS = etags
+CTAGS = ctags
+DIST_SUBDIRS = $(SUBDIRS)
 DISTFILES = $(DIST_COMMON) $(DIST_SOURCES) $(TEXINFOS) $(EXTRA_DIST)
+am__relativize = \
+  dir0=`pwd`; \
+  sed_first='s,^\([^/]*\)/.*$$,\1,'; \
+  sed_rest='s,^[^/]*/*,,'; \
+  sed_last='s,^.*/\([^/]*\)$$,\1,'; \
+  sed_butlast='s,/*[^/]*$$,,'; \
+  while test -n "$$dir1"; do \
+    first=`echo "$$dir1" | sed -e "$$sed_first"`; \
+    if test "$$first" != "."; then \
+      if test "$$first" = ".."; then \
+        dir2=`echo "$$dir0" | sed -e "$$sed_last"`/"$$dir2"; \
+        dir0=`echo "$$dir0" | sed -e "$$sed_butlast"`; \
+      else \
+        first2=`echo "$$dir2" | sed -e "$$sed_first"`; \
+        if test "$$first2" = "$$first"; then \
+          dir2=`echo "$$dir2" | sed -e "$$sed_rest"`; \
+        else \
+          dir2="../$$dir2"; \
+        fi; \
+        dir0="$$dir0"/"$$first"; \
+      fi; \
+    fi; \
+    dir1=`echo "$$dir1" | sed -e "$$sed_rest"`; \
+  done; \
+  reldir="$$dir2"
 ACLOCAL = @ACLOCAL@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -212,7 +273,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -326,13 +390,15 @@
 top_build_prefix = @top_build_prefix@
 top_builddir = @top_builddir@
 top_srcdir = @top_srcdir@
+SUBDIRS = . examples
 info_TEXINFOS = gsl-ref.texi
 noinst_TEXINFOS = gsl-design.texi
 gsl_ref_TEXINFOS = err.texi cblas.texi blas.texi min.texi fft.texi \
-	rng.texi randist.texi roots.texi statistics.texi specfunc.texi \
-	specfunc-airy.texi specfunc-bessel.texi specfunc-clausen.texi \
-	specfunc-coulomb.texi specfunc-coupling.texi \
-	specfunc-dawson.texi specfunc-debye.texi specfunc-dilog.texi \
+	rng.texi randist.texi roots.texi rstat.texi statistics.texi \
+	specfunc.texi specfunc-airy.texi specfunc-bessel.texi \
+	specfunc-clausen.texi specfunc-coulomb.texi \
+	specfunc-coupling.texi specfunc-dawson.texi \
+	specfunc-debye.texi specfunc-dilog.texi \
 	specfunc-elementary.texi specfunc-ellint.texi \
 	specfunc-elljac.texi specfunc-erf.texi specfunc-exp.texi \
 	specfunc-expint.texi specfunc-fermi-dirac.texi \
@@ -347,9 +413,10 @@
 	sum.texi intro.texi usage.texi dwt.texi dht.texi interp.texi \
 	poly.texi linalg.texi eigen.texi multiroots.texi sort.texi \
 	permutation.texi combination.texi multiset.texi complex.texi \
-	math.texi fitting.texi multifit.texi const.texi ntuple.texi \
-	diff.texi qrng.texi cheb.texi multimin.texi gpl.texi fdl.texi \
-	autoconf.texi bspline.texi
+	math.texi fitting.texi multifit-nlinear.texi const.texi \
+	ntuple.texi diff.texi qrng.texi cheb.texi multimin.texi \
+	gpl.texi fdl.texi autoconf.texi bspline.texi spblas.texi \
+	spmatrix.texi splinalg.texi
 man_MANS = gsl.3 gsl-config.1 gsl-randist.1 gsl-histogram.1
 figures = multimin.eps siman-test.eps siman-energy.eps 12-cities.eps \
 	initial-route.eps final-route.eps fft-complex-radix2-f.eps \
@@ -358,47 +425,26 @@
 	roots-false-position.eps roots-newtons-method.eps \
 	roots-secant-method.eps histogram.eps histogram2d.eps \
 	min-interval.eps fit-wlinear.eps fit-wlinear2.eps fit-exp.eps \
-	ntuple.eps qrng.eps cheb.eps vdp.eps interp2.eps rand-beta.tex \
-	rand-binomial.tex rand-cauchy.tex rand-chisq.tex \
-	rand-erlang.tex rand-exponential.tex rand-fdist.tex \
-	rand-flat.tex rand-gamma.tex rand-gaussian.tex \
-	rand-geometric.tex rand-laplace.tex rand-logarithmic.tex \
-	rand-logistic.tex rand-lognormal.tex rand-pareto.tex \
-	rand-poisson.tex rand-hypergeometric.tex rand-nbinomial.tex \
-	rand-pascal.tex rand-bivariate-gaussian.tex rand-rayleigh.tex \
+	ntuple.eps qrng.eps cheb.eps vdp.eps interp2.eps interp2d.eps \
+	nlfit2.eps nlfit3.eps rand-beta.tex rand-binomial.tex \
+	rand-cauchy.tex rand-chisq.tex rand-erlang.tex \
+	rand-exponential.tex rand-fdist.tex rand-flat.tex \
+	rand-gamma.tex rand-gaussian.tex rand-geometric.tex \
+	rand-laplace.tex rand-logarithmic.tex rand-logistic.tex \
+	rand-lognormal.tex rand-pareto.tex rand-poisson.tex \
+	rand-hypergeometric.tex rand-nbinomial.tex rand-pascal.tex \
+	rand-bivariate-gaussian.tex rand-rayleigh.tex \
 	rand-rayleigh-tail.tex rand-tdist.tex rand-weibull.tex \
 	random-walk.tex randplots.gnp rand-exppow.tex rand-levy.tex \
 	rand-levyskew.tex rand-gumbel.tex rand-bernoulli.tex \
 	rand-gaussian-tail.tex rand-gumbel1.tex rand-gumbel2.tex \
 	landau.dat rand-landau.tex dwt-orig.eps dwt-samp.eps \
-	interpp2.eps bspline.eps robust.eps
-examples_src = examples/blas.c examples/block.c examples/cblas.c \
-	examples/cdf.c examples/cheb.c examples/combination.c \
-	examples/multiset.c examples/const.c examples/demo_fn.c \
-	examples/diff.c examples/eigen.c examples/fft.c \
-	examples/fftmr.c examples/fftreal.c examples/fitting.c \
-	examples/fitting2.c examples/fitting3.c examples/histogram.c \
-	examples/histogram2d.c examples/ieee.c examples/ieeeround.c \
-	examples/integration.c examples/interp.c examples/intro.c \
-	examples/linalglu.c examples/matrix.c examples/matrixw.c \
-	examples/min.c examples/monte.c examples/ntupler.c \
-	examples/ntuplew.c examples/ode-initval.c examples/odefixed.c \
-	examples/permseq.c examples/permshuffle.c examples/polyroots.c \
-	examples/qrng.c examples/randpoisson.c examples/randwalk.c \
-	examples/rng.c examples/rngunif.c examples/robfit.c \
-	examples/rootnewt.c examples/roots.c examples/siman.c \
-	examples/sortsmall.c examples/specfun.c examples/specfun_e.c \
-	examples/stat.c examples/statsort.c examples/sum.c \
-	examples/vector.c examples/vectorr.c examples/vectorview.c \
-	examples/vectorw.c examples/demo_fn.h examples/dwt.c \
-	examples/expfit.c examples/nlfit.c examples/interpp.c \
-	examples/eigen_nonsymm.c examples/bspline.c \
-	examples/multimin.c examples/multiminfn.c examples/nmsimplex.c \
-	examples/ode-initval-low-level.c
-examples_out = examples/blas.out examples/block.out examples/cblas.out examples/cdf.out examples/combination.out examples/multiset.out examples/const.out examples/diff.out examples/integration.out examples/intro.out examples/linalglu.out examples/min.out examples/polyroots.out examples/randpoisson.2.out examples/randpoisson.out examples/rng.out examples/rngunif.2.out examples/rngunif.out examples/sortsmall.out examples/specfun.out examples/specfun_e.out examples/stat.out examples/statsort.out examples/sum.out examples/vectorview.out examples/ecg.dat examples/dwt.dat examples/multimin.out examples/nmsimplex.out
-noinst_DATA = $(examples_src) $(examples_out) $(figures)
+	interpp2.eps bspline.eps robust.eps sparse_poisson.eps \
+	interp_compare.eps regularized.eps regularized2.eps \
+	multilarge.eps
+noinst_DATA = $(figures)
 EXTRA_DIST = $(man_MANS) $(noinst_DATA) gsl-design.texi fftalgorithms.tex fftalgorithms.bib algorithm.sty algorithmic.sty calc.sty statnotes.tex
-all: all-am
+all: all-recursive
 
 .SUFFIXES:
 .SUFFIXES: .dvi .html .info .pdf .ps .texi
@@ -688,12 +734,105 @@
 	} | sed -e 's,.*/,,;h;s,.*\.,,;s,^[^3][0-9a-z]*$$,3,;x' \
 	      -e 's,\.[0-9a-z]*$$,,;$(transform);G;s,\n,.,'`; \
 	dir='$(DESTDIR)$(man3dir)'; $(am__uninstall_files_from_dir)
-tags TAGS:
 
-ctags CTAGS:
+# This directory's subdirectories are mostly independent; you can cd
+# into them and run 'make' without going through this Makefile.
+# To change the values of 'make' variables: instead of editing Makefiles,
+# (1) if the variable is set in 'config.status', edit 'config.status'
+#     (which will cause the Makefiles to be regenerated when you run 'make');
+# (2) otherwise, pass the desired values on the 'make' command line.
+$(am__recursive_targets):
+	@fail=; \
+	if $(am__make_keepgoing); then \
+	  failcom='fail=yes'; \
+	else \
+	  failcom='exit 1'; \
+	fi; \
+	dot_seen=no; \
+	target=`echo $@ | sed s/-recursive//`; \
+	case "$@" in \
+	  distclean-* | maintainer-clean-*) list='$(DIST_SUBDIRS)' ;; \
+	  *) list='$(SUBDIRS)' ;; \
+	esac; \
+	for subdir in $$list; do \
+	  echo "Making $$target in $$subdir"; \
+	  if test "$$subdir" = "."; then \
+	    dot_seen=yes; \
+	    local_target="$$target-am"; \
+	  else \
+	    local_target="$$target"; \
+	  fi; \
+	  ($(am__cd) $$subdir && $(MAKE) $(AM_MAKEFLAGS) $$local_target) \
+	  || eval $$failcom; \
+	done; \
+	if test "$$dot_seen" = "no"; then \
+	  $(MAKE) $(AM_MAKEFLAGS) "$$target-am" || exit 1; \
+	fi; test -z "$$fail"
+
+ID: $(am__tagged_files)
+	$(am__define_uniq_tagged_files); mkid -fID $$unique
+tags: tags-recursive
+TAGS: tags
+
+tags-am: $(TAGS_DEPENDENCIES) $(am__tagged_files)
+	set x; \
+	here=`pwd`; \
+	if ($(ETAGS) --etags-include --version) >/dev/null 2>&1; then \
+	  include_option=--etags-include; \
+	  empty_fix=.; \
+	else \
+	  include_option=--include; \
+	  empty_fix=; \
+	fi; \
+	list='$(SUBDIRS)'; for subdir in $$list; do \
+	  if test "$$subdir" = .; then :; else \
+	    test ! -f $$subdir/TAGS || \
+	      set "$$@" "$$include_option=$$here/$$subdir/TAGS"; \
+	  fi; \
+	done; \
+	$(am__define_uniq_tagged_files); \
+	shift; \
+	if test -z "$(ETAGS_ARGS)$$*$$unique"; then :; else \
+	  test -n "$$unique" || unique=$$empty_fix; \
+	  if test $$# -gt 0; then \
+	    $(ETAGS) $(ETAGSFLAGS) $(AM_ETAGSFLAGS) $(ETAGS_ARGS) \
+	      "$$@" $$unique; \
+	  else \
+	    $(ETAGS) $(ETAGSFLAGS) $(AM_ETAGSFLAGS) $(ETAGS_ARGS) \
+	      $$unique; \
+	  fi; \
+	fi
+ctags: ctags-recursive
 
-cscope cscopelist:
+CTAGS: ctags
+ctags-am: $(TAGS_DEPENDENCIES) $(am__tagged_files)
+	$(am__define_uniq_tagged_files); \
+	test -z "$(CTAGS_ARGS)$$unique" \
+	  || $(CTAGS) $(CTAGSFLAGS) $(AM_CTAGSFLAGS) $(CTAGS_ARGS) \
+	     $$unique
+
+GTAGS:
+	here=`$(am__cd) $(top_builddir) && pwd` \
+	  && $(am__cd) $(top_srcdir) \
+	  && gtags -i $(GTAGS_ARGS) "$$here"
+cscopelist: cscopelist-recursive
+
+cscopelist-am: $(am__tagged_files)
+	list='$(am__tagged_files)'; \
+	case "$(srcdir)" in \
+	  [\\/]* | ?:[\\/]*) sdir="$(srcdir)" ;; \
+	  *) sdir=$(subdir)/$(srcdir) ;; \
+	esac; \
+	for i in $$list; do \
+	  if test -f "$$i"; then \
+	    echo "$(subdir)/$$i"; \
+	  else \
+	    echo "$$sdir/$$i"; \
+	  fi; \
+	done >> $(top_builddir)/cscope.files
 
+distclean-tags:
+	-rm -f TAGS ID GTAGS GRTAGS GSYMS GPATH tags
 
 distdir: $(DISTFILES)
 	@srcdirstrip=`echo "$(srcdir)" | sed 's/[].[^$$\\*]/\\\\&/g'`; \
@@ -725,25 +864,51 @@
 	    || exit 1; \
 	  fi; \
 	done
+	@list='$(DIST_SUBDIRS)'; for subdir in $$list; do \
+	  if test "$$subdir" = .; then :; else \
+	    $(am__make_dryrun) \
+	      || test -d "$(distdir)/$$subdir" \
+	      || $(MKDIR_P) "$(distdir)/$$subdir" \
+	      || exit 1; \
+	    dir1=$$subdir; dir2="$(distdir)/$$subdir"; \
+	    $(am__relativize); \
+	    new_distdir=$$reldir; \
+	    dir1=$$subdir; dir2="$(top_distdir)"; \
+	    $(am__relativize); \
+	    new_top_distdir=$$reldir; \
+	    echo " (cd $$subdir && $(MAKE) $(AM_MAKEFLAGS) top_distdir="$$new_top_distdir" distdir="$$new_distdir" \\"; \
+	    echo "     am__remove_distdir=: am__skip_length_check=: am__skip_mode_fix=: distdir)"; \
+	    ($(am__cd) $$subdir && \
+	      $(MAKE) $(AM_MAKEFLAGS) \
+	        top_distdir="$$new_top_distdir" \
+	        distdir="$$new_distdir" \
+		am__remove_distdir=: \
+		am__skip_length_check=: \
+		am__skip_mode_fix=: \
+	        distdir) \
+	      || exit 1; \
+	  fi; \
+	done
 	$(MAKE) $(AM_MAKEFLAGS) \
 	  top_distdir="$(top_distdir)" distdir="$(distdir)" \
 	  dist-info
 check-am: all-am
-check: check-am
+check: check-recursive
 all-am: Makefile $(INFO_DEPS) $(MANS) $(DATA)
-installdirs:
+installdirs: installdirs-recursive
+installdirs-am:
 	for dir in "$(DESTDIR)$(infodir)" "$(DESTDIR)$(man1dir)" "$(DESTDIR)$(man3dir)"; do \
 	  test -z "$$dir" || $(MKDIR_P) "$$dir"; \
 	done
-install: install-am
-install-exec: install-exec-am
-install-data: install-data-am
-uninstall: uninstall-am
+install: install-recursive
+install-exec: install-exec-recursive
+install-data: install-data-recursive
+uninstall: uninstall-recursive
 
 install-am: all-am
 	@$(MAKE) $(AM_MAKEFLAGS) install-exec-am install-data-am
 
-installcheck: installcheck-am
+installcheck: installcheck-recursive
 install-strip:
 	if test -z '$(STRIP)'; then \
 	  $(MAKE) $(AM_MAKEFLAGS) INSTALL_PROGRAM="$(INSTALL_STRIP_PROGRAM)" \
@@ -765,29 +930,29 @@
 maintainer-clean-generic:
 	@echo "This command is intended for maintainers to use"
 	@echo "it deletes files that may require special tools to rebuild."
-clean: clean-am
+clean: clean-recursive
 
 clean-am: clean-aminfo clean-generic clean-libtool mostlyclean-am
 
-distclean: distclean-am
+distclean: distclean-recursive
 	-rm -f Makefile
-distclean-am: clean-am distclean-generic
+distclean-am: clean-am distclean-generic distclean-tags
 
-dvi: dvi-am
+dvi: dvi-recursive
 
 dvi-am: $(DVIS)
 
-html: html-am
+html: html-recursive
 
 html-am: $(HTMLS)
 
-info: info-am
+info: info-recursive
 
 info-am: $(INFO_DEPS)
 
 install-data-am: install-info-am install-man
 
-install-dvi: install-dvi-am
+install-dvi: install-dvi-recursive
 
 install-dvi-am: $(DVIS)
 	@$(NORMAL_INSTALL)
@@ -806,7 +971,7 @@
 	done
 install-exec-am:
 
-install-html: install-html-am
+install-html: install-html-recursive
 
 install-html-am: $(HTMLS)
 	@$(NORMAL_INSTALL)
@@ -833,7 +998,7 @@
 	  echo " $(INSTALL_DATA) $$files '$(DESTDIR)$(htmldir)'"; \
 	  $(INSTALL_DATA) $$files "$(DESTDIR)$(htmldir)" || exit $$?; \
 	done; }
-install-info: install-info-am
+install-info: install-info-recursive
 
 install-info-am: $(INFO_DEPS)
 	@$(NORMAL_INSTALL)
@@ -870,7 +1035,7 @@
 	else : ; fi
 install-man: install-man1 install-man3
 
-install-pdf: install-pdf-am
+install-pdf: install-pdf-recursive
 
 install-pdf-am: $(PDFS)
 	@$(NORMAL_INSTALL)
@@ -886,7 +1051,7 @@
 	while read files; do \
 	  echo " $(INSTALL_DATA) $$files '$(DESTDIR)$(pdfdir)'"; \
 	  $(INSTALL_DATA) $$files "$(DESTDIR)$(pdfdir)" || exit $$?; done
-install-ps: install-ps-am
+install-ps: install-ps-recursive
 
 install-ps-am: $(PSS)
 	@$(NORMAL_INSTALL)
@@ -904,19 +1069,19 @@
 	  $(INSTALL_DATA) $$files "$(DESTDIR)$(psdir)" || exit $$?; done
 installcheck-am:
 
-maintainer-clean: maintainer-clean-am
+maintainer-clean: maintainer-clean-recursive
 	-rm -f Makefile
 maintainer-clean-am: distclean-am maintainer-clean-aminfo \
 	maintainer-clean-generic maintainer-clean-vti
 
-mostlyclean: mostlyclean-am
+mostlyclean: mostlyclean-recursive
 
 mostlyclean-am: mostlyclean-aminfo mostlyclean-generic \
 	mostlyclean-libtool mostlyclean-vti
 
 pdf-am: $(PDFS)
 
-ps: ps-am
+ps: ps-recursive
 
 ps-am: $(PSS)
 
@@ -925,24 +1090,26 @@
 
 uninstall-man: uninstall-man1 uninstall-man3
 
-.MAKE: install-am install-strip
+.MAKE: $(am__recursive_targets) install-am install-strip
 
-.PHONY: all all-am check check-am clean clean-aminfo clean-generic \
-	clean-libtool cscopelist-am ctags-am dist-info distclean \
-	distclean-generic distclean-libtool distdir dvi dvi-am html \
-	html-am info info-am install install-am install-data \
-	install-data-am install-dvi install-dvi-am install-exec \
-	install-exec-am install-html install-html-am install-info \
-	install-info-am install-man install-man1 install-man3 \
-	install-pdf install-pdf-am install-ps install-ps-am \
-	install-strip installcheck installcheck-am installdirs \
-	maintainer-clean maintainer-clean-aminfo \
-	maintainer-clean-generic maintainer-clean-vti mostlyclean \
-	mostlyclean-aminfo mostlyclean-generic mostlyclean-libtool \
-	mostlyclean-vti pdf pdf-am ps ps-am tags-am uninstall \
-	uninstall-am uninstall-dvi-am uninstall-html-am \
-	uninstall-info-am uninstall-man uninstall-man1 uninstall-man3 \
-	uninstall-pdf-am uninstall-ps-am
+.PHONY: $(am__recursive_targets) CTAGS GTAGS TAGS all all-am check \
+	check-am clean clean-aminfo clean-generic clean-libtool \
+	cscopelist-am ctags ctags-am dist-info distclean \
+	distclean-generic distclean-libtool distclean-tags distdir dvi \
+	dvi-am html html-am info info-am install install-am \
+	install-data install-data-am install-dvi install-dvi-am \
+	install-exec install-exec-am install-html install-html-am \
+	install-info install-info-am install-man install-man1 \
+	install-man3 install-pdf install-pdf-am install-ps \
+	install-ps-am install-strip installcheck installcheck-am \
+	installdirs installdirs-am maintainer-clean \
+	maintainer-clean-aminfo maintainer-clean-generic \
+	maintainer-clean-vti mostlyclean mostlyclean-aminfo \
+	mostlyclean-generic mostlyclean-libtool mostlyclean-vti pdf \
+	pdf-am ps ps-am tags tags-am uninstall uninstall-am \
+	uninstall-dvi-am uninstall-html-am uninstall-info-am \
+	uninstall-man uninstall-man1 uninstall-man3 uninstall-pdf-am \
+	uninstall-ps-am
 
 
 # pdf disabled, use postscript and ps2pdf
diff -Nru gsl-doc-1.16/doc/min.texi gsl-doc-2.3/doc/min.texi
--- gsl-doc-1.16/doc/min.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/min.texi	2016-09-15 16:30:25.000000000 +0000
@@ -131,8 +131,8 @@
 @section Initializing the Minimizer
 
 @deftypefun {gsl_min_fminimizer *} gsl_min_fminimizer_alloc (const gsl_min_fminimizer_type * @var{T})
-@tpindex gsl_min_fminimizer
-@tpindex gsl_min_fminimizer_type
+@tindex gsl_min_fminimizer
+@tindex gsl_min_fminimizer_type
 This function returns a pointer to a newly allocated instance of a
 minimizer of type @var{T}.  For example, the following code
 creates an instance of a golden section minimizer,
@@ -334,7 +334,7 @@
 On each iteration, the algorithm first compares the subintervals from
 the endpoints to the current minimum.  The larger subinterval is divided
 in a golden section (using the famous ratio @math{(3-\sqrt 5)/2 =
-0.3189660}@dots{}) and the value of the function at this new point is
+0.3819660}@dots{}) and the value of the function at this new point is
 calculated.  The new value is used with the constraint @math{f(a') >
 f(x') < f(b')} to a select new interval containing the minimum, by
 discarding the least useful point.  This procedure can be continued
@@ -390,7 +390,7 @@
 
 @smallexample
 $ ./a.out 
-@verbatiminclude examples/min.out
+@verbatiminclude examples/min.txt
 @end smallexample
 
 @node Minimization References and Further Reading
diff -Nru gsl-doc-1.16/doc/montecarlo.texi gsl-doc-2.3/doc/montecarlo.texi
--- gsl-doc-1.16/doc/montecarlo.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/montecarlo.texi	2015-11-03 16:21:55.000000000 +0000
@@ -195,7 +195,7 @@
 @file{gsl_monte_plain.h}.
 
 @deftypefun {gsl_monte_plain_state *} gsl_monte_plain_alloc (size_t @var{dim})
-@tpindex gsl_monte_plain_state
+@tindex gsl_monte_plain_state
 This function allocates and initializes a workspace for Monte Carlo
 integration in @var{dim} dimensions.  
 @end deftypefun
@@ -295,7 +295,7 @@
 @file{gsl_monte_miser.h}.
 
 @deftypefun {gsl_monte_miser_state *} gsl_monte_miser_alloc (size_t @var{dim})
-@tpindex gsl_monte_miser_state
+@tindex gsl_monte_miser_state
 This function allocates and initializes a workspace for Monte Carlo
 integration in @var{dim} dimensions.  The workspace is used to maintain
 the state of the integration.
@@ -485,7 +485,7 @@
 
 
 @deftypefun {gsl_monte_vegas_state *} gsl_monte_vegas_alloc (size_t @var{dim})
-@tpindex gsl_monte_vegas_state
+@tindex gsl_monte_vegas_state
 This function allocates and initializes a workspace for Monte Carlo
 integration in @var{dim} dimensions.  The workspace is used to maintain
 the state of the integration.
diff -Nru gsl-doc-1.16/doc/multifit-nlinear.texi gsl-doc-2.3/doc/multifit-nlinear.texi
--- gsl-doc-1.16/doc/multifit-nlinear.texi	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/multifit-nlinear.texi	2016-11-21 18:05:19.000000000 +0000
@@ -0,0 +1,1963 @@
+@cindex nonlinear least squares
+@cindex least squares, nonlinear
+
+This chapter describes functions for multidimensional nonlinear
+least-squares fitting.  There are generally two classes of
+algorithms for solving nonlinear least squares problems, which
+fall under line search methods and trust region methods.
+GSL currently implements only trust region methods and
+provides the user with
+full access to intermediate steps of the iteration. The user
+also has the ability to tune a number of parameters which affect
+low-level aspects of the algorithm which can help to accelerate
+convergence for the specific problem at hand. GSL provides
+two separate interfaces for nonlinear least squares fitting. The
+first is designed for small to moderate sized problems, and the
+second is designed for very large problems, which may or may not
+have significant sparse structure.
+
+The header file @file{gsl_multifit_nlinear.h} contains prototypes for the
+multidimensional nonlinear fitting functions and related declarations
+relating to the small to moderate sized systems.
+
+The header file @file{gsl_multilarge_nlinear.h} contains prototypes for the
+multidimensional nonlinear fitting functions and related declarations
+relating to large systems.
+
+@menu
+* Nonlinear Least-Squares Overview::
+* Nonlinear Least-Squares TRS Overview::
+* Nonlinear Least-Squares Weighted Overview::
+* Nonlinear Least-Squares Tunable Parameters::
+* Nonlinear Least-Squares Initialization::
+* Nonlinear Least-Squares Function Definition::
+* Nonlinear Least-Squares Iteration::
+* Nonlinear Least-Squares Testing for Convergence::
+* Nonlinear Least-Squares High Level Driver::
+* Nonlinear Least-Squares Covariance Matrix::
+* Nonlinear Least-Squares Troubleshooting::
+* Nonlinear Least-Squares Examples::
+* Nonlinear Least-Squares References and Further Reading::
+@end menu
+
+@node Nonlinear Least-Squares Overview
+@section Overview
+@cindex nonlinear least squares, overview
+
+The problem of multidimensional nonlinear least-squares fitting requires
+the minimization of the squared residuals of @math{n} functions,
+@math{f_i}, in @math{p} parameters, @math{x_i},
+@tex
+\beforedisplay
+$$
+\Phi(x)  = {1 \over 2} || f(x) ||^2
+         = {1 \over 2} \sum_{i=1}^{n} f_i (x_1, \dots, x_p)^2
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+\Phi(x) = (1/2) || f(x) ||^2
+        = (1/2) \sum_@{i=1@}^@{n@} f_i(x_1, ..., x_p)^2 
+@end example
+
+@end ifinfo
+@noindent
+In trust region methods, the objective (or cost) function @math{\Phi(x)} is approximated
+by a model function @math{m_k(\delta)} in the vicinity of some point @math{x_k}. The
+model function is often simply a second order Taylor series expansion around the
+point @math{x_k}, ie:
+@tex
+\beforedisplay
+$$
+\Phi(x_k + \delta) \approx m_k(\delta) = \Phi(x_k) + g_k^T \delta + {1 \over 2} \delta^T B_k \delta
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+\Phi(x_k + \delta) ~=~ m_k(\delta) = \Phi(x_k) + g_k^T \delta + 1/2 \delta^T B_k \delta
+@end example
+
+@end ifinfo
+where @math{g_k = \nabla \Phi(x_k) = J^T f} is the gradient vector at the point @math{x_k},
+@math{B_k = \nabla^2 \Phi(x_k)} is the Hessian matrix at @math{x_k}, or some
+approximation to it, and @math{J} is the @math{n}-by-@math{p} Jacobian matrix
+@c{$J_{ij} = \partial f_i / \partial x_j$}
+@math{J_@{ij@} = d f_i / d x_j}.
+In order to find the next step @math{\delta}, we minimize the model function
+@math{m_k(\delta)}, but search for solutions only within a region where
+we trust that @math{m_k(\delta)} is a good approximation to the objective
+function @math{\Phi(x_k + \delta)}. In other words,
+we seek a solution of the trust region subproblem (TRS)
+@tex
+\beforedisplay
+$$
+\min_{\delta \in R^p} m_k(\delta) = \Phi(x_k) + g_k^T \delta + {1 \over 2} \delta^T B_k \delta, \qquad\hbox{s.t.}\quad || D_k \delta || \le \Delta_k
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+\min_(\delta \in R^p) m_k(\delta), s.t. || D_k \delta || <= \Delta_k
+@end example
+
+@end ifinfo
+where @math{\Delta_k > 0} is the trust region radius and @math{D_k} is
+a scaling matrix. If @math{D_k = I}, then the trust region is a ball
+of radius @math{\Delta_k} centered at @math{x_k}. In some applications,
+the parameter vector @math{x} may have widely different scales. For
+example, one parameter might be a temperature on the order of
+@math{10^3} K, while another might be a length on the order of
+@math{10^{-6}} m. In such cases, a spherical trust region may not
+be the best choice, since if @math{\Phi} changes rapidly along
+directions with one scale, and more slowly along directions with
+a different scale, the model function @math{m_k} may be a poor
+approximation to @math{\Phi} along the rapidly changing directions.
+In such problems, it may be best to use an elliptical trust region,
+by setting @math{D_k} to a diagonal matrix whose entries are designed
+so that the scaled step @math{D_k \delta} has entries of approximately the same
+order of magnitude.
+
+The trust region subproblem above normally amounts to solving a
+linear least squares system (or multiple systems) for the step
+@math{\delta}. Once @math{\delta} is computed, it is checked whether
+or not it reduces the objective function @math{\Phi(x)}. A useful
+statistic for this is to look at the ratio
+@tex
+\beforedisplay
+$$
+\rho_k = { \Phi(x_k) - \Phi(x_k + \delta_k) \over m_k(0) - m_k(\delta_k) }
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+\rho_k = ( \Phi(x_k) - \Phi(x_k + \delta_k) / ( m_k(0) - m_k(\delta_k) )
+@end example
+
+@end ifinfo
+where the numerator is the actual reduction of the objective function
+due to the step @math{\delta_k}, and the denominator is the predicted
+reduction due to the model @math{m_k}. If @math{\rho_k} is negative,
+it means that the step @math{\delta_k} increased the objective function
+and so it is rejected. If @math{\rho_k} is positive,
+then we have found a step which reduced the objective function and
+it is accepted. Furthermore, if @math{\rho_k} is close to 1,
+then this indicates that the model function is a good approximation
+to the objective function in the trust region, and so on the next
+iteration the trust region is enlarged in order to take more ambitious
+steps. When a step is rejected, the trust region is made smaller and
+the TRS is solved again. An outline for the general trust region method
+used by GSL can now be given.
+
+@noindent
+@b{Trust Region Algorithm}
+@enumerate
+
+@item Initialize: given @math{x_0}, construct @math{m_0(\delta)}, @math{D_0} and @math{\Delta_0 > 0}
+
+@item For k = 0, 1, 2, ...
+
+@enumerate a
+
+@item If converged, then stop
+
+@item Solve TRS for trial step @math{\delta_k}
+
+@item Evaluate trial step by computing @math{\rho_k}
+
+@enumerate
+@item if step is accepted, set @math{x_{k+1} = x_k + \delta_k} and increase radius, @math{\Delta_{k+1} = \alpha \Delta_k}
+@item if step is rejected, set @math{x_{k+1} = x_k} and decrease radius, @math{\Delta_{k+1} = {\Delta_k \over \beta}}; goto 2(b)
+@end enumerate
+
+@item Construct @math{m_{k+1}(\delta)} and @math{D_{k+1}}
+
+@end enumerate
+
+@end enumerate
+
+@noindent
+GSL offers the user a number of different algorithms for solving the trust
+region subproblem in 2(b), as well as different choices of scaling matrices
+@math{D_k} and different methods of updating the trust region radius
+@math{\Delta_k}. Therefore, while reasonable default methods are provided,
+the user has a lot of control to fine-tune the various steps of the
+algorithm for their specific problem.
+
+@node Nonlinear Least-Squares TRS Overview
+@section Solving the Trust Region Subproblem (TRS)
+
+@menu
+* Nonlinear Least-Squares TRS Levenberg-Marquardt::
+* Nonlinear Least-Squares TRS Levenberg-Marquardt with Geodesic Acceleration::
+* Nonlinear Least-Squares TRS Dogleg::
+* Nonlinear Least-Squares TRS Double Dogleg::
+* Nonlinear Least-Squares TRS 2D Subspace::
+* Nonlinear Least-Squares TRS Steihaug-Toint Conjugate Gradient::
+@end menu
+
+Below we describe the methods available for solving the trust region
+subproblem. The methods available provide either exact or approximate
+solutions to the trust region subproblem. In all algorithms below,
+the Hessian matrix @math{B_k} is approximated as @math{B_k \approx J_k^T J_k},
+where @math{J_k = J(x_k)}. In all methods, the solution of the TRS
+involves solving a linear least squares system involving the Jacobian
+matrix. For small to moderate sized problems (@code{gsl_multifit_nlinear} interface),
+this is accomplished by factoring the full Jacobian matrix, which is provided
+by the user, with the Cholesky, QR, or SVD decompositions. For large systems
+(@code{gsl_multilarge_nlinear} interface), the user has two choices. One
+is to solve the system iteratively, without needing to store the full
+Jacobian matrix in memory. With this method, the user must provide a routine
+to calculate the matrix-vector products @math{J u} or @math{J^T u} for a given vector @math{u}.
+This iterative method is particularly useful for systems where the Jacobian has
+sparse structure, since forming matrix-vector products can be done cheaply. The
+second option for large systems involves forming the normal equations matrix
+@math{J^T J} and then factoring it using a Cholesky decomposition. The normal
+equations matrix is @math{p}-by-@math{p}, typically much smaller than the full
+@math{n}-by-@math{p} Jacobian, and can usually be stored in memory even if the full
+Jacobian matrix cannot. This option is useful for large, dense systems, or if the
+iterative method has difficulty converging.
+
+@node Nonlinear Least-Squares TRS Levenberg-Marquardt
+@subsection Levenberg-Marquardt
+@cindex Levenberg-Marquardt algorithm
+@cindex nonlinear least squares, levenberg-marquardt
+
+There is a theorem which states that if @math{\delta_k} is a solution
+to the trust region subproblem given above, then there exists
+@math{\mu_k \ge 0} such that
+@tex
+\beforedisplay
+$$
+\left( B_k + \mu_k D_k^T D_k \right) \delta_k = -g_k
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+( B_k + \mu_k D_k^T D_k ) \delta_k = -g_k
+@end example
+
+@end ifinfo
+with @math{\mu_k (\Delta_k - ||D_k \delta_k||) = 0}. This
+forms the basis of the Levenberg-Marquardt algorithm, which controls
+the trust region size by adjusting the parameter @math{\mu_k}
+rather than the radius @math{\Delta_k} directly. For each radius
+@math{\Delta_k}, there is a unique parameter @math{\mu_k} which
+solves the TRS, and they have an inverse relationship, so that large values of
+@math{\mu_k} correspond to smaller trust regions, while small
+values of @math{\mu_k} correspond to larger trust regions.
+
+@noindent
+With the approximation @math{B_k \approx J_k^T J_k}, on each iteration,
+in order to calculate the step @math{\delta_k},
+the following linear least squares problem is solved:
+@tex
+\beforedisplay
+$$
+\left[
+\matrix{
+J_k \cr
+\sqrt{\mu_k} D_k
+}
+\right]
+\delta_k =
+-
+\left[
+\matrix{
+f_k \cr
+0
+}
+\right]
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+[J_k; sqrt(mu_k) D_k] \delta_k = - [f_k; 0]
+@end example
+
+@end ifinfo
+@noindent
+If the step @math{\delta_k} is accepted, then
+@math{\mu_k} is decreased on the next iteration in order
+to take a larger step, otherwise it is increased to take
+a smaller step. The Levenberg-Marquardt algorithm provides
+an exact solution of the trust region subproblem, but
+typically has a higher computational cost per iteration
+than the approximate methods discussed below, since it
+may need to solve the least squares system above several
+times for different values of @math{\mu_k}.
+
+@node Nonlinear Least-Squares TRS Levenberg-Marquardt with Geodesic Acceleration
+@subsection Levenberg-Marquardt with Geodesic Acceleration
+@cindex Levenberg-Marquardt algorithm, geodesic acceleration
+@cindex nonlinear least squares, levenberg-marquardt, geodesic acceleration
+
+This method applies a so-called geodesic acceleration correction to
+the standard Levenberg-Marquardt step @math{\delta_k} (Transtrum et al, 2011).
+By interpreting @math{\delta_k} as a first order step along a geodesic in the
+model parameter space (ie: a velocity @math{\delta_k = v_k}), the geodesic
+acceleration @math{a_k} is a second order correction along the
+geodesic which is determined by solving the linear least squares system
+@tex
+\beforedisplay
+$$
+\left[
+\matrix{
+J_k \cr
+\sqrt{\mu_k} D_k
+}
+\right]
+a_k =
+-
+\left[
+\matrix{
+f_{vv}(x_k) \cr
+0
+}
+\right]
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+[J_k; sqrt(mu_k) D_k] a_k = - [f_vv(x_k); 0]
+@end example
+
+@end ifinfo
+@noindent
+where @math{f_{vv}} is the second directional derivative of
+the residual vector in the velocity direction @math{v},
+@math{f_{vv}(x) = D_v^2 f = \sum_{\alpha\beta} v_{\alpha} v_{\beta} \partial_{\alpha} \partial_{\beta} f(x)},
+where @math{\alpha} and @math{\beta} are summed over the @math{p}
+parameters. The new total step is then @math{\delta_k' = v_k + {1 \over 2}a_k}.
+The second order correction @math{a_k} can be calculated with a modest additional
+cost, and has been shown to dramatically reduce the number of iterations
+(and expensive Jacobian evaluations) required to reach convergence on a variety
+of different problems. In order to utilize the geodesic acceleration, the user must supply a
+function which provides the second directional derivative vector
+@math{f_{vv}(x)}, or alternatively the library can use a finite
+difference method to estimate this vector with one additional function
+evaluation of @math{f(x + h v)} where @math{h} is a tunable step size
+(see the @code{h_fvv} parameter description).
+
+@node Nonlinear Least-Squares TRS Dogleg
+@subsection Dogleg
+@cindex Dogleg algorithm
+@cindex nonlinear least squares, dogleg
+
+This is Powell's dogleg method, which finds an approximate
+solution to the trust region subproblem, by restricting
+its search to a piecewise linear ``dogleg'' path,
+composed of the origin, the Cauchy point which represents
+the model minimizer along the steepest descent direction,
+and the Gauss-Newton point, which is the overall minimizer
+of the unconstrained model. The Gauss-Newton step is calculated by
+solving
+@tex
+\beforedisplay
+$$
+J_k \delta_{gn} = -f_k
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+J_k \delta_gn = -f_k
+@end example
+
+@end ifinfo
+which is the main computational task for each iteration,
+but only needs to be performed once per iteration. If
+the Gauss-Newton point is inside the trust region, it is
+selected as the step. If it is outside, the method then
+calculates the Cauchy point, which is located along the
+gradient direction. If the Cauchy point is also outside
+the trust region, the method assumes that it is still far
+from the minimum and so proceeds along the gradient
+direction, truncating the step at the trust region
+boundary. If the Cauchy point is inside the trust region,
+with the Gauss-Newton point outside, the method
+uses a dogleg step, which is a linear combination of the
+gradient direction and the Gauss-Newton direction, stopping at the trust
+region boundary.
+
+@node Nonlinear Least-Squares TRS Double Dogleg
+@subsection Double Dogleg
+@cindex double Dogleg algorithm
+@cindex Dogleg algorithm, double
+@cindex nonlinear least squares, double dogleg
+
+This method is an improvement over the classical dogleg
+algorithm, which attempts to include information about
+the Gauss-Newton step while the iteration is still far from
+the minimum. When the Cauchy point is inside the trust region
+and the Gauss-Newton point is outside, the method computes
+a scaled Gauss-Newton point and then takes a dogleg step
+between the Cauchy point and the scaled Gauss-Newton point.
+The scaling is calculated to ensure that the reduction
+in the model @math{m_k} is about the same as the reduction
+provided by the Cauchy point.
+
+@node Nonlinear Least-Squares TRS 2D Subspace
+@subsection Two Dimensional Subspace
+
+The dogleg methods restrict the search for the TRS solution
+to a 1D curve defined by the Cauchy and Gauss-Newton points.
+An improvement to this is to search for a solution using
+the full two dimensional subspace spanned by the Cauchy
+and Gauss-Newton directions. The dogleg path is of course
+inside this subspace, and so this method solves the TRS
+at least as accurately as the dogleg methods. Since this
+method searches a larger subspace for a solution, it can
+converge more quickly than dogleg on some problems. Because
+the subspace is only two dimensional, this method is
+very efficient and the main computation per iteration is
+to determine the Gauss-Newton point.
+
+@node Nonlinear Least-Squares TRS Steihaug-Toint Conjugate Gradient
+@subsection Steihaug-Toint Conjugate Gradient
+
+One difficulty of the dogleg methods is calculating the
+Gauss-Newton step when the Jacobian matrix is singular. The
+Steihaug-Toint method also computes a generalized dogleg
+step, but avoids solving for the Gauss-Newton step directly,
+instead using an iterative conjugate gradient algorithm. This
+method performs well at points where the Jacobian is singular,
+and is also suitable for large-scale problems where factoring
+the Jacobian matrix could be prohibitively expensive.
+
+@node Nonlinear Least-Squares Weighted Overview
+@section Weighted Nonlinear Least-Squares
+
+Weighted nonlinear least-squares fitting minimizes the function
+@tex
+\beforedisplay
+$$
+\Phi(x)  = {1 \over 2} || f ||_W^2
+         = {1 \over 2} \sum_{i=1}^{n} w_i f_i (x_1, \dots, x_p)^2
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+\Phi(x) = (1/2) || f(x) ||_W^2
+        = (1/2) \sum_@{i=1@}^@{n@} f_i(x_1, ..., x_p)^2 
+@end example
+
+@end ifinfo
+where @math{W = diag(w_1,w_2,...,w_n)} is the weighting matrix,
+and @math{||f||_W^2 = f^T W f}.
+The weights @math{w_i} are commonly defined as @math{w_i = 1/\sigma_i^2},
+where @math{\sigma_i} is the error in the @math{i}th measurement.
+A simple change of variables @math{\tilde{f} = W^{1 \over 2} f} yields
+@math{\Phi(x) = {1 \over 2} ||\tilde{f}||^2}, which is in the
+same form as the unweighted case. The user can either perform this
+transform directly on their function residuals and Jacobian, or use
+the @code{gsl_multifit_nlinear_winit} interface which automatically
+performs the correct scaling. To manually perform this transformation,
+the residuals and Jacobian should be modified according to
+@tex
+\beforedisplay
+$$
+\eqalign{
+\tilde{f}_i & = \sqrt{w_i} f_i = {f_i \over \sigma_i} \cr
+\tilde{J}_{ij} & = \sqrt{w_i} { \partial f_i \over \partial x_j } = { 1 \over \sigma_i} { \partial f_i \over \partial x_j }
+}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+f~_i = f_i / \sigma_i
+J~_ij = 1 / \sigma_i df_i/dx_j
+@end example
+
+@end ifinfo
+
+@noindent
+For large systems, the user must perform their own weighting.
+
+@node Nonlinear Least-Squares Tunable Parameters
+@section Tunable Parameters
+
+@noindent
+The user can tune nearly all aspects of the iteration at allocation
+time. For the @code{gsl_multifit_nlinear} interface, the user may
+modify the @code{gsl_multifit_nlinear_parameters} structure, which is
+defined as follows:
+
+@example
+typedef struct
+@{
+  const gsl_multifit_nlinear_trs *trs;        /* trust region subproblem method */
+  const gsl_multifit_nlinear_scale *scale;    /* scaling method */
+  const gsl_multifit_nlinear_solver *solver;  /* solver method */
+  gsl_multifit_nlinear_fdtype fdtype;         /* finite difference method */
+  double factor_up;                           /* factor for increasing trust radius */
+  double factor_down;                         /* factor for decreasing trust radius */
+  double avmax;                               /* max allowed |a|/|v| */
+  double h_df;                                /* step size for finite difference Jacobian */
+  double h_fvv;                               /* step size for finite difference fvv */
+@} gsl_multifit_nlinear_parameters;
+@end example
+
+@noindent
+For the @code{gsl_multilarge_nlinear} interface, the user may
+modify the @code{gsl_multilarge_nlinear_parameters} structure, which is
+defined as follows:
+
+@example
+typedef struct
+@{
+  const gsl_multilarge_nlinear_trs *trs;       /* trust region subproblem method */
+  const gsl_multilarge_nlinear_scale *scale;   /* scaling method */
+  const gsl_multilarge_nlinear_solver *solver; /* solver method */
+  gsl_multilarge_nlinear_fdtype fdtype;        /* finite difference method */
+  double factor_up;                            /* factor for increasing trust radius */
+  double factor_down;                          /* factor for decreasing trust radius */
+  double avmax;                                /* max allowed |a|/|v| */
+  double h_df;                                 /* step size for finite difference Jacobian */
+  double h_fvv;                                /* step size for finite difference fvv */
+  size_t max_iter;                             /* maximum iterations for trs method */
+  double tol;                                  /* tolerance for solving trs */
+@} gsl_multilarge_nlinear_parameters;
+@end example
+
+@noindent
+Each of these parameters is discussed in further detail below.
+
+@deftypevr {Parameter} {const gsl_multifit_nlinear_trs *} trs
+@deftypevrx {Parameter} {const gsl_multilarge_nlinear_trs *} trs
+
+This parameter determines the method used to solve the trust region
+subproblem, and may be selected from the following choices,
+
+@defvr {Default} gsl_multifit_nlinear_trs_lm
+@defvrx {Default} gsl_multilarge_nlinear_trs_lm
+This selects the Levenberg-Marquardt algorithm.
+@end defvr
+
+@defvr {Option} gsl_multifit_nlinear_trs_lmaccel
+@defvrx {Option} gsl_multilarge_nlinear_trs_lmaccel
+This selects the Levenberg-Marquardt algorithm with geodesic
+acceleration.
+@end defvr
+
+@defvr {Option} gsl_multifit_nlinear_trs_dogleg
+@defvrx {Option} gsl_multilarge_nlinear_trs_dogleg
+This selects the dogleg algorithm.
+@end defvr
+
+@defvr {Option} gsl_multifit_nlinear_trs_ddogleg
+@defvrx {Option} gsl_multilarge_nlinear_trs_ddogleg
+This selects the double dogleg algorithm.
+@end defvr
+
+@defvr {Option} gsl_multifit_nlinear_trs_subspace2D
+@defvrx {Option} gsl_multilarge_nlinear_trs_subspace2D
+This selects the 2D subspace algorithm.
+@end defvr
+
+@defvr {Option} gsl_multilarge_nlinear_trs_cgst
+This selects the Steihaug-Toint conjugate gradient algorithm. This
+method is available only for large systems.
+@end defvr
+
+@end deftypevr
+
+@deftypevr {Parameter} {const gsl_multifit_nlinear_scale *} scale
+@deftypevrx {Parameter} {const gsl_multilarge_nlinear_scale *} scale
+
+This parameter determines the diagonal scaling matrix @math{D} and
+may be selected from the following choices,
+
+@defvr {Default} gsl_multifit_nlinear_scale_more
+@defvrx {Default} gsl_multilarge_nlinear_scale_more
+This damping strategy was suggested by Mor@'e, and
+corresponds to @math{D^T D = } max(diag(@math{J^T J})),
+in other words the maximum elements of
+diag(@math{J^T J}) encountered thus far in the iteration.
+This choice of @math{D} makes the problem scale-invariant,
+so that if the model parameters @math{x_i} are each scaled
+by an arbitrary constant, @math{\tilde{x}_i = a_i x_i}, then
+the sequence of iterates produced by the algorithm would
+be unchanged. This method can work very well in cases
+where the model parameters have widely different scales
+(ie: if some parameters are measured in nanometers, while others
+are measured in degrees Kelvin). This strategy has been proven
+effective on a large class of problems and so it is the library
+default, but it may not be the best choice for all problems.
+@end defvr
+
+@defvr {Option} gsl_multifit_nlinear_scale_levenberg
+@defvrx {Option} gsl_multilarge_nlinear_scale_levenberg
+This damping strategy was originally suggested by Levenberg, and
+corresponds to @math{D^T D = I}. This method has also proven
+effective on a large class of problems, but is not scale-invariant.
+However, some authors (e.g. Transtrum and Sethna 2012) argue
+that this choice is better for problems which are susceptible
+to parameter evaporation (ie: parameters go to infinity)
+@end defvr
+
+@defvr {Option} gsl_multifit_nlinear_scale_marquardt
+@defvrx {Option} gsl_multilarge_nlinear_scale_marquardt
+This damping strategy was suggested by Marquardt, and
+corresponds to @math{D^T D = } diag(@math{J^T J}). This
+method is scale-invariant, but it is generally considered
+inferior to both the Levenberg and Mor@'e strategies, though
+may work well on certain classes of problems.
+@end defvr
+
+@end deftypevr
+
+@deftypevr {Parameter} {const gsl_multifit_nlinear_solver *} solver
+@deftypevrx {Parameter} {const gsl_multilarge_nlinear_solver *} solver
+
+@noindent
+Solving the trust region subproblem on each iteration almost always
+requires the solution of the following linear least squares system
+@tex
+\beforedisplay
+$$
+\left[
+\matrix{
+J \cr
+\sqrt{\mu} D
+}
+\right]
+\delta =
+-
+\left[
+\matrix{
+f \cr
+0
+}
+\right]
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+[J; sqrt(mu) D] \delta = - [f; 0]
+@end example
+
+@end ifinfo
+
+The @var{solver} parameter determines how the system is
+solved and can be selected from the following choices:
+
+@defvr {Default} gsl_multifit_nlinear_solver_qr
+This method solves the system using a rank revealing QR
+decomposition of the Jacobian @math{J}. This method will
+produce reliable solutions in cases where the Jacobian
+is rank deficient or near-singular but does require about
+twice as many operations as the Cholesky method discussed
+below.
+@end defvr
+
+@defvr {Option} gsl_multifit_nlinear_solver_cholesky
+@defvrx {Default} gsl_multilarge_nlinear_solver_cholesky
+This method solves the alternate normal equations problem
+@tex
+\beforedisplay
+$$
+\left( J^T J + \mu D^T D \right) \delta = -J^T f
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+( J^T J + \mu D^T D ) \delta = -J^T f
+@end example
+
+@end ifinfo
+
+by using a Cholesky decomposition of the matrix
+@math{J^T J + \mu D^T D}. This method is faster than the
+QR approach, however it is susceptible to numerical instabilities
+if the Jacobian matrix is rank deficient or near-singular. In
+these cases, an attempt is made to reduce the condition number
+of the matrix using Jacobi preconditioning, but for highly
+ill-conditioned problems the QR approach is better. If it is
+known that the Jacobian matrix is well conditioned, this method
+is accurate and will perform faster than the QR approach.
+@end defvr
+
+@defvr {Option} gsl_multifit_nlinear_solver_svd
+This method solves the system using a singular value
+decomposition of the Jacobian @math{J}. This method will
+produce the most reliable solutions for ill-conditioned Jacobians
+but is also the slowest solver method.
+@end defvr
+
+@end deftypevr
+
+@deftypevr {Parameter} {gsl_multifit_nlinear_fdtype} fdtype
+
+This parameter specifies whether to use forward or centered
+differences when approximating the Jacobian. This is only
+used when an analytic Jacobian is not provided to the solver.
+This parameter may be set to one of the following choices.
+
+@defvr {Default} GSL_MULTIFIT_NLINEAR_FWDIFF
+This specifies a forward finite difference to approximate
+the Jacobian matrix. The Jacobian matrix will be calculated as
+@tex
+\beforedisplay
+$$
+J_{ij} = {1 \over \Delta_j} \left( f_i(x + \Delta_j e_j) - f_i(x) \right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+J_ij = 1 / \Delta_j ( f_i(x + \Delta_j e_j) - f_i(x) )
+@end example
+
+@end ifinfo
+where @math{\Delta_j = h |x_j|} and @math{e_j} is the standard
+@math{j}th Cartesian unit basis vector so that
+@math{x + \Delta_j e_j} represents a small (forward) perturbation of
+the @math{j}th parameter by an amount @math{\Delta_j}. The perturbation
+@math{\Delta_j} is proportional to the current value @math{|x_j|} which
+helps to calculate an accurate Jacobian when the various parameters have
+different scale sizes. The value of @math{h} is specified by the @code{h_df}
+parameter. The accuracy of this method is @math{O(h)}, and evaluating this
+matrix requires an additional @math{p} function evaluations.
+@end defvr
+
+@defvr {Option} GSL_MULTIFIT_NLINEAR_CTRDIFF
+This specifies a centered finite difference to approximate
+the Jacobian matrix. The Jacobian matrix will be calculated as
+@tex
+\beforedisplay
+$$
+J_{ij} = {1 \over \Delta_j} \left( f_i(x + {1 \over 2} \Delta_j e_j) - f_i(x - {1 \over 2} \Delta_j e_j) \right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+J_ij = 1 / \Delta_j ( f_i(x + 1/2 \Delta_j e_j) - f_i(x - 1/2 \Delta_j e_j) )
+@end example
+
+@end ifinfo
+See above for a description of @math{\Delta_j}. The accuracy of this
+method is @math{O(h^2)}, but evaluating this
+matrix requires an additional @math{2p} function evaluations.
+@end defvr
+
+@end deftypevr
+
+@deftypevr {Parameter} {double} factor_up
+
+When a step is accepted, the trust region radius will be increased
+by this factor. The default value is @math{3}.
+
+@end deftypevr
+
+@deftypevr {Parameter} {double} factor_down
+
+When a step is rejected, the trust region radius will be decreased
+by this factor. The default value is @math{2}.
+
+@end deftypevr
+
+@deftypevr {Parameter} {double} avmax
+
+When using geodesic acceleration to solve a nonlinear least squares problem,
+an important parameter to monitor is the ratio of the acceleration term
+to the velocity term,
+@tex
+\beforedisplay
+$$
+{ ||a|| \over ||v|| }
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+|a| / |v|
+@end example
+
+@end ifinfo
+
+If this ratio is small, it means the acceleration correction
+is contributing very little to the step. This could be because
+the problem is not ``nonlinear'' enough to benefit from
+the acceleration. If the ratio is large (@math{> 1}) it
+means that the acceleration is larger than the velocity,
+which shouldn't happen since the step represents a truncated
+series and so the second order term @math{a} should be smaller than
+the first order term @math{v} to guarantee convergence.
+Therefore any steps with a ratio larger than the parameter
+@var{avmax} are rejected. @var{avmax} is set to 0.75 by default.
+For problems which experience difficulty converging, this threshold
+could be lowered.
+
+@end deftypevr
+
+@deftypevr {Parameter} {double} h_df
+
+This parameter specifies the step size for approximating the
+Jacobian matrix with finite differences. It is set to
+@math{\sqrt{\epsilon}} by default, where @math{\epsilon}
+is @code{GSL_DBL_EPSILON}.
+
+@end deftypevr
+
+@deftypevr {Parameter} {double} h_fvv
+
+When using geodesic acceleration, the user must either supply
+a function to calculate @math{f_{vv}(x)} or the library
+can estimate this second directional derivative using a finite
+difference method. When using finite differences, the library
+must calculate @math{f(x + h v)} where @math{h} represents
+a small step in the velocity direction. The parameter
+@var{h_fvv} defines this step size and is set to 0.02 by
+default.
+
+@end deftypevr
+
+@node Nonlinear Least-Squares Initialization
+@section Initializing the Solver
+
+@deftypefun {gsl_multifit_nlinear_workspace *} gsl_multifit_nlinear_alloc (const gsl_multifit_nlinear_type * @var{T}, const gsl_multifit_nlinear_parameters * @var{params}, const size_t @var{n}, const size_t @var{p})
+@deftypefunx {gsl_multilarge_nlinear_workspace *} gsl_multilarge_nlinear_alloc (const gsl_multilarge_nlinear_type * @var{T}, const gsl_multilarge_nlinear_parameters * @var{params}, const size_t @var{n}, const size_t @var{p})
+@tindex gsl_multifit_nlinear_alloc
+@tindex gsl_multifit_nlinear_type
+These functions return a pointer to a newly allocated instance of a
+derivative solver of type @var{T} for @var{n} observations and @var{p}
+parameters. The @var{params} input specifies a tunable set of
+parameters which will affect important details in each iteration
+of the trust region subproblem algorithm. It is recommended to start
+with the suggested default parameters (see
+@code{gsl_multifit_nlinear_default_parameters} and
+@code{gsl_multilarge_nlinear_default_parameters}) and then tune
+the parameters once the code is working correctly. See
+@ref{Nonlinear Least-Squares Tunable Parameters}
+for descriptions of the various parameters.
+For example, the following code creates an instance of a
+Levenberg-Marquardt solver for 100 data points and 3 parameters,
+using suggested defaults:
+
+@example
+const gsl_multifit_nlinear_type * T 
+    = gsl_multifit_nlinear_lm;
+gsl_multifit_nlinear_parameters params
+    = gsl_multifit_nlinear_default_parameters();
+gsl_multifit_nlinear_workspace * w 
+    = gsl_multifit_nlinear_alloc (T, &params, 100, 3);
+@end example
+
+@noindent
+The number of observations @var{n} must be greater than or equal to
+parameters @var{p}.
+
+If there is insufficient memory to create the solver then the function
+returns a null pointer and the error handler is invoked with an error
+code of @code{GSL_ENOMEM}.
+@end deftypefun
+
+@deftypefun gsl_multifit_nlinear_parameters gsl_multifit_nlinear_default_parameters (void)
+@deftypefunx gsl_multilarge_nlinear_parameters gsl_multilarge_nlinear_default_parameters (void)
+These functions return a set of recommended default parameters
+for use in solving nonlinear least squares problems. The user
+can tune each parameter to improve the performance on their
+particular problem, see
+@ref{Nonlinear Least-Squares Tunable Parameters}.
+@end deftypefun
+
+@deftypefun int gsl_multifit_nlinear_init (const gsl_vector * @var{x}, gsl_multifit_nlinear_fdf * @var{fdf}, gsl_multifit_nlinear_workspace * @var{w})
+@deftypefunx int gsl_multifit_nlinear_winit (const gsl_vector * @var{x}, const gsl_vector * @var{wts}, gsl_multifit_nlinear_fdf * @var{fdf}, gsl_multifit_nlinear_workspace * @var{w})
+@deftypefunx int gsl_multilarge_nlinear_init (const gsl_vector * @var{x}, gsl_multilarge_nlinear_fdf * @var{fdf}, gsl_multilarge_nlinear_workspace * @var{w})
+@deftypefunx int gsl_multilarge_nlinear_winit (const gsl_vector * @var{x}, const gsl_vector * @var{wts}, gsl_multilarge_nlinear_fdf * @var{fdf}, gsl_multilarge_nlinear_workspace * @var{w})
+These functions initialize, or reinitialize, an existing workspace @var{w}
+to use the system @var{fdf} and the initial guess
+@var{x}. See @ref{Nonlinear Least-Squares Function Definition}
+for a description of the @var{fdf} structure.
+
+Optionally, a weight vector @var{wts} can be given to perform
+a weighted nonlinear regression. Here, the weighting matrix is
+@math{W = diag(w_1,w_2,...,w_n)}.
+@end deftypefun
+
+@deftypefun void gsl_multifit_nlinear_free (gsl_multifit_nlinear_workspace * @var{w})
+@deftypefunx void gsl_multilarge_nlinear_free (gsl_multilarge_nlinear_workspace * @var{w})
+These functions free all the memory associated with the workspace @var{w}.
+@end deftypefun
+
+@deftypefun {const char *} gsl_multifit_nlinear_name (const gsl_multifit_nlinear_workspace * @var{w})
+@deftypefunx {const char *} gsl_multilarge_nlinear_name (const gsl_multilarge_nlinear_workspace * @var{w})
+These functions return a pointer to the name of the solver.  For example,
+
+@example
+printf ("w is a '%s' solver\n", 
+        gsl_multifit_nlinear_name (w));
+@end example
+
+@noindent
+would print something like @code{w is a 'trust-region' solver}.
+@end deftypefun
+
+@deftypefun {const char *} gsl_multifit_nlinear_trs_name (const gsl_multifit_nlinear_workspace * @var{w})
+@deftypefunx {const char *} gsl_multilarge_nlinear_trs_name (const gsl_multilarge_nlinear_workspace * @var{w})
+These functions return a pointer to the name of the trust region subproblem
+method.  For example,
+
+@example
+printf ("w is a '%s' solver\n", 
+        gsl_multifit_nlinear_trs_name (w));
+@end example
+
+@noindent
+would print something like @code{w is a 'levenberg-marquardt' solver}.
+@end deftypefun
+
+@node Nonlinear Least-Squares Function Definition
+@section Providing the Function to be Minimized
+
+The user must provide @math{n} functions of @math{p} variables for the
+minimization algorithm to operate on.  In order to allow for
+arbitrary parameters the functions are defined by the following data
+types:
+
+@deftp {Data Type} gsl_multifit_nlinear_fdf
+This data type defines a general system of functions with arbitrary parameters,
+the corresponding Jacobian matrix of derivatives, and optionally the
+second directional derivative of the functions for geodesic acceleration.
+
+@table @code
+@item int (* f) (const gsl_vector * @var{x}, void * @var{params}, gsl_vector * @var{f})
+This function should store the @math{n} components of the vector
+@c{$f(x)$}
+@math{f(x)} in @var{f} for argument @var{x} and arbitrary parameters @var{params},
+returning an appropriate error code if the function cannot be computed.
+
+@item int (* df) (const gsl_vector * @var{x}, void * @var{params}, gsl_matrix * @var{J})
+This function should store the @var{n}-by-@var{p} matrix result
+@c{$J_{ij} = \partial f_i(x) / \partial x_j$}
+@math{J_ij = d f_i(x) / d x_j} in @var{J} for argument @var{x} 
+and arbitrary parameters @var{params}, returning an appropriate error code if the
+matrix cannot be computed. If an analytic Jacobian is unavailable, or too expensive
+to compute, this function pointer may be set to NULL, in which
+case the Jacobian will be internally computed using finite difference approximations
+of the function @var{f}.
+
+@item int (* fvv) (const gsl_vector * @var{x}, const gsl_vector * @var{v}, void * @var{params}, gsl_vector * @var{fvv})
+When geodesic acceleration is enabled, this function should store the
+@math{n} components of the vector
+@math{f_{vv}(x) = \sum_{\alpha\beta} v_{\alpha} v_{\beta} {\partial \over \partial x_{\alpha}} {\partial \over \partial x_{\beta}} f(x)},
+representing second directional derivatives of the function to be minimized,
+into the output @var{fvv}. The parameter vector is provided in @var{x} and
+the velocity vector is provided in @var{v}, both of which have @math{p}
+components. The arbitrary parameters are given in @var{params}. If
+analytic expressions for @math{f_{vv}(x)} are unavailable or too difficult
+to compute, this function pointer may be set to NULL, in which case
+@math{f_{vv}(x)} will be computed internally using a finite difference
+approximation.
+
+@item size_t n
+the number of functions, i.e. the number of components of the
+vector @var{f}.
+
+@item size_t p
+the number of independent variables, i.e. the number of components of
+the vector @var{x}.
+
+@item void * params
+a pointer to the arbitrary parameters of the function.
+
+@item size_t nevalf
+This does not need to be set by the user. It counts the number of
+function evaluations and is initialized by the @code{_init} function.
+
+@item size_t nevaldf
+This does not need to be set by the user. It counts the number of
+Jacobian evaluations and is initialized by the @code{_init} function.
+
+@item size_t nevalfvv
+This does not need to be set by the user. It counts the number of
+@math{f_{vv}(x)} evaluations and is initialized by the @code{_init} function.
+@end table
+@end deftp
+
+@deftp {Data Type} gsl_multilarge_nlinear_fdf
+This data type defines a general system of functions with arbitrary parameters,
+a function to compute @math{J u} or @math{J^T u} for a given vector @math{u},
+the normal equations matrix @math{J^T J},
+and optionally the second directional derivative of the functions for geodesic acceleration.
+
+@table @code
+@item int (* f) (const gsl_vector * @var{x}, void * @var{params}, gsl_vector * @var{f})
+This function should store the @math{n} components of the vector
+@c{$f(x)$}
+@math{f(x)} in @var{f} for argument @var{x} and arbitrary parameters @var{params},
+returning an appropriate error code if the function cannot be computed.
+
+@item int (* df) (CBLAS_TRANSPOSE_t @var{TransJ}, const gsl_vector * @var{x}, const gsl_vector * @var{u}, void * @var{params}, gsl_vector * @var{v}, gsl_matrix * @var{JTJ})
+If @var{TransJ} is equal to @code{CblasNoTrans}, then this function should
+compute the matrix-vector product @math{J u} and store the result in @var{v}.
+If @var{TransJ} is equal to @code{CblasTrans}, then this function should
+compute the matrix-vector product @math{J^T u} and store the result in @var{v}.
+Additionally, the normal equations matrix @math{J^T J} should be stored in the
+lower half of @var{JTJ}. The input matrix @var{JTJ} could be set to NULL,
+for example by iterative methods which do not require this matrix, so the user
+should check for this prior to constructing the matrix.
+The input @var{params} contains the arbitrary parameters.
+
+@item int (* fvv) (const gsl_vector * @var{x}, const gsl_vector * @var{v}, void * @var{params}, gsl_vector * @var{fvv})
+When geodesic acceleration is enabled, this function should store the
+@math{n} components of the vector
+@math{f_{vv}(x) = \sum_{\alpha\beta} v_{\alpha} v_{\beta} {\partial \over \partial x_{\alpha}} {\partial \over \partial x_{\beta}} f(x)},
+representing second directional derivatives of the function to be minimized,
+into the output @var{fvv}. The parameter vector is provided in @var{x} and
+the velocity vector is provided in @var{v}, both of which have @math{p}
+components. The arbitrary parameters are given in @var{params}. If
+analytic expressions for @math{f_{vv}(x)} are unavailable or too difficult
+to compute, this function pointer may be set to NULL, in which case
+@math{f_{vv}(x)} will be computed internally using a finite difference
+approximation.
+
+@item size_t n
+the number of functions, i.e. the number of components of the
+vector @var{f}.
+
+@item size_t p
+the number of independent variables, i.e. the number of components of
+the vector @var{x}.
+
+@item void * params
+a pointer to the arbitrary parameters of the function.
+
+@item size_t nevalf
+This does not need to be set by the user. It counts the number of
+function evaluations and is initialized by the @code{_init} function.
+
+@item size_t nevaldfu
+This does not need to be set by the user. It counts the number of
+Jacobian matrix-vector evaluations (@math{J u} or @math{J^T u}) and
+is initialized by the @code{_init} function.
+
+@item size_t nevaldf2
+This does not need to be set by the user. It counts the number of
+@math{J^T J} evaluations and is initialized by the @code{_init} function.
+
+@item size_t nevalfvv
+This does not need to be set by the user. It counts the number of
+@math{f_{vv}(x)} evaluations and is initialized by the @code{_init} function.
+@end table
+@end deftp
+
+@noindent
+Note that when fitting a non-linear model against experimental data,
+the data is passed to the functions above using the
+@var{params} argument and the trial best-fit parameters through the
+@var{x} argument.
+
+@node Nonlinear Least-Squares Iteration
+@section Iteration
+
+The following functions drive the iteration of each algorithm.  Each
+function performs one iteration of the trust region method and updates
+the state of the solver.
+
+@deftypefun int gsl_multifit_nlinear_iterate (gsl_multifit_nlinear_workspace * @var{w})
+@deftypefunx int gsl_multilarge_nlinear_iterate (gsl_multilarge_nlinear_workspace * @var{w})
+These functions perform a single iteration of the solver @var{w}.  If
+the iteration encounters an unexpected problem then an error code will
+be returned.  The solver workspace maintains a current estimate of the
+best-fit parameters at all times.
+@end deftypefun
+
+@noindent
+The solver workspace @var{w} contains the following entries, which can
+be used to track the progress of the solution:
+
+@table @code
+@item gsl_vector * x
+The current position, length @math{p}.
+
+@item gsl_vector * f
+The function residual vector at the current position @math{f(x)}, length
+@math{n}.
+
+@item gsl_matrix * J
+The Jacobian matrix at the current position @math{J(x)}, size
+@math{n}-by-@math{p} (only for @code{gsl_multifit_nlinear} interface).
+
+@item gsl_vector * dx
+The difference between the current position and the previous position,
+i.e. the last step @math{\delta}, taken as a vector, length @math{p}.
+
+@end table
+
+@noindent
+These quantities can be accessed with the following functions,
+
+@deftypefun {gsl_vector *} gsl_multifit_nlinear_position (const gsl_multifit_nlinear_workspace * @var{w})
+@deftypefunx {gsl_vector *} gsl_multilarge_nlinear_position (const gsl_multilarge_nlinear_workspace * @var{w})
+These functions return the current position @math{x} (i.e. best-fit
+parameters) of the solver @var{w}.
+@end deftypefun
+
+@deftypefun {gsl_vector *} gsl_multifit_nlinear_residual (const gsl_multifit_nlinear_workspace * @var{w})
+@deftypefunx {gsl_vector *} gsl_multilarge_nlinear_residual (const gsl_multilarge_nlinear_workspace * @var{w})
+These functions return the current residual vector @math{f(x)} of the
+solver @var{w}.  For weighted systems, the residual vector includes the
+weighting factor @math{\sqrt{W}}.
+@end deftypefun
+
+@deftypefun {gsl_matrix *} gsl_multifit_nlinear_jac (const gsl_multifit_nlinear_workspace * @var{w})
+This function returns a pointer to the @math{n}-by-@math{p} Jacobian matrix for the
+current iteration of the solver @var{w}. This function is available only for the
+@code{gsl_multifit_nlinear} interface.
+@end deftypefun
+
+@deftypefun size_t gsl_multifit_nlinear_niter (const gsl_multifit_nlinear_workspace * @var{w})
+@deftypefunx size_t gsl_multilarge_nlinear_niter (const gsl_multilarge_nlinear_workspace * @var{w})
+These functions return the number of iterations performed so far.
+The iteration counter is updated on each call to the
+@code{_iterate} functions above, and reset to 0 in the
+@code{_init} functions.
+@end deftypefun
+
+@deftypefun int gsl_multifit_nlinear_rcond (double * @var{rcond}, const gsl_multifit_nlinear_workspace * @var{w})
+@deftypefunx int gsl_multilarge_nlinear_rcond (double * @var{rcond}, const gsl_multilarge_nlinear_workspace * @var{w})
+This function estimates the reciprocal condition number
+of the Jacobian matrix at the current position @math{x} and
+stores it in @var{rcond}. The computed value is only an estimate
+to give the user a guideline as to the conditioning of their particular
+problem. Its calculation is based on which factorization
+method is used (Cholesky, QR, or SVD). 
+
+@itemize @bullet
+
+@item For the Cholesky solver, the matrix @math{J^T J} is factored at each
+iteration. Therefore this function will estimate the 1-norm condition number
+@math{rcond^2 = 1/(||J^T J||_1 \cdot ||(J^T J)^{-1}||_1)}
+
+@item For the QR solver, @math{J} is factored as @math{J = Q R} at each
+iteration. For simplicity, this function calculates the 1-norm conditioning of
+only the @math{R} factor, @math{rcond = 1 / (||R||_1 \cdot ||R^{-1}||_1)}.
+This can be computed efficiently since @math{R} is upper triangular.
+
+@item For the SVD solver, in order to efficiently solve the trust region
+subproblem, the matrix which is factored is @math{J D^{-1}}, instead of
+@math{J} itself. The resulting singular values are used to provide
+the 2-norm reciprocal condition number, as @math{rcond = \sigma_{min} / \sigma_{max}}.
+Note that when using Mor@'e scaling, @math{D \ne I} and the resulting
+@var{rcond} estimate may be significantly different from the true
+@var{rcond} of @math{J} itself.
+
+@end itemize
+@end deftypefun
+
+@node Nonlinear Least-Squares Testing for Convergence
+@section Testing for Convergence
+@cindex nonlinear fitting, stopping parameters, convergence
+
+A minimization procedure should stop when one of the following conditions is
+true:
+
+@itemize @bullet
+@item
+A minimum has been found to within the user-specified precision.
+
+@item
+A user-specified maximum number of iterations has been reached.
+
+@item
+An error has occurred.
+@end itemize
+
+@noindent
+The handling of these conditions is under user control.  The functions
+below allow the user to test the current estimate of the best-fit
+parameters in several standard ways.
+
+@deftypefun int gsl_multifit_nlinear_test (const double @var{xtol}, const double @var{gtol}, const double @var{ftol}, int * @var{info}, const gsl_multifit_nlinear_workspace * @var{w})
+@deftypefunx int gsl_multilarge_nlinear_test (const double @var{xtol}, const double @var{gtol}, const double @var{ftol}, int * @var{info}, const gsl_multilarge_nlinear_workspace * @var{w})
+These functions test for convergence of the minimization method
+using the following criteria:
+
+@itemize @bullet
+@item
+Testing for a small step size relative to the current parameter vector
+@tex
+\beforedisplay
+$$
+|\delta_i| \le xtol (|x_i| + xtol)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+|\delta_i| <= xtol (|x_i| + xtol)
+@end example
+@end ifinfo
+for each @math{0 <= i < p}. Each element of the step vector @math{\delta}
+is tested individually in case the different parameters have widely
+different scales. Adding @var{xtol} to @math{|x_i|} helps the test avoid
+breaking down in situations where the true solution value @math{x_i = 0}.
+If this test succeeds, @var{info} is set to 1 and the function
+returns @code{GSL_SUCCESS}.
+
+A general guideline for selecting the step tolerance is to choose
+@math{xtol = 10^{-d}} where @math{d} is the number of accurate
+decimal digits desired in the solution @math{x}. See Dennis and
+Schnabel for more information.
+
+@item
+Testing for a small gradient (@math{g = \nabla \Phi(x) = J^T f})
+indicating a local function minimum:
+@tex
+\beforedisplay
+$$
+max_i |g_i \times max(x_i, 1)| \le gtol \times max(\Phi(x), 1)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+||g||_inf <= gtol
+@end example
+@end ifinfo
+This expression tests whether the ratio
+@math{(\nabla \Phi)_i x_i / \Phi} is small. Testing this scaled gradient
+is a better than @math{\nabla \Phi} alone since it is a dimensionless
+quantity and so independent of the scale of the problem. The
+@code{max} arguments help ensure the test doesn't break down in
+regions where @math{x_i} or @math{\Phi(x)} are close to 0.
+If this test succeeds, @var{info} is set to 2 and the function
+returns @code{GSL_SUCCESS}.
+
+A general guideline for choosing the gradient tolerance is to set
+@code{gtol = GSL_DBL_EPSILON^(1/3)}. See Dennis and Schnabel for
+more information.
+
+@end itemize
+
+If none of the tests succeed, @var{info} is set to 0 and the
+function returns @code{GSL_CONTINUE}, indicating further iterations
+are required.
+
+@end deftypefun
+
+@node Nonlinear Least-Squares High Level Driver
+@section High Level Driver
+
+These routines provide a high level wrapper that combines the iteration
+and convergence testing for easy use.
+
+@deftypefun int gsl_multifit_nlinear_driver (const size_t @var{maxiter}, const double @var{xtol}, const double @var{gtol}, const double @var{ftol}, void (* @var{callback})(const size_t @var{iter}, void * @var{params}, const gsl_multifit_linear_workspace * @var{w}), void * @var{callback_params}, int * @var{info}, gsl_multifit_nlinear_workspace * @var{w})
+@deftypefunx int gsl_multilarge_nlinear_driver (const size_t @var{maxiter}, const double @var{xtol}, const double @var{gtol}, const double @var{ftol}, void (* @var{callback})(const size_t @var{iter}, void * @var{params}, const gsl_multilarge_linear_workspace * @var{w}), void * @var{callback_params}, int * @var{info}, gsl_multilarge_nlinear_workspace * @var{w})
+These functions iterate the nonlinear least squares solver @var{w} for a
+maximum of @var{maxiter} iterations. After each iteration, the system is
+tested for convergence with the error tolerances @var{xtol}, @var{gtol} and @var{ftol}.
+Additionally, the user may supply a callback function @var{callback}
+which is called after each iteration, so that the user may save or print
+relevant quantities for each iteration. The parameter @var{callback_params}
+is passed to the @var{callback} function. The parameters @var{callback}
+and @var{callback_params} may be set to NULL to disable this feature.
+Upon successful convergence, the function returns @code{GSL_SUCCESS}
+and sets @var{info} to the reason for convergence (see
+@code{gsl_multifit_nlinear_test}). If the function has not
+converged after @var{maxiter} iterations, @code{GSL_EMAXITER} is
+returned. In rare cases, during an iteration the algorithm may
+be unable to find a new acceptable step @math{\delta} to take. In
+this case, @code{GSL_ENOPROG} is returned indicating no further
+progress can be made. If your problem is having difficulty converging,
+see @ref{Nonlinear Least-Squares Troubleshooting} for further guidance.
+@end deftypefun
+
+@node Nonlinear Least-Squares Covariance Matrix
+@section Covariance matrix of best fit parameters
+@cindex best-fit parameters, covariance
+@cindex least squares, covariance of best-fit parameters
+@cindex covariance matrix, nonlinear fits
+
+@deftypefun int gsl_multifit_nlinear_covar (const gsl_matrix * @var{J}, const double @var{epsrel}, gsl_matrix * @var{covar})
+@deftypefunx int gsl_multilarge_nlinear_covar (gsl_matrix * @var{covar}, gsl_multilarge_nlinear_workspace * @var{w})
+This function computes the covariance matrix of best-fit parameters
+using the Jacobian matrix @var{J} and stores it in @var{covar}.
+The parameter @var{epsrel} is used to remove linear-dependent columns
+when @var{J} is rank deficient.
+
+The covariance matrix is given by,
+@tex
+\beforedisplay
+$$
+C = (J^T J)^{-1}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+covar = (J^T J)^@{-1@}
+@end example
+
+@end ifinfo
+or in the weighted case,
+@tex
+\beforedisplay
+$$
+C = (J^T W J)^{-1}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+covar = (J^T W J)^@{-1@}
+@end example
+
+@end ifinfo
+@noindent
+and is computed using the factored form of the Jacobian (Cholesky, QR, or SVD).
+Any columns of @math{R} which satisfy 
+@tex
+\beforedisplay
+$$
+|R_{kk}| \leq epsrel |R_{11}|
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+|R_@{kk@}| <= epsrel |R_@{11@}|
+@end example
+
+@end ifinfo
+@noindent
+are considered linearly-dependent and are excluded from the covariance
+matrix (the corresponding rows and columns of the covariance matrix are
+set to zero).
+
+If the minimisation uses the weighted least-squares function
+@math{f_i = (Y(x, t_i) - y_i) / \sigma_i} then the covariance
+matrix above gives the statistical error on the best-fit parameters
+resulting from the Gaussian errors @math{\sigma_i} on 
+the underlying data @math{y_i}.  This can be verified from the relation 
+@math{\delta f = J \delta c} and the fact that the fluctuations in @math{f}
+from the data @math{y_i} are normalised by @math{\sigma_i} and 
+so satisfy @c{$\langle \delta f \delta f^T \rangle = I$}
+@math{<\delta f \delta f^T> = I}.
+
+For an unweighted least-squares function @math{f_i = (Y(x, t_i) -
+y_i)} the covariance matrix above should be multiplied by the variance
+of the residuals about the best-fit @math{\sigma^2 = \sum (y_i - Y(x,t_i))^2 / (n-p)}
+to give the variance-covariance
+matrix @math{\sigma^2 C}.  This estimates the statistical error on the
+best-fit parameters from the scatter of the underlying data.
+
+For more information about covariance matrices see @ref{Fitting Overview}.
+@end deftypefun
+
+@node Nonlinear Least-Squares Troubleshooting
+@section Troubleshooting
+
+When developing a code to solve a nonlinear least squares problem,
+here are a few considerations to keep in mind.
+
+@enumerate
+
+@item
+The most common difficulty is the accurate implementation of the Jacobian
+matrix. If the analytic Jacobian is not properly provided to the
+solver, this can hinder and many times prevent convergence of the method.
+When developing a new nonlinear least squares code, it often helps
+to compare the program output with the internally computed finite
+difference Jacobian and the user supplied analytic Jacobian. If there
+is a large difference in coefficients, it is likely the analytic
+Jacobian is incorrectly implemented.
+
+@item
+If your code is having difficulty converging, the next thing to
+check is the starting point provided to the solver. The methods
+of this chapter are local methods, meaning if you provide a starting
+point far away from the true minimum, the method may converge to
+a local minimum or not converge at all. Sometimes it is possible
+to solve a linearized approximation to the nonlinear problem,
+and use the linear solution as the starting point to the nonlinear
+problem.
+
+@item
+If the various parameters of the coefficient vector @math{x}
+vary widely in magnitude, then the problem is said to be badly scaled.
+The methods of this chapter do attempt to automatically rescale
+the elements of @math{x} to have roughly the same order of magnitude,
+but in extreme cases this could still cause problems for convergence.
+In these cases it is recommended for the user to scale their
+parameter vector @math{x} so that each parameter spans roughly the
+same range, say @math{[-1,1]}. The solution vector can be backscaled
+to recover the original units of the problem.
+
+@end enumerate
+
+@node Nonlinear Least-Squares Examples
+@section Examples
+
+The following example programs demonstrate the nonlinear least
+squares fitting capabilities.
+
+@menu
+* Nonlinear Least-Squares Exponential Fit Example::
+* Nonlinear Least-Squares Geodesic Acceleration Example::
+* Nonlinear Least-Squares Comparison Example::
+* Nonlinear Least-Squares Large Example::
+@end menu
+
+@node Nonlinear Least-Squares Exponential Fit Example
+@subsection Exponential Fitting Example
+
+The following example program fits a weighted exponential model with
+background to experimental data, @math{Y = A \exp(-\lambda t) + b}. The
+first part of the program sets up the functions @code{expb_f} and
+@code{expb_df} to calculate the model and its Jacobian.  The appropriate
+fitting function is given by,
+@tex
+\beforedisplay
+$$
+f_i = (A \exp(-\lambda t_i) + b) - y_i
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+f_i = (A \exp(-\lambda t_i) + b) - y_i
+@end example
+
+@end ifinfo
+@noindent
+where we have chosen @math{t_i = i}.  The Jacobian matrix @math{J} is
+the derivative of these functions with respect to the three parameters
+(@math{A}, @math{\lambda}, @math{b}).  It is given by,
+@tex
+\beforedisplay
+$$
+J_{ij} = {\partial f_i \over \partial x_j}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+J_@{ij@} = d f_i / d x_j
+@end example
+
+@end ifinfo
+@noindent
+where @math{x_0 = A}, @math{x_1 = \lambda} and @math{x_2 = b}.
+The @math{i}th row of the Jacobian is therefore
+@tex
+\beforedisplay
+$$
+J_{i\cdot} = \left(
+\matrix{
+\exp(-\lambda t_i) & -t_i A \exp(-\lambda t_i) & 1
+}
+\right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+@end example
+
+@end ifinfo
+
+@noindent
+The main part of the program sets up a Levenberg-Marquardt solver and
+some simulated random data. The data uses the known parameters
+(5.0,0.1,1.0) combined with Gaussian noise (standard deviation = 0.1)
+over a range of 40 timesteps. The initial guess for the parameters is
+chosen as (1.0, 1.0, 0.0). The iteration terminates when the relative
+change in x is smaller than @math{10^{-8}}, or when the magnitude of
+the gradient falls below @math{10^{-8}}. Here are the results of running
+the program:
+
+@smallexample
+iter  0: A = 1.0000, lambda = 1.0000, b = 0.0000, cond(J) =      inf, |f(x)| = 62.2029
+iter  1: A = 1.2196, lambda = 0.3663, b = 0.0436, cond(J) =  53.6368, |f(x)| = 59.8062
+iter  2: A = 1.6062, lambda = 0.1506, b = 0.1054, cond(J) =  23.8178, |f(x)| = 53.9039
+iter  3: A = 2.4528, lambda = 0.0583, b = 0.2470, cond(J) =  20.0493, |f(x)| = 28.8039
+iter  4: A = 2.9723, lambda = 0.0494, b = 0.3727, cond(J) =  94.5601, |f(x)| = 15.3252
+iter  5: A = 3.3473, lambda = 0.0477, b = 0.4410, cond(J) = 229.3627, |f(x)| = 10.7511
+iter  6: A = 3.6690, lambda = 0.0508, b = 0.4617, cond(J) = 298.3589, |f(x)| = 9.7373
+iter  7: A = 3.9907, lambda = 0.0580, b = 0.5433, cond(J) = 250.0194, |f(x)| = 8.7661
+iter  8: A = 4.2353, lambda = 0.0731, b = 0.7989, cond(J) = 154.8571, |f(x)| = 7.4299
+iter  9: A = 4.6573, lambda = 0.0958, b = 1.0302, cond(J) = 140.2265, |f(x)| = 6.1893
+iter 10: A = 5.0138, lambda = 0.1060, b = 1.0329, cond(J) = 109.4141, |f(x)| = 5.4961
+iter 11: A = 5.1505, lambda = 0.1103, b = 1.0497, cond(J) = 100.8762, |f(x)| = 5.4552
+iter 12: A = 5.1724, lambda = 0.1110, b = 1.0526, cond(J) =  97.3403, |f(x)| = 5.4542
+iter 13: A = 5.1737, lambda = 0.1110, b = 1.0528, cond(J) =  96.7136, |f(x)| = 5.4542
+iter 14: A = 5.1738, lambda = 0.1110, b = 1.0528, cond(J) =  96.6678, |f(x)| = 5.4542
+iter 15: A = 5.1738, lambda = 0.1110, b = 1.0528, cond(J) =  96.6663, |f(x)| = 5.4542
+iter 16: A = 5.1738, lambda = 0.1110, b = 1.0528, cond(J) =  96.6663, |f(x)| = 5.4542
+summary from method 'trust-region/levenberg-marquardt'
+number of iterations: 16
+function evaluations: 23
+Jacobian evaluations: 17
+reason for stopping: small step size
+initial |f(x)| = 62.202928
+final   |f(x)| = 5.454180
+chisq/dof = 0.804002
+A      = 5.17379 +/- 0.27938
+lambda = 0.11104 +/- 0.00817
+b      = 1.05283 +/- 0.05365
+status = success
+@end smallexample
+
+@noindent
+The approximate values of the parameters are found correctly, and the
+chi-squared value indicates a good fit (the chi-squared per degree of
+freedom is approximately 1).  In this case the errors on the parameters
+can be estimated from the square roots of the diagonal elements of the
+covariance matrix. If the chi-squared value shows a poor fit (i.e.
+@c{$\chi^2/(n-p) \gg 1$}
+@math{chi^2/dof >> 1}) then the error estimates obtained from the
+covariance matrix will be too small.  In the example program the error estimates
+are multiplied by @c{$\sqrt{\chi^2/(n-p)}$}
+@math{\sqrt@{\chi^2/dof@}} in this case, a common way of increasing the
+errors for a poor fit.  Note that a poor fit will result from the use
+of an inappropriate model, and the scaled error estimates may then
+be outside the range of validity for Gaussian errors.
+
+@noindent
+Additionally, we see that the condition number of @math{J(x)} stays
+reasonably small throughout the iteration. This indicates we could
+safely switch to the Cholesky solver for speed improvement,
+although this particular system is too small to really benefit.
+
+@iftex
+@sp 1
+@center @image{fit-exp,3.4in}
+@end iftex
+
+@example
+@verbatiminclude examples/nlfit.c
+@end example
+
+@node Nonlinear Least-Squares Geodesic Acceleration Example
+@subsection Geodesic Acceleration Example
+
+The following example program minimizes a modified Rosenbrock function,
+which is characterized by a narrow canyon with steep walls. The
+starting point is selected high on the canyon wall, so the solver
+must first find the canyon bottom and then navigate to the minimum.
+The problem is solved both with and without using geodesic acceleration
+for comparison. The cost function is given by
+@tex
+\beforedisplay
+$$
+\eqalign{
+\Phi(x) &= {1 \over 2} (f_1^2 + f_2^2) \cr
+f_1 &= 100 \left( x_2 - x_1^2 \right) \cr
+f_2 &= 1 - x_1
+}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+Phi(x) = 1/2 (f1^2 + f2^2)
+f1 = 100 ( x2 - x1^2 )
+f2 = 1 - x1
+@end example
+
+@end ifinfo
+@noindent
+The Jacobian matrix is given by
+@tex
+\beforedisplay
+$$
+J =
+\left(
+\matrix{
+{\partial f_1 \over \partial x_1} & {\partial f_1 \over \partial x_2} \cr
+{\partial f_2 \over \partial x_1} & {\partial f_2 \over \partial x_2}
+}
+\right) =
+\left(
+\matrix{
+-200 x_1 & 100 \cr
+-1 & 0
+}
+\right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+J = [ -200*x1 100 ; -1 0 ]
+@end example
+
+@end ifinfo
+@noindent
+In order to use geodesic acceleration, the user must provide
+the second directional derivative of each residual in the
+velocity direction,
+@math{D_v^2 f_i = \sum_{\alpha\beta} v_{\alpha} v_{\beta} \partial_{\alpha} \partial_{\beta} f_i}.
+The velocity vector @math{v} is provided by the solver. For this example,
+these derivatives are given by
+@tex
+\beforedisplay
+$$
+f_{vv} =
+D_v^2
+\left(
+\matrix{
+f_1 \cr
+f_2
+}
+\right) =
+\left(
+\matrix{
+-200 v_1^2 \cr
+0
+}
+\right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+fvv = [ -200 v1^2 ; 0 ]
+@end example
+
+@end ifinfo
+@noindent
+The solution of this minimization problem is given by
+@tex
+\beforedisplay
+$$
+\eqalign{
+x^{*} &= \left(
+\matrix{
+1 \cr
+1
+}
+\right) \cr
+\Phi(x^{*}) &= 0
+}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+x* = [ 1 ; 1 ]
+Phi(x*) = 0
+@end example
+
+@end ifinfo
+@noindent
+The program output is shown below.
+
+@smallexample
+=== Solving system without acceleration ===
+NITER         = 53
+NFEV          = 56
+NJEV          = 54
+NAEV          = 0
+initial cost  = 2.250225000000e+04
+final cost    = 6.674986031430e-18
+final x       = (9.999999974165e-01, 9.999999948328e-01)
+final cond(J) = 6.000096055094e+02
+=== Solving system with acceleration ===
+NITER         = 15
+NFEV          = 17
+NJEV          = 16
+NAEV          = 16
+initial cost  = 2.250225000000e+04
+final cost    = 7.518932873279e-19
+final x       = (9.999999991329e-01, 9.999999982657e-01)
+final cond(J) = 6.000097233278e+02
+@end smallexample
+
+@noindent
+We can see that enabling geodesic acceleration requires less
+than a third of the number of Jacobian evaluations in order to locate
+the minimum. The path taken by both methods is shown in the
+figure below. The contours show the cost function
+@math{\Phi(x_1,x_2)}. We see that both methods quickly
+find the canyon bottom, but the geodesic acceleration method
+navigates along the bottom to the solution with significantly
+fewer iterations.
+
+@iftex
+@sp 1
+@center @image{nlfit2,6in}
+@end iftex
+
+@noindent
+The program is given below.
+
+@example
+@verbatiminclude examples/nlfit2.c
+@end example
+
+@node Nonlinear Least-Squares Comparison Example
+@subsection Comparing TRS Methods Example
+
+The following program compares all available nonlinear least squares
+trust-region subproblem (TRS) methods on the Branin function, a common
+optimization test problem. The cost function is given by
+@tex
+\beforedisplay
+$$
+\eqalign{
+\Phi(x) &= {1 \over 2} (f_1^2 + f_2^2) \cr
+f_1 &= x_2 + a_1 x_1^2 + a_2 x_1 + a_3 \cr
+f_2 &= \sqrt{a_4} \sqrt{1 + (1 - a_5) \cos{x_1}}
+}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+\Phi(x) &= 1/2 (f_1^2 + f_2^2)
+f_1 &= x_2 + a_1 x_1^2 + a_2 x_1 + a_3
+f_2 &= sqrt(a_4) sqrt(1 + (1 - a_5) cos(x_1))
+@end example
+
+@end ifinfo
+with @math{a_1 = -{5.1 \over 4 \pi^2}, a_2 = {5 \over \pi}, a_3 = -6, a_4 = 10, a_5 = {1 \over 8\pi}}.
+There are three minima of this function in the range
+@math{(x_1,x_2) \in [-5,15] \times [-5,15]}. The program
+below uses the starting point @math{(x_1,x_2) = (6,14.5)}
+and calculates the solution with all available nonlinear
+least squares TRS methods. The program output is shown below.
+
+@smallformat
+@verbatim
+Method                    NITER  NFEV  NJEV  Initial Cost  Final cost   Final cond(J) Final x        
+levenberg-marquardt       20     27    21    1.9874e+02    3.9789e-01   6.1399e+07    (-3.14e+00, 1.23e+01)
+levenberg-marquardt+accel 27     36    28    1.9874e+02    3.9789e-01   1.4465e+07    (3.14e+00, 2.27e+00)
+dogleg                    23     64    23    1.9874e+02    3.9789e-01   5.0692e+08    (3.14e+00, 2.28e+00)
+double-dogleg             24     69    24    1.9874e+02    3.9789e-01   3.4879e+07    (3.14e+00, 2.27e+00)
+2D-subspace               23     54    24    1.9874e+02    3.9789e-01   2.5142e+07    (3.14e+00, 2.27e+00)
+@end verbatim
+@end smallformat
+
+@noindent
+The first row of output above corresponds to standard Levenberg-Marquardt, while
+the second row includes geodesic acceleration. We see that the standard LM method
+converges to the minimum at @math{(-\pi,12.275)} and also uses the least number
+of iterations and Jacobian evaluations. All other methods converge to the minimum
+@math{(\pi,2.275)} and perform similarly in terms of number of Jacobian evaluations.
+We see that @math{J} is fairly ill-conditioned
+at both minima, indicating that the QR (or SVD) solver is the best choice for this problem.
+Since there are only two parameters in this optimization problem, we can easily
+visualize the paths taken by each method, which are shown in the figure below.
+The figure shows contours of the cost function @math{\Phi(x_1,x_2)} which exhibits
+three global minima in the range @math{[-5,15] \times [-5,15]}. The paths taken
+by each solver are shown as colored lines.
+
+@iftex
+@sp 1
+@center @image{nlfit3,6in}
+@end iftex
+
+@noindent
+The program is given below.
+
+@example
+@verbatiminclude examples/nlfit3.c
+@end example
+
+@node Nonlinear Least-Squares Large Example
+@subsection Large Nonlinear Least Squares Example
+
+The following program illustrates the large nonlinear least
+squares solvers on a system with significant sparse structure
+in the Jacobian. The cost function is given by
+@tex
+\beforedisplay
+$$
+\eqalign{
+\Phi(x) &= {1 \over 2} \sum_{i=1}^{p+1} f_i^2 \cr
+f_i &= \sqrt{\alpha} (x_i - 1), \quad 1 \le i \le p \cr
+f_{p+1} &= ||x||^2 - {1 \over 4}
+}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+\Phi(x) &= 1/2 \sum_@{i=1@}^@{p+1@} f_i^2
+f_i &= \sqrt@{\alpha@} (x_i - 1), 1 \le i \le p
+f_@{p+1@} &= ||x||^2 - 1/4
+@end example
+
+@end ifinfo
+with @math{\alpha = 10^{-5}}. The residual @math{f_{p+1}} imposes a constraint on the @math{p}
+parameters @math{x}, to ensure that @math{||x||^2 \approx {1 \over 4}}.
+The @math{(p+1)}-by-@math{p} Jacobian for this system is given by
+@tex
+\beforedisplay
+$$
+J(x) =
+\left(
+\matrix{
+\sqrt{\alpha} I_p \cr
+2 x^T
+}
+\right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+J(x) = [ \sqrt@{alpha@} I_p; 2 x^T ]
+@end example
+
+@end ifinfo
+and the normal equations matrix is given by
+@tex
+\beforedisplay
+$$
+J^T J =
+\alpha I_p + 4 x x^T
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+J^T J = [ \alpha I_p + 4 x x^T ]
+@end example
+
+@end ifinfo
+@noindent
+Finally, the second directional derivative of @math{f} for the
+geodesic acceleration method is given by
+@tex
+\beforedisplay
+$$
+f_{vv} = D_v^2 f =
+\left(
+\matrix{
+0 \cr
+2 ||v||^2
+}
+\right)
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+fvv = [ 0; 2 ||v||^2 ]
+@end example
+
+@end ifinfo
+@noindent
+Since the upper @math{p}-by-@math{p} block of @math{J} is diagonal,
+this sparse structure should be exploited in the nonlinear solver.
+For comparison, the following program solves the system for @math{p = 2000}
+using the dense direct Cholesky solver based on the normal equations matrix
+@math{J^T J}, as well as the iterative Steihaug-Toint solver, based on
+sparse matrix-vector products @math{J u} and @math{J^T u}. The
+program output is shown below.
+
+@smallformat
+@verbatim
+Method                    NITER NFEV NJUEV NJTJEV NAEV Init Cost  Final cost cond(J) Final |x|^2 Time (s)  
+levenberg-marquardt       25    31   26    26     0    7.1218e+18 1.9555e-02 447.50  2.5044e-01  46.28
+levenberg-marquardt+accel 22    23   45    23     22   7.1218e+18 1.9555e-02 447.64  2.5044e-01  33.92
+dogleg                    37    87   36    36     0    7.1218e+18 1.9555e-02 447.59  2.5044e-01  56.05
+double-dogleg             35    88   34    34     0    7.1218e+18 1.9555e-02 447.62  2.5044e-01  52.65
+2D-subspace               37    88   36    36     0    7.1218e+18 1.9555e-02 447.71  2.5044e-01  59.75
+steihaug-toint            35    88   345   0      0    7.1218e+18 1.9555e-02 inf     2.5044e-01  0.09
+@end verbatim
+@end smallformat
+
+@noindent
+The first five rows use methods based on factoring the dense @math{J^T J} matrix
+while the last row uses the iterative Steihaug-Toint method. While the number
+of Jacobian matrix-vector products (NJUEV) is less for the dense methods, the added time
+to construct and factor the @math{J^T J} matrix (NJTJEV) results in a much larger runtime than the
+iterative method (see last column).
+
+@noindent
+The program is given below.
+
+@example
+@verbatiminclude examples/nlfit4.c
+@end example
+
+@node Nonlinear Least-Squares References and Further Reading
+@section References and Further Reading
+
+@noindent
+The following publications are relevant to the algorithms described
+in this section,
+
+@itemize @w{}
+@item
+J.J. Mor@'e, @cite{The Levenberg-Marquardt Algorithm: Implementation and
+Theory}, Lecture Notes in Mathematics, v630 (1978), ed G. Watson.
+
+@item
+H. B. Nielsen, ``Damping Parameter in Marquardt's Method'',
+IMM Department of Mathematical Modeling, DTU, Tech. Report IMM-REP-1999-05
+(1999).
+
+@item
+K. Madsen and H. B. Nielsen, ``Introduction to Optimization and Data
+Fitting'', IMM Department of Mathematical Modeling, DTU, 2010.
+
+@item
+J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained
+Optimization and Nonlinear Equations, SIAM, 1996.
+
+@item
+M. K. Transtrum, B. B. Machta, and J. P. Sethna,
+Geometry of nonlinear least squares with applications to sloppy models and optimization,
+Phys. Rev. E 83, 036701, 2011.
+
+@item
+M. K. Transtrum and J. P. Sethna, Improvements to the Levenberg-Marquardt
+algorithm for nonlinear least-squares minimization, arXiv:1201.5885, 2012.
+
+@item 
+J.J. Mor@'e, B.S. Garbow, K.E. Hillstrom, ``Testing Unconstrained
+Optimization Software'', ACM Transactions on Mathematical Software, Vol
+7, No 1 (1981), p 17--41.
+
+@item 
+H. B. Nielsen, ``UCTP Test Problems for Unconstrained Optimization'',
+IMM Department of Mathematical Modeling, DTU, Tech. Report IMM-REP-2000-17
+(2000).
+@end itemize
diff -Nru gsl-doc-1.16/doc/multifit.texi gsl-doc-2.3/doc/multifit.texi
--- gsl-doc-1.16/doc/multifit.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/multifit.texi	1970-01-01 00:00:00.000000000 +0000
@@ -1,708 +0,0 @@
-@cindex nonlinear least squares fitting
-@cindex least squares fitting, nonlinear
-
-This chapter describes functions for multidimensional nonlinear
-least-squares fitting.  The library provides low level components for a
-variety of iterative solvers and convergence tests.  These can be
-combined by the user to achieve the desired solution, with full access
-to the intermediate steps of the iteration.  Each class of methods uses
-the same framework, so that you can switch between solvers at runtime
-without needing to recompile your program.  Each instance of a solver
-keeps track of its own state, allowing the solvers to be used in
-multi-threaded programs.
-
-The header file @file{gsl_multifit_nlin.h} contains prototypes for the
-multidimensional nonlinear fitting functions and related declarations.
-
-@menu
-* Overview of Nonlinear Least-Squares Fitting::  
-* Initializing the Nonlinear Least-Squares Solver::  
-* Providing the Function to be Minimized::  
-* Finite Difference Jacobian::  
-* Iteration of the Minimization Algorithm::  
-* Search Stopping Parameters for Minimization Algorithms::  
-* High Level Driver::
-* Minimization Algorithms using Derivatives::  
-* Minimization Algorithms without Derivatives::  
-* Computing the covariance matrix of best fit parameters::  
-* Example programs for Nonlinear Least-Squares Fitting::  
-* References and Further Reading for Nonlinear Least-Squares Fitting::  
-@end menu
-
-@node Overview of Nonlinear Least-Squares Fitting
-@section Overview
-@cindex nonlinear least squares fitting, overview
-
-The problem of multidimensional nonlinear least-squares fitting requires
-the minimization of the squared residuals of @math{n} functions,
-@math{f_i}, in @math{p} parameters, @math{x_i},
-@tex
-\beforedisplay
-$$
-\Phi(x)  = {1 \over 2} || F(x) ||^2
-         = {1 \over 2} \sum_{i=1}^{n} f_i (x_1, \dots, x_p)^2
-$$
-\afterdisplay
-@end tex
-@ifinfo
-
-@example
-\Phi(x) = (1/2) || F(x) ||^2
-        = (1/2) \sum_@{i=1@}^@{n@} f_i(x_1, ..., x_p)^2 
-@end example
-
-@end ifinfo
-@noindent
-All algorithms proceed from an initial guess using the linearization,
-@tex
-\beforedisplay
-$$
-\psi(p) = || F(x+p) || \approx || F(x) + J p\, ||
-$$
-\afterdisplay
-@end tex
-@ifinfo
-
-@example
-\psi(p) = || F(x+p) || ~=~ || F(x) + J p ||
-@end example
-
-@end ifinfo
-@noindent
-where @math{x} is the initial point, @math{p} is the proposed step
-and @math{J} is the
-Jacobian matrix @c{$J_{ij} = \partial f_i / \partial x_j$}
-@math{J_@{ij@} = d f_i / d x_j}.  
-Additional strategies are used to enlarge the region of convergence.
-These include requiring a decrease in the norm @math{||F||} on each
-step or using a trust region to avoid steps which fall outside the linear 
-regime.
-
-To perform a weighted least-squares fit of a nonlinear model
-@math{Y(x,t)} to data (@math{t_i}, @math{y_i}) with independent Gaussian
-errors @math{\sigma_i}, use function components of the following form,
-@tex
-\beforedisplay
-$$
-f_i = {(Y(x, t_i) - y_i) \over \sigma_i}
-$$
-\afterdisplay
-@end tex
-@ifinfo
-
-@example
-f_i = (Y(x, t_i) - y_i) / \sigma_i
-@end example
-
-@end ifinfo
-@noindent
-Note that the model parameters are denoted by @math{x} in this chapter
-since the non-linear least-squares algorithms are described
-geometrically (i.e. finding the minimum of a surface).  The
-independent variable of any data to be fitted is denoted by @math{t}.
-
-@cindex Jacobian matrix, fitting
-With the definition above the Jacobian is 
-@c{$J_{ij} = (1 / \sigma_i) \partial Y_i / \partial x_j$}
-@math{J_@{ij@} =(1 / \sigma_i)  d Y_i / d x_j}, where @math{Y_i = Y(x,t_i)}.  
-
-
-@node Initializing the Nonlinear Least-Squares Solver
-@section Initializing the Solver
-
-@deftypefun {gsl_multifit_fsolver *} gsl_multifit_fsolver_alloc (const gsl_multifit_fsolver_type * @var{T}, size_t @var{n}, size_t @var{p})
-@tpindex gsl_multifit_fsolver
-@tpindex gsl_multifit_fsolver_type
-This function returns a pointer to a newly allocated instance of a
-solver of type @var{T} for @var{n} observations and @var{p} parameters.
-The number of observations @var{n} must be greater than or equal to
-parameters @var{p}. 
-
-If there is insufficient memory to create the solver then the function
-returns a null pointer and the error handler is invoked with an error
-code of @code{GSL_ENOMEM}.
-@end deftypefun
-
-@deftypefun {gsl_multifit_fdfsolver *} gsl_multifit_fdfsolver_alloc (const gsl_multifit_fdfsolver_type * @var{T}, size_t @var{n}, size_t @var{p})
-@tpindex gsl_multifit_fdfsolver
-@tpindex gsl_multifit_fdfsolver_type
-This function returns a pointer to a newly allocated instance of a
-derivative solver of type @var{T} for @var{n} observations and @var{p}
-parameters.  For example, the following code creates an instance of a
-Levenberg-Marquardt solver for 100 data points and 3 parameters,
-
-@example
-const gsl_multifit_fdfsolver_type * T 
-    = gsl_multifit_fdfsolver_lmder;
-gsl_multifit_fdfsolver * s 
-    = gsl_multifit_fdfsolver_alloc (T, 100, 3);
-@end example
-
-@noindent
-The number of observations @var{n} must be greater than or equal to
-parameters @var{p}.
-
-If there is insufficient memory to create the solver then the function
-returns a null pointer and the error handler is invoked with an error
-code of @code{GSL_ENOMEM}.
-@end deftypefun
-
-@deftypefun int gsl_multifit_fsolver_set (gsl_multifit_fsolver * @var{s}, gsl_multifit_function * @var{f}, const gsl_vector * @var{x})
-This function initializes, or reinitializes, an existing solver @var{s}
-to use the function @var{f} and the initial guess @var{x}.
-@end deftypefun
-
-@deftypefun int gsl_multifit_fdfsolver_set (gsl_multifit_fdfsolver * @var{s}, gsl_multifit_function_fdf * @var{fdf}, const gsl_vector * @var{x})
-This function initializes, or reinitializes, an existing solver @var{s}
-to use the function and derivative @var{fdf} and the initial guess
-@var{x}.
-@end deftypefun
-
-@deftypefun void gsl_multifit_fsolver_free (gsl_multifit_fsolver * @var{s})
-@deftypefunx void gsl_multifit_fdfsolver_free (gsl_multifit_fdfsolver * @var{s})
-These functions free all the memory associated with the solver @var{s}.
-@end deftypefun
-
-@deftypefun {const char *} gsl_multifit_fsolver_name (const gsl_multifit_fsolver * @var{s})
-@deftypefunx {const char *} gsl_multifit_fdfsolver_name (const gsl_multifit_fdfsolver * @var{s})
-These functions return a pointer to the name of the solver.  For example,
-
-@example
-printf ("s is a '%s' solver\n", 
-        gsl_multifit_fdfsolver_name (s));
-@end example
-
-@noindent
-would print something like @code{s is a 'lmder' solver}.
-@end deftypefun
-
-@node Providing the Function to be Minimized
-@section Providing the Function to be Minimized
-
-You must provide @math{n} functions of @math{p} variables for the
-minimization algorithms to operate on.  In order to allow for
-arbitrary parameters the functions are defined by the following data
-types:
-
-@deftp {Data Type} gsl_multifit_function 
-This data type defines a general system of functions with arbitrary parameters.  
-
-@table @code
-@item int (* f) (const gsl_vector * @var{x}, void * @var{params}, gsl_vector * @var{f})
-this function should store the vector result
-@c{$f(x,\hbox{\it params})$}
-@math{f(x,params)} in @var{f} for argument @var{x} and arbitrary parameters @var{params},
-returning an appropriate error code if the function cannot be computed.
-
-@item size_t n
-the number of functions, i.e. the number of components of the
-vector @var{f}.
-
-@item size_t p
-the number of independent variables, i.e. the number of components of
-the vector @var{x}.
-
-@item void * params
-a pointer to the arbitrary parameters of the function.
-@end table
-@end deftp
-
-@deftp {Data Type} gsl_multifit_function_fdf
-This data type defines a general system of functions with arbitrary parameters and
-the corresponding Jacobian matrix of derivatives,
-
-@table @code
-@item int (* f) (const gsl_vector * @var{x}, void * @var{params}, gsl_vector * @var{f})
-this function should store the vector result
-@c{$f(x,\hbox{\it params})$}
-@math{f(x,params)} in @var{f} for argument @var{x} and arbitrary parameters @var{params},
-returning an appropriate error code if the function cannot be computed.
-
-@item int (* df) (const gsl_vector * @var{x}, void * @var{params}, gsl_matrix * @var{J})
-this function should store the @var{n}-by-@var{p} matrix result
-@c{$J_{ij} = \partial f_i(x,\hbox{\it params}) / \partial x_j$}
-@math{J_ij = d f_i(x,params) / d x_j} in @var{J} for argument @var{x} 
-and arbitrary parameters @var{params}, returning an appropriate error code if the
-function cannot be computed. If an analytic Jacobian is unavailable, or too expensive
-to compute, this function pointer may be set to NULL, in which
-case the Jacobian will be internally computed using finite difference approximations
-of the function @var{f}.
-
-@item int (* fdf) (const gsl_vector * @var{x}, void * @var{params}, gsl_vector * @var{f}, gsl_matrix * @var{J})
-This function should set the values of the @var{f} and @var{J} as above,
-for arguments @var{x} and arbitrary parameters @var{params}.  This function
-provides an optimization of the separate functions for @math{f(x)} and
-@math{J(x)}---it is always faster to compute the function and its
-derivative at the same time. If an analytic Jacobian is unavailable, or too expensive
-to compute, this function pointer may be set to NULL, in which
-case the Jacobian will be internally computed using finite difference approximations
-of the function @var{f}.
-
-@item size_t n
-the number of functions, i.e. the number of components of the
-vector @var{f}.
-
-@item size_t p
-the number of independent variables, i.e. the number of components of
-the vector @var{x}.
-
-@item void * params
-a pointer to the arbitrary parameters of the function.
-@end table
-@end deftp
-
-Note that when fitting a non-linear model against experimental data,
-the data is passed to the functions above using the
-@var{params} argument and the trial best-fit parameters through the
-@var{x} argument.
-
-@node Finite Difference Jacobian
-@section Finite Difference Jacobian
-
-For the algorithms which require a Jacobian matrix of derivatives of
-the fit functions, there are times when an analytic Jacobian may be
-unavailable or too expensive to compute. Therefore GSL supports
-approximating the Jacobian numerically using finite differences of the fit
-functions. This is typically done by setting the relevant function pointers
-of the @code{gsl_multifit_function_fdf} data type to NULL, however the
-following functions allow the user to access the approximate Jacobian
-directly if needed.
-
-@deftypefun int gsl_multifit_fdfsolver_dif_df (const gsl_vector * @var{x}, gsl_multifit_function_fdf * @var{fdf}, const gsl_vector * @var{f}, gsl_matrix * @var{J})
-This function takes as input the current position @var{x} with the function
-values computed at the current position @var{f}, along with @var{fdf}
-which specifies the fit function and parameters and approximates the
-@var{n}-by-@var{p} Jacobian @var{J} using forward finite differences:
-@c{$J_{ij} = \partial f_i(x,\hbox{\it params}) / \partial x_j \approx (f_i(x^{*}, \hbox{\it params}) - f_i(x, \hbox{\it params})) / \Delta x_j$}
-@math{J_ij = d f_i(x,params) / d x_j = (f_i(x^*,params) - f_i(x,params)) / d x_j}.
-where @math{x^*} has the @math{j}th element perturbed by @math{\Delta x_j}
-and @math{\Delta x_j = \epsilon |x_j|}, where @math{\epsilon} is the
-square root of the machine precision @code{GSL_DBL_EPSILON}.
-@end deftypefun
-
-@deftypefun int gsl_multifit_fdfsolver_dif_fdf (const gsl_vector * @var{x}, gsl_multifit_function_fdf * @var{fdf}, gsl_vector * @var{f}, gsl_matrix * @var{J})
-This function computes the vector of function values @var{f} and
-the approximate Jacobian @var{J} at the position vector @var{x} using
-the system described in @var{fdf}. See @code{gsl_multifit_fdfsolver_dif_df}
-for a description of how the Jacobian is computed.
-@end deftypefun
-
-@node Iteration of the Minimization Algorithm
-@section Iteration
-
-The following functions drive the iteration of each algorithm.  Each
-function performs one iteration to update the state of any solver of the
-corresponding type.  The same functions work for all solvers so that
-different methods can be substituted at runtime without modifications to
-the code.
-
-@deftypefun int gsl_multifit_fsolver_iterate (gsl_multifit_fsolver * @var{s})
-@deftypefunx int gsl_multifit_fdfsolver_iterate (gsl_multifit_fdfsolver * @var{s})
-These functions perform a single iteration of the solver @var{s}.  If
-the iteration encounters an unexpected problem then an error code will
-be returned.  The solver maintains a current estimate of the best-fit
-parameters at all times. 
-@end deftypefun
-
-The solver struct @var{s} contains the following entries, which can
-be used to track the progress of the solution:
-
-@table @code
-@item gsl_vector * x
-The current position.
-
-@item gsl_vector * f
-The function value at the current position.
-
-@item gsl_vector * dx
-The difference between the current position and the previous position,
-i.e. the last step, taken as a vector.
-
-@item gsl_matrix * J
-The Jacobian matrix at the current position (for the
-@code{gsl_multifit_fdfsolver} struct only)
-@end table
-
-The best-fit information also can be accessed with the following
-auxiliary functions,
-
-@deftypefun {gsl_vector *} gsl_multifit_fsolver_position (const gsl_multifit_fsolver * @var{s})
-@deftypefunx {gsl_vector *} gsl_multifit_fdfsolver_position (const gsl_multifit_fdfsolver * @var{s})
-These functions return the current position (i.e. best-fit parameters)
-@code{s->x} of the solver @var{s}.
-@end deftypefun
-
-@node Search Stopping Parameters for Minimization Algorithms
-@section Search Stopping Parameters
-@cindex nonlinear fitting, stopping parameters
-
-A minimization procedure should stop when one of the following conditions is
-true:
-
-@itemize @bullet
-@item
-A minimum has been found to within the user-specified precision.
-
-@item
-A user-specified maximum number of iterations has been reached.
-
-@item
-An error has occurred.
-@end itemize
-
-@noindent
-The handling of these conditions is under user control.  The functions
-below allow the user to test the current estimate of the best-fit
-parameters in several standard ways.
-
-@deftypefun int gsl_multifit_test_delta (const gsl_vector * @var{dx}, const gsl_vector * @var{x}, double @var{epsabs}, double @var{epsrel})
-
-This function tests for the convergence of the sequence by comparing the
-last step @var{dx} with the absolute error @var{epsabs} and relative
-error @var{epsrel} to the current position @var{x}.  The test returns
-@code{GSL_SUCCESS} if the following condition is achieved,
-@tex
-\beforedisplay
-$$
-|dx_i| < \hbox{\it epsabs} + \hbox{\it epsrel\/}\, |x_i|
-$$
-\afterdisplay
-@end tex
-@ifinfo
-
-@example
-|dx_i| < epsabs + epsrel |x_i|
-@end example
-
-@end ifinfo
-@noindent
-for each component of @var{x} and returns @code{GSL_CONTINUE} otherwise.
-@end deftypefun
-
-@cindex residual, in nonlinear systems of equations
-@deftypefun int gsl_multifit_test_gradient (const gsl_vector * @var{g}, double @var{epsabs})
-This function tests the residual gradient @var{g} against the absolute
-error bound @var{epsabs}.  Mathematically, the gradient should be
-exactly zero at the minimum. The test returns @code{GSL_SUCCESS} if the
-following condition is achieved,
-@tex
-\beforedisplay
-$$
-\sum_i |g_i| < \hbox{\it epsabs}
-$$
-\afterdisplay
-@end tex
-@ifinfo
-
-@example
-\sum_i |g_i| < epsabs
-@end example
-
-@end ifinfo
-@noindent
-and returns @code{GSL_CONTINUE} otherwise.  This criterion is suitable
-for situations where the precise location of the minimum, @math{x},
-is unimportant provided a value can be found where the gradient is small
-enough.
-@end deftypefun
-
-
-@deftypefun int gsl_multifit_gradient (const gsl_matrix * @var{J}, const gsl_vector * @var{f}, gsl_vector * @var{g})
-This function computes the gradient @var{g} of @math{\Phi(x) = (1/2)
-||F(x)||^2} from the Jacobian matrix @math{J} and the function values
-@var{f}, using the formula @math{g = J^T f}.
-@end deftypefun
-
-@node High Level Driver
-@section High Level Driver
-
-These routines provide a high level wrapper that combine the iteration
-and convergence testing for easy use.
-
-@deftypefun int gsl_multifit_fsolver_driver (gsl_multifit_fsolver * @var{s}, const size_t @var{maxiter}, const double @var{epsabs}, const double @var{epsrel})
-@deftypefunx int gsl_multifit_fdfsolver_driver (gsl_multifit_fdfsolver * @var{s}, const size_t @var{maxiter}, const double @var{epsabs}, const double @var{epsrel})
-These functions iterate the solver @var{s} for a maximum of @var{maxiter}
-iterations. After each iteration, the system is tested for convergence
-using @code{gsl_multifit_test_delta} with the error tolerances @var{epsabs}
-and @var{epsrel}.
-@end deftypefun
-
-@node Minimization Algorithms using Derivatives
-@section Minimization Algorithms using Derivatives
-
-The minimization algorithms described in this section make use of both
-the function and its derivative.  They require an initial guess for the
-location of the minimum. There is no absolute guarantee of
-convergence---the function must be suitable for this technique and the
-initial guess must be sufficiently close to the minimum for it to work.
-
-@comment ============================================================
-@cindex Levenberg-Marquardt algorithms
-@deffn {Derivative Solver} gsl_multifit_fdfsolver_lmsder
-@cindex LMDER algorithm
-@cindex MINPACK, minimization algorithms
-This is a robust and efficient version of the Levenberg-Marquardt
-algorithm as implemented in the scaled @sc{lmder} routine in
-@sc{minpack}.  Minpack was written by Jorge J. Mor@'e, Burton S. Garbow
-and Kenneth E. Hillstrom.
-
-The algorithm uses a generalized trust region to keep each step under
-control.  In order to be accepted a proposed new position @math{x'} must
-satisfy the condition @math{|D (x' - x)| < \delta}, where @math{D} is a
-diagonal scaling matrix and @math{\delta} is the size of the trust
-region.  The components of @math{D} are computed internally, using the
-column norms of the Jacobian to estimate the sensitivity of the residual
-to each component of @math{x}.  This improves the behavior of the
-algorithm for badly scaled functions.
-
-On each iteration the algorithm attempts to minimize the linear system
-@math{|F + J p|} subject to the constraint @math{|D p| < \Delta}.  The
-solution to this constrained linear system is found using the
-Levenberg-Marquardt method.
-
-The proposed step is now tested by evaluating the function at the
-resulting point, @math{x'}.  If the step reduces the norm of the
-function sufficiently, and follows the predicted behavior of the
-function within the trust region, then it is accepted and the size of the
-trust region is increased.  If the proposed step fails to improve the
-solution, or differs significantly from the expected behavior within
-the trust region, then the size of the trust region is decreased and
-another trial step is computed.
-
-The algorithm also monitors the progress of the solution and returns an
-error if the changes in the solution are smaller than the machine
-precision.  The possible error codes are,
-
-@table @code
-@item GSL_ETOLF
-the decrease in the function falls below machine precision
-
-@item GSL_ETOLX
-the change in the position vector falls below machine precision
-
-@item GSL_ETOLG
-the norm of the gradient, relative to the norm of the function, falls
-below machine precision
-
-@item GSL_ENOPROG
-the routine has made 10 or more attempts to find a suitable trial step
-without success (but subsequent calls can be made to continue the
-search).@footnote{The return code @code{GSL_CONTINUE} was used for
-this case in versions prior to 1.14.}
-@end table
-
-@noindent
-These error codes indicate that further iterations will be unlikely to
-change the solution from its current value.  
-@end deffn
-
-@deffn {Derivative Solver} gsl_multifit_fdfsolver_lmder
-This is an unscaled version of the @sc{lmder} algorithm.  The elements of the
-diagonal scaling matrix @math{D} are set to 1.  This algorithm may be
-useful in circumstances where the scaled version of @sc{lmder} converges too
-slowly, or the function is already scaled appropriately.
-@end deffn
-
-@node Minimization Algorithms without Derivatives
-@section Minimization Algorithms without Derivatives
-
-There are no algorithms implemented in this section at the moment.
-
-@node Computing the covariance matrix of best fit parameters
-@section Computing the covariance matrix of best fit parameters
-@cindex best-fit parameters, covariance
-@cindex least squares, covariance of best-fit parameters
-@cindex covariance matrix, nonlinear fits
-
-@deftypefun int gsl_multifit_covar (const gsl_matrix * @var{J}, double @var{epsrel}, gsl_matrix * @var{covar})
-This function uses the Jacobian matrix @var{J} to compute the covariance
-matrix of the best-fit parameters, @var{covar}.  The parameter
-@var{epsrel} is used to remove linear-dependent columns when @var{J} is
-rank deficient.
-
-The covariance matrix is given by,
-@tex
-\beforedisplay
-$$
-C = (J^T J)^{-1}
-$$
-\afterdisplay
-@end tex
-@ifinfo
-
-@example
-covar = (J^T J)^@{-1@}
-@end example
-
-@end ifinfo
-@noindent
-and is computed by QR decomposition of J with column-pivoting.  Any
-columns of @math{R} which satisfy 
-@tex
-\beforedisplay
-$$
-|R_{kk}| \leq epsrel |R_{11}|
-$$
-\afterdisplay
-@end tex
-@ifinfo
-
-@example
-|R_@{kk@}| <= epsrel |R_@{11@}|
-@end example
-
-@end ifinfo
-@noindent
-are considered linearly-dependent and are excluded from the covariance
-matrix (the corresponding rows and columns of the covariance matrix are
-set to zero).
-
-If the minimisation uses the weighted least-squares function
-@math{f_i = (Y(x, t_i) - y_i) / \sigma_i} then the covariance
-matrix above gives the statistical error on the best-fit parameters
-resulting from the Gaussian errors @math{\sigma_i} on 
-the underlying data @math{y_i}.  This can be verified from the relation 
-@math{\delta f = J \delta c} and the fact that the fluctuations in @math{f}
-from the data @math{y_i} are normalised by @math{\sigma_i} and 
-so satisfy @c{$\langle \delta f \delta f^T \rangle = I$}
-@math{<\delta f \delta f^T> = I}.
-
-For an unweighted least-squares function @math{f_i = (Y(x, t_i) -
-y_i)} the covariance matrix above should be multiplied by the variance
-of the residuals about the best-fit @math{\sigma^2 = \sum (y_i - Y(x,t_i))^2 / (n-p)}
-to give the variance-covariance
-matrix @math{\sigma^2 C}.  This estimates the statistical error on the
-best-fit parameters from the scatter of the underlying data.
-
-For more information about covariance matrices see @ref{Fitting Overview}.
-@end deftypefun
-
-@comment ============================================================
-
-@node Example programs for Nonlinear Least-Squares Fitting
-@section Examples
-
-The following example program fits a weighted exponential model with
-background to experimental data, @math{Y = A \exp(-\lambda t) + b}. The
-first part of the program sets up the functions @code{expb_f} and
-@code{expb_df} to calculate the model and its Jacobian.  The appropriate
-fitting function is given by,
-@tex
-\beforedisplay
-$$
-f_i = ((A \exp(-\lambda t_i) + b) - y_i)/\sigma_i
-$$
-\afterdisplay
-@end tex
-@ifinfo
-
-@example
-f_i = ((A \exp(-\lambda t_i) + b) - y_i)/\sigma_i
-@end example
-
-@end ifinfo
-@noindent
-where we have chosen @math{t_i = i}.  The Jacobian matrix @math{J} is
-the derivative of these functions with respect to the three parameters
-(@math{A}, @math{\lambda}, @math{b}).  It is given by,
-@tex
-\beforedisplay
-$$
-J_{ij} = {\partial f_i \over \partial x_j}
-$$
-\afterdisplay
-@end tex
-@ifinfo
-
-@example
-J_@{ij@} = d f_i / d x_j
-@end example
-
-@end ifinfo
-@noindent
-where @math{x_0 = A}, @math{x_1 = \lambda} and @math{x_2 = b}.
-
-@example
-@verbatiminclude examples/expfit.c
-@end example
-
-@noindent
-The main part of the program sets up a Levenberg-Marquardt solver and
-some simulated random data. The data uses the known parameters
-(1.0,5.0,0.1) combined with Gaussian noise (standard deviation = 0.1)
-over a range of 40 timesteps. The initial guess for the parameters is
-chosen as (0.0, 1.0, 0.0).
-
-@example
-@verbatiminclude examples/nlfit.c
-@end example
-
-@noindent
-The iteration terminates when the change in x is smaller than 0.0001, as
-both an absolute and relative change.  Here are the results of running
-the program:
-
-@smallexample
-iter: 0 x=1.00000000 0.00000000 0.00000000 |f(x)|=117.349
-status=success
-iter: 1 x=1.64659312 0.01814772 0.64659312 |f(x)|=76.4578
-status=success
-iter: 2 x=2.85876037 0.08092095 1.44796363 |f(x)|=37.6838
-status=success
-iter: 3 x=4.94899512 0.11942928 1.09457665 |f(x)|=9.58079
-status=success
-iter: 4 x=5.02175572 0.10287787 1.03388354 |f(x)|=5.63049
-status=success
-iter: 5 x=5.04520433 0.10405523 1.01941607 |f(x)|=5.44398
-status=success
-iter: 6 x=5.04535782 0.10404906 1.01924871 |f(x)|=5.44397
-chisq/dof = 0.800996
-A      = 5.04536 +/- 0.06028
-lambda = 0.10405 +/- 0.00316
-b      = 1.01925 +/- 0.03782
-status = success
-@end smallexample
-
-@noindent
-The approximate values of the parameters are found correctly, and the
-chi-squared value indicates a good fit (the chi-squared per degree of
-freedom is approximately 1).  In this case the errors on the parameters
-can be estimated from the square roots of the diagonal elements of the
-covariance matrix.  
-
-If the chi-squared value shows a poor fit (i.e. @c{$\chi^2/(n-p) \gg 1$}
-@math{chi^2/dof >> 1}) then the error estimates obtained from the
-covariance matrix will be too small.  In the example program the error estimates
-are multiplied by @c{$\sqrt{\chi^2/(n-p)}$}
-@math{\sqrt@{\chi^2/dof@}} in this case, a common way of increasing the
-errors for a poor fit.  Note that a poor fit will result from the use
-an inappropriate model, and the scaled error estimates may then
-be outside the range of validity for Gaussian errors.
-
-@iftex
-@sp 1
-@center @image{fit-exp,3.4in}
-@end iftex
-
-@node References and Further Reading for Nonlinear Least-Squares Fitting
-@section References and Further Reading
-
-The @sc{minpack} algorithm is described in the following article,
-
-@itemize @w{}
-@item
-J.J. Mor@'e, @cite{The Levenberg-Marquardt Algorithm: Implementation and
-Theory}, Lecture Notes in Mathematics, v630 (1978), ed G. Watson.
-@end itemize
-
-@noindent
-The following paper is also relevant to the algorithms described in this
-section,
-
-@itemize @w{}
-@item 
-J.J. Mor@'e, B.S. Garbow, K.E. Hillstrom, ``Testing Unconstrained
-Optimization Software'', ACM Transactions on Mathematical Software, Vol
-7, No 1 (1981), p 17--41.
-@end itemize
-
diff -Nru gsl-doc-1.16/doc/multilarge.eps gsl-doc-2.3/doc/multilarge.eps
--- gsl-doc-1.16/doc/multilarge.eps	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/multilarge.eps	2016-08-12 17:55:12.000000000 +0000
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diff -Nru gsl-doc-1.16/doc/multimin.texi gsl-doc-2.3/doc/multimin.texi
--- gsl-doc-1.16/doc/multimin.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/multimin.texi	2016-07-07 20:36:10.000000000 +0000
@@ -115,10 +115,10 @@
 
 @deftypefun {gsl_multimin_fdfminimizer *} gsl_multimin_fdfminimizer_alloc (const gsl_multimin_fdfminimizer_type * @var{T}, size_t @var{n})
 @deftypefunx {gsl_multimin_fminimizer *} gsl_multimin_fminimizer_alloc (const gsl_multimin_fminimizer_type * @var{T}, size_t @var{n})
-@tpindex gsl_multimin_fdfminimizer
-@tpindex gsl_multimin_fminimizer
-@tpindex gsl_multimin_fdfminimizer_type
-@tpindex gsl_multimin_fminimizer_type
+@tindex gsl_multimin_fdfminimizer
+@tindex gsl_multimin_fminimizer
+@tindex gsl_multimin_fdfminimizer_type
+@tindex gsl_multimin_fminimizer_type
 This function returns a pointer to a newly allocated instance of a
 minimizer of type @var{T} for an @var{n}-dimension function.  If there
 is insufficient memory to create the minimizer then the function returns
@@ -285,10 +285,11 @@
 @deftypefunx double gsl_multimin_fdfminimizer_minimum (const gsl_multimin_fdfminimizer * @var{s})
 @deftypefunx double gsl_multimin_fminimizer_minimum (const gsl_multimin_fminimizer * @var{s})
 @deftypefunx {gsl_vector *} gsl_multimin_fdfminimizer_gradient (const gsl_multimin_fdfminimizer * @var{s})
+@deftypefunx {gsl_vector *} gsl_multimin_fdfminimizer_dx (const gsl_multimin_fdfminimizer * @var{s})
 @deftypefunx double gsl_multimin_fminimizer_size (const gsl_multimin_fminimizer * @var{s})
 These functions return the current best estimate of the location of the
-minimum, the value of the function at that point, its gradient, 
-and minimizer specific characteristic size for the minimizer @var{s}.
+minimum, the value of the function at that point, its gradient, the last
+step increment of the estimate, and minimizer specific characteristic size for the minimizer @var{s}.
 @end deftypefun
 
 @deftypefun int gsl_multimin_fdfminimizer_restart (gsl_multimin_fdfminimizer * @var{s})
@@ -525,7 +526,7 @@
 0.001. The output of the program is shown below,
 
 @example
-@verbatiminclude examples/multimin.out
+@verbatiminclude examples/multimin.txt
 @end example
 
 @noindent
@@ -555,7 +556,7 @@
 shown below.
 
 @example
-@verbatiminclude examples/nmsimplex.out
+@verbatiminclude examples/nmsimplex.txt
 @end example
 
 @noindent
diff -Nru gsl-doc-1.16/doc/multiroots.texi gsl-doc-2.3/doc/multiroots.texi
--- gsl-doc-1.16/doc/multiroots.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/multiroots.texi	2015-11-03 16:21:55.000000000 +0000
@@ -121,8 +121,8 @@
 different problems.
 
 @deftypefun {gsl_multiroot_fsolver *} gsl_multiroot_fsolver_alloc (const gsl_multiroot_fsolver_type * @var{T}, size_t @var{n})
-@tpindex gsl_multiroot_fsolver
-@tpindex gsl_multiroot_fsolver_type
+@tindex gsl_multiroot_fsolver
+@tindex gsl_multiroot_fsolver_type
 This function returns a pointer to a newly allocated instance of a
 solver of type @var{T} for a system of @var{n} dimensions.
 For example, the following code creates an instance of a hybrid solver, 
@@ -142,8 +142,8 @@
 @end deftypefun
 
 @deftypefun {gsl_multiroot_fdfsolver *} gsl_multiroot_fdfsolver_alloc (const gsl_multiroot_fdfsolver_type * @var{T}, size_t @var{n})
-@tpindex gsl_multiroot_fdfsolver
-@tpindex gsl_multiroot_fdfsolver_type
+@tindex gsl_multiroot_fdfsolver
+@tindex gsl_multiroot_fdfsolver_type
 This function returns a pointer to a newly allocated instance of a
 derivative solver of type @var{T} for a system of @var{n} dimensions.
 For example, the following code creates an instance of a Newton-Raphson solver,
diff -Nru gsl-doc-1.16/doc/multiset.texi gsl-doc-2.3/doc/multiset.texi
--- gsl-doc-1.16/doc/multiset.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/multiset.texi	2015-11-09 05:23:40.000000000 +0000
@@ -24,7 +24,7 @@
 
 @node The Multiset struct
 @section The Multiset struct
-@tpindex gsl_multiset
+@tindex gsl_multiset
 A multiset is defined by a structure containing three components, the
 values of @math{n} and @math{k}, and a pointer to the multiset array.
 The elements of the multiset array are all of type @code{size_t}, and
@@ -194,7 +194,7 @@
 
 @example
 $ ./a.out
-@verbatiminclude examples/multiset.out
+@verbatiminclude examples/multiset.txt
 @end example
 
 @noindent
diff -Nru gsl-doc-1.16/doc/nlfit2.eps gsl-doc-2.3/doc/nlfit2.eps
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+++ gsl-doc-2.3/doc/nlfit2.eps	2016-07-07 20:36:10.000000000 +0000
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diff -Nru gsl-doc-1.16/doc/ntuple.texi gsl-doc-2.3/doc/ntuple.texi
--- gsl-doc-1.16/doc/ntuple.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/ntuple.texi	2015-11-03 16:21:55.000000000 +0000
@@ -33,7 +33,7 @@
 
 @node The ntuple struct
 @section The ntuple struct
-@tpindex gsl_ntuple
+@tindex gsl_ntuple
 Ntuples are manipulated using the @code{gsl_ntuple} struct. This struct
 contains information on the file where the ntuple data is stored, a
 pointer to the current ntuple data row and the size of the user-defined
@@ -109,7 +109,7 @@
 parameters as a second argument.
 
 @cindex selection function, ntuples
-@tpindex gsl_ntuple_select_fn
+@tindex gsl_ntuple_select_fn
 The @dfn{selection function} determines which ntuple rows are selected
 for histogramming.  It is defined by the following struct,
 
@@ -125,7 +125,7 @@
 each ntuple row that is to be included in the histogram.
 
 @cindex value function, ntuples
-@tpindex gsl_ntuple_value_fn
+@tindex gsl_ntuple_value_fn
 The @dfn{value function} computes scalar values for those ntuple rows
 selected by the selection function,
 
diff -Nru gsl-doc-1.16/doc/ode-initval.texi gsl-doc-2.3/doc/ode-initval.texi
--- gsl-doc-1.16/doc/ode-initval.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/ode-initval.texi	2015-11-03 16:21:55.000000000 +0000
@@ -67,9 +67,11 @@
 The function should return @code{GSL_SUCCESS} if the calculation was
 completed successfully. Any other return value indicates an error. A
 special return value @code{GSL_EBADFUNC} causes @code{gsl_odeiv2}
-routines to immediately stop and return. The user must call an
-appropriate reset function (e.g. @code{gsl_odeiv2_driver_reset} or
-@code{gsl_odeiv2_step_reset}) before continuing. Use return values
+routines to immediately stop and return. If @code{function} 
+is modified (for example contents of @var{params}), the user must call an
+appropriate reset function (@code{gsl_odeiv2_driver_reset}, 
+@code{gsl_odeiv2_evolve_reset} or @code{gsl_odeiv2_step_reset}) 
+before continuing. Use return values
 distinct from standard GSL error codes to distinguish your function as
 the source of the error.
 
@@ -90,9 +92,11 @@
 The function should return @code{GSL_SUCCESS} if the calculation was
 completed successfully. Any other return value indicates an error. A
 special return value @code{GSL_EBADFUNC} causes @code{gsl_odeiv2}
-routines to immediately stop and return. The user must call an
-appropriate reset function (e.g. @code{gsl_odeiv2_driver_reset} or
-@code{gsl_odeiv2_step_reset}) before continuing. Use return values
+routines to immediately stop and return. If @code{jacobian} 
+is modified (for example contents of @var{params}), the user must call an
+appropriate reset function (@code{gsl_odeiv2_driver_reset}, 
+@code{gsl_odeiv2_evolve_reset} or @code{gsl_odeiv2_step_reset}) 
+before continuing. Use return values
 distinct from standard GSL error codes to distinguish your function as
 the source of the error.
 
@@ -112,8 +116,8 @@
 step-size @math{h} and estimate the resulting local error.
 
 @deftypefun {gsl_odeiv2_step *} gsl_odeiv2_step_alloc (const gsl_odeiv2_step_type * @var{T}, size_t @var{dim})
-@tpindex gsl_odeiv2_step
-@tpindex gsl_odeiv2_step_type
+@tindex gsl_odeiv2_step
+@tindex gsl_odeiv2_step_type
 This function returns a pointer to a newly allocated instance of a
 stepping function of type @var{T} for a system of @var{dim}
 dimensions. Please note that if you use a stepper method that
@@ -291,8 +295,8 @@
 step-size for a user-specified level of error.
 
 @deftypefun {gsl_odeiv2_control *} gsl_odeiv2_control_standard_new (double @var{eps_abs}, double @var{eps_rel}, double @var{a_y}, double @var{a_dydt})
-@tpindex gsl_odeiv2_control
-@tpindex gsl_odeiv2_control_type
+@tindex gsl_odeiv2_control
+@tindex gsl_odeiv2_control_type
 The standard control object is a four parameter heuristic based on
 absolute and relative errors @var{eps_abs} and @var{eps_rel}, and
 scaling factors @var{a_y} and @var{a_dydt} for the system state
@@ -467,7 +471,7 @@
 using an acceptable step-size.
 
 @deftypefun {gsl_odeiv2_evolve *} gsl_odeiv2_evolve_alloc (size_t @var{dim})
-@tpindex gsl_odeiv2_evolve
+@tindex gsl_odeiv2_evolve
 This function returns a pointer to a newly allocated instance of an
 evolution function for a system of @var{dim} dimensions.
 @end deftypefun
diff -Nru gsl-doc-1.16/doc/permutation.texi gsl-doc-2.3/doc/permutation.texi
--- gsl-doc-1.16/doc/permutation.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/permutation.texi	2016-07-07 20:36:10.000000000 +0000
@@ -34,7 +34,7 @@
 
 @node The Permutation struct
 @section The Permutation struct
-@tpindex gsl_permutation
+@tindex gsl_permutation
 A permutation is defined by a structure containing two components, the size
 of the permutation and a pointer to the permutation array.  The elements
 of the permutation array are all of type @code{size_t}.  The
@@ -185,6 +185,15 @@
 and the vector @var{v} must have the same length.
 @end deftypefun
 
+@deftypefun int gsl_permute_matrix (const gsl_permutation * @var{p}, gsl_matrix * @var{A})
+This function applies the permutation @var{p} to the matrix @var{A} from
+the right, @math{A' = A P}.  The @math{j}-th column of the
+permutation matrix @math{P} is given by the @math{@var{p}_j}-th column of the
+identity matrix. This effectively permutes the columns of @var{A} according
+to the permutation @var{p}, and so the number of columns of @var{A} must
+equal the size of the permutation @var{p}.
+@end deftypefun
+
 @deftypefun int gsl_permutation_mul (gsl_permutation * @var{p}, const gsl_permutation * @var{pa}, const gsl_permutation * @var{pb})
 This function combines the two permutations @var{pa} and @var{pb} into a
 single permutation @var{p}, where @c{$@var{p} = @var{pa} \ast @var{pb}$}
diff -Nru gsl-doc-1.16/doc/poly.texi gsl-doc-2.3/doc/poly.texi
--- gsl-doc-1.16/doc/poly.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/poly.texi	2015-11-09 05:23:40.000000000 +0000
@@ -276,7 +276,7 @@
 approximate locations of roots of higher order polynomials.
 
 @deftypefun {gsl_poly_complex_workspace *} gsl_poly_complex_workspace_alloc (size_t @var{n})
-@tpindex gsl_poly_complex_workspace
+@tindex gsl_poly_complex_workspace
 This function allocates space for a @code{gsl_poly_complex_workspace}
 struct and a workspace suitable for solving a polynomial with @var{n}
 coefficients using the routine @code{gsl_poly_complex_solve}.
@@ -344,7 +344,7 @@
 
 @example
 $ ./a.out 
-@verbatiminclude examples/polyroots.out
+@verbatiminclude examples/polyroots.txt
 @end example
 
 @noindent
diff -Nru gsl-doc-1.16/doc/qrng.texi gsl-doc-2.3/doc/qrng.texi
--- gsl-doc-1.16/doc/qrng.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/qrng.texi	2015-11-03 16:21:55.000000000 +0000
@@ -17,7 +17,7 @@
 * Quasi-random number generator initialization::  
 * Sampling from a quasi-random number generator::  
 * Auxiliary quasi-random number generator functions::  
-* Saving and resorting quasi-random number generator state::  
+* Saving and restoring quasi-random number generator state::  
 * Quasi-random number generator algorithms::  
 * Quasi-random number generator examples::  
 * Quasi-random number references::  
@@ -27,8 +27,8 @@
 @section Quasi-random number generator initialization
 
 @deftypefun {gsl_qrng *} gsl_qrng_alloc (const gsl_qrng_type * @var{T}, unsigned int @var{d})
-@tpindex gsl_qrng
-@tpindex gsl_qrng_type
+@tindex gsl_qrng
+@tindex gsl_qrng_type
 This function returns a pointer to a newly-created instance of a
 quasi-random sequence generator of type @var{T} and dimension @var{d}.
 If there is insufficient memory to create the generator then the
@@ -79,8 +79,8 @@
 @end deftypefun
 
 
-@node Saving and resorting quasi-random number generator state
-@section Saving and resorting quasi-random number generator state
+@node Saving and restoring quasi-random number generator state
+@section Saving and restoring quasi-random number generator state
 
 @deftypefun int gsl_qrng_memcpy (gsl_qrng * @var{dest}, const gsl_qrng * @var{src})
 This function copies the quasi-random sequence generator @var{src} into the
diff -Nru gsl-doc-1.16/doc/randist.texi gsl-doc-2.3/doc/randist.texi
--- gsl-doc-1.16/doc/randist.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/randist.texi	2016-08-10 21:24:45.000000000 +0000
@@ -41,6 +41,7 @@
 * The Gaussian Distribution::   
 * The Gaussian Tail Distribution::  
 * The Bivariate Gaussian Distribution::  
+* The Multivariate Gaussian Distribution::  
 * The Exponential Distribution::  
 * The Laplace Distribution::    
 * The Exponential Power Distribution::  
@@ -366,6 +367,87 @@
 @end tex
 
 @page
+@node The Multivariate Gaussian Distribution
+@section The Multivariate Gaussian Distribution
+
+@deftypefun int gsl_ran_multivariate_gaussian (const gsl_rng * @var{r}, const gsl_vector * @var{mu}, const gsl_matrix * @var{L}, gsl_vector * @var{result})
+@cindex Bivariate Gaussian distribution
+@cindex two dimensional Gaussian distribution
+@cindex Gaussian distribution, bivariate
+This function generates a random vector satisfying the @math{k}-dimensional multivariate Gaussian
+distribution with mean @math{\mu} and variance-covariance matrix
+@math{\Sigma}. On input, the @math{k}-vector @math{\mu} is given in @var{mu}, and
+the Cholesky factor of the @math{k}-by-@math{k} matrix @math{\Sigma = L L^T} is
+given in the lower triangle of @var{L}, as output from @code{gsl_linalg_cholesky_decomp}.
+The random vector is stored in @var{result} on output. The probability distribution
+for multivariate Gaussian random variates is
+@tex
+\beforedisplay
+$$
+p(x_1,\dots,x_k) dx_1 \dots dx_k = {1 \over \sqrt{(2 \pi)^k |\Sigma|}} \exp \left(-{1 \over 2} (x - \mu)^T \Sigma^{-1} (x - \mu)\right) dx_1 \dots dx_k
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+p(x_1,...,x_k) dx_1 ... dx_k = @{1 \over \sqrt@{(2 \pi)^k |\Sigma|@} \exp \left(-@{1 \over 2@} (x - \mu)^T \Sigma^@{-1@} (x - \mu)\right) dx_1 \dots dx_k
+@end example
+
+@end ifinfo
+@end deftypefun
+
+@deftypefun int gsl_ran_multivariate_gaussian_pdf (const gsl_vector * @var{x}, const gsl_vector * @var{mu}, const gsl_matrix * @var{L}, double * @var{result}, gsl_vector * @var{work})
+@deftypefunx int gsl_ran_multivariate_gaussian_log_pdf (const gsl_vector * @var{x}, const gsl_vector * @var{mu}, const gsl_matrix * @var{L}, double * @var{result}, gsl_vector * @var{work})
+These functions compute @math{p(x)} or @math{\log{p(x)}} at the point @var{x}, using mean vector
+@var{mu} and variance-covariance matrix specified by its Cholesky factor @var{L} using the formula
+above. Additional workspace of length @math{k} is required in @var{work}.
+@end deftypefun
+
+@deftypefun int gsl_ran_multivariate_gaussian_mean (const gsl_matrix * @var{X}, gsl_vector * @var{mu_hat})
+Given a set of @math{n} samples @math{X_j} from a @math{k}-dimensional multivariate Gaussian distribution,
+this function computes the maximum likelihood estimate of the mean of the distribution, given by
+@tex
+\beforedisplay
+$$
+\Hat{\mu} = {1 \over n} \sum_{j=1}^n X_j
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+\Hat@{\mu@} = @{1 \over n@} \sum_@{j=1@}^n X_j
+@end example
+
+@end ifinfo
+The samples @math{X_1,X_2,\dots,X_n} are given in the @math{n}-by-@math{k} matrix @var{X}, and the maximum
+likelihood estimate of the mean is stored in @var{mu_hat} on output.
+@end deftypefun
+
+@deftypefun int gsl_ran_multivariate_gaussian_vcov (const gsl_matrix * @var{X}, gsl_matrix * @var{sigma_hat})
+Given a set of @math{n} samples @math{X_j} from a @math{k}-dimensional multivariate Gaussian distribution,
+this function computes the maximum likelihood estimate of the variance-covariance matrix of the distribution,
+given by
+@tex
+\beforedisplay
+$$
+\Hat{\Sigma} = {1 \over n} \sum_{j=1}^n \left( X_j - \Hat{\mu} \right) \left( X_j - \Hat{\mu} \right)^T
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+\Hat@{\Sigma@} = @{1 \over n@} \sum_@{j=1@}^n \left( X_j - \Hat@{\mu@} \right) \left( X_j - \Hat@{\mu@} \right)^T
+@end example
+
+@end ifinfo
+The samples @math{X_1,X_2,\dots,X_n} are given in the @math{n}-by-@math{k} matrix @var{X} and the maximum
+likelihood estimate of the variance-covariance matrix is stored in @var{sigma_hat} on output.
+@end deftypefun
+
+@page
 @node The Exponential Distribution
 @section The Exponential Distribution
 @deftypefun double gsl_ran_exponential (const gsl_rng * @var{r}, double @var{mu})
@@ -1626,7 +1708,7 @@
 be made, since it only takes a finite set of @math{K} outcomes.
 
 @deftypefun {gsl_ran_discrete_t *} gsl_ran_discrete_preproc (size_t @var{K}, const double * @var{P})
-@tpindex gsl_ran_discrete_t
+@tindex gsl_ran_discrete_t
 @cindex Discrete random numbers
 @cindex Discrete random numbers, preprocessing
 This function returns a pointer to a structure that contains the lookup
@@ -2180,7 +2262,7 @@
 
 @example
 $ ./a.out 
-@verbatiminclude examples/randpoisson.out
+@verbatiminclude examples/randpoisson.txt
 @end example
 
 @noindent
@@ -2191,7 +2273,7 @@
 
 @example
 $ GSL_RNG_SEED=123 ./a.out 
-@verbatiminclude examples/randpoisson.2.out
+@verbatiminclude examples/randpoisson2.txt
 @end example
 
 @noindent
@@ -2220,7 +2302,7 @@
 Here is the output of the program,
 
 @example
-@verbatiminclude examples/cdf.out
+@verbatiminclude examples/cdf.txt
 @end example
 
 @node Random Number Distribution References and Further Reading
diff -Nru gsl-doc-1.16/doc/regularized2.eps gsl-doc-2.3/doc/regularized2.eps
--- gsl-doc-1.16/doc/regularized2.eps	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/regularized2.eps	2016-10-27 11:20:46.000000000 +0000
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diff -Nru gsl-doc-1.16/doc/regularized.eps gsl-doc-2.3/doc/regularized.eps
--- gsl-doc-1.16/doc/regularized.eps	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/regularized.eps	2016-10-27 11:20:46.000000000 +0000
@@ -0,0 +1,1857 @@
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diff -Nru gsl-doc-1.16/doc/rng.texi gsl-doc-2.3/doc/rng.texi
--- gsl-doc-1.16/doc/rng.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/rng.texi	2015-11-10 19:35:58.000000000 +0000
@@ -83,7 +83,7 @@
 generators, you do not need to know the details of what comprises the
 state, and besides that varies from algorithm to algorithm.
 
-@tpindex gsl_rng_type
+@tindex gsl_rng_type
 The random number generator library uses two special structs,
 @code{gsl_rng_type} which holds static information about each type of
 generator and @code{gsl_rng} which describes an instance of a generator
@@ -96,7 +96,7 @@
 @section Random number generator initialization
 
 @deftypefun {gsl_rng *} gsl_rng_alloc (const gsl_rng_type * @var{T})
-@tpindex gsl_rng
+@tindex gsl_rng
 This function returns a pointer to a newly-created
 instance of a random number generator of type @var{T}.
 For example, the following code creates an instance of the Tausworthe
@@ -110,8 +110,8 @@
 function returns a null pointer and the error handler is invoked with an
 error code of @code{GSL_ENOMEM}.
 
-@vrindex gsl_rng_default_seed
-@vrindex @env{GSL_RNG_SEED}
+@vindex gsl_rng_default_seed
+@vindex @env{GSL_RNG_SEED}
 @cindex @code{GSL_RNG_SEED}
 The generator is automatically initialized with the default seed,
 @code{gsl_rng_default_seed}.  This is zero by default but can be changed
@@ -282,10 +282,10 @@
 different generators and seeds without having to recompile your program.
 
 @deftypefun {const gsl_rng_type *} gsl_rng_env_setup (void)
-@vrindex @env{GSL_RNG_TYPE}
-@vrindex @env{GSL_RNG_SEED}
-@vrindex gsl_rng_default
-@vrindex gsl_rng_default_seed
+@vindex @env{GSL_RNG_TYPE}
+@vindex @env{GSL_RNG_SEED}
+@vindex gsl_rng_default
+@vindex gsl_rng_default_seed
 This function reads the environment variables @code{GSL_RNG_TYPE} and
 @code{GSL_RNG_SEED} and uses their values to set the corresponding
 library variables @code{gsl_rng_default} and
@@ -325,7 +325,7 @@
 
 @example
 $ ./a.out 
-@verbatiminclude examples/rng.out
+@verbatiminclude examples/rng.txt
 @end example
 
 @noindent
@@ -1376,7 +1376,7 @@
 
 @example
 $ ./a.out 
-@verbatiminclude examples/rngunif.out
+@verbatiminclude examples/rngunif.txt
 @end example
 
 @noindent
@@ -1389,7 +1389,7 @@
 
 @example
 $ GSL_RNG_SEED=123 GSL_RNG_TYPE=mrg ./a.out 
-@verbatiminclude examples/rngunif.2.out
+@verbatiminclude examples/rngunif2.txt
 @end example
 
 @node Random Number References and Further Reading
diff -Nru gsl-doc-1.16/doc/roots.texi gsl-doc-2.3/doc/roots.texi
--- gsl-doc-1.16/doc/roots.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/roots.texi	2015-11-03 16:21:55.000000000 +0000
@@ -116,8 +116,8 @@
 @section Initializing the Solver
 
 @deftypefun {gsl_root_fsolver *} gsl_root_fsolver_alloc (const gsl_root_fsolver_type * @var{T})
-@tpindex gsl_root_fsolver
-@tpindex gsl_root_fsolver_type
+@tindex gsl_root_fsolver
+@tindex gsl_root_fsolver_type
 This function returns a pointer to a newly allocated instance of a
 solver of type @var{T}.  For example, the following code creates an
 instance of a bisection solver,
@@ -135,8 +135,8 @@
 @end deftypefun
 
 @deftypefun {gsl_root_fdfsolver *} gsl_root_fdfsolver_alloc (const gsl_root_fdfsolver_type * @var{T})
-@tpindex gsl_root_fdfsolver
-@tpindex gsl_root_fdfsolver_type
+@tindex gsl_root_fdfsolver
+@tindex gsl_root_fdfsolver_type
 This function returns a pointer to a newly allocated instance of a
 derivative-based solver of type @var{T}.  For example, the following
 code creates an instance of a Newton-Raphson solver,
diff -Nru gsl-doc-1.16/doc/rstat.texi gsl-doc-2.3/doc/rstat.texi
--- gsl-doc-1.16/doc/rstat.texi	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/rstat.texi	2016-10-03 09:08:46.000000000 +0000
@@ -0,0 +1,276 @@
+@cindex running statistics
+@cindex online statistics
+
+This chapter describes routines for computing running statistics,
+also known as online statistics, of data. These routines are
+suitable for handling large datasets for which it may be
+inconvenient or impractical to store in memory all at once.
+The data can be processed in a single pass, one point at a time.
+Each time a data point is added to the accumulator, internal
+parameters are updated in order to compute the current mean, variance,
+standard deviation, skewness, and kurtosis. These statistics are
+exact, and are updated with numerically stable single-pass algorithms.
+The median and arbitrary quantiles are also available, however these
+calculations use algorithms which provide approximations, and grow
+more accurate as more data is added to the accumulator.
+
+The functions described in this chapter are declared in the header file
+@file{gsl_rstat.h}.
+
+@menu
+* Running Statistics Initializing the Accumulator::
+* Running Statistics Adding Data to the Accumulator::
+* Running Statistics Current Statistics::
+* Running Statistics Quantiles::      
+* Running Statistics Example programs::  
+* Running Statistics References and Further Reading::  
+@end menu
+
+@node Running Statistics Initializing the Accumulator
+@section Initializing the Accumulator
+
+@deftypefun {gsl_rstat_workspace *} gsl_rstat_alloc (void)
+This function allocates a workspace for computing running statistics.
+The size of the workspace is @math{O(1)}.
+@end deftypefun
+
+@deftypefun void gsl_rstat_free (gsl_rstat_workspace * @var{w})
+This function frees the memory associated with the workspace @var{w}.
+@end deftypefun
+
+@deftypefun int gsl_rstat_reset (gsl_rstat_workspace * @var{w})
+This function resets the workspace @var{w} to its initial state,
+so it can begin working on a new set of data.
+@end deftypefun
+
+@node Running Statistics Adding Data to the Accumulator
+@section Adding Data to the Accumulator
+
+@deftypefun int gsl_rstat_add (const double @var{x}, gsl_rstat_workspace * @var{w})
+This function adds the data point @var{x} to the statistical
+accumulator, updating calculations of the mean, variance,
+standard deviation, skewness, kurtosis, and median.
+@end deftypefun
+
+@deftypefun size_t gsl_rstat_n (gsl_rstat_workspace * @var{w})
+This function returns the number of data so far added to the accumulator.
+@end deftypefun
+
+@node Running Statistics Current Statistics
+@section Current Statistics
+
+@deftypefun double gsl_rstat_min (gsl_rstat_workspace * @var{w})
+This function returns the minimum value added to the accumulator.
+@end deftypefun
+
+@deftypefun double gsl_rstat_max (gsl_rstat_workspace * @var{w})
+This function returns the maximum value added to the accumulator.
+@end deftypefun
+
+@deftypefun double gsl_rstat_mean (gsl_rstat_workspace * @var{w})
+This function returns the mean of all data added to the accumulator,
+defined as
+@tex
+\beforedisplay
+$$
+{\Hat\mu} = {1 \over N} \sum x_i
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+\Hat\mu = (1/N) \sum x_i
+@end example
+
+@end ifinfo
+@end deftypefun
+
+@deftypefun double gsl_rstat_variance (gsl_rstat_workspace * @var{w})
+This function returns the variance of all data added to the accumulator,
+defined as
+@tex
+\beforedisplay
+$$
+{\Hat\sigma}^2 = {1 \over (N-1)} \sum (x_i - {\Hat\mu})^2
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+\Hat\sigma^2 = (1/(N-1)) \sum (x_i - \Hat\mu)^2
+@end example
+
+@end ifinfo
+@end deftypefun
+
+@deftypefun double gsl_rstat_sd (gsl_rstat_workspace * @var{w})
+This function returns the standard deviation of all data added to the
+accumulator, defined as the square root of the variance given above.
+@end deftypefun
+
+@deftypefun double gsl_rstat_sd_mean (gsl_rstat_workspace * @var{w})
+This function returns the standard deviation of the mean, defined as
+@tex
+\beforedisplay
+$$
+\Hat\sigma_{\Hat\mu} = {\Hat\sigma \over \sqrt{N}}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+sd_mean = \Hat\sigma / \sqrt@{N@}
+@end example
+
+@end ifinfo
+@end deftypefun
+
+@deftypefun double gsl_rstat_rms (gsl_rstat_workspace * @var{w})
+This function returns the root mean square of all data added to the
+accumulator, defined as
+@tex
+\beforedisplay
+$$
+rms = \sqrt{{1 \over N} \sum x_i^2}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+rms = \sqrt ( 1/N \sum x_i^2 )
+@end example
+
+@end ifinfo
+@end deftypefun
+
+@deftypefun double gsl_rstat_skew (gsl_rstat_workspace * @var{w})
+This function returns the skewness of all data added to the accumulator,
+defined as
+@tex
+\beforedisplay
+$$
+skew = {1 \over N} \sum 
+ {\left( x_i - {\Hat\mu} \over {\Hat\sigma} \right)}^3
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+skew = (1/N) \sum ((x_i - \Hat\mu)/\Hat\sigma)^3
+@end example
+
+@end ifinfo
+@end deftypefun
+
+@deftypefun double gsl_rstat_kurtosis (gsl_rstat_workspace * @var{w})
+This function returns the kurtosis of all data added to the accumulator,
+defined as
+@tex
+\beforedisplay
+$$
+kurtosis = \left( {1 \over N} \sum 
+ {\left(x_i - {\Hat\mu} \over {\Hat\sigma} \right)}^4 
+ \right) 
+ - 3
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+kurtosis = ((1/N) \sum ((x_i - \Hat\mu)/\Hat\sigma)^4)  - 3
+@end example
+
+@end ifinfo
+@end deftypefun
+
+@deftypefun double gsl_rstat_median (gsl_rstat_workspace * @var{w})
+This function returns an estimate of the median of the data added to
+the accumulator.
+@end deftypefun
+
+@node Running Statistics Quantiles
+@section Quantiles
+
+The functions in this section estimate quantiles dynamically without
+storing the entire dataset, using the algorithm of Jain and Chlamtec, 1985.
+Only five points (markers) are stored which represent the minimum
+and maximum of the data, as well as current estimates of the
+@math{p/2}-, @math{p}-, and @math{(1+p)/2}-quantiles. Each time
+a new data point is added, the marker positions and heights are
+updated.
+
+@deftypefun {gsl_rstat_quantile_workspace *} gsl_rstat_quantile_alloc (const double @var{p})
+This function allocates a workspace for the dynamic estimation of
+@var{p}-quantiles, where @var{p} is between @math{0} and @math{1}.
+The median corresponds to @math{p = 0.5}. The size of the workspace
+is @math{O(1)}.
+@end deftypefun
+
+@deftypefun void gsl_rstat_quantile_free (gsl_rstat_quantile_workspace * @var{w})
+This function frees the memory associated with the workspace @var{w}.
+@end deftypefun
+
+@deftypefun int gsl_rstat_quantile_reset (gsl_rstat_quantile_workspace * @var{w})
+This function resets the workspace @var{w} to its initial state,
+so it can begin working on a new set of data.
+@end deftypefun
+
+@deftypefun int gsl_rstat_quantile_add (const double @var{x}, gsl_rstat_quantile_workspace * @var{w})
+This function updates the estimate of the @math{p}-quantile with
+the new data point @var{x}.
+@end deftypefun
+
+@deftypefun double gsl_rstat_quantile_get (gsl_rstat_quantile_workspace * @var{w})
+This function returns the current estimate of the @math{p}-quantile.
+@end deftypefun
+
+@node Running Statistics Example programs
+@section Examples
+
+Here is a basic example of how to use the statistical functions:
+
+@example
+@verbatiminclude examples/rstat.c
+@end example
+
+The program should produce the following output,
+
+@example
+@verbatiminclude examples/rstat.txt
+@end example
+
+@noindent
+This next program estimates the lower quartile, median and upper
+quartile from 10,000 samples of a random Rayleigh distribution,
+using the @math{P^2} algorithm of Jain and Chlamtec. For
+comparison, the exact values are also computed from the sorted
+dataset.
+
+@example
+@verbatiminclude examples/rquantile.c
+@end example
+
+The program should produce the following output,
+
+@example
+@verbatiminclude examples/rquantile.txt
+@end example
+
+@node Running Statistics References and Further Reading
+@section References and Further Reading
+
+The algorithm used to dynamically estimate @math{p}-quantiles is described
+in the paper,
+@itemize @w{}
+@item
+R. Jain and I. Chlamtac.
+@cite{The P^2 algorithm for dynamic calculation of quantiles and histograms without storing observations},
+Communications of the ACM, Volume 28 (October), Number 10, 1985,
+p. 1076-1085.
+@end itemize
diff -Nru gsl-doc-1.16/doc/sort.texi gsl-doc-2.3/doc/sort.texi
--- gsl-doc-1.16/doc/sort.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/sort.texi	2015-11-09 05:23:40.000000000 +0000
@@ -301,7 +301,7 @@
 
 @example
 $ ./a.out 
-@verbatiminclude examples/sortsmall.out
+@verbatiminclude examples/sortsmall.txt
 @end example
 
 @node Sorting References and Further Reading
diff -Nru gsl-doc-1.16/doc/sparse_poisson.eps gsl-doc-2.3/doc/sparse_poisson.eps
--- gsl-doc-1.16/doc/sparse_poisson.eps	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/sparse_poisson.eps	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,1190 @@
+%!PS-Adobe-2.0 EPSF-2.0
+%%Title: sparse_poisson.eps
+%%Creator: gnuplot 4.6 patchlevel 2
+%%CreationDate: Sun Jan 31 14:49:44 2016
+%%DocumentFonts: (atend)
+%%BoundingBox: 50 50 410 302
+%%EndComments
+%%BeginProlog
+/gnudict 256 dict def
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diff -Nru gsl-doc-1.16/doc/spblas.texi gsl-doc-2.3/doc/spblas.texi
--- gsl-doc-1.16/doc/spblas.texi	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/spblas.texi	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,49 @@
+@cindex sparse BLAS
+@cindex BLAS, sparse
+
+The Sparse Basic Linear Algebra Subprograms (@sc{blas}) define a set of
+fundamental operations on vectors and sparse matrices which can be used
+to create optimized higher-level linear algebra functionality.
+GSL supports a limited number of BLAS operations for sparse matrices.
+
+@noindent
+The header file @file{gsl_spblas.h} contains the prototypes for the
+sparse BLAS functions and related declarations.
+
+@menu
+* Sparse BLAS operations::
+* Sparse BLAS References and Further Reading::
+@end menu
+
+@node Sparse BLAS operations
+@section Sparse BLAS operations
+@cindex sparse matrices, BLAS operations
+
+@deftypefun int gsl_spblas_dgemv (const CBLAS_TRANSPOSE_t TransA, const double @var{alpha}, const gsl_spmatrix * @var{A}, const gsl_vector * @var{x}, const double @var{beta}, gsl_vector * @var{y})
+This function computes the matrix-vector product and sum
+@math{y \leftarrow \alpha op(A) x + \beta y}, where
+@math{op(A) = A}, @math{A^T} for @var{TransA} = @code{CblasNoTrans},
+@code{CblasTrans}. In-place computations are not supported, so
+@var{x} and @var{y} must be distinct vectors.
+The matrix @var{A} may be in triplet or compressed format.
+@end deftypefun
+
+@deftypefun int gsl_spblas_dgemm (const double @var{alpha}, const gsl_spmatrix * @var{A}, const gsl_spmatrix * @var{B}, gsl_spmatrix * @var{C})
+This function computes the sparse matrix-matrix product
+@math{C = \alpha A B}. The matrices must be in compressed format.
+@end deftypefun
+
+@node Sparse BLAS References and Further Reading
+@section References and Further Reading
+@cindex sparse matrices, references
+
+The algorithms used by these functions are described in the
+following sources:
+
+@itemize @w{}
+@item
+T. A. Davis, Direct Methods for Sparse Linear Systems, SIAM, 2006.
+
+@item
+CSparse software library, @uref{https://www.cise.ufl.edu/research/sparse/CSparse}
+@end itemize
diff -Nru gsl-doc-1.16/doc/specfunc-bessel.texi gsl-doc-2.3/doc/specfunc-bessel.texi
--- gsl-doc-1.16/doc/specfunc-bessel.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/specfunc-bessel.texi	2015-11-03 16:21:55.000000000 +0000
@@ -405,7 +405,7 @@
 
 @deftypefun int gsl_sf_bessel_il_scaled_array (int @var{lmax}, double @var{x}, double @var{result_array}[])
 This routine computes the values of the scaled regular modified
-cylindrical Bessel functions @math{\exp(-|x|) i_l(x)} for @math{l} from
+spherical Bessel functions @math{\exp(-|x|) i_l(x)} for @math{l} from
 0 to @var{lmax} inclusive for @c{$lmax \geq 0$}
 @math{lmax >= 0}, storing the results in
 the array @var{result_array}. 
diff -Nru gsl-doc-1.16/doc/specfunc-ellint.texi gsl-doc-2.3/doc/specfunc-ellint.texi
--- gsl-doc-1.16/doc/specfunc-ellint.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/specfunc-ellint.texi	2015-11-03 16:21:55.000000000 +0000
@@ -142,25 +142,24 @@
 @comment Exceptional Return Values: GSL_EDOM
 @end deftypefun
 
-@deftypefun double gsl_sf_ellint_D (double @var{phi}, double @var{k}, double @var{n}, gsl_mode_t @var{mode})
-@deftypefunx int gsl_sf_ellint_D_e (double @var{phi}, double @var{k}, double @var{n}, gsl_mode_t @var{mode}, gsl_sf_result * @var{result})
+@deftypefun double gsl_sf_ellint_D (double @var{phi}, double @var{k}, gsl_mode_t @var{mode})
+@deftypefunx int gsl_sf_ellint_D_e (double @var{phi}, double @var{k}, gsl_mode_t @var{mode}, gsl_sf_result * @var{result})
 These functions compute the incomplete elliptic integral
 @math{D(\phi,k)} which is defined through the Carlson form @math{RD(x,y,z)}
 by the following relation, 
 @tex
 \beforedisplay
 $$
-D(\phi,k,n) = {1 \over 3} (\sin \phi)^3 RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1).
+D(\phi,k) = {1 \over 3} (\sin \phi)^3 RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1).
 $$
 \afterdisplay
 @end tex
 @ifinfo
 
 @example
-D(\phi,k,n) = (1/3)(\sin(\phi))^3 RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1).
+D(\phi,k) = (1/3)(\sin(\phi))^3 RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1).
 @end example
 @end ifinfo
-The argument @var{n} is not used and will be removed in a future release.
 
 @comment Exceptional Return Values: GSL_EDOM
 @end deftypefun
diff -Nru gsl-doc-1.16/doc/specfunc-legendre.texi gsl-doc-2.3/doc/specfunc-legendre.texi
--- gsl-doc-1.16/doc/specfunc-legendre.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/specfunc-legendre.texi	2015-11-03 16:21:55.000000000 +0000
@@ -84,17 +84,233 @@
 @node Associated Legendre Polynomials and Spherical Harmonics
 @subsection Associated Legendre Polynomials and Spherical Harmonics
 
-The following functions compute the associated Legendre Polynomials
-@math{P_l^m(x)}.  Note that this function grows combinatorially with
-@math{l} and can overflow for @math{l} larger than about 150.  There is
-no trouble for small @math{m}, but overflow occurs when @math{m} and
-@math{l} are both large.  Rather than allow overflows, these functions
-refuse to calculate @math{P_l^m(x)} and return @code{GSL_EOVRFLW} when
-they can sense that @math{l} and @math{m} are too big.
-
-If you want to calculate a spherical harmonic, then @emph{do not} use
-these functions.  Instead use @code{gsl_sf_legendre_sphPlm} below,
-which uses a similar recursion, but with the normalized functions.
+The following functions compute the associated Legendre polynomials
+@math{P_l^m(x)} which are solutions of the differential equation
+@tex
+\beforedisplay
+$$
+(1 - x^2) {d^2 \over dx^2} P_l^m(x) - 2x {d \over dx} P_l^m(x) +
+\left( l(l+1) - {m^2 \over 1 - x^2} \right) P_l^m(x) = 0
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+(1 - x^2) d^2 P_l^m(x) / dx^2 P_l^m(x) - 2x d/dx P_l^m(x) +
+( l(l+1) - m^2 / (1 - x^2) ) P_l^m(x) = 0
+@end example
+
+@end ifinfo
+where the degree @math{l} and order @math{m} satisfy @math{0 \le l} and
+@math{0 \le m \le l}.
+The functions @math{P_l^m(x)} grow combinatorially with
+@math{l} and can overflow for @math{l} larger than about 150.
+Alternatively, one may calculate normalized associated Legendre
+polynomials. There are a number of different normalization conventions,
+and these
+functions can be stably computed up to degree and order 2700. The
+following normalizations are provided:
+@table @code
+@item Schmidt semi-normalization
+Schmidt semi-normalized associated Legendre polynomials are often
+used in the magnetics community and are defined as
+@tex
+\beforedisplay
+$$
+\eqalign{
+S_l^0(x) &= P_l^0(x) \cr 
+S_l^m(x) &= (-1)^m \sqrt{2 {(l-m)! \over (l+m)!}} P_l^m(x), m > 0 
+}
+$$
+\afterdisplay
+@end tex 
+@ifinfo
+@example
+S_l^0(x) = P_l^0(x)
+S_l^m(x) = (-1)^m \sqrt((2(l-m)! / (l+m)!)) P_l^m(x), m > 0 
+@end example
+@end ifinfo
+The factor of @math{(-1)^m} is called the Condon-Shortley phase
+factor and can be excluded if desired by setting the parameter
+@code{csphase = 1} in the functions below.
+
+@item Spherical Harmonic Normalization
+The associated Legendre polynomials suitable for calculating spherical
+harmonics are defined as
+@tex
+\beforedisplay
+$$
+Y_l^m(x) = (-1)^m \sqrt{{2l + 1 \over 4 \pi} {(l-m)! \over (l+m)!}} P_l^m(x)
+$$
+\afterdisplay
+@end tex 
+@ifinfo
+@example
+Y_l^m(x) = (-1)^m \sqrt((2l + 1) * (l-m)! / (4 \pi) / (l+m)!) P_l^m(x)
+@end example
+@end ifinfo
+where again the phase factor @math{(-1)^m} can be included or excluded
+if desired.
+
+@item Full Normalization
+The fully normalized associated Legendre polynomials are defined as
+@tex
+\beforedisplay
+$$
+N_l^m(x) = (-1)^m \sqrt{(l + {1 \over 2}) {(l-m)! \over (l+m)!}} P_l^m(x)
+$$
+\afterdisplay
+@end tex 
+@ifinfo
+@example
+N_l^m(x) = (-1)^m \sqrt((l + 1/2) * (l-m)! / (l+m)!) P_l^m(x)
+@end example
+@end ifinfo
+and have the property
+@tex
+\beforedisplay
+$$
+\int_{-1}^1 N_l^m(x)^2 dx = 1
+$$
+\afterdisplay
+@end tex 
+@ifinfo
+@example
+\int_(-1)^1 ( N_l^m(x) )^2 dx = 1
+@end example
+@end ifinfo
+
+@end table
+The normalized associated Legendre routines below use a recurrence
+relation which is stable up to a degree and order of about 2700.
+Beyond this, the computed functions could suffer from underflow
+leading to incorrect results. Routines are provided to compute
+first and second derivatives
+@math{dP_l^m(x)/dx} and @math{d^2 P_l^m(x)/dx^2} as well as their alternate
+versions @math{d P_l^m(\cos{\theta})/d\theta} and
+@math{d^2 P_l^m(\cos{\theta})/d\theta^2}. While there is a simple
+scaling relationship between the two forms, the derivatives
+involving @math{\theta} are heavily used in spherical harmonic
+expansions and so these routines are also provided.
+
+In the functions below, a parameter of type @code{gsl_sf_legendre_t}
+specifies the type of normalization to use. The possible values are
+@table @code
+@item GSL_SF_LEGENDRE_NONE
+This specifies the computation of the unnormalized associated
+Legendre polynomials @math{P_l^m(x)}.
+
+@item GSL_SF_LEGENDRE_SCHMIDT
+This specifies the computation of the Schmidt semi-normalized associated
+Legendre polynomials @math{S_l^m(x)}.
+
+@item GSL_SF_LEGENDRE_SPHARM
+This specifies the computation of the spherical harmonic associated
+Legendre polynomials @math{Y_l^m(x)}.
+
+@item GSL_SF_LEGENDRE_FULL
+This specifies the computation of the fully normalized associated
+Legendre polynomials @math{N_l^m(x)}.
+@end table
+
+@deftypefun int gsl_sf_legendre_array (const gsl_sf_legendre_t @var{norm}, const size_t @var{lmax}, const double @var{x}, double @var{result_array}[])
+@deftypefunx int gsl_sf_legendre_array_e (const gsl_sf_legendre_t @var{norm}, const size_t @var{lmax}, const double @var{x}, const double @var{csphase}, double @var{result_array}[])
+These functions calculate all normalized associated Legendre
+polynomials for @math{0 \le l \le lmax} and
+@math{0 \le m \le l} for
+@c{$|x| \le 1$}
+@math{|x| <= 1}.
+The @var{norm} parameter specifies which normalization is used.
+The normalized @math{P_l^m(x)} values are stored in @var{result_array}, whose
+minimum size can be obtained from calling @code{gsl_sf_legendre_array_n}.
+The array index of @math{P_l^m(x)} is obtained from calling
+@code{gsl_sf_legendre_array_index(l, m)}. To include or exclude
+the Condon-Shortley phase factor of @math{(-1)^m}, set the parameter
+@var{csphase} to either @math{-1} or @math{1} respectively in the
+@code{_e} function. This factor is included by default.
+@end deftypefun
+
+@deftypefun int gsl_sf_legendre_deriv_array (const gsl_sf_legendre_t @var{norm}, const size_t @var{lmax}, const double @var{x}, double @var{result_array}[], double @var{result_deriv_array}[])
+@deftypefunx int gsl_sf_legendre_deriv_array_e (const gsl_sf_legendre_t @var{norm}, const size_t @var{lmax}, const double @var{x}, const double @var{csphase}, double @var{result_array}[], double @var{result_deriv_array}[])
+These functions calculate all normalized associated Legendre
+functions and their first derivatives up to degree @var{lmax} for
+@c{$|x| < 1$}
+@math{|x| < 1}.
+The parameter @var{norm} specifies the normalization used. The
+normalized @math{P_l^m(x)} values and their derivatives
+@math{dP_l^m(x)/dx} are stored in @var{result_array} and
+@var{result_deriv_array} respectively.
+To include or exclude
+the Condon-Shortley phase factor of @math{(-1)^m}, set the parameter
+@var{csphase} to either @math{-1} or @math{1} respectively in the
+@code{_e} function. This factor is included by default.
+@end deftypefun
+
+@deftypefun int gsl_sf_legendre_deriv_alt_array (const gsl_sf_legendre_t @var{norm}, const size_t @var{lmax}, const double @var{x}, double @var{result_array}[], double @var{result_deriv_array}[])
+@deftypefunx int gsl_sf_legendre_deriv_alt_array_e (const gsl_sf_legendre_t @var{norm}, const size_t @var{lmax}, const double @var{x}, const double @var{csphase}, double @var{result_array}[], double @var{result_deriv_array}[])
+These functions calculate all normalized associated Legendre
+functions and their (alternate) first derivatives up to degree @var{lmax} for
+@c{$|x| < 1$}
+@math{|x| < 1}.
+The normalized @math{P_l^m(x)} values and their derivatives
+@math{dP_l^m(\cos{\theta})/d\theta} are stored in @var{result_array} and
+@var{result_deriv_array} respectively.
+To include or exclude
+the Condon-Shortley phase factor of @math{(-1)^m}, set the parameter
+@var{csphase} to either @math{-1} or @math{1} respectively in the
+@code{_e} function. This factor is included by default.
+@end deftypefun
+
+@deftypefun int gsl_sf_legendre_deriv2_array (const gsl_sf_legendre_t @var{norm}, const size_t @var{lmax}, const double @var{x}, double @var{result_array}[], double @var{result_deriv_array}[], double @var{result_deriv2_array}[])
+@deftypefunx int gsl_sf_legendre_deriv2_array_e (const gsl_sf_legendre_t @var{norm}, const size_t @var{lmax}, const double @var{x}, const double @var{csphase}, double @var{result_array}[], double @var{result_deriv_array}[], double @var{result_deriv2_array}[])
+These functions calculate all normalized associated Legendre
+functions and their first and second derivatives up to degree @var{lmax} for
+@c{$|x| < 1$}
+@math{|x| < 1}.
+The parameter @var{norm} specifies the normalization used. The
+normalized @math{P_l^m(x)}, their first derivatives
+@math{dP_l^m(x)/dx}, and their second derivatives
+@math{d^2 P_l^m(x)/dx^2} are stored in @var{result_array},
+@var{result_deriv_array}, and @var{result_deriv2_array} respectively.
+To include or exclude
+the Condon-Shortley phase factor of @math{(-1)^m}, set the parameter
+@var{csphase} to either @math{-1} or @math{1} respectively in the
+@code{_e} function. This factor is included by default.
+@end deftypefun
+
+@deftypefun int gsl_sf_legendre_deriv2_alt_array (const gsl_sf_legendre_t @var{norm}, const size_t @var{lmax}, const double @var{x}, double @var{result_array}[], double @var{result_deriv_array}[], double @var{result_deriv2_array}[])
+@deftypefunx int gsl_sf_legendre_deriv2_alt_array_e (const gsl_sf_legendre_t @var{norm}, const size_t @var{lmax}, const double @var{x}, const double @var{csphase}, double @var{result_array}[], double @var{result_deriv_array}[], double @var{result_deriv2_array}[])
+These functions calculate all normalized associated Legendre
+functions and their (alternate) first and second derivatives up to degree
+@var{lmax} for
+@c{$|x| < 1$}
+@math{|x| < 1}.
+The parameter @var{norm} specifies the normalization used. The
+normalized @math{P_l^m(x)}, their first derivatives
+@math{dP_l^m(\cos{\theta})/d\theta}, and their second derivatives
+@math{d^2 P_l^m(\cos{\theta})/d\theta^2} are stored in @var{result_array},
+@var{result_deriv_array}, and @var{result_deriv2_array} respectively.
+To include or exclude
+the Condon-Shortley phase factor of @math{(-1)^m}, set the parameter
+@var{csphase} to either @math{-1} or @math{1} respectively in the
+@code{_e} function. This factor is included by default.
+@end deftypefun
+
+@deftypefun size_t gsl_sf_legendre_array_n (const size_t @var{lmax})
+This function returns the minimum array size for maximum degree @var{lmax}
+needed for the array versions of the associated Legendre functions.
+Size is calculated as the total number of @math{P_l^m(x)} functions,
+plus extra space for precomputing multiplicative factors used in the
+recurrence relations.
+@end deftypefun
+
+@deftypefun size_t gsl_sf_legendre_array_index (const size_t @var{l}, const size_t @var{m})
+This function returns the index into @var{result_array},
+@var{result_deriv_array}, or @var{result_deriv2_array} corresponding
+to @math{P_l^m(x)}, @math{P_l^{'m}(x)}, or @math{P_l^{''m}(x)}. The
+index is given by @math{l(l+1)/2 + m}.
+@end deftypefun
 
 @deftypefun double gsl_sf_legendre_Plm (int @var{l}, int @var{m}, double @var{x})
 @deftypefunx int gsl_sf_legendre_Plm_e (int @var{l}, int @var{m}, double @var{x}, gsl_sf_result * @var{result})
@@ -106,18 +322,6 @@
 @comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW
 @end deftypefun
 
-@deftypefun int gsl_sf_legendre_Plm_array (int @var{lmax}, int @var{m}, double @var{x}, double @var{result_array}[])
-@deftypefunx int gsl_sf_legendre_Plm_deriv_array (int @var{lmax}, int @var{m}, double @var{x}, double @var{result_array}[], double @var{result_deriv_array}[])
-These functions compute arrays of Legendre polynomials
-@math{P_l^m(x)} and derivatives @math{dP_l^m(x)/dx},
-for @c{$m \ge 0$}
-@math{m >= 0}, @c{$l = |m|, \dots, lmax$}
-@math{l = |m|, ..., lmax}, @c{$|x| \le 1$}
-@math{|x| <= 1}.
-@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW
-@end deftypefun
-
-
 @deftypefun double gsl_sf_legendre_sphPlm (int @var{l}, int @var{m}, double @var{x})
 @deftypefunx int gsl_sf_legendre_sphPlm_e (int @var{l}, int @var{m}, double @var{x}, gsl_sf_result * @var{result})
 These routines compute the normalized associated Legendre polynomial
@@ -131,23 +335,23 @@
 @comment Exceptional Return Values: GSL_EDOM
 @end deftypefun
 
+@deftypefun int gsl_sf_legendre_Plm_array (int @var{lmax}, int @var{m}, double @var{x}, double @var{result_array}[])
+@deftypefunx int gsl_sf_legendre_Plm_deriv_array (int @var{lmax}, int @var{m}, double @var{x}, double @var{result_array}[], double @var{result_deriv_array}[])
+These functions are now deprecated and will be removed in a future
+release; see @code{gsl_sf_legendre_array} and
+@code{gsl_sf_legendre_deriv_array}.
+@end deftypefun
+
 @deftypefun int gsl_sf_legendre_sphPlm_array (int @var{lmax}, int @var{m}, double @var{x}, double @var{result_array}[])
 @deftypefunx int gsl_sf_legendre_sphPlm_deriv_array (int @var{lmax}, int @var{m}, double @var{x}, double @var{result_array}[], double @var{result_deriv_array}[])
-These functions compute arrays of normalized associated Legendre functions
-@c{$\sqrt{(2l+1)/(4\pi)} \sqrt{(l-m)!/(l+m)!} P_l^m(x)$}
-@math{\sqrt@{(2l+1)/(4\pi)@} \sqrt@{(l-m)!/(l+m)!@} P_l^m(x)},
-and derivatives,
-for @c{$m \ge 0$}
-@math{m >= 0}, @c{$l = |m|, \dots, lmax$}
-@math{l = |m|, ..., lmax}, @c{$|x| \le 1$}
-@math{|x| <= 1.0}
-@comment Exceptional Return Values: GSL_EDOM
+These functions are now deprecated and will be removed in a future
+release; see @code{gsl_sf_legendre_array} and
+@code{gsl_sf_legendre_deriv_array}.
 @end deftypefun
 
 @deftypefun int gsl_sf_legendre_array_size (const int @var{lmax}, const int @var{m})
-This function returns the size of @var{result_array}[] needed for the array
-versions of @math{P_l^m(x)}, @math{@var{lmax} - @var{m} + 1}.  @inlinefn{}
-@comment Exceptional Return Values: none
+This function is now deprecated and will be removed in a future
+release.
 @end deftypefun
 
 @node Conical Functions
diff -Nru gsl-doc-1.16/doc/specfunc-mathieu.texi gsl-doc-2.3/doc/specfunc-mathieu.texi
--- gsl-doc-1.16/doc/specfunc-mathieu.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/specfunc-mathieu.texi	2015-11-03 16:21:55.000000000 +0000
@@ -170,7 +170,7 @@
 routines require a preallocated workspace.
 
 @deftypefun {gsl_sf_mathieu_workspace *} gsl_sf_mathieu_alloc (size_t @var{n}, double @var{qmax})
-@tpindex gsl_sf_mathieu_workspace
+@tindex gsl_sf_mathieu_workspace
 This function returns a workspace for the array versions of the
 Mathieu routines.  The arguments @var{n} and @var{qmax} specify the
 maximum order and @math{q}-value of Mathieu functions which can be
@@ -190,8 +190,10 @@
 @subsection Mathieu Function Characteristic Values
 @cindex Mathieu Function Characteristic Values
 
-@deftypefun int gsl_sf_mathieu_a (int @var{n}, double @var{q}, gsl_sf_result * @var{result})
-@deftypefunx int gsl_sf_mathieu_b (int @var{n}, double @var{q}, gsl_sf_result * @var{result})
+@deftypefun int gsl_sf_mathieu_a (int @var{n}, double @var{q})
+@deftypefunx int gsl_sf_mathieu_a_e (int @var{n}, double @var{q}, gsl_sf_result * @var{result})
+@deftypefunx int gsl_sf_mathieu_b (int @var{n}, double @var{q})
+@deftypefunx int gsl_sf_mathieu_b_e (int @var{n}, double @var{q}, gsl_sf_result * @var{result})
 These routines compute the characteristic values @math{a_n(q)},
 @math{b_n(q)} of the Mathieu functions @math{ce_n(q,x)} and
 @math{se_n(q,x)}, respectively.
@@ -210,8 +212,10 @@
 @cindex @math{ce(q,x)}, Mathieu function
 @cindex @math{se(q,x)}, Mathieu function
 
-@deftypefun int gsl_sf_mathieu_ce (int @var{n}, double @var{q}, double @var{x}, gsl_sf_result * @var{result})
-@deftypefunx int gsl_sf_mathieu_se (int @var{n}, double @var{q}, double @var{x}, gsl_sf_result * @var{result})
+@deftypefun int gsl_sf_mathieu_ce (int @var{n}, double @var{q}, double @var{x})
+@deftypefunx int gsl_sf_mathieu_ce_e (int @var{n}, double @var{q}, double @var{x}, gsl_sf_result * @var{result})
+@deftypefunx int gsl_sf_mathieu_se (int @var{n}, double @var{q}, double @var{x})
+@deftypefunx int gsl_sf_mathieu_se_e (int @var{n}, double @var{q}, double @var{x}, gsl_sf_result * @var{result})
 These routines compute the angular Mathieu functions @math{ce_n(q,x)}
 and @math{se_n(q,x)}, respectively.
 @end deftypefun
@@ -228,8 +232,10 @@
 @subsection Radial Mathieu Functions
 @cindex Radial Mathieu Functions
 
-@deftypefun int gsl_sf_mathieu_Mc (int @var{j}, int @var{n}, double @var{q}, double @var{x}, gsl_sf_result * @var{result})
-@deftypefunx int gsl_sf_mathieu_Ms (int @var{j}, int @var{n}, double @var{q}, double @var{x}, gsl_sf_result * @var{result})
+@deftypefun int gsl_sf_mathieu_Mc (int @var{j}, int @var{n}, double @var{q}, double @var{x})
+@deftypefunx int gsl_sf_mathieu_Mc_e (int @var{j}, int @var{n}, double @var{q}, double @var{x}, gsl_sf_result * @var{result})
+@deftypefunx int gsl_sf_mathieu_Ms (int @var{j}, int @var{n}, double @var{q}, double @var{x})
+@deftypefunx int gsl_sf_mathieu_Ms_e (int @var{j}, int @var{n}, double @var{q}, double @var{x}, gsl_sf_result * @var{result})
 These routines compute the radial @var{j}-th kind Mathieu functions
 @c{$Mc_n^{(j)}(q,x)$}
 @math{Mc_n^@{(j)@}(q,x)} and 
diff -Nru gsl-doc-1.16/doc/specfunc.texi gsl-doc-2.3/doc/specfunc.texi
--- gsl-doc-1.16/doc/specfunc.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/specfunc.texi	2015-11-09 05:23:40.000000000 +0000
@@ -91,8 +91,8 @@
 @section The gsl_sf_result struct
 @cindex gsl_sf_result
 @cindex gsl_sf_result_e10
-@tpindex gsl_sf_result
-@tpindex gsl_sf_result_e10
+@tindex gsl_sf_result
+@tindex gsl_sf_result_e10
 
 The error handling form of the special functions always calculate an
 error estimate along with the value of the result.  Therefore,
@@ -288,7 +288,7 @@
 
 @example
 $ ./a.out 
-@verbatiminclude examples/specfun_e.out
+@verbatiminclude examples/specfun_e.txt
 @end example
 
 @noindent
@@ -305,7 +305,7 @@
 
 @example
 $ ./a.out 
-@verbatiminclude examples/specfun.out
+@verbatiminclude examples/specfun.txt
 @end example
 
 
@@ -353,6 +353,12 @@
 Y.Y. Luke, Algorithms for the Computation of Mathematical Functions, Academic
 Press, New York (1977).
 
+@item
+S. A. Holmes and W. E. Featherstone, A unified approach to the Clenshaw
+summation and the recursive computation of very high degree and order
+normalised associated Legendre functions, Journal of Geodesy, 76,
+pg. 279-299, 2002.
+
 @comment @item
 @comment Fermi-Dirac functions of orders @math{-1/2}, @math{1/2}, @math{3/2}, and
 @comment @math{5/2}.  @cite{ACM Trans. Math. Soft.}, vol. 24, 1998, 1-12.
diff -Nru gsl-doc-1.16/doc/splinalg.texi gsl-doc-2.3/doc/splinalg.texi
--- gsl-doc-1.16/doc/splinalg.texi	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/splinalg.texi	2016-01-31 21:50:21.000000000 +0000
@@ -0,0 +1,296 @@
+@cindex sparse linear algebra
+@cindex linear algebra, sparse
+
+This chapter describes functions for solving sparse linear systems
+of equations. The library provides linear algebra routines which
+operate directly on the @code{gsl_spmatrix} and @code{gsl_vector}
+objects.
+
+@noindent
+The functions described in this chapter are declared in the header file
+@file{gsl_splinalg.h}.
+
+@menu
+* Overview of Sparse Linear Algebra::
+* Sparse Iterative Solvers::
+* Sparse Linear Algebra Examples::
+* Sparse Linear Algebra References and Further Reading::
+@end menu
+
+@node Overview of Sparse Linear Algebra
+@section Overview
+@cindex sparse linear algebra, overview
+
+This chapter is primarily concerned with the solution of the
+linear system
+@tex
+\beforedisplay
+$$
+A x = b
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+A x = b
+@end example
+@end ifinfo
+where @math{A} is a general square @math{n}-by-@math{n} non-singular
+sparse matrix, @math{x} is an unknown @math{n}-by-@math{1} vector, and
+@math{b} is a given @math{n}-by-1 right hand side vector. There exist
+many methods for solving such sparse linear systems, which broadly
+fall into either direct or iterative categories. Direct methods include
+LU and QR decompositions, while iterative methods start with an
+initial guess for the vector @math{x} and update the guess through
+iteration until convergence. GSL does not currently provide any
+direct sparse solvers.
+
+@node Sparse Iterative Solvers
+@section Sparse Iterative Solvers
+@cindex sparse matrices, iterative solvers
+@cindex sparse linear algebra, iterative solvers
+@cindex sparse, iterative solvers
+
+@menu
+* Sparse Iterative Solver Overview::
+* Sparse Iterative Solvers Types::
+* Iterating the Sparse Linear System::
+@end menu
+
+@node Sparse Iterative Solver Overview
+@subsection Overview
+
+Many practical iterative methods of solving large @math{n}-by-@math{n}
+sparse linear systems involve projecting an approximate solution for
+@var{x} onto a subspace of @math{{\bf R}^n}. If we define a @math{m}-dimensional
+subspace @math{{\cal K}} as the subspace of approximations to the solution
+@var{x}, then @math{m} constraints must be imposed to determine
+the next approximation. These @math{m} constraints define another
+@math{m}-dimensional subspace denoted by @math{{\cal L}}. The
+subspace dimension @math{m} is typically chosen to be much smaller than
+@math{n} in order to reduce the computational
+effort needed to generate the next approximate solution vector.
+The many iterative algorithms which exist differ mainly
+in their choice of @math{{\cal K}} and @math{{\cal L}}.
+
+@node Sparse Iterative Solvers Types
+@subsection Types of Sparse Iterative Solvers
+
+The sparse linear algebra library provides the following types
+of iterative solvers:
+
+@deffn {Sparse Iterative Type} gsl_splinalg_itersolve_gmres
+@cindex gmres
+This specifies the Generalized Minimum Residual Method (GMRES).
+This is a projection method using @math{{\cal K} = {\cal K}_m}
+and @math{{\cal L} = A {\cal K}_m} where @math{{\cal K}_m} is
+the @math{m}-th Krylov subspace
+@tex
+\beforedisplay
+$$
+{\cal K}_m = span \left\{ r_0, A r_0, ..., A^{m-1} r_0 \right\}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+K_m = span( r_0, A r_0, ..., A^(m-1) r_0)
+@end example
+@end ifinfo
+and @math{r_0 = b - A x_0} is the residual vector of the initial guess
+@math{x_0}. If @math{m} is set equal to @math{n}, then the Krylov
+subspace is @math{{\bf R}^n} and GMRES will provide the exact solution
+@var{x}.  However, the goal is for the method to arrive at a very good
+approximation to @var{x} using a much smaller subspace @math{{\cal K}_m}. By
+default, the GMRES method selects @math{m = MIN(n,10)} but the user
+may specify a different value for @math{m}. The GMRES storage
+requirements grow as @math{O(n(m+1))} and the number of flops
+grow as @math{O(4 m^2 n - 4 m^3 / 3)}.
+
+In the below function @code{gsl_splinalg_itersolve_iterate}, one
+GMRES iteration is defined as projecting the approximate solution
+vector onto each Krylov subspace @math{{\cal K}_1, ..., {\cal K}_m},
+and so @math{m} can be kept smaller by "restarting" the method
+and calling @code{gsl_splinalg_itersolve_iterate} multiple times,
+providing the updated approximation @var{x} to each new call. If
+the method is not adequately converging, the user may try increasing
+the parameter @math{m}.
+
+GMRES is considered a robust general purpose iterative solver, however
+there are cases where the method stagnates if the matrix is not
+positive-definite and fails to reduce the residual until the very last
+projection onto the subspace @math{{\cal K}_n = {\bf R}^n}. In these
+cases, preconditioning the linear system can help, but GSL does not
+currently provide any preconditioners.
+@end deffn
+
+@node Iterating the Sparse Linear System
+@subsection Iterating the Sparse Linear System
+
+The following functions are provided to allocate storage for the
+sparse linear solvers and iterate the system to a solution.
+
+@deftypefun {gsl_splinalg_itersolve *} gsl_splinalg_itersolve_alloc (const gsl_splinalg_itersolve_type * @var{T}, const size_t @var{n}, const size_t @var{m})
+This function allocates a workspace for the iterative solution of
+@var{n}-by-@var{n} sparse matrix systems. The iterative solver type
+is specified by @var{T}. The argument @var{m} specifies the size
+of the solution candidate subspace @math{{\cal K}_m}. The dimension
+@var{m} may be set to 0 in which case a reasonable default value is used.
+@end deftypefun
+
+@deftypefun void gsl_splinalg_itersolve_free (gsl_splinalg_itersolve * @var{w})
+This function frees the memory associated with the workspace @var{w}.
+@end deftypefun
+
+@deftypefun {const char *} gsl_splinalg_itersolve_name (const gsl_splinalg_itersolve * @var{w})
+This function returns a string pointer to the name of the solver.
+@end deftypefun
+
+@deftypefun int gsl_splinalg_itersolve_iterate (const gsl_spmatrix *@var{A}, const gsl_vector *@var{b}, const double @var{tol}, gsl_vector *@var{x}, gsl_splinalg_itersolve *@var{w})
+This function performs one iteration of the iterative method for
+the sparse linear system specfied by the matrix @var{A}, right hand
+side vector @var{b} and solution vector @var{x}. On input, @var{x}
+must be set to an initial guess for the solution. On output,
+@var{x} is updated to give the current solution estimate. The
+parameter @var{tol} specifies the relative tolerance between the residual
+norm and norm of @var{b} in order to check for convergence.
+When the following condition is satisfied:
+@tex
+\beforedisplay
+$$
+|| A x - b || \le tol \times || b ||
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+|| A x - b || <= tol * || b ||
+@end example
+@end ifinfo
+the method has converged, the function returns @code{GSL_SUCCESS} and
+the final solution is provided in @var{x}. Otherwise, the function
+returns @code{GSL_CONTINUE} to signal that more iterations are
+required. Here, @math{|| \cdot ||} represents the Euclidean norm.
+The input matrix @var{A} may be in triplet or compressed column
+format.
+@end deftypefun
+
+@deftypefun double gsl_splinalg_itersolve_normr (const gsl_splinalg_itersolve *@var{w})
+This function returns the current residual norm
+@math{||r|| = ||A x - b||}, which is updated after each call to
+@code{gsl_splinalg_itersolve_iterate}.
+@end deftypefun
+
+@node Sparse Linear Algebra Examples
+@section Examples
+@cindex sparse linear algebra, examples
+
+This example program demonstrates the sparse linear algebra routines on
+the solution of a simple 1D Poisson equation on @math{[0,1]}:
+@tex
+\beforedisplay
+$$
+{d^2 u(x) \over dx^2} = f(x) = -\pi^2 \sin{(\pi x)}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+u''(x) = f(x) = -\pi^2 \sin(\pi x)
+@end example
+@end ifinfo
+with boundary conditions @math{u(0) = u(1) = 0}. The analytic solution of
+this simple problem is @math{u(x) = \sin{\pi x}}. We will solve this
+problem by finite differencing the left hand side to give
+@tex
+\beforedisplay
+$$
+{1 \over h^2} \left( u_{i+1} - 2 u_i + u_{i-1} \right) = f_i
+$$
+\afterdisplay
+@end tex
+@ifinfo
+@example
+1/h^2 ( u_(i+1) - 2 u_i + u_(i-1) ) = f_i
+@end example
+@end ifinfo
+Defining a grid of @math{N} points, @math{h = 1/(N-1)}. In the finite
+difference equation above, @math{u_0 = u_{N-1} = 0} are known from
+the boundary conditions, so we will only put the equations for
+@math{i = 1, ..., N-2} into the matrix system. The resulting
+@math{(N-2) \times (N-2)} matrix equation is
+@tex
+\beforedisplay
+$$
+{1 \over h^2}
+\left(
+\matrix{
+-2 & 1 & 0 & 0 & \ldots & 0 \cr
+1 & -2 & 1 & 0 & \ldots & 0 \cr
+0 & 1 & -2 & 1 & \ldots & 0 \cr
+\vdots & \vdots & \ddots & \ddots & \ddots & \vdots \cr
+0 & \ldots & \ldots & 1 & -2 & 1 \cr
+0 & \ldots & \ldots & \ldots & 1 & -2 \cr
+}
+\right)
+\left(
+\matrix{
+u_1 \cr
+u_2 \cr
+u_3 \cr
+\vdots \cr
+u_{N-3} \cr
+u_{N-2} \cr
+}
+\right) =
+\left(
+\matrix{
+f_1 \cr
+f_2 \cr
+f_3 \cr
+\vdots \cr
+f_{N-3} \cr
+f_{N-2} \cr
+}
+\right)
+$$
+\afterdisplay
+@end tex
+An example program which constructs and solves this system is given below.
+The system is solved using the iterative GMRES solver. Here is
+the output of the program:
+
+@example
+iter 0 residual = 4.297275996844e-11
+Converged
+@end example
+@noindent
+showing that the method converged in a single iteration.
+The calculated solution is shown in the following plot.
+
+@page
+@iftex
+@center @image{sparse_poisson,6in}
+@end iftex
+
+@example
+@verbatiminclude examples/poisson.c
+@end example
+
+@node Sparse Linear Algebra References and Further Reading
+@section References and Further Reading
+@cindex sparse linear algebra, references
+
+The implementation of the GMRES iterative solver closely follows
+the publications
+
+@itemize @w{}
+@item
+H. F. Walker, Implementation of the GMRES method using
+Householder transformations, SIAM J. Sci. Stat. Comput.
+9(1), 1988.
+
+@item
+Y. Saad, Iterative methods for sparse linear systems, 2nd edition,
+SIAM, 2003.
+@end itemize
diff -Nru gsl-doc-1.16/doc/spmatrix.texi gsl-doc-2.3/doc/spmatrix.texi
--- gsl-doc-1.16/doc/spmatrix.texi	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/doc/spmatrix.texi	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,445 @@
+@cindex sparse matrices
+@cindex matrices, sparse
+
+This chapter describes functions for the construction and
+manipulation of sparse matrices, matrices which are populated
+primarily with zeros and contain only a few non-zero elements.
+Sparse matrices often appear in the solution of partial
+differential equations. It is beneficial to use specialized
+data structures and algorithms for storing and working with
+sparse matrices, since dense matrix algorithms and structures
+can be very slow and use huge amounts of memory when applied
+to sparse matrices.
+
+@noindent
+The header file @file{gsl_spmatrix.h} contains the prototypes for the
+sparse matrix functions and related declarations.
+
+@menu
+* Sparse Matrices Overview::
+* Sparse Matrices Allocation::
+* Sparse Matrices Accessing Elements::
+* Sparse Matrices Initializing Elements::
+* Sparse Matrices Reading and Writing::
+* Sparse Matrices Copying::
+* Sparse Matrices Exchanging Rows and Columns::
+* Sparse Matrices Operations::
+* Sparse Matrices Properties::
+* Sparse Matrices Finding Maximum and Minimum Elements::
+* Sparse Matrices Compressed Format::
+* Sparse Matrices Conversion Between Sparse and Dense::
+* Sparse Matrices Examples::
+* Sparse Matrices References and Further Reading::
+@end menu
+
+@node Sparse Matrices Overview
+@section Overview
+@cindex sparse matrices, overview
+
+These routines provide support for constructing and manipulating
+sparse matrices in GSL, using an API similar to @code{gsl_matrix}.
+The basic structure is called @code{gsl_spmatrix}. There are
+three supported storage formats for sparse matrices: the triplet,
+compressed column storage (CCS) and compressed row storage (CRS)
+formats. The triplet format stores triplets @math{(i,j,x)} for each
+non-zero element of the matrix. This notation means that the
+@math{(i,j)} element of the matrix @math{A}
+is @math{A_{ij} = x}. Compressed column storage stores each column of
+non-zero values in the sparse matrix in a continuous memory block, keeping
+pointers to the beginning of each column in that memory block, and storing
+the row indices of each non-zero element. Compressed row storage stores
+each row of non-zero values in a continuous memory block, keeping pointers
+to the beginning of each row in the block and storing the column indices
+of each non-zero element. The triplet format is ideal
+for adding elements to the sparse matrix structure while it is being
+constructed, while the compressed storage formats are better suited for
+matrix-matrix multiplication or linear solvers.
+
+@tindex gsl_spmatrix
+@noindent
+The @code{gsl_spmatrix} structure is defined as
+
+@example
+typedef struct
+@{
+  size_t size1;
+  size_t size2;
+  size_t *i;
+  double *data;
+  size_t *p;
+  size_t nzmax;
+  size_t nz;
+  gsl_spmatrix_tree *tree_data;
+  void *work;
+  size_t sptype;
+@} gsl_spmatrix;
+@end example
+
+@noindent
+This defines a @var{size1}-by-@var{size2} sparse matrix. The number of non-zero
+elements currently in the matrix is given by @var{nz}. For the triplet
+representation, @var{i}, @var{p}, and @var{data} are arrays of size @var{nz}
+which contain the row indices, column indices, and element value, respectively.
+So if @math{data[k] = A(i,j)}, then @math{i = i[k]} and @math{j = p[k]}.
+
+@noindent
+For compressed column storage, @var{i} and @var{data} are arrays of size
+@var{nz} containing the row indices and element values, identical to the triplet
+case. @var{p} is an array of size @math{size2 + 1} where @math{p[j]} points
+to the index in @var{data} of the start of column @var{j}. Thus, if
+@math{data[k] = A(i,j)}, then @math{i = i[k]} and @math{p[j] <= k < p[j+1]}.
+
+@noindent
+For compressed row storage, @var{i} and @var{data} are arrays of size
+@var{nz} containing the column indices and element values, identical to the triplet
+case. @var{p} is an array of size @math{size1 + 1} where @math{p[i]} points
+to the index in @var{data} of the start of row @var{i}. Thus, if
+@math{data[k] = A(i,j)}, then @math{j = i[k]} and @math{p[i] <= k < p[i+1]}.
+
+@noindent
+The parameter @var{tree_data} is a binary tree structure used in the triplet
+representation, specifically a balanced AVL tree. This speeds up element
+searches and duplicate detection during the matrix assembly process.
+The parameter @var{work} is additional workspace needed for various operations like
+converting from triplet to compressed storage. @var{sptype} indicates
+the type of storage format being used (triplet, CCS or CRS).
+
+@noindent
+The compressed storage format defined above makes it very simple
+to interface with sophisticated external linear solver libraries
+which accept compressed storage input. The user can simply
+pass the arrays @var{i}, @var{p}, and @var{data} as the
+inputs to external libraries.
+
+@node Sparse Matrices Allocation
+@section Allocation
+@cindex sparse matrices, allocation
+
+The functions for allocating memory for a sparse matrix follow the style of
+@code{malloc} and @code{free}. They also perform their own error checking. If
+there is insufficient memory available to allocate a matrix then the functions
+call the GSL error handler with an error code of @code{GSL_ENOMEM} in addition
+to returning a null pointer.
+
+@deftypefun {gsl_spmatrix *} gsl_spmatrix_alloc (const size_t @var{n1}, const size_t @var{n2})
+This function allocates a sparse matrix of size @var{n1}-by-@var{n2} and
+initializes it to all zeros. If the size of the matrix is not known at allocation
+time, both @var{n1} and @var{n2} may be set to 1, and they will automatically
+grow as elements are added to the matrix. This function sets the
+matrix to the triplet representation, which is the easiest for adding
+and accessing matrix elements. This function tries to make a reasonable guess
+for the number of non-zero elements (@var{nzmax}) which will be added to the matrix by
+assuming a sparse density of @math{10\%}. The function
+@code{gsl_spmatrix_alloc_nzmax} can be used if this number is known more
+accurately. The workspace is of size @math{O(nzmax)}.
+@end deftypefun
+
+@deftypefun {gsl_spmatrix *} gsl_spmatrix_alloc_nzmax (const size_t @var{n1}, const size_t @var{n2}, const size_t @var{nzmax}, const size_t @var{sptype})
+This function allocates a sparse matrix of size @var{n1}-by-@var{n2} and
+initializes it to all zeros. If the size of the matrix is not known at allocation
+time, both @var{n1} and @var{n2} may be set to 1, and they will automatically
+grow as elements are added to the matrix. The parameter @var{nzmax} specifies
+the maximum number of non-zero elements which will be added to the matrix.
+It does not need to be precisely known in advance, since storage space will 
+automatically grow using @code{gsl_spmatrix_realloc} if @var{nzmax} is not
+large enough. Accurate knowledge of this parameter reduces the number of
+reallocation calls required. The parameter @var{sptype} specifies the
+storage format of the sparse matrix. Possible values are
+@table @code
+@item GSL_SPMATRIX_TRIPLET
+This flag specifies triplet storage.
+
+@item GSL_SPMATRIX_CCS
+This flag specifies compressed column storage.
+
+@item GSL_SPMATRIX_CRS
+This flag specifies compressed row storage.
+@end table
+The allocated @code{gsl_spmatrix} structure is of size @math{O(nzmax)}.
+@end deftypefun
+
+@deftypefun int gsl_spmatrix_realloc (const size_t @var{nzmax}, gsl_spmatrix * @var{m})
+This function reallocates the storage space for @var{m} to accomodate
+@var{nzmax} non-zero elements. It is typically called internally by
+@code{gsl_spmatrix_set} if the user wants to add more elements to the
+sparse matrix than the previously specified @var{nzmax}.
+@end deftypefun
+
+@deftypefun void gsl_spmatrix_free (gsl_spmatrix * @var{m})
+This function frees the memory associated with the sparse matrix @var{m}.
+@end deftypefun
+
+@node Sparse Matrices Accessing Elements
+@section Accessing Matrix Elements
+@cindex sparse matrices, accessing elements
+
+@deftypefun double gsl_spmatrix_get (const gsl_spmatrix * @var{m}, const size_t @var{i}, const size_t @var{j})
+This function returns element (@var{i},@var{j}) of the matrix @var{m}.
+The matrix may be in triplet or compressed format.
+@end deftypefun
+
+@deftypefun int gsl_spmatrix_set (gsl_spmatrix * @var{m}, const size_t @var{i}, const size_t @var{j}, const double @var{x})
+This function sets element (@var{i},@var{j}) of the matrix @var{m} to
+the value @var{x}. The matrix must be in triplet representation.
+@end deftypefun
+
+@deftypefun {double *} gsl_spmatrix_ptr (gsl_spmatrix * @var{m}, const size_t @var{i}, const size_t @var{j})
+This function returns a pointer to the (@var{i},@var{j}) element of the matrix @var{m}.
+If the (@var{i},@var{j}) element is not explicitly stored in the matrix,
+a null pointer is returned.
+@end deftypefun
+
+@node Sparse Matrices Initializing Elements
+@section Initializing Matrix Elements
+@cindex sparse matrices, initializing elements
+
+Since the sparse matrix format only stores the non-zero elements, it is automatically
+initialized to zero upon allocation. The function @code{gsl_spmatrix_set_zero} may
+be used to re-initialize a matrix to zero after elements have been added to it.
+
+@deftypefun int gsl_spmatrix_set_zero (gsl_spmatrix * @var{m})
+This function sets (or resets) all the elements of the matrix @var{m} to zero.
+@end deftypefun
+
+@node Sparse Matrices Reading and Writing
+@section Reading and Writing Matrices
+@cindex sparse matrices, reading
+@cindex sparse matrices, writing
+
+@deftypefun int gsl_spmatrix_fwrite (FILE * @var{stream}, const gsl_spmatrix * @var{m})
+This function writes the elements of the matrix @var{m} to the stream
+@var{stream} in binary format.  The return value is 0 for success and
+@code{GSL_EFAILED} if there was a problem writing to the file.  Since the
+data is written in the native binary format it may not be portable
+between different architectures.
+@end deftypefun
+
+@deftypefun int gsl_spmatrix_fread (FILE * @var{stream}, gsl_spmatrix * @var{m})
+This function reads into the matrix @var{m} from the open stream
+@var{stream} in binary format.  The matrix @var{m} must be preallocated
+with the correct storage format, dimensions and have a sufficiently large @code{nzmax}
+in order to read in all matrix elements, otherwise @code{GSL_EBADLEN}
+is returned. The return value is 0 for success and
+@code{GSL_EFAILED} if there was a problem reading from the file.  The
+data is assumed to have been written in the native binary format on the
+same architecture.
+@end deftypefun
+
+@deftypefun int gsl_spmatrix_fprintf (FILE * @var{stream}, const gsl_spmatrix * @var{m}, const char * @var{format})
+This function writes the elements of the matrix @var{m} line-by-line to
+the stream @var{stream} using the format specifier @var{format}, which
+should be one of the @code{%g}, @code{%e} or @code{%f} formats for
+floating point numbers.  The function returns 0 for success and
+@code{GSL_EFAILED} if there was a problem writing to the file. The
+input matrix @var{m} may be in any storage format, and the output file
+will be written in MatrixMarket format.
+@end deftypefun
+
+@deftypefun {gsl_spmatrix *} gsl_spmatrix_fscanf (FILE * @var{stream})
+This function reads sparse matrix data in the MatrixMarket format
+from the stream @var{stream} and stores it in a newly allocated matrix
+which is returned in triplet format.  The function returns 0 for success and
+@code{GSL_EFAILED} if there was a problem reading from the file. The
+user should free the returned matrix when it is no longer needed.
+@end deftypefun
+
+@node Sparse Matrices Copying
+@section Copying Matrices
+@cindex sparse matrices, copying
+
+@deftypefun int gsl_spmatrix_memcpy (gsl_spmatrix * @var{dest}, const gsl_spmatrix * @var{src})
+This function copies the elements of the sparse matrix @var{src} into
+@var{dest}. The two matrices must have the same dimensions and be in the
+same storage format.
+@end deftypefun
+
+@node Sparse Matrices Exchanging Rows and Columns
+@section Exchanging Rows and Columns
+@cindex sparse matrices, exchanging rows and columns
+
+@deftypefun int gsl_spmatrix_transpose_memcpy (gsl_spmatrix * @var{dest}, const gsl_spmatrix * @var{src})
+This function copies the transpose of the sparse matrix @var{src} into
+@var{dest}. The dimensions of @var{dest} must match the transpose of the
+matrix @var{src}. Also, both matrices must use the same sparse storage
+format.
+@end deftypefun
+
+@deftypefun int gsl_spmatrix_transpose (gsl_spmatrix * @var{m})
+This function replaces the matrix @var{m} by its transpose,
+preserving the storage format of the input matrix. Currently,
+only triplet matrix inputs are supported.
+@end deftypefun
+
+@deftypefun int gsl_spmatrix_transpose2 (gsl_spmatrix * @var{m})
+This function replaces the matrix @var{m} by its transpose, but
+changes the storage format for compressed matrix inputs. Since
+compressed column storage is the transpose of compressed row storage,
+this function simply converts a CCS matrix to CRS and vice versa.
+This is the most efficient way to transpose a compressed storage
+matrix, but the user should note that the storage format of their
+compressed matrix will change on output. For triplet matrices,
+the output matrix is also in triplet storage.
+@end deftypefun
+
+
+@node Sparse Matrices Operations
+@section Matrix Operations
+@cindex sparse matrices, operations
+
+@deftypefun int gsl_spmatrix_add (gsl_spmatrix * @var{c}, const gsl_spmatrix * @var{a}, const gsl_spmatrix * @var{b})
+This function computes the sum @math{c = a + b}. The three matrices must
+have the same dimensions and be stored in a compressed format.
+@end deftypefun
+
+@deftypefun int gsl_spmatrix_scale (gsl_spmatrix * @var{m}, const double @var{x})
+This function scales all elements of the matrix @var{m} by the constant
+factor @var{x}. The result @math{m(i,j) \leftarrow x m(i,j)} is stored in @var{m}.
+@end deftypefun
+
+@node Sparse Matrices Properties
+@section Matrix Properties
+@cindex sparse matrices, properties
+
+@deftypefun size_t gsl_spmatrix_nnz (const gsl_spmatrix * @var{m})
+This function returns the number of non-zero elements in @var{m}.
+@end deftypefun
+
+@deftypefun int gsl_spmatrix_equal (const gsl_spmatrix * @var{a}, const gsl_spmatrix * @var{b})
+This function returns 1 if the matrices @var{a} and @var{b} are equal (by comparison of
+element values) and 0 otherwise. The matrices @var{a} and @var{b} must be in the same
+sparse storage format for comparison.
+@end deftypefun
+
+@node Sparse Matrices Finding Maximum and Minimum Elements
+@section Finding Maximum and Minimum Elements
+@cindex sparse matrices, min/max elements
+
+@deftypefun int gsl_spmatrix_minmax (const gsl_spmatrix * @var{m}, double * @var{min_out}, double * @var{max_out})
+This function returns the minimum and maximum elements of the matrix
+@var{m}, storing them in @var{min_out} and @var{max_out}, and searching
+only the non-zero values.
+@end deftypefun
+
+@node Sparse Matrices Compressed Format
+@section Compressed Format
+@cindex sparse matrices, compression
+
+GSL supports compressed column storage (CCS) and compressed row storage (CRS)
+formats.
+
+@deftypefun {gsl_spmatrix *} gsl_spmatrix_ccs (const gsl_spmatrix * @var{T})
+This function creates a sparse matrix in compressed column format
+from the input sparse matrix @var{T} which must be in triplet format.
+A pointer to a newly allocated matrix is returned. The calling function
+should free the newly allocated matrix when it is no longer needed.
+@end deftypefun
+
+@deftypefun {gsl_spmatrix *} gsl_spmatrix_crs (const gsl_spmatrix * @var{T})
+This function creates a sparse matrix in compressed row format
+from the input sparse matrix @var{T} which must be in triplet format.
+A pointer to a newly allocated matrix is returned. The calling function
+should free the newly allocated matrix when it is no longer needed.
+@end deftypefun
+
+@node Sparse Matrices Conversion Between Sparse and Dense
+@section Conversion Between Sparse and Dense Matrices
+@cindex sparse matrices, conversion
+
+The @code{gsl_spmatrix} structure can be converted into the dense @code{gsl_matrix}
+format and vice versa with the following routines.
+
+@deftypefun int gsl_spmatrix_d2sp (gsl_spmatrix * @var{S}, const gsl_matrix * @var{A})
+This function converts the dense matrix @var{A} into sparse triplet format
+and stores the result in @var{S}.
+@end deftypefun
+
+@deftypefun int gsl_spmatrix_sp2d (gsl_matrix * @var{A}, const gsl_spmatrix * @var{S})
+This function converts the sparse matrix @var{S} into a dense matrix and
+stores the result in @var{A}. @var{S} must be in triplet format.
+@end deftypefun
+
+@node Sparse Matrices Examples
+@section Examples
+@cindex sparse matrices, examples
+
+The following example program builds a 5-by-4 sparse matrix
+and prints it in triplet, compressed column, and compressed
+row format. The matrix which is constructed is
+@tex
+\beforedisplay
+$$
+\left(
+\matrix{
+0 & 0 & 3.1 & 4.6 \cr
+1 & 0 & 7.2 & 0 \cr
+0 & 0 & 0 & 0 \cr
+2.1 & 2.9 & 0 & 8.5 \cr
+4.1 & 0 & 0 & 0 \cr
+}
+\right)
+$$
+\afterdisplay
+@end tex
+The output of the program is
+
+@example
+printing all matrix elements:
+A(0,0) = 0
+A(0,1) = 0
+A(0,2) = 3.1
+A(0,3) = 4.6
+A(1,0) = 1
+.
+.
+.
+A(4,0) = 4.1
+A(4,1) = 0
+A(4,2) = 0
+A(4,3) = 0
+matrix in triplet format (i,j,Aij):
+(0, 2, 3.1)
+(0, 3, 4.6)
+(1, 0, 1.0)
+(1, 2, 7.2)
+(3, 0, 2.1)
+(3, 1, 2.9)
+(3, 3, 8.5)
+(4, 0, 4.1)
+matrix in compressed column format:
+i = [ 1, 3, 4, 3, 0, 1, 0, 3, ]
+p = [ 0, 3, 4, 6, 8, ]
+d = [ 1, 2.1, 4.1, 2.9, 3.1, 7.2, 4.6, 8.5, ]
+matrix in compressed row format:
+i = [ 2, 3, 0, 2, 0, 1, 3, 0, ]
+p = [ 0, 2, 4, 4, 7, 8, ]
+d = [ 3.1, 4.6, 1, 7.2, 2.1, 2.9, 8.5, 4.1, ]
+@end example
+@noindent
+We see in the compressed column output, the data array stores
+each column contiguously, the array @math{i} stores
+the row index of the corresponding data element, and the
+array @math{p} stores the index of the start of each column in the
+data array. Similarly, for the compressed row output, the
+data array stores each row contiguously, the array @math{i}
+stores the column index of the corresponding data element, and
+the @math{p} array stores the index of the start of each row
+in the data array.
+
+@example
+@verbatiminclude examples/spmatrix.c
+@end example
+
+@node Sparse Matrices References and Further Reading
+@section References and Further Reading
+@cindex sparse matrices, references
+
+The algorithms used by these functions are described in the
+following sources:
+
+@itemize @w{}
+@item
+T. A. Davis, Direct Methods for Sparse Linear Systems, SIAM, 2006.
+
+@item
+CSparse software library, @uref{https://www.cise.ufl.edu/research/sparse/CSparse}
+@end itemize
diff -Nru gsl-doc-1.16/doc/stamp-vti gsl-doc-2.3/doc/stamp-vti
--- gsl-doc-1.16/doc/stamp-vti	2013-07-19 15:17:08.000000000 +0000
+++ gsl-doc-2.3/doc/stamp-vti	2016-12-09 00:06:07.000000000 +0000
@@ -1,4 +1,4 @@
-@set UPDATED 17 July 2013
-@set UPDATED-MONTH July 2013
-@set EDITION 1.16
-@set VERSION 1.16
+@set UPDATED 29 August 2016
+@set UPDATED-MONTH August 2016
+@set EDITION 2.3
+@set VERSION 2.3
diff -Nru gsl-doc-1.16/doc/statistics.texi gsl-doc-2.3/doc/statistics.texi
--- gsl-doc-1.16/doc/statistics.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/statistics.texi	2016-07-07 20:36:10.000000000 +0000
@@ -336,7 +336,7 @@
 @tex
 \beforedisplay
 $$
-a_1 = {\sum_{i = 1}^{n} (x_{i} - \Hat\mu) (x_{i-1} - \Hat\mu)
+a_1 = {\sum_{i = 2}^{n} (x_{i} - \Hat\mu) (x_{i-1} - \Hat\mu)
 \over
 \sum_{i = 1}^{n} (x_{i} - \Hat\mu) (x_{i} - \Hat\mu)}
 $$
@@ -345,7 +345,7 @@
 @ifinfo
 
 @example
-a_1 = @{\sum_@{i = 1@}^@{n@} (x_@{i@} - \Hat\mu) (x_@{i-1@} - \Hat\mu)
+a_1 = @{\sum_@{i = 2@}^@{n@} (x_@{i@} - \Hat\mu) (x_@{i-1@} - \Hat\mu)
        \over
        \sum_@{i = 1@}^@{n@} (x_@{i@} - \Hat\mu) (x_@{i@} - \Hat\mu)@}
 @end example
@@ -767,7 +767,7 @@
 The program should produce the following output,
 
 @example
-@verbatiminclude examples/stat.out
+@verbatiminclude examples/stat.txt
 @end example
 
 
@@ -780,7 +780,7 @@
 This program should produce the following output,
 
 @example
-@verbatiminclude examples/statsort.out
+@verbatiminclude examples/statsort.txt
 @end example
 
 @node Statistics References and Further Reading
diff -Nru gsl-doc-1.16/doc/sum.texi gsl-doc-2.3/doc/sum.texi
--- gsl-doc-1.16/doc/sum.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/sum.texi	2015-11-09 05:23:40.000000000 +0000
@@ -42,7 +42,7 @@
 does give a reliable error estimate.
 
 @deftypefun {gsl_sum_levin_u_workspace *} gsl_sum_levin_u_alloc (size_t @var{n})
-@tpindex gsl_sum_levin_u_workspace
+@tindex gsl_sum_levin_u_workspace
 This function allocates a workspace for a Levin @math{u}-transform of @var{n}
 terms.  The size of the workspace is @math{O(2n^2 + 3n)}.
 @end deftypefun
@@ -85,7 +85,7 @@
 results.
 
 @deftypefun {gsl_sum_levin_utrunc_workspace *} gsl_sum_levin_utrunc_alloc (size_t @var{n})
-@tpindex gsl_sum_levin_utrunc_workspace
+@tindex gsl_sum_levin_utrunc_workspace
 This function allocates a workspace for a Levin @math{u}-transform of @var{n}
 terms, without error estimation.  The size of the workspace is
 @math{O(3n)}.
@@ -147,7 +147,7 @@
 
 @example
 $ ./a.out 
-@verbatiminclude examples/sum.out
+@verbatiminclude examples/sum.txt
 @end example
 
 @noindent
diff -Nru gsl-doc-1.16/doc/usage.texi gsl-doc-2.3/doc/usage.texi
--- gsl-doc-1.16/doc/usage.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/usage.texi	2015-11-09 05:23:40.000000000 +0000
@@ -38,7 +38,7 @@
 the compiler and platform used---this is normal.}
 
 @example
-@verbatiminclude examples/intro.out
+@verbatiminclude examples/intro.txt
 @end example
 
 @noindent
@@ -235,8 +235,8 @@
 
 @node Inline functions
 @section Inline functions
-@vrindex @code{HAVE_INLINE}
-@vrindex @code{GSL_C99_INLINE}
+@vindex @code{HAVE_INLINE}
+@vindex @code{GSL_C99_INLINE}
 @cindex inline functions
 @cindex HAVE_INLINE
 @cindex GSL_C99_INLINE
diff -Nru gsl-doc-1.16/doc/vectors.texi gsl-doc-2.3/doc/vectors.texi
--- gsl-doc-1.16/doc/vectors.texi	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/doc/vectors.texi	2015-11-09 05:23:40.000000000 +0000
@@ -55,7 +55,7 @@
 
 @node Blocks
 @section Blocks
-@tpindex gsl_block
+@tindex gsl_block
 For consistency all memory is allocated through a @code{gsl_block}
 structure.  The structure contains two components, the size of an area of
 memory and a pointer to the memory.  The @code{gsl_block} structure looks
@@ -174,7 +174,7 @@
 Here is the output from the program,
 
 @example
-@verbatiminclude examples/block.out
+@verbatiminclude examples/block.txt
 @end example
 @comment
 
@@ -188,7 +188,7 @@
 same block.  A vector slice is a set of equally-spaced elements of an
 area of memory.
 
-@tpindex gsl_vector
+@tindex gsl_vector
 The @code{gsl_vector} structure contains five components, the
 @dfn{size}, the @dfn{stride}, a pointer to the memory where the elements
 are stored, @var{data}, a pointer to the block owned by the vector,
@@ -293,7 +293,7 @@
 the preprocessor macro @code{HAVE_INLINE} defined to use these
 functions.
 
-@vrindex @code{GSL_RANGE_CHECK_OFF}
+@vindex @code{GSL_RANGE_CHECK_OFF}
 If necessary you can turn off range checking completely without
 modifying any source files by recompiling your program with the
 preprocessor definition @code{GSL_RANGE_CHECK_OFF}.  Provided your
@@ -304,14 +304,14 @@
 penalty for using the range checking functions when range checking is
 turned off.
 
-@vrindex @code{GSL_C99_INLINE}
+@vindex @code{GSL_C99_INLINE}
 If you use a C99 compiler which requires inline functions in header
 files to be declared @code{inline} instead of @code{extern inline},
 define the macro @code{GSL_C99_INLINE} (@pxref{Inline functions}).
 With GCC this is selected automatically when compiling in C99 mode
 (@code{-std=c99}).
 
-@vrindex gsl_check_range
+@vindex gsl_check_range
 If inline functions are not used, calls to the functions
 @code{gsl_vector_get} and @code{gsl_vector_set} will link to the
 compiled versions of these functions in the library itself.  The range
@@ -321,13 +321,13 @@
 overhead, there is less benefit in disabling range checking here than
 for inline functions.
 
-@deftypefun double gsl_vector_get (const gsl_vector * @var{v}, size_t @var{i})
+@deftypefun double gsl_vector_get (const gsl_vector * @var{v}, const size_t @var{i})
 This function returns the @var{i}-th element of a vector @var{v}.  If
 @var{i} lies outside the allowed range of 0 to @math{@var{n}-1} then the error
 handler is invoked and 0 is returned.  @inlinefn{}
 @end deftypefun
 
-@deftypefun void gsl_vector_set (gsl_vector * @var{v}, size_t @var{i}, double @var{x})
+@deftypefun void gsl_vector_set (gsl_vector * @var{v}, const size_t @var{i}, double @var{x})
 This function sets the value of the @var{i}-th element of a vector
 @var{v} to @var{x}.  If @var{i} lies outside the allowed range of 0 to
 @math{@var{n}-1} then the error handler is invoked.  @inlinefn{}
@@ -410,8 +410,8 @@
 can be made which provide access to the even and odd elements of a
 vector.
 
-@tpindex gsl_vector_view
-@tpindex gsl_vector_const_view
+@tindex gsl_vector_view
+@tindex gsl_vector_const_view
 A vector view is a temporary object, stored on the stack, which can be
 used to operate on a subset of vector elements.  Vector views can be
 defined for both constant and non-constant vectors, using separate types
@@ -843,7 +843,7 @@
 generalized slice of a block.  Like a vector it represents a set of
 elements in an area of memory, but uses two indices instead of one.
 
-@tpindex gsl_matrix
+@tindex gsl_matrix
 The @code{gsl_matrix} structure contains six components, the two
 dimensions of the matrix, a physical dimension, a pointer to the memory
 where the elements of the matrix are stored, @var{data}, a pointer to
@@ -974,14 +974,14 @@
 @noindent
 where @var{tda} is the physical row-length of the matrix.
 
-@deftypefun double gsl_matrix_get (const gsl_matrix * @var{m}, size_t @var{i}, size_t @var{j})
+@deftypefun double gsl_matrix_get (const gsl_matrix * @var{m}, const size_t @var{i}, const size_t @var{j})
 This function returns the @math{(i,j)}-th element of a matrix
 @var{m}.  If @var{i} or @var{j} lie outside the allowed range of 0 to
 @math{@var{n1}-1} and 0 to @math{@var{n2}-1} then the error handler is invoked and 0
 is returned.  @inlinefn{}
 @end deftypefun
 
-@deftypefun void gsl_matrix_set (gsl_matrix * @var{m}, size_t @var{i}, size_t @var{j}, double @var{x})
+@deftypefun void gsl_matrix_set (gsl_matrix * @var{m}, const size_t @var{i}, const size_t @var{j}, double @var{x})
 This function sets the value of the @math{(i,j)}-th element of a
 matrix @var{m} to @var{x}.  If @var{i} or @var{j} lies outside the
 allowed range of 0 to @math{@var{n1}-1} and 0 to @math{@var{n2}-1} then the error
@@ -1066,8 +1066,8 @@
 
 @node Matrix views
 @subsection Matrix views
-@tpindex gsl_matrix_view
-@tpindex gsl_matrix_const_view
+@tindex gsl_matrix_view
+@tindex gsl_matrix_const_view
 
 A matrix view is a temporary object, stored on the stack, which can be
 used to operate on a subset of matrix elements.  Matrix views can be
@@ -1663,7 +1663,7 @@
 
 @example
 $ ./a.out
-@verbatiminclude examples/vectorview.out
+@verbatiminclude examples/vectorview.txt
 @end example
 
 @noindent
diff -Nru gsl-doc-1.16/doc/version.texi gsl-doc-2.3/doc/version.texi
--- gsl-doc-1.16/doc/version.texi	2013-07-19 15:17:08.000000000 +0000
+++ gsl-doc-2.3/doc/version.texi	2016-12-09 00:06:07.000000000 +0000
@@ -1,4 +1,4 @@
-@set UPDATED 17 July 2013
-@set UPDATED-MONTH July 2013
-@set EDITION 1.16
-@set VERSION 1.16
+@set UPDATED 29 August 2016
+@set UPDATED-MONTH August 2016
+@set EDITION 2.3
+@set VERSION 2.3
diff -Nru gsl-doc-1.16/eigen/francis.c gsl-doc-2.3/eigen/francis.c
--- gsl-doc-1.16/eigen/francis.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/eigen/francis.c	2016-07-07 20:36:10.000000000 +0000
@@ -27,7 +27,6 @@
 #include <gsl/gsl_vector.h>
 #include <gsl/gsl_vector_complex.h>
 #include <gsl/gsl_matrix.h>
-#include <gsl/gsl_cblas.h>
 #include <gsl/gsl_complex.h>
 #include <gsl/gsl_complex_math.h>
 
diff -Nru gsl-doc-1.16/eigen/gen.c gsl-doc-2.3/eigen/gen.c
--- gsl-doc-1.16/eigen/gen.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/eigen/gen.c	2016-08-19 15:37:27.000000000 +0000
@@ -94,7 +94,6 @@
 
 /*FIX**/
 inline static double normF (gsl_matrix * A);
-inline static void create_givens (const double a, const double b, double *c, double *s);
 
 /*
 gsl_eigen_gen_alloc()
@@ -606,7 +605,7 @@
          temp2;
   size_t j;               /* looping */
   gsl_vector_view xv, yv; /* temporary views */
-  size_t top;
+  size_t top = 0;
   size_t rows;
 
   if (w->n_iter % 10 == 0)
@@ -703,7 +702,7 @@
   temp = scale1*gsl_matrix_get(H, 0, 0) - wr1*gsl_matrix_get(R, 0, 0);
   temp2 = scale1*gsl_matrix_get(H, 1, 0);
 
-  create_givens(temp, temp2, &cs, &sn);
+  gsl_linalg_givens(temp, temp2, &cs, &sn);
   sn = -sn;
 
   for (j = 0; j < N - 1; ++j)
@@ -712,7 +711,7 @@
         {
           temp = gsl_matrix_get(H, j, j - 1);
           temp2 = gsl_matrix_get(H, j + 1, j - 1);
-          create_givens(temp, temp2, &cs, &sn);
+          gsl_linalg_givens(temp, temp2, &cs, &sn);
           sn = -sn;
 
           /* apply to column (j - 1) */
@@ -760,7 +759,7 @@
 
       temp = gsl_matrix_get(R, j + 1, j + 1);
       temp2 = gsl_matrix_get(R, j + 1, j);
-      create_givens(temp, temp2, &cs, &sn);
+      gsl_linalg_givens(temp, temp2, &cs, &sn);
 
       rows = GSL_MIN(j + 3, N);
 
@@ -826,7 +825,7 @@
   gsl_matrix_view m;      /* temporary view */
   double tmp;
   size_t q, r;
-  size_t top;             /* location of H in original matrix */
+  size_t top = 0;         /* location of H in original matrix */
   double scale;
   double AB11,            /* various matrix element ratios */
          AB22,
@@ -1229,7 +1228,7 @@
 gen_tri_split_top(gsl_matrix *H, gsl_matrix *R, gsl_eigen_gen_workspace *w)
 {
   const size_t N = H->size1;
-  size_t j, top;
+  size_t j, top = 0;
   double cs, sn;
   gsl_vector_view xv, yv;
 
@@ -1238,10 +1237,10 @@
 
   j = 0;
 
-  create_givens(gsl_matrix_get(H, j, j),
-                gsl_matrix_get(H, j + 1, j),
-                &cs,
-                &sn);
+  gsl_linalg_givens(gsl_matrix_get(H, j, j),
+                    gsl_matrix_get(H, j + 1, j),
+                    &cs,
+                    &sn);
   sn = -sn;
 
   if (w->compute_s)
@@ -1296,7 +1295,7 @@
                    gsl_eigen_gen_workspace *w)
 {
   const size_t N = H->size1;
-  size_t j, top;
+  size_t j, top = 0;
   double cs, sn;
   gsl_vector_view xv, yv;
 
@@ -1305,10 +1304,10 @@
 
   for (j = q; j < N - 1; ++j)
     {
-      create_givens(gsl_matrix_get(R, j, j + 1),
-                    gsl_matrix_get(R, j + 1, j + 1),
-                    &cs,
-                    &sn);
+      gsl_linalg_givens(gsl_matrix_get(R, j, j + 1),
+                        gsl_matrix_get(R, j + 1, j + 1),
+                        &cs,
+                        &sn);
       sn = -sn;
 
       if (w->compute_t)
@@ -1346,10 +1345,10 @@
           gsl_blas_drot(&xv.vector, &yv.vector, cs, sn);
         }
 
-      create_givens(gsl_matrix_get(H, j + 1, j),
-                    gsl_matrix_get(H, j + 1, j - 1),
-                    &cs,
-                    &sn);
+      gsl_linalg_givens(gsl_matrix_get(H, j + 1, j),
+                        gsl_matrix_get(H, j + 1, j - 1),
+                        &cs,
+                        &sn);
       sn = -sn;
 
       if (w->compute_s)
@@ -1400,17 +1399,17 @@
 gen_tri_zero_H(gsl_matrix *H, gsl_matrix *R, gsl_eigen_gen_workspace *w)
 {
   const size_t N = H->size1;
-  size_t top;
+  size_t top = 0;
   double cs, sn;
   gsl_vector_view xv, yv;
 
   if (w->needtop)
     top = gen_get_submatrix(w->H, H);
 
-  create_givens(gsl_matrix_get(H, N - 1, N - 1),
-                gsl_matrix_get(H, N - 1, N - 2),
-                &cs,
-                &sn);
+  gsl_linalg_givens(gsl_matrix_get(H, N - 1, N - 1),
+                    gsl_matrix_get(H, N - 1, N - 2),
+                    &cs,
+                    &sn);
   sn = -sn;
 
   if (w->compute_s)
@@ -1555,7 +1554,7 @@
                        double *beta, gsl_eigen_gen_workspace *w)
 {
   size_t i;
-  size_t top;
+  size_t top = 0;
 
   /*
    * it is a 1-by-1 block - the only requirement is that
@@ -1635,7 +1634,7 @@
   gsl_vector_view sv = gsl_vector_view_array(datS, 2);
   gsl_vector_view wv = gsl_vector_view_array(work, 2);
   double B11, B22;
-  size_t top;
+  size_t top = 0;
   double det;
   double cr, sr, cl, sl;
   gsl_vector_view xv, yv;
@@ -2086,31 +2085,3 @@
 
   return sum;
 }
-
-/* Generate a Givens rotation (cos,sin) which takes v=(x,y) to (|v|,0) 
-
-   From Golub and Van Loan, "Matrix Computations", Section 5.1.8 */
-
-inline static void
-create_givens (const double a, const double b, double *c, double *s)
-{
-  if (b == 0)
-    {
-      *c = 1;
-      *s = 0;
-    }
-  else if (fabs (b) > fabs (a))
-    {
-      double t = -a / b;
-      double s1 = 1.0 / sqrt (1 + t * t);
-      *s = s1;
-      *c = s1 * t;
-    }
-  else
-    {
-      double t = -b / a;
-      double c1 = 1.0 / sqrt (1 + t * t);
-      *c = c1;
-      *s = c1 * t;
-    }
-}
diff -Nru gsl-doc-1.16/eigen/gensymm.c gsl-doc-2.3/eigen/gensymm.c
--- gsl-doc-1.16/eigen/gensymm.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/eigen/gensymm.c	2016-08-30 15:14:04.000000000 +0000
@@ -136,7 +136,7 @@
       int s;
 
       /* compute Cholesky factorization of B */
-      s = gsl_linalg_cholesky_decomp(B);
+      s = gsl_linalg_cholesky_decomp1(B);
       if (s != GSL_SUCCESS)
         return s; /* B is not positive definite */
 
diff -Nru gsl-doc-1.16/eigen/gensymmv.c gsl-doc-2.3/eigen/gensymmv.c
--- gsl-doc-1.16/eigen/gensymmv.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/eigen/gensymmv.c	2016-08-30 15:14:12.000000000 +0000
@@ -147,7 +147,7 @@
       int s;
 
       /* compute Cholesky factorization of B */
-      s = gsl_linalg_cholesky_decomp(B);
+      s = gsl_linalg_cholesky_decomp1(B);
       if (s != GSL_SUCCESS)
         return s; /* B is not positive definite */
 
diff -Nru gsl-doc-1.16/eigen/Makefile.am gsl-doc-2.3/eigen/Makefile.am
--- gsl-doc-1.16/eigen/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/eigen/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -5,7 +5,7 @@
 pkginclude_HEADERS = gsl_eigen.h
 libgsleigen_la_SOURCES =  jacobi.c symm.c symmv.c nonsymm.c nonsymmv.c herm.c hermv.c gensymm.c gensymmv.c genherm.c genhermv.c gen.c genv.c sort.c francis.c schur.c
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 noinst_HEADERS =  qrstep.c
 
diff -Nru gsl-doc-1.16/eigen/Makefile.in gsl-doc-2.3/eigen/Makefile.in
--- gsl-doc-1.16/eigen/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/eigen/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -384,6 +384,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -406,7 +407,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -523,7 +527,7 @@
 noinst_LTLIBRARIES = libgsleigen.la 
 pkginclude_HEADERS = gsl_eigen.h
 libgsleigen_la_SOURCES = jacobi.c symm.c symmv.c nonsymm.c nonsymmv.c herm.c hermv.c gensymm.c gensymmv.c genherm.c genhermv.c gen.c genv.c sort.c francis.c schur.c
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 noinst_HEADERS = qrstep.c
 TESTS = $(check_PROGRAMS)
 test_LDADD = libgsleigen.la  ../test/libgsltest.la ../linalg/libgsllinalg.la ../permutation/libgslpermutation.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la  ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../sys/libgslsys.la ../err/libgslerr.la ../utils/libutils.la ../rng/libgslrng.la ../sort/libgslsort.la
diff -Nru gsl-doc-1.16/eigen/nonsymmv.c gsl-doc-2.3/eigen/nonsymmv.c
--- gsl-doc-1.16/eigen/nonsymmv.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/eigen/nonsymmv.c	2016-07-07 20:36:10.000000000 +0000
@@ -27,7 +27,6 @@
 #include <gsl/gsl_linalg.h>
 #include <gsl/gsl_math.h>
 #include <gsl/gsl_blas.h>
-#include <gsl/gsl_cblas.h>
 #include <gsl/gsl_vector.h>
 #include <gsl/gsl_vector_complex.h>
 #include <gsl/gsl_matrix.h>
diff -Nru gsl-doc-1.16/eigen/sort.c gsl-doc-2.3/eigen/sort.c
--- gsl-doc-1.16/eigen/sort.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/eigen/sort.c	2016-08-12 14:46:36.000000000 +0000
@@ -26,6 +26,15 @@
 #include <gsl/gsl_complex.h>
 #include <gsl/gsl_complex_math.h>
 
+/* Compares real parts of a and b and, if they are not approximately equal,
+ * returns Re(a) < Re(b); otherwise returns Im(a) < Im(b). */
+static int
+complex_less(gsl_complex a, gsl_complex b)
+{
+  return gsl_fcmp(GSL_REAL(a), GSL_REAL(b), GSL_DBL_EPSILON) == 0 ?
+    GSL_IMAG(a) < GSL_IMAG(b) : GSL_REAL(a) < GSL_REAL(b);
+}
+
 /* The eigen_sort below is not very good, but it is simple and
  * self-contained. We can always implement an improved sort later.  */
 
@@ -208,7 +217,11 @@
                   test = (gsl_complex_abs (ej) > gsl_complex_abs (ek));
                   break;
                 case GSL_EIGEN_SORT_VAL_ASC:
+                  test = complex_less(ej, ek);
+                  break;
                 case GSL_EIGEN_SORT_VAL_DESC:
+                  test = complex_less(ek, ej);
+                  break;
                 default:
                   GSL_ERROR ("invalid sort type", GSL_EINVAL);
                 }
diff -Nru gsl-doc-1.16/eigen/symm.c gsl-doc-2.3/eigen/symm.c
--- gsl-doc-1.16/eigen/symm.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/eigen/symm.c	2016-07-07 20:36:10.000000000 +0000
@@ -84,7 +84,7 @@
 
 int
 gsl_eigen_symm (gsl_matrix * A, gsl_vector * eval,
-                     gsl_eigen_symm_workspace * w)
+                gsl_eigen_symm_workspace * w)
 {
   if (A->size1 != A->size2)
     {
@@ -94,6 +94,10 @@
     {
       GSL_ERROR ("eigenvalue vector must match matrix size", GSL_EBADLEN);
     }
+  else if (A->size1 != w->size)
+    {
+      GSL_ERROR ("matrix does not match workspace", GSL_EBADLEN);
+    }
   else
     {
       const size_t N = A->size1;
diff -Nru gsl-doc-1.16/eigen/test.c gsl-doc-2.3/eigen/test.c
--- gsl-doc-1.16/eigen/test.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/eigen/test.c	2016-08-12 14:45:17.000000000 +0000
@@ -1267,8 +1267,8 @@
     }
 
   /* sort eval and evalv and test them */
-  gsl_eigen_nonsymmv_sort(w->eval, NULL, GSL_EIGEN_SORT_ABS_ASC);
-  gsl_eigen_nonsymmv_sort(w->evalv, NULL, GSL_EIGEN_SORT_ABS_ASC);
+  gsl_eigen_nonsymmv_sort(w->eval, NULL, GSL_EIGEN_SORT_VAL_ASC);
+  gsl_eigen_nonsymmv_sort(w->evalv, NULL, GSL_EIGEN_SORT_VAL_ASC);
   test_eigenvalues_complex(w->evalv, w->eval, "gen", desc);
 
   gsl_eigen_genv_sort(w->alphav, w->betav, w->evec, GSL_EIGEN_SORT_ABS_ASC);
diff -Nru gsl-doc-1.16/err/Makefile.in gsl-doc-2.3/err/Makefile.in
--- gsl-doc-1.16/err/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/err/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -375,6 +375,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -397,7 +398,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
diff -Nru gsl-doc-1.16/fft/Makefile.am gsl-doc-2.3/fft/Makefile.am
--- gsl-doc-1.16/fft/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/fft/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_fft.h gsl_fft_complex.h gsl_fft_halfcomplex.h gsl_fft_real.h gsl_dft_complex.h gsl_dft_complex_float.h gsl_fft_complex_float.h gsl_fft_halfcomplex_float.h gsl_fft_real_float.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslfft_la_SOURCES =  dft.c fft.c
 
diff -Nru gsl-doc-1.16/fft/Makefile.in gsl-doc-2.3/fft/Makefile.in
--- gsl-doc-1.16/fft/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/fft/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -377,6 +377,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -399,7 +400,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -515,7 +519,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslfft.la 
 pkginclude_HEADERS = gsl_fft.h gsl_fft_complex.h gsl_fft_halfcomplex.h gsl_fft_real.h gsl_dft_complex.h gsl_dft_complex_float.h gsl_fft_complex_float.h gsl_fft_halfcomplex_float.h gsl_fft_real_float.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslfft_la_SOURCES = dft.c fft.c
 noinst_HEADERS = c_pass.h hc_pass.h real_pass.h signals.h signals_source.c c_main.c c_init.c c_pass_2.c c_pass_3.c c_pass_4.c c_pass_5.c c_pass_6.c c_pass_7.c c_pass_n.c c_radix2.c bitreverse.c bitreverse.h factorize.c factorize.h hc_init.c hc_pass_2.c hc_pass_3.c hc_pass_4.c hc_pass_5.c hc_pass_n.c hc_radix2.c hc_unpack.c real_init.c real_pass_2.c real_pass_3.c real_pass_4.c real_pass_5.c real_pass_n.c real_radix2.c real_unpack.c compare.h compare_source.c dft_source.c hc_main.c real_main.c test_complex_source.c test_real_source.c test_trap_source.c urand.c complex_internal.h
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/fit/Makefile.am gsl-doc-2.3/fit/Makefile.am
--- gsl-doc-1.16/fit/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/fit/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_fit.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslfit_la_SOURCES = linear.c
 
diff -Nru gsl-doc-1.16/fit/Makefile.in gsl-doc-2.3/fit/Makefile.in
--- gsl-doc-1.16/fit/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/fit/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -376,6 +376,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -398,7 +399,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -514,7 +518,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslfit.la 
 pkginclude_HEADERS = gsl_fit.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslfit_la_SOURCES = linear.c
 TESTS = $(check_PROGRAMS)
 test_SOURCES = test.c
diff -Nru gsl-doc-1.16/gsl/Makefile.am gsl-doc-2.3/gsl/Makefile.am
--- gsl-doc-1.16/gsl/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/gsl/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -12,6 +12,5 @@
 
 all: all-am header-links
 
-clean: clean-am remove-links
-distclean: distclean-am remove-links
-	-rm -f Makefile
+clean-local: remove-links
+distclean-local: remove-links
diff -Nru gsl-doc-1.16/gsl/Makefile.in gsl-doc-2.3/gsl/Makefile.in
--- gsl-doc-1.16/gsl/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/gsl/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -113,6 +113,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -135,7 +136,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -359,9 +363,13 @@
 maintainer-clean-generic:
 	@echo "This command is intended for maintainers to use"
 	@echo "it deletes files that may require special tools to rebuild."
-clean-am: clean-generic clean-libtool mostlyclean-am
+clean: clean-am
 
-distclean-am: clean-am distclean-generic
+clean-am: clean-generic clean-libtool clean-local mostlyclean-am
+
+distclean: distclean-am
+	-rm -f Makefile
+distclean-am: clean-am distclean-generic distclean-local
 
 dvi: dvi-am
 
@@ -424,16 +432,17 @@
 .MAKE: install-am install-strip
 
 .PHONY: all all-am check check-am clean clean-generic clean-libtool \
-	cscopelist-am ctags-am distclean distclean-generic \
-	distclean-libtool distdir dvi dvi-am html html-am info info-am \
-	install install-am install-data install-data-am install-dvi \
-	install-dvi-am install-exec install-exec-am install-html \
-	install-html-am install-info install-info-am install-man \
-	install-pdf install-pdf-am install-ps install-ps-am \
-	install-strip installcheck installcheck-am installdirs \
-	maintainer-clean maintainer-clean-generic mostlyclean \
-	mostlyclean-generic mostlyclean-libtool pdf pdf-am ps ps-am \
-	tags-am uninstall uninstall-am
+	clean-local cscopelist-am ctags-am distclean distclean-generic \
+	distclean-libtool distclean-local distdir dvi dvi-am html \
+	html-am info info-am install install-am install-data \
+	install-data-am install-dvi install-dvi-am install-exec \
+	install-exec-am install-html install-html-am install-info \
+	install-info-am install-man install-pdf install-pdf-am \
+	install-ps install-ps-am install-strip installcheck \
+	installcheck-am installdirs maintainer-clean \
+	maintainer-clean-generic mostlyclean mostlyclean-generic \
+	mostlyclean-libtool pdf pdf-am ps ps-am tags-am uninstall \
+	uninstall-am
 
 
 header-links: remove-links
@@ -448,9 +457,8 @@
 
 all: all-am header-links
 
-clean: clean-am remove-links
-distclean: distclean-am remove-links
-	-rm -f Makefile
+clean-local: remove-links
+distclean-local: remove-links
 
 # Tell versions [3.59,3.63) of GNU make to not export all variables.
 # Otherwise a system limit (for SysV at least) may be exceeded.
diff -Nru gsl-doc-1.16/gsl-histogram.c gsl-doc-2.3/gsl-histogram.c
--- gsl-doc-1.16/gsl-histogram.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/gsl-histogram.c	2015-11-03 16:21:55.000000000 +0000
@@ -20,34 +20,54 @@
 #include <config.h>
 #include <stdio.h>
 #include <stdlib.h>
+#include <getopt.h>
 #include <gsl/gsl_histogram.h>
 
+void
+print_help(void)
+{
+  fprintf (stderr, "Usage: gsl-histogram [-u] xmin xmax [n]\n");
+  fprintf (stderr, "Computes a histogram of the data on stdin using n bins from xmin to xmax.\n"
+                   "If n is unspecified then bins of integer width are used.\n"
+                   "If -u is given, histogram is normalized so that sum of all bins is unity.\n");
+}
+
 int
 main (int argc, char **argv)
 {
   double a = 0.0, b = 1.0;
   size_t n = 10;
+  int unit = 0;
+  int c;
 
-  if (argc != 3 && argc !=4)
+  while ((c = getopt(argc, argv, "u")) != (-1))
     {
-      printf ("Usage: gsl-histogram xmin xmax [n]\n");
-      printf (
-"Computes a histogram of the data on stdin using n bins from xmin to xmax.\n"
-"If n is unspecified then bins of integer width are used.\n");
-      exit (0);
+      switch (c)
+        {
+          case 'u':
+            unit = 1;
+            break;
+
+          default:
+            print_help();
+            exit(0);
+            break;
+        }
     }
 
-  a = atof (argv[1]);
-  b = atof (argv[2]);
-
-  if (argc == 4) 
+  if (argc - optind < 2)
     {
-      n = atoi (argv[3]);
+      print_help();
+      exit(0);
     }
+
+  a = atof (argv[optind++]);
+  b = atof (argv[optind++]);
+
+  if (argc - optind > 0)
+    n = atoi (argv[optind++]);
   else
-    {
-      n = (int)(b - a) ;
-    }
+    n = (int)(b - a) ;
 
   {
     double x;
@@ -69,6 +89,15 @@
     }
 #endif
 
+    /* normalize histogram if needed */
+    if (unit)
+      {
+        double sum = gsl_histogram_sum(h);
+
+        if (sum > 0.0)
+          gsl_histogram_scale(h, 1.0 / sum);
+      }
+
     gsl_histogram_fprintf (stdout, h, "%g", "%g");
 
     gsl_histogram_free (h);
diff -Nru gsl-doc-1.16/gsl_version.h gsl-doc-2.3/gsl_version.h
--- gsl-doc-1.16/gsl_version.h	2013-07-19 15:16:58.000000000 +0000
+++ gsl-doc-2.3/gsl_version.h	2016-12-09 00:04:34.000000000 +0000
@@ -15,9 +15,9 @@
 __BEGIN_DECLS
 
 
-#define GSL_VERSION "1.16"
-#define GSL_MAJOR_VERSION 1
-#define GSL_MINOR_VERSION 16
+#define GSL_VERSION "2.3"
+#define GSL_MAJOR_VERSION 2
+#define GSL_MINOR_VERSION 3
 
 GSL_VAR const char * gsl_version;
 
diff -Nru gsl-doc-1.16/histogram/Makefile.am gsl-doc-2.3/histogram/Makefile.am
--- gsl-doc-1.16/histogram/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/histogram/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_histogram.h gsl_histogram2d.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslhistogram_la_SOURCES = add.c  get.c init.c params.c reset.c file.c pdf.c gsl_histogram.h add2d.c get2d.c init2d.c params2d.c reset2d.c file2d.c pdf2d.c gsl_histogram2d.h calloc_range.c calloc_range2d.c copy.c copy2d.c maxval.c maxval2d.c oper.c oper2d.c stat.c stat2d.c
 
diff -Nru gsl-doc-1.16/histogram/Makefile.in gsl-doc-2.3/histogram/Makefile.in
--- gsl-doc-1.16/histogram/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/histogram/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -383,6 +383,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -405,7 +406,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -521,7 +525,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslhistogram.la 
 pkginclude_HEADERS = gsl_histogram.h gsl_histogram2d.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslhistogram_la_SOURCES = add.c  get.c init.c params.c reset.c file.c pdf.c gsl_histogram.h add2d.c get2d.c init2d.c params2d.c reset2d.c file2d.c pdf2d.c gsl_histogram2d.h calloc_range.c calloc_range2d.c copy.c copy2d.c maxval.c maxval2d.c oper.c oper2d.c stat.c stat2d.c
 noinst_HEADERS = urand.c find.c find2d.c
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/ieee-utils/env.c gsl-doc-2.3/ieee-utils/env.c
--- gsl-doc-1.16/ieee-utils/env.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/ieee-utils/env.c	2015-11-03 16:21:55.000000000 +0000
@@ -31,12 +31,21 @@
 
   int comma = 0 ;
 
+#if defined( _MSC_VER )
+
+    extern const char *fp_env_string;
+    p = fp_env_string;
+
+#else
+
   if (p == 0)  /* GSL_IEEE_MODE environment variable is not set */
     return ;
 
   if (*p == '\0') /* GSL_IEEE_MODE environment variable is empty */
     return ;
 
+#endif
+
   gsl_ieee_read_mode_string (p, &precision, &rounding, &exception_mask) ;
 
   gsl_ieee_set_mode (precision, rounding, exception_mask) ;
diff -Nru gsl-doc-1.16/ieee-utils/Makefile.am gsl-doc-2.3/ieee-utils/Makefile.am
--- gsl-doc-1.16/ieee-utils/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/ieee-utils/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -6,7 +6,7 @@
 
 noinst_HEADERS = fp-aix.c fp-darwin.c fp-darwin86.c fp-hpux.c fp-hpux11.c fp-irix.c fp-gnum68k.c fp-gnuppc.c fp-solaris.c fp-gnusparc.c fp-sunos4.c fp-tru64.c fp-unknown.c fp-gnux86.c fp-freebsd.c fp-os2emx.c fp-netbsd.c fp-openbsd.c fp-gnuc99.c endian.c standardize.c
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 TESTS = $(check_PROGRAMS)
 check_PROGRAMS = test
diff -Nru gsl-doc-1.16/ieee-utils/Makefile.in gsl-doc-2.3/ieee-utils/Makefile.in
--- gsl-doc-1.16/ieee-utils/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/ieee-utils/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -377,6 +377,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -399,7 +400,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -517,7 +521,7 @@
 pkginclude_HEADERS = gsl_ieee_utils.h
 libgslieeeutils_la_SOURCES = print.c make_rep.c gsl_ieee_utils.h env.c fp.c read.c
 noinst_HEADERS = fp-aix.c fp-darwin.c fp-darwin86.c fp-hpux.c fp-hpux11.c fp-irix.c fp-gnum68k.c fp-gnuppc.c fp-solaris.c fp-gnusparc.c fp-sunos4.c fp-tru64.c fp-unknown.c fp-gnux86.c fp-freebsd.c fp-os2emx.c fp-netbsd.c fp-openbsd.c fp-gnuc99.c endian.c standardize.c
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 TESTS = $(check_PROGRAMS)
 test_LDADD = libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
 test_SOURCES = test.c
diff -Nru gsl-doc-1.16/ieee-utils/read.c gsl-doc-2.3/ieee-utils/read.c
--- gsl-doc-1.16/ieee-utils/read.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/ieee-utils/read.c	2016-08-19 15:37:27.000000000 +0000
@@ -79,23 +79,29 @@
     status = lookup_string (p, &new_precision, &new_rounding, &new_exception) ;
 
     if (status)
-      GSL_ERROR ("unrecognized GSL_IEEE_MODE string.\nValid settings are:\n\n" 
-                 "  single-precision double-precision extended-precision\n"
-                 "  round-to-nearest round-down round-up round-to-zero\n"
-                 "  mask-invalid mask-denormalized mask-division-by-zero\n"
-                 "  mask-overflow mask-underflow mask-all\n"
-                 "  trap-common trap-inexact\n"
-                 "\n"
-                 "separated by commas. "
-                 "(e.g. GSL_IEEE_MODE=\"round-down,mask-underflow\")",
-                 GSL_EINVAL) ;
+      {
+        free(start);
+        GSL_ERROR ("unrecognized GSL_IEEE_MODE string.\nValid settings are:\n\n" 
+                   "  single-precision double-precision extended-precision\n"
+                   "  round-to-nearest round-down round-up round-to-zero\n"
+                   "  mask-invalid mask-denormalized mask-division-by-zero\n"
+                   "  mask-overflow mask-underflow mask-all\n"
+                   "  trap-common trap-inexact\n"
+                   "\n"
+                   "separated by commas. "
+                   "(e.g. GSL_IEEE_MODE=\"round-down,mask-underflow\")",
+                   GSL_EINVAL) ;
+      }
 
     if (new_precision) 
       {
         *precision = new_precision ;
         precision_count ++ ;
         if (precision_count > 1)
-          GSL_ERROR ("attempted to set IEEE precision twice", GSL_EINVAL) ;
+          {
+            free(start);
+            GSL_ERROR ("attempted to set IEEE precision twice", GSL_EINVAL) ;
+          }
       }
 
     if (new_rounding) 
@@ -103,7 +109,10 @@
         *rounding = new_rounding ;
         rounding_count ++ ;
         if (rounding_count > 1)
-          GSL_ERROR ("attempted to set IEEE rounding mode twice", GSL_EINVAL) ;
+          {
+            free(start);
+            GSL_ERROR ("attempted to set IEEE rounding mode twice", GSL_EINVAL) ;
+          }
       }
 
     if (new_exception) 
diff -Nru gsl-doc-1.16/INSTALL gsl-doc-2.3/INSTALL
--- gsl-doc-1.16/INSTALL	2013-07-18 21:29:23.000000000 +0000
+++ gsl-doc-2.3/INSTALL	2015-12-03 18:34:33.000000000 +0000
@@ -1,426 +1,80 @@
-GSL - GNU Scientific Library
-============================
-
 Installation Instructions
-=========================
-
-GSL follows the standard GNU installation procedure.  To compile GSL
-you will need an ANSI C-compiler.  After unpacking the distribution
-the Makefiles can be prepared using the configure command,
-
-  ./configure
-
-You can then build the library by typing,
-
-  make
-
-Both static and shared versions of the libraries will be compiled by
-default.  Compilation of shared libraries can be turned off by
-specifying the `--disable-shared' option to `configure', e.g.
-  
-  ./configure --disable-shared
-
-If you encounter problems building the library try using the above
-option, because some platforms do not support shared libraries.  If
-you change any compilation options you will need to remove any
-existing compiled files with,
-
-  make clean
-
-before running "make" again, so the new settings take effect.
-
-For notes about problems with specific platforms and compilers see the
-next section of this file (below).
-
-An extensive test suite is available.  After compiling the library
-with "make", it can be invoked with "make check" at the top level.
-The test output should be directed to a file rather than a terminal,
-with the command,
-
-   make check > log 2>&1
-
-to allow any errors to be examined in detail.  By default, only test
-failures are shown.  To see the complete output, set the environment
-variable GSL_TEST_VERBOSE=1.  Use "make -k check" to continue running
-the remaining tests in the event of failures.
-
-If you run the tests and get some failures, please see the notes on
-platform specific problems below.  If you find failures that are not
-mentioned, please report them to bug-gsl@gnu.org.
-
-The library can be installed using the command,
-
-  make install
-
-The default installation directory prefix is /usr/local.  Installing
-in this directory will require root privileges on most systems (use
-"su" or "sudo").
-
-The installation directory can be changed with the --prefix option to
-configure.  Consult the "Further Information" section below for
-instructions on installing the library in another location or changing
-other default compilation options.
-
-When building from source, GNU packages are compiled with debugging
-symbols enabled by default (CFLAGS="-g -O2").  It's part of the
-philosophy that anyone should be able to examine any program on the
-system.
-
-                    ------------------------------
-
-Platform Specific Compilation Notes
-===================================
-
-This section documents any known issues with installing GSL on
-specific platforms.
-
-  * General hints for all platforms
-  * AIX
-  * Compaq/DEC Alpha
-  * HP-UX
-  * IRIX
-  * MacOS X / PowerPC
-  * Microsoft Windows
-  * OpenBSD
-  * OS/2
-  * Solaris
-
-Hints for any platform
-======================
-
-1) If there are problems building the library try using
-
-        ./configure --disable-shared --disable-dependency-tracking
-
-This will turn off the compilation of shared libraries and dependency
-tracking and may allow the build process to complete successfully.
-
-If you get any problems try this first.
-
-2) If your compiler uses the C99-style inline keyword, use
-
-    ./configure CFLAGS="-DGSL_C99_INLINE -g -O2"
-
-to avoid problems with duplicate function definitions.  For gcc this
-is handled automatically.  See the file gsl_inline.h for the
-preprocessor definitions that are used.
-
-3) If you want to pass C++ functions with exceptions to GSL, the
-library needs to be compiled with the GCC option -fexceptions
-
-    ./confugire CFLAGS="-fexceptions ..."
-
-to allow C++ exceptions to be handled.
-
-4) With gcc-4.3.2 the tests in the poly/ directory fail due to a
-compiler optimization bug which is fixed in later versions of GCC
-(http://gcc.gnu.org/bugzilla/show_bug.cgi?id=38478).
-
-FAIL: y.real, gsl_complex_poly_complex_eval ({-2.31 + 0.44i, 4.21 - 3.19i, 0.93 + 1.04i, -0.42 + 0.68i}, 0.49 + 0.95i) (-1.68450788000000018 observed vs 1.82462012000000007 expected) [9]
-FAIL: y.imag, gsl_complex_poly_complex_eval ({-2.31 + 0.44i, 4.21 - 3.19i, 0.93 + 1.04i, -0.42 + 0.68i}, 0.49 + 0.95i) (-0.30943988 observed vs 2.30389411999999982 expected) [10]
-
-With gcc-2.95/2.96 the tests fail in the eigen/ directory.  This is
-due to a compiler optimization bug which causes errors in the
-manipulation of complex numbers.  
-
-If you encounter these problems, install a different version of gcc.
-
-5) Attempts to run 'strip' on the static library libgsl.a will probably
-produce a broken library (it is known to happen with GNU binutils
-strip, and probably affects others too). The libgsl.a ar archive made
-by libtool contains files with the same filenames from different
-directories, and this causes the strip program to overwrite these
-archive entries.  If you need to produce a compact version of the
-library compile without -g instead of using strip.
-
-make install-strip does not work, due to a minor problem with autoconf
-which is fixed in the 2.5 development version of autoconf.  In the
-meantime compile without -g instead if you need to reduce the file size.
-
-6) The configure script can fail with a segmentation fault on bash-2.01
-
-    $ ./configure
-    Segmentation fault
-
-This is due to a bug in bash, related to the MAIL environment
-variable.  To work around it use 
-
-    $ unset ENV MAIL MAILPATH
-    $ ./configure
-
-which should avoid the problem.
-
-Hints for AIX
-=============
-
-For compilation problems with the native compiler xlc, try disabling
-shared libraries,
-
-    setenv CC 'xlc'
-    setenv CFLAGS '-O -qmaxmem=8192'
-    ./configure --disable-shared
-    make
-
-If you compile with higher optimisation -O3 you will also need
--qstrict.  The -O3 flag causes the -nostrict option to be
-enabled. This affects the accuracy of the results and causes some of
-the tests to fail.
-
-If you get errors like
-
- ld: 0711-593 SEVERE ERROR: Symbol C_BSTAT (entry 635) in object siman_tsp.o:
-          The symbol refers to a csect with symbol number 0, which was not
-          found. The new symbol cannot be associated with a csect and
-          is being ignored.
-
-this is due to problems with some versions of the IBM assembler.  Try
-compiling with CFLAGS="-g0" as a workaround.  For details and other
-solutions see https://www-304.ibm.com/support/docview.wss?uid=isg1IZ98134 and
-http://gcc.gnu.org/bugzilla/show_bug.cgi?id=46072
-
-If you get the error,
-
-   ld: 0711-781 ERROR: TOC overflow. 
-
-you can try building the library with a larger linker
-table-of-contents by setting LDFLAGS before compilation,
-
-   ./configure LDFLAGS="-Wl,-bbigtoc" 
-
-On older versions of AIX (e.g. 4.2) the size of the command-line is
-limited to 24kb, which causes linking to fail (due to the large number
-of files to be linked). Unfortunately this limit cannot be increased.
-To link the library you may need to use a manual approach of
-incrementally combining the object files in smaller groups. 
-
-On more recent versions of AIX (e.g >= 5.1) use
-
-  chdev -l sys0 -a ncargs=NNN
-
-to increase the allowed number of arguments. NNN is the amount of
-space measured in 4k blocks (default 6, maximum 1024)
-
-Hints for Compaq/DEC Alpha
-==========================
-
-When comping with GCC use the -mieee and -mfp-rounding-mode options 
-as appropriate, e.g.
-
-    ./configure CFLAGS="-mieee -mfp-rounding-mode=d -g -O2"
-
-The library should compile successfully with Compaq's C compiler on
-Tru64 Unix 'cc' using the -std, -ieee and -fprm options.  Use
-
-    ./configure CC=cc 
-    make CFLAGS="-std -ieee -fprm d"
-
-to build the library this way.
-
-Use GNU tar to unpack the tar file, as Tru64 tar gives an error
-halfway through.
-
-Hints for HP-UX
-===============
-
-The default mode of the HP-UX C compiler does not use ANSI C.
-
-To compile GSL you need to select ANSI C mode with the following
-configuration option:
-
-      ./configure CFLAGS="-Ae"  
-
-To switch on optimization use CFLAGS="-Ae -O".
-
-Hints for IRIX (SGI)
-====================
-
-The library should be compiled with the CFLAGS option
--OPT:IEEE_NaN_inf=ON to ensure correct IEEE arithmetic.  The tests in
-sys/ will fail without this option.  The older deprecated option
--OPT:IEEE_comparisons=ON will also work.
-
-The 32 bit IRIX compiler gives warnings about "long double" not being
-supported. These can be ignored or turned off with,
-
-   ./configure CFLAGS="-woff 728" 
-
-or 
-
-   make CFLAGS="-woff 728"
-
-The compiler also gives warnings about certain libraries that are "not
-used for resolving any symbol". This is harmless and the warnings can
-be ignored.
-
-You may get warnings about " /usr/bin/ld: arg list too long" when
-building shared libraries.  If so, try increasing the ncargs kernel
-parameter with the systune(1m) command.
-
-For 64-bit compilation use the following options,
-
-  ./configure CC=cc CFLAGS="-64" LDFLAGS="-64" 
-
-or for gcc
+*************************
 
-  CFLAGS="-mabi-64" LDFLAGS="-mabi=64 -mips4 -L/usr/local/lib/mabi=64"
+Copyright (C) 1994-1996, 1999-2002, 2004-2013 Free Software Foundation,
+Inc.
 
-Hints for MacOS X and PowerPC
-=============================
-
-To install in /usr/local on MacOS systems, do "sudo make install" to
-gain root privileges.
-
-Note that GSL contains files with filenames of 32 characters or more.
-Therefore you need to be careful in unpacking the tar file, as some
-MacOS applications such as Stuffit Expander will truncate filenames to
-31 characters.  Using GNU tar and gunzip directly is the safe way to
-unpack the distribution.
-
-There are problems with dynamic linker, so the library should be
-compiled with,
-
-  ./configure --disable-shared --disable-dependency-tracking
-
-It has been reported that shared libraries can be built if MacOS X
-specific versions of libtool, automake and autoconf from
-http://fink.sourceforge.net/ are installed, and the GSL source is
-reconfigured from scratch (./autogen.sh; ./configure; make)
-
-To avoid warnings about long-double, use the flag
-
-  CFLAGS="-Wno-long-double ....(other options here)"
-
-in addition to the normal compilation options.
-
-If you get make check failures with OS X 10.x try using CC=gcc-4.2 or
-CC=clang since the llvm compiler has bugs that make the tests fail.
-
-The GCC 3.3 compiler shipped by Apple contains a bug which causes the
-wavelet tests to fail on "data untouched" tests at optimisation level
--O2.  You may be able work around this by compiling with CFLAGS="-O1
-..." instead.
-
-F J Frankin <MEP95JFF@sheffield.ac.uk> reported that some early
-versions of GCC-2.95 have a problem with long argument lists on PPC
-architecture, and this prevents GSL from compiling correctly (e.g. the
-test program in the blas directory gives a segmentation fault when
-run).  This problem is fixed in more recent versions of GCC.
-
-
-Hints for Microsoft Windows
-===========================
-
-GSL should compile with GCC under Cygwin on Microsoft Windows.  
-There is a gsl package in the standard Cygwin distribution which
-contains any patches needed.
-
-With Mingw/MSYS some floating point issues have been reported which
-cause failures in the monte/ test directory.
-
-Hints for OpenBSD
-=================
-
-As of July 2001 the OpenBSD log1p() function on i386 causes failures
-in the gsl complex tests.  The configure script has been hardcoded to
-substitute gsl_log1p instead on OpenBSD.  The log1p() bug has been
-reported and so may be fixed in future versions of OpenBSD.
-
-Hints for OS/2
-==============
-
-The configure script fails to detect the function 'isnan', leading to
-a slew of errors 'isnan redefined'.
-
-To work around this problem, run configure and edit the resulting
-config.h file to comment out the line which defines HAVE_ISINF.
-
-Hints for Solaris
-=================
-
-If you are using the Sun compilers then the library should be compiled
-with the Sun C compiler 'cc', not 'CC' which is the C++ compiler.
-
-The Sun compiler tools are stored in non-standard directories -- make
-sure that all the compiler and linker tools (cc, ar, ranlib, ld) are
-on the PATH.  A typical PATH should include the directories
-/opt/SUNWspro/bin:/usr/ccs/bin:/usr/ucb in that order.
-
-For example,
-
-  $ PATH=/opt/SUNWspro/bin:/usr/ccs/bin:/usr/ucb:$PATH
-  $ ./configure CC=cc CFLAGS=-O
-
-If you see configure output 
-  
-   checking for ar... :
-
-it means that 'ar' has not been found, and the library will fail to
-build.
-
-If you use the Sun compiler you should use the Sun linker and
-assembler.  If you use GCC, you can use the GNU linker and assembler
-or the Sun linker and assembler.
-
-There may be some warnings about "end of loop code not reached". These
-can be ignored -- they come from the do { ... ; return ; } while(0)
-statement in the GSL_ERROR macro.
-
-If you get errors such as symbol `gsl_complex_rect' is	multiply-defined
-you will need to use ./configure CFLAGS="-DGSL_C99_INLINE -g -O2"
-
-                    ------------------------------
-
-Further information on the standard GNU installation procedure
-==============================================================
-
-The sections below describe the general features of the standard GNU
-installation procedure.
+   Copying and distribution of this file, with or without modification,
+are permitted in any medium without royalty provided the copyright
+notice and this notice are preserved.  This file is offered as-is,
+without warranty of any kind.
 
 Basic Installation
 ==================
 
-   These are generic installation instructions.
+   Briefly, the shell commands `./configure; make; make install' should
+configure, build, and install this package.  The following
+more-detailed instructions are generic; see the `README' file for
+instructions specific to this package.  Some packages provide this
+`INSTALL' file but do not implement all of the features documented
+below.  The lack of an optional feature in a given package is not
+necessarily a bug.  More recommendations for GNU packages can be found
+in *note Makefile Conventions: (standards)Makefile Conventions.
 
    The `configure' shell script attempts to guess correct values for
 various system-dependent variables used during compilation.  It uses
 those values to create a `Makefile' in each directory of the package.
 It may also create one or more `.h' files containing system-dependent
 definitions.  Finally, it creates a shell script `config.status' that
-you can run in the future to recreate the current configuration, a file
-`config.cache' that saves the results of its tests to speed up
-reconfiguring, and a file `config.log' containing compiler output
-(useful mainly for debugging `configure').
+you can run in the future to recreate the current configuration, and a
+file `config.log' containing compiler output (useful mainly for
+debugging `configure').
+
+   It can also use an optional file (typically called `config.cache'
+and enabled with `--cache-file=config.cache' or simply `-C') that saves
+the results of its tests to speed up reconfiguring.  Caching is
+disabled by default to prevent problems with accidental use of stale
+cache files.
 
    If you need to do unusual things to compile the package, please try
 to figure out how `configure' could check whether to do them, and mail
 diffs or instructions to the address given in the `README' so they can
-be considered for the next release.  If at some point `config.cache'
-contains results you don't want to keep, you may remove or edit it.
-
-   The file `configure.in' is used to create `configure' by a program
-called `autoconf'.  You only need `configure.in' if you want to change
-it or regenerate `configure' using a newer version of `autoconf'.
+be considered for the next release.  If you are using the cache, and at
+some point `config.cache' contains results you don't want to keep, you
+may remove or edit it.
+
+   The file `configure.ac' (or `configure.in') is used to create
+`configure' by a program called `autoconf'.  You need `configure.ac' if
+you want to change it or regenerate `configure' using a newer version
+of `autoconf'.
 
-The simplest way to compile this package is:
+   The simplest way to compile this package is:
 
   1. `cd' to the directory containing the package's source code and type
-     `./configure' to configure the package for your system.  If you're
-     using `csh' on an old version of System V, you might need to type
-     `sh ./configure' instead to prevent `csh' from trying to execute
-     `configure' itself.
+     `./configure' to configure the package for your system.
 
-     Running `configure' takes a while.  While running, it prints some
-     messages telling which features it is checking for.
+     Running `configure' might take a while.  While running, it prints
+     some messages telling which features it is checking for.
 
   2. Type `make' to compile the package.
 
   3. Optionally, type `make check' to run any self-tests that come with
-     the package.
+     the package, generally using the just-built uninstalled binaries.
 
   4. Type `make install' to install the programs and any data files and
-     documentation.
+     documentation.  When installing into a prefix owned by root, it is
+     recommended that the package be configured and built as a regular
+     user, and only the `make install' phase executed with root
+     privileges.
+
+  5. Optionally, type `make installcheck' to repeat any self-tests, but
+     this time using the binaries in their final installed location.
+     This target does not install anything.  Running this target as a
+     regular user, particularly if the prior `make install' required
+     root privileges, verifies that the installation completed
+     correctly.
 
-  5. You can remove the program binaries and object files from the
+  6. You can remove the program binaries and object files from the
      source code directory by typing `make clean'.  To also remove the
      files that `configure' created (so you can compile the package for
      a different kind of computer), type `make distclean'.  There is
@@ -429,57 +83,119 @@
      all sorts of other programs in order to regenerate files that came
      with the distribution.
 
+  7. Often, you can also type `make uninstall' to remove the installed
+     files again.  In practice, not all packages have tested that
+     uninstallation works correctly, even though it is required by the
+     GNU Coding Standards.
+
+  8. Some packages, particularly those that use Automake, provide `make
+     distcheck', which can by used by developers to test that all other
+     targets like `make install' and `make uninstall' work correctly.
+     This target is generally not run by end users.
+
 Compilers and Options
 =====================
 
    Some systems require unusual options for compilation or linking that
-the `configure' script does not know about.  You can give `configure'
-initial values for variables by setting them in the environment.  Using
-a Bourne-compatible shell, you can do that on the command line like
-this:
-     CC=c89 CFLAGS=-O2 LIBS=-lposix ./configure
+the `configure' script does not know about.  Run `./configure --help'
+for details on some of the pertinent environment variables.
 
-Or on systems that have the `env' program, you can do it like this:
-     env CPPFLAGS=-I/usr/local/include LDFLAGS=-s ./configure
+   You can give `configure' initial values for configuration parameters
+by setting variables in the command line or in the environment.  Here
+is an example:
+
+     ./configure CC=c99 CFLAGS=-g LIBS=-lposix
+
+   *Note Defining Variables::, for more details.
 
 Compiling For Multiple Architectures
 ====================================
 
    You can compile the package for more than one kind of computer at the
 same time, by placing the object files for each architecture in their
-own directory.  To do this, you must use a version of `make' that
-supports the `VPATH' variable, such as GNU `make'.  `cd' to the
+own directory.  To do this, you can use GNU `make'.  `cd' to the
 directory where you want the object files and executables to go and run
 the `configure' script.  `configure' automatically checks for the
-source code in the directory that `configure' is in and in `..'.
+source code in the directory that `configure' is in and in `..'.  This
+is known as a "VPATH" build.
 
-   If you have to use a `make' that does not supports the `VPATH'
-variable, you have to compile the package for one architecture at a time
-in the source code directory.  After you have installed the package for
-one architecture, use `make distclean' before reconfiguring for another
-architecture.
+   With a non-GNU `make', it is safer to compile the package for one
+architecture at a time in the source code directory.  After you have
+installed the package for one architecture, use `make distclean' before
+reconfiguring for another architecture.
+
+   On MacOS X 10.5 and later systems, you can create libraries and
+executables that work on multiple system types--known as "fat" or
+"universal" binaries--by specifying multiple `-arch' options to the
+compiler but only a single `-arch' option to the preprocessor.  Like
+this:
+
+     ./configure CC="gcc -arch i386 -arch x86_64 -arch ppc -arch ppc64" \
+                 CXX="g++ -arch i386 -arch x86_64 -arch ppc -arch ppc64" \
+                 CPP="gcc -E" CXXCPP="g++ -E"
+
+   This is not guaranteed to produce working output in all cases, you
+may have to build one architecture at a time and combine the results
+using the `lipo' tool if you have problems.
 
 Installation Names
 ==================
 
-   By default, `make install' will install the package's files in
-`/usr/local/bin', `/usr/local/man', etc.  You can specify an
-installation prefix other than `/usr/local' by giving `configure' the
-option `--prefix=PATH'.
+   By default, `make install' installs the package's commands under
+`/usr/local/bin', include files under `/usr/local/include', etc.  You
+can specify an installation prefix other than `/usr/local' by giving
+`configure' the option `--prefix=PREFIX', where PREFIX must be an
+absolute file name.
 
    You can specify separate installation prefixes for
 architecture-specific files and architecture-independent files.  If you
-give `configure' the option `--exec-prefix=PATH', the package will use
-PATH as the prefix for installing programs and libraries.
-Documentation and other data files will still use the regular prefix.
+pass the option `--exec-prefix=PREFIX' to `configure', the package uses
+PREFIX as the prefix for installing programs and libraries.
+Documentation and other data files still use the regular prefix.
+
+   In addition, if you use an unusual directory layout you can give
+options like `--bindir=DIR' to specify different values for particular
+kinds of files.  Run `configure --help' for a list of the directories
+you can set and what kinds of files go in them.  In general, the
+default for these options is expressed in terms of `${prefix}', so that
+specifying just `--prefix' will affect all of the other directory
+specifications that were not explicitly provided.
+
+   The most portable way to affect installation locations is to pass the
+correct locations to `configure'; however, many packages provide one or
+both of the following shortcuts of passing variable assignments to the
+`make install' command line to change installation locations without
+having to reconfigure or recompile.
+
+   The first method involves providing an override variable for each
+affected directory.  For example, `make install
+prefix=/alternate/directory' will choose an alternate location for all
+directory configuration variables that were expressed in terms of
+`${prefix}'.  Any directories that were specified during `configure',
+but not in terms of `${prefix}', must each be overridden at install
+time for the entire installation to be relocated.  The approach of
+makefile variable overrides for each directory variable is required by
+the GNU Coding Standards, and ideally causes no recompilation.
+However, some platforms have known limitations with the semantics of
+shared libraries that end up requiring recompilation when using this
+method, particularly noticeable in packages that use GNU Libtool.
+
+   The second method involves providing the `DESTDIR' variable.  For
+example, `make install DESTDIR=/alternate/directory' will prepend
+`/alternate/directory' before all installation names.  The approach of
+`DESTDIR' overrides is not required by the GNU Coding Standards, and
+does not work on platforms that have drive letters.  On the other hand,
+it does better at avoiding recompilation issues, and works well even
+when some directory options were not specified in terms of `${prefix}'
+at `configure' time.
+
+Optional Features
+=================
 
    If the package supports it, you can cause programs to be installed
 with an extra prefix or suffix on their names by giving `configure' the
 option `--program-prefix=PREFIX' or `--program-suffix=SUFFIX'.
 
-Optional Features
-=================
-
    Some packages pay attention to `--enable-FEATURE' options to
 `configure', where FEATURE indicates an optional part of the package.
 They may also pay attention to `--with-PACKAGE' options, where PACKAGE
@@ -492,25 +208,80 @@
 you can use the `configure' options `--x-includes=DIR' and
 `--x-libraries=DIR' to specify their locations.
 
+   Some packages offer the ability to configure how verbose the
+execution of `make' will be.  For these packages, running `./configure
+--enable-silent-rules' sets the default to minimal output, which can be
+overridden with `make V=1'; while running `./configure
+--disable-silent-rules' sets the default to verbose, which can be
+overridden with `make V=0'.
+
+Particular systems
+==================
+
+   On HP-UX, the default C compiler is not ANSI C compatible.  If GNU
+CC is not installed, it is recommended to use the following options in
+order to use an ANSI C compiler:
+
+     ./configure CC="cc -Ae -D_XOPEN_SOURCE=500"
+
+and if that doesn't work, install pre-built binaries of GCC for HP-UX.
+
+   HP-UX `make' updates targets which have the same time stamps as
+their prerequisites, which makes it generally unusable when shipped
+generated files such as `configure' are involved.  Use GNU `make'
+instead.
+
+   On OSF/1 a.k.a. Tru64, some versions of the default C compiler cannot
+parse its `<wchar.h>' header file.  The option `-nodtk' can be used as
+a workaround.  If GNU CC is not installed, it is therefore recommended
+to try
+
+     ./configure CC="cc"
+
+and if that doesn't work, try
+
+     ./configure CC="cc -nodtk"
+
+   On Solaris, don't put `/usr/ucb' early in your `PATH'.  This
+directory contains several dysfunctional programs; working variants of
+these programs are available in `/usr/bin'.  So, if you need `/usr/ucb'
+in your `PATH', put it _after_ `/usr/bin'.
+
+   On Haiku, software installed for all users goes in `/boot/common',
+not `/usr/local'.  It is recommended to use the following options:
+
+     ./configure --prefix=/boot/common
+
 Specifying the System Type
 ==========================
 
-   There may be some features `configure' can not figure out
-automatically, but needs to determine by the type of host the package
-will run on.  Usually `configure' can figure that out, but if it prints
-a message saying it can not guess the host type, give it the
-`--host=TYPE' option.  TYPE can either be a short name for the system
-type, such as `sun4', or a canonical name with three fields:
+   There may be some features `configure' cannot figure out
+automatically, but needs to determine by the type of machine the package
+will run on.  Usually, assuming the package is built to be run on the
+_same_ architectures, `configure' can figure that out, but if it prints
+a message saying it cannot guess the machine type, give it the
+`--build=TYPE' option.  TYPE can either be a short name for the system
+type, such as `sun4', or a canonical name which has the form:
+
      CPU-COMPANY-SYSTEM
 
-See the file `config.sub' for the possible values of each field.  If
+where SYSTEM can have one of these forms:
+
+     OS
+     KERNEL-OS
+
+   See the file `config.sub' for the possible values of each field.  If
 `config.sub' isn't included in this package, then this package doesn't
-need to know the host type.
+need to know the machine type.
 
-   If you are building compiler tools for cross-compiling, you can also
-use the `--target=TYPE' option to select the type of system they will
-produce code for and the `--build=TYPE' option to select the type of
-system on which you are compiling the package.
+   If you are _building_ compiler tools for cross-compiling, you should
+use the option `--target=TYPE' to select the type of system they will
+produce code for.
+
+   If you want to _use_ a cross compiler, that generates code for a
+platform different from the build platform, you should specify the
+"host" platform (i.e., that on which the generated programs will
+eventually be run) with `--host=TYPE'.
 
 Sharing Defaults
 ================
@@ -523,32 +294,77 @@
 `CONFIG_SITE' environment variable to the location of the site script.
 A warning: not all `configure' scripts look for a site script.
 
-Operation Controls
+Defining Variables
 ==================
 
+   Variables not defined in a site shell script can be set in the
+environment passed to `configure'.  However, some packages may run
+configure again during the build, and the customized values of these
+variables may be lost.  In order to avoid this problem, you should set
+them in the `configure' command line, using `VAR=value'.  For example:
+
+     ./configure CC=/usr/local2/bin/gcc
+
+causes the specified `gcc' to be used as the C compiler (unless it is
+overridden in the site shell script).
+
+Unfortunately, this technique does not work for `CONFIG_SHELL' due to
+an Autoconf limitation.  Until the limitation is lifted, you can use
+this workaround:
+
+     CONFIG_SHELL=/bin/bash ./configure CONFIG_SHELL=/bin/bash
+
+`configure' Invocation
+======================
+
    `configure' recognizes the following options to control how it
 operates.
 
-`--cache-file=FILE'
-     Use and save the results of the tests in FILE instead of
-     `./config.cache'.  Set FILE to `/dev/null' to disable caching, for
-     debugging `configure'.
-
 `--help'
-     Print a summary of the options to `configure', and exit.
+`-h'
+     Print a summary of all of the options to `configure', and exit.
+
+`--help=short'
+`--help=recursive'
+     Print a summary of the options unique to this package's
+     `configure', and exit.  The `short' variant lists options used
+     only in the top level, while the `recursive' variant lists options
+     also present in any nested packages.
+
+`--version'
+`-V'
+     Print the version of Autoconf used to generate the `configure'
+     script, and exit.
+
+`--cache-file=FILE'
+     Enable the cache: use and save the results of the tests in FILE,
+     traditionally `config.cache'.  FILE defaults to `/dev/null' to
+     disable caching.
+
+`--config-cache'
+`-C'
+     Alias for `--cache-file=config.cache'.
 
 `--quiet'
 `--silent'
 `-q'
-     Do not print messages saying which checks are being made.
+     Do not print messages saying which checks are being made.  To
+     suppress all normal output, redirect it to `/dev/null' (any error
+     messages will still be shown).
 
 `--srcdir=DIR'
      Look for the package's source code in directory DIR.  Usually
      `configure' can determine that directory automatically.
 
-`--version'
-     Print the version of Autoconf used to generate the `configure'
-     script, and exit.
-
-`configure' also accepts some other, not widely useful, options.
+`--prefix=DIR'
+     Use DIR as the installation prefix.  *note Installation Names::
+     for more details, including other options available for fine-tuning
+     the installation locations.
+
+`--no-create'
+`-n'
+     Run the configure checks, but stop before creating any output
+     files.
 
+`configure' also accepts some other, not widely useful, options.  Run
+`configure --help' for more details.
diff -Nru gsl-doc-1.16/integration/cquad.c gsl-doc-2.3/integration/cquad.c
--- gsl-doc-1.16/integration/cquad.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/integration/cquad.c	2015-11-03 16:21:55.000000000 +0000
@@ -235,7 +235,7 @@
     {
       iv->fx[i] = GSL_FN_EVAL (f, m + xi[i] * h);
       neval++;
-      if (!finite (iv->fx[i]))
+      if (!gsl_finite (iv->fx[i]))
 	{
 	  nans[nnans++] = i;
 	  iv->fx[i] = 0.0;
@@ -319,7 +319,7 @@
 	  nnans = 0;
 	  for (i = 0; i <= 32; i += skip[d])
 	    {
-	      if (!finite (iv->fx[i]))
+	      if (!gsl_finite (iv->fx[i]))
 		{
 		  nans[nnans++] = i;
 		  iv->fx[i] = 0.0;
@@ -444,7 +444,7 @@
 	  nnans = 0;
 	  for (i = 0; i <= 32; i += skip[0])
 	    {
-	      if (!finite (ivl->fx[i]))
+	      if (!gsl_finite (ivl->fx[i]))
 		{
 		  nans[nnans++] = i;
 		  ivl->fx[i] = 0.0;
@@ -510,7 +510,7 @@
 	  nnans = 0;
 	  for (i = 0; i <= 32; i += skip[0])
 	    {
-	      if (!finite (ivr->fx[i]))
+	      if (!gsl_finite (ivr->fx[i]))
 		{
 		  nans[nnans++] = i;
 		  ivr->fx[i] = 0.0;
diff -Nru gsl-doc-1.16/integration/Makefile.am gsl-doc-2.3/integration/Makefile.am
--- gsl-doc-1.16/integration/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/integration/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -1,6 +1,6 @@
 noinst_LTLIBRARIES = libgslintegration.la
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslintegration_la_SOURCES = qk15.c qk21.c qk31.c qk41.c qk51.c qk61.c qk.c qng.c qng.h qag.c	qags.c qagp.c workspace.c qcheb.c qawc.c qmomo.c qaws.c	qmomof.c qawo.c	qawf.c glfixed.c cquad.c
 
diff -Nru gsl-doc-1.16/integration/Makefile.in gsl-doc-2.3/integration/Makefile.in
--- gsl-doc-1.16/integration/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/integration/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -380,6 +380,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -402,7 +403,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -517,7 +521,7 @@
 top_builddir = @top_builddir@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslintegration.la
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslintegration_la_SOURCES = qk15.c qk21.c qk31.c qk41.c qk51.c qk61.c qk.c qng.c qng.h qag.c	qags.c qagp.c workspace.c qcheb.c qawc.c qmomo.c qaws.c	qmomof.c qawo.c	qawf.c glfixed.c cquad.c
 pkginclude_HEADERS = gsl_integration.h
 noinst_HEADERS = qpsrt.c qpsrt2.c qelg.c qc25c.c qc25s.c qc25f.c ptsort.c util.c err.c positivity.c append.c initialise.c set_initial.c reset.c cquad_const.c
diff -Nru gsl-doc-1.16/integration/qag.c gsl-doc-2.3/integration/qag.c
--- gsl-doc-1.16/integration/qag.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/integration/qag.c	2015-11-03 16:21:55.000000000 +0000
@@ -121,7 +121,7 @@
 
   if (epsabs <= 0 && (epsrel < 50 * GSL_DBL_EPSILON || epsrel < 0.5e-28))
     {
-      GSL_ERROR ("tolerance cannot be acheived with given epsabs and epsrel",
+      GSL_ERROR ("tolerance cannot be achieved with given epsabs and epsrel",
                  GSL_EBADTOL);
     }
 
diff -Nru gsl-doc-1.16/integration/qagp.c gsl-doc-2.3/integration/qagp.c
--- gsl-doc-1.16/integration/qagp.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/integration/qagp.c	2015-11-03 16:21:55.000000000 +0000
@@ -111,7 +111,7 @@
 
   if (epsabs <= 0 && (epsrel < 50 * GSL_DBL_EPSILON || epsrel < 0.5e-28))
     {
-      GSL_ERROR ("tolerance cannot be acheived with given epsabs and epsrel",
+      GSL_ERROR ("tolerance cannot be achieved with given epsabs and epsrel",
                  GSL_EBADTOL);
     }
 
diff -Nru gsl-doc-1.16/integration/qags.c gsl-doc-2.3/integration/qags.c
--- gsl-doc-1.16/integration/qags.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/integration/qags.c	2015-11-03 16:21:55.000000000 +0000
@@ -236,7 +236,7 @@
 
   if (epsabs <= 0 && (epsrel < 50 * GSL_DBL_EPSILON || epsrel < 0.5e-28))
     {
-      GSL_ERROR ("tolerance cannot be acheived with given epsabs and epsrel",
+      GSL_ERROR ("tolerance cannot be achieved with given epsabs and epsrel",
                  GSL_EBADTOL);
     }
 
diff -Nru gsl-doc-1.16/integration/qawc.c gsl-doc-2.3/integration/qawc.c
--- gsl-doc-1.16/integration/qawc.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/integration/qawc.c	2015-11-03 16:21:55.000000000 +0000
@@ -73,7 +73,7 @@
 
   if (epsabs <= 0 && (epsrel < 50 * GSL_DBL_EPSILON || epsrel < 0.5e-28))
     {
-      GSL_ERROR ("tolerance cannot be acheived with given epsabs and epsrel",
+      GSL_ERROR ("tolerance cannot be achieved with given epsabs and epsrel",
                  GSL_EBADTOL);
     }
 
diff -Nru gsl-doc-1.16/integration/qawo.c gsl-doc-2.3/integration/qawo.c
--- gsl-doc-1.16/integration/qawo.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/integration/qawo.c	2015-11-03 16:21:55.000000000 +0000
@@ -84,7 +84,7 @@
 
   if (epsabs <= 0 && (epsrel < 50 * GSL_DBL_EPSILON || epsrel < 0.5e-28))
     {
-      GSL_ERROR ("tolerance cannot be acheived with given epsabs and epsrel",
+      GSL_ERROR ("tolerance cannot be achieved with given epsabs and epsrel",
                  GSL_EBADTOL);
     }
 
diff -Nru gsl-doc-1.16/integration/qaws.c gsl-doc-2.3/integration/qaws.c
--- gsl-doc-1.16/integration/qaws.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/integration/qaws.c	2015-11-03 16:21:55.000000000 +0000
@@ -64,7 +64,7 @@
 
   if (epsabs <= 0 && (epsrel < 50 * GSL_DBL_EPSILON || epsrel < 0.5e-28))
     {
-      GSL_ERROR ("tolerance cannot be acheived with given epsabs and epsrel",
+      GSL_ERROR ("tolerance cannot be achieved with given epsabs and epsrel",
                  GSL_EBADTOL);
     }
 
diff -Nru gsl-doc-1.16/integration/qk41.c gsl-doc-2.3/integration/qk41.c
--- gsl-doc-1.16/integration/qk41.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/integration/qk41.c	2015-11-03 16:21:55.000000000 +0000
@@ -52,7 +52,7 @@
 /* xgk[1], xgk[3], ... abscissae of the 20-point gauss rule. 
    xgk[0], xgk[2], ... abscissae to optimally extend the 20-point gauss rule */
 
-static const double wg[11] =    /* weights of the 20-point gauss rule */
+static const double wg[10] =    /* weights of the 20-point gauss rule */
 {
   0.017614007139152118311861962351853,
   0.040601429800386941331039952274932,
diff -Nru gsl-doc-1.16/integration/qng.c gsl-doc-2.3/integration/qng.c
--- gsl-doc-1.16/integration/qng.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/integration/qng.c	2015-11-03 16:21:55.000000000 +0000
@@ -52,7 +52,7 @@
       * result = 0;
       * abserr = 0;
       * neval = 0;
-      GSL_ERROR ("tolerance cannot be acheived with given epsabs and epsrel",
+      GSL_ERROR ("tolerance cannot be achieved with given epsabs and epsrel",
                  GSL_EBADTOL);
     };
 
diff -Nru gsl-doc-1.16/interpolation/bicubic.c gsl-doc-2.3/interpolation/bicubic.c
--- gsl-doc-1.16/interpolation/bicubic.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/interpolation/bicubic.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,805 @@
+/* interpolation/bicubic.c
+ * 
+ * Copyright 2012 David Zaslavsky
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_spline.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_interp.h>
+#include <gsl/gsl_interp2d.h>
+
+#define IDX2D(i, j, w) ((j) * ((w)->xsize) + (i))
+
+typedef struct
+{
+  double * zx;
+  double * zy;
+  double * zxy;
+  size_t xsize;
+  size_t ysize;
+} bicubic_state_t;
+
+static void bicubic_free (void * vstate);
+
+static void *
+bicubic_alloc(size_t xsize, size_t ysize)
+{
+  bicubic_state_t *state;
+  
+  state = calloc(1, sizeof (bicubic_state_t));
+
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL("failed to allocate space for state", GSL_ENOMEM);
+    }
+
+  state->zx = (double *) malloc (xsize * ysize * sizeof (double));
+  if (state->zx == NULL)
+    {
+      bicubic_free(state);
+      GSL_ERROR_NULL("failed to allocate space for zx", GSL_ENOMEM);
+    }
+
+  state->zy = (double *) malloc (xsize * ysize * sizeof (double));
+  if (state->zy == NULL)
+    {
+      bicubic_free(state);
+      GSL_ERROR_NULL("failed to allocate space for zy", GSL_ENOMEM);
+    }
+
+  state->zxy = (double *) malloc (xsize * ysize * sizeof (double));
+  if (state->zxy == NULL)
+    {
+      bicubic_free(state);
+      GSL_ERROR_NULL("failed to allocate space for zxy", GSL_ENOMEM);
+    }
+
+  state->xsize = xsize;
+  state->ysize = ysize;
+
+  return state;
+} /* bicubic_alloc() */
+
+static void
+bicubic_free (void * vstate)
+{
+  bicubic_state_t *state = (bicubic_state_t *) vstate;
+
+  RETURN_IF_NULL(state);
+
+  if (state->zx)
+    free (state->zx);
+
+  if (state->zy)
+    free (state->zy);
+
+  if (state->zxy)
+    free (state->zxy);
+
+  free (state);
+} /* bicubic_free() */
+
+static int
+bicubic_init(void * vstate, const double xa[], const double ya[],
+             const double za[], size_t xsize, size_t ysize)
+{
+  bicubic_state_t *state = (bicubic_state_t *) vstate;
+
+  gsl_interp_accel *acc = gsl_interp_accel_alloc();
+  gsl_spline *spline;
+  gsl_vector *x;
+  gsl_vector *y;
+  size_t i, j;
+
+  x = gsl_vector_alloc(xsize);
+  y = gsl_vector_alloc(xsize);
+  spline = gsl_spline_alloc(gsl_interp_cspline, xsize);
+  for (j = 0; j <= ysize - 1; j++)
+    {
+      for (i = 0; i <= xsize - 1; i++)
+        {
+          gsl_vector_set(x, i, xa[i]);
+          gsl_vector_set(y, i, za[IDX2D(i, j, state)]);
+        }
+      gsl_spline_init(spline, x->data, y->data, xsize);
+      for (i = 0; i <= xsize - 1; i++)
+        {
+          state->zx[IDX2D(i, j, state)] = gsl_spline_eval_deriv(spline, xa[i], acc);
+        }
+    }
+  gsl_vector_free(x);
+  gsl_vector_free(y);
+  gsl_spline_free(spline);
+  gsl_interp_accel_reset(acc);
+
+  x = gsl_vector_alloc(ysize);
+  y = gsl_vector_alloc(ysize);
+  spline = gsl_spline_alloc(gsl_interp_cspline, ysize);
+  for (i = 0; i <= xsize - 1; i++)
+    {
+      for (j = 0; j <= ysize - 1; j++)
+        {
+          gsl_vector_set(x, j, ya[j]);
+          gsl_vector_set(y, j, za[IDX2D(i, j, state)]);
+        }
+      gsl_spline_init(spline, x->data, y->data, ysize);
+      for (j = 0; j <= ysize - 1; j++)
+        {
+          state->zy[IDX2D(i, j, state)] = gsl_spline_eval_deriv(spline, ya[j], acc);
+        }
+    }
+  gsl_vector_free(x);
+  gsl_vector_free(y);
+  gsl_spline_free(spline);
+  gsl_interp_accel_reset(acc);
+
+  x = gsl_vector_alloc(xsize);
+  y = gsl_vector_alloc(xsize);
+  spline = gsl_spline_alloc(gsl_interp_cspline, xsize);
+  for (j = 0; j <= ysize - 1; j++)
+    {
+      for (i = 0; i <= xsize - 1; i++)
+        {
+          gsl_vector_set(x, i, xa[i]);
+          gsl_vector_set(y, i, state->zy[IDX2D(i, j, state)]);
+        }
+      gsl_spline_init(spline, x->data, y->data, xsize);
+      for (i = 0; i <= xsize - 1; i++)
+        {
+          state->zxy[IDX2D(i, j, state)] = gsl_spline_eval_deriv(spline, xa[i], acc);
+        }
+    }
+  gsl_vector_free(x);
+  gsl_vector_free(y);
+  gsl_spline_free(spline);
+  gsl_interp_accel_free(acc);
+
+  return GSL_SUCCESS;
+} /* bicubic_init() */
+
+
+static int
+bicubic_eval(const void * vstate, const double xarr[], const double yarr[],
+             const double zarr[], size_t xsize, size_t ysize,
+             double x, double y, gsl_interp_accel * xa,
+             gsl_interp_accel * ya, double * z)
+{
+  bicubic_state_t *state = (bicubic_state_t *) vstate;
+
+  double xmin, xmax, ymin, ymax;
+  double zminmin, zminmax, zmaxmin, zmaxmax;
+  double zxminmin, zxminmax, zxmaxmin, zxmaxmax;
+  double zyminmin, zyminmax, zymaxmin, zymaxmax;
+  double zxyminmin, zxyminmax, zxymaxmin, zxymaxmax;
+
+  double dx, dy;   /* size of the grid cell */
+  double dt, du;
+
+  /*
+   * t and u are the positions within the grid cell at which we are computing
+   * the interpolation, in units of grid cell size
+   */
+  double t, u;
+  double t0, t1, t2, t3, u0, u1, u2, u3;
+  double v;
+  size_t xi, yi;
+
+  /* first compute the indices into the data arrays where we are interpolating */
+  if (xa != NULL)
+    xi = gsl_interp_accel_find(xa, xarr, xsize, x);
+  else
+    xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
+
+  if (ya != NULL)
+    yi = gsl_interp_accel_find(ya, yarr, ysize, y);
+  else
+    yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
+
+  /* find the minimum and maximum values on the grid cell in each dimension */
+  xmin = xarr[xi];
+  xmax = xarr[xi + 1];
+  ymin = yarr[yi];
+  ymax = yarr[yi + 1];
+  zminmin = zarr[IDX2D(xi, yi, state)];
+  zminmax = zarr[IDX2D(xi, yi + 1, state)];
+  zmaxmin = zarr[IDX2D(xi + 1, yi, state)];
+  zmaxmax = zarr[IDX2D(xi + 1, yi + 1, state)];
+  /* Get the width and height of the grid cell */
+  dx = xmax - xmin;
+  dy = ymax - ymin;
+  t = (x - xmin)/dx;
+  u = (y - ymin)/dy;
+  dt = 1./dx; /* partial t / partial x */
+  du = 1./dy; /* partial u / partial y */
+  zxminmin = state->zx[IDX2D(xi, yi, state)]/dt;
+  zxminmax = state->zx[IDX2D(xi, yi + 1, state)]/dt;
+  zxmaxmin = state->zx[IDX2D(xi + 1, yi, state)]/dt;
+  zxmaxmax = state->zx[IDX2D(xi + 1, yi + 1, state)]/dt;
+  zyminmin = state->zy[IDX2D(xi, yi, state)]/du;
+  zyminmax = state->zy[IDX2D(xi, yi + 1, state)]/du;
+  zymaxmin = state->zy[IDX2D(xi + 1, yi, state)]/du;
+  zymaxmax = state->zy[IDX2D(xi + 1, yi + 1, state)]/du;
+  zxyminmin = state->zxy[IDX2D(xi, yi, state)]/(dt*du);
+  zxyminmax = state->zxy[IDX2D(xi, yi + 1, state)]/(dt*du);
+  zxymaxmin = state->zxy[IDX2D(xi + 1, yi, state)]/(dt*du);
+  zxymaxmax = state->zxy[IDX2D(xi + 1, yi + 1, state)]/(dt*du);
+  t0 = 1;
+  t1 = t;
+  t2 = t*t;
+  t3 = t*t2;
+  u0 = 1;
+  u1 = u;
+  u2 = u*u;
+  u3 = u*u2;
+
+  *z = 0;
+  v = zminmin;
+  *z += v*t0*u0;
+  v = zyminmin;
+  *z += v*t0*u1;
+  v = -3*zminmin + 3*zminmax - 2*zyminmin - zyminmax;
+  *z += v*t0*u2;
+  v = 2*zminmin - 2*zminmax + zyminmin + zyminmax;
+  *z += v*t0*u3;
+  v = zxminmin;
+  *z += v*t1*u0;
+  v = zxyminmin;
+  *z += v*t1*u1;
+  v = -3*zxminmin + 3*zxminmax - 2*zxyminmin - zxyminmax;
+  *z += v*t1*u2;
+  v = 2*zxminmin - 2*zxminmax + zxyminmin + zxyminmax;
+  *z += v*t1*u3;
+  v = -3*zminmin + 3*zmaxmin - 2*zxminmin - zxmaxmin;
+  *z += v*t2*u0;
+  v = -3*zyminmin + 3*zymaxmin - 2*zxyminmin - zxymaxmin;
+  *z += v*t2*u1;
+  v = 9*zminmin - 9*zmaxmin + 9*zmaxmax - 9*zminmax + 6*zxminmin + 3*zxmaxmin - 3*zxmaxmax - 6*zxminmax + 6*zyminmin - 6*zymaxmin - 3*zymaxmax + 3*zyminmax + 4*zxyminmin + 2*zxymaxmin + zxymaxmax + 2*zxyminmax;
+  *z += v*t2*u2;
+  v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 4*zxminmin - 2*zxmaxmin + 2*zxmaxmax + 4*zxminmax - 3*zyminmin + 3*zymaxmin + 3*zymaxmax - 3*zyminmax - 2*zxyminmin - zxymaxmin - zxymaxmax - 2*zxyminmax;
+  *z += v*t2*u3;
+  v = 2*zminmin - 2*zmaxmin + zxminmin + zxmaxmin;
+  *z += v*t3*u0;
+  v = 2*zyminmin - 2*zymaxmin + zxyminmin + zxymaxmin;
+  *z += v*t3*u1;
+  v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 3*zxminmin - 3*zxmaxmin + 3*zxmaxmax + 3*zxminmax - 4*zyminmin + 4*zymaxmin + 2*zymaxmax - 2*zyminmax - 2*zxyminmin - 2*zxymaxmin - zxymaxmax - zxyminmax;
+  *z += v*t3*u2;
+  v = 4*zminmin - 4*zmaxmin + 4*zmaxmax - 4*zminmax + 2*zxminmin + 2*zxmaxmin - 2*zxmaxmax - 2*zxminmax + 2*zyminmin - 2*zymaxmin - 2*zymaxmax + 2*zyminmax + zxyminmin + zxymaxmin + zxymaxmax + zxyminmax;
+  *z += v*t3*u3;
+
+  return GSL_SUCCESS;
+} /* bicubic_eval() */
+
+static int
+bicubic_deriv_x(const void * vstate, const double xarr[], const double yarr[],
+                const double zarr[], size_t xsize, size_t ysize,
+                double x, double y,
+                gsl_interp_accel * xa, gsl_interp_accel * ya, double * z_p)
+{
+  bicubic_state_t *state = (bicubic_state_t *) vstate;
+
+  double xmin, xmax, ymin, ymax;
+  double zminmin, zminmax, zmaxmin, zmaxmax;
+  double zxminmin, zxminmax, zxmaxmin, zxmaxmax;
+  double zyminmin, zyminmax, zymaxmin, zymaxmax;
+  double zxyminmin, zxyminmax, zxymaxmin, zxymaxmax;
+  double dx, dy; /* size of the grid cell */
+  double dt, du;
+
+  /*
+   * t and u are the positions within the grid cell at which we are computing
+   * the interpolation, in units of grid cell size
+   */
+  double t, u;
+  double t0, t1, t2, u0, u1, u2, u3;
+  double v;
+  size_t xi, yi;
+
+  /* first compute the indices into the data arrays where we are interpolating */
+  if (xa != NULL)
+    xi = gsl_interp_accel_find(xa, xarr, xsize, x);
+  else
+    xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
+
+  if (ya != NULL)
+    yi = gsl_interp_accel_find(ya, yarr, ysize, y);
+  else
+    yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
+
+  /* find the minimum and maximum values on the grid cell in each dimension */
+  xmin = xarr[xi];
+  xmax = xarr[xi + 1];
+  ymin = yarr[yi];
+  ymax = yarr[yi + 1];
+  zminmin = zarr[IDX2D(xi, yi, state)];
+  zminmax = zarr[IDX2D(xi, yi + 1, state)];
+  zmaxmin = zarr[IDX2D(xi + 1, yi, state)];
+  zmaxmax = zarr[IDX2D(xi + 1, yi + 1, state)];
+
+  /* get the width and height of the grid cell */
+  dx = xmax - xmin;
+  dy = ymax - ymin;
+  t = (x - xmin)/dx;
+  u = (y - ymin)/dy;
+  dt = 1./dx; /* partial t / partial x */
+  du = 1./dy; /* partial u / partial y */
+
+  zxminmin = state->zx[IDX2D(xi, yi, state)]/dt;
+  zxminmax = state->zx[IDX2D(xi, yi + 1, state)]/dt;
+  zxmaxmin = state->zx[IDX2D(xi + 1, yi, state)]/dt;
+  zxmaxmax = state->zx[IDX2D(xi + 1, yi + 1, state)]/dt;
+  zyminmin = state->zy[IDX2D(xi, yi, state)]/du;
+  zyminmax = state->zy[IDX2D(xi, yi + 1, state)]/du;
+  zymaxmin = state->zy[IDX2D(xi + 1, yi, state)]/du;
+  zymaxmax = state->zy[IDX2D(xi + 1, yi + 1, state)]/du;
+  zxyminmin = state->zxy[IDX2D(xi, yi, state)]/(dt*du);
+  zxyminmax = state->zxy[IDX2D(xi, yi + 1, state)]/(dt*du);
+  zxymaxmin = state->zxy[IDX2D(xi + 1, yi, state)]/(dt*du);
+  zxymaxmax = state->zxy[IDX2D(xi + 1, yi + 1, state)]/(dt*du);
+
+  t0 = 1;
+  t1 = t;
+  t2 = t*t;
+  u0 = 1;
+  u1 = u;
+  u2 = u*u;
+  u3 = u*u2;
+
+  *z_p = 0;
+  v = zxminmin;
+  *z_p += v*t0*u0;
+  v = zxyminmin;
+  *z_p += v*t0*u1;
+  v = -3*zxminmin + 3*zxminmax - 2*zxyminmin - zxyminmax;
+  *z_p += v*t0*u2;
+  v = 2*zxminmin - 2*zxminmax + zxyminmin + zxyminmax;
+  *z_p += v*t0*u3;
+  v = -3*zminmin + 3*zmaxmin - 2*zxminmin - zxmaxmin;
+  *z_p += 2*v*t1*u0;
+  v = -3*zyminmin + 3*zymaxmin - 2*zxyminmin - zxymaxmin;
+  *z_p += 2*v*t1*u1;
+  v = 9*zminmin - 9*zmaxmin + 9*zmaxmax - 9*zminmax + 6*zxminmin + 3*zxmaxmin - 3*zxmaxmax - 6*zxminmax + 6*zyminmin - 6*zymaxmin - 3*zymaxmax + 3*zyminmax + 4*zxyminmin + 2*zxymaxmin + zxymaxmax + 2*zxyminmax;
+  *z_p += 2*v*t1*u2;
+  v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 4*zxminmin - 2*zxmaxmin + 2*zxmaxmax + 4*zxminmax - 3*zyminmin + 3*zymaxmin + 3*zymaxmax - 3*zyminmax - 2*zxyminmin - zxymaxmin - zxymaxmax - 2*zxyminmax;
+  *z_p += 2*v*t1*u3;
+  v = 2*zminmin - 2*zmaxmin + zxminmin + zxmaxmin;
+  *z_p += 3*v*t2*u0;
+  v = 2*zyminmin - 2*zymaxmin + zxyminmin + zxymaxmin;
+  *z_p += 3*v*t2*u1;
+  v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 3*zxminmin - 3*zxmaxmin + 3*zxmaxmax + 3*zxminmax - 4*zyminmin + 4*zymaxmin + 2*zymaxmax - 2*zyminmax - 2*zxyminmin - 2*zxymaxmin - zxymaxmax - zxyminmax;
+  *z_p += 3*v*t2*u2;
+  v = 4*zminmin - 4*zmaxmin + 4*zmaxmax - 4*zminmax + 2*zxminmin + 2*zxmaxmin - 2*zxmaxmax - 2*zxminmax + 2*zyminmin - 2*zymaxmin - 2*zymaxmax + 2*zyminmax + zxyminmin + zxymaxmin + zxymaxmax + zxyminmax;
+  *z_p += 3*v*t2*u3;
+  *z_p *= dt;
+
+  return GSL_SUCCESS;
+} /* bicubic_deriv_x() */
+
+static int
+bicubic_deriv_y(const void * vstate, const double xarr[], const double yarr[],
+                const double zarr[], size_t xsize, size_t ysize,
+                double x, double y,
+                gsl_interp_accel * xa, gsl_interp_accel * ya, double * z_p)
+{
+  bicubic_state_t *state = (bicubic_state_t *) vstate;
+
+  double xmin, xmax, ymin, ymax;
+  double zminmin, zminmax, zmaxmin, zmaxmax;
+  double zxminmin, zxminmax, zxmaxmin, zxmaxmax;
+  double zyminmin, zyminmax, zymaxmin, zymaxmax;
+  double zxyminmin, zxyminmax, zxymaxmin, zxymaxmax;
+  /* dx and dy are the size of the grid cell */
+  double dx, dy;
+  double dt, du;
+  /* t and u are the positions within the grid cell at which we are
+   * computing the interpolation, in units of grid cell size */
+  double t, u;
+  double t0, t1, t2, t3, u0, u1, u2;
+  double v;
+  size_t xi, yi;
+
+  /* first compute the indices into the data arrays where we are interpolating */
+  if (xa != NULL)
+    xi = gsl_interp_accel_find(xa, xarr, xsize, x);
+  else
+    xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
+
+  if (ya != NULL)
+    yi = gsl_interp_accel_find(ya, yarr, ysize, y);
+  else
+    yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
+
+  /* find the minimum and maximum values on the grid cell in each dimension */
+  xmin = xarr[xi];
+  xmax = xarr[xi + 1];
+  ymin = yarr[yi];
+  ymax = yarr[yi + 1];
+  zminmin = zarr[IDX2D(xi, yi, state)];
+  zminmax = zarr[IDX2D(xi, yi + 1, state)];
+  zmaxmin = zarr[IDX2D(xi + 1, yi, state)];
+  zmaxmax = zarr[IDX2D(xi + 1, yi + 1, state)];
+
+  /* get the width and height of the grid cell */
+  dx = xmax - xmin;
+  dy = ymax - ymin;
+  t = (x - xmin)/dx;
+  u = (y - ymin)/dy;
+  dt = 1./dx; /* partial t / partial x */
+  du = 1./dy; /* partial u / partial y */
+
+  zxminmin = state->zx[IDX2D(xi, yi, state)]/dt;
+  zxminmax = state->zx[IDX2D(xi, yi + 1, state)]/dt;
+  zxmaxmin = state->zx[IDX2D(xi + 1, yi, state)]/dt;
+  zxmaxmax = state->zx[IDX2D(xi + 1, yi + 1, state)]/dt;
+  zyminmin = state->zy[IDX2D(xi, yi, state)]/du;
+  zyminmax = state->zy[IDX2D(xi, yi + 1, state)]/du;
+  zymaxmin = state->zy[IDX2D(xi + 1, yi, state)]/du;
+  zymaxmax = state->zy[IDX2D(xi + 1, yi + 1, state)]/du;
+  zxyminmin = state->zxy[IDX2D(xi, yi, state)]/(dt*du);
+  zxyminmax = state->zxy[IDX2D(xi, yi + 1, state)]/(dt*du);
+  zxymaxmin = state->zxy[IDX2D(xi + 1, yi, state)]/(dt*du);
+  zxymaxmax = state->zxy[IDX2D(xi + 1, yi + 1, state)]/(dt*du);
+
+  t0 = 1;
+  t1 = t;
+  t2 = t*t;
+  t3 = t*t2;
+  u0 = 1;
+  u1 = u;
+  u2 = u*u;
+
+  *z_p = 0;
+  v = zyminmin;
+  *z_p += v*t0*u0;
+  v = -3*zminmin + 3*zminmax - 2*zyminmin - zyminmax;
+  *z_p += 2*v*t0*u1;
+  v = 2*zminmin-2*zminmax + zyminmin + zyminmax;
+  *z_p += 3*v*t0*u2;
+  v = zxyminmin;
+  *z_p += v*t1*u0;
+  v = -3*zxminmin + 3*zxminmax - 2*zxyminmin - zxyminmax;
+  *z_p += 2*v*t1*u1;
+  v = 2*zxminmin - 2*zxminmax + zxyminmin + zxyminmax;
+  *z_p += 3*v*t1*u2;
+  v = -3*zyminmin + 3*zymaxmin - 2*zxyminmin - zxymaxmin;
+  *z_p += v*t2*u0;
+  v = 9*zminmin - 9*zmaxmin + 9*zmaxmax - 9*zminmax + 6*zxminmin + 3*zxmaxmin - 3*zxmaxmax - 6*zxminmax + 6*zyminmin - 6*zymaxmin - 3*zymaxmax + 3*zyminmax + 4*zxyminmin + 2*zxymaxmin + zxymaxmax + 2*zxyminmax;
+  *z_p += 2*v*t2*u1;
+  v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 4*zxminmin - 2*zxmaxmin + 2*zxmaxmax + 4*zxminmax - 3*zyminmin + 3*zymaxmin + 3*zymaxmax - 3*zyminmax - 2*zxyminmin - zxymaxmin - zxymaxmax - 2*zxyminmax;
+  *z_p += 3*v*t2*u2;
+  v = 2*zyminmin - 2*zymaxmin + zxyminmin + zxymaxmin;
+  *z_p += v*t3*u0;
+  v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 3*zxminmin - 3*zxmaxmin + 3*zxmaxmax + 3*zxminmax - 4*zyminmin + 4*zymaxmin + 2*zymaxmax - 2*zyminmax - 2*zxyminmin - 2*zxymaxmin - zxymaxmax - zxyminmax;
+  *z_p += 2*v*t3*u1;
+  v = 4*zminmin - 4*zmaxmin + 4*zmaxmax - 4*zminmax + 2*zxminmin + 2*zxmaxmin - 2*zxmaxmax - 2*zxminmax + 2*zyminmin - 2*zymaxmin - 2*zymaxmax + 2*zyminmax + zxyminmin + zxymaxmin + zxymaxmax + zxyminmax;
+  *z_p += 3*v*t3*u2;
+  *z_p *= du;
+
+  return GSL_SUCCESS;
+}
+
+static int
+bicubic_deriv_xx(const void * vstate, const double xarr[], const double yarr[],
+                 const double zarr[], size_t xsize, size_t ysize,
+                 double x, double y,
+                 gsl_interp_accel * xa, gsl_interp_accel * ya, double * z_pp)
+{
+  bicubic_state_t *state = (bicubic_state_t *) vstate;
+
+  double xmin, xmax, ymin, ymax;
+  double zminmin, zminmax, zmaxmin, zmaxmax;
+  double zxminmin, zxminmax, zxmaxmin, zxmaxmax;
+  double zyminmin, zyminmax, zymaxmin, zymaxmax;
+  double zxyminmin, zxyminmax, zxymaxmin, zxymaxmax;
+
+  double dx, dy; /* size of the grid cell */
+  double dt, du;
+
+  /*
+   * t and u are the positions within the grid cell at which we are computing
+   * the interpolation, in units of grid cell size
+   */
+  double t, u;
+  double t0, t1, u0, u1, u2, u3;
+  double v;
+  size_t xi, yi;
+
+  /* first compute the indices into the data arrays where we are interpolating */
+  if (xa != NULL)
+    xi = gsl_interp_accel_find(xa, xarr, xsize, x);
+  else
+    xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
+
+  if (ya != NULL)
+    yi = gsl_interp_accel_find(ya, yarr, ysize, y);
+  else
+    yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
+
+  /* find the minimum and maximum values on the grid cell in each dimension */
+  xmin = xarr[xi];
+  xmax = xarr[xi + 1];
+  ymin = yarr[yi];
+  ymax = yarr[yi + 1];
+  zminmin = zarr[IDX2D(xi, yi, state)];
+  zminmax = zarr[IDX2D(xi, yi + 1, state)];
+  zmaxmin = zarr[IDX2D(xi + 1, yi, state)];
+  zmaxmax = zarr[IDX2D(xi + 1, yi + 1, state)];
+
+  /* get the width and height of the grid cell */
+  dx = xmax - xmin;
+  dy = ymax - ymin;
+  t = (x - xmin)/dx;
+  u = (y - ymin)/dy;
+  dt = 1./dx; /* partial t / partial x */
+  du = 1./dy; /* partial u / partial y */
+
+  zxminmin = state->zx[IDX2D(xi, yi, state)]/dt;
+  zxminmax = state->zx[IDX2D(xi, yi + 1, state)]/dt;
+  zxmaxmin = state->zx[IDX2D(xi + 1, yi, state)]/dt;
+  zxmaxmax = state->zx[IDX2D(xi + 1, yi + 1, state)]/dt;
+  zyminmin = state->zy[IDX2D(xi, yi, state)]/du;
+  zyminmax = state->zy[IDX2D(xi, yi + 1, state)]/du;
+  zymaxmin = state->zy[IDX2D(xi + 1, yi, state)]/du;
+  zymaxmax = state->zy[IDX2D(xi + 1, yi + 1, state)]/du;
+  zxyminmin = state->zxy[IDX2D(xi, yi, state)]/(dt*du);
+  zxyminmax = state->zxy[IDX2D(xi, yi + 1, state)]/(dt*du);
+  zxymaxmin = state->zxy[IDX2D(xi + 1, yi, state)]/(dt*du);
+  zxymaxmax = state->zxy[IDX2D(xi + 1, yi + 1, state)]/(dt*du);
+
+  t0 = 1;
+  t1 = t;
+  u0 = 1;
+  u1 = u;
+  u2 = u*u;
+  u3 = u*u2;
+
+  *z_pp = 0;
+  v = -3*zminmin + 3*zmaxmin - 2*zxminmin - zxmaxmin;
+  *z_pp += 2*v*t0*u0;
+  v = -3*zyminmin + 3*zymaxmin - 2*zxyminmin - zxymaxmin;
+  *z_pp += 2*v*t0*u1;
+  v = 9*zminmin - 9*zmaxmin + 9*zmaxmax - 9*zminmax + 6*zxminmin + 3*zxmaxmin - 3*zxmaxmax - 6*zxminmax + 6*zyminmin - 6*zymaxmin - 3*zymaxmax + 3*zyminmax + 4*zxyminmin + 2*zxymaxmin + zxymaxmax + 2*zxyminmax;
+  *z_pp += 2*v*t0*u2;
+  v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 4*zxminmin - 2*zxmaxmin + 2*zxmaxmax + 4*zxminmax - 3*zyminmin + 3*zymaxmin + 3*zymaxmax - 3*zyminmax - 2*zxyminmin - zxymaxmin - zxymaxmax - 2*zxyminmax;
+  *z_pp += 2*v*t0*u3;
+  v = 2*zminmin - 2*zmaxmin + zxminmin + zxmaxmin;
+  *z_pp += 6*v*t1*u0;
+  v = 2*zyminmin - 2*zymaxmin + zxyminmin + zxymaxmin;
+  *z_pp += 6*v*t1*u1;
+  v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 3*zxminmin - 3*zxmaxmin + 3*zxmaxmax + 3*zxminmax - 4*zyminmin + 4*zymaxmin + 2*zymaxmax - 2*zyminmax - 2*zxyminmin - 2*zxymaxmin - zxymaxmax - zxyminmax;
+  *z_pp += 6*v*t1*u2;
+  v = 4*zminmin - 4*zmaxmin + 4*zmaxmax - 4*zminmax + 2*zxminmin + 2*zxmaxmin - 2*zxmaxmax - 2*zxminmax + 2*zyminmin - 2*zymaxmin - 2*zymaxmax + 2*zyminmax + zxyminmin + zxymaxmin + zxymaxmax + zxyminmax;
+  *z_pp += 6*v*t1*u3;
+  *z_pp *= dt*dt;
+
+  return GSL_SUCCESS;
+}
+
+static int
+bicubic_deriv_xy(const void * vstate, const double xarr[], const double yarr[],
+                 const double zarr[], size_t xsize, size_t ysize,
+                 double x, double y,
+                 gsl_interp_accel * xa, gsl_interp_accel * ya, double * z_pp)
+{
+  bicubic_state_t *state = (bicubic_state_t *) vstate;
+
+  double xmin, xmax, ymin, ymax;
+  double zminmin, zminmax, zmaxmin, zmaxmax;
+  double zxminmin, zxminmax, zxmaxmin, zxmaxmax;
+  double zyminmin, zyminmax, zymaxmin, zymaxmax;
+  double zxyminmin, zxyminmax, zxymaxmin, zxymaxmax;
+
+  double dx, dy; /* size of the grid cell */
+  double dt, du;
+
+  /*
+   * t and u are the positions within the grid cell at which we are computing
+   * the interpolation, in units of grid cell size
+   */
+  double t, u;
+  double t0, t1, t2, u0, u1, u2;
+  double v;
+  size_t xi, yi;
+
+  /* first compute the indices into the data arrays where we are interpolating */
+  if (xa != NULL)
+    xi = gsl_interp_accel_find(xa, xarr, xsize, x);
+  else
+    xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
+
+  if (ya != NULL)
+    yi = gsl_interp_accel_find(ya, yarr, ysize, y);
+  else
+    yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
+
+  /* find the minimum and maximum values on the grid cell in each dimension */
+  xmin = xarr[xi];
+  xmax = xarr[xi + 1];
+  ymin = yarr[yi];
+  ymax = yarr[yi + 1];
+  zminmin = zarr[IDX2D(xi, yi, state)];
+  zminmax = zarr[IDX2D(xi, yi + 1, state)];
+  zmaxmin = zarr[IDX2D(xi + 1, yi, state)];
+  zmaxmax = zarr[IDX2D(xi + 1, yi + 1, state)];
+
+  /* get the width and height of the grid cell */
+  dx = xmax - xmin;
+  dy = ymax - ymin;
+  t = (x - xmin)/dx;
+  u = (y - ymin)/dy;
+  dt = 1./dx; /* partial t / partial x */
+  du = 1./dy; /* partial u / partial y */
+
+  zxminmin = state->zx[IDX2D(xi, yi, state)]/dt;
+  zxminmax = state->zx[IDX2D(xi, yi + 1, state)]/dt;
+  zxmaxmin = state->zx[IDX2D(xi + 1, yi, state)]/dt;
+  zxmaxmax = state->zx[IDX2D(xi + 1, yi + 1, state)]/dt;
+  zyminmin = state->zy[IDX2D(xi, yi, state)]/du;
+  zyminmax = state->zy[IDX2D(xi, yi + 1, state)]/du;
+  zymaxmin = state->zy[IDX2D(xi + 1, yi, state)]/du;
+  zymaxmax = state->zy[IDX2D(xi + 1, yi + 1, state)]/du;
+  zxyminmin = state->zxy[IDX2D(xi, yi, state)]/(dt*du);
+  zxyminmax = state->zxy[IDX2D(xi, yi + 1, state)]/(dt*du);
+  zxymaxmin = state->zxy[IDX2D(xi + 1, yi, state)]/(dt*du);
+  zxymaxmax = state->zxy[IDX2D(xi + 1, yi + 1, state)]/(dt*du);
+
+  t0 = 1;
+  t1 = t;
+  t2 = t*t;
+  u0 = 1;
+  u1 = u;
+  u2 = u*u;
+
+  *z_pp = 0;
+  v = zxyminmin;
+  *z_pp += v*t0*u0;
+  v = -3*zxminmin + 3*zxminmax - 2*zxyminmin - zxyminmax;
+  *z_pp += 2*v*t0*u1;
+  v = 2*zxminmin - 2*zxminmax + zxyminmin + zxyminmax;
+  *z_pp += 3*v*t0*u2;
+  v = -3*zyminmin + 3*zymaxmin - 2*zxyminmin - zxymaxmin;
+  *z_pp += 2*v*t1*u0;
+  v = 9*zminmin - 9*zmaxmin + 9*zmaxmax - 9*zminmax + 6*zxminmin + 3*zxmaxmin - 3*zxmaxmax - 6*zxminmax + 6*zyminmin - 6*zymaxmin - 3*zymaxmax + 3*zyminmax + 4*zxyminmin + 2*zxymaxmin + zxymaxmax + 2*zxyminmax;
+  *z_pp += 4*v*t1*u1;
+  v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 4*zxminmin - 2*zxmaxmin + 2*zxmaxmax + 4*zxminmax - 3*zyminmin + 3*zymaxmin + 3*zymaxmax - 3*zyminmax - 2*zxyminmin - zxymaxmin - zxymaxmax - 2*zxyminmax;
+  *z_pp += 6*v*t1*u2;
+  v = 2*zyminmin - 2*zymaxmin + zxyminmin + zxymaxmin;
+  *z_pp += 3*v*t2*u0;
+  v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 3*zxminmin - 3*zxmaxmin + 3*zxmaxmax + 3*zxminmax - 4*zyminmin + 4*zymaxmin + 2*zymaxmax - 2*zyminmax - 2*zxyminmin - 2*zxymaxmin - zxymaxmax - zxyminmax;
+  *z_pp += 6*v*t2*u1;
+  v = 4*zminmin - 4*zmaxmin + 4*zmaxmax - 4*zminmax + 2*zxminmin + 2*zxmaxmin - 2*zxmaxmax - 2*zxminmax + 2*zyminmin - 2*zymaxmin - 2*zymaxmax + 2*zyminmax + zxyminmin + zxymaxmin + zxymaxmax + zxyminmax;
+  *z_pp += 9*v*t2*u2;
+  *z_pp *= dt*du;
+
+  return GSL_SUCCESS;
+}
+
+static int
+bicubic_deriv_yy(const void * vstate, const double xarr[], const double yarr[],
+                 const double zarr[], size_t xsize, size_t ysize,
+                 double x, double y,
+                 gsl_interp_accel * xa, gsl_interp_accel * ya, double * z_pp)
+{
+  bicubic_state_t *state = (bicubic_state_t *) vstate;
+
+  double xmin, xmax, ymin, ymax;
+  double zminmin, zminmax, zmaxmin, zmaxmax;
+  double zxminmin, zxminmax, zxmaxmin, zxmaxmax;
+  double zyminmin, zyminmax, zymaxmin, zymaxmax;
+  double zxyminmin, zxyminmax, zxymaxmin, zxymaxmax;
+
+  double dx, dy; /* size of the grid cell */
+  double dt, du;
+
+  /*
+   * t and u are the positions within the grid cell at which we are computing
+   * the interpolation, in units of grid cell size
+   */
+  double t, u;
+  double t0, t1, t2, t3, u0, u1;
+  double v;
+  size_t xi, yi;
+
+  /* first compute the indices into the data arrays where we are interpolating */
+  if (xa != NULL)
+    xi = gsl_interp_accel_find(xa, xarr, xsize, x);
+  else
+    xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
+
+  if (ya != NULL)
+    yi = gsl_interp_accel_find(ya, yarr, ysize, y);
+  else
+    yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
+
+  /* find the minimum and maximum values on the grid cell in each dimension */
+  xmin = xarr[xi];
+  xmax = xarr[xi + 1];
+  ymin = yarr[yi];
+  ymax = yarr[yi + 1];
+  zminmin = zarr[IDX2D(xi, yi, state)];
+  zminmax = zarr[IDX2D(xi, yi + 1, state)];
+  zmaxmin = zarr[IDX2D(xi + 1, yi, state)];
+  zmaxmax = zarr[IDX2D(xi + 1, yi + 1, state)];
+
+  /* get the width and height of the grid cell */
+  dx = xmax - xmin;
+  dy = ymax - ymin;
+  t = (x - xmin)/dx;
+  u = (y - ymin)/dy;
+  dt = 1./dx; /* partial t / partial x */
+  du = 1./dy; /* partial u / partial y */
+
+  zxminmin = state->zx[IDX2D(xi, yi, state)]/dt;
+  zxminmax = state->zx[IDX2D(xi, yi + 1, state)]/dt;
+  zxmaxmin = state->zx[IDX2D(xi + 1, yi, state)]/dt;
+  zxmaxmax = state->zx[IDX2D(xi + 1, yi + 1, state)]/dt;
+  zyminmin = state->zy[IDX2D(xi, yi, state)]/du;
+  zyminmax = state->zy[IDX2D(xi, yi + 1, state)]/du;
+  zymaxmin = state->zy[IDX2D(xi + 1, yi, state)]/du;
+  zymaxmax = state->zy[IDX2D(xi + 1, yi + 1, state)]/du;
+  zxyminmin = state->zxy[IDX2D(xi, yi, state)]/(dt*du);
+  zxyminmax = state->zxy[IDX2D(xi, yi + 1, state)]/(dt*du);
+  zxymaxmin = state->zxy[IDX2D(xi + 1, yi, state)]/(dt*du);
+  zxymaxmax = state->zxy[IDX2D(xi + 1, yi + 1, state)]/(dt*du);
+
+  t0 = 1;
+  t1 = t;
+  t2 = t*t;
+  t3 = t*t2;
+  u0 = 1;
+  u1 = u;
+
+  *z_pp = 0;
+  v = -3*zminmin + 3*zminmax - 2*zyminmin - zyminmax;
+  *z_pp += 2*v*t0*u0;
+  v = 2*zminmin-2*zminmax + zyminmin + zyminmax;
+  *z_pp += 6*v*t0*u1;
+  v = -3*zxminmin + 3*zxminmax - 2*zxyminmin - zxyminmax;
+  *z_pp += 2*v*t1*u0;
+  v = 2*zxminmin - 2*zxminmax + zxyminmin + zxyminmax;
+  *z_pp += 6*v*t1*u1;
+  v = 9*zminmin - 9*zmaxmin + 9*zmaxmax - 9*zminmax + 6*zxminmin + 3*zxmaxmin - 3*zxmaxmax - 6*zxminmax + 6*zyminmin - 6*zymaxmin - 3*zymaxmax + 3*zyminmax + 4*zxyminmin + 2*zxymaxmin + zxymaxmax + 2*zxyminmax;
+  *z_pp += 2*v*t2*u0;
+  v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 4*zxminmin - 2*zxmaxmin + 2*zxmaxmax + 4*zxminmax - 3*zyminmin + 3*zymaxmin + 3*zymaxmax - 3*zyminmax - 2*zxyminmin - zxymaxmin - zxymaxmax - 2*zxyminmax;
+  *z_pp += 6*v*t2*u1;
+  v = -6*zminmin + 6*zmaxmin - 6*zmaxmax + 6*zminmax - 3*zxminmin - 3*zxmaxmin + 3*zxmaxmax + 3*zxminmax - 4*zyminmin + 4*zymaxmin + 2*zymaxmax - 2*zyminmax - 2*zxyminmin - 2*zxymaxmin - zxymaxmax - zxyminmax;
+  *z_pp += 2*v*t3*u0;
+  v = 4*zminmin - 4*zmaxmin + 4*zmaxmax - 4*zminmax + 2*zxminmin + 2*zxmaxmin - 2*zxmaxmax - 2*zxminmax + 2*zyminmin - 2*zymaxmin - 2*zymaxmax + 2*zyminmax + zxyminmin + zxymaxmin + zxymaxmax + zxyminmax;
+  *z_pp += 6*v*t3*u1;
+  *z_pp *= du*du;
+
+  return GSL_SUCCESS;
+}
+
+static const gsl_interp2d_type bicubic_type = {
+  "bicubic",
+  4,
+  &bicubic_alloc,
+  &bicubic_init,
+  &bicubic_eval,
+  &bicubic_deriv_x,
+  &bicubic_deriv_y,
+  &bicubic_deriv_xx,
+  &bicubic_deriv_xy,
+  &bicubic_deriv_yy,
+  &bicubic_free
+};
+
+const gsl_interp2d_type * gsl_interp2d_bicubic = &bicubic_type;
+
+#undef IDX2D
diff -Nru gsl-doc-1.16/interpolation/bilinear.c gsl-doc-2.3/interpolation/bilinear.c
--- gsl-doc-1.16/interpolation/bilinear.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/interpolation/bilinear.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,212 @@
+/* interpolation/bilinear.c
+ * 
+ * Copyright 2012 David Zaslavsky
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_interp.h>
+#include <gsl/gsl_interp2d.h>
+
+#define IDX2D(i, j, xsize, ysize) ((j) * (xsize) + (i))
+
+static int
+bilinear_init(void * state, const double xa[], const double ya[],
+              const double za[], size_t xsize, size_t ysize)
+{
+  return GSL_SUCCESS;
+}
+
+static int
+bilinear_eval(const void * state, const double xarr[], const double yarr[],
+              const double zarr[], size_t xsize, size_t ysize,
+              double x, double y, gsl_interp_accel * xa,
+              gsl_interp_accel * ya, double * z)
+{
+  double xmin, xmax, ymin, ymax, zminmin, zminmax, zmaxmin, zmaxmax;
+  double dx, dy;
+  double t, u;
+  size_t xi, yi;
+
+  if (xa != NULL)
+    xi = gsl_interp_accel_find(xa, xarr, xsize, x);
+  else
+    xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
+
+  if (ya != NULL)
+    yi = gsl_interp_accel_find(ya, yarr, ysize, y);
+  else
+    yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
+
+  xmin = xarr[xi];
+  xmax = xarr[xi + 1];
+  ymin = yarr[yi];
+  ymax = yarr[yi + 1];
+  zminmin = zarr[IDX2D(xi, yi, xsize, ysize)];
+  zminmax = zarr[IDX2D(xi, yi + 1, xsize, ysize)];
+  zmaxmin = zarr[IDX2D(xi + 1, yi, xsize, ysize)];
+  zmaxmax = zarr[IDX2D(xi + 1, yi + 1, xsize, ysize)];
+  dx = xmax - xmin;
+  dy = ymax - ymin;
+  t = (x - xmin)/dx;
+  u = (y - ymin)/dy;
+  *z = (1.-t)*(1.-u)*zminmin + t*(1.-u)*zmaxmin + (1.-t)*u*zminmax + t*u*zmaxmax;
+
+  return GSL_SUCCESS;
+}
+
+static int
+bilinear_deriv_x(const void * state, const double xarr[],
+                 const double yarr[], const double zarr[],
+                 size_t xsize, size_t ysize, double x, double y,
+                 gsl_interp_accel * xa, gsl_interp_accel * ya, double * z_p)
+{
+  double xmin, xmax, ymin, ymax, zminmin, zminmax, zmaxmin, zmaxmax;
+  double dx, dy;
+  double dt, u;
+  size_t xi, yi;
+
+  if (xa != NULL)
+    xi = gsl_interp_accel_find(xa, xarr, xsize, x);
+  else
+    xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
+
+  if (ya != NULL)
+    yi = gsl_interp_accel_find(ya, yarr, ysize, y);
+  else
+    yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
+
+  xmin = xarr[xi];
+  xmax = xarr[xi + 1];
+  ymin = yarr[yi];
+  ymax = yarr[yi + 1];
+  zminmin = zarr[IDX2D(xi, yi, xsize, ysize)];
+  zminmax = zarr[IDX2D(xi, yi + 1, xsize, ysize)];
+  zmaxmin = zarr[IDX2D(xi + 1, yi, xsize, ysize)];
+  zmaxmax = zarr[IDX2D(xi + 1, yi + 1, xsize, ysize)];
+  dx = xmax - xmin;
+  dy = ymax - ymin;
+  dt = 1./dx; /* partial t / partial x */
+  u = (y - ymin)/dy;
+  *z_p = dt*(-(1.-u)*zminmin + (1.-u)*zmaxmin - u*zminmax + u*zmaxmax);
+
+  return GSL_SUCCESS;
+}
+
+static int
+bilinear_deriv_y(const void * state, const double xarr[],
+                 const double yarr[], const double zarr[],
+                 size_t xsize, size_t ysize, double x, double y,
+                 gsl_interp_accel * xa, gsl_interp_accel * ya, double * z_p)
+{
+  double xmin, xmax, ymin, ymax, zminmin, zminmax, zmaxmin, zmaxmax;
+  double dx, dy;
+  double t, du;
+  size_t xi, yi;
+
+  if (xa != NULL)
+    xi = gsl_interp_accel_find(xa, xarr, xsize, x);
+  else
+    xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
+
+  if (ya != NULL)
+    yi = gsl_interp_accel_find(ya, yarr, ysize, y);
+  else
+    yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
+
+  xmin = xarr[xi];
+  xmax = xarr[xi + 1];
+  ymin = yarr[yi];
+  ymax = yarr[yi + 1];
+  zminmin = zarr[IDX2D(xi, yi, xsize, ysize)];
+  zminmax = zarr[IDX2D(xi, yi + 1, xsize, ysize)];
+  zmaxmin = zarr[IDX2D(xi + 1, yi, xsize, ysize)];
+  zmaxmax = zarr[IDX2D(xi + 1, yi + 1, xsize, ysize)];
+  dx = xmax - xmin;
+  dy = ymax - ymin;
+  t = (x - xmin)/dx;
+  du = 1./dy; /* partial u / partial y */
+  *z_p = du*(-(1.-t)*zminmin - t*zmaxmin + (1.-t)*zminmax + t*zmaxmax);
+
+  return GSL_SUCCESS;
+}
+
+static int
+bilinear_deriv2(const void * state, const double xarr[],
+                const double yarr[], const double zarr[],
+                size_t xsize, size_t ysize, double x, double y,
+                gsl_interp_accel * xa, gsl_interp_accel * ya, double * z_pp)
+{
+  *z_pp = 0.0;
+  return GSL_SUCCESS;
+}
+
+static int
+bilinear_derivxy(const void * state, const double xarr[],
+                 const double yarr[], const double zarr[],
+                 size_t xsize, size_t ysize, double x, double y,
+                 gsl_interp_accel * xa, gsl_interp_accel * ya, double * z_pp)
+{
+  double xmin, xmax, ymin, ymax, zminmin, zminmax, zmaxmin, zmaxmax;
+  double dx, dy;
+  double dt, du;
+  size_t xi, yi;
+
+  if (xa != NULL)
+    xi = gsl_interp_accel_find(xa, xarr, xsize, x);
+  else
+    xi = gsl_interp_bsearch(xarr, x, 0, xsize - 1);
+
+  if (ya != NULL)
+    yi = gsl_interp_accel_find(ya, yarr, ysize, y);
+  else
+    yi = gsl_interp_bsearch(yarr, y, 0, ysize - 1);
+
+  xmin = xarr[xi];
+  xmax = xarr[xi + 1];
+  ymin = yarr[yi];
+  ymax = yarr[yi + 1];
+  zminmin = zarr[IDX2D(xi, yi, xsize, ysize)];
+  zminmax = zarr[IDX2D(xi, yi + 1, xsize, ysize)];
+  zmaxmin = zarr[IDX2D(xi + 1, yi, xsize, ysize)];
+  zmaxmax = zarr[IDX2D(xi + 1, yi + 1, xsize, ysize)];
+  dx = xmax - xmin;
+  dy = ymax - ymin;
+  dt = 1./dx; /* partial t / partial x */
+  du = 1./dy; /* partial u / partial y */
+  *z_pp = dt*du*(zminmin-zmaxmin-zminmax+zmaxmax);
+
+  return GSL_SUCCESS;
+}
+
+static const gsl_interp2d_type bilinear_type = {
+  "bilinear",
+  2,
+  NULL,
+  &bilinear_init,
+  &bilinear_eval,
+  &bilinear_deriv_x,
+  &bilinear_deriv_y,
+  &bilinear_deriv2,
+  &bilinear_derivxy,
+  &bilinear_deriv2,
+  NULL
+};
+
+const gsl_interp2d_type * gsl_interp2d_bilinear = &bilinear_type;
+
+#undef IDX2D
diff -Nru gsl-doc-1.16/interpolation/gsl_interp2d.h gsl-doc-2.3/interpolation/gsl_interp2d.h
--- gsl-doc-1.16/interpolation/gsl_interp2d.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/interpolation/gsl_interp2d.h	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,160 @@
+/* interpolation/gsl_interp2d.h
+ * 
+ * Copyright 2012 David Zaslavsky
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_INTERP2D_H__
+#define __GSL_INTERP2D_H__
+
+#include <gsl/gsl_interp.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+typedef struct {
+    const char* name;
+    unsigned int min_size;
+    void * (*alloc)(size_t xsize, size_t ysize);
+    int    (*init)(void *, const double xa[], const double ya[], const double za[], size_t xsize, size_t ysize);
+    int    (*eval)(const void *, const double xa[], const double ya[], const double za[], size_t xsize, size_t ysize, double x, double y, gsl_interp_accel*, gsl_interp_accel*, double* z);
+    int    (*eval_deriv_x) (const void *, const double xa[], const double ya[], const double za[], size_t xsize, size_t ysize, double x, double y, gsl_interp_accel*, gsl_interp_accel*, double* z_p);
+    int    (*eval_deriv_y) (const void *, const double xa[], const double ya[], const double za[], size_t xsize, size_t ysize, double x, double y, gsl_interp_accel*, gsl_interp_accel*, double* z_p);
+    int    (*eval_deriv_xx) (const void *, const double xa[], const double ya[], const double za[], size_t xsize, size_t ysize, double x, double y, gsl_interp_accel*, gsl_interp_accel*, double* z_pp);
+    int    (*eval_deriv_xy) (const void *, const double xa[], const double ya[], const double za[], size_t xsize, size_t ysize, double x, double y, gsl_interp_accel*, gsl_interp_accel*, double* z_pp);
+    int    (*eval_deriv_yy) (const void *, const double xa[], const double ya[], const double za[], size_t xsize, size_t ysize, double x, double y, gsl_interp_accel*, gsl_interp_accel*, double* z_pp);
+    void   (*free)(void *);
+} gsl_interp2d_type;
+
+typedef struct {
+    const gsl_interp2d_type * type; /* interpolation type */
+    double xmin;                    /* minimum value of x for which data have been provided */
+    double xmax;                    /* maximum value of x for which data have been provided */
+    double ymin;                    /* minimum value of y for which data have been provided */
+    double ymax;                    /* maximum value of y for which data have been provided */
+    size_t xsize;                   /* number of x values provided */
+    size_t ysize;                   /* number of y values provided */
+    void * state;                   /* internal state object specific to the interpolation type */
+} gsl_interp2d;
+
+/* available types */
+GSL_VAR const gsl_interp2d_type * gsl_interp2d_bilinear;
+GSL_VAR const gsl_interp2d_type * gsl_interp2d_bicubic;
+
+gsl_interp2d * gsl_interp2d_alloc(const gsl_interp2d_type * T, const size_t xsize,
+                                  const size_t ysize);
+
+const char * gsl_interp2d_name(const gsl_interp2d * interp);
+size_t gsl_interp2d_min_size(const gsl_interp2d * interp);
+size_t gsl_interp2d_type_min_size(const gsl_interp2d_type * T);
+int gsl_interp2d_set(const gsl_interp2d * interp, double zarr[],
+                     const size_t i, const size_t j, const double z);
+double gsl_interp2d_get(const gsl_interp2d * interp, const double zarr[],
+                        const size_t i, const size_t j);
+size_t gsl_interp2d_idx(const gsl_interp2d * interp,
+                        const size_t i, const size_t j);
+int gsl_interp2d_init(gsl_interp2d * interp, const double xa[], const double ya[],
+                      const double za[], const size_t xsize, const size_t ysize);
+void gsl_interp2d_free(gsl_interp2d * interp);
+
+double gsl_interp2d_eval(const gsl_interp2d * interp, const double xarr[],
+                         const double yarr[], const double zarr[], const double x,
+                         const double y, gsl_interp_accel * xa, gsl_interp_accel * ya);
+
+double gsl_interp2d_eval_extrap(const gsl_interp2d * interp,
+                                const double xarr[], const double yarr[],
+                                const double zarr[], const double x,
+                                const double y, gsl_interp_accel * xa,
+                                gsl_interp_accel * ya);
+
+int gsl_interp2d_eval_e(const gsl_interp2d * interp, const double xarr[],
+                        const double yarr[], const double zarr[],
+                        const double x, const double y, gsl_interp_accel* xa,
+                        gsl_interp_accel* ya, double * z);
+
+int gsl_interp2d_eval_e_extrap(const gsl_interp2d * interp,
+                               const double xarr[],
+                               const double yarr[],
+                               const double zarr[],
+                               const double x,
+                               const double y,
+                               gsl_interp_accel * xa,
+                               gsl_interp_accel * ya,
+                               double * z);
+
+double gsl_interp2d_eval_deriv_x(const gsl_interp2d * interp, const double xarr[],
+                                 const double yarr[], const double zarr[],
+                                 const double x, const double y, gsl_interp_accel * xa,
+                                 gsl_interp_accel * ya);
+
+int gsl_interp2d_eval_deriv_x_e(const gsl_interp2d * interp, const double xarr[],
+                                const double yarr[], const double zarr[],
+                                const double x, const double y,
+                                gsl_interp_accel * xa, gsl_interp_accel * ya, double * z);
+
+double gsl_interp2d_eval_deriv_y(const gsl_interp2d * interp, const double xarr[],
+                                 const double yarr[], const double zarr[],
+                                 const double x, const double y,
+                                 gsl_interp_accel* xa, gsl_interp_accel* ya);
+
+int gsl_interp2d_eval_deriv_y_e(const gsl_interp2d * interp, const double xarr[],
+                                const double yarr[], const double zarr[],
+                                const double x, const double y,
+                                gsl_interp_accel * xa, gsl_interp_accel * ya, double * z);
+
+double gsl_interp2d_eval_deriv_xx(const gsl_interp2d * interp, const double xarr[],
+                                  const double yarr[], const double zarr[],
+                                  const double x, const double y,
+                                  gsl_interp_accel * xa, gsl_interp_accel * ya);
+
+int gsl_interp2d_eval_deriv_xx_e(const gsl_interp2d * interp, const double xarr[],
+                                 const double yarr[], const double zarr[],
+                                 const double x, const double y,
+                                 gsl_interp_accel * xa, gsl_interp_accel * ya, double * z);
+
+double gsl_interp2d_eval_deriv_yy(const gsl_interp2d * interp, const double xarr[],
+                                  const double yarr[], const double zarr[],
+                                  const double x, const double y,
+                                  gsl_interp_accel * xa, gsl_interp_accel * ya);
+
+int gsl_interp2d_eval_deriv_yy_e(const gsl_interp2d * interp, const double xarr[],
+                                 const double yarr[], const double zarr[],
+                                 const double x, const double y,
+                                 gsl_interp_accel * xa, gsl_interp_accel * ya, double * z);
+
+double gsl_interp2d_eval_deriv_xy(const gsl_interp2d * interp, const double xarr[],
+                                  const double yarr[], const double zarr[],
+                                  const double x, const double y,
+                                  gsl_interp_accel * xa, gsl_interp_accel * ya);
+
+int gsl_interp2d_eval_deriv_xy_e(const gsl_interp2d * interp, const double xarr[],
+                                 const double yarr[], const double zarr[],
+                                 const double x, const double y,
+                                 gsl_interp_accel * xa, gsl_interp_accel * ya, double * z);
+
+
+__END_DECLS
+
+#endif /* __GSL_INTERP2D_H__ */
diff -Nru gsl-doc-1.16/interpolation/gsl_interp.h gsl-doc-2.3/interpolation/gsl_interp.h
--- gsl-doc-1.16/interpolation/gsl_interp.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/interpolation/gsl_interp.h	2015-11-03 16:21:55.000000000 +0000
@@ -78,6 +78,7 @@
 GSL_VAR const gsl_interp_type * gsl_interp_cspline_periodic;
 GSL_VAR const gsl_interp_type * gsl_interp_akima;
 GSL_VAR const gsl_interp_type * gsl_interp_akima_periodic;
+GSL_VAR const gsl_interp_type * gsl_interp_steffen;
 
 gsl_interp_accel *
 gsl_interp_accel_alloc(void);
diff -Nru gsl-doc-1.16/interpolation/gsl_spline2d.h gsl-doc-2.3/interpolation/gsl_spline2d.h
--- gsl-doc-1.16/interpolation/gsl_spline2d.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/interpolation/gsl_spline2d.h	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,113 @@
+/* interpolation/gsl_spline2d.h
+ * 
+ * Copyright 2012 David Zaslavsky
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_SPLINE2D_H__
+#define __GSL_SPLINE2D_H__
+
+#include <gsl/gsl_interp.h>
+#include <gsl/gsl_interp2d.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+
+/*
+ * A 2D interpolation object which stores the arrays defining the function.
+ * In all other respects, this is just like a gsl_interp2d object.
+ */
+typedef struct
+{
+  gsl_interp2d interp_object; /* low-level interpolation object */
+  double * xarr;              /* x data array */
+  double * yarr;              /* y data array */
+  double * zarr;              /* z data array */
+} gsl_spline2d;
+
+gsl_spline2d * gsl_spline2d_alloc(const gsl_interp2d_type * T, size_t xsize, size_t ysize);
+
+int gsl_spline2d_init(gsl_spline2d * interp, const double xa[],
+                      const double ya[], const double za[],
+                      size_t xsize, size_t ysize);
+
+void gsl_spline2d_free(gsl_spline2d * interp);
+
+double gsl_spline2d_eval(const gsl_spline2d * interp, const double x,
+                         const double y, gsl_interp_accel* xa, gsl_interp_accel* ya);
+
+int gsl_spline2d_eval_e(const gsl_spline2d * interp, const double x,
+                        const double y, gsl_interp_accel* xa, gsl_interp_accel* ya,
+                        double * z);
+
+double gsl_spline2d_eval_deriv_x(const gsl_spline2d * interp, const double x,
+                                 const double y, gsl_interp_accel* xa, gsl_interp_accel* ya);
+
+int gsl_spline2d_eval_deriv_x_e(const gsl_spline2d * interp, const double x,
+                                const double y, gsl_interp_accel* xa,
+                                gsl_interp_accel* ya, double * z);
+
+double gsl_spline2d_eval_deriv_y(const gsl_spline2d * interp, const double x,
+                                 const double y, gsl_interp_accel* xa,
+                                 gsl_interp_accel* ya);
+
+int gsl_spline2d_eval_deriv_y_e(const gsl_spline2d * interp, const double x,
+                                const double y, gsl_interp_accel* xa,
+                                gsl_interp_accel* ya, double * z);
+
+double gsl_spline2d_eval_deriv_xx(const gsl_spline2d * interp, const double x,
+                                  const double y, gsl_interp_accel* xa, gsl_interp_accel* ya);
+
+int gsl_spline2d_eval_deriv_xx_e(const gsl_spline2d * interp, const double x,
+                                 const double y, gsl_interp_accel* xa,
+                                 gsl_interp_accel* ya, double * z);
+
+double gsl_spline2d_eval_deriv_yy(const gsl_spline2d * interp, const double x,
+                                  const double y, gsl_interp_accel* xa, gsl_interp_accel* ya);
+
+int gsl_spline2d_eval_deriv_yy_e(const gsl_spline2d * interp, const double x,
+                                 const double y, gsl_interp_accel* xa,
+                                 gsl_interp_accel* ya, double * z);
+
+double gsl_spline2d_eval_deriv_xy(const gsl_spline2d * interp, const double x,
+                                  const double y, gsl_interp_accel* xa, gsl_interp_accel* ya);
+
+int gsl_spline2d_eval_deriv_xy_e(const gsl_spline2d * interp, const double x,
+                                 const double y, gsl_interp_accel* xa,
+                                 gsl_interp_accel* ya, double * z);
+
+size_t gsl_spline2d_min_size(const gsl_spline2d * interp);
+
+const char * gsl_spline2d_name(const gsl_spline2d * interp);
+
+int gsl_spline2d_set(const gsl_spline2d * interp, double zarr[],
+                     const size_t i, const size_t j, const double z);
+double gsl_spline2d_get(const gsl_spline2d * interp, const double zarr[],
+                        const size_t i, const size_t j);
+
+__END_DECLS
+
+#endif /* __GSL_SPLINE2D_H__ */
diff -Nru gsl-doc-1.16/interpolation/interp2d.c gsl-doc-2.3/interpolation/interp2d.c
--- gsl-doc-1.16/interpolation/interp2d.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/interpolation/interp2d.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,411 @@
+/* interpolation/interp2d.c
+ * 
+ * Copyright 2012 David Zaslavsky
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_interp.h>
+#include <gsl/gsl_interp2d.h>
+
+/**
+ * Triggers a GSL error if the argument is not equal to GSL_SUCCESS.
+ * If the argument is GSL_SUCCESS, this does nothing.
+ */
+#define DISCARD_STATUS(s) if ((s) != GSL_SUCCESS) { GSL_ERROR_VAL("interpolation error", (s),  GSL_NAN); }
+
+#define IDX2D(i, j, w) ((j) * ((w)->xsize) + (i))
+
+gsl_interp2d *
+gsl_interp2d_alloc(const gsl_interp2d_type * T, const size_t xsize,
+                   const size_t ysize)
+{
+  gsl_interp2d * interp;
+
+  if (xsize < T->min_size || ysize < T->min_size)
+    {
+      GSL_ERROR_NULL ("insufficient number of points for interpolation type",
+                      GSL_EINVAL);
+    }
+
+  interp = (gsl_interp2d *) calloc(1, sizeof(gsl_interp2d));
+  if (interp == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for gsl_interp2d struct",
+                      GSL_ENOMEM);
+    }
+
+  interp->type = T;
+  interp->xsize = xsize;
+  interp->ysize = ysize;
+
+  if (interp->type->alloc == NULL)
+    {
+      interp->state = NULL;
+      return interp;
+    }
+
+  interp->state = interp->type->alloc(xsize, ysize);
+  if (interp->state == NULL)
+    {
+      free(interp);
+      GSL_ERROR_NULL ("failed to allocate space for gsl_interp2d state",
+                      GSL_ENOMEM);
+    }
+
+  return interp;
+} /* gsl_interp2d_alloc() */
+
+void
+gsl_interp2d_free (gsl_interp2d * interp)
+{
+  RETURN_IF_NULL(interp);
+
+  if (interp->type->free)
+    interp->type->free(interp->state);
+
+  free(interp);
+} /* gsl_interp2d_free() */
+
+int
+gsl_interp2d_init (gsl_interp2d * interp, const double xarr[], const double yarr[],
+                   const double zarr[], const size_t xsize, const size_t ysize)
+{
+  size_t i;
+
+  if (xsize != interp->xsize || ysize != interp->ysize)
+    {
+      GSL_ERROR("data must match size of interpolation object", GSL_EINVAL);
+    }
+
+  for (i = 1; i < xsize; i++)
+    {
+      if (xarr[i-1] >= xarr[i])
+        {
+          GSL_ERROR("x values must be strictly increasing", GSL_EINVAL);
+        }
+    }
+
+  for (i = 1; i < ysize; i++)
+    {
+      if (yarr[i-1] >= yarr[i])
+        {
+          GSL_ERROR("y values must be strictly increasing", GSL_EINVAL);
+        }
+    }
+
+  interp->xmin = xarr[0];
+  interp->xmax = xarr[xsize - 1];
+  interp->ymin = yarr[0];
+  interp->ymax = yarr[ysize - 1];
+
+  {
+    int status = interp->type->init(interp->state, xarr, yarr, zarr,
+                                    xsize, ysize);
+    return status;
+  }
+} /* gsl_interp2d_init() */
+
+/*
+ * A wrapper function that checks boundary conditions, calls an evaluator
+ * which implements the actual calculation of the function value or 
+ * derivative etc., and checks the return status.
+ */
+static int
+interp2d_eval(int (*evaluator)(const void *, const double xa[], const double ya[],
+                               const double za[], size_t xsize, size_t ysize,
+                               double x, double y, gsl_interp_accel *,
+                               gsl_interp_accel *, double * z),
+              const gsl_interp2d * interp, const double xarr[],
+              const double yarr[], const double zarr[],
+              const double x, const double y,
+              gsl_interp_accel * xa, gsl_interp_accel * ya,
+              double * result)
+{
+  if (x < interp->xmin || x > interp->xmax)
+    {
+      GSL_ERROR ("interpolation x value out of range", GSL_EDOM);
+    }
+  else if (y < interp->ymin || y > interp->ymax)
+    {
+      GSL_ERROR ("interpolation y value out of range", GSL_EDOM);
+    }
+
+  return evaluator(interp->state, xarr, yarr, zarr,
+                   interp->xsize, interp->ysize,
+                   x, y, xa, ya, result);
+}
+
+/*
+ * Another wrapper function that serves as a drop-in replacement for
+ * interp2d_eval but does not check the bounds. This can be used
+ * for extrapolation.
+ */
+static int
+interp2d_eval_extrap(int (*evaluator)(const void *, const double xa[],
+                                      const double ya[], const double za[],
+                                      size_t xsize, size_t ysize,
+                                      double x, double y,
+                                      gsl_interp_accel *,
+                                      gsl_interp_accel *, double * z),
+                     const gsl_interp2d * interp, const double xarr[],
+                     const double yarr[], const double zarr[],
+                     const double x, const double y,
+                     gsl_interp_accel * xa, gsl_interp_accel * ya,
+                     double * result)
+{
+  return evaluator(interp->state, xarr, yarr, zarr,
+                   interp->xsize, interp->ysize, x, y, xa, ya, result);
+}
+
+double
+gsl_interp2d_eval (const gsl_interp2d * interp, const double xarr[],
+                   const double yarr[], const double zarr[],
+                   const double x, const double y,
+                   gsl_interp_accel * xa, gsl_interp_accel * ya)
+{
+  double z;
+  int status = gsl_interp2d_eval_e(interp, xarr, yarr, zarr, x, y, xa, ya, &z);
+  DISCARD_STATUS(status)
+  return z;
+} /* gsl_interp2d_eval() */
+
+double
+gsl_interp2d_eval_extrap (const gsl_interp2d * interp,
+                          const double xarr[],
+                          const double yarr[],
+                          const double zarr[],
+                          const double x,
+                          const double y,
+                          gsl_interp_accel * xa,
+                          gsl_interp_accel * ya)
+{
+  double z;
+  int status =
+    interp2d_eval_extrap(interp->type->eval, interp,
+                         xarr, yarr, zarr, x, y, xa, ya, &z);
+  DISCARD_STATUS(status)
+  return z;
+}
+
+int
+gsl_interp2d_eval_e (const gsl_interp2d * interp, const double xarr[],
+                     const double yarr[], const double zarr[],
+                     const double x, const double y,
+                     gsl_interp_accel * xa, gsl_interp_accel * ya, double * z)
+{
+  return interp2d_eval(interp->type->eval, interp,
+                       xarr, yarr, zarr, x, y, xa, ya, z);
+} /* gsl_interp2d_eval_e() */
+
+int
+gsl_interp2d_eval_e_extrap (const gsl_interp2d * interp,
+                            const double xarr[], const double yarr[],
+                            const double zarr[], const double x,
+                            const double y, gsl_interp_accel * xa,
+                            gsl_interp_accel * ya, double * z)
+{
+  return interp2d_eval_extrap(interp->type->eval, interp,
+                              xarr, yarr, zarr, x, y, xa, ya, z);
+}
+
+double
+gsl_interp2d_eval_deriv_x (const gsl_interp2d * interp, const double xarr[],
+                           const double yarr[], const double zarr[],
+                           const double x, const double y,
+                           gsl_interp_accel * xa, gsl_interp_accel * ya)
+{
+  double z;
+  int status = gsl_interp2d_eval_deriv_x_e(interp, xarr, yarr, zarr, x, y, xa, ya, &z);
+  DISCARD_STATUS(status)
+  return z;
+}
+
+int
+gsl_interp2d_eval_deriv_x_e (const gsl_interp2d * interp, const double xarr[],
+                             const double yarr[], const double zarr[],
+                             const double x, const double y,
+                             gsl_interp_accel * xa, gsl_interp_accel * ya, double * z)
+{
+  return interp2d_eval(interp->type->eval_deriv_x, interp,
+                       xarr, yarr, zarr, x, y, xa, ya, z);
+}
+
+double
+gsl_interp2d_eval_deriv_y (const gsl_interp2d * interp, const double xarr[],
+                           const double yarr[], const double zarr[],
+                           const double x, const double y,
+                           gsl_interp_accel * xa, gsl_interp_accel * ya)
+{
+  double z;
+  int status = gsl_interp2d_eval_deriv_y_e(interp, xarr, yarr, zarr, x, y, xa, ya, &z);
+  DISCARD_STATUS(status)
+  return z;
+}
+
+int
+gsl_interp2d_eval_deriv_y_e (const gsl_interp2d * interp, const double xarr[],
+                             const double yarr[], const double zarr[],
+                             const double x, const double y,
+                             gsl_interp_accel * xa, gsl_interp_accel * ya, double * z)
+{
+  return interp2d_eval(interp->type->eval_deriv_y, interp,
+                       xarr, yarr, zarr, x, y, xa, ya, z);
+}
+
+double
+gsl_interp2d_eval_deriv_xx (const gsl_interp2d * interp, const double xarr[],
+                            const double yarr[], const double zarr[],
+                            const double x, const double y,
+                            gsl_interp_accel * xa, gsl_interp_accel * ya)
+{
+  double z;
+  int status = gsl_interp2d_eval_deriv_xx_e(interp, xarr, yarr, zarr, x, y, xa, ya, &z);
+  DISCARD_STATUS(status)
+  return z;
+}
+
+int
+gsl_interp2d_eval_deriv_xx_e (const gsl_interp2d * interp, const double xarr[],
+                              const double yarr[], const double zarr[],
+                              const double x, const double y,
+                              gsl_interp_accel * xa, gsl_interp_accel * ya, double * z)
+{
+  return interp2d_eval(interp->type->eval_deriv_xx, interp,
+                       xarr, yarr, zarr, x, y, xa, ya, z);
+}
+
+double
+gsl_interp2d_eval_deriv_yy (const gsl_interp2d * interp, const double xarr[],
+                            const double yarr[], const double zarr[],
+                            const double x, const double y,
+                            gsl_interp_accel * xa, gsl_interp_accel * ya)
+{
+  double z;
+  int status = gsl_interp2d_eval_deriv_yy_e(interp, xarr, yarr, zarr, x, y, xa, ya, &z);
+  DISCARD_STATUS(status)
+  return z;
+}
+
+int
+gsl_interp2d_eval_deriv_yy_e (const gsl_interp2d * interp, const double xarr[],
+                              const double yarr[], const double zarr[],
+                              const double x, const double y,
+                              gsl_interp_accel * xa, gsl_interp_accel * ya, double * z)
+{
+  return interp2d_eval(interp->type->eval_deriv_yy, interp,
+                       xarr, yarr, zarr, x, y, xa, ya, z);
+}
+
+double
+gsl_interp2d_eval_deriv_xy (const gsl_interp2d * interp, const double xarr[],
+                            const double yarr[], const double zarr[],
+                            const double x, const double y,
+                            gsl_interp_accel * xa, gsl_interp_accel * ya)
+{
+  double z;
+  int status = gsl_interp2d_eval_deriv_xy_e(interp, xarr, yarr, zarr, x, y, xa, ya, &z);
+  DISCARD_STATUS(status)
+  return z;
+}
+
+int
+gsl_interp2d_eval_deriv_xy_e (const gsl_interp2d * interp, const double xarr[],
+                              const double yarr[], const double zarr[],
+                              const double x, const double y,
+                              gsl_interp_accel * xa, gsl_interp_accel * ya, double * z)
+{
+  return interp2d_eval(interp->type->eval_deriv_xy, interp,
+                       xarr, yarr, zarr, x, y, xa, ya, z);
+}
+
+size_t
+gsl_interp2d_type_min_size(const gsl_interp2d_type * T)
+{
+  return T->min_size;
+}
+
+size_t
+gsl_interp2d_min_size(const gsl_interp2d * interp)
+{
+  return interp->type->min_size;
+}
+
+const char *
+gsl_interp2d_name(const gsl_interp2d * interp)
+{
+  return interp->type->name;
+}
+
+size_t
+gsl_interp2d_idx(const gsl_interp2d * interp,
+                 const size_t i, const size_t j)
+{
+  if (i >= interp->xsize)
+    {
+      GSL_ERROR_VAL ("x index out of range", GSL_ERANGE, 0);
+    }
+  else if (j >= interp->ysize)
+    {
+      GSL_ERROR_VAL ("y index out of range", GSL_ERANGE, 0);
+    }
+  else
+    {
+      return IDX2D(i, j, interp);
+    }
+} /* gsl_interp2d_idx() */
+
+int
+gsl_interp2d_set(const gsl_interp2d * interp, double zarr[],
+                 const size_t i, const size_t j, const double z)
+{
+  if (i >= interp->xsize)
+    {
+      GSL_ERROR ("x index out of range", GSL_ERANGE);
+    }
+  else if (j >= interp->ysize)
+    {
+      GSL_ERROR ("y index out of range", GSL_ERANGE);
+    }
+  else
+    {
+      zarr[IDX2D(i, j, interp)] = z;
+      return GSL_SUCCESS;
+    }
+} /* gsl_interp2d_set() */
+
+double
+gsl_interp2d_get(const gsl_interp2d * interp, const double zarr[],
+                 const size_t i, const size_t j)
+{
+  if (i >= interp->xsize)
+    {
+      GSL_ERROR_VAL ("x index out of range", GSL_ERANGE, 0);
+    }
+  else if (j >= interp->ysize)
+    {
+      GSL_ERROR_VAL ("y index out of range", GSL_ERANGE, 0);
+    }
+  else
+    {
+      return zarr[IDX2D(i, j, interp)];
+    }
+} /* gsl_interp2d_get() */
+
+#undef IDX2D
diff -Nru gsl-doc-1.16/interpolation/Makefile.am gsl-doc-2.3/interpolation/Makefile.am
--- gsl-doc-1.16/interpolation/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/interpolation/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,11 +2,13 @@
 
 check_PROGRAMS = test
 
-pkginclude_HEADERS = gsl_interp.h gsl_spline.h
+pkginclude_HEADERS = gsl_interp.h gsl_spline.h gsl_interp2d.h gsl_spline2d.h
 
-libgslinterpolation_la_SOURCES = accel.c akima.c cspline.c interp.c linear.c integ_eval.h spline.c poly.c inline.c
+libgslinterpolation_la_SOURCES = accel.c akima.c cspline.c interp.c linear.c integ_eval.h spline.c poly.c steffen.c inline.c interp2d.c bilinear.c bicubic.c spline2d.c
 
-INCLUDES = -I$(top_srcdir)
+noinst_HEADERS = test2d.c
+
+AM_CPPFLAGS = -I$(top_srcdir)
 
 TESTS = $(check_PROGRAMS)
 
diff -Nru gsl-doc-1.16/interpolation/Makefile.in gsl-doc-2.3/interpolation/Makefile.in
--- gsl-doc-1.16/interpolation/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/interpolation/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -83,7 +83,8 @@
 subdir = interpolation
 DIST_COMMON = $(srcdir)/Makefile.in $(srcdir)/Makefile.am \
 	$(top_srcdir)/mkinstalldirs $(top_srcdir)/depcomp \
-	$(pkginclude_HEADERS) $(top_srcdir)/test-driver ChangeLog TODO
+	$(noinst_HEADERS) $(pkginclude_HEADERS) \
+	$(top_srcdir)/test-driver ChangeLog TODO
 ACLOCAL_M4 = $(top_srcdir)/aclocal.m4
 am__aclocal_m4_deps = $(top_srcdir)/configure.ac
 am__configure_deps = $(am__aclocal_m4_deps) $(CONFIGURE_DEPENDENCIES) \
@@ -95,7 +96,8 @@
 LTLIBRARIES = $(noinst_LTLIBRARIES)
 libgslinterpolation_la_LIBADD =
 am_libgslinterpolation_la_OBJECTS = accel.lo akima.lo cspline.lo \
-	interp.lo linear.lo spline.lo poly.lo inline.lo
+	interp.lo linear.lo spline.lo poly.lo steffen.lo inline.lo \
+	interp2d.lo bilinear.lo bicubic.lo spline2d.lo
 libgslinterpolation_la_OBJECTS = $(am_libgslinterpolation_la_OBJECTS)
 AM_V_lt = $(am__v_lt_@AM_V@)
 am__v_lt_ = $(am__v_lt_@AM_DEFAULT_V@)
@@ -179,7 +181,7 @@
          $(am__cd) "$$dir" && rm -f $$files; }; \
   }
 am__installdirs = "$(DESTDIR)$(pkgincludedir)"
-HEADERS = $(pkginclude_HEADERS)
+HEADERS = $(noinst_HEADERS) $(pkginclude_HEADERS)
 am__tagged_files = $(HEADERS) $(SOURCES) $(TAGS_FILES) $(LISP)
 # Read a list of newline-separated strings from the standard input,
 # and print each of them once, without duplicates.  Input order is
@@ -381,6 +383,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -403,7 +406,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -518,9 +524,10 @@
 top_builddir = @top_builddir@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslinterpolation.la 
-pkginclude_HEADERS = gsl_interp.h gsl_spline.h
-libgslinterpolation_la_SOURCES = accel.c akima.c cspline.c interp.c linear.c integ_eval.h spline.c poly.c inline.c
-INCLUDES = -I$(top_srcdir)
+pkginclude_HEADERS = gsl_interp.h gsl_spline.h gsl_interp2d.h gsl_spline2d.h
+libgslinterpolation_la_SOURCES = accel.c akima.c cspline.c interp.c linear.c integ_eval.h spline.c poly.c steffen.c inline.c interp2d.c bilinear.c bicubic.c spline2d.c
+noinst_HEADERS = test2d.c
+AM_CPPFLAGS = -I$(top_srcdir)
 TESTS = $(check_PROGRAMS)
 test_LDADD = libgslinterpolation.la ../poly/libgslpoly.la ../linalg/libgsllinalg.la ../permutation/libgslpermutation.la ../blas/libgslblas.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la ../complex/libgslcomplex.la ../cblas/libgslcblas.la ../ieee-utils/libgslieeeutils.la  ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
 test_SOURCES = test.c
@@ -594,12 +601,17 @@
 
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/accel.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/akima.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/bicubic.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/bilinear.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/cspline.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/inline.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/interp.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/interp2d.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/linear.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/poly.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/spline.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/spline2d.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/steffen.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/test.Po@am__quote@
 
 .c.o:
diff -Nru gsl-doc-1.16/interpolation/spline2d.c gsl-doc-2.3/interpolation/spline2d.c
--- gsl-doc-1.16/interpolation/spline2d.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/interpolation/spline2d.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,241 @@
+/* interpolation/spline2d.c
+ * 
+ * Copyright 2012 David Zaslavsky
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <string.h>
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_interp.h>
+#include <gsl/gsl_interp2d.h>
+#include <gsl/gsl_spline2d.h>
+
+gsl_spline2d *
+gsl_spline2d_alloc(const gsl_interp2d_type * T, size_t xsize, size_t ysize)
+{
+  double * array_mem;
+  gsl_spline2d * interp;
+
+  if (xsize < T->min_size || ysize < T->min_size)
+    {
+      GSL_ERROR_NULL("insufficient number of points for interpolation type", GSL_EINVAL);
+    }
+
+  interp = calloc(1, sizeof(gsl_spline2d));
+  if (interp == NULL)
+    {
+      GSL_ERROR_NULL("failed to allocate space for gsl_spline2d struct", GSL_ENOMEM);
+    }
+
+  interp->interp_object.type = T;
+  interp->interp_object.xsize = xsize;
+  interp->interp_object.ysize = ysize;
+  if (interp->interp_object.type->alloc == NULL)
+    {
+      interp->interp_object.state = NULL;
+    }
+  else
+    {
+      interp->interp_object.state = interp->interp_object.type->alloc(xsize, ysize);
+      if (interp->interp_object.state == NULL)
+        {
+          gsl_spline2d_free(interp);
+          GSL_ERROR_NULL("failed to allocate space for gsl_spline2d state", GSL_ENOMEM);
+        }
+    }
+
+  /*
+   * Use one contiguous block of memory for all three data arrays.
+   * That way the code fails immediately if there isn't sufficient space for everything,
+   * rather than allocating one or two and then having to free them.
+   */
+  array_mem = (double *)calloc(xsize + ysize + xsize * ysize, sizeof(double));
+  if (array_mem == NULL)
+    {
+      gsl_spline2d_free(interp);
+      GSL_ERROR_NULL("failed to allocate space for data arrays", GSL_ENOMEM);
+    }
+
+  interp->xarr = array_mem;
+  interp->yarr = array_mem + xsize;
+  interp->zarr = array_mem + xsize + ysize;
+
+  return interp;
+} /* gsl_spline2d_alloc() */
+
+int
+gsl_spline2d_init(gsl_spline2d * interp, const double xarr[],
+                  const double yarr[], const double zarr[],
+                  size_t xsize, size_t ysize)
+{
+  int status = gsl_interp2d_init(&(interp->interp_object), xarr, yarr, zarr, xsize, ysize);
+
+  memcpy(interp->xarr, xarr, xsize * sizeof(double));
+  memcpy(interp->yarr, yarr, ysize * sizeof(double));
+  memcpy(interp->zarr, zarr, xsize * ysize * sizeof(double));
+
+  return status;
+} /* gsl_spline2d_init() */
+
+void
+gsl_spline2d_free(gsl_spline2d * interp)
+{
+  RETURN_IF_NULL(interp);
+
+  if (interp->interp_object.type->free)
+    interp->interp_object.type->free(interp->interp_object.state);
+
+  /*
+   * interp->xarr points to the beginning of one contiguous block of memory
+   * that holds interp->xarr, interp->yarr, and interp->zarr. So it all gets
+   * freed with one call. cf. gsl_spline2d_alloc() implementation
+   */
+  if (interp->xarr)
+    free(interp->xarr);
+
+  free(interp);
+} /* gsl_spline2d_free() */
+
+double
+gsl_spline2d_eval(const gsl_spline2d * interp, const double x,
+                  const double y, gsl_interp_accel * xa, gsl_interp_accel * ya)
+{
+  return gsl_interp2d_eval(&(interp->interp_object), interp->xarr, interp->yarr,
+                           interp->zarr, x, y, xa, ya);
+}
+
+int
+gsl_spline2d_eval_e(const gsl_spline2d * interp, const double x,
+                    const double y, gsl_interp_accel * xa, gsl_interp_accel * ya,
+                    double * z)
+{
+  return gsl_interp2d_eval_e(&(interp->interp_object), interp->xarr, interp->yarr,
+                             interp->zarr, x, y, xa, ya, z);
+}
+
+double
+gsl_spline2d_eval_deriv_x(const gsl_spline2d * interp, const double x,
+                          const double y, gsl_interp_accel * xa, gsl_interp_accel * ya)
+{
+  return gsl_interp2d_eval_deriv_x(&(interp->interp_object), interp->xarr, interp->yarr,
+                                   interp->zarr, x, y, xa, ya);
+}
+
+int
+gsl_spline2d_eval_deriv_x_e(const gsl_spline2d * interp, const double x,
+                            const double y, gsl_interp_accel * xa, gsl_interp_accel * ya,
+                            double * z)
+{
+  return gsl_interp2d_eval_deriv_x_e(&(interp->interp_object), interp->xarr, interp->yarr,
+                                     interp->zarr, x, y, xa, ya, z);
+}
+
+double
+gsl_spline2d_eval_deriv_y(const gsl_spline2d * interp, const double x,
+                          const double y, gsl_interp_accel * xa, gsl_interp_accel * ya)
+{
+  return gsl_interp2d_eval_deriv_y(&(interp->interp_object), interp->xarr, interp->yarr,
+                                   interp->zarr, x, y, xa, ya);
+}
+
+int
+gsl_spline2d_eval_deriv_y_e(const gsl_spline2d * interp, const double x,
+                            const double y, gsl_interp_accel * xa, gsl_interp_accel * ya,
+                            double * z)
+{
+  return gsl_interp2d_eval_deriv_y_e(&(interp->interp_object), interp->xarr, interp->yarr,
+                                     interp->zarr, x, y, xa, ya, z);
+}
+
+double
+gsl_spline2d_eval_deriv_xx(const gsl_spline2d * interp, const double x,
+                           const double y, gsl_interp_accel * xa, gsl_interp_accel * ya)
+{
+  return gsl_interp2d_eval_deriv_xx(&(interp->interp_object), interp->xarr, interp->yarr,
+                                    interp->zarr, x, y, xa, ya);
+}
+
+int
+gsl_spline2d_eval_deriv_xx_e(const gsl_spline2d * interp, const double x,
+                             const double y, gsl_interp_accel * xa, gsl_interp_accel * ya,
+                             double * z)
+{
+  return gsl_interp2d_eval_deriv_xx_e(&(interp->interp_object), interp->xarr, interp->yarr,
+                                      interp->zarr, x, y, xa, ya, z);
+}
+
+double
+gsl_spline2d_eval_deriv_yy(const gsl_spline2d * interp, const double x,
+                           const double y, gsl_interp_accel * xa, gsl_interp_accel * ya)
+{
+  return gsl_interp2d_eval_deriv_yy(&(interp->interp_object), interp->xarr, interp->yarr,
+                                    interp->zarr, x, y, xa, ya);
+}
+
+int
+gsl_spline2d_eval_deriv_yy_e(const gsl_spline2d * interp, const double x,
+                             const double y, gsl_interp_accel * xa, gsl_interp_accel * ya,
+                             double * z)
+{
+  return gsl_interp2d_eval_deriv_yy_e(&(interp->interp_object), interp->xarr, interp->yarr,
+                                      interp->zarr, x, y, xa, ya, z);
+}
+
+double
+gsl_spline2d_eval_deriv_xy(const gsl_spline2d * interp, const double x,
+                           const double y, gsl_interp_accel * xa, gsl_interp_accel * ya)
+{
+  return gsl_interp2d_eval_deriv_xy(&(interp->interp_object), interp->xarr, interp->yarr,
+                                    interp->zarr, x, y, xa, ya);
+}
+
+int
+gsl_spline2d_eval_deriv_xy_e(const gsl_spline2d * interp, const double x,
+                             const double y, gsl_interp_accel * xa, gsl_interp_accel * ya,
+                             double * z)
+{
+  return gsl_interp2d_eval_deriv_xy_e(&(interp->interp_object), interp->xarr, interp->yarr,
+                                      interp->zarr, x, y, xa, ya, z);
+}
+
+size_t
+gsl_spline2d_min_size(const gsl_spline2d * interp)
+{
+  return gsl_interp2d_min_size(&(interp->interp_object));
+}
+
+const char *
+gsl_spline2d_name(const gsl_spline2d * interp)
+{
+  return gsl_interp2d_name(&(interp->interp_object));
+}
+
+int
+gsl_spline2d_set(const gsl_spline2d * interp, double zarr[],
+                 const size_t i, const size_t j, const double z)
+{
+  return gsl_interp2d_set(&(interp->interp_object), zarr, i, j, z);
+} /* gsl_spline2d_set() */
+
+double
+gsl_spline2d_get(const gsl_spline2d * interp, const double zarr[],
+                 const size_t i, const size_t j)
+{
+  return gsl_interp2d_get(&(interp->interp_object), zarr, i, j);
+} /* gsl_spline2d_get() */
diff -Nru gsl-doc-1.16/interpolation/steffen.c gsl-doc-2.3/interpolation/steffen.c
--- gsl-doc-1.16/interpolation/steffen.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/interpolation/steffen.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,386 @@
+/* interpolation/steffen.c
+ * 
+ * Copyright (C) 2014 Jean-François Caron
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/* Author:  J.-F. Caron
+ *
+ * This interpolation method is taken from 
+ * M.Steffen, "A simple method for monotonic interpolation in one dimension",
+ * Astron. Astrophys. 239, 443-450 (1990).
+ *
+ * This interpolation method guarantees monotonic interpolation functions between
+ * the given data points.  A consequence of this is that extremal values can only
+ * occur at the data points.  The interpolating function and its first derivative
+ * are guaranteed to be continuous, but the second derivative is not.
+ *
+ * The implementation is modelled on the existing Akima interpolation method
+ * previously included in GSL by Gerard Jungman.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include "integ_eval.h"
+#include <gsl/gsl_interp.h>
+
+typedef struct
+{
+  double * a;       /* eqs 2-5 of paper */
+  double * b;
+  double * c;
+  double * d;
+
+  double * y_prime; /* eq 11 of paper */
+} steffen_state_t;
+
+static void steffen_free (void * vstate);
+static double steffen_copysign(const double x, const double y);
+
+static void *
+steffen_alloc (size_t size)
+{
+  steffen_state_t *state;
+  
+  state = (steffen_state_t *) calloc (1, sizeof (steffen_state_t));
+  
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL("failed to allocate space for state", GSL_ENOMEM);
+    }
+
+  state->a = (double *) malloc (size * sizeof (double));
+  
+  if (state->a == NULL)
+    {
+      steffen_free(state);
+      GSL_ERROR_NULL("failed to allocate space for a", GSL_ENOMEM);
+    }
+  
+  state->b = (double *) malloc (size * sizeof (double));
+  
+  if (state->b == NULL)
+    {
+      steffen_free(state);
+      GSL_ERROR_NULL("failed to allocate space for b", GSL_ENOMEM);
+    }
+  
+  state->c = (double *) malloc (size * sizeof (double));
+  
+  if (state->c == NULL)
+    {
+      steffen_free(state);
+      GSL_ERROR_NULL("failed to allocate space for c", GSL_ENOMEM);
+    }
+  
+  state->d = (double *) malloc (size * sizeof (double));
+  
+  if (state->d == NULL)
+    {
+      steffen_free(state);
+      GSL_ERROR_NULL("failed to allocate space for d", GSL_ENOMEM);
+    }
+
+  state->y_prime = (double *) malloc (size * sizeof (double));
+  if (state->y_prime == NULL)
+    {
+      steffen_free(state);
+      GSL_ERROR_NULL("failed to allocate space for y_prime", GSL_ENOMEM);
+    }
+
+  return state;
+}
+
+static int
+steffen_init (void * vstate, const double x_array[],
+              const double y_array[], size_t size)
+{
+  steffen_state_t *state = (steffen_state_t *) vstate;
+  size_t i;
+  double *a = state->a;
+  double *b = state->b;
+  double *c = state->c;
+  double *d = state->d;
+  double *y_prime = state->y_prime;
+
+  /*
+   * first assign the interval and slopes for the left boundary.
+   * We use the "simplest possibility" method described in the paper
+   * in section 2.2
+   */
+  double h0 = (x_array[1] - x_array[0]);
+  double s0 = (y_array[1] - y_array[0]) / h0;
+
+  y_prime[0] = s0;
+
+  /* Now we calculate all the necessary s, h, p, and y' variables 
+     from 1 to N-2 (0 to size - 2 inclusive) */
+  for (i = 1; i < (size - 1); i++)
+    {
+      double pi;
+
+      /* equation 6 in the paper */
+      double hi = (x_array[i+1] - x_array[i]);
+      double him1 = (x_array[i] - x_array[i - 1]);
+
+      /* equation 7 in the paper */
+      double si = (y_array[i+1] - y_array[i]) / hi;
+      double sim1 = (y_array[i] - y_array[i - 1]) / him1;
+
+      /* equation 8 in the paper */
+      pi = (sim1*hi + si*him1) / (him1 + hi);
+
+      /* This is a C equivalent of the FORTRAN statement below eqn 11 */
+      y_prime[i] = (steffen_copysign(1.0,sim1) + steffen_copysign(1.0,si)) *
+                    GSL_MIN(fabs(sim1),
+                            GSL_MIN(fabs(si), 0.5*fabs(pi))); 
+    }
+
+  /*
+   * we also need y' for the rightmost boundary; we use the
+   * "simplest possibility" method described in the paper in
+   * section 2.2
+   *
+   * y' = s_{n-1}
+   */
+  y_prime[size-1] = (y_array[size - 1] - y_array[size - 2]) /
+                    (x_array[size - 1] - x_array[size - 2]);
+
+  /* Now we can calculate all the coefficients for the whole range. */
+  for (i = 0; i < (size - 1); i++)
+    {
+      double hi = (x_array[i+1] - x_array[i]);
+      double si = (y_array[i+1] - y_array[i]) / hi;
+
+      /* These are from equations 2-5 in the paper. */
+      a[i] = (y_prime[i] + y_prime[i+1] - 2*si) / hi / hi;
+      b[i] = (3*si - 2*y_prime[i] - y_prime[i+1]) / hi;
+      c[i] = y_prime[i];
+      d[i] = y_array[i];
+    }
+
+  return GSL_SUCCESS;
+}
+
+static void
+steffen_free (void * vstate)
+{
+  steffen_state_t *state = (steffen_state_t *) vstate;
+
+  RETURN_IF_NULL(state);
+
+  if (state->a)
+    free (state->a);
+
+  if (state->b)
+    free (state->b);
+
+  if (state->c)
+    free (state->c);
+
+  if (state->d)
+    free (state->d);
+
+  if (state->y_prime)
+    free (state->y_prime);
+
+  free (state);
+}
+
+static int
+steffen_eval (const void * vstate,
+              const double x_array[], const double y_array[], size_t size,
+              double x, gsl_interp_accel * a, double *y)
+{
+  const steffen_state_t *state = (const steffen_state_t *) vstate;
+
+  size_t index;
+  
+  if (a != 0)
+    {
+      index = gsl_interp_accel_find (a, x_array, size, x);
+    }
+  else
+    {
+      index = gsl_interp_bsearch (x_array, x, 0, size - 1);
+    }
+  
+  /* evaluate */
+  {
+    const double x_lo = x_array[index];
+    const double delx = x - x_lo;
+    const double a = state->a[index];
+    const double b = state->b[index];
+    const double c = state->c[index];
+    const double d = state->d[index];
+    /* Use Horner's scheme for efficient evaluation of polynomials. */
+    /* *y = a*delx*delx*delx + b*delx*delx + c*delx + d; */
+    *y = d + delx*(c + delx*(b + delx*a));
+
+    return GSL_SUCCESS;
+  }
+}
+
+static int
+steffen_eval_deriv (const void * vstate,
+                    const double x_array[], const double y_array[], size_t size,
+                    double x, gsl_interp_accel * a, double *dydx)
+{
+  const steffen_state_t *state = (const steffen_state_t *) vstate;
+
+  size_t index;
+
+  /* DISCARD_POINTER(y_array); /\* prevent warning about unused parameter *\/ */
+  
+  if (a != 0)
+    {
+      index = gsl_interp_accel_find (a, x_array, size, x);
+    }
+  else
+    {
+      index = gsl_interp_bsearch (x_array, x, 0, size - 1);
+    }
+  
+  /* evaluate */
+  {
+    double x_lo = x_array[index];
+    double delx = x - x_lo;
+    double a = state->a[index];
+    double b = state->b[index];
+    double c = state->c[index];
+    /*double d = state->d[index];*/
+    /* *dydx = 3*a*delx*delx*delx + 2*b*delx + c; */
+    *dydx = c + delx*(2*b + delx*3*a);
+    return GSL_SUCCESS;
+  }
+}
+
+static int
+steffen_eval_deriv2 (const void * vstate,
+                     const double x_array[], const double y_array[], size_t size,
+                     double x, gsl_interp_accel * a, double *y_pp)
+{
+  const steffen_state_t *state = (const steffen_state_t *) vstate;
+
+  size_t index;
+
+  /* DISCARD_POINTER(y_array); /\* prevent warning about unused parameter *\/ */
+
+  if (a != 0)
+    {
+      index = gsl_interp_accel_find (a, x_array, size, x);
+    }
+  else
+    {
+      index = gsl_interp_bsearch (x_array, x, 0, size - 1);
+    }
+  
+  /* evaluate */
+  {
+    const double x_lo = x_array[index];
+    const double delx = x - x_lo;
+    const double a = state->a[index];
+    const double b = state->b[index];
+    *y_pp = 6*a*delx + 2*b;
+    return GSL_SUCCESS;
+  }
+}
+
+static int
+steffen_eval_integ (const void * vstate,
+                    const double x_array[], const double y_array[], size_t size,
+                    gsl_interp_accel * acc, double a, double b,
+                    double * result)
+{
+  /* a and b are the boundaries of the integration. */
+  
+  const steffen_state_t *state = (const steffen_state_t *) vstate;
+
+  size_t i, index_a, index_b;
+
+  /* Find the data points in the x_array that are nearest to the desired */
+  /* a and b integration boundaries. */
+
+  if (acc != 0)
+    {
+      index_a = gsl_interp_accel_find (acc, x_array, size, a);
+      index_b = gsl_interp_accel_find (acc, x_array, size, b);
+    }
+  else
+    {
+      index_a = gsl_interp_bsearch (x_array, a, 0, size - 1);
+      index_b = gsl_interp_bsearch (x_array, b, 0, size - 1);
+    }
+  
+  *result = 0.0;
+
+  /* Iterate over all the segments between data points and sum the */
+  /* contributions into result. */
+  for(i=index_a; i<=index_b; i++) 
+    {
+      const double x_hi = x_array[i + 1];
+      const double x_lo = x_array[i];
+      const double dx = x_hi - x_lo;
+      if(dx != 0.0) 
+        {
+          /*
+           * check if we are at a boundary point, so take the
+           * a and b parameters instead of the data points.
+           */
+          double x1 = (i == index_a) ? a-x_lo : 0.0;
+          double x2 = (i == index_b) ? b-x_lo : x_hi-x_lo;
+
+          *result += (1.0/4.0)*state->a[i]*(x2*x2*x2*x2 - x1*x1*x1*x1)
+                    +(1.0/3.0)*state->b[i]*(x2*x2*x2 - x1*x1*x1)
+                    +(1.0/2.0)*state->c[i]*(x2*x2 - x1*x1)
+                    +state->d[i]*(x2-x1);
+        }
+      else /* if the interval was zero, i.e. consecutive x values in data. */
+        {
+          *result = 0.0;
+          return GSL_EINVAL;
+        }
+    }
+  
+  return GSL_SUCCESS;
+}
+
+static double
+steffen_copysign(const double x, const double y)
+{
+  if ((x < 0 && y > 0) || (x > 0 && y < 0))
+    return -x;
+
+  return x;
+}
+
+static const gsl_interp_type steffen_type = 
+{
+  "steffen", 
+  3,
+  &steffen_alloc,
+  &steffen_init,
+  &steffen_eval,
+  &steffen_eval_deriv,
+  &steffen_eval_deriv2,
+  &steffen_eval_integ,
+  &steffen_free
+};
+
+const gsl_interp_type * gsl_interp_steffen = &steffen_type;
diff -Nru gsl-doc-1.16/interpolation/test2d.c gsl-doc-2.3/interpolation/test2d.c
--- gsl-doc-1.16/interpolation/test2d.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/interpolation/test2d.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,344 @@
+/* interpolation/test2d.c
+ * 
+ * Copyright 2012 David Zaslavsky
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_ieee_utils.h>
+#include <gsl/gsl_test.h>
+#include <gsl/gsl_interp.h>
+#include <gsl/gsl_interp2d.h>
+#include <gsl/gsl_spline2d.h>
+
+/* tests a single evaluator function from the low-level interface */
+static int
+test_single_low_level(
+  double (*evaluator)(const gsl_interp2d *, const double[], const double[],
+                      const double[], const double, const double,
+                      gsl_interp_accel *, gsl_interp_accel *),
+  int (*evaluator_e)(const gsl_interp2d *, const double[], const double[],
+                     const double[], const double, const double,
+                     gsl_interp_accel *, gsl_interp_accel *, double *),
+  const gsl_interp2d * interp, const double xarr[], const double yarr[],
+  const double zarr[], const double x, const double y,
+  gsl_interp_accel * xa, gsl_interp_accel * ya,
+  const double expected_results[], size_t i)
+{
+  if (expected_results != NULL)
+    {
+      int status;
+      double result = evaluator(interp, xarr, yarr, zarr, x, y, xa, ya);
+      gsl_test_rel(result, expected_results[i], 1e-10,
+                   "low level %s %d", gsl_interp2d_name(interp), i);
+
+      status = evaluator_e(interp, xarr, yarr, zarr, x, y, xa, ya, &result);
+      if (status == GSL_SUCCESS)
+        {
+          gsl_test_rel(result, expected_results[i], 1e-10,
+                       "low level _e %s %d", gsl_interp2d_name(interp), i);
+        }
+    }
+
+  return 0;
+}
+
+/* tests a single evaluator function from the high-level interface */
+static int
+test_single_high_level(
+    double (*evaluator)(const gsl_spline2d *, const double, const double,
+                        gsl_interp_accel *, gsl_interp_accel *),
+    int (*evaluator_e)(const gsl_spline2d *, const double, const double,
+                       gsl_interp_accel *, gsl_interp_accel *, double *),
+    const gsl_spline2d * interp, const double x, const double y,
+    gsl_interp_accel * xa, gsl_interp_accel * ya,
+    const double expected_results[], size_t i)
+{
+  if (expected_results != NULL)
+    {
+      int status;
+      double result = evaluator(interp, x, y, xa, ya);
+
+      gsl_test_rel(result, expected_results[i], 1e-10,
+                   "high level %s %d", gsl_spline2d_name(interp), i);
+
+      status = evaluator_e(interp, x, y, xa, ya, &result);
+      if (status == GSL_SUCCESS)
+        {
+          gsl_test_rel(result, expected_results[i], 1e-10,
+                       "high level _e %s %d", gsl_spline2d_name(interp), i);
+        }
+    }
+
+  return 0;
+}
+
+/*
+ * Tests that a given interpolation type reproduces the data points
+ * it is given, and then tests that it correctly reproduces additional
+ * values.
+ */
+static int
+test_interp2d(
+const double xarr[], const double yarr[], const double zarr[], /* data */
+              size_t xsize, size_t ysize,                /* array sizes */
+              const double xval[], const double yval[],  /* test points */
+              const double zval[],                       /* expected results */
+              const double zxval[], const double zyval[],
+              const double zxxval[], const double zyyval[], const double zxyval[],
+              size_t test_size,                          /* number of test points */
+              const gsl_interp2d_type * T)
+{
+  gsl_interp_accel *xa = gsl_interp_accel_alloc();
+  gsl_interp_accel *ya = gsl_interp_accel_alloc();
+  int status = 0;
+  size_t xi, yi, zi, i;
+  gsl_interp2d * interp = gsl_interp2d_alloc(T, xsize, ysize);
+  gsl_spline2d * interp_s = gsl_spline2d_alloc(T, xsize, ysize);
+  unsigned int min_size = gsl_interp2d_type_min_size(T);
+
+  gsl_test_int(min_size, T->min_size, "gsl_interp2d_type_min_size on %s", gsl_interp2d_name(interp));
+
+  gsl_interp2d_init(interp, xarr, yarr, zarr, xsize, ysize);
+  gsl_spline2d_init(interp_s, xarr, yarr, zarr, xsize, ysize);
+
+  /* First check that the interpolation reproduces the given points */
+  for (xi = 0; xi < xsize; xi++)
+    {
+      double x = xarr[xi];
+      for (yi = 0; yi < ysize; yi++)
+        {
+          double y = yarr[yi];
+          
+          zi = gsl_interp2d_idx(interp, xi, yi);
+          test_single_low_level(&gsl_interp2d_eval, &gsl_interp2d_eval_e,
+                                interp, xarr, yarr, zarr, x, y,
+                                xa, ya, zarr, zi);
+          test_single_low_level(&gsl_interp2d_eval_extrap,
+                                &gsl_interp2d_eval_e_extrap, interp,
+                                xarr, yarr, zarr, x, y, xa, ya, zarr, zi);
+          test_single_high_level(&gsl_spline2d_eval, &gsl_spline2d_eval_e,
+                                 interp_s, x, y, xa, ya, zarr, zi);
+        }
+    }
+
+  /* Then check additional points provided */
+  for (i = 0; i < test_size; i++)
+    {
+      double x = xval[i];
+      double y = yval[i];
+        
+      test_single_low_level(&gsl_interp2d_eval,         &gsl_interp2d_eval_e,          interp, xarr, yarr, zarr, x, y, xa, ya, zval, i);
+      test_single_low_level(&gsl_interp2d_eval_deriv_x, &gsl_interp2d_eval_deriv_x_e,  interp, xarr, yarr, zarr, x, y, xa, ya, zxval, i);
+      test_single_low_level(&gsl_interp2d_eval_deriv_y, &gsl_interp2d_eval_deriv_y_e,  interp, xarr, yarr, zarr, x, y, xa, ya, zyval, i);
+      test_single_low_level(&gsl_interp2d_eval_deriv_xx,&gsl_interp2d_eval_deriv_xx_e, interp, xarr, yarr, zarr, x, y, xa, ya, zxxval, i);
+      test_single_low_level(&gsl_interp2d_eval_deriv_yy,&gsl_interp2d_eval_deriv_yy_e, interp, xarr, yarr, zarr, x, y, xa, ya, zyyval, i);
+      test_single_low_level(&gsl_interp2d_eval_deriv_xy,&gsl_interp2d_eval_deriv_xy_e, interp, xarr, yarr, zarr, x, y, xa, ya, zxyval, i);
+
+      test_single_high_level(&gsl_spline2d_eval,         &gsl_spline2d_eval_e,          interp_s, x, y, xa, ya, zval, i);
+      test_single_high_level(&gsl_spline2d_eval_deriv_x, &gsl_spline2d_eval_deriv_x_e,  interp_s, x, y, xa, ya, zxval, i);
+      test_single_high_level(&gsl_spline2d_eval_deriv_y, &gsl_spline2d_eval_deriv_y_e,  interp_s, x, y, xa, ya, zyval, i);
+      test_single_high_level(&gsl_spline2d_eval_deriv_xx,&gsl_spline2d_eval_deriv_xx_e, interp_s, x, y, xa, ya, zxxval, i);
+      test_single_high_level(&gsl_spline2d_eval_deriv_yy,&gsl_spline2d_eval_deriv_yy_e, interp_s, x, y, xa, ya, zyyval, i);
+      test_single_high_level(&gsl_spline2d_eval_deriv_xy,&gsl_spline2d_eval_deriv_xy_e, interp_s, x, y, xa, ya, zxyval, i);
+
+      test_single_low_level(&gsl_interp2d_eval_extrap, &gsl_interp2d_eval_e_extrap, interp, xarr, yarr, zarr, x, y, xa, ya, zval, i);
+    }
+
+  gsl_interp_accel_free(xa);
+  gsl_interp_accel_free(ya);
+  gsl_interp2d_free(interp);
+  gsl_spline2d_free(interp_s);
+
+  return status;
+}
+
+/*
+ * Tests bilinear interpolation using a symmetric function, f(x,y)==f(y,x),
+ * and diagonal interpolation points (x,y) where x==y. If these tests don't
+ * pass, something is seriously broken.
+ */
+static int
+test_bilinear_symmetric()
+{
+  int status;
+  double xarr[] = {0.0, 1.0, 2.0, 3.0};
+  double yarr[] = {0.0, 1.0, 2.0, 3.0};
+  double zarr[] = {1.0, 1.1, 1.2, 1.3,
+                   1.1, 1.2, 1.3, 1.4,
+                   1.2, 1.3, 1.4, 1.5,
+                   1.3, 1.4, 1.5, 1.6};
+  double xval[] = {0.0, 0.5, 1.0, 1.5, 2.5, 3.0};
+  double yval[] = {0.0, 0.5, 1.0, 1.5, 2.5, 3.0};
+  double zval[] = {1.0, 1.1, 1.2, 1.3, 1.5, 1.6};
+  size_t xsize = sizeof(xarr) / sizeof(xarr[0]);
+  size_t ysize = sizeof(yarr) / sizeof(yarr[0]);
+  size_t test_size = sizeof(xval) / sizeof(xval[0]);
+
+  status = test_interp2d(xarr, yarr, zarr, xsize, ysize, xval, yval, zval,
+                         NULL, NULL, NULL, NULL, NULL, test_size,
+                         gsl_interp2d_bilinear);
+  gsl_test(status, "bilinear interpolation with symmetric values");
+
+  return status;
+}
+
+/*
+ * Tests bilinear interpolation with an asymmetric function, f(x,y)!=f(y,x),
+ * and off-diagonal interpolation points (x,y) where x and y may or may not
+ * be equal.
+ */
+static int
+test_bilinear_asymmetric_z()
+{
+  int status;
+  double xarr[] = {0.0, 1.0, 2.0, 3.0};
+  double yarr[] = {0.0, 1.0, 2.0, 3.0};
+  double zarr[] = {1.0, 1.1, 1.2, 1.4,
+                   1.3, 1.4, 1.5, 1.7,
+                   1.5, 1.6, 1.7, 1.9,
+                   1.6, 1.9, 2.2, 2.3};
+  double xval[] = { 0.0, 0.5, 1.0, 1.5,  2.5, 3.0,
+                    1.3954, 1.6476, 0.824957,
+                    2.41108,  2.98619, 1.36485 };
+  double yval[] = {0.0, 0.5, 1.0, 1.5,  2.5, 3.0,
+                   0.265371, 2.13849, 1.62114,
+                   1.22198, 0.724681, 0.0596087 };
+
+  /* results computed using Mathematica 9.0.1.0 */
+  double zval[] = {1.0, 1.2, 1.4, 1.55, 2.025, 2.3,
+                   1.2191513, 1.7242442248, 1.5067237,
+                   1.626612, 1.6146423, 1.15436761};
+  size_t xsize = sizeof(xarr) / sizeof(xarr[0]);
+  size_t ysize = sizeof(yarr) / sizeof(yarr[0]);
+  size_t test_size = sizeof(xval) / sizeof(xval[0]);
+
+  status = test_interp2d(xarr, yarr, zarr, xsize, ysize, xval, yval, zval,
+                         NULL, NULL, NULL, NULL, NULL, test_size,
+                         gsl_interp2d_bilinear);
+  gsl_test(status, "bilinear interpolation with asymmetric z values");
+
+  return status;
+}
+
+static int
+test_bicubic()
+{
+  int status;
+  double xarr[] = {0.0, 1.0, 2.0, 3.0};
+  double yarr[] = {0.0, 1.0, 2.0, 3.0};
+  double zarr[] = {1.0, 1.1, 1.2, 1.3,
+                   1.1, 1.2, 1.3, 1.4,
+                   1.2, 1.3, 1.4, 1.5,
+                   1.3, 1.4, 1.5, 1.6};
+  double xval[] = {1.0, 1.5, 2.0};
+  double yval[] = {1.0, 1.5, 2.0};
+  double zval[] = {1.2, 1.3, 1.4};
+  size_t xsize = sizeof(xarr) / sizeof(xarr[0]);
+  size_t ysize = sizeof(yarr) / sizeof(yarr[0]);
+  size_t test_size = sizeof(xval) / sizeof(xval[0]);
+
+  status = test_interp2d(xarr, yarr, zarr, xsize, ysize, xval, yval, zval,
+                         NULL, NULL, NULL, NULL, NULL, test_size,
+                         gsl_interp2d_bicubic);
+  gsl_test(status, "bicubic interpolation on linear function");
+
+  return status;
+}
+
+static int
+test_bicubic_nonlinear()
+{
+  int status;
+  double xarr[] = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0};
+  double yarr[] = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0};
+  /* least common multiple of x and y */
+  double zarr[] = { 1,  2,  3,  4,  5,  6,  7,  8,
+                    2,  2,  6,  4, 10,  6, 14,  8,
+                    3,  6,  3, 12, 15,  6, 21, 24,
+                    4,  4, 12,  4, 20, 12, 28,  8,
+                    5, 10, 15, 20,  5, 30, 35, 40,
+                    6,  6,  6, 12, 30,  6, 42, 24,
+                    7, 14, 21, 28, 35, 42,  7, 56,
+                    8,  8, 24,  8, 40, 24, 56,  8};
+  double xval[] = {1.4, 2.3, 4.7, 3.3, 7.5, 6.6, 5.1};
+  double yval[] = {1.0, 1.8, 1.9, 2.5, 2.7, 4.1, 3.3};
+
+  /* results computed using GSL 1D cubic interpolation twice */
+  double zval[] = { 1.4, 3.11183531264736, 8.27114315792559, 5.03218982537718,
+                    22.13230634702637, 23.63206834997871, 17.28553080971182 };
+  size_t xsize = sizeof(xarr) / sizeof(xarr[0]);
+  size_t ysize = sizeof(yarr) / sizeof(yarr[0]);
+  size_t test_size = sizeof(xval) / sizeof(xval[0]);
+
+  status = test_interp2d(xarr, yarr, zarr, xsize, ysize, xval, yval, zval,
+                         NULL, NULL, NULL, NULL, NULL, test_size,
+                         gsl_interp2d_bicubic);
+  gsl_test(status, "bicubic interpolation on nonlinear symmetric function");
+
+  return status;
+}
+
+/* This function contributed by Andrew W. Steiner <awsteiner@gmail.com> */
+static int
+test_bicubic_nonlinear_nonsq()
+{
+  int status;
+  double xarr[] = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0};
+  double yarr[] = {1.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0};
+  double zarr[] = { 1,  2,  3,  4,  5,  6,  7,  8, 9, 10,
+                    2,  2,  6,  4, 10,  6, 14,  8, 11, 12,
+                    3,  6,  3, 12, 15,  6, 21, 24, 13, 14,
+                    4,  4, 12,  4, 20, 12, 28,  8, 15, 16,
+                    5, 10, 15, 20,  5, 30, 35, 40, 17, 18,
+                    6,  6,  6, 12, 30,  6, 42, 24, 19, 20,
+                    7, 14, 21, 28, 35, 42,  7, 56, 21, 22,
+                    8,  8, 24,  8, 40, 24, 56,  8, 23, 24};
+  double xval[] = {1.4, 2.3, 9.7, 3.3, 9.5, 6.6, 5.1};
+  double yval[] = {1.0, 1.8, 1.9, 2.5, 2.7, 4.1, 3.3};
+
+  /* results computed using GSL 1D cubic interpolation twice */
+  double zval[] = { 1.4, 2.46782030941187003, 10.7717721621846465,
+                    4.80725067958096375, 11.6747032398627297,
+                    11.2619968682970111, 9.00168877916872567};
+  size_t xsize = sizeof(xarr) / sizeof(xarr[0]);
+  size_t ysize = sizeof(yarr) / sizeof(yarr[0]);
+  size_t test_size = sizeof(xval) / sizeof(xval[0]);
+
+  status = test_interp2d(xarr, yarr, zarr, xsize, ysize, xval, yval, zval,
+                         NULL, NULL, NULL, NULL, NULL, test_size,
+                         gsl_interp2d_bicubic);
+  gsl_test(status, "bicubic interpolation on nonlinear symmetric function");
+
+  return status;
+}
+
+/* runs all the tests */
+int
+test_interp2d_main(void)
+{
+  int status = 0;
+
+  status += test_bilinear_symmetric();
+  status += test_bilinear_asymmetric_z();
+  status += test_bicubic();
+  status += test_bicubic_nonlinear();
+  status += test_bicubic_nonlinear_nonsq();
+
+  return status;
+}
diff -Nru gsl-doc-1.16/interpolation/test.c gsl-doc-2.3/interpolation/test.c
--- gsl-doc-1.16/interpolation/test.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/interpolation/test.c	2015-11-03 16:21:55.000000000 +0000
@@ -1,6 +1,7 @@
 /* interpolation/test.c
  * 
- * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2014 Gerard Jungman
+ * Copyright (C) 2014 Jean-François Caron
  * 
  * This program is free software; you can redistribute it and/or modify
  * it under the terms of the GNU General Public License as published by
@@ -30,6 +31,8 @@
 #include <gsl/gsl_interp.h>
 #include <gsl/gsl_ieee_utils.h>
 
+#include "test2d.c"
+
 int
 test_bsearch(void)
 {
@@ -938,8 +941,6 @@
   return s;
 }
 
-
-
 static int
 test_akima (void)
 {
@@ -962,6 +963,247 @@
   return s;
 }
 
+static int
+test_steffen1 (void)
+{
+  int s;
+
+  double data_x[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
+  double data_y[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
+
+  double test_x[6] = { 0.0, 0.5, 1.0, 2.0, 2.5, 3.95 };
+  double test_y[6] = { 0.0, 0.5, 1.0, 2.0, 2.5, 3.95 };
+  double test_dy[6] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
+  double test_iy[6] = { 0.0, 0.125, 0.5, 2.0, 3.125, 7.80125 };
+
+  xy_table data_table = make_xy_table(data_x, data_y, 5);
+  xy_table test_table = make_xy_table(test_x, test_y, 4);
+  xy_table test_d_table = make_xy_table(test_x, test_dy, 4);
+  xy_table test_i_table = make_xy_table(test_x, test_iy, 4);
+
+  s = test_interp (&data_table, gsl_interp_steffen, &test_table, &test_d_table, &test_i_table);
+  gsl_test (s, "steffen interpolation test 1");
+  return s;
+}
+
+static int
+test_steffen2 (void)
+{
+  int s;
+
+  double data_x[30] = { 
+    4.673405471947611, 4.851675778029557, 6.185473620119991,
+    7.066003430727031, 7.236222118389267, 7.82067161881444,
+    8.054504031621493, 8.615033792800752, 9.16666529764867,
+    9.442092828126395, 10.719577968900381, 11.741967577609238,
+    12.564881194673035, 12.938424721515084, 12.985892202096888,
+    13.995771653255744, 14.459157783380315, 15.834857667614848,
+    15.887779086499942, 18.64645279534696, 19.256361741244287,
+    19.85100457105047, 19.943627313550987, 20.5033910115468,
+    20.895380493234843, 21.759942483053962, 21.948984866760803,
+    22.2504057728461, 22.741860290952104, 23.088720630939164 };
+
+  double data_y[30] = {
+    -6.131584089652438, 4.997132870704837, 9.50359639889188,
+    -3.788474042493764, 1.98825324341826, -6.553460294945401,
+    8.44565760012345, -3.643687601520438, -4.720262269613782,
+    -5.31956608504474, 4.7484698519996655, 1.8191111043001218,
+    2.7234424260251124, -7.282776099988966, -6.966038807035955,
+    2.6047260012112545, -3.6363485275348033, -4.124714595822157,
+    -4.820986899771757, -2.8550035950284602, 6.017204757558943,
+    6.7275899382734075, -9.423359755713639, -0.3645325139870703,
+    6.925739188986089, -0.07843256857855074, 1.6744315603866244,
+    -8.332083151442944, 6.059246349756446, -7.360159198725659 };
+
+  double test_x[129] = {
+    4.6734054719476106,4.8516757780295574,4.8575586235375265,
+    5.0417117751274407,5.2258649267173567,5.4100180783072727,
+    5.5941712298971886,5.7783243814871028,5.9624775330770188,
+    6.1466306846669347,6.1854736201199909,6.3307838362568507,
+    6.5149369878467667,6.6990901394366809,6.8832432910265968,
+    7.0660034307270312,7.0673964426165128,7.236222118389267,
+    7.2515495942064288,7.4357027457963438,7.6198558973862589,
+    7.8040090489761749,7.8206716188144396,7.9881622005660908,
+    8.0545040316214926,8.172315352156005,8.356468503745921,
+    8.5406216553358369,8.6150337928007517,8.7247748069257529,
+    8.9089279585156689,9.0930811101055831,9.1666652976486702,
+    9.277234261695499,9.4420928281263947,9.461387413285415,
+    9.645540564875331,9.8296937164652469,10.013846868055161,
+    10.198000019645077,10.382153171234993,10.566306322824907,
+    10.719577968900381,10.750459474414823,10.934612626004739,
+    11.118765777594655,11.302918929184571,11.487072080774485,
+    11.671225232364399,11.741967577609238,11.855378383954315,
+    12.039531535544231,12.223684687134147,12.407837838724063,
+    12.564881194673035,12.591990990313979,12.776144141903895,
+    12.938424721515084,12.960297293493811,12.985892202096888,
+    13.144450445083727,13.328603596673641,13.512756748263556,
+    13.696909899853472,13.881063051443387,13.995771653255744,
+    14.065216203033303,14.249369354623219,14.433522506213134,
+    14.459157783380315,14.617675657803051,14.801828809392966,
+    14.985981960982881,15.170135112572796,15.354288264162712,
+    15.538441415752628,15.722594567342544,15.834857667614848,
+    15.90674771893246,15.887779086499942,16.090900870522375,
+    16.27505402211229,16.459207173702204,16.643360325292122,
+    16.827513476882036,17.01166662847195,17.195819780061868,
+    17.379972931651782,17.5641260832417,17.748279234831614,
+    17.932432386421532,18.116585538011446,18.300738689601364,
+    18.484891841191278,18.64645279534696,18.669044992781188,
+    18.853198144371106,19.03735129596102,19.221504447550938,
+    19.256361741244287,19.405657599140852,19.58981075073077,
+    19.773963902320684,19.851004571050471,19.958117053910598,
+    19.943627313550987,20.142270205500516,20.32642335709043,
+    20.5033910115468,20.510576508680348,20.694729660270262,
+    20.87888281186018,20.895380493234843,21.063035963450094,
+    21.247189115040012,21.431342266629926,21.61549541821984,
+    21.759942483053962,21.799648569809754,21.948984866760803,
+    21.983801721399669,22.167954872989586,22.250405772846101,
+    22.352108024579501,22.536261176169418,22.720414327759332,
+    22.741860290952104,22.90456747934925,23.088720630939164 };
+
+  double test_y[129] = {
+    -6.1315840896524376, 4.9971328707048368, 5.0367975988827167,
+    6.1897906340782765, 7.170975366812117, 7.9803517970842286,
+    8.6179199248946077, 9.083679750243256, 9.3776312731301772,
+    9.4997744935553676, 9.5035963988918795, 8.5371013292095554,
+    5.3135045284256019, 1.2120062346303317, -2.3083133782071208,
+    -3.788474042493764, -3.7873197326712797, 1.98825324341826,
+    1.9709370138809248, -0.31768851396215103, -4.2211558425051745,
+    -6.5330277558649303, -6.5534602949454008, 5.5087083141507147,
+    8.4456576001234502, 7.1443430435268214, 1.9932653799771245,
+    -2.8426372908118083, -3.6436876015204378, -3.9926784426485034,
+    -4.3315242293057175, -4.5849882013553547, -4.7202622696137819,
+    -5.0157009305506106, -5.3195660850447402, -5.3127453670702938,
+    -4.6348437675141847, -3.1014810884327102, -1.0745634258401102,
+    1.0840031242494419, 3.0123124658217071, 4.3484585028624627,
+    4.7484698519996655, 4.740613456600772, 4.4142234654988952,
+    3.7574719541934956, 2.9757785771330334, 2.274562988765974,
+    1.8592448435407634, 1.8191111043001218, 1.8659054809992697,
+    2.0883298868527498, 2.3859686670095699, 2.6372078307738107,
+    2.7234424260251124, 2.5729816013335247, -3.258105131647655,
+    -7.2827760999889657, -7.179945071809863, -6.9660388070359547,
+    -5.5662805880783406, -3.3905902235190721, -1.0497645733987406,
+    1.0095869363327665, 2.3408548797255095, 2.6047260012112545,
+    2.2325150500282476, -0.91241316251151927, -3.5649171021138555,
+    -3.6363485275348033, -3.7309363021244821, -3.8038342533632736,
+    -3.8503835649797429, -3.8846412514674595, -3.920664327319995,
+    -3.9725098070309213, -4.0542347050938083, -4.1247145958221569,
+    -4.8208939493861829, -4.8209868997717571, -4.8103284962540727,
+    -4.7822416973267625, -4.7366335526042516, -4.6735040620865389,
+    -4.5928532257736272, -4.4946810436655156, -4.3789875157622005,
+    -4.2457726420636881, -4.0950364225699714, -3.9267788572810582,
+    -3.7409999461969403, -3.537699689317626, -3.3168780866431069,
+    -3.0785351381733914, -2.8550035950284602, -2.7914506045621672,
+    -0.46968123806956008, 3.263658433044764, 5.8622198554846658,
+    6.0172047575589431, 6.3291356295622618, 6.5905310151592165,
+    6.7156659481449141, 6.7275899382734075, -9.4118959280855066,
+    -9.4233597557136388, -7.6111870705157543, -3.9651685725226056,
+    -0.36453251398707032, -0.23537781181431175, 4.0332797539781309,
+    6.899794364641159, 6.9257391889860891, 6.2377210430025594,
+    4.3902665602806792, 2.1878722453596344, 0.44278317319805183,
+    -0.078432568578550743, 0.12107113682074738, 1.6744315603866244,
+    1.3047436323966959, -6.4955024539509765, -8.3320831514429443,
+    -6.7382472104931805, 0.61052993339902706, 5.9794239504090552,
+    6.0592463497564459, 1.5387265272596853, -7.3601591987256612 };
+
+  double test_dy[129] = {
+    62.426083204466224, 6.757341159173202, 6.727537246743899,
+    5.7945730211610407, 4.8616087955781726, 3.9286445699953054,
+    2.9956803444124378, 2.0627161188295791, 1.1297518932467119,
+    0.1967876676638447, 0, -12.480296842307126,
+    -21.209126982426163, -22.014768399615317, -14.897221093874615,
+    0, 1.65274069980919, 0,
+    -2.2393981239975669, -19.714311699236049, -19.77742868994725,
+    -2.4287490961310456, 0, 78.213312807624717,
+    0, -20.358420305108574, -31.350476855816961,
+    -16.93545425712459, -3.9032385156832157, -2.5401833171916435,
+    -1.3740294011308083, -1.6128919418291603, -2.1012124848241789,
+    -2.8800570317456784, 0, 0.70341285683675259,
+    6.3314138906742139, 9.9941697310971538, 11.69168037810557,
+    11.42394583169949, 9.1909660918788916, 4.992741158643824,
+    0, -0.50358091648162351, -2.8552721239834269,
+    -4.0914806331173992, -4.2122064438835425, -3.2174495562818706,
+    -1.1072099703123885, 0, 0.78347408424733667,
+    1.5221058615312819, 1.6003417148468082, 1.018181644193916,
+    0, -10.817925943273289, -39.490030870551372,
+    0, 8.0126635338650072, 6.7986203849007927,
+    10.557804177353285, 12.667135433334296, 12.351260158262027,
+    9.6101783521364421, 4.44389001495753, 0,
+    -10.1306309231183, -19.882866043398995, -4.7826445467139278,
+    -0.70998925548225966, -0.49283947499262398, -0.31159279753453034,
+    -0.20667940230488324, -0.17809928930368468, -0.22585245853093405,
+    -0.3499389099866323, -0.55035864367077902, -0.70998925548225966,
+    0.0098004308855327432, 0, 0.10494594234665755,
+    0.20009145380778143, 0.2952369652689053, 0.39038247673003107,
+    0.48552798819115495, 0.58067349965227877, 0.67581901111340459,
+    0.77096452257452841, 0.86611003403565412, 0.96125554549677805,
+    1.0564010569579039, 1.1515465684190276, 1.2466920798801533,
+    1.3418375913412772, 1.4253105022449177, 4.1661049863071913,
+    18.74497348837053, 19.496500284294363, 6.4206853740787171,
+    2.3892836005304425, 1.7894106566060179, 1.0494805960296585,
+    0.30955053545331346, 0, 1.5724451183167569,
+    0, 16.386389851530527, 21.613477536080744,
+    17.603560096681914, 18.338573561497682, 23.697110333020628,
+    3.1105642331329868, 0, -7.5982202651552164,
+    -11.73098890423519, -11.453053366134201, -6.7644136508523696,
+    0, 9.2309078320594402, 0,
+    -20.350273706124355, -39.581660196515507, 0,
+    28.835095151183879, 42.753317235684989, 7.3325239511975031,
+    0, -47.053315974301256, -38.688209637869583 };
+
+  double test_iy[129] = { 
+    0, 0.046311303303274043, 0.07582542065258166,
+    1.1121678097008914, 2.345017979757877, 3.7427368904558875,
+    5.2736855014272832, 6.9062247723044061, 8.6087156627196464,
+    10.349519132305348, 10.718617229125304, 12.051326255780914,
+    13.351310568583624, 13.954434023333466, 13.833375399536308,
+    13.23478503216295, 13.229508179502936, 13.081569421202504,
+    13.111955459764134, 13.313565584429645, 12.895822708651364,
+    11.856586384851303, 11.747502930901248, 11.477166081331394,
+    11.968731461589641, 12.910617813249443, 13.783041410703255,
+    13.664096839344904, 13.416752727534579, 12.996373500853053,
+    12.226613834386363, 11.406286934906419, 11.064147626707395,
+    10.526693424249395, 9.6682418398824055, 9.5656469982362644,
+    8.633802142647145, 7.911116775692733, 7.5218036771498298,
+    7.5234294786346014, 7.9069146636026106, 8.5965335673487839,
+    9.3034583640488648, 9.4500169740341917, 10.299608964240058,
+    11.055524261651918, 11.675840089542856, 12.156462347951148,
+    12.53112561368027, 12.660771626086403, 12.868892222896084,
+    13.230897278463143, 13.642654271367054, 14.106816365848598,
+    14.529836204259333, 14.602291235557717, 14.620235691106975,
+    13.678281413948246, 13.51979351456291, 13.338827208895861,
+    12.337400222501822, 11.506721190837634, 11.098761199438101,
+    11.102808164918775, 11.425905470576772, 11.714428553431798,
+    11.886459852625201, 12.035570442032403, 11.580639494361572,
+    11.488113239473538, 10.903735363611753, 10.209447282562856,
+    9.5043766268555689, 8.7920812597559994, 8.0735304010092825,
+    7.347104626839644, 6.6085958699503662, 6.1496664193039994,
+    5.821344166329677, 5.9127911070795323, 4.9342652985615576,
+    4.050745397809842, 3.1740110751228041, 2.3072889415487108,
+    1.4538056081358768, 0.61678768593257072, -0.20053821401294236,
+    -0.99494548065234767, -1.7632075029373926, -2.5020976698197641,
+    -3.2083893702512087, -3.8788559931834152, -4.5102709275681283,
+    -5.0994075623570394, -5.5789032190742072, -5.6428026999265457,
+    -5.9842769011998804, -5.729140886963938, -4.8519085924998322,
+    -4.6444581063590329, -3.7217151397093993, -2.5300254086689806,
+    -1.3027452894525609, -0.78475347239267057, -1.0460847630211827,
+    -0.90959826921338605, -2.6553766359304607, -3.7360597404585745,
+    -4.1087031972797643, -4.1108616867222691, -3.776307276733156,
+    -2.7114490122334045, -2.5973338374383879, -1.4760729895576692,
+    -0.48580494729501034, 0.11910209432525942, 0.34807359178739627,
+    0.36262668088219696, 0.3622604193055981, 0.51348240778475363,
+    0.56740090208414018, 0.14380211642697149, -0.48989527970345625,
+    -1.2810928311228711, -1.8846453955503084, -1.1777647142370817,
+    -1.0483932372566702, -0.32646483194908105, -0.88612247621927298 };
+
+  xy_table data_table = make_xy_table(data_x, data_y, 30);
+  xy_table test_table = make_xy_table(test_x, test_y, 129);
+  xy_table test_d_table = make_xy_table(test_x, test_dy, 129);
+  xy_table test_i_table = make_xy_table(test_x, test_iy, 129);
+
+  s = test_interp (&data_table, gsl_interp_steffen, &test_table, &test_d_table, &test_i_table);
+  gsl_test (s, "steffen interpolation test 2");
+  return s;
+}
 
 int 
 main (int argc, char **argv)
@@ -982,6 +1224,10 @@
   status += test_csplinep();
   status += test_csplinep2();
   status += test_akima();
+  status += test_steffen1();
+  status += test_steffen2();
+
+  status += test_interp2d_main();
 
   exit (gsl_test_summary());
 }
diff -Nru gsl-doc-1.16/linalg/apply_givens.c gsl-doc-2.3/linalg/apply_givens.c
--- gsl-doc-1.16/linalg/apply_givens.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/apply_givens.c	2015-11-03 16:21:55.000000000 +0000
@@ -111,15 +111,3 @@
     }
 #endif
 }
-
-inline static void
-apply_givens_vec (gsl_vector * v, size_t i, size_t j, double c, double s)
-{
-  /* Apply rotation to vector v' = G^T v */
-
-  double vi = gsl_vector_get (v, i);
-  double vj = gsl_vector_get (v, j);
-  gsl_vector_set (v, i, c * vi - s * vj);
-  gsl_vector_set (v, j, s * vi + c * vj);
-}
-
diff -Nru gsl-doc-1.16/linalg/balance.c gsl-doc-2.3/linalg/balance.c
--- gsl-doc-1.16/linalg/balance.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/balance.c	2015-11-03 16:21:55.000000000 +0000
@@ -19,7 +19,7 @@
 
 /* Balance a general matrix by scaling the columns
  *
- * B =  A D
+ * A_new = A D^{-1}
  *
  * where D is a diagonal matrix
  */
diff -Nru gsl-doc-1.16/linalg/cholesky.c gsl-doc-2.3/linalg/cholesky.c
--- gsl-doc-1.16/linalg/cholesky.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/cholesky.c	2016-08-30 15:20:38.000000000 +0000
@@ -1,10 +1,8 @@
 /* Cholesky Decomposition
  *
- * Copyright (C) 2000  Thomas Walter
- *
- * 03 May 2000: Modified for GSL by Brian Gough
- * 29 Jul 2005: Additions by Gerard Jungman
- * Copyright (C) 2000,2001, 2002, 2003, 2005, 2007 Brian Gough, Gerard Jungman
+ * Copyright (C) 2000 Thomas Walter
+ * Copyright (C) 2000, 2001, 2002, 2003, 2005, 2007 Brian Gough, Gerard Jungman
+ * Copyright (C) 2016 Patrick Alken
  *
  * This is free software; you can redistribute it and/or modify it
  * under the terms of the GNU General Public License as published by the
@@ -15,6 +13,10 @@
  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  * for more details.
+ *
+ * 03 May 2000: Modified for GSL by Brian Gough
+ * 29 Jul 2005: Additions by Gerard Jungman
+ * 04 Mar 2016: Change Cholesky algorithm to gaxpy version by Patrick Alken
  */
 
 /*
@@ -40,16 +42,49 @@
 #include <gsl/gsl_blas.h>
 #include <gsl/gsl_linalg.h>
 
-static inline 
-double
-quiet_sqrt (double x)  
-     /* avoids runtime error, for checking matrix for positive definiteness */
+static double cholesky_norm1(const gsl_matrix * LLT, gsl_vector * work);
+static int cholesky_Ainv(CBLAS_TRANSPOSE_t TransA, gsl_vector * x, void * params);
+
+/*
+In GSL 2.2, we decided to modify the behavior of the Cholesky decomposition
+to store the Cholesky factor in the lower triangle, and store the original
+matrix in the upper triangle. Previous versions stored the Cholesky factor in
+both places. The routine gsl_linalg_cholesky_decomp1 was added for the new
+behavior, and gsl_linalg_cholesky_decomp is maintained for backward compatibility.
+It will be removed in a future release.
+*/
+
+int
+gsl_linalg_cholesky_decomp (gsl_matrix * A)
 {
-  return (x >= 0) ? sqrt(x) : GSL_NAN;
+  int status;
+
+  status = gsl_linalg_cholesky_decomp1(A);
+  if (status == GSL_SUCCESS)
+    {
+      gsl_matrix_transpose_tricpy('L', 0, A, A);
+    }
+
+  return status;
 }
 
+/*
+gsl_linalg_cholesky_decomp1()
+  Perform Cholesky decomposition of a symmetric positive
+definite matrix
+
+Inputs: A - (input) symmetric, positive definite matrix
+            (output) lower triangle contains Cholesky factor
+
+Return: success/error
+
+Notes:
+1) Based on algorithm 4.2.1 (Gaxpy Cholesky) of Golub and
+Van Loan, Matrix Computations (4th ed).
+*/
+
 int
-gsl_linalg_cholesky_decomp (gsl_matrix * A)
+gsl_linalg_cholesky_decomp1 (gsl_matrix * A)
 {
   const size_t M = A->size1;
   const size_t N = A->size2;
@@ -60,108 +95,36 @@
     }
   else
     {
-      size_t i,j,k;
-      int status = 0;
-
-      /* Do the first 2 rows explicitly.  It is simple, and faster.  And
-       * one can return if the matrix has only 1 or 2 rows.  
-       */
+      size_t j;
 
-      double A_00 = gsl_matrix_get (A, 0, 0);
-      
-      double L_00 = quiet_sqrt(A_00);
-      
-      if (A_00 <= 0)
+      for (j = 0; j < N; ++j)
         {
-          status = GSL_EDOM ;
-        }
-
-      gsl_matrix_set (A, 0, 0, L_00);
-  
-      if (M > 1)
-        {
-          double A_10 = gsl_matrix_get (A, 1, 0);
-          double A_11 = gsl_matrix_get (A, 1, 1);
-          
-          double L_10 = A_10 / L_00;
-          double diag = A_11 - L_10 * L_10;
-          double L_11 = quiet_sqrt(diag);
-          
-          if (diag <= 0)
-            {
-              status = GSL_EDOM;
-            }
+          double ajj;
+          gsl_vector_view v = gsl_matrix_subcolumn(A, j, j, N - j); /* A(j:n,j) */
 
-          gsl_matrix_set (A, 1, 0, L_10);        
-          gsl_matrix_set (A, 1, 1, L_11);
-        }
-      
-      for (k = 2; k < M; k++)
-        {
-          double A_kk = gsl_matrix_get (A, k, k);
-          
-          for (i = 0; i < k; i++)
+          if (j > 0)
             {
-              double sum = 0;
+              gsl_vector_view w = gsl_matrix_subrow(A, j, 0, j);           /* A(j,1:j-1)^T */
+              gsl_matrix_view m = gsl_matrix_submatrix(A, j, 0, N - j, j); /* A(j:n,1:j-1) */
 
-              double A_ki = gsl_matrix_get (A, k, i);
-              double A_ii = gsl_matrix_get (A, i, i);
-
-              gsl_vector_view ci = gsl_matrix_row (A, i);
-              gsl_vector_view ck = gsl_matrix_row (A, k);
+              gsl_blas_dgemv(CblasNoTrans, -1.0, &m.matrix, &w.vector, 1.0, &v.vector);
+            }
 
-              if (i > 0) {
-                gsl_vector_view di = gsl_vector_subvector(&ci.vector, 0, i);
-                gsl_vector_view dk = gsl_vector_subvector(&ck.vector, 0, i);
-                
-                gsl_blas_ddot (&di.vector, &dk.vector, &sum);
-              }
-
-              A_ki = (A_ki - sum) / A_ii;
-              gsl_matrix_set (A, k, i, A_ki);
-            } 
-
-          {
-            gsl_vector_view ck = gsl_matrix_row (A, k);
-            gsl_vector_view dk = gsl_vector_subvector (&ck.vector, 0, k);
-            
-            double sum = gsl_blas_dnrm2 (&dk.vector);
-            double diag = A_kk - sum * sum;
-
-            double L_kk = quiet_sqrt(diag);
-            
-            if (diag <= 0)
-              {
-                status = GSL_EDOM;
-              }
-            
-            gsl_matrix_set (A, k, k, L_kk);
-          }
-        }
+          ajj = gsl_matrix_get(A, j, j);
 
-      /* Now copy the transposed lower triangle to the upper triangle,
-       * the diagonal is common.  
-       */
-      
-      for (i = 1; i < M; i++)
-        {
-          for (j = 0; j < i; j++)
+          if (ajj <= 0.0)
             {
-              double A_ij = gsl_matrix_get (A, i, j);
-              gsl_matrix_set (A, j, i, A_ij);
+              GSL_ERROR("matrix is not positive definite", GSL_EDOM);
             }
-        } 
-      
-      if (status == GSL_EDOM)
-        {
-          GSL_ERROR ("matrix must be positive definite", GSL_EDOM);
+
+          ajj = sqrt(ajj);
+          gsl_vector_scale(&v.vector, 1.0 / ajj);
         }
-      
+
       return GSL_SUCCESS;
     }
 }
 
-
 int
 gsl_linalg_cholesky_solve (const gsl_matrix * LLT,
                            const gsl_vector * b,
@@ -181,20 +144,14 @@
     }
   else
     {
-      /* Copy x <- b */
+      int status;
 
+      /* copy x <- b */
       gsl_vector_memcpy (x, b);
 
-      /* Solve for c using forward-substitution, L c = b */
-
-      gsl_blas_dtrsv (CblasLower, CblasNoTrans, CblasNonUnit, LLT, x);
-
-      /* Perform back-substitution, U x = c */
-
-      gsl_blas_dtrsv (CblasUpper, CblasNoTrans, CblasNonUnit, LLT, x);
-
+      status = gsl_linalg_cholesky_svx(LLT, x);
 
-      return GSL_SUCCESS;
+      return status;
     }
 }
 
@@ -212,13 +169,11 @@
     }
   else
     {
-      /* Solve for c using forward-substitution, L c = b */
-
+      /* solve for c using forward-substitution, L c = b */
       gsl_blas_dtrsv (CblasLower, CblasNoTrans, CblasNonUnit, LLT, x);
 
-      /* Perform back-substitution, U x = c */
-
-      gsl_blas_dtrsv (CblasUpper, CblasNoTrans, CblasNonUnit, LLT, x);
+      /* perform back-substitution, L^T x = c */
+      gsl_blas_dtrsv (CblasLower, CblasTrans, CblasNonUnit, LLT, x);
 
       return GSL_SUCCESS;
     }
@@ -244,74 +199,49 @@
     }
   else
     {
-      size_t N = LLT->size1;
-      size_t i, j;
-      double sum;
+      const size_t N = LLT->size1;
+      size_t i;
       gsl_vector_view v1, v2;
 
       /* invert the lower triangle of LLT */
-      for (i = 0; i < N; ++i)
-        {
-          double ajj;
-
-          j = N - i - 1;
-
-          gsl_matrix_set(LLT, j, j, 1.0 / gsl_matrix_get(LLT, j, j));
-          ajj = -gsl_matrix_get(LLT, j, j);
-
-          if (j < N - 1)
-            {
-              gsl_matrix_view m;
-              
-              m = gsl_matrix_submatrix(LLT, j + 1, j + 1,
-                                       N - j - 1, N - j - 1);
-              v1 = gsl_matrix_subcolumn(LLT, j, j + 1, N - j - 1);
-
-              gsl_blas_dtrmv(CblasLower, CblasNoTrans, CblasNonUnit,
-                             &m.matrix, &v1.vector);
-
-              gsl_blas_dscal(ajj, &v1.vector);
-            }
-        } /* for (i = 0; i < N; ++i) */
+      gsl_linalg_tri_lower_invert(LLT);
 
       /*
        * The lower triangle of LLT now contains L^{-1}. Now compute
-       * A^{-1} = L^{-t} L^{-1}
-       *
-       * The (ij) element of A^{-1} is column i of L^{-1} dotted into
-       * column j of L^{-1}
+       * A^{-1} = L^{-T} L^{-1}
        */
 
       for (i = 0; i < N; ++i)
         {
-          for (j = i + 1; j < N; ++j)
-            {
-              v1 = gsl_matrix_subcolumn(LLT, i, j, N - j);
-              v2 = gsl_matrix_subcolumn(LLT, j, j, N - j);
+          double aii = gsl_matrix_get(LLT, i, i);
 
-              /* compute Ainv_{ij} = sum_k Linv_{ki} Linv_{kj} */
-              gsl_blas_ddot(&v1.vector, &v2.vector, &sum);
+          if (i < N - 1)
+            {
+              double tmp;
 
-              /* store in upper triangle */
-              gsl_matrix_set(LLT, i, j, sum);
-            }
+              v1 = gsl_matrix_subcolumn(LLT, i, i, N - i);
+              gsl_blas_ddot(&v1.vector, &v1.vector, &tmp);
+              gsl_matrix_set(LLT, i, i, tmp);
 
-          /* now compute the diagonal element */
-          v1 = gsl_matrix_subcolumn(LLT, i, i, N - i);
-          gsl_blas_ddot(&v1.vector, &v1.vector, &sum);
-          gsl_matrix_set(LLT, i, i, sum);
-        }
+              if (i > 0)
+                {
+                  gsl_matrix_view m = gsl_matrix_submatrix(LLT, i + 1, 0, N - i - 1, i);
 
-      /* copy the transposed upper triangle to the lower triangle */
+                  v1 = gsl_matrix_subcolumn(LLT, i, i + 1, N - i - 1);
+                  v2 = gsl_matrix_subrow(LLT, i, 0, i);
 
-      for (j = 1; j < N; j++)
-        {
-          for (i = 0; i < j; i++)
+                  gsl_blas_dgemv(CblasTrans, 1.0, &m.matrix, &v1.vector, aii, &v2.vector);
+                }
+            }
+          else
             {
-              double A_ij = gsl_matrix_get (LLT, i, j);
-              gsl_matrix_set (LLT, j, i, A_ij);
+              v1 = gsl_matrix_row(LLT, N - 1);
+              gsl_blas_dscal(aii, &v1.vector);
             }
-        } 
+        }
+
+      /* copy lower triangle to upper */
+      gsl_matrix_transpose_tricpy('L', 0, LLT, LLT);
 
       return GSL_SUCCESS;
     }
@@ -324,7 +254,7 @@
   size_t i, j;
 
   /* initial Cholesky */
-  int stat_chol = gsl_linalg_cholesky_decomp(A);
+  int stat_chol = gsl_linalg_cholesky_decomp1(A);
 
   if(stat_chol == GSL_SUCCESS)
   {
@@ -356,3 +286,309 @@
 
   return stat_chol;
 }
+
+/*
+gsl_linalg_cholesky_scale()
+  This function computes scale factors diag(S), such that
+
+diag(S) A diag(S)
+
+has a condition number within a factor N of the matrix
+with the smallest condition number over all possible
+diagonal scalings. See Corollary 7.6 of:
+
+N. J. Higham, Accuracy and Stability of Numerical Algorithms (2nd Edition),
+SIAM, 2002.
+
+Inputs: A - symmetric positive definite matrix
+        S - (output) scale factors, S_i = 1 / sqrt(A_ii)
+*/
+
+int
+gsl_linalg_cholesky_scale(const gsl_matrix * A, gsl_vector * S)
+{
+  const size_t M = A->size1;
+  const size_t N = A->size2;
+
+  if (M != N)
+    {
+      GSL_ERROR("A is not a square matrix", GSL_ENOTSQR);
+    }
+  else if (N != S->size)
+    {
+      GSL_ERROR("S must have length N", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i;
+
+      /* compute S_i = 1/sqrt(A_{ii}) */
+      for (i = 0; i < N; ++i)
+        {
+          double Aii = gsl_matrix_get(A, i, i);
+
+          if (Aii <= 0.0)
+            gsl_vector_set(S, i, 1.0); /* matrix not positive definite */
+          else
+            gsl_vector_set(S, i, 1.0 / sqrt(Aii));
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+gsl_linalg_cholesky_scale_apply()
+  This function applies scale transformation to A:
+
+A <- diag(S) A diag(S)
+
+Inputs: A     - (input/output)
+                on input, symmetric positive definite matrix
+                on output, diag(S) * A * diag(S) in lower triangle
+        S     - (input) scale factors
+*/
+
+int
+gsl_linalg_cholesky_scale_apply(gsl_matrix * A, const gsl_vector * S)
+{
+  const size_t M = A->size1;
+  const size_t N = A->size2;
+
+  if (M != N)
+    {
+      GSL_ERROR("A is not a square matrix", GSL_ENOTSQR);
+    }
+  else if (N != S->size)
+    {
+      GSL_ERROR("S must have length N", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i, j;
+
+      /* compute: A <- diag(S) A diag(S) using lower triangle */
+      for (j = 0; j < N; ++j)
+        {
+          double sj = gsl_vector_get(S, j);
+
+          for (i = j; i < N; ++i)
+            {
+              double si = gsl_vector_get(S, i);
+              double *Aij = gsl_matrix_ptr(A, i, j);
+              *Aij *= si * sj;
+            }
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+int
+gsl_linalg_cholesky_decomp2(gsl_matrix * A, gsl_vector * S)
+{
+  const size_t M = A->size1;
+  const size_t N = A->size2;
+
+  if (M != N)
+    {
+      GSL_ERROR("cholesky decomposition requires square matrix", GSL_ENOTSQR);
+    }
+  else if (N != S->size)
+    {
+      GSL_ERROR("S must have length N", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+
+      /* compute scaling factors to reduce cond(A) */
+      status = gsl_linalg_cholesky_scale(A, S);
+      if (status)
+        return status;
+
+      /* apply scaling factors */
+      status = gsl_linalg_cholesky_scale_apply(A, S);
+      if (status)
+        return status;
+
+      /* compute Cholesky decomposition of diag(S) A diag(S) */
+      status = gsl_linalg_cholesky_decomp1(A);
+      if (status)
+        return status;
+
+      return GSL_SUCCESS;
+    }
+}
+
+int
+gsl_linalg_cholesky_svx2 (const gsl_matrix * LLT,
+                          const gsl_vector * S,
+                          gsl_vector * x)
+{
+  if (LLT->size1 != LLT->size2)
+    {
+      GSL_ERROR ("cholesky matrix must be square", GSL_ENOTSQR);
+    }
+  else if (LLT->size2 != S->size)
+    {
+      GSL_ERROR ("matrix size must match S", GSL_EBADLEN);
+    }
+  else if (LLT->size2 != x->size)
+    {
+      GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
+    }
+  else
+    {
+      /* b~ = diag(S) b */
+      gsl_vector_mul(x, S);
+
+      /* Solve for c using forward-substitution, L c = b~ */
+      gsl_blas_dtrsv (CblasLower, CblasNoTrans, CblasNonUnit, LLT, x);
+
+      /* Perform back-substitution, L^T x~ = c */
+      gsl_blas_dtrsv (CblasLower, CblasTrans, CblasNonUnit, LLT, x);
+
+      /* compute original solution vector x = S x~ */
+      gsl_vector_mul(x, S);
+
+      return GSL_SUCCESS;
+    }
+}
+
+int
+gsl_linalg_cholesky_solve2 (const gsl_matrix * LLT,
+                            const gsl_vector * S,
+                            const gsl_vector * b,
+                            gsl_vector * x)
+{
+  if (LLT->size1 != LLT->size2)
+    {
+      GSL_ERROR ("cholesky matrix must be square", GSL_ENOTSQR);
+    }
+  else if (LLT->size1 != S->size)
+    {
+      GSL_ERROR ("matrix size must match S size", GSL_EBADLEN);
+    }
+  else if (LLT->size1 != b->size)
+    {
+      GSL_ERROR ("matrix size must match b size", GSL_EBADLEN);
+    }
+  else if (LLT->size2 != x->size)
+    {
+      GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+
+      /* Copy x <- b */
+      gsl_vector_memcpy (x, b);
+
+      status = gsl_linalg_cholesky_svx2(LLT, S, x);
+
+      return status;
+    }
+}
+
+int
+gsl_linalg_cholesky_rcond (const gsl_matrix * LLT, double * rcond,
+                           gsl_vector * work)
+{
+  const size_t M = LLT->size1;
+  const size_t N = LLT->size2;
+
+  if (M != N)
+    {
+      GSL_ERROR ("cholesky matrix must be square", GSL_ENOTSQR);
+    }
+  else if (work->size != 3 * N)
+    {
+      GSL_ERROR ("work vector must have length 3*N", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+      double Anorm = cholesky_norm1(LLT, work); /* ||A||_1 */
+      double Ainvnorm;                          /* ||A^{-1}||_1 */
+
+      *rcond = 0.0;
+
+      /* don't continue if matrix is singular */
+      if (Anorm == 0.0)
+        return GSL_SUCCESS;
+
+      /* estimate ||A^{-1}||_1 */
+      status = gsl_linalg_invnorm1(N, cholesky_Ainv, (void *) LLT, &Ainvnorm, work);
+
+      if (status)
+        return status;
+
+      if (Ainvnorm != 0.0)
+        *rcond = (1.0 / Anorm) / Ainvnorm;
+
+      return GSL_SUCCESS;
+    }
+}
+
+/* compute 1-norm of original matrix, stored in upper triangle of LLT;
+ * diagonal entries have to be reconstructed */
+static double
+cholesky_norm1(const gsl_matrix * LLT, gsl_vector * work)
+{
+  const size_t N = LLT->size1;
+  double max = 0.0;
+  size_t i, j;
+
+  for (j = 0; j < N; ++j)
+    {
+      double sum = 0.0;
+      gsl_vector_const_view lj = gsl_matrix_const_subrow(LLT, j, 0, j + 1);
+      double Ajj;
+
+      /* compute diagonal (j,j) entry of A */
+      gsl_blas_ddot(&lj.vector, &lj.vector, &Ajj);
+
+      for (i = 0; i < j; ++i)
+        {
+          double *wi = gsl_vector_ptr(work, i);
+          double Aij = gsl_matrix_get(LLT, i, j);
+          double absAij = fabs(Aij);
+
+          sum += absAij;
+          *wi += absAij;
+        }
+
+      gsl_vector_set(work, j, sum + fabs(Ajj));
+    }
+
+  for (i = 0; i < N; ++i)
+    {
+      double wi = gsl_vector_get(work, i);
+      max = GSL_MAX(max, wi);
+    }
+
+  return max;
+}
+
+/* x := A^{-1} x = A^{-t} x, A = L L^T */
+static int
+cholesky_Ainv(CBLAS_TRANSPOSE_t TransA, gsl_vector * x, void * params)
+{
+  int status;
+  gsl_matrix * A = (gsl_matrix * ) params;
+
+  (void) TransA; /* unused parameter warning */
+
+  /* compute L^{-1} x */
+  status = gsl_blas_dtrsv(CblasLower, CblasNoTrans, CblasNonUnit, A, x);
+  if (status)
+    return status;
+
+  /* compute L^{-t} x */
+  status = gsl_blas_dtrsv(CblasLower, CblasTrans, CblasNonUnit, A, x);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+}
diff -Nru gsl-doc-1.16/linalg/cholesky_common.c gsl-doc-2.3/linalg/cholesky_common.c
--- gsl-doc-1.16/linalg/cholesky_common.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/linalg/cholesky_common.c	2016-08-10 21:03:42.000000000 +0000
@@ -0,0 +1,86 @@
+/* linalg/cholesky_common.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#define SWAP(a,b) do { double tmp = b ; b = a ; a = tmp ; } while(0)
+
+/*
+cholesky_swap_rowcol()
+  Swap rows and columns i and j of symmetric matrix A, updating only the
+lower triangle
+
+Inputs: A - symmetric matrix A, stored in lower triangle
+        i - index i
+        j - index j
+
+Return: success/error
+*/
+
+static int
+cholesky_swap_rowcol(gsl_matrix * A, const size_t i, const size_t j)
+{
+  if (i != j)
+    {
+      const size_t N = A->size1;
+      double *Aii, *Ajj;
+      size_t ii, jj, k;
+
+      /* organize so that ii < jj */
+      if (i < j)
+        {
+          ii = i;
+          jj = j;
+        }
+      else
+        {
+          ii = j;
+          jj = i;
+        }
+
+      /* swap subrows A(i,1:i-1) with A(j,1:i-1) */
+      for (k = 0; k < ii; ++k)
+        {
+          double *Aik = gsl_matrix_ptr(A, ii, k);
+          double *Ajk = gsl_matrix_ptr(A, jj, k);
+          SWAP(*Aik, *Ajk);
+        }
+
+      /* swap subrow A(j,i+1:j-1) with subcolumn A(i+1:j-1,i) */
+      for (k = ii + 1; k < jj; ++k)
+        {
+          double *Ajk = gsl_matrix_ptr(A, jj, k);
+          double *Aki = gsl_matrix_ptr(A, k, ii);
+          SWAP(*Ajk, *Aki);
+        }
+
+      /* swap subcolumns A(j+1:N,i) with A(j+1:N,j) */
+      for (k = jj + 1; k < N; ++k)
+        {
+          double *Aki = gsl_matrix_ptr(A, k, ii);
+          double *Akj = gsl_matrix_ptr(A, k, jj);
+          SWAP(*Aki, *Akj);
+        }
+
+      /* now swap diagonal elements A(i,i) and A(j,j) */
+      Aii = gsl_matrix_ptr(A, ii, ii);
+      Ajj = gsl_matrix_ptr(A, jj, jj);
+      SWAP(*Aii, *Ajj);
+    }
+
+  return GSL_SUCCESS;
+}
diff -Nru gsl-doc-1.16/linalg/cod.c gsl-doc-2.3/linalg/cod.c
--- gsl-doc-1.16/linalg/cod.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/linalg/cod.c	2016-08-23 14:30:22.000000000 +0000
@@ -0,0 +1,570 @@
+/* linalg/cod.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_permute_vector.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_linalg.h>
+
+/*
+ * This module contains routines for factoring an M-by-N matrix A as:
+ *
+ * A P = Q R Z
+ *
+ * known as the Complete Orthogonal Decomposition, where:
+ *
+ * P is a N-by-N permutation matrix
+ * Q is M-by-M orthogonal
+ * R has an r-by-r upper triangular block
+ * Z is N-by-N orthogonal
+ *
+ * When A is full rank, Z = I and this becomes the QR decomposition
+ * with column pivoting. When A is rank deficient, then
+ *
+ * R = [ R11 0 ] where R11 is r-by-r and r = rank(A)
+ *     [  0  0 ]
+ */
+
+static int cod_RZ(gsl_matrix * A, gsl_vector * tau);
+static double cod_householder_transform(double *alpha, gsl_vector * v);
+static int cod_householder_mh(const double tau, const gsl_vector * v,
+                              gsl_matrix * A, gsl_vector * work);
+static int cod_householder_hv(const double tau, const gsl_vector * v, gsl_vector * w);
+static int cod_householder_ZTvec(const gsl_matrix * QRZ, const gsl_vector * tau_Z, const size_t rank,
+                                 gsl_vector * v);
+
+int
+gsl_linalg_COD_decomp_e(gsl_matrix * A, gsl_vector * tau_Q, gsl_vector * tau_Z,
+                        gsl_permutation * p, double tol, size_t * rank, gsl_vector * work)
+{
+  const size_t M = A->size1;
+  const size_t N = A->size2;
+
+  if (tau_Q->size != GSL_MIN (M, N))
+    {
+      GSL_ERROR ("size of tau_Q must be MIN(M,N)", GSL_EBADLEN);
+    }
+  else if (tau_Z->size != GSL_MIN (M, N))
+    {
+      GSL_ERROR ("size of tau_Z must be MIN(M,N)", GSL_EBADLEN);
+    }
+  else if (p->size != N)
+    {
+      GSL_ERROR ("permutation size must be N", GSL_EBADLEN);
+    }
+  else if (work->size != N)
+    {
+      GSL_ERROR ("work size must be N", GSL_EBADLEN);
+    }
+  else
+    {
+      int status, signum;
+      size_t r;
+
+      /* decompose: A P = Q R */
+      status = gsl_linalg_QRPT_decomp(A, tau_Q, p, &signum, work);
+      if (status)
+        return status;
+
+      /* estimate rank of A */
+      r = gsl_linalg_QRPT_rank(A, tol);
+
+      if (r < N)
+        {
+          /*
+           * matrix is rank-deficient, so that the R factor is
+           *
+           * R = [ R11 R12 ] =~ [ R11 R12 ]
+           *     [  0  R22 ]    [  0   0  ]
+           *
+           * compute RZ decomposition of upper trapezoidal matrix
+           * [ R11 R12 ] = [ R11~ 0 ] Z
+           */
+          gsl_matrix_view R_upper = gsl_matrix_submatrix(A, 0, 0, r, N);
+          gsl_vector_view t = gsl_vector_subvector(tau_Z, 0, r);
+
+          cod_RZ(&R_upper.matrix, &t.vector);
+        }
+
+      *rank = r;
+
+      return GSL_SUCCESS;
+    }
+}
+
+int
+gsl_linalg_COD_decomp(gsl_matrix * A, gsl_vector * tau_Q, gsl_vector * tau_Z,
+                      gsl_permutation * p, size_t * rank, gsl_vector * work)
+{
+  return gsl_linalg_COD_decomp_e(A, tau_Q, tau_Z, p, -1.0, rank, work);
+}
+
+/*
+gsl_linalg_COD_lssolve()
+  Find the least squares solution to the overdetermined system 
+
+   A x = b 
+
+for M >= N using the COD factorization A P = Q R Z
+
+Inputs: QRZ      - matrix A, in COD compressed format, M-by-N
+        tau_Q    - Householder scalars for Q, length min(M,N)
+        tau_Z    - Householder scalars for Z, length min(M,N)
+        perm     - permutation matrix
+        rank     - rank of A
+        b        - rhs vector, length M
+        x        - (output) solution vector, length N
+        residual - (output) residual vector, b - A x, length M
+*/
+
+int
+gsl_linalg_COD_lssolve (const gsl_matrix * QRZ, const gsl_vector * tau_Q, const gsl_vector * tau_Z,
+                        const gsl_permutation * perm, const size_t rank, const gsl_vector * b,
+                        gsl_vector * x, gsl_vector * residual)
+{
+  const size_t M = QRZ->size1;
+  const size_t N = QRZ->size2;
+
+  if (M < N)
+    {
+      GSL_ERROR ("QRZ matrix must have M>=N", GSL_EBADLEN);
+    }
+  else if (M != b->size)
+    {
+      GSL_ERROR ("matrix size must match b size", GSL_EBADLEN);
+    }
+  else if (rank > GSL_MIN (M, N))
+    {
+      GSL_ERROR ("rank must be <= MIN(M,N)", GSL_EBADLEN);
+    }
+  else if (N != x->size)
+    {
+      GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
+    }
+  else if (M != residual->size)
+    {
+      GSL_ERROR ("matrix size must match residual size", GSL_EBADLEN);
+    }
+  else
+    {
+      gsl_matrix_const_view R11 = gsl_matrix_const_submatrix (QRZ, 0, 0, rank, rank);
+      gsl_vector_view QTb1 = gsl_vector_subvector(residual, 0, rank);
+      gsl_vector_view x1 = gsl_vector_subvector(x, 0, rank);
+
+      gsl_vector_set_zero(x);
+
+      /* compute residual = Q^T b */
+      gsl_vector_memcpy(residual, b);
+      gsl_linalg_QR_QTvec (QRZ, tau_Q, residual);
+
+      /* solve x1 := R11^{-1} (Q^T b)(1:r) */
+      gsl_vector_memcpy(&(x1.vector), &(QTb1.vector));
+      gsl_blas_dtrsv(CblasUpper, CblasNoTrans, CblasNonUnit, &(R11.matrix), &(x1.vector));
+
+      /* compute Z^T ( R11^{-1} x1; 0 ) */
+      cod_householder_ZTvec(QRZ, tau_Z, rank, x);
+
+      /* compute x = P Z^T ( R11^{-1} x1; 0 ) */
+      gsl_permute_vector_inverse(perm, x);
+
+      /* compute residual = b - A x = Q (Q^T b - R [ R11^{-1} x1; 0 ]) */
+      gsl_vector_set_zero(&(QTb1.vector));
+      gsl_linalg_QR_Qvec(QRZ, tau_Q, residual);
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+gsl_linalg_COD_unpack()
+  Unpack encoded COD decomposition into the matrices Q,R,Z,P
+
+Inputs: QRZ   - encoded COD decomposition
+        tau_Q - Householder scalars for Q
+        tau_Z - Householder scalars for Z
+        rank  - rank of matrix (as determined from gsl_linalg_COD_decomp)
+        Q     - (output) M-by-M matrix Q
+        R     - (output) M-by-N matrix R
+        Z     - (output) N-by-N matrix Z
+*/
+
+int
+gsl_linalg_COD_unpack(const gsl_matrix * QRZ, const gsl_vector * tau_Q,
+                      const gsl_vector * tau_Z, const size_t rank, gsl_matrix * Q,
+                      gsl_matrix * R, gsl_matrix * Z)
+{
+  const size_t M = QRZ->size1;
+  const size_t N = QRZ->size2;
+
+  if (tau_Q->size != GSL_MIN (M, N))
+    {
+      GSL_ERROR ("size of tau_Q must be MIN(M,N)", GSL_EBADLEN);
+    }
+  else if (tau_Z->size != GSL_MIN (M, N))
+    {
+      GSL_ERROR ("size of tau_Z must be MIN(M,N)", GSL_EBADLEN);
+    }
+  else if (rank > GSL_MIN (M, N))
+    {
+      GSL_ERROR ("rank must be <= MIN(M,N)", GSL_EBADLEN);
+    }
+  else if (Q->size1 != M || Q->size2 != M)
+    {
+      GSL_ERROR ("Q must by M-by-M", GSL_EBADLEN);
+    }
+  else if (R->size1 != M || R->size2 != N)
+    {
+      GSL_ERROR ("R must by M-by-N", GSL_EBADLEN);
+    }
+  else if (Z->size1 != N || Z->size2 != N)
+    {
+      GSL_ERROR ("Z must by N-by-N", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i;
+      gsl_matrix_view R11 = gsl_matrix_submatrix(R, 0, 0, rank, rank);
+      gsl_matrix_const_view QRZ11 = gsl_matrix_const_submatrix(QRZ, 0, 0, rank, rank);
+
+      /* form Q matrix */
+
+      gsl_matrix_set_identity(Q);
+
+      for (i = GSL_MIN (M, N); i-- > 0;)
+        {
+          gsl_vector_const_view h = gsl_matrix_const_subcolumn (QRZ, i, i, M - i);
+          gsl_matrix_view m = gsl_matrix_submatrix (Q, i, i, M - i, M - i);
+          double ti = gsl_vector_get (tau_Q, i);
+          gsl_linalg_householder_hm (ti, &h.vector, &m.matrix);
+        }
+
+      /* form Z matrix */
+      gsl_matrix_set_identity(Z);
+
+      if (rank < N)
+        {
+          gsl_vector_view work = gsl_matrix_row(R, 0); /* temporary workspace, size N */
+
+          /* multiply I by Z from the right */
+          gsl_linalg_COD_matZ(QRZ, tau_Z, rank, Z, &work.vector);
+        }
+
+      /* copy rank-by-rank upper triangle of QRZ into R and zero the rest */
+      gsl_matrix_set_zero(R);
+      gsl_matrix_tricpy('U', 1, &R11.matrix, &QRZ11.matrix);
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+gsl_linalg_COD_matZ
+  Multiply an M-by-N matrix A on the right by Z (N-by-N)
+
+Inputs: QRZ   - encoded COD matrix
+        tau_Z - Householder scalars for Z
+        rank  - matrix rank
+        A     - on input, M-by-N matrix
+                on output, A * Z
+        work  - workspace of length M
+*/
+
+int
+gsl_linalg_COD_matZ(const gsl_matrix * QRZ, const gsl_vector * tau_Z, const size_t rank,
+                    gsl_matrix * A, gsl_vector * work)
+{
+  const size_t M = A->size1;
+  const size_t N = A->size2;
+
+  if (tau_Z->size != GSL_MIN (QRZ->size1, QRZ->size2))
+    {
+      GSL_ERROR("tau_Z must be GSL_MIN(M,N)", GSL_EBADLEN);
+    }
+  else if (QRZ->size2 != N)
+    {
+      GSL_ERROR("QRZ must have N columns", GSL_EBADLEN);
+    }
+  else if (work->size != M)
+    {
+      GSL_ERROR("workspace must be length M", GSL_EBADLEN);
+    }
+  else
+    {
+      /* if rank == N, then Z = I and there is nothing to do */
+      if (rank < N)
+        {
+          size_t i;
+
+          for (i = 0; i < rank; ++i)
+            {
+              gsl_vector_const_view h = gsl_matrix_const_subrow (QRZ, i, rank, N - rank);
+              gsl_matrix_view m = gsl_matrix_submatrix (A, 0, i, M, N - i);
+              double ti = gsl_vector_get (tau_Z, i);
+              cod_householder_mh (ti, &h.vector, &m.matrix, work);
+            }
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+
+/*********************************************
+ * INTERNAL ROUTINES                         *
+ *********************************************/
+
+/*
+cod_RZ()
+  Perform RZ decomposition of an upper trapezoidal matrix,
+
+A = [ A11 A12 ] = [ R 0 ] Z
+
+where A is M-by-N with N >= M, A11 is M-by-M upper triangular,
+and A12 is M-by-(N-M). On output, Z is stored as Householder
+reflectors in the A12 portion of A,
+
+Z = Z(1) Z(2) ... Z(M)
+
+Inputs: A   - M-by-N matrix with N >= M
+              On input, upper trapezoidal matrix [ A11 A12 ]
+              On output, A11 is overwritten by R (subdiagonal elements
+              are not touched), and A12 is overwritten by Z in packed storage
+        tau - (output) Householder scalars, size M
+*/
+
+static int
+cod_RZ(gsl_matrix * A, gsl_vector * tau)
+{
+  const size_t M = A->size1;
+  const size_t N = A->size2;
+
+  if (tau->size != M)
+    {
+      GSL_ERROR("tau has wrong size", GSL_EBADLEN);
+    }
+  else if (N < M)
+    {
+      GSL_ERROR("N must be >= M", GSL_EINVAL);
+    }
+  else if (M == N)
+    {
+      /* quick return */
+      gsl_vector_set_all(tau, 0.0);
+      return GSL_SUCCESS;
+    }
+  else
+    {
+      size_t k;
+
+      for (k = M; k > 0 && k--; )
+        {
+          double *alpha = gsl_matrix_ptr(A, k, k);
+          gsl_vector_view z = gsl_matrix_subrow(A, k, M, N - M);
+          double tauk;
+
+          /* compute Householder reflection to zero [ A(k,k) A(k,M+1:N) ] */
+          tauk = cod_householder_transform(alpha, &z.vector);
+          gsl_vector_set(tau, k, tauk);
+
+          if ((tauk != 0) && (k > 0))
+            {
+              gsl_vector_view w = gsl_vector_subvector(tau, 0, k);
+              gsl_matrix_view B = gsl_matrix_submatrix(A, 0, k, k, N - k);
+
+              cod_householder_mh(tauk, &z.vector, &B.matrix, &w.vector);
+            }
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+static double
+cod_householder_transform(double *alpha, gsl_vector * v)
+{
+  double beta, tau;
+  double xnorm = gsl_blas_dnrm2(v);
+
+  if (xnorm == 0)
+    {
+      return 0.0; /* tau = 0 */
+    }
+
+  beta = - (*alpha >= 0.0 ? +1.0 : -1.0) * gsl_hypot(*alpha, xnorm);
+  tau = (beta - *alpha) / beta;
+
+  {
+    double s = (*alpha - beta);
+    
+    if (fabs(s) > GSL_DBL_MIN) 
+      {
+        gsl_blas_dscal (1.0 / s, v);
+      }
+    else
+      {
+        gsl_blas_dscal (GSL_DBL_EPSILON / s, v);
+        gsl_blas_dscal (1.0 / GSL_DBL_EPSILON, v);
+      }
+
+    *alpha = beta;
+  }
+  
+  return tau;
+}
+
+/*
+cod_householder_hv
+  Apply Householder reflection H = (I - tau*v*v') to vector v from the left,
+
+w' = H * w
+
+Inputs: tau  - Householder scalar
+        v    - Householder vector, size M
+        w    - on input, w vector, size M
+               on output, H * w
+
+Notes:
+1) Based on LAPACK routine DLARZ
+*/
+
+static int
+cod_householder_hv(const double tau, const gsl_vector * v, gsl_vector * w)
+{
+  if (tau == 0)
+    {
+      return GSL_SUCCESS; /* H = I */
+    }
+  else
+    {
+      const size_t M = w->size;
+      const size_t L = v->size;
+      double w0 = gsl_vector_get(w, 0);
+      gsl_vector_view w1 = gsl_vector_subvector(w, M - L, L);
+      double d1, d;
+
+      /* d1 := v . w(M-L:M) */
+      gsl_blas_ddot(v, &w1.vector, &d1);
+
+      /* d := w(1) + v . w(M-L:M) */
+      d = w0 + d1;
+
+      /* w(1) = w(1) - tau * d */
+      gsl_vector_set(w, 0, w0 - tau * d);
+
+      /* w(M-L:M) = w(M-L:M) - tau * d * v */
+      gsl_blas_daxpy(-tau * d, v, &w1.vector);
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+cod_householder_mh
+  Apply Householder reflection H = (I - tau*v*v') to matrix A from the right
+
+Inputs: tau  - Householder scalar
+        v    - Householder vector, size N-M
+        A    - matrix, size M-by-N
+        work - workspace, size M
+
+Notes:
+1) Based on LAPACK routine DLARZ
+*/
+
+static int
+cod_householder_mh(const double tau, const gsl_vector * v, gsl_matrix * A,
+                   gsl_vector * work)
+{
+  if (tau == 0)
+    {
+      return GSL_SUCCESS; /* H = I */
+    }
+  else
+    {
+      const size_t M = A->size1;
+      const size_t N = A->size2;
+      const size_t L = v->size;
+      gsl_vector_view A1 = gsl_matrix_subcolumn(A, 0, 0, M);
+      gsl_matrix_view C = gsl_matrix_submatrix(A, 0, N - L, M, L);
+
+      /* work(1:M) = A(1:M,1) */
+      gsl_vector_memcpy(work, &A1.vector);
+
+      /* work(1:M) = work(1:M) + A(1:M,M+1:N) * v(1:N-M) */
+      gsl_blas_dgemv(CblasNoTrans, 1.0, &C.matrix, v, 1.0, work);
+
+      /* A(1:M,1) = A(1:M,1) - tau * work(1:M) */
+      gsl_blas_daxpy(-tau, work, &A1.vector);
+
+      /* A(1:M,M+1:N) = A(1:M,M+1:N) - tau * work(1:M) * v(1:N-M)' */
+      gsl_blas_dger(-tau, work, v, &C.matrix);
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+cod_householder_ZTvec
+  Multiply a vector by Z^T
+
+Inputs: QRZ   - encoded COD matrix
+        tau_Z - Householder scalars for Z
+        rank  - matrix rank
+        v     - on input, vector of length N
+                on output, Z^T * v
+*/
+
+static int
+cod_householder_ZTvec(const gsl_matrix * QRZ, const gsl_vector * tau_Z, const size_t rank,
+                      gsl_vector * v)
+{
+  const size_t M = QRZ->size1;
+  const size_t N = QRZ->size2;
+
+  if (tau_Z->size != GSL_MIN (M, N))
+    {
+      GSL_ERROR("tau_Z must be GSL_MIN(M,N)", GSL_EBADLEN);
+    }
+  else if (v->size != N)
+    {
+      GSL_ERROR("v must be length N", GSL_EBADLEN);
+    }
+  else
+    {
+      if (rank < N)
+        {
+          size_t i;
+
+          for (i = 0; i < rank; ++i)
+            {
+              gsl_vector_const_view h = gsl_matrix_const_subrow (QRZ, i, rank, N - rank);
+              gsl_vector_view w = gsl_vector_subvector (v, i, N - i);
+              double ti = gsl_vector_get (tau_Z, i);
+              cod_householder_hv(ti, &h.vector, &w.vector);
+            }
+        }
+
+      return GSL_SUCCESS;
+    }
+}
diff -Nru gsl-doc-1.16/linalg/condest.c gsl-doc-2.3/linalg/condest.c
--- gsl-doc-1.16/linalg/condest.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/linalg/condest.c	2016-08-23 14:34:05.000000000 +0000
@@ -0,0 +1,299 @@
+/* linalg/condest.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_linalg.h>
+
+/*
+ * This module contains routines for estimating the condition number
+ * of matrices in the 1-norm. The algorithm is based on the paper,
+ *
+ * [1] N. J. Higham, "FORTRAN codes for estimating the one-norm of
+ * a real or complex matrix, with applications to condition estimation",
+ * ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
+ */
+
+static double condest_tri_norm1(CBLAS_UPLO_t Uplo, const gsl_matrix * A);
+static int condest_tri_rcond(CBLAS_UPLO_t Uplo, const gsl_matrix * A,
+                             double * rcond, gsl_vector * work);
+static int condest_same_sign(const gsl_vector * x, const gsl_vector * y);
+static int condest_invtriu(CBLAS_TRANSPOSE_t TransA, gsl_vector * x, void * params);
+static int condest_invtril(CBLAS_TRANSPOSE_t TransA, gsl_vector * x, void * params);
+
+/*
+gsl_linalg_tri_upper_rcond()
+  Estimate reciprocal condition number of upper triangular matrix
+
+Inputs: A     - upper triangular matrix, N-by-N
+        rcond - (output) reciprocal condition number estimate
+        work  - workspace, length 3*N
+
+Return: success/error
+*/
+
+int
+gsl_linalg_tri_upper_rcond(const gsl_matrix * A, double * rcond, gsl_vector * work)
+{
+  int status = condest_tri_rcond(CblasUpper, A, rcond, work);
+  return status;
+}
+
+/*
+gsl_linalg_tri_lower_rcond()
+  Estimate reciprocal condition number of lower triangular matrix
+
+Inputs: A     - lower triangular matrix, N-by-N
+        rcond - (output) reciprocal condition number estimate
+        work  - workspace, length 3*N
+
+Return: success/error
+*/
+
+int
+gsl_linalg_tri_lower_rcond(const gsl_matrix * A, double * rcond, gsl_vector * work)
+{
+  int status = condest_tri_rcond(CblasLower, A, rcond, work);
+  return status;
+}
+
+/*
+gsl_linalg_invnorm1()
+  Estimate the 1-norm of ||A^{-1}||, where A is a square
+N-by-N matrix
+
+Inputs: N        - size of matrix
+        Ainvx    - pointer to function which calculates:
+                   x := A^{-1} x or x := A^{-t} x
+        params   - parameters to pass to Ainvx
+        Ainvnorm - (output) estimate of ||A^{-1}||_1
+        work     - workspace, length 3*N
+*/
+
+int
+gsl_linalg_invnorm1(const size_t N,
+                    int (* Ainvx)(CBLAS_TRANSPOSE_t TransA, gsl_vector * x, void * params),
+                    void * params, double * Ainvnorm, gsl_vector * work)
+{
+  if (work->size != 3 * N)
+    {
+      GSL_ERROR ("work vector must have length 3*N", GSL_EBADLEN);
+    }
+  else
+    {
+      const size_t maxit = 5;
+      gsl_vector_view x = gsl_vector_subvector(work, 0, N);
+      gsl_vector_view v = gsl_vector_subvector(work, N, N);
+      gsl_vector_view xi = gsl_vector_subvector(work, 2*N, N);
+      double gamma, gamma_old, temp;
+      size_t i, k;
+
+      for (i = 0; i < N; ++i)
+        gsl_vector_set(&x.vector, i, 1.0 / (double) N);
+
+      /* compute v = A^{-1} x */
+      gsl_vector_memcpy(&v.vector, &x.vector);
+      (*Ainvx)(CblasNoTrans, &v.vector, params);
+
+      /* gamma = ||v||_1 */
+      gamma = gsl_blas_dasum(&v.vector);
+
+      /* xi = sign(v) */
+      for (i = 0; i < N; ++i)
+        {
+          double vi = gsl_vector_get(&v.vector, i);
+          gsl_vector_set(&xi.vector, i, GSL_SIGN(vi));
+        }
+
+      /* x = A^{-t} xi */
+      gsl_vector_memcpy(&x.vector, &xi.vector);
+      (*Ainvx)(CblasTrans, &x.vector, params);
+
+      for (k = 0; k < maxit; ++k)
+        {
+          size_t j = (size_t) gsl_blas_idamax(&x.vector);
+
+          /* v := A^{-1} e_j */
+          gsl_vector_set_zero(&v.vector);
+          gsl_vector_set(&v.vector, j, 1.0);
+          (*Ainvx)(CblasNoTrans, &v.vector, params);
+
+          gamma_old = gamma;
+          gamma = gsl_blas_dasum(&v.vector);
+
+          /* check for repeated sign vector (algorithm has converged) */
+          if (condest_same_sign(&v.vector, &xi.vector) || (gamma < gamma_old))
+            break;
+
+          /* xi = sign(v) */
+          for (i = 0; i < N; ++i)
+            {
+              double vi = gsl_vector_get(&v.vector, i);
+              gsl_vector_set(&xi.vector, i, GSL_SIGN(vi));
+            }
+
+          /* x = A^{-t} sign(v) */
+          gsl_vector_memcpy(&x.vector, &xi.vector);
+          (*Ainvx)(CblasTrans, &x.vector, params);
+        }
+
+      temp = 1.0; /* (-1)^i */
+      for (i = 0; i < N; ++i)
+        {
+          double term = 1.0 + (double) i / (N - 1.0);
+          gsl_vector_set(&x.vector, i, temp * term);
+          temp = -temp;
+        }
+
+      /* x := A^{-1} x */
+      (*Ainvx)(CblasNoTrans, &x.vector, params);
+
+      temp = 2.0 * gsl_blas_dasum(&x.vector) / (3.0 * N);
+      if (temp > gamma)
+        {
+          gsl_vector_memcpy(&v.vector, &x.vector);
+          gamma = temp;
+        }
+
+      *Ainvnorm = gamma;
+
+      return GSL_SUCCESS;
+    }
+}
+
+static int
+condest_tri_rcond(CBLAS_UPLO_t Uplo, const gsl_matrix * A, double * rcond, gsl_vector * work)
+{
+  const size_t M = A->size1;
+  const size_t N = A->size2;
+
+  if (M != N)
+    {
+      GSL_ERROR ("matrix must be square", GSL_ENOTSQR);
+    }
+  else if (work->size != 3 * N)
+    {
+      GSL_ERROR ("work vector must have length 3*N", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+      double Anorm = condest_tri_norm1(Uplo, A); /* ||A||_1 */
+      double Ainvnorm;                           /* ||A^{-1}||_1 */
+
+      *rcond = 0.0;
+
+      /* don't continue if matrix is singular */
+      if (Anorm == 0.0)
+        return GSL_SUCCESS;
+
+      /* estimate ||A^{-1}||_1 */
+      if (Uplo == CblasUpper)
+        status = gsl_linalg_invnorm1(N, condest_invtriu, (void *) A, &Ainvnorm, work);
+      else
+        status = gsl_linalg_invnorm1(N, condest_invtril, (void *) A, &Ainvnorm, work);
+
+      if (status)
+        return status;
+
+      if (Ainvnorm != 0.0)
+        *rcond = (1.0 / Anorm) / Ainvnorm;
+
+      return GSL_SUCCESS;
+    }
+}
+
+/* calculate 1 norm of triangular matrix */
+static double
+condest_tri_norm1(CBLAS_UPLO_t Uplo, const gsl_matrix * A)
+{
+  const size_t N = A->size2;
+  double max = 0.0;
+  size_t i, j;
+
+  if (Uplo == CblasUpper)
+    {
+      for (j = 0; j < N; ++j)
+        {
+          double sum = 0.0;
+          for (i = 0; i <= j; ++i)
+            {
+              double Aij = gsl_matrix_get(A, i, j);
+              sum += fabs(Aij);
+            }
+
+          max = GSL_MAX(max, sum);
+        }
+    }
+  else
+    {
+      for (j = 0; j < N; ++j)
+        {
+          double sum = 0.0;
+          for (i = j; i < N; ++i)
+            {
+              double Aij = gsl_matrix_get(A, i, j);
+              sum += fabs(Aij);
+            }
+
+          max = GSL_MAX(max, sum);
+        }
+    }
+
+  return max;
+}
+
+/* return 1 if sign(x) = sign(y), 0 otherwise */
+static int
+condest_same_sign(const gsl_vector * x, const gsl_vector * y)
+{
+  const size_t n = x->size;
+  size_t i;
+
+  for (i = 0; i < n; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      double yi = gsl_vector_get(y, i);
+      if (GSL_SIGN(xi) != GSL_SIGN(yi))
+        return 0;
+    }
+
+  return 1;
+}
+
+/* x := A^{-1} x, A upper triangular */
+static int
+condest_invtriu(CBLAS_TRANSPOSE_t TransA, gsl_vector * x, void * params)
+{
+  gsl_matrix * A = (gsl_matrix *) params;
+  return gsl_blas_dtrsv(CblasUpper, TransA, CblasNonUnit, A, x);
+}
+
+/* x := A^{-1} x, A lower triangular */
+static int
+condest_invtril(CBLAS_TRANSPOSE_t TransA, gsl_vector * x, void * params)
+{
+  gsl_matrix * A = (gsl_matrix *) params;
+  return gsl_blas_dtrsv(CblasLower, TransA, CblasNonUnit, A, x);
+}
diff -Nru gsl-doc-1.16/linalg/givens.c gsl-doc-2.3/linalg/givens.c
--- gsl-doc-1.16/linalg/givens.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/givens.c	1970-01-01 00:00:00.000000000 +0000
@@ -1,46 +0,0 @@
-/* linalg/givens.c
- * 
- * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Gerard Jungman, Brian Gough
- * 
- * This program is free software; you can redistribute it and/or modify
- * it under the terms of the GNU General Public License as published by
- * the Free Software Foundation; either version 3 of the License, or (at
- * your option) any later version.
- * 
- * This program is distributed in the hope that it will be useful, but
- * WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
- * General Public License for more details.
- * 
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
- */
-
-/* Generate a Givens rotation (cos,sin) which takes v=(x,y) to (|v|,0) 
-
-   From Golub and Van Loan, "Matrix Computations", Section 5.1.8 */
-
-inline static void
-create_givens (const double a, const double b, double *c, double *s)
-{
-  if (b == 0)
-    {
-      *c = 1;
-      *s = 0;
-    }
-  else if (fabs (b) > fabs (a))
-    {
-      double t = -a / b;
-      double s1 = 1.0 / sqrt (1 + t * t);
-      *s = s1;
-      *c = s1 * t;
-    }
-  else
-    {
-      double t = -b / a;
-      double c1 = 1.0 / sqrt (1 + t * t);
-      *c = c1;
-      *s = c1 * t;
-    }
-}
diff -Nru gsl-doc-1.16/linalg/gsl_linalg.h gsl-doc-2.3/linalg/gsl_linalg.h
--- gsl-doc-1.16/linalg/gsl_linalg.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/gsl_linalg.h	2016-11-29 21:53:35.000000000 +0000
@@ -20,10 +20,14 @@
 #ifndef __GSL_LINALG_H__
 #define __GSL_LINALG_H__
 
+#include <stdlib.h>
 #include <gsl/gsl_mode.h>
 #include <gsl/gsl_permutation.h>
 #include <gsl/gsl_vector.h>
 #include <gsl/gsl_matrix.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_inline.h>
+#include <gsl/gsl_blas.h>
 
 #undef __BEGIN_DECLS
 #undef __END_DECLS
@@ -189,7 +193,7 @@
                           const gsl_permutation * p,
                           const gsl_vector * b,
                           gsl_vector * x,
-                          gsl_vector * residual);
+                          gsl_vector * work);
 
 int gsl_linalg_LU_invert (const gsl_matrix * LU,
                           const gsl_permutation * p,
@@ -219,7 +223,7 @@
                                   const gsl_permutation * p,
                                   const gsl_vector_complex * b,
                                   gsl_vector_complex * x,
-                                  gsl_vector_complex * residual);
+                                  gsl_vector_complex * work);
 
 int gsl_linalg_complex_LU_invert (const gsl_matrix_complex * LU,
                                   const gsl_permutation * p,
@@ -283,6 +287,10 @@
                          const gsl_vector * tau,
                          gsl_matrix * A);
 
+int gsl_linalg_QR_matQ (const gsl_matrix * QR,
+                        const gsl_vector * tau,
+                        gsl_matrix * A);
+
 int gsl_linalg_QR_unpack (const gsl_matrix * QR,
                           const gsl_vector * tau,
                           gsl_matrix * Q,
@@ -317,6 +325,20 @@
                            const gsl_vector * b,
                            gsl_vector * x);
 
+int gsl_linalg_QRPT_lssolve (const gsl_matrix * QR,
+                             const gsl_vector * tau,
+                             const gsl_permutation * p,
+                             const gsl_vector * b,
+                             gsl_vector * x,
+                             gsl_vector * residual);
+
+int gsl_linalg_QRPT_lssolve2 (const gsl_matrix * QR,
+                              const gsl_vector * tau,
+                              const gsl_permutation * p,
+                              const gsl_vector * b,
+                              const size_t rank,
+                              gsl_vector * x,
+                              gsl_vector * residual);
 
 int gsl_linalg_QRPT_svx (const gsl_matrix * QR,
                          const gsl_vector * tau,
@@ -344,6 +366,29 @@
                             gsl_vector * u,
                             const gsl_vector * v);
 
+size_t gsl_linalg_QRPT_rank (const gsl_matrix * QR, const double tol);
+
+int gsl_linalg_QRPT_rcond(const gsl_matrix * QR, double * rcond, gsl_vector * work);
+
+/* COD decomposition */
+
+int gsl_linalg_COD_decomp(gsl_matrix * A, gsl_vector * tau_Q, gsl_vector * tau_Z,
+                          gsl_permutation * p, size_t * rank, gsl_vector * work);
+
+int gsl_linalg_COD_decomp_e(gsl_matrix * A, gsl_vector * tau_Q, gsl_vector * tau_Z,
+                            gsl_permutation * p, double tol, size_t * rank, gsl_vector * work);
+
+int gsl_linalg_COD_lssolve (const gsl_matrix * QRZ, const gsl_vector * tau_Q, const gsl_vector * tau_Z,
+                            const gsl_permutation * perm, const size_t rank, const gsl_vector * b,
+                            gsl_vector * x, gsl_vector * residual);
+
+int gsl_linalg_COD_unpack(const gsl_matrix * QRZ, const gsl_vector * tau_Q,
+                          const gsl_vector * tau_Z, const size_t rank, gsl_matrix * Q,
+                          gsl_matrix * R, gsl_matrix * Z);
+
+int gsl_linalg_COD_matZ(const gsl_matrix * QRZ, const gsl_vector * tau_Z, const size_t rank,
+                        gsl_matrix * A, gsl_vector * work);
+
 /* LQ decomposition */
 
 int gsl_linalg_LQ_decomp (gsl_matrix * A, gsl_vector * tau);
@@ -423,6 +468,7 @@
 /* Cholesky Decomposition */
 
 int gsl_linalg_cholesky_decomp (gsl_matrix * A);
+int gsl_linalg_cholesky_decomp1 (gsl_matrix * A);
 
 int gsl_linalg_cholesky_solve (const gsl_matrix * cholesky,
                                const gsl_vector * b,
@@ -441,6 +487,24 @@
  */
 int gsl_linalg_cholesky_decomp_unit(gsl_matrix * A, gsl_vector * D);
 
+int gsl_linalg_cholesky_scale(const gsl_matrix * A, gsl_vector * S);
+
+int gsl_linalg_cholesky_scale_apply(gsl_matrix * A, const gsl_vector * S);
+
+int gsl_linalg_cholesky_decomp2(gsl_matrix * A, gsl_vector * S);
+
+int gsl_linalg_cholesky_svx2 (const gsl_matrix * LLT,
+                              const gsl_vector * S,
+                              gsl_vector * x);
+
+int gsl_linalg_cholesky_solve2 (const gsl_matrix * LLT,
+                                const gsl_vector * S,
+                                const gsl_vector * b,
+                                gsl_vector * x);
+
+int gsl_linalg_cholesky_rcond (const gsl_matrix * LLT, double * rcond,
+                               gsl_vector * work);
+
 /* Complex Cholesky Decomposition */
 
 int gsl_linalg_complex_cholesky_decomp (gsl_matrix_complex * A);
@@ -454,6 +518,58 @@
 
 int gsl_linalg_complex_cholesky_invert(gsl_matrix_complex * cholesky);
 
+/* Pivoted Cholesky LDLT decomposition */
+
+int gsl_linalg_pcholesky_decomp (gsl_matrix * A, gsl_permutation * p);
+
+int gsl_linalg_pcholesky_solve(const gsl_matrix * LDLT,
+                               const gsl_permutation * p,
+                               const gsl_vector * b,
+                               gsl_vector * x);
+
+int gsl_linalg_pcholesky_svx(const gsl_matrix * LDLT,
+                             const gsl_permutation * p,
+                             gsl_vector * x);
+
+int gsl_linalg_pcholesky_decomp2(gsl_matrix * A, gsl_permutation * p,
+                                 gsl_vector * S);
+
+int gsl_linalg_pcholesky_solve2(const gsl_matrix * LDLT,
+                                const gsl_permutation * p,
+                                const gsl_vector * S,
+                                const gsl_vector * b,
+                                gsl_vector * x);
+
+int gsl_linalg_pcholesky_svx2(const gsl_matrix * LDLT,
+                              const gsl_permutation * p,
+                              const gsl_vector * S,
+                              gsl_vector * x);
+
+int gsl_linalg_pcholesky_invert(const gsl_matrix * LDLT, const gsl_permutation * p,
+                                gsl_matrix * Ainv);
+
+int gsl_linalg_pcholesky_rcond (const gsl_matrix * LDLT, const gsl_permutation * p,
+                                double * rcond, gsl_vector * work);
+
+/* Modified Cholesky decomposition */
+
+int gsl_linalg_mcholesky_decomp (gsl_matrix * A, gsl_permutation * p,
+                                 gsl_vector * E);
+
+int gsl_linalg_mcholesky_solve(const gsl_matrix * LDLT,
+                               const gsl_permutation * p,
+                               const gsl_vector * b,
+                               gsl_vector * x);
+
+int gsl_linalg_mcholesky_svx(const gsl_matrix * LDLT,
+                             const gsl_permutation * p,
+                             gsl_vector * x);
+
+int gsl_linalg_mcholesky_rcond (const gsl_matrix * LDLT, const gsl_permutation * p,
+                                double * rcond, gsl_vector * work);
+
+int gsl_linalg_mcholesky_invert(const gsl_matrix * LDLT, const gsl_permutation * p,
+                                gsl_matrix * Ainv);
 
 /* Symmetric to symmetric tridiagonal decomposition */
 
@@ -588,6 +704,70 @@
 int gsl_linalg_balance_accum (gsl_matrix * A, gsl_vector * D);
 int gsl_linalg_balance_columns (gsl_matrix * A, gsl_vector * D);
 
+/* condition estimation */
+
+int gsl_linalg_tri_upper_rcond(const gsl_matrix * A, double * rcond, gsl_vector * work);
+int gsl_linalg_tri_lower_rcond(const gsl_matrix * A, double * rcond, gsl_vector * work);
+int gsl_linalg_invnorm1(const size_t N,
+                        int (* Ainvx)(CBLAS_TRANSPOSE_t TransA, gsl_vector * x, void * params),
+                        void * params, double * Ainvnorm, gsl_vector * work);
+
+/* triangular matrices */
+
+int gsl_linalg_tri_upper_invert(gsl_matrix * T);
+int gsl_linalg_tri_lower_invert(gsl_matrix * T);
+int gsl_linalg_tri_upper_unit_invert(gsl_matrix * T);
+int gsl_linalg_tri_lower_unit_invert(gsl_matrix * T);
+
+INLINE_DECL void gsl_linalg_givens (const double a, const double b,
+                                    double *c, double *s);
+INLINE_DECL void gsl_linalg_givens_gv (gsl_vector * v, const size_t i,
+                                       const size_t j, const double c,
+                                       const double s);
+
+#ifdef HAVE_INLINE
+
+/* Generate a Givens rotation (cos,sin) which takes v=(x,y) to (|v|,0) 
+   From Golub and Van Loan, "Matrix Computations", Section 5.1.8 */
+INLINE_FUN
+void
+gsl_linalg_givens (const double a, const double b, double *c, double *s)
+{
+  if (b == 0)
+    {
+      *c = 1;
+      *s = 0;
+    }
+  else if (fabs (b) > fabs (a))
+    {
+      double t = -a / b;
+      double s1 = 1.0 / sqrt (1 + t * t);
+      *s = s1;
+      *c = s1 * t;
+    }
+  else
+    {
+      double t = -b / a;
+      double c1 = 1.0 / sqrt (1 + t * t);
+      *c = c1;
+      *s = c1 * t;
+    }
+} /* gsl_linalg_givens() */
+
+INLINE_FUN
+void
+gsl_linalg_givens_gv (gsl_vector * v, const size_t i, const size_t j,
+                      const double c, const double s)
+{
+  /* Apply rotation to vector v' = G^T v */
+
+  double vi = gsl_vector_get (v, i);
+  double vj = gsl_vector_get (v, j);
+  gsl_vector_set (v, i, c * vi - s * vj);
+  gsl_vector_set (v, j, s * vi + c * vj);
+}
+
+#endif /* HAVE_INLINE */
 
 __END_DECLS
 
diff -Nru gsl-doc-1.16/linalg/hesstri.c gsl-doc-2.3/linalg/hesstri.c
--- gsl-doc-1.16/linalg/hesstri.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/hesstri.c	2015-11-03 16:21:55.000000000 +0000
@@ -26,8 +26,6 @@
 #include <gsl/gsl_vector.h>
 #include <gsl/gsl_blas.h>
 
-#include "givens.c"
-
 /*
  * This module contains routines related to the Hessenberg-Triangular
  * reduction of two general real matrices
@@ -114,10 +112,10 @@
                * compute G = [ CS SN ] so that G^t [ A(i-1,j) ] = [ * ]
                *             [-SN CS ]             [ A(i, j)  ]   [ 0 ]
                */
-              create_givens(gsl_matrix_get(A, i - 1, j),
-                            gsl_matrix_get(A, i, j),
-                            &cs,
-                            &sn);
+              gsl_linalg_givens(gsl_matrix_get(A, i - 1, j),
+                                gsl_matrix_get(A, i, j),
+                                &cs,
+                                &sn);
               /* invert so drot() works correctly (G -> G^t) */
               sn = -sn;
 
@@ -141,10 +139,10 @@
 
               /* step 2: rotate columns i, i - 1 to kill B(i, i - 1) */
 
-              create_givens(-gsl_matrix_get(B, i, i),
-                            gsl_matrix_get(B, i, i - 1),
-                            &cs,
-                            &sn);
+              gsl_linalg_givens(-gsl_matrix_get(B, i, i),
+                                gsl_matrix_get(B, i, i - 1),
+                                &cs,
+                                &sn);
               /* invert so drot() works correctly (G -> G^t) */
               sn = -sn;
 
diff -Nru gsl-doc-1.16/linalg/householder.c gsl-doc-2.3/linalg/householder.c
--- gsl-doc-1.16/linalg/householder.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/householder.c	2015-11-03 16:21:55.000000000 +0000
@@ -26,6 +26,26 @@
 
 #include <gsl/gsl_linalg.h>
 
+/*
+gsl_linalg_householder_transform()
+  Compute a householder transformation (tau,v) of a vector
+x so that P x = [ I - tau*v*v' ] x annihilates x(1:n-1)
+
+Inputs: v - on input, x vector
+            on output, householder vector v
+
+Notes:
+1) on output, v is normalized so that v[0] = 1. The 1 is
+not actually stored; instead v[0] = -sign(x[0])*||x|| so
+that:
+
+P x = v[0] * e_1
+
+Therefore external routines should take care when applying
+the projection matrix P to vectors, taking into account
+that v[0] should be 1 when doing so.
+*/
+
 double
 gsl_linalg_householder_transform (gsl_vector * v)
 {
@@ -223,23 +243,21 @@
   {
     /* compute d = v'w */
 
-    double d0 = gsl_vector_get(w,0);
+    double w0 = gsl_vector_get(w,0);
     double d1, d;
 
     gsl_vector_const_view v1 = gsl_vector_const_subvector(v, 1, N-1);
     gsl_vector_view w1 = gsl_vector_subvector(w, 1, N-1);
 
+    /* compute d1 = v(2:n)'w(2:n) */
     gsl_blas_ddot (&v1.vector, &w1.vector, &d1);
-    
-    d = d0 + d1;
+
+    /* compute d = v'w = w(1) + d1 since v(1) = 1 */
+    d = w0 + d1;
 
     /* compute w = w - tau (v) (v'w) */
-  
-    {
-      double w0 = gsl_vector_get (w,0);
-      gsl_vector_set (w, 0, w0 - tau * d);
-    }
-    
+
+    gsl_vector_set (w, 0, w0 - tau * d);
     gsl_blas_daxpy (-tau * d, &v1.vector, &w1.vector);
   }
   
diff -Nru gsl-doc-1.16/linalg/inline.c gsl-doc-2.3/linalg/inline.c
--- gsl-doc-1.16/linalg/inline.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/linalg/inline.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,32 @@
+/* linalg/inline.c
+ * 
+ * Copyright (C) 2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_mode.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_permutation.h>
+
+/* Compile all the inline functions */
+
+#define COMPILE_INLINE_STATIC
+#include "build.h"
+#include <gsl/gsl_linalg.h>
+
diff -Nru gsl-doc-1.16/linalg/invtri.c gsl-doc-2.3/linalg/invtri.c
--- gsl-doc-1.16/linalg/invtri.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/linalg/invtri.c	2016-08-22 15:16:24.000000000 +0000
@@ -0,0 +1,151 @@
+/* linalg/invtri.c
+ *
+ * Copyright (C) 2016 Patrick Alken
+ *
+ * This is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by the
+ * Free Software Foundation; either version 3, or (at your option) any
+ * later version.
+ *
+ * This source is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+ * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+ * for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ *
+ * This module contains code to invert triangular matrices
+ */
+
+#include <config.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_linalg.h>
+
+static int triangular_inverse(CBLAS_UPLO_t Uplo, CBLAS_DIAG_t Diag, gsl_matrix * T);
+
+int
+gsl_linalg_tri_upper_invert(gsl_matrix * T)
+{
+  int status = triangular_inverse(CblasUpper, CblasNonUnit, T);
+  return status;
+}
+
+int
+gsl_linalg_tri_lower_invert(gsl_matrix * T)
+{
+  int status = triangular_inverse(CblasLower, CblasNonUnit, T);
+  return status;
+}
+
+int
+gsl_linalg_tri_upper_unit_invert(gsl_matrix * T)
+{
+  int status = triangular_inverse(CblasUpper, CblasUnit, T);
+  return status;
+}
+
+int
+gsl_linalg_tri_lower_unit_invert(gsl_matrix * T)
+{
+  int status = triangular_inverse(CblasLower, CblasUnit, T);
+  return status;
+}
+
+/*
+triangular_inverse()
+  Invert a triangular matrix T
+
+Inputs: Uplo - CblasUpper or CblasLower
+        Diag - unit triangular?
+        T    - on output the upper (or lower) part of T
+               is replaced by its inverse
+
+Return: success/error
+*/
+
+static int
+triangular_inverse(CBLAS_UPLO_t Uplo, CBLAS_DIAG_t Diag, gsl_matrix * T)
+{
+  const size_t N = T->size1;
+
+  if (N != T->size2)
+    {
+      GSL_ERROR ("matrix must be square", GSL_ENOTSQR);
+    }
+  else
+    {
+      gsl_matrix_view m;
+      gsl_vector_view v;
+      size_t i;
+
+      if (Uplo == CblasUpper)
+        {
+          for (i = 0; i < N; ++i)
+            {
+              double aii;
+
+              if (Diag == CblasNonUnit)
+                {
+                  double *Tii = gsl_matrix_ptr(T, i, i);
+                  *Tii = 1.0 / *Tii;
+                  aii = -(*Tii);
+                }
+              else
+                {
+                  aii = -1.0;
+                }
+
+              if (i > 0)
+                {
+                  m = gsl_matrix_submatrix(T, 0, 0, i, i);
+                  v = gsl_matrix_subcolumn(T, i, 0, i);
+
+                  gsl_blas_dtrmv(CblasUpper, CblasNoTrans, Diag,
+                                 &m.matrix, &v.vector);
+
+                  gsl_blas_dscal(aii, &v.vector);
+                }
+            } /* for (i = 0; i < N; ++i) */
+        }
+      else
+        {
+          for (i = 0; i < N; ++i)
+            {
+              double ajj;
+              size_t j = N - i - 1;
+
+              if (Diag == CblasNonUnit)
+                {
+                  double *Tjj = gsl_matrix_ptr(T, j, j);
+                  *Tjj = 1.0 / *Tjj;
+                  ajj = -(*Tjj);
+                }
+              else
+                {
+                  ajj = -1.0;
+                }
+
+              if (j < N - 1)
+                {
+                  m = gsl_matrix_submatrix(T, j + 1, j + 1,
+                                           N - j - 1, N - j - 1);
+                  v = gsl_matrix_subcolumn(T, j, j + 1, N - j - 1);
+
+                  gsl_blas_dtrmv(CblasLower, CblasNoTrans, Diag,
+                                 &m.matrix, &v.vector);
+
+                  gsl_blas_dscal(ajj, &v.vector);
+                }
+            } /* for (i = 0; i < N; ++i) */
+        }
+
+      return GSL_SUCCESS;
+    }
+}
diff -Nru gsl-doc-1.16/linalg/lq.c gsl-doc-2.3/linalg/lq.c
--- gsl-doc-1.16/linalg/lq.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/lq.c	2015-11-03 16:21:55.000000000 +0000
@@ -28,7 +28,6 @@
 
 #include <gsl/gsl_linalg.h>
 
-#include "givens.c"
 #include "apply_givens.c"
 
 /* Note: The standard in numerical linear algebra is to solve A x = b
@@ -501,8 +500,8 @@
           double wk = gsl_vector_get (w, k);
           double wkm1 = gsl_vector_get (w, k - 1);
 
-          create_givens (wkm1, wk, &c, &s);
-          apply_givens_vec (w, k - 1, k, c, s);
+          gsl_linalg_givens (wkm1, wk, &c, &s);
+          gsl_linalg_givens_gv (w, k - 1, k, c, s);
           apply_givens_lq (M, N, Q, L, k - 1, k, c, s);
        }
 
@@ -526,7 +525,7 @@
           double diag = gsl_matrix_get (L, k - 1, k - 1);
           double offdiag = gsl_matrix_get (L, k - 1 , k);
 
-          create_givens (diag, offdiag, &c, &s);
+          gsl_linalg_givens (diag, offdiag, &c, &s);
           apply_givens_lq (M, N, Q, L, k - 1, k, c, s);
 
           gsl_matrix_set (L, k - 1, k, 0.0);    /* exact zero of G^T */
diff -Nru gsl-doc-1.16/linalg/lu.c gsl-doc-2.3/linalg/lu.c
--- gsl-doc-1.16/linalg/lu.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/lu.c	2016-11-29 21:51:39.000000000 +0000
@@ -202,7 +202,7 @@
 
 
 int
-gsl_linalg_LU_refine (const gsl_matrix * A, const gsl_matrix * LU, const gsl_permutation * p, const gsl_vector * b, gsl_vector * x, gsl_vector * residual)
+gsl_linalg_LU_refine (const gsl_matrix * A, const gsl_matrix * LU, const gsl_permutation * p, const gsl_vector * b, gsl_vector * x, gsl_vector * work)
 {
   if (A->size1 != A->size2)
     {
@@ -228,6 +228,10 @@
     {
       GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
     }
+  else if (LU->size1 != work->size)
+    {
+      GSL_ERROR ("matrix size must match workspace size", GSL_EBADLEN);
+    }
   else if (singular (LU)) 
     {
       GSL_ERROR ("matrix is singular", GSL_EDOM);
@@ -236,15 +240,15 @@
     {
       int status;
 
-      /* Compute residual, residual = (A * x  - b) */
+      /* Compute residual = (A * x  - b) */
 
-      gsl_vector_memcpy (residual, b);
-      gsl_blas_dgemv (CblasNoTrans, 1.0, A, x, -1.0, residual);
+      gsl_vector_memcpy (work, b);
+      gsl_blas_dgemv (CblasNoTrans, 1.0, A, x, -1.0, work);
 
       /* Find correction, delta = - (A^-1) * residual, and apply it */
 
-      status = gsl_linalg_LU_svx (LU, p, residual);
-      gsl_blas_daxpy (-1.0, residual, x);
+      status = gsl_linalg_LU_svx (LU, p, work);
+      gsl_blas_daxpy (-1.0, work, x);
 
       return status;
     }
diff -Nru gsl-doc-1.16/linalg/luc.c gsl-doc-2.3/linalg/luc.c
--- gsl-doc-1.16/linalg/luc.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/luc.c	2016-11-29 21:53:25.000000000 +0000
@@ -211,7 +211,7 @@
 
 
 int
-gsl_linalg_complex_LU_refine (const gsl_matrix_complex * A, const gsl_matrix_complex * LU, const gsl_permutation * p, const gsl_vector_complex * b, gsl_vector_complex * x, gsl_vector_complex * residual)
+gsl_linalg_complex_LU_refine (const gsl_matrix_complex * A, const gsl_matrix_complex * LU, const gsl_permutation * p, const gsl_vector_complex * b, gsl_vector_complex * x, gsl_vector_complex * work)
 {
   if (A->size1 != A->size2)
     {
@@ -237,6 +237,10 @@
     {
       GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
     }
+  else if (LU->size1 != work->size)
+    {
+      GSL_ERROR ("matrix size must match workspace size", GSL_EBADLEN);
+    }
   else if (singular (LU)) 
     {
       GSL_ERROR ("matrix is singular", GSL_EDOM);
@@ -245,23 +249,23 @@
     {
       int status;
 
-      /* Compute residual, residual = (A * x  - b) */
+      /* Compute residual = (A * x  - b) */
 
-      gsl_vector_complex_memcpy (residual, b);
+      gsl_vector_complex_memcpy (work, b);
 
       {
         gsl_complex one = GSL_COMPLEX_ONE;
         gsl_complex negone = GSL_COMPLEX_NEGONE;
-        gsl_blas_zgemv (CblasNoTrans, one, A, x, negone, residual);
+        gsl_blas_zgemv (CblasNoTrans, one, A, x, negone, work);
       }
 
       /* Find correction, delta = - (A^-1) * residual, and apply it */
 
-      status = gsl_linalg_complex_LU_svx (LU, p, residual);
+      status = gsl_linalg_complex_LU_svx (LU, p, work);
 
       {
         gsl_complex negone= GSL_COMPLEX_NEGONE;
-        gsl_blas_zaxpy (negone, residual, x);
+        gsl_blas_zaxpy (negone, work, x);
       }
 
       return status;
diff -Nru gsl-doc-1.16/linalg/Makefile.am gsl-doc-2.3/linalg/Makefile.am
--- gsl-doc-1.16/linalg/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/Makefile.am	2016-08-15 16:58:52.000000000 +0000
@@ -2,18 +2,15 @@
 
 pkginclude_HEADERS = gsl_linalg.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
-libgsllinalg_la_SOURCES = multiply.c exponential.c tridiag.c tridiag.h lu.c luc.c hh.c qr.c qrpt.c lq.c ptlq.c svd.c householder.c householdercomplex.c hessenberg.c hesstri.c cholesky.c choleskyc.c symmtd.c hermtd.c bidiag.c balance.c balancemat.c
+libgsllinalg_la_SOURCES = cod.c condest.c invtri.c multiply.c exponential.c tridiag.c tridiag.h lu.c luc.c hh.c qr.c qrpt.c lq.c ptlq.c svd.c householder.c householdercomplex.c hessenberg.c hesstri.c cholesky.c choleskyc.c mcholesky.c pcholesky.c symmtd.c hermtd.c bidiag.c balance.c balancemat.c inline.c
 
-noinst_HEADERS =  givens.c apply_givens.c svdstep.c tridiag.h 
+noinst_HEADERS = apply_givens.c cholesky_common.c svdstep.c tridiag.h test_cholesky.c
 
 TESTS = $(check_PROGRAMS)
 
 check_PROGRAMS = test
 
-test_LDADD = libgsllinalg.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../permutation/libgslpermutation.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
-
 test_SOURCES = test.c
-
-
+test_LDADD = libgsllinalg.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../permutation/libgslpermutation.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la ../rng/libgslrng.la
diff -Nru gsl-doc-1.16/linalg/Makefile.in gsl-doc-2.3/linalg/Makefile.in
--- gsl-doc-1.16/linalg/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/linalg/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -95,11 +95,12 @@
 CONFIG_CLEAN_VPATH_FILES =
 LTLIBRARIES = $(noinst_LTLIBRARIES)
 libgsllinalg_la_LIBADD =
-am_libgsllinalg_la_OBJECTS = multiply.lo exponential.lo tridiag.lo \
-	lu.lo luc.lo hh.lo qr.lo qrpt.lo lq.lo ptlq.lo svd.lo \
-	householder.lo householdercomplex.lo hessenberg.lo hesstri.lo \
-	cholesky.lo choleskyc.lo symmtd.lo hermtd.lo bidiag.lo \
-	balance.lo balancemat.lo
+am_libgsllinalg_la_OBJECTS = cod.lo condest.lo invtri.lo multiply.lo \
+	exponential.lo tridiag.lo lu.lo luc.lo hh.lo qr.lo qrpt.lo \
+	lq.lo ptlq.lo svd.lo householder.lo householdercomplex.lo \
+	hessenberg.lo hesstri.lo cholesky.lo choleskyc.lo mcholesky.lo \
+	pcholesky.lo symmtd.lo hermtd.lo bidiag.lo balance.lo \
+	balancemat.lo inline.lo
 libgsllinalg_la_OBJECTS = $(am_libgsllinalg_la_OBJECTS)
 AM_V_lt = $(am__v_lt_@AM_V@)
 am__v_lt_ = $(am__v_lt_@AM_DEFAULT_V@)
@@ -112,7 +113,8 @@
 	../matrix/libgslmatrix.la ../vector/libgslvector.la \
 	../block/libgslblock.la ../complex/libgslcomplex.la \
 	../ieee-utils/libgslieeeutils.la ../err/libgslerr.la \
-	../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
+	../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la \
+	../rng/libgslrng.la
 AM_V_P = $(am__v_P_@AM_V@)
 am__v_P_ = $(am__v_P_@AM_DEFAULT_V@)
 am__v_P_0 = false
@@ -384,6 +386,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -406,7 +409,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -522,12 +528,12 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgsllinalg.la 
 pkginclude_HEADERS = gsl_linalg.h
-INCLUDES = -I$(top_srcdir)
-libgsllinalg_la_SOURCES = multiply.c exponential.c tridiag.c tridiag.h lu.c luc.c hh.c qr.c qrpt.c lq.c ptlq.c svd.c householder.c householdercomplex.c hessenberg.c hesstri.c cholesky.c choleskyc.c symmtd.c hermtd.c bidiag.c balance.c balancemat.c
-noinst_HEADERS = givens.c apply_givens.c svdstep.c tridiag.h 
+AM_CPPFLAGS = -I$(top_srcdir)
+libgsllinalg_la_SOURCES = cod.c condest.c invtri.c multiply.c exponential.c tridiag.c tridiag.h lu.c luc.c hh.c qr.c qrpt.c lq.c ptlq.c svd.c householder.c householdercomplex.c hessenberg.c hesstri.c cholesky.c choleskyc.c mcholesky.c pcholesky.c symmtd.c hermtd.c bidiag.c balance.c balancemat.c inline.c
+noinst_HEADERS = apply_givens.c cholesky_common.c svdstep.c tridiag.h test_cholesky.c
 TESTS = $(check_PROGRAMS)
-test_LDADD = libgsllinalg.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../permutation/libgslpermutation.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
 test_SOURCES = test.c
+test_LDADD = libgsllinalg.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../permutation/libgslpermutation.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la ../rng/libgslrng.la
 all: all-am
 
 .SUFFIXES:
@@ -601,6 +607,8 @@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/bidiag.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/cholesky.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/choleskyc.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/cod.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/condest.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/exponential.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/hermtd.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/hessenberg.Plo@am__quote@
@@ -608,10 +616,14 @@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/hh.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/householder.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/householdercomplex.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/inline.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/invtri.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/lq.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/lu.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/luc.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/mcholesky.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/multiply.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/pcholesky.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/ptlq.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/qr.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/qrpt.Plo@am__quote@
diff -Nru gsl-doc-1.16/linalg/mcholesky.c gsl-doc-2.3/linalg/mcholesky.c
--- gsl-doc-1.16/linalg/mcholesky.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/linalg/mcholesky.c	2016-08-19 16:47:27.000000000 +0000
@@ -0,0 +1,271 @@
+/* Modified Cholesky Decomposition
+ *
+ * Copyright (C) 2016 Patrick Alken
+ *
+ * This is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by the
+ * Free Software Foundation; either version 3, or (at your option) any
+ * later version.
+ *
+ * This source is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+ * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+ * for more details.
+ */
+
+#include <config.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_permute_vector.h>
+
+#include "cholesky_common.c"
+
+/*
+ * This module contains routines related to the Modified Cholesky
+ * Decomposition, which factors a symmetric indefinite matrix A as
+ *
+ * P (A + E) P^T = L D L^T
+ *
+ * where:
+ * P: permutation matrix
+ * E: small, non-negative diagonal matrix
+ * L: unit lower triangular matrix
+ * D: strictly positive diagonal matrix
+ *
+ * These routines follow these works closely:
+ *
+ * [1] P. E. Gill, W. Murray, M. H. Wright, Practical Optimization,
+ *     Academic Press, 1981.
+ *
+ * [2] Dennis and Schnabel, Numerical Methods for Unconstrained Optimization
+ *     and Nonlinear Equations, SIAM, 1996
+ */
+
+static size_t mcholesky_maxabs(const gsl_vector * v, double *maxabs);
+
+/*
+gsl_linalg_mcholesky_decomp()
+  Perform Pivoted Modified Cholesky LDLT decomposition of a symmetric positive
+indefinite matrix:
+
+P (A + E) P^T = L D L^T
+
+Inputs: A - (input) symmetric, positive indefinite matrix,
+                    stored in lower triangle
+            (output) lower triangle contains L; diagonal contains D
+        p - (output) permutation matrix P
+        E - (output) perturbation matrix E
+
+Return: success/error
+
+Notes:
+1) Based on algorithm 4.2.2 (Outer Product LDLT with Pivoting) of
+Golub and Van Loan, Matrix Computations (4th ed), with modifications
+described in [1] and [2]
+
+2) E can be set to NULL if not required
+*/
+
+int
+gsl_linalg_mcholesky_decomp (gsl_matrix * A, gsl_permutation * p,
+                             gsl_vector * E)
+{
+  const size_t N = A->size1;
+
+  if (N != A->size2)
+    {
+      GSL_ERROR("LDLT decomposition requires square matrix", GSL_ENOTSQR);
+    }
+  else if (p->size != N)
+    {
+      GSL_ERROR ("permutation length must match matrix size", GSL_EBADLEN);
+    }
+  else
+    {
+      const double delta = GSL_DBL_EPSILON;
+      double beta;
+      double gamma = 0.0;
+      double xi = 0.0;
+      gsl_vector_view diag = gsl_matrix_diagonal(A);
+      size_t i, j;
+
+      /* save a copy of A in upper triangle (for later rcond calculation) */
+      gsl_matrix_transpose_tricpy('L', 0, A, A);
+
+      gsl_permutation_init(p);
+
+      /* compute:
+       * gamma = max | A_{ii} |
+       * xi = max_{i \ne j} | A_{ij} |
+       */
+      for (i = 0; i < N; ++i)
+        {
+          double aii = gsl_matrix_get(A, i, i);
+
+          gamma = GSL_MAX(gamma, fabs(aii));
+
+          for (j = 0; j < i; ++j)
+            {
+              double aij = gsl_matrix_get(A, i, j);
+              xi = GSL_MAX(xi, fabs(aij));
+            }
+        }
+
+      /* compute:
+       * beta = sqrt[ max { gamma, xi/nu, eps } ]
+       * with: nu = max{ sqrt(N^2 - 1), 1 }
+       */
+      if (N == 1)
+        {
+          beta = GSL_MAX(GSL_MAX(gamma, xi), GSL_DBL_EPSILON);
+        }
+      else
+        {
+          double nu = sqrt(N*N - 1.0);
+          beta = GSL_MAX(GSL_MAX(gamma, xi / nu), GSL_DBL_EPSILON);
+        }
+
+      beta = sqrt(beta);
+
+      for (j = 0; j < N; ++j)
+        {
+          double ajj, thetaj, u, alpha, alphainv;
+          gsl_vector_view w;
+          size_t q;
+
+          /* compute q = max_idx { A_jj, ..., A_nn } */
+          w = gsl_vector_subvector(&diag.vector, j, N - j);
+          q = mcholesky_maxabs(&w.vector, NULL) + j;
+
+          gsl_permutation_swap(p, q, j);
+          cholesky_swap_rowcol(A, q, j);
+
+          /* theta_j = max_{j+1 <= i <= n} |A_{ij}| */
+          if (j < N - 1)
+            {
+              w = gsl_matrix_subcolumn(A, j, j + 1, N - j - 1);
+              mcholesky_maxabs(&w.vector, &thetaj);
+            }
+          else
+            {
+              thetaj = 0.0;
+            }
+
+          u = thetaj / beta;
+
+          /* compute alpha = d_j */
+          ajj = gsl_matrix_get(A, j, j);
+          alpha = GSL_MAX(GSL_MAX(delta, fabs(ajj)), u * u);
+          alphainv = 1.0 / alpha;
+
+          if (j < N - 1)
+            {
+              /* v = A(j+1:n, j) */
+              gsl_vector_view v = gsl_matrix_subcolumn(A, j, j + 1, N - j - 1);
+
+              /* m = A(j+1:n, j+1:n) */
+              gsl_matrix_view m = gsl_matrix_submatrix(A, j + 1, j + 1, N - j - 1, N - j - 1);
+
+              /* m = m - v v^T / alpha */
+              gsl_blas_dsyr(CblasLower, -alphainv, &v.vector, &m.matrix);
+
+              /* v = v / alpha */
+              gsl_vector_scale(&v.vector, alphainv);
+
+            }
+
+          if (E)
+            gsl_vector_set(E, j, alpha - ajj);
+
+          gsl_matrix_set(A, j, j, alpha);
+        }
+
+      if (E)
+        {
+          /* we currently have: P A P^T + E = L D L^T, permute E
+           * so that we have: P (A + E) P^T = L D L^T */
+          gsl_permute_vector_inverse(p, E);
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+int
+gsl_linalg_mcholesky_solve(const gsl_matrix * LDLT,
+                           const gsl_permutation * p,
+                           const gsl_vector * b,
+                           gsl_vector * x)
+{
+  int status = gsl_linalg_pcholesky_solve(LDLT, p, b, x);
+  return status;
+}
+
+int
+gsl_linalg_mcholesky_svx(const gsl_matrix * LDLT,
+                         const gsl_permutation * p,
+                         gsl_vector * x)
+{
+  int status = gsl_linalg_pcholesky_svx(LDLT, p, x);
+  return status;
+}
+
+int
+gsl_linalg_mcholesky_rcond (const gsl_matrix * LDLT, const gsl_permutation * p,
+                            double * rcond, gsl_vector * work)
+{
+  int status = gsl_linalg_pcholesky_rcond(LDLT, p, rcond, work);
+  return status;
+}
+
+int
+gsl_linalg_mcholesky_invert(const gsl_matrix * LDLT, const gsl_permutation * p,
+                            gsl_matrix * Ainv)
+{
+  int status = gsl_linalg_pcholesky_invert(LDLT, p, Ainv);
+  return status;
+}
+
+/*
+mcholesky_maxabs()
+  Compute:
+
+val = max_i |v_i|
+
+Inputs: v      - vector
+        maxabs - (output) max abs value
+
+Return: index corresponding to max_i |v_i|
+*/
+
+static size_t
+mcholesky_maxabs(const gsl_vector * v, double *maxabs)
+{
+  const size_t n = v->size;
+  size_t i;
+  size_t idx = 0;
+  double max = gsl_vector_get(v, idx);
+
+  for (i = 1; i < n; ++i)
+    {
+      double vi = gsl_vector_get(v, i);
+      double absvi = fabs(vi);
+
+      if (absvi > max)
+        {
+          max = absvi;
+          idx = i;
+        }
+    }
+
+  if (maxabs)
+    *maxabs = max;
+
+  return idx;
+}
diff -Nru gsl-doc-1.16/linalg/pcholesky.c gsl-doc-2.3/linalg/pcholesky.c
--- gsl-doc-1.16/linalg/pcholesky.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/linalg/pcholesky.c	2016-08-22 15:21:15.000000000 +0000
@@ -0,0 +1,594 @@
+/* L D L^T Decomposition
+ *
+ * Copyright (C) 2016 Patrick Alken
+ *
+ * This is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by the
+ * Free Software Foundation; either version 3, or (at your option) any
+ * later version.
+ *
+ * This source is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+ * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+ * for more details.
+ */
+
+/*
+ * L D L^T decomposition of a symmetrix positive definite matrix.
+ *
+ * This algorithm does:
+ *   P A P' = L D L'
+ * with
+ *   L  := unit lower left triangle matrix
+ *   D  := diagonal matrix
+ *   L' := the transposed form of L.
+ *   P  := permutation matrix
+ *
+ */
+
+#include <config.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_permute_vector.h>
+
+#include "cholesky_common.c"
+
+static double cholesky_LDLT_norm1(const gsl_matrix * LDLT, const gsl_permutation * p,
+                                  gsl_vector * work);
+static int cholesky_LDLT_Ainv(CBLAS_TRANSPOSE_t TransA, gsl_vector * x, void * params);
+
+typedef struct
+{
+  const gsl_matrix * LDLT;
+  const gsl_permutation * perm;
+} pcholesky_params;
+
+/*
+pcholesky_decomp()
+  Perform Pivoted Cholesky LDLT decomposition of a symmetric positive
+semidefinite matrix
+
+Inputs: copy_uplo - copy lower triangle to upper to save original matrix
+                    for rcond calculation later
+        A         - (input) symmetric, positive semidefinite matrix,
+                    stored in lower triangle
+                    (output) lower triangle contains L; diagonal contains D
+        p         - permutation vector
+
+Return: success/error
+
+Notes:
+1) Based on algorithm 4.2.2 (Outer Product LDLT with Pivoting) of
+Golub and Van Loan, Matrix Computations (4th ed).
+*/
+
+static int
+pcholesky_decomp (const int copy_uplo, gsl_matrix * A, gsl_permutation * p)
+{
+  const size_t N = A->size1;
+
+  if (N != A->size2)
+    {
+      GSL_ERROR("LDLT decomposition requires square matrix", GSL_ENOTSQR);
+    }
+  else if (p->size != N)
+    {
+      GSL_ERROR ("permutation length must match matrix size", GSL_EBADLEN);
+    }
+  else
+    {
+      gsl_vector_view diag = gsl_matrix_diagonal(A);
+      size_t k;
+
+      if (copy_uplo)
+        {
+          /* save a copy of A in upper triangle (for later rcond calculation) */
+          gsl_matrix_transpose_tricpy('L', 0, A, A);
+        }
+
+      gsl_permutation_init(p);
+
+      for (k = 0; k < N; ++k)
+        {
+          gsl_vector_view w;
+          size_t j;
+
+          /* compute j = max_idx { A_kk, ..., A_nn } */
+          w = gsl_vector_subvector(&diag.vector, k, N - k);
+          j = gsl_vector_max_index(&w.vector) + k;
+          gsl_permutation_swap(p, k, j);
+
+          cholesky_swap_rowcol(A, k, j);
+
+          if (k < N - 1)
+            {
+              double alpha = gsl_matrix_get(A, k, k);
+              double alphainv = 1.0 / alpha;
+
+              /* v = A(k+1:n, k) */
+              gsl_vector_view v = gsl_matrix_subcolumn(A, k, k + 1, N - k - 1);
+
+              /* m = A(k+1:n, k+1:n) */
+              gsl_matrix_view m = gsl_matrix_submatrix(A, k + 1, k + 1, N - k - 1, N - k - 1);
+
+              /* m = m - v v^T / alpha */
+              gsl_blas_dsyr(CblasLower, -alphainv, &v.vector, &m.matrix);
+
+              /* v = v / alpha */
+              gsl_vector_scale(&v.vector, alphainv);
+            }
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+gsl_linalg_pcholesky_decomp()
+  Perform Pivoted Cholesky LDLT decomposition of a symmetric positive
+semidefinite matrix
+
+Inputs: A - (input) symmetric, positive semidefinite matrix,
+                    stored in lower triangle
+            (output) lower triangle contains L; diagonal contains D
+        p - permutation vector
+
+Return: success/error
+
+Notes:
+1) Based on algorithm 4.2.2 (Outer Product LDLT with Pivoting) of
+Golub and Van Loan, Matrix Computations (4th ed).
+*/
+
+int
+gsl_linalg_pcholesky_decomp (gsl_matrix * A, gsl_permutation * p)
+{
+  int status = pcholesky_decomp(1, A, p);
+  return status;
+}
+
+int
+gsl_linalg_pcholesky_solve(const gsl_matrix * LDLT,
+                           const gsl_permutation * p,
+                           const gsl_vector * b,
+                           gsl_vector * x)
+{
+  if (LDLT->size1 != LDLT->size2)
+    {
+      GSL_ERROR ("LDLT matrix must be square", GSL_ENOTSQR);
+    }
+  else if (LDLT->size1 != p->size)
+    {
+      GSL_ERROR ("matrix size must match permutation size", GSL_EBADLEN);
+    }
+  else if (LDLT->size1 != b->size)
+    {
+      GSL_ERROR ("matrix size must match b size", GSL_EBADLEN);
+    }
+  else if (LDLT->size2 != x->size)
+    {
+      GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+
+      gsl_vector_memcpy (x, b);
+
+      status = gsl_linalg_pcholesky_svx (LDLT, p, x);
+      
+      return status;
+    }
+}
+
+int
+gsl_linalg_pcholesky_svx(const gsl_matrix * LDLT,
+                         const gsl_permutation * p,
+                         gsl_vector * x)
+{
+  if (LDLT->size1 != LDLT->size2)
+    {
+      GSL_ERROR ("LDLT matrix must be square", GSL_ENOTSQR);
+    }
+  else if (LDLT->size1 != p->size)
+    {
+      GSL_ERROR ("matrix size must match permutation size", GSL_EBADLEN);
+    }
+  else if (LDLT->size2 != x->size)
+    {
+      GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
+    }
+  else
+    {
+      gsl_vector_const_view D = gsl_matrix_const_diagonal(LDLT);
+
+      /* x := P b */
+      gsl_permute_vector(p, x);
+
+      /* solve: L w = P b */
+      gsl_blas_dtrsv(CblasLower, CblasNoTrans, CblasUnit, LDLT, x);
+
+      /* solve: D y = w */
+      gsl_vector_div(x, &D.vector);
+
+      /* solve: L^T z = y */
+      gsl_blas_dtrsv(CblasLower, CblasTrans, CblasUnit, LDLT, x);
+
+      /* compute: x = P^T z */
+      gsl_permute_vector_inverse(p, x);
+
+      return GSL_SUCCESS;
+    }
+}
+
+int
+gsl_linalg_pcholesky_decomp2(gsl_matrix * A, gsl_permutation * p,
+                             gsl_vector * S)
+{
+  const size_t M = A->size1;
+  const size_t N = A->size2;
+
+  if (M != N)
+    {
+      GSL_ERROR("cholesky decomposition requires square matrix", GSL_ENOTSQR);
+    }
+  else if (N != p->size)
+    {
+      GSL_ERROR ("matrix size must match permutation size", GSL_EBADLEN);
+    }
+  else if (N != S->size)
+    {
+      GSL_ERROR("S must have length N", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+
+      /* save a copy of A in upper triangle (for later rcond calculation) */
+      gsl_matrix_transpose_tricpy('L', 0, A, A);
+
+      /* compute scaling factors to reduce cond(A) */
+      status = gsl_linalg_cholesky_scale(A, S);
+      if (status)
+        return status;
+
+      /* apply scaling factors */
+      status = gsl_linalg_cholesky_scale_apply(A, S);
+      if (status)
+        return status;
+
+      /* compute Cholesky decomposition of diag(S) A diag(S) */
+      status = pcholesky_decomp(0, A, p);
+      if (status)
+        return status;
+
+      return GSL_SUCCESS;
+    }
+}
+
+int
+gsl_linalg_pcholesky_solve2(const gsl_matrix * LDLT,
+                            const gsl_permutation * p,
+                            const gsl_vector * S,
+                            const gsl_vector * b,
+                            gsl_vector * x)
+{
+  if (LDLT->size1 != LDLT->size2)
+    {
+      GSL_ERROR ("LDLT matrix must be square", GSL_ENOTSQR);
+    }
+  else if (LDLT->size1 != p->size)
+    {
+      GSL_ERROR ("matrix size must match permutation size", GSL_EBADLEN);
+    }
+  else if (LDLT->size1 != S->size)
+    {
+      GSL_ERROR ("matrix size must match S", GSL_EBADLEN);
+    }
+  else if (LDLT->size1 != b->size)
+    {
+      GSL_ERROR ("matrix size must match b size", GSL_EBADLEN);
+    }
+  else if (LDLT->size2 != x->size)
+    {
+      GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+
+      gsl_vector_memcpy (x, b);
+
+      status = gsl_linalg_pcholesky_svx2 (LDLT, p, S, x);
+      
+      return status;
+    }
+}
+
+int
+gsl_linalg_pcholesky_svx2(const gsl_matrix * LDLT,
+                          const gsl_permutation * p,
+                          const gsl_vector * S,
+                          gsl_vector * x)
+{
+  if (LDLT->size1 != LDLT->size2)
+    {
+      GSL_ERROR ("LDLT matrix must be square", GSL_ENOTSQR);
+    }
+  else if (LDLT->size1 != p->size)
+    {
+      GSL_ERROR ("matrix size must match permutation size", GSL_EBADLEN);
+    }
+  else if (LDLT->size1 != S->size)
+    {
+      GSL_ERROR ("matrix size must match S", GSL_EBADLEN);
+    }
+  else if (LDLT->size2 != x->size)
+    {
+      GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+
+      /* x := S b */
+      gsl_vector_mul(x, S);
+
+      /* solve: A~ x~ = b~, with A~ = S A S, b~ = S b */
+      status = gsl_linalg_pcholesky_svx(LDLT, p, x);
+      if (status)
+        return status;
+
+      /* compute: x = S x~ */
+      gsl_vector_mul(x, S);
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+gsl_linalg_pcholesky_invert()
+  Compute the inverse of a symmetric positive definite matrix in
+Cholesky form.
+
+Inputs: LDLT - matrix in cholesky form
+        p    - permutation
+        Ainv - (output) A^{-1}
+
+Return: success or error
+*/
+
+int
+gsl_linalg_pcholesky_invert(const gsl_matrix * LDLT, const gsl_permutation * p,
+                            gsl_matrix * Ainv)
+{
+  const size_t M = LDLT->size1;
+  const size_t N = LDLT->size2;
+
+  if (M != N)
+    {
+      GSL_ERROR ("LDLT matrix must be square", GSL_ENOTSQR);
+    }
+  else if (LDLT->size1 != p->size)
+    {
+      GSL_ERROR ("matrix size must match permutation size", GSL_EBADLEN);
+    }
+  else if (Ainv->size1 != Ainv->size2)
+    {
+      GSL_ERROR ("Ainv matrix must be square", GSL_ENOTSQR);
+    }
+  else if (Ainv->size1 != M)
+    {
+      GSL_ERROR ("Ainv matrix has wrong dimensions", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i, j;
+      gsl_vector_view v1, v2;
+
+      /* invert the lower triangle of LDLT */
+      gsl_matrix_memcpy(Ainv, LDLT);
+      gsl_linalg_tri_lower_unit_invert(Ainv);
+
+      /* compute sqrt(D^{-1}) L^{-1} in the lower triangle of Ainv */
+      for (i = 0; i < N; ++i)
+        {
+          double di = gsl_matrix_get(LDLT, i, i);
+          double sqrt_di = sqrt(di);
+
+          for (j = 0; j < i; ++j)
+            {
+              double *Lij = gsl_matrix_ptr(Ainv, i, j);
+              *Lij /= sqrt_di;
+            }
+
+          gsl_matrix_set(Ainv, i, i, 1.0 / sqrt_di);
+        }
+
+      /*
+       * The lower triangle of Ainv now contains D^{-1/2} L^{-1}. Now compute
+       * A^{-1} = L^{-T} D^{-1} L^{-1}
+       */
+
+      for (i = 0; i < N; ++i)
+        {
+          double aii = gsl_matrix_get(Ainv, i, i);
+
+          if (i < N - 1)
+            {
+              double tmp;
+
+              v1 = gsl_matrix_subcolumn(Ainv, i, i, N - i);
+              gsl_blas_ddot(&v1.vector, &v1.vector, &tmp);
+              gsl_matrix_set(Ainv, i, i, tmp);
+
+              if (i > 0)
+                {
+                  gsl_matrix_view m = gsl_matrix_submatrix(Ainv, i + 1, 0, N - i - 1, i);
+
+                  v1 = gsl_matrix_subcolumn(Ainv, i, i + 1, N - i - 1);
+                  v2 = gsl_matrix_subrow(Ainv, i, 0, i);
+
+                  gsl_blas_dgemv(CblasTrans, 1.0, &m.matrix, &v1.vector, aii, &v2.vector);
+                }
+            }
+          else
+            {
+              v1 = gsl_matrix_row(Ainv, N - 1);
+              gsl_blas_dscal(aii, &v1.vector);
+            }
+        }
+
+      /* copy lower triangle to upper */
+      gsl_matrix_transpose_tricpy('L', 0, Ainv, Ainv);
+
+      /* now apply permutation p to the matrix */
+
+      /* compute L^{-T} D^{-1} L^{-1} P^T */
+      for (i = 0; i < N; ++i)
+        {
+          v1 = gsl_matrix_row(Ainv, i);
+          gsl_permute_vector_inverse(p, &v1.vector);
+        }
+
+      /* compute P L^{-T} D^{-1} L^{-1} P^T */
+      for (i = 0; i < N; ++i)
+        {
+          v1 = gsl_matrix_column(Ainv, i);
+          gsl_permute_vector_inverse(p, &v1.vector);
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+int
+gsl_linalg_pcholesky_rcond (const gsl_matrix * LDLT, const gsl_permutation * p,
+                            double * rcond, gsl_vector * work)
+{
+  const size_t M = LDLT->size1;
+  const size_t N = LDLT->size2;
+
+  if (M != N)
+    {
+      GSL_ERROR ("cholesky matrix must be square", GSL_ENOTSQR);
+    }
+  else if (work->size != 3 * N)
+    {
+      GSL_ERROR ("work vector must have length 3*N", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+      double Anorm = cholesky_LDLT_norm1(LDLT, p, work); /* ||A||_1 */
+      double Ainvnorm;                                   /* ||A^{-1}||_1 */
+      pcholesky_params params;
+
+      *rcond = 0.0;
+
+      /* don't continue if matrix is singular */
+      if (Anorm == 0.0)
+        return GSL_SUCCESS;
+
+      params.LDLT = LDLT;
+      params.perm = p;
+
+      /* estimate ||A^{-1}||_1 */
+      status = gsl_linalg_invnorm1(N, cholesky_LDLT_Ainv, &params, &Ainvnorm, work);
+
+      if (status)
+        return status;
+
+      if (Ainvnorm != 0.0)
+        *rcond = (1.0 / Anorm) / Ainvnorm;
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+cholesky_LDLT_norm1
+  Compute 1-norm of original matrix A, stored in upper triangle of LDLT;
+diagonal entries have to be reconstructed
+
+Inputs: LDLT - Cholesky L D L^T decomposition (lower triangle) with
+               original matrix in upper triangle
+        p    - permutation vector
+        work - workspace, length 2*N
+*/
+
+static double
+cholesky_LDLT_norm1(const gsl_matrix * LDLT, const gsl_permutation * p, gsl_vector * work)
+{
+  const size_t N = LDLT->size1;
+  gsl_vector_const_view D = gsl_matrix_const_diagonal(LDLT);
+  gsl_vector_view diagA = gsl_vector_subvector(work, N, N);
+  double max = 0.0;
+  size_t i, j;
+
+  /* reconstruct diagonal entries of original matrix A */
+  for (j = 0; j < N; ++j)
+    {
+      double Ajj;
+
+      /* compute diagonal (j,j) entry of A */
+      Ajj = gsl_vector_get(&D.vector, j);
+      for (i = 0; i < j; ++i)
+        {
+          double Di = gsl_vector_get(&D.vector, i);
+          double Lji = gsl_matrix_get(LDLT, j, i);
+
+          Ajj += Di * Lji * Lji;
+        }
+
+      gsl_vector_set(&diagA.vector, j, Ajj);
+    }
+
+  gsl_permute_vector_inverse(p, &diagA.vector);
+
+  for (j = 0; j < N; ++j)
+    {
+      double sum = 0.0;
+      double Ajj = gsl_vector_get(&diagA.vector, j);
+
+      for (i = 0; i < j; ++i)
+        {
+          double *wi = gsl_vector_ptr(work, i);
+          double Aij = gsl_matrix_get(LDLT, i, j);
+          double absAij = fabs(Aij);
+
+          sum += absAij;
+          *wi += absAij;
+        }
+
+      gsl_vector_set(work, j, sum + fabs(Ajj));
+    }
+
+  for (i = 0; i < N; ++i)
+    {
+      double wi = gsl_vector_get(work, i);
+      max = GSL_MAX(max, wi);
+    }
+
+  return max;
+}
+
+/* x := A^{-1} x = A^{-t} x, A = L D L^T */
+static int
+cholesky_LDLT_Ainv(CBLAS_TRANSPOSE_t TransA, gsl_vector * x, void * params)
+{
+  int status;
+  pcholesky_params *par = (pcholesky_params *) params;
+
+  (void) TransA; /* unused parameter warning */
+
+  status = gsl_linalg_pcholesky_svx(par->LDLT, par->perm, x);
+
+  return status;
+}
diff -Nru gsl-doc-1.16/linalg/ptlq.c gsl-doc-2.3/linalg/ptlq.c
--- gsl-doc-1.16/linalg/ptlq.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/ptlq.c	2015-11-03 16:21:55.000000000 +0000
@@ -28,7 +28,6 @@
 #include <gsl/gsl_permute_vector.h>
 #include <gsl/gsl_linalg.h>
 
-#include "givens.c"
 #include "apply_givens.c"
 
 /* The purpose of this package is to speed up QR-decomposition for
@@ -458,8 +457,8 @@
           double wk = gsl_vector_get (w, k);
           double wkm1 = gsl_vector_get (w, k - 1);
 
-          create_givens (wkm1, wk, &c, &s);
-          apply_givens_vec (w, k - 1, k, c, s);
+          gsl_linalg_givens (wkm1, wk, &c, &s);
+          gsl_linalg_givens_gv (w, k - 1, k, c, s);
           apply_givens_lq (M, N, Q, L, k - 1, k, c, s);
         }
 
@@ -484,7 +483,7 @@
           double diag = gsl_matrix_get (L, k - 1, k - 1);
           double offdiag = gsl_matrix_get (L, k - 1, k );
 
-          create_givens (diag, offdiag, &c, &s);
+          gsl_linalg_givens (diag, offdiag, &c, &s);
           apply_givens_lq (M, N, Q, L, k - 1, k, c, s);
         }
 
diff -Nru gsl-doc-1.16/linalg/qr.c gsl-doc-2.3/linalg/qr.c
--- gsl-doc-1.16/linalg/qr.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/qr.c	2016-04-05 21:01:16.000000000 +0000
@@ -22,14 +22,12 @@
 #include <config.h>
 #include <stdlib.h>
 #include <string.h>
+#include <gsl/gsl_linalg.h>
 #include <gsl/gsl_math.h>
 #include <gsl/gsl_vector.h>
 #include <gsl/gsl_matrix.h>
 #include <gsl/gsl_blas.h>
 
-#include <gsl/gsl_linalg.h>
-
-#include "givens.c"
 #include "apply_givens.c"
 
 /* Factorise a general M x N matrix A into
@@ -381,7 +379,7 @@
     {
       size_t i;
 
-      /* compute Q^T v */
+      /* compute Q v */
 
       for (i = GSL_MIN (M, N); i-- > 0;)
         {
@@ -396,7 +394,7 @@
     }
 }
 
-/* Form the product Q^T A  from a QR factorized matrix */
+/* Form the product Q^T A from a QR factorized matrix */
 
 int
 gsl_linalg_QR_QTmat (const gsl_matrix * QR, const gsl_vector * tau, gsl_matrix * A)
@@ -430,6 +428,38 @@
     }
 }
 
+/* Form the product A Q from a QR factorized matrix */
+int
+gsl_linalg_QR_matQ (const gsl_matrix * QR, const gsl_vector * tau, gsl_matrix * A)
+{
+  const size_t M = QR->size1;
+  const size_t N = QR->size2;
+
+  if (tau->size != GSL_MIN (M, N))
+    {
+      GSL_ERROR ("size of tau must be MIN(M,N)", GSL_EBADLEN);
+    }
+  else if (A->size2 != M)
+    {
+      GSL_ERROR ("matrix must have M columns", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i;
+
+      /* compute A Q */
+
+      for (i = 0; i < GSL_MIN (M, N); i++)
+        {
+          gsl_vector_const_view c = gsl_matrix_const_column (QR, i);
+          gsl_vector_const_view h = gsl_vector_const_subvector (&(c.vector), i, M - i);
+          gsl_matrix_view m = gsl_matrix_submatrix(A, 0, i, A->size1, M - i);
+          double ti = gsl_vector_get (tau, i);
+          gsl_linalg_householder_mh (ti, &(h.vector), &(m.matrix));
+        }
+      return GSL_SUCCESS;
+    }
+}
 
 /*  Form the orthogonal matrix Q from the packed QR matrix */
 
@@ -534,8 +564,8 @@
           double wk = gsl_vector_get (w, k);
           double wkm1 = gsl_vector_get (w, k - 1);
 
-          create_givens (wkm1, wk, &c, &s);
-          apply_givens_vec (w, k - 1, k, c, s);
+          gsl_linalg_givens (wkm1, wk, &c, &s);
+          gsl_linalg_givens_gv (w, k - 1, k, c, s);
           apply_givens_qr (M, N, Q, R, k - 1, k, c, s);
         }
 
@@ -559,7 +589,7 @@
           double diag = gsl_matrix_get (R, k - 1, k - 1);
           double offdiag = gsl_matrix_get (R, k, k - 1);
 
-          create_givens (diag, offdiag, &c, &s);
+          gsl_linalg_givens (diag, offdiag, &c, &s);
           apply_givens_qr (M, N, Q, R, k - 1, k, c, s);
 
           gsl_matrix_set (R, k, k - 1, 0.0);    /* exact zero of G^T */
diff -Nru gsl-doc-1.16/linalg/qrpt.c gsl-doc-2.3/linalg/qrpt.c
--- gsl-doc-1.16/linalg/qrpt.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/qrpt.c	2016-08-22 15:08:48.000000000 +0000
@@ -28,9 +28,6 @@
 
 #include <gsl/gsl_linalg.h>
 
-#define REAL double
-
-#include "givens.c"
 #include "apply_givens.c"
 
 /* Factorise a general M x N matrix A into
@@ -303,6 +300,87 @@
     }
 }
 
+/* Find the least squares solution to the overdetermined system 
+ *
+ *   A x = b 
+ *  
+ * for M >= N using the QRPT factorization A P = Q R. Assumes
+ * A has full column rank.
+ */
+
+int
+gsl_linalg_QRPT_lssolve (const gsl_matrix * QR, const gsl_vector * tau, const gsl_permutation * p,
+                         const gsl_vector * b, gsl_vector * x, gsl_vector * residual)
+{
+  const size_t N = QR->size2;
+  int status = gsl_linalg_QRPT_lssolve2(QR, tau, p, b, N, x, residual);
+  return status;
+}
+
+/* Find the least squares solution to the overdetermined system 
+ *
+ *   A x = b 
+ *  
+ * for M >= N using the QRPT factorization A P = Q R, where A
+ * is assumed rank deficient with a given rank.
+ */
+
+int
+gsl_linalg_QRPT_lssolve2 (const gsl_matrix * QR, const gsl_vector * tau, const gsl_permutation * p,
+                          const gsl_vector * b, const size_t rank, gsl_vector * x, gsl_vector * residual)
+{
+  const size_t M = QR->size1;
+  const size_t N = QR->size2;
+
+  if (M < N)
+    {
+      GSL_ERROR ("QR matrix must have M>=N", GSL_EBADLEN);
+    }
+  else if (M != b->size)
+    {
+      GSL_ERROR ("matrix size must match b size", GSL_EBADLEN);
+    }
+  else if (rank == 0 || rank > N)
+    {
+      GSL_ERROR ("rank must have 0 < rank <= N", GSL_EBADLEN);
+    }
+  else if (N != x->size)
+    {
+      GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
+    }
+  else if (M != residual->size)
+    {
+      GSL_ERROR ("matrix size must match residual size", GSL_EBADLEN);
+    }
+  else
+    {
+      gsl_matrix_const_view R11 = gsl_matrix_const_submatrix (QR, 0, 0, rank, rank);
+      gsl_vector_view QTb1 = gsl_vector_subvector(residual, 0, rank);
+      gsl_vector_view x1 = gsl_vector_subvector(x, 0, rank);
+      size_t i;
+
+      /* compute work = Q^T b */
+      gsl_vector_memcpy(residual, b);
+      gsl_linalg_QR_QTvec (QR, tau, residual);
+
+      /* solve R_{11} x(1:r) = [Q^T b](1:r) */
+      gsl_vector_memcpy(&(x1.vector), &(QTb1.vector));
+      gsl_blas_dtrsv (CblasUpper, CblasNoTrans, CblasNonUnit, &(R11.matrix), &(x1.vector));
+
+      /* x(r+1:N) = 0 */
+      for (i = rank; i < N; ++i)
+        gsl_vector_set(x, i, 0.0);
+
+      /* compute x = P y */
+      gsl_permute_vector_inverse (p, x);
+
+      /* compute residual = b - A x = Q (Q^T b - R x) */
+      gsl_vector_set_zero(&(QTb1.vector));
+      gsl_linalg_QR_Qvec(QR, tau, residual);
+
+      return GSL_SUCCESS;
+    }
+}
 
 int
 gsl_linalg_QRPT_QRsolve (const gsl_matrix * Q, const gsl_matrix * R,
@@ -456,8 +534,8 @@
           double wk = gsl_vector_get (w, k);
           double wkm1 = gsl_vector_get (w, k - 1);
 
-          create_givens (wkm1, wk, &c, &s);
-          apply_givens_vec (w, k - 1, k, c, s);
+          gsl_linalg_givens (wkm1, wk, &c, &s);
+          gsl_linalg_givens_gv (w, k - 1, k, c, s);
           apply_givens_qr (M, N, Q, R, k - 1, k, c, s);
         }
 
@@ -482,7 +560,7 @@
           double diag = gsl_matrix_get (R, k - 1, k - 1);
           double offdiag = gsl_matrix_get (R, k, k - 1);
 
-          create_givens (diag, offdiag, &c, &s);
+          gsl_linalg_givens (diag, offdiag, &c, &s);
           apply_givens_qr (M, N, Q, R, k - 1, k, c, s);
 
           gsl_matrix_set (R, k, k - 1, 0.0);    /* exact zero of G^T */
@@ -491,3 +569,75 @@
       return GSL_SUCCESS;
     }
 }
+
+/*
+gsl_linalg_QRPT_rank()
+  Estimate rank of triangular matrix from QRPT decomposition
+
+Inputs: QR  - QRPT decomposed matrix
+        tol - tolerance for rank determination; if < 0,
+              a default value is used:
+              20 * (M + N) * eps(max(|diag(R)|))
+
+Return: rank estimate
+*/
+
+size_t
+gsl_linalg_QRPT_rank (const gsl_matrix * QR, const double tol)
+{
+  const size_t M = QR->size1;
+  const size_t N = QR->size2;
+  gsl_vector_const_view diag = gsl_matrix_const_diagonal(QR);
+  double eps;
+  size_t i;
+  size_t r = 0;
+
+  if (tol < 0.0)
+    {
+      double min, max, absmax;
+      int ee;
+
+      gsl_vector_minmax(&diag.vector, &min, &max);
+      absmax = GSL_MAX(fabs(min), fabs(max));
+      ee = (int) log2(absmax);
+
+      eps = 20.0 * (M + N) * pow(2.0, (double) ee) * GSL_DBL_EPSILON;
+    }
+  else
+    eps = tol;
+
+  /* count number of diagonal elements with |di| > eps */
+  for (i = 0; i < GSL_MIN(M, N); ++i)
+    {
+      double di = gsl_vector_get(&diag.vector, i);
+      if (fabs(di) > eps)
+        ++r;
+    }
+
+  return r;
+}
+
+int
+gsl_linalg_QRPT_rcond(const gsl_matrix * QR, double * rcond, gsl_vector * work)
+{
+  const size_t M = QR->size1;
+  const size_t N = QR->size2;
+
+  if (M < N)
+    {
+      GSL_ERROR ("M must be >= N", GSL_EBADLEN);
+    }
+  else if (work->size != 3 * N)
+    {
+      GSL_ERROR ("work vector must have length 3*N", GSL_EBADLEN);
+    }
+  else
+    {
+      gsl_matrix_const_view R = gsl_matrix_const_submatrix (QR, 0, 0, N, N);
+      int status;
+
+      status = gsl_linalg_tri_upper_rcond(&R.matrix, rcond, work);
+
+      return status;
+    }
+}
diff -Nru gsl-doc-1.16/linalg/svd.c gsl-doc-2.3/linalg/svd.c
--- gsl-doc-1.16/linalg/svd.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/svd.c	2015-11-03 16:21:55.000000000 +0000
@@ -27,7 +27,6 @@
 
 #include <gsl/gsl_linalg.h>
 
-#include "givens.c"
 #include "svdstep.c"
 
 /* Factorise a general M x N matrix A into,
diff -Nru gsl-doc-1.16/linalg/svdstep.c gsl-doc-2.3/linalg/svdstep.c
--- gsl-doc-1.16/linalg/svdstep.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/svdstep.c	2015-11-13 22:21:39.000000000 +0000
@@ -185,7 +185,7 @@
     {
       /* Eliminate off-diagonal element in [0,f0;0,d1] to make [d,0;0,0] */
 
-      create_givens (f0, d1, &c, &s);
+      gsl_linalg_givens (f0, d1, &c, &s);
 
       /* compute B <= G^T B X,  where X = [0,1;1,0] */
 
@@ -213,7 +213,7 @@
     {
       /* Eliminate off-diagonal element in [d0,f0;0,0] */
 
-      create_givens (d0, f0, &c, &s);
+      gsl_linalg_givens (d0, f0, &c, &s);
 
       /* compute B <= B G */
 
@@ -273,7 +273,7 @@
           gsl_matrix_swap_columns(V, 0, 1);
         } 
 
-      create_givens (a11, a21, &c, &s);
+      gsl_linalg_givens (a11, a21, &c, &s);
       
       /* compute B <= G^T B */
       
@@ -312,7 +312,7 @@
 
   for (k = k0; k < n - 1; k++)
     {
-      create_givens (y, -x, &c, &s);
+      gsl_linalg_givens (y, -x, &c, &s);
       
       /* Compute U <= U G */
 
@@ -370,7 +370,7 @@
 
   for (k = n - 1; k-- > 0;)
     {
-      create_givens (x, y, &c, &s);
+      gsl_linalg_givens (x, y, &c, &s);
 
       /* Compute V <= V G where G = [c, s ; -s, c] */
 
@@ -421,7 +421,7 @@
 #endif
   const size_t n = d->size;
   double y, z;
-  double ak, bk, zk, ap, bp, aq, bq;
+  double ak, bk, zk, ap, bp, aq;
   size_t i, k;
 
   if (n == 1)
@@ -468,7 +468,6 @@
     double f0 = gsl_vector_get (f, 0);
     
     double d1 = gsl_vector_get (d, 1);
-    double f1 = gsl_vector_get (f, 1);
     
     {
       double mu = trailing_eigenvalue (d, f);
@@ -486,13 +485,12 @@
     bp = f0;
     
     aq = d1;
-    bq = f1;
   }
 
   for (k = 0; k < n - 1; k++)
     {
       double c, s;
-      create_givens (y, z, &c, &s);
+      gsl_linalg_givens (y, z, &c, &s);
 
       /* Compute V <= V G */
 
@@ -547,7 +545,7 @@
         z = zk;
       }
 
-      create_givens (y, z, &c, &s);
+      gsl_linalg_givens (y, z, &c, &s);
 
       /* Compute U <= U G */
 
diff -Nru gsl-doc-1.16/linalg/test.c gsl-doc-2.3/linalg/test.c
--- gsl-doc-1.16/linalg/test.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/test.c	2016-08-30 15:12:44.000000000 +0000
@@ -26,9 +26,13 @@
 #include <gsl/gsl_math.h>
 #include <gsl/gsl_ieee_utils.h>
 #include <gsl/gsl_permute_vector.h>
+#include <gsl/gsl_permute_matrix.h>
 #include <gsl/gsl_blas.h>
 #include <gsl/gsl_complex_math.h>
 #include <gsl/gsl_linalg.h>
+#include <gsl/gsl_rng.h>
+
+#include "test_cholesky.c"
 
 #define TEST_SVD_4X4 1
 
@@ -60,12 +64,18 @@
 int test_QRPT_solve(void);
 int test_QRPT_QRsolve_dim(const gsl_matrix * m, const double * actual, double eps);
 int test_QRPT_QRsolve(void);
-int test_QRPT_decomp_dim(const gsl_matrix * m, double eps);
+int test_QRPT_decomp_dim(const gsl_matrix * m, const double expected_rcond, double eps);
 int test_QRPT_decomp(void);
+int test_QRPT_lssolve_dim(const gsl_matrix * m, const double * actual, double eps);
+int test_QRPT_lssolve(void);
+int test_QRPT_lssolve2_dim(const gsl_matrix * m, const double * actual, double eps);
+int test_QRPT_lssolve2(void);
 int test_QR_update_dim(const gsl_matrix * m, double eps);
 int test_QR_update(void);
 int test_QRPT_update_dim(const gsl_matrix * m, double eps);
 int test_QRPT_update(void);
+int test_COD_decomp_dim(const gsl_matrix * m, double eps);
+int test_COD_decomp(void);
 
 int test_LQ_solve_dim(const gsl_matrix * m, const double * actual, double eps);
 int test_LQ_solve(void);
@@ -94,10 +104,6 @@
 int test_SV_decomp_jacobi(void);
 int test_cholesky_solve_dim(const gsl_matrix * m, const double * actual, double eps);
 int test_cholesky_solve(void);
-int test_cholesky_decomp_dim(const gsl_matrix * m, double eps);
-int test_cholesky_decomp(void);
-int test_cholesky_invert_dim(const gsl_matrix * m, double eps);
-int test_cholesky_invert(void);
 int test_HH_solve_dim(const gsl_matrix * m, const double * actual, double eps);
 int test_HH_solve(void);
 int test_TDS_solve_dim(unsigned long dim, double d, double od, const double * actual, double eps);
@@ -308,6 +314,36 @@
   return A;
 }
 
+static int
+create_tri_matrix(CBLAS_UPLO_t Uplo, CBLAS_DIAG_t Diag, gsl_matrix * m, gsl_rng * r)
+{
+  const size_t N = m->size1;
+  size_t i, j;
+
+  gsl_matrix_set_zero(m);
+
+  for (i = 0; i < N; ++i)
+    {
+      for (j = 0; j <= i; ++j)
+        {
+          double mij = gsl_rng_uniform(r);
+
+          /* put lower bound on diagonal entries to ensure invertibility */
+          if (i == j)
+            mij = GSL_MAX(mij, 0.3);
+
+          if (Uplo == CblasLower)
+            gsl_matrix_set(m, i, j, mij);
+          else
+            gsl_matrix_set(m, j, i, mij);
+
+          if (Diag == CblasUnit && i == j)
+            gsl_matrix_set(m, i, j, 1.0);
+        }
+    }
+
+  return GSL_SUCCESS;
+}
 
 
 gsl_matrix * m11;
@@ -1023,6 +1059,237 @@
 }
 
 int
+test_QRPT_lssolve_dim(const gsl_matrix * m, const double * actual, double eps)
+{
+  int s = 0;
+  size_t i, M = m->size1, N = m->size2;
+
+  gsl_vector * rhs = gsl_vector_alloc(M);
+  gsl_matrix * QRPT  = gsl_matrix_alloc(M,N);
+  gsl_vector * tau = gsl_vector_alloc(N);
+  gsl_vector * x = gsl_vector_alloc(N);
+  gsl_vector * r = gsl_vector_alloc(M);
+  gsl_vector * res = gsl_vector_alloc(M);
+  gsl_permutation * perm = gsl_permutation_alloc(N);
+  gsl_vector * work = gsl_vector_alloc(N);
+  int signum;
+
+  gsl_matrix_memcpy(QRPT, m);
+
+  for(i = 0; i < M; i++)
+    gsl_vector_set(rhs, i, i + 1.0);
+
+  s += gsl_linalg_QRPT_decomp(QRPT, tau, perm, &signum, work);
+  s += gsl_linalg_QRPT_lssolve(QRPT, tau, perm, rhs, x, res);
+
+  for (i = 0; i < N; i++)
+    {
+      int foo = check(gsl_vector_get(x, i), actual[i], eps);
+      if(foo)
+        {
+          printf("(%3lu,%3lu)[%lu]: %22.18g   %22.18g\n", M, N, i, gsl_vector_get(x, i), actual[i]);
+        }
+      s += foo;
+    }
+
+  /* compute residual r = b - m x */
+  if (M == N)
+    {
+      gsl_vector_set_zero(r);
+    }
+  else
+    {
+      gsl_vector_memcpy(r, rhs);
+      gsl_blas_dgemv(CblasNoTrans, -1.0, m, x, 1.0, r);
+    }
+
+  for (i = 0; i < N; i++)
+    {
+      int foo = check(gsl_vector_get(res, i), gsl_vector_get(r,i), sqrt(eps));
+      if(foo)
+        {
+          printf("(%3lu,%3lu)[%lu]: %22.18g   %22.18g\n", M, N, i, gsl_vector_get(res, i), gsl_vector_get(r,i));
+        }
+      s += foo;
+    }
+
+  gsl_vector_free(r);
+  gsl_vector_free(res);
+  gsl_vector_free(x);
+  gsl_vector_free(tau);
+  gsl_matrix_free(QRPT);
+  gsl_vector_free(rhs);
+  gsl_permutation_free(perm);
+  gsl_vector_free(work);
+
+  return s;
+}
+
+int
+test_QRPT_lssolve(void)
+{
+  int f;
+  int s = 0;
+
+  f = test_QRPT_lssolve_dim(m53, m53_lssolution, 2 * 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve m(5,3)");
+  s += f;
+
+  f = test_QRPT_lssolve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve hilbert(2)");
+  s += f;
+
+  f = test_QRPT_lssolve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve hilbert(3)");
+  s += f;
+
+  f = test_QRPT_lssolve_dim(hilb4, hilb4_solution, 2 * 2048.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve hilbert(4)");
+  s += f;
+
+  f = test_QRPT_lssolve_dim(hilb12, hilb12_solution, 0.5);
+  gsl_test(f, "  QRPT_lssolve hilbert(12)");
+  s += f;
+
+  f = test_QRPT_lssolve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve vander(2)");
+  s += f;
+
+  f = test_QRPT_lssolve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve vander(3)");
+  s += f;
+
+  f = test_QRPT_lssolve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve vander(4)");
+  s += f;
+
+  f = test_QRPT_lssolve_dim(vander12, vander12_solution, 0.05);
+  gsl_test(f, "  QRPT_lssolve vander(12)");
+  s += f;
+
+  return s;
+}
+
+int
+test_QRPT_lssolve2_dim(const gsl_matrix * m, const double * actual, double eps)
+{
+  int s = 0;
+  size_t i, M = m->size1, N = m->size2;
+
+  gsl_vector * rhs = gsl_vector_alloc(M);
+  gsl_matrix * QRPT  = gsl_matrix_alloc(M,N);
+  gsl_vector * tau = gsl_vector_alloc(N);
+  gsl_vector * x = gsl_vector_alloc(N);
+  gsl_vector * r = gsl_vector_alloc(M);
+  gsl_vector * res = gsl_vector_alloc(M);
+  gsl_permutation * perm = gsl_permutation_alloc(N);
+  gsl_vector * work = gsl_vector_alloc(N);
+  int signum;
+  size_t rank;
+
+  gsl_matrix_memcpy(QRPT, m);
+
+  for(i = 0; i < M; i++)
+    gsl_vector_set(rhs, i, i + 1.0);
+
+  s += gsl_linalg_QRPT_decomp(QRPT, tau, perm, &signum, work);
+
+  rank = gsl_linalg_QRPT_rank(QRPT, -1.0);
+
+  s += gsl_linalg_QRPT_lssolve2(QRPT, tau, perm, rhs, rank, x, res);
+
+  if (M > N)
+    {
+      for (i = 0; i < N; i++)
+        {
+          int foo = check(gsl_vector_get(x, i), actual[i], eps);
+          if(foo)
+            {
+              printf("(%3lu,%3lu)[%lu]: %22.18g   %22.18g\n", M, N, i, gsl_vector_get(x, i), actual[i]);
+            }
+          s += foo;
+        }
+    }
+
+  /* compute residual r = b - m x */
+  if (M == N)
+    {
+      gsl_vector_set_zero(r);
+    }
+  else
+    {
+      gsl_vector_memcpy(r, rhs);
+      gsl_blas_dgemv(CblasNoTrans, -1.0, m, x, 1.0, r);
+    }
+
+  for (i = 0; i < N; i++)
+    {
+      int foo = check(gsl_vector_get(res, i), gsl_vector_get(r,i), sqrt(eps));
+      if(foo)
+        {
+          printf("(%3lu,%3lu)[%lu]: %22.18g   %22.18g\n", M, N, i, gsl_vector_get(res, i), gsl_vector_get(r,i));
+        }
+      s += foo;
+    }
+
+  gsl_vector_free(r);
+  gsl_vector_free(res);
+  gsl_vector_free(x);
+  gsl_vector_free(tau);
+  gsl_matrix_free(QRPT);
+  gsl_vector_free(rhs);
+  gsl_permutation_free(perm);
+  gsl_vector_free(work);
+
+  return s;
+}
+
+int
+test_QRPT_lssolve2(void)
+{
+  int f;
+  int s = 0;
+
+  f = test_QRPT_lssolve2_dim(m53, m53_lssolution, 2 * 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve2 m(5,3)");
+  s += f;
+
+  f = test_QRPT_lssolve2_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve2 hilbert(2)");
+  s += f;
+
+  f = test_QRPT_lssolve2_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve2 hilbert(3)");
+  s += f;
+
+  f = test_QRPT_lssolve2_dim(hilb4, hilb4_solution, 2 * 2048.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve2 hilbert(4)");
+  s += f;
+
+  f = test_QRPT_lssolve2_dim(hilb12, hilb12_solution, 0.5);
+  gsl_test(f, "  QRPT_lssolve2 hilbert(12)");
+  s += f;
+
+  f = test_QRPT_lssolve2_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve2 vander(2)");
+  s += f;
+
+  f = test_QRPT_lssolve2_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve2 vander(3)");
+  s += f;
+
+  f = test_QRPT_lssolve2_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  QRPT_lssolve2 vander(4)");
+  s += f;
+
+  f = test_QRPT_lssolve2_dim(vander12, vander12_solution, 0.05);
+  gsl_test(f, "  QRPT_lssolve2 vander(12)");
+  s += f;
+
+  return s;
+}
+
+int
 test_QRPT_solve_dim(const gsl_matrix * m, const double * actual, double eps)
 {
   int s = 0;
@@ -1179,55 +1446,71 @@
 }
 
 int
-test_QRPT_decomp_dim(const gsl_matrix * m, double eps)
+test_QRPT_decomp_dim(const gsl_matrix * m, const double expected_rcond, double eps)
 {
   int s = 0, signum;
   unsigned long i,j, M = m->size1, N = m->size2;
 
-  gsl_matrix * qr = gsl_matrix_alloc(M,N);
-  gsl_matrix * a  = gsl_matrix_alloc(M,N);
-  gsl_matrix * q  = gsl_matrix_alloc(M,M);
-  gsl_matrix * r  = gsl_matrix_alloc(M,N);
-  gsl_vector * d = gsl_vector_alloc(GSL_MIN(M,N));
+  gsl_matrix * QR = gsl_matrix_alloc(M, N);
+  gsl_matrix * A  = gsl_matrix_alloc(M, N);
+  gsl_matrix * Q  = gsl_matrix_alloc(M, M);
+  gsl_matrix * R  = gsl_matrix_alloc(M, N);
+  gsl_vector * tau = gsl_vector_alloc(GSL_MIN(M, N));
   gsl_vector * norm = gsl_vector_alloc(N);
 
   gsl_permutation * perm = gsl_permutation_alloc(N);
 
-  gsl_matrix_memcpy(qr,m);
+  gsl_matrix_memcpy(QR, m);
+  s += gsl_linalg_QRPT_decomp(QR, tau, perm, &signum, norm);
+  s += gsl_linalg_QR_unpack(QR, tau, Q, R);
 
-  s += gsl_linalg_QRPT_decomp(qr, d, perm, &signum, norm);
-  s += gsl_linalg_QR_unpack(qr, d, q, r);
+  /* compute A = Q R */
+  gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, Q, R, 0.0, A);
 
-  /* compute a = q r */
-  gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, q, r, 0.0, a);
+  /* Compute QR P^T by permuting the elements of the rows of QR */
 
+  for (i = 0; i < M; i++)
+    {
+      gsl_vector_view row = gsl_matrix_row (A, i);
+      gsl_permute_vector_inverse (perm, &row.vector);
+    }
 
-  /* Compute QR P^T by permuting the elements of the rows of QR */
+  for (i = 0; i < M; i++)
+    {
+      for (j = 0; j < N; j++)
+        {
+          double aij = gsl_matrix_get(A, i, j);
+          double mij = gsl_matrix_get(m, i, j);
+          int foo = check(aij, mij, eps);
+          if(foo)
+            printf("(%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n", M, N, i,j, aij, mij);
+          s += foo;
+        }
+    }
 
-  for (i = 0; i < M; i++) {
-    gsl_vector_view row = gsl_matrix_row (a, i);
-    gsl_permute_vector_inverse (perm, &row.vector);
-  }
+  if (expected_rcond > 0.0)
+    {
+      double rcond;
+      int foo;
+      gsl_vector * work = gsl_vector_alloc(3 * N);
+
+      gsl_linalg_QRPT_rcond(QR, &rcond, work);
+      foo = check(rcond, expected_rcond, 1.0e-10);
+      if (foo)
+        printf("QRPT_rcond (%3lu,%3lu): %22.18g   %22.18g\n", M, N, rcond, expected_rcond);
 
-  for(i=0; i<M; i++) {
-    for(j=0; j<N; j++) {
-      double aij = gsl_matrix_get(a, i, j);
-      double mij = gsl_matrix_get(m, i, j);
-      int foo = check(aij, mij, eps);
-      if(foo) {
-        printf("(%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n", M, N, i,j, aij, mij);
-      }
       s += foo;
+
+      gsl_vector_free(work);
     }
-  }
 
   gsl_permutation_free (perm);
   gsl_vector_free(norm);
-  gsl_vector_free(d);
-  gsl_matrix_free(qr);
-  gsl_matrix_free(a);
-  gsl_matrix_free(q);
-  gsl_matrix_free(r);
+  gsl_vector_free(tau);
+  gsl_matrix_free(QR);
+  gsl_matrix_free(A);
+  gsl_matrix_free(Q);
+  gsl_matrix_free(R);
 
   return s;
 }
@@ -1237,51 +1520,52 @@
   int f;
   int s = 0;
 
-  f = test_QRPT_decomp_dim(m35, 2 * 8.0 * GSL_DBL_EPSILON);
+  f = test_QRPT_decomp_dim(m35, -1.0, 2 * 8.0 * GSL_DBL_EPSILON);
   gsl_test(f, "  QRPT_decomp m(3,5)");
   s += f;
 
-  f = test_QRPT_decomp_dim(m53, 2 * 8.0 * GSL_DBL_EPSILON);
+  /* rcond value from LAPACK DTRCON */
+  f = test_QRPT_decomp_dim(m53, 2.915362697820e-03, 2 * 8.0 * GSL_DBL_EPSILON);
   gsl_test(f, "  QRPT_decomp m(5,3)");
   s += f;
 
-  f = test_QRPT_decomp_dim(s35, 2 * 8.0 * GSL_DBL_EPSILON);
+  f = test_QRPT_decomp_dim(s35, -1.0, 2 * 8.0 * GSL_DBL_EPSILON);
   gsl_test(f, "  QRPT_decomp s(3,5)");
   s += f;
 
-  f = test_QRPT_decomp_dim(s53, 2 * 8.0 * GSL_DBL_EPSILON);
+  f = test_QRPT_decomp_dim(s53, 1.002045825443827e-03, 2 * 8.0 * GSL_DBL_EPSILON);
   gsl_test(f, "  QRPT_decomp s(5,3)");
   s += f;
 
-  f = test_QRPT_decomp_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
+  f = test_QRPT_decomp_dim(hilb2, 4.347826086956522e-02, 2 * 8.0 * GSL_DBL_EPSILON);
   gsl_test(f, "  QRPT_decomp hilbert(2)");
   s += f;
 
-  f = test_QRPT_decomp_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
+  f = test_QRPT_decomp_dim(hilb3, 1.505488055305100e-03, 2 * 64.0 * GSL_DBL_EPSILON);
   gsl_test(f, "  QRPT_decomp hilbert(3)");
   s += f;
 
-  f = test_QRPT_decomp_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
+  f = test_QRPT_decomp_dim(hilb4, 4.872100915910022e-05, 2 * 1024.0 * GSL_DBL_EPSILON);
   gsl_test(f, "  QRPT_decomp hilbert(4)");
   s += f;
 
-  f = test_QRPT_decomp_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
+  f = test_QRPT_decomp_dim(hilb12, -1.0, 2 * 1024.0 * GSL_DBL_EPSILON);
   gsl_test(f, "  QRPT_decomp hilbert(12)");
   s += f;
 
-  f = test_QRPT_decomp_dim(vander2, 8.0 * GSL_DBL_EPSILON);
+  f = test_QRPT_decomp_dim(vander2, 1.249999999999999e-01, 8.0 * GSL_DBL_EPSILON);
   gsl_test(f, "  QRPT_decomp vander(2)");
   s += f;
 
-  f = test_QRPT_decomp_dim(vander3, 64.0 * GSL_DBL_EPSILON);
+  f = test_QRPT_decomp_dim(vander3, 9.708737864077667e-03, 64.0 * GSL_DBL_EPSILON);
   gsl_test(f, "  QRPT_decomp vander(3)");
   s += f;
 
-  f = test_QRPT_decomp_dim(vander4, 1024.0 * GSL_DBL_EPSILON);
+  f = test_QRPT_decomp_dim(vander4, 5.255631229339451e-04, 1024.0 * GSL_DBL_EPSILON);
   gsl_test(f, "  QRPT_decomp vander(4)");
   s += f;
 
-  f = test_QRPT_decomp_dim(vander12, 0.0005); /* FIXME: bad accuracy */
+  f = test_QRPT_decomp_dim(vander12, -1.0, 0.0005); /* FIXME: bad accuracy */
   gsl_test(f, "  QRPT_decomp vander(12)");
   s += f;
 
@@ -1592,6 +1876,245 @@
 }
 
 int
+test_COD_decomp_dim(const gsl_matrix * m, double eps)
+{
+  int s = 0;
+  size_t i, j, M = m->size1, N = m->size2;
+  size_t rank;
+
+  gsl_matrix * QRZT = gsl_matrix_alloc(M, N);
+  gsl_matrix * Q = gsl_matrix_alloc(M, M);
+  gsl_matrix * R = gsl_matrix_alloc(M, N);
+  gsl_matrix * QR = gsl_matrix_alloc(M, N);
+  gsl_matrix * Z = gsl_matrix_alloc(N, N);
+  gsl_vector * tau_Q = gsl_vector_alloc(GSL_MIN(M, N));
+  gsl_vector * tau_Z = gsl_vector_alloc(GSL_MIN(M, N));
+  gsl_vector * work = gsl_vector_alloc(N);
+  gsl_matrix * lhs = gsl_matrix_alloc(M, N);
+  gsl_matrix * rhs = gsl_matrix_alloc(M, N);
+
+  gsl_permutation * perm = gsl_permutation_alloc(N);
+
+  gsl_matrix_memcpy(QRZT, m);
+
+  s += gsl_linalg_COD_decomp(QRZT, tau_Q, tau_Z, perm, &rank, work);
+  s += gsl_linalg_COD_unpack(QRZT, tau_Q, tau_Z, rank, Q, R, Z);
+
+  /* compute lhs = m P */
+  gsl_matrix_memcpy(lhs, m);
+  gsl_permute_matrix(perm, lhs);
+
+  /* compute rhs = Q R Z */
+  gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, Q, R, 0.0, QR);
+  gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, QR, Z, 0.0, rhs);
+
+  for (i = 0; i < M; i++)
+    {
+      for (j = 0; j < N; j++)
+        {
+          double aij = gsl_matrix_get(rhs, i, j);
+          double bij = gsl_matrix_get(lhs, i, j);
+          int foo = check(aij, bij, eps);
+          if (foo)
+            {
+              printf("(%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n", M, N, i, j, aij, bij);
+            }
+          s += foo;
+        }
+    }
+
+  gsl_permutation_free (perm);
+  gsl_vector_free(work);
+  gsl_vector_free(tau_Q);
+  gsl_vector_free(tau_Z);
+  gsl_matrix_free(QRZT);
+  gsl_matrix_free(lhs);
+  gsl_matrix_free(rhs);
+  gsl_matrix_free(QR);
+  gsl_matrix_free(Q);
+  gsl_matrix_free(R);
+  gsl_matrix_free(Z);
+
+  return s;
+}
+
+int
+test_COD_decomp(void)
+{
+  int f;
+  int s = 0;
+
+  f = test_COD_decomp_dim(m35, 2 * 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_decomp m(3,5)");
+  s += f;
+
+  f = test_COD_decomp_dim(m53, 2 * 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_decomp m(5,3)");
+  s += f;
+
+  f = test_COD_decomp_dim(s35, 2 * 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_decomp s(3,5)");
+  s += f;
+
+  f = test_COD_decomp_dim(s53, 2 * 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_decomp s(5,3)");
+  s += f;
+
+  f = test_COD_decomp_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_decomp hilbert(2)");
+  s += f;
+
+  f = test_COD_decomp_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_decomp hilbert(3)");
+  s += f;
+
+  f = test_COD_decomp_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_decomp hilbert(4)");
+  s += f;
+
+  f = test_COD_decomp_dim(hilb12, 2 * 2048.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_decomp hilbert(12)");
+  s += f;
+
+  f = test_COD_decomp_dim(vander2, 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_decomp vander(2)");
+  s += f;
+
+  f = test_COD_decomp_dim(vander3, 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_decomp vander(3)");
+  s += f;
+
+  f = test_COD_decomp_dim(vander4, 1024.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_decomp vander(4)");
+  s += f;
+
+  f = test_COD_decomp_dim(vander12, 0.001); /* FIXME: bad accuracy */
+  gsl_test(f, "  COD_decomp vander(12)");
+  s += f;
+
+  return s;
+}
+
+int
+test_COD_lssolve_dim(const gsl_matrix * m, const double * actual, double eps)
+{
+  int s = 0;
+  size_t i, M = m->size1, N = m->size2;
+
+  gsl_vector * lhs = gsl_vector_alloc(M);
+  gsl_vector * rhs = gsl_vector_alloc(M);
+  gsl_matrix * QRZT  = gsl_matrix_alloc(M, N);
+  gsl_vector * tau_Q = gsl_vector_alloc(GSL_MIN(M, N));
+  gsl_vector * tau_Z = gsl_vector_alloc(GSL_MIN(M, N));
+  gsl_vector * work = gsl_vector_alloc(N);
+  gsl_vector * x = gsl_vector_alloc(N);
+  gsl_vector * r = gsl_vector_alloc(M);
+  gsl_vector * res = gsl_vector_alloc(M);
+  gsl_permutation * perm = gsl_permutation_alloc(N);
+  size_t rank;
+
+  gsl_matrix_memcpy(QRZT, m);
+
+  for (i = 0; i < M; i++)
+    gsl_vector_set(rhs, i, i + 1.0);
+
+  s += gsl_linalg_COD_decomp(QRZT, tau_Q, tau_Z, perm, &rank, work);
+  s += gsl_linalg_COD_lssolve(QRZT, tau_Q, tau_Z, perm, rank, rhs, x, res);
+
+  if (M > N)
+    {
+      for (i = 0; i < N; i++)
+        {
+          int foo = check(gsl_vector_get(x, i), actual[i], eps);
+          if(foo)
+            {
+              printf("(%3lu,%3lu)[%lu]: %22.18g   %22.18g\n", M, N, i, gsl_vector_get(x, i), actual[i]);
+            }
+          s += foo;
+        }
+    }
+
+  /* compute residual r = b - m x */
+  if (M == N)
+    {
+      gsl_vector_set_zero(r);
+    }
+  else
+    {
+      gsl_vector_memcpy(r, rhs);
+      gsl_blas_dgemv(CblasNoTrans, -1.0, m, x, 1.0, r);
+    }
+
+  for (i = 0; i < N; i++)
+    {
+      int foo = check(gsl_vector_get(res, i), gsl_vector_get(r, i), sqrt(eps));
+      if(foo)
+        {
+          printf("res (%3lu,%3lu)[%lu]: %22.18g   %22.18g\n", M, N, i, gsl_vector_get(res, i), gsl_vector_get(r,i));
+        }
+      s += foo;
+    }
+
+  gsl_vector_free(r);
+  gsl_vector_free(res);
+  gsl_vector_free(x);
+  gsl_vector_free(tau_Q);
+  gsl_vector_free(tau_Z);
+  gsl_matrix_free(QRZT);
+  gsl_vector_free(rhs);
+  gsl_vector_free(lhs);
+  gsl_vector_free(work);
+  gsl_permutation_free(perm);
+
+  return s;
+}
+
+int
+test_COD_lssolve(void)
+{
+  int f;
+  int s = 0;
+
+  f = test_COD_lssolve_dim(m53, m53_lssolution, 2 * 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_lssolve m(5,3)");
+  s += f;
+
+  f = test_COD_lssolve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_lssolve hilbert(2)");
+  s += f;
+
+  f = test_COD_lssolve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_lssolve hilbert(3)");
+  s += f;
+
+  f = test_COD_lssolve_dim(hilb4, hilb4_solution, 2 * 2048.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_lssolve hilbert(4)");
+  s += f;
+
+  f = test_COD_lssolve_dim(hilb12, hilb12_solution, 1.0e-5);
+  gsl_test(f, "  COD_lssolve hilbert(12)");
+  s += f;
+
+  f = test_COD_lssolve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_lssolve vander(2)");
+  s += f;
+
+  f = test_COD_lssolve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_lssolve vander(3)");
+  s += f;
+
+  f = test_COD_lssolve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  COD_lssolve vander(4)");
+  s += f;
+
+  f = test_COD_lssolve_dim(vander12, vander12_solution, 0.05);
+  gsl_test(f, "  COD_lssolve vander(12)");
+  s += f;
+
+  return s;
+}
+
+int
 test_LQ_solve_dim(const gsl_matrix * m, const double * actual, double eps)
 {
   int s = 0;
@@ -2288,7 +2811,7 @@
   gsl_test(f, "  LQ_update m(3,5)");
   s += f;
 
-  f = test_LQ_update_dim(m53, 2 * 512.0 * GSL_DBL_EPSILON);
+  f = test_LQ_update_dim(m53, 2 * 2048.0 * GSL_DBL_EPSILON);
   gsl_test(f, "  LQ_update m(5,3)");
   s += f;
 
@@ -3213,7 +3736,7 @@
   gsl_vector * x = gsl_vector_calloc(dim);
   gsl_matrix_memcpy(u,m);
   for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
-  s += gsl_linalg_cholesky_decomp(u);
+  s += gsl_linalg_cholesky_decomp1(u);
   s += gsl_linalg_cholesky_solve(u, rhs, x);
   for(i=0; i<dim; i++) {
     int foo = check(gsl_vector_get(x, i), actual[i], eps);
@@ -3229,173 +3752,78 @@
   return s;
 }
 
-int test_cholesky_solve(void)
-{
-  int f;
-  int s = 0;
-
-  f = test_cholesky_solve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
-  gsl_test(f, "  cholesky_solve hilbert(2)");
-  s += f;
-
-  f = test_cholesky_solve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
-  gsl_test(f, "  cholesky_solve hilbert(3)");
-  s += f;
-
-  f = test_cholesky_solve_dim(hilb4, hilb4_solution, 2 * 1024.0 * GSL_DBL_EPSILON);
-  gsl_test(f, "  cholesky_solve hilbert(4)");
-  s += f;
-
-  f = test_cholesky_solve_dim(hilb12, hilb12_solution, 0.5);
-  gsl_test(f, "  cholesky_solve hilbert(12)");
-  s += f;
-
-  return s;
-}
-
-
 int
-test_cholesky_decomp_dim(const gsl_matrix * m, double eps)
+test_cholesky_solve2_dim(const gsl_matrix * m, const double * actual, double eps)
 {
   int s = 0;
-  unsigned long i,j, M = m->size1, N = m->size2;
-
-  gsl_matrix * v  = gsl_matrix_alloc(M,N);
-  gsl_matrix * a  = gsl_matrix_alloc(M,N);
-  gsl_matrix * l  = gsl_matrix_alloc(M,N);
-  gsl_matrix * lt  = gsl_matrix_alloc(N,N);
-
-  gsl_matrix_memcpy(v,m);
-
-  s += gsl_linalg_cholesky_decomp(v);
-  
-  /* Compute L LT */
-  
-  for (i = 0; i < N ; i++)
-    {
-      for (j = 0; j < N; j++)
-        {
-          double vij = gsl_matrix_get(v, i, j);
-          gsl_matrix_set (l, i, j, i>=j ? vij : 0);
-          gsl_matrix_set (lt, i, j, i<=j ? vij : 0);
-        }
-    }
-            
-  /* compute a = l lt */
-  gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, l, lt, 0.0, a);
+  unsigned long i, dim = m->size1;
 
-  for(i=0; i<M; i++) {
-    for(j=0; j<N; j++) {
-      double aij = gsl_matrix_get(a, i, j);
-      double mij = gsl_matrix_get(m, i, j);
-      int foo = check(aij, mij, eps);
-      if(foo) {
-        printf("(%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n", M, N, i,j, aij, mij);
-      }
-      s += foo;
+  gsl_vector * rhs = gsl_vector_alloc(dim);
+  gsl_matrix * u  = gsl_matrix_alloc(dim,dim);
+  gsl_vector * x = gsl_vector_calloc(dim);
+  gsl_vector * D = gsl_vector_calloc(dim);
+  gsl_matrix_memcpy(u,m);
+  for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
+  s += gsl_linalg_cholesky_decomp2(u, D);
+  s += gsl_linalg_cholesky_solve2(u, D, rhs, x);
+  for(i=0; i<dim; i++) {
+    int foo = check(gsl_vector_get(x, i), actual[i], eps);
+    if(foo) {
+      printf("%3lu[%lu]: %22.18g   %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
     }
+    s += foo;
   }
-
-  gsl_matrix_free(v);
-  gsl_matrix_free(a);
-  gsl_matrix_free(l);
-  gsl_matrix_free(lt);
+  gsl_vector_free(x);
+  gsl_matrix_free(u);
+  gsl_vector_free(rhs);
+  gsl_vector_free(D);
 
   return s;
 }
 
-int test_cholesky_decomp(void)
+int
+test_cholesky_solve(void)
 {
   int f;
   int s = 0;
 
-  f = test_cholesky_decomp_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
-  gsl_test(f, "  cholesky_decomp hilbert(2)");
+  f = test_cholesky_solve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  cholesky_solve hilbert(2)");
   s += f;
 
-  f = test_cholesky_decomp_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
-  gsl_test(f, "  cholesky_decomp hilbert(3)");
+  f = test_cholesky_solve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  cholesky_solve hilbert(3)");
   s += f;
 
-  f = test_cholesky_decomp_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
-  gsl_test(f, "  cholesky_decomp hilbert(4)");
+  f = test_cholesky_solve_dim(hilb4, hilb4_solution, 2 * 1024.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  cholesky_solve hilbert(4)");
   s += f;
 
-  f = test_cholesky_decomp_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
-  gsl_test(f, "  cholesky_decomp hilbert(12)");
+  f = test_cholesky_solve_dim(hilb12, hilb12_solution, 0.5);
+  gsl_test(f, "  cholesky_solve hilbert(12)");
   s += f;
 
-  return s;
-}
-
-int
-test_cholesky_invert_dim(const gsl_matrix * m, double eps)
-{
-  int s = 0;
-  unsigned long i, j, N = m->size1;
-
-  gsl_matrix * v  = gsl_matrix_alloc(N, N);
-  gsl_matrix * c  = gsl_matrix_alloc(N, N);
-
-  gsl_matrix_memcpy(v,m);
-
-  s += gsl_linalg_cholesky_decomp(v);
-  s += gsl_linalg_cholesky_invert(v);
-
-  gsl_blas_dsymm(CblasLeft, CblasUpper, 1.0, m, v, 0.0, c);
-
-  /* c should be the identity matrix */
-
-  for (i = 0; i < N; ++i)
-    {
-      for (j = 0; j < N; ++j)
-        {
-          int foo;
-          double cij = gsl_matrix_get(c, i, j);
-          double expected;
-
-          if (i == j)
-            expected = 1.0;
-          else
-            expected = 0.0;
-
-          foo = check(cij, expected, eps);
-
-          if (foo)
-            printf("(%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n", N, N, i,j, cij, expected);
-
-          s += foo;
-        }
-    }
-
-  gsl_matrix_free(v);
-  gsl_matrix_free(c);
-
-  return s;
-}
+  /* test scaled Cholesky routines */
 
-int
-test_cholesky_invert(void)
-{
-  int f;
-  int s = 0;
+  f = test_cholesky_solve2_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  cholesky_solve2 hilbert(2)");
+  s += f;
 
-  f = test_cholesky_invert_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
-  gsl_test(f, "  cholesky_invert hilbert(2)");
+  f = test_cholesky_solve2_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  cholesky_solve2 hilbert(3)");
   s += f;
 
-  f = test_cholesky_invert_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
-  gsl_test(f, "  cholesky_invert hilbert(3)");
+  f = test_cholesky_solve2_dim(hilb4, hilb4_solution, 2 * 2048.0 * GSL_DBL_EPSILON);
+  gsl_test(f, "  cholesky_solve2 hilbert(4)");
   s += f;
 
-  f = test_cholesky_invert_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
-  gsl_test(f, "  cholesky_invert hilbert(4)");
+  f = test_cholesky_solve2_dim(hilb12, hilb12_solution, 0.5);
+  gsl_test(f, "  cholesky_solve2 hilbert(12)");
   s += f;
 
   return s;
 }
 
-
 int
 test_cholesky_decomp_unit_dim(const gsl_matrix * m, double eps)
 {
@@ -3752,8 +4180,6 @@
   return s;
 }
 
-
-
 int
 test_HH_solve_dim(const gsl_matrix * m, const double * actual, double eps)
 {
@@ -4240,14 +4666,85 @@
   return s;
 }
 
+int
+test_tri_invert2(CBLAS_UPLO_t Uplo, CBLAS_DIAG_t Diag, gsl_rng * r, const double tol)
+{
+  const size_t N_max = 30;
+  int s = 0;
+  size_t n, i, j;
+  int (*invert_func) (gsl_matrix * T) = NULL;
+
+  if (Uplo == CblasUpper && Diag == CblasNonUnit)
+    invert_func = gsl_linalg_tri_upper_invert;
+  else if (Uplo == CblasLower && Diag == CblasNonUnit)
+    invert_func = gsl_linalg_tri_lower_invert;
+  else if (Uplo == CblasUpper && Diag == CblasUnit)
+    invert_func = gsl_linalg_tri_upper_unit_invert;
+  else if (Uplo == CblasLower && Diag == CblasUnit)
+    invert_func = gsl_linalg_tri_lower_unit_invert;
+
+  for (n = 1; n <= N_max; ++n)
+    {
+      gsl_matrix *T = gsl_matrix_alloc(n, n);
+      gsl_matrix *B = gsl_matrix_alloc(n, n);
+
+      /* generate random triangular matrix */
+      create_tri_matrix(Uplo, Diag, T, r);
+
+      /* compute B = T^{-1} */
+      gsl_matrix_memcpy(B, T);
+      (invert_func)(B);
+
+      /* compute B = T * T^{-1} */
+      gsl_blas_dtrmm(CblasLeft, Uplo, CblasNoTrans, Diag, 1.0, T, B);
+
+      /* test B = I */
+      for (i = 0; i < n; ++i)
+        {
+          for (j = 0; j < n; ++j)
+            {
+              double Bij = gsl_matrix_get(B, i, j);
+              double expected = (i == j) ? 1.0 : 0.0;
+
+              gsl_test_rel(Bij, expected, tol, "tri_invert N=%zu %s %s",
+                           n,
+                           (Uplo == CblasUpper) ? "Upper" : "Lower",
+                           (Diag == CblasNonUnit) ? "NonUnit" : "Unit");
+            }
+        }
+
+      gsl_matrix_free(T);
+      gsl_matrix_free(B);
+    }
+
+  return s;
+}
+
+int
+test_tri_invert(gsl_rng * r)
+{
+  int s = 0;
+
+  s += test_tri_invert2(CblasLower, CblasNonUnit, r, 1.0e-10);
+  s += test_tri_invert2(CblasLower, CblasUnit, r, 1.0e-10);
+
+  s += test_tri_invert2(CblasUpper, CblasNonUnit, r, 1.0e-10);
+  s += test_tri_invert2(CblasUpper, CblasUnit, r, 1.0e-10);
+
+  return s;
+}
+
 void
 my_error_handler (const char *reason, const char *file, int line, int err)
 {
   if (1) printf ("(caught [%s:%d: %s (%d)])\n", file, line, reason, err) ;
 }
 
-int main(void)
+int
+main(void)
 {
+  gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+
   gsl_ieee_env_setup ();
   gsl_set_error_handler (&my_error_handler);
 
@@ -4307,6 +4804,9 @@
   gsl_test(test_matmult(),               "Matrix Multiply"); 
   gsl_test(test_matmult_mod(),           "Matrix Multiply with Modification"); 
 #endif
+
+  gsl_test(test_tri_invert(r),           "Triangular Inverse");
+
   gsl_test(test_bidiag_decomp(),         "Bidiagonal Decomposition");
   gsl_test(test_LU_solve(),              "LU Decomposition and Solve");
   gsl_test(test_LUc_solve(),             "Complex LU Decomposition and Solve");
@@ -4326,17 +4826,32 @@
   gsl_test(test_QR_lssolve(),            "QR LS Solve");
   gsl_test(test_QR_update(),             "QR Rank-1 Update");
   gsl_test(test_QRPT_decomp(),           "QRPT Decomposition");
+  gsl_test(test_QRPT_lssolve(),          "QRPT LS Solve");
+  gsl_test(test_QRPT_lssolve2(),         "QRPT LS Solve 2");
   gsl_test(test_QRPT_solve(),            "QRPT Solve");
   gsl_test(test_QRPT_QRsolve(),          "QRPT QR Solve");
   gsl_test(test_QRPT_update(),           "QRPT Rank-1 Update");
+
+  gsl_test(test_COD_decomp(),            "COD Decomposition");
+  gsl_test(test_COD_lssolve(),           "COD LS Solve");
+
   gsl_test(test_SV_decomp(),             "Singular Value Decomposition");
-  gsl_test(test_SV_decomp_jacobi(),        "Singular Value Decomposition (Jacobi)");
+  gsl_test(test_SV_decomp_jacobi(),      "Singular Value Decomposition (Jacobi)");
   gsl_test(test_SV_decomp_mod(),         "Singular Value Decomposition (Mod)");
   gsl_test(test_SV_solve(),              "SVD Solve");
-  gsl_test(test_cholesky_decomp(),       "Cholesky Decomposition");
+
   gsl_test(test_cholesky_decomp_unit(),  "Cholesky Decomposition [unit triangular]");
   gsl_test(test_cholesky_solve(),        "Cholesky Solve");
-  gsl_test(test_cholesky_invert(),       "Cholesky Inverse");
+
+  gsl_test(test_cholesky_decomp(r),      "Cholesky Decomposition");
+  gsl_test(test_cholesky_invert(r),      "Cholesky Inverse");
+  gsl_test(test_pcholesky_decomp(r),     "Pivoted Cholesky Decomposition");
+  gsl_test(test_pcholesky_solve(r),      "Pivoted Cholesky Solve");
+  gsl_test(test_pcholesky_invert(r),     "Pivoted Cholesky Inverse");
+  gsl_test(test_mcholesky_decomp(r),     "Modified Cholesky Decomposition");
+  gsl_test(test_mcholesky_solve(r),      "Modified Cholesky Solve");
+  gsl_test(test_mcholesky_invert(r),     "Modified Cholesky Inverse");
+
   gsl_test(test_choleskyc_decomp(),      "Complex Cholesky Decomposition");
   gsl_test(test_choleskyc_solve(),       "Complex Cholesky Solve");
   gsl_test(test_choleskyc_invert(),      "Complex Cholesky Inverse");
@@ -4386,5 +4901,7 @@
 
   gsl_matrix_free (bigsparse);
 
+  gsl_rng_free(r);
+
   exit (gsl_test_summary());
 }
diff -Nru gsl-doc-1.16/linalg/test_cholesky.c gsl-doc-2.3/linalg/test_cholesky.c
--- gsl-doc-1.16/linalg/test_cholesky.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/linalg/test_cholesky.c	2016-12-07 17:40:50.000000000 +0000
@@ -0,0 +1,955 @@
+/* linalg/test_cholesky.c
+ *
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <gsl/gsl_test.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_ieee_utils.h>
+#include <gsl/gsl_permute_vector.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_permutation.h>
+
+static int create_random_vector(gsl_vector * v, gsl_rng * r);
+static int create_posdef_matrix(gsl_matrix * m, gsl_rng * r);
+static int create_hilbert_matrix2(gsl_matrix * m);
+
+static int test_cholesky_decomp_eps(const int scale, const gsl_matrix * m,
+                                    const double expected_rcond, const double eps,
+                                    const char * desc);
+static int test_cholesky_decomp(gsl_rng * r);
+int test_cholesky_invert_eps(const gsl_matrix * m, const double eps, const char *desc);
+int test_cholesky_invert(gsl_rng * r);
+static int test_pcholesky_decomp_eps(const int scale, const gsl_matrix * m,
+                                     const double expected_rcond, const double eps,
+                                     const char * desc);
+static int test_pcholesky_decomp(gsl_rng * r);
+int test_pcholesky_solve_eps(const int scale, const gsl_matrix * m, const gsl_vector * rhs,
+                             const gsl_vector * sol, const double eps,
+                             const char * desc);
+static int test_pcholesky_solve(gsl_rng * r);
+int test_pcholesky_invert_eps(const gsl_matrix * m, const double eps, const char *desc);
+int test_pcholesky_invert(gsl_rng * r);
+
+static int test_mcholesky_decomp_eps(const int posdef, const int scale, const gsl_matrix * m,
+                                     const double expected_rcond, const double eps, const char * desc);
+
+/* Hilbert matrix condition numbers, as calculated by LAPACK DPOSVX */
+double hilb_rcond[] = { 1.000000000000e+00, 3.703703703704e-02, 1.336898395722e-03,
+                        3.524229074890e-05, 1.059708198754e-06, 3.439939465186e-08,
+                        1.015027593823e-09, 2.952221630602e-11, 9.093751565191e-13,
+                        2.828277420229e-14, 8.110242564869e-16, 2.409320075800e-17 };
+
+static int
+create_random_vector(gsl_vector * v, gsl_rng * r)
+{
+  const size_t N = v->size;
+  size_t i;
+
+  for (i = 0; i < N; ++i)
+    {
+      double vi = gsl_rng_uniform(r);
+      gsl_vector_set(v, i, vi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+create_symm_matrix(gsl_matrix * m, gsl_rng * r)
+{
+  const size_t N = m->size1;
+  size_t i, j;
+
+  for (i = 0; i < N; ++i)
+    {
+      for (j = 0; j <= i; ++j)
+        {
+          double mij = gsl_rng_uniform(r);
+          gsl_matrix_set(m, i, j, mij);
+        }
+    }
+
+  /* copy lower triangle to upper */
+  gsl_matrix_transpose_tricpy('L', 0, m, m);
+
+  return GSL_SUCCESS;
+}
+
+static int
+create_posdef_matrix(gsl_matrix * m, gsl_rng * r)
+{
+  const size_t N = m->size1;
+  const double alpha = 10.0 * N;
+  size_t i;
+
+  /* The idea is to make a symmetric diagonally dominant
+   * matrix. Make a symmetric matrix and add alpha*I to
+   * its diagonal */
+
+  create_symm_matrix(m, r);
+
+  for (i = 0; i < N; ++i)
+    {
+      double mii = gsl_matrix_get(m, i, i);
+      gsl_matrix_set(m, i, i, mii + alpha);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+create_hilbert_matrix2(gsl_matrix * m)
+{
+  const size_t N = m->size1;
+  size_t i, j;
+
+  for (i = 0; i < N; i++)
+    {
+      for (j = 0; j < N; j++)
+        {
+          gsl_matrix_set(m, i, j, 1.0/(i+j+1.0));
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+test_cholesky_decomp_eps(const int scale, const gsl_matrix * m,
+                         const double expected_rcond, const double eps,
+                         const char * desc)
+{
+  int s = 0;
+  size_t i, j, N = m->size2;
+
+  gsl_matrix * V  = gsl_matrix_alloc(N, N);
+  gsl_matrix * A  = gsl_matrix_alloc(N, N);
+  gsl_matrix * L  = gsl_matrix_calloc(N, N);
+  gsl_matrix * LT = gsl_matrix_calloc(N, N);
+  gsl_vector * S = gsl_vector_alloc(N);
+
+  gsl_matrix_memcpy(V, m);
+
+  if (scale)
+    s += gsl_linalg_cholesky_decomp2(V, S);
+  else
+    s += gsl_linalg_cholesky_decomp1(V);
+
+  /* compute L and LT */
+  gsl_matrix_tricpy('L', 1, L, V);
+  gsl_matrix_transpose_tricpy('L', 1, LT, L);
+  
+  if (scale)
+    {
+      /* L <- S^{-1} L, LT <- LT S^{-1} */
+      for (i = 0; i < N; ++i)
+        {
+          double Si = gsl_vector_get(S, i);
+          gsl_vector_view v = gsl_matrix_row(L, i);
+          gsl_vector_view w = gsl_matrix_column(LT, i);
+
+          gsl_vector_scale(&v.vector, 1.0 / Si);
+          gsl_vector_scale(&w.vector, 1.0 / Si);
+        }
+    }
+            
+  /* compute A = L LT */
+  gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, L, LT, 0.0, A);
+
+  for (i = 0; i < N; i++)
+    {
+      for (j = 0; j < N; j++)
+        {
+          double Aij = gsl_matrix_get(A, i, j);
+          double mij = gsl_matrix_get(m, i, j);
+
+          gsl_test_rel(Aij, mij, eps,
+                       "%s: (%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n",
+                       desc, N, N, i, j, Aij, mij);
+        }
+    }
+
+  if (expected_rcond > 0 && !scale)
+    {
+      gsl_vector *work = gsl_vector_alloc(3 * N);
+      double rcond;
+
+      gsl_linalg_cholesky_rcond(V, &rcond, work);
+
+      gsl_test_rel(rcond, expected_rcond, 1.0e-6,
+                   "%s rcond: (%3lu,%3lu): %22.18g   %22.18g\n",
+                   desc, N, N, rcond, expected_rcond);
+
+      gsl_vector_free(work);
+    }
+
+  gsl_matrix_free(V);
+  gsl_matrix_free(A);
+  gsl_matrix_free(L);
+  gsl_matrix_free(LT);
+  gsl_vector_free(S);
+
+  return s;
+}
+
+static int
+test_cholesky_decomp(gsl_rng * r)
+{
+  int s = 0;
+  const size_t N_max = 50;
+  size_t N;
+
+  for (N = 1; N <= N_max; ++N)
+    {
+      gsl_matrix * m = gsl_matrix_alloc(N, N);
+
+      create_posdef_matrix(m, r);
+      test_cholesky_decomp_eps(0, m, -1.0, 10.0 * N * GSL_DBL_EPSILON, "cholesky_decomp unscaled random");
+      test_cholesky_decomp_eps(1, m, -1.0, 20.0 * N * GSL_DBL_EPSILON, "cholesky_decomp scaled random");
+
+      if (N <= 12)
+        {
+          double expected_rcond = -1.0;
+          
+          if (hilb_rcond[N - 1] > 1.0e-12)
+            expected_rcond = hilb_rcond[N - 1];
+
+          create_hilbert_matrix2(m);
+
+          test_cholesky_decomp_eps(0, m, expected_rcond, GSL_DBL_EPSILON, "cholesky_decomp unscaled hilbert");
+          test_cholesky_decomp_eps(1, m, expected_rcond, N * GSL_DBL_EPSILON, "cholesky_decomp scaled hilbert");
+        }
+
+      gsl_matrix_free(m);
+    }
+
+  return s;
+}
+
+int
+test_cholesky_invert_eps(const gsl_matrix * m, const double eps, const char *desc)
+{
+  int s = 0;
+  size_t i, j, N = m->size1;
+
+  gsl_matrix * v  = gsl_matrix_alloc(N, N);
+  gsl_matrix * c  = gsl_matrix_alloc(N, N);
+
+  gsl_matrix_memcpy(v, m);
+
+  s += gsl_linalg_cholesky_decomp1(v);
+  s += gsl_linalg_cholesky_invert(v);
+
+  /* c = m m^{-1} */
+  gsl_blas_dsymm(CblasLeft, CblasUpper, 1.0, m, v, 0.0, c);
+
+  /* c should be the identity matrix */
+
+  for (i = 0; i < N; ++i)
+    {
+      for (j = 0; j < N; ++j)
+        {
+          double cij = gsl_matrix_get(c, i, j);
+          double expected = (i == j) ? 1.0 : 0.0;
+
+          gsl_test_rel(cij, expected, eps, "%s (%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n",
+                       desc, N, N, i, j, cij, expected);
+        }
+    }
+
+  gsl_matrix_free(v);
+  gsl_matrix_free(c);
+
+  return s;
+}
+
+int
+test_cholesky_invert(gsl_rng * r)
+{
+  int s = 0;
+  const size_t N_max = 50;
+  size_t N;
+
+  for (N = 1; N <= N_max; ++N)
+    {
+      gsl_matrix * m = gsl_matrix_alloc(N, N);
+
+      create_posdef_matrix(m, r);
+
+      test_cholesky_invert_eps(m, N * GSL_DBL_EPSILON, "cholesky_invert unscaled random");
+
+      if (N <= 4)
+        {
+          create_hilbert_matrix2(m);
+          test_cholesky_invert_eps(m, N * 256.0 * GSL_DBL_EPSILON, "cholesky_invert unscaled hilbert");
+        }
+
+      gsl_matrix_free(m);
+    }
+
+  return s;
+}
+
+static int
+test_mcholesky_decomp_eps(const int posdef, const int scale, const gsl_matrix * m,
+                          const double expected_rcond, const double eps, const char * desc)
+{
+  int s = 0;
+  size_t i, j, N = m->size2;
+
+  gsl_matrix * LDLT = gsl_matrix_alloc(N, N);
+  gsl_matrix * V  = gsl_matrix_alloc(N, N);
+  gsl_matrix * A  = gsl_matrix_alloc(N, N);
+  gsl_matrix * L  = gsl_matrix_alloc(N, N);
+  gsl_matrix * LT = gsl_matrix_alloc(N, N);
+  gsl_vector * S = gsl_vector_alloc(N);
+  gsl_vector * E = gsl_vector_alloc(N);
+  gsl_permutation * perm = gsl_permutation_alloc(N);
+
+  gsl_vector_view D = gsl_matrix_diagonal(LDLT);
+
+  gsl_matrix_memcpy(LDLT, m);
+  s += gsl_linalg_mcholesky_decomp(LDLT, perm, E);
+
+  /* check that the upper triangle of LDLT equals original matrix */
+  for (i = 0; i < N; ++i)
+    {
+      for (j = i + 1; j < N; ++j)
+        {
+          double mij = gsl_matrix_get(m, i, j);
+          double aij = gsl_matrix_get(LDLT, i, j);
+
+          gsl_test_rel(aij, mij, 1.0e-12,
+                       "%s upper triangle: (%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n",
+                       desc, N, N, i, j, aij, mij);
+        }
+    }
+
+  if (posdef)
+    {
+      /* ||E|| should be 0 */
+      double norm = gsl_blas_dnrm2(E);
+      s = norm != 0.0;
+      gsl_test(s, "%s: (%zu,%zu): ||E|| = %.12e",
+               desc, N, N, norm);
+
+      /* check that D is decreasing */
+      s = 0;
+      for (i = 1; i < N; ++i)
+        {
+          double dprev = gsl_vector_get(&D.vector, i - 1);
+          double di = gsl_vector_get(&D.vector, i);
+
+          if (di > dprev)
+            s = 1;
+        }
+
+      gsl_test(s, "%s: (%zu,%zu): D is not decreasing",
+               desc, N, N);
+    }
+  
+  /* compute L and LT */
+  gsl_matrix_set_identity(L);
+  gsl_matrix_set_identity(LT);
+
+  gsl_matrix_tricpy('L', 0, L, LDLT);
+  gsl_matrix_transpose_tricpy('L', 0, LT, L);
+
+  /* compute (L sqrt(D)) and (sqrt(D) LT) */
+  for (i = 0; i < N; ++i)
+    {
+      gsl_vector_view v = gsl_matrix_column(L, i);
+      gsl_vector_view w = gsl_matrix_row(LT, i);
+      double di = gsl_vector_get(&D.vector, i);
+
+      gsl_vector_scale(&v.vector, sqrt(di));
+      gsl_vector_scale(&w.vector, sqrt(di));
+    }
+
+  /* compute A = L D LT */
+  gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, L, LT, 0.0, A);
+
+  /* compute V = P (S M S + E) P^T */
+
+  gsl_matrix_memcpy(V, m);
+  D = gsl_matrix_diagonal(V);
+
+  /* compute S M S */
+  if (scale)
+    {
+      gsl_linalg_cholesky_scale_apply(V, S);
+      gsl_matrix_transpose_tricpy('L', 0, V, V);
+    }
+
+  /* compute S M S + E */
+  gsl_vector_add(&D.vector, E);
+
+  /* compute M P^T */
+  for (i = 0; i < N; ++i)
+    {
+      gsl_vector_view v = gsl_matrix_row(V, i);
+      gsl_permute_vector(perm, &v.vector);
+    }
+
+  /* compute P M P^T */
+  for (i = 0; i < N; ++i)
+    {
+      gsl_vector_view v = gsl_matrix_column(V, i);
+      gsl_permute_vector(perm, &v.vector);
+    }
+
+  for (i = 0; i < N; i++)
+    {
+      double Ei = gsl_vector_get(E, i);
+
+      for (j = 0; j < N; j++)
+        {
+          double Aij = gsl_matrix_get(A, i, j); /* L D L^T */
+          double Bij = gsl_matrix_get(V, i, j); /* P M P^T */
+          double Cij;                           /* P M P^T + E */
+
+          if (i == j)
+            Cij = Bij + Ei*0;
+          else
+            Cij = Bij;
+
+          gsl_test_rel(Aij, Cij, eps,
+                       "%s: (%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n",
+                       desc, N, N, i, j, Aij, Cij);
+        }
+    }
+
+  if (expected_rcond > 0 && !scale)
+    {
+      gsl_vector *work = gsl_vector_alloc(3 * N);
+      double rcond;
+
+      gsl_linalg_mcholesky_rcond(LDLT, perm, &rcond, work);
+
+      gsl_test_rel(rcond, expected_rcond, 1.0e-6,
+                   "%s rcond: (%3lu,%3lu): %22.18g   %22.18g\n",
+                   desc, N, N, rcond, expected_rcond);
+
+      gsl_vector_free(work);
+    }
+
+  gsl_matrix_free(LDLT);
+  gsl_matrix_free(V);
+  gsl_matrix_free(A);
+  gsl_matrix_free(L);
+  gsl_matrix_free(LT);
+  gsl_vector_free(S);
+  gsl_vector_free(E);
+  gsl_permutation_free(perm);
+
+  return s;
+}
+
+static int
+test_mcholesky_decomp(gsl_rng * r)
+{
+  int s = 0;
+  const size_t N_max = 50;
+  size_t N;
+
+  for (N = 1; N <= N_max; ++N)
+    {
+      gsl_matrix * m = gsl_matrix_alloc(N, N);
+
+      create_posdef_matrix(m, r);
+      test_mcholesky_decomp_eps(1, 0, m, -1.0, 128.0 * N * GSL_DBL_EPSILON, "mcholesky_decomp unscaled random posdef");
+
+      create_symm_matrix(m, r);
+      test_mcholesky_decomp_eps(0, 0, m, -1.0, 8192.0 * N * GSL_DBL_EPSILON, "mcholesky_decomp unscaled random symm");
+
+      if (N <= 8)
+        {
+          double expected_rcond = -1.0;
+          
+          if (hilb_rcond[N - 1] > 1.0e-12)
+            expected_rcond = hilb_rcond[N - 1];
+
+          create_hilbert_matrix2(m);
+
+          test_mcholesky_decomp_eps(1, 0, m, expected_rcond, N * GSL_DBL_EPSILON, "mcholesky_decomp unscaled hilbert");
+        }
+
+      gsl_matrix_free(m);
+    }
+
+  return s;
+}
+
+int
+test_mcholesky_solve_eps(const gsl_matrix * m, const gsl_vector * rhs,
+                         const gsl_vector * sol, const double eps,
+                         const char * desc)
+{
+  int s = 0;
+  size_t i, N = m->size1;
+  gsl_matrix * u  = gsl_matrix_alloc(N, N);
+  gsl_vector * x = gsl_vector_calloc(N);
+  gsl_vector * S = gsl_vector_alloc(N);
+  gsl_permutation * perm = gsl_permutation_alloc(N);
+
+  gsl_matrix_memcpy(u, m);
+
+  s += gsl_linalg_mcholesky_decomp(u, perm, NULL);
+  s += gsl_linalg_mcholesky_solve(u, perm, rhs, x);
+
+  for (i = 0; i < N; i++)
+    {
+      double xi = gsl_vector_get(x, i);
+      double yi = gsl_vector_get(sol, i);
+
+      gsl_test_rel(xi, yi, eps,
+                   "%s: %3lu[%lu]: %22.18g   %22.18g\n",
+                   desc, N, i, xi, yi);
+    }
+
+  gsl_vector_free(x);
+  gsl_vector_free(S);
+  gsl_matrix_free(u);
+  gsl_permutation_free(perm);
+
+  return s;
+}
+
+static int
+test_mcholesky_solve(gsl_rng * r)
+{
+  int s = 0;
+  const size_t N_max = 50;
+  size_t N;
+
+  for (N = 1; N <= N_max; ++N)
+    {
+      gsl_matrix * m = gsl_matrix_alloc(N, N);
+      gsl_vector * rhs = gsl_vector_alloc(N);
+      gsl_vector * sol = gsl_vector_alloc(N);
+
+      create_posdef_matrix(m, r);
+      create_random_vector(sol, r);
+      gsl_blas_dsymv(CblasLower, 1.0, m, sol, 0.0, rhs);
+
+      test_mcholesky_solve_eps(m, rhs, sol, 64.0 * N * GSL_DBL_EPSILON, "mcholesky_solve random");
+
+      if (N <= 3)
+        {
+          create_hilbert_matrix2(m);
+          gsl_blas_dsymv(CblasLower, 1.0, m, sol, 0.0, rhs);
+          test_mcholesky_solve_eps(m, rhs, sol, 512.0 * N * GSL_DBL_EPSILON, "mcholesky_solve hilbert");
+        }
+
+      gsl_matrix_free(m);
+      gsl_vector_free(rhs);
+      gsl_vector_free(sol);
+    }
+
+  return s;
+}
+
+int
+test_mcholesky_invert_eps(const gsl_matrix * m, const double eps, const char *desc)
+{
+  int s = 0;
+  size_t i, j, N = m->size1;
+
+  gsl_matrix * v  = gsl_matrix_alloc(N, N);
+  gsl_matrix * c  = gsl_matrix_alloc(N, N);
+  gsl_matrix * minv = gsl_matrix_alloc(N, N);
+  gsl_vector * E = gsl_vector_alloc(N);
+  gsl_permutation * p = gsl_permutation_alloc(N);
+
+  gsl_matrix_memcpy(v, m);
+
+  s += gsl_linalg_mcholesky_decomp(v, p, E);
+  s += gsl_linalg_mcholesky_invert(v, p, minv);
+
+  /* c = m m^{-1} */
+  gsl_blas_dsymm(CblasLeft, CblasUpper, 1.0, m, minv, 0.0, c);
+
+  /* c should be the identity matrix */
+
+  for (i = 0; i < N; ++i)
+    {
+      for (j = 0; j < N; ++j)
+        {
+          double cij = gsl_matrix_get(c, i, j);
+          double expected = (i == j) ? 1.0 : 0.0;
+
+          gsl_test_rel(cij, expected, eps, "%s (%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n",
+                       desc, N, N, i, j, cij, expected);
+        }
+    }
+
+  gsl_matrix_free(v);
+  gsl_matrix_free(c);
+  gsl_matrix_free(minv);
+  gsl_vector_free(E);
+  gsl_permutation_free(p);
+
+  return s;
+}
+
+int
+test_mcholesky_invert(gsl_rng * r)
+{
+  int s = 0;
+  const size_t N_max = 30;
+  size_t N;
+
+  for (N = 1; N <= N_max; ++N)
+    {
+      gsl_matrix * m = gsl_matrix_alloc(N, N);
+
+      create_posdef_matrix(m, r);
+      test_mcholesky_invert_eps(m, N * GSL_DBL_EPSILON, "mcholesky_invert unscaled random");
+
+      if (N <= 4)
+        {
+          create_hilbert_matrix2(m);
+          test_mcholesky_invert_eps(m, 256.0 * N * GSL_DBL_EPSILON, "mcholesky_invert unscaled hilbert");
+        }
+
+      gsl_matrix_free(m);
+    }
+
+  return s;
+}
+
+static int
+test_pcholesky_decomp_eps(const int scale, const gsl_matrix * m,
+                          const double expected_rcond, const double eps,
+                          const char * desc)
+{
+  int s = 0;
+  size_t i, j, N = m->size2;
+
+  gsl_matrix * LDLT = gsl_matrix_alloc(N, N);
+  gsl_matrix * V  = gsl_matrix_alloc(N, N);
+  gsl_matrix * A  = gsl_matrix_alloc(N, N);
+  gsl_matrix * L  = gsl_matrix_alloc(N, N);
+  gsl_matrix * LT = gsl_matrix_alloc(N, N);
+  gsl_vector * S = gsl_vector_alloc(N);
+  gsl_permutation * perm = gsl_permutation_alloc(N);
+
+  gsl_vector_view D = gsl_matrix_diagonal(LDLT);
+
+  gsl_matrix_memcpy(LDLT, m);
+
+  if (scale)
+    s += gsl_linalg_pcholesky_decomp2(LDLT, perm, S);
+  else
+    s += gsl_linalg_pcholesky_decomp(LDLT, perm);
+
+  /* check that the upper triangle of LDLT equals original matrix */
+  for (i = 0; i < N; ++i)
+    {
+      for (j = i + 1; j < N; ++j)
+        {
+          double mij = gsl_matrix_get(m, i, j);
+          double aij = gsl_matrix_get(LDLT, i, j);
+
+          gsl_test_rel(aij, mij, 1.0e-12,
+                       "%s upper triangle: (%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n",
+                       desc, N, N, i, j, aij, mij);
+        }
+    }
+
+  /* check that D is decreasing */
+  s = 0;
+  for (i = 1; i < N; ++i)
+    {
+      double dprev = gsl_vector_get(&D.vector, i - 1);
+      double di = gsl_vector_get(&D.vector, i);
+
+      if (di > dprev)
+        s = 1;
+    }
+
+  gsl_test(s, "%s: (%zu,%zu): D is not decreasing",
+           desc, N, N);
+  
+  /* compute L and LT */
+  gsl_matrix_set_identity(L);
+  gsl_matrix_set_identity(LT);
+
+  gsl_matrix_tricpy('L', 0, L, LDLT);
+  gsl_matrix_transpose_tricpy('L', 0, LT, L);
+
+  /* compute (L sqrt(D)) and (sqrt(D) LT) */
+  for (i = 0; i < N; ++i)
+    {
+      gsl_vector_view v = gsl_matrix_column(L, i);
+      gsl_vector_view w = gsl_matrix_row(LT, i);
+      double di = gsl_vector_get(&D.vector, i);
+
+      gsl_vector_scale(&v.vector, sqrt(di));
+      gsl_vector_scale(&w.vector, sqrt(di));
+    }
+
+  /* compute A = L D LT */
+  gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, L, LT, 0.0, A);
+
+  /* compute V = P S M S P^T */
+
+  gsl_matrix_memcpy(V, m);
+
+  /* compute S M S */
+  if (scale)
+    {
+      gsl_linalg_cholesky_scale_apply(V, S);
+      gsl_matrix_transpose_tricpy('L', 0, V, V);
+    }
+
+  /* compute M P^T */
+  for (i = 0; i < N; ++i)
+    {
+      gsl_vector_view v = gsl_matrix_row(V, i);
+      gsl_permute_vector(perm, &v.vector);
+    }
+
+  /* compute P M P^T */
+  for (i = 0; i < N; ++i)
+    {
+      gsl_vector_view v = gsl_matrix_column(V, i);
+      gsl_permute_vector(perm, &v.vector);
+    }
+
+  for (i = 0; i < N; i++)
+    {
+      for (j = 0; j < N; j++)
+        {
+          double Aij = gsl_matrix_get(A, i, j); /* L D L^T */
+          double Bij = gsl_matrix_get(V, i, j); /* P M P^T */
+
+          gsl_test_rel(Aij, Bij, eps,
+                       "%s: (%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n",
+                       desc, N, N, i, j, Aij, Bij);
+        }
+    }
+
+  if (expected_rcond > 0 && !scale)
+    {
+      gsl_vector *work = gsl_vector_alloc(3 * N);
+      double rcond;
+
+      gsl_linalg_pcholesky_rcond(LDLT, perm, &rcond, work);
+
+      gsl_test_rel(rcond, expected_rcond, 1.0e-6,
+                   "%s rcond: (%3lu,%3lu): %22.18g   %22.18g\n",
+                   desc, N, N, rcond, expected_rcond);
+
+      gsl_vector_free(work);
+    }
+
+  gsl_matrix_free(LDLT);
+  gsl_matrix_free(V);
+  gsl_matrix_free(A);
+  gsl_matrix_free(L);
+  gsl_matrix_free(LT);
+  gsl_vector_free(S);
+  gsl_permutation_free(perm);
+
+  return s;
+}
+
+static int
+test_pcholesky_decomp(gsl_rng * r)
+{
+  int s = 0;
+  const size_t N_max = 50;
+  size_t N;
+
+  for (N = 1; N <= N_max; ++N)
+    {
+      gsl_matrix * m = gsl_matrix_alloc(N, N);
+
+      create_posdef_matrix(m, r);
+      test_pcholesky_decomp_eps(0, m, -1.0, 1024.0 * N * GSL_DBL_EPSILON, "pcholesky_decomp unscaled random");
+      test_pcholesky_decomp_eps(1, m, -1.0, 1024.0 * N * GSL_DBL_EPSILON, "pcholesky_decomp scaled random");
+
+      if (N <= 12)
+        {
+          double expected_rcond = -1.0;
+          
+          if (hilb_rcond[N - 1] > 1.0e-12)
+            expected_rcond = hilb_rcond[N - 1];
+
+          create_hilbert_matrix2(m);
+
+          test_pcholesky_decomp_eps(0, m, expected_rcond, N * GSL_DBL_EPSILON, "pcholesky_decomp unscaled hilbert");
+          test_pcholesky_decomp_eps(1, m, expected_rcond, N * GSL_DBL_EPSILON, "pcholesky_decomp scaled hilbert");
+        }
+
+      gsl_matrix_free(m);
+    }
+
+  return s;
+}
+
+int
+test_pcholesky_solve_eps(const int scale, const gsl_matrix * m, const gsl_vector * rhs,
+                         const gsl_vector * sol, const double eps,
+                         const char * desc)
+{
+  int s = 0;
+  size_t i, N = m->size1;
+  gsl_matrix * u  = gsl_matrix_alloc(N, N);
+  gsl_vector * x = gsl_vector_calloc(N);
+  gsl_vector * S = gsl_vector_alloc(N);
+  gsl_permutation * perm = gsl_permutation_alloc(N);
+
+  gsl_matrix_memcpy(u, m);
+
+  if (scale)
+    {
+      s += gsl_linalg_pcholesky_decomp2(u, perm, S);
+      s += gsl_linalg_pcholesky_solve2(u, perm, S, rhs, x);
+    }
+  else
+    {
+      s += gsl_linalg_pcholesky_decomp(u, perm);
+      s += gsl_linalg_pcholesky_solve(u, perm, rhs, x);
+    }
+
+  for (i = 0; i < N; i++)
+    {
+      double xi = gsl_vector_get(x, i);
+      double yi = gsl_vector_get(sol, i);
+
+      gsl_test_rel(xi, yi, eps,
+                   "%s: %3lu[%lu]: %22.18g   %22.18g\n",
+                   desc, N, i, xi, yi);
+    }
+
+  gsl_vector_free(x);
+  gsl_vector_free(S);
+  gsl_matrix_free(u);
+  gsl_permutation_free(perm);
+
+  return s;
+}
+
+static int
+test_pcholesky_solve(gsl_rng * r)
+{
+  int s = 0;
+  const size_t N_max = 50;
+  size_t N;
+
+  for (N = 1; N <= N_max; ++N)
+    {
+      gsl_matrix * m = gsl_matrix_alloc(N, N);
+      gsl_vector * rhs = gsl_vector_alloc(N);
+      gsl_vector * sol = gsl_vector_alloc(N);
+
+      create_posdef_matrix(m, r);
+      create_random_vector(sol, r);
+      gsl_blas_dsymv(CblasLower, 1.0, m, sol, 0.0, rhs);
+
+      test_pcholesky_solve_eps(0, m, rhs, sol, 64.0 * N * GSL_DBL_EPSILON, "pcholesky_solve unscaled random");
+      test_pcholesky_solve_eps(1, m, rhs, sol, 64.0 * N * GSL_DBL_EPSILON, "pcholesky_solve scaled random");
+
+      if (N <= 4)
+        {
+          create_hilbert_matrix2(m);
+          gsl_blas_dsymv(CblasLower, 1.0, m, sol, 0.0, rhs);
+          test_pcholesky_solve_eps(0, m, rhs, sol, 1024.0 * N * GSL_DBL_EPSILON, "pcholesky_solve unscaled hilbert");
+          test_pcholesky_solve_eps(1, m, rhs, sol, 2048.0 * N * GSL_DBL_EPSILON, "pcholesky_solve scaled hilbert");
+        }
+
+      gsl_matrix_free(m);
+      gsl_vector_free(rhs);
+      gsl_vector_free(sol);
+    }
+
+  return s;
+}
+
+int
+test_pcholesky_invert_eps(const gsl_matrix * m, const double eps, const char *desc)
+{
+  int s = 0;
+  size_t i, j, N = m->size1;
+
+  gsl_matrix * v  = gsl_matrix_alloc(N, N);
+  gsl_matrix * c  = gsl_matrix_alloc(N, N);
+  gsl_matrix * minv = gsl_matrix_alloc(N, N);
+  gsl_permutation * p = gsl_permutation_alloc(N);
+
+  gsl_matrix_memcpy(v, m);
+
+  s += gsl_linalg_pcholesky_decomp(v, p);
+  s += gsl_linalg_pcholesky_invert(v, p, minv);
+
+  /* c = m m^{-1} */
+  gsl_blas_dsymm(CblasLeft, CblasUpper, 1.0, m, minv, 0.0, c);
+
+  /* c should be the identity matrix */
+
+  for (i = 0; i < N; ++i)
+    {
+      for (j = 0; j < N; ++j)
+        {
+          double cij = gsl_matrix_get(c, i, j);
+          double expected = (i == j) ? 1.0 : 0.0;
+
+          gsl_test_rel(cij, expected, eps, "%s (%3lu,%3lu)[%lu,%lu]: %22.18g   %22.18g\n",
+                       desc, N, N, i, j, cij, expected);
+        }
+    }
+
+  gsl_matrix_free(v);
+  gsl_matrix_free(c);
+  gsl_matrix_free(minv);
+  gsl_permutation_free(p);
+
+  return s;
+}
+
+int
+test_pcholesky_invert(gsl_rng * r)
+{
+  int s = 0;
+  const size_t N_max = 30;
+  size_t N;
+
+  for (N = 1; N <= N_max; ++N)
+    {
+      gsl_matrix * m = gsl_matrix_alloc(N, N);
+
+      create_posdef_matrix(m, r);
+      test_pcholesky_invert_eps(m, N * GSL_DBL_EPSILON, "pcholesky_invert unscaled random");
+
+      if (N <= 4)
+        {
+          create_hilbert_matrix2(m);
+          test_pcholesky_invert_eps(m, 256.0 * N * GSL_DBL_EPSILON, "pcholesky_invert unscaled hilbert");
+        }
+
+      gsl_matrix_free(m);
+    }
+
+  return s;
+}
diff -Nru gsl-doc-1.16/linalg/TODO gsl-doc-2.3/linalg/TODO
--- gsl-doc-1.16/linalg/TODO	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/TODO	2016-08-10 21:03:42.000000000 +0000
@@ -11,5 +11,3 @@
 
    TAUCS is a C library of sparse linear solvers.
     http://www.tau.ac.il/~stoledo/taucs/
-
-
diff -Nru gsl-doc-1.16/linalg/tridiag.c gsl-doc-2.3/linalg/tridiag.c
--- gsl-doc-1.16/linalg/tridiag.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/linalg/tridiag.c	2015-11-03 16:21:55.000000000 +0000
@@ -234,6 +234,11 @@
       if (N == 1) 
         {
           x[0] = b[0] / diag[0];
+          free(delta);
+          free(gamma);
+          free(alpha);
+          free(c);
+          free(z);
           return GSL_SUCCESS;
         }
 
diff -Nru gsl-doc-1.16/Makefile.am gsl-doc-2.3/Makefile.am
--- gsl-doc-1.16/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/Makefile.am	2016-07-07 20:36:10.000000000 +0000
@@ -2,9 +2,9 @@
 
 # AUTOMAKE_OPTIONS = readme-alpha
 
-SUBDIRS = gsl utils sys test err const complex cheb block vector matrix permutation combination multiset sort ieee-utils cblas blas linalg eigen specfunc dht qrng rng randist fft poly fit multifit statistics siman sum integration interpolation histogram ode-initval ode-initval2 roots multiroots min multimin monte ntuple diff deriv cdf wavelet bspline doc
+SUBDIRS = gsl utils sys test err const complex cheb block vector matrix permutation combination multiset sort ieee-utils cblas blas linalg eigen specfunc dht qrng rng randist fft poly fit multifit multifit_nlinear multilarge multilarge_nlinear rstat statistics siman sum integration interpolation histogram ode-initval ode-initval2 roots multiroots min multimin monte ntuple diff deriv cdf wavelet bspline spblas spmatrix splinalg doc
 
-SUBLIBS = block/libgslblock.la blas/libgslblas.la bspline/libgslbspline.la complex/libgslcomplex.la cheb/libgslcheb.la dht/libgsldht.la diff/libgsldiff.la deriv/libgslderiv.la eigen/libgsleigen.la err/libgslerr.la fft/libgslfft.la fit/libgslfit.la histogram/libgslhistogram.la ieee-utils/libgslieeeutils.la integration/libgslintegration.la interpolation/libgslinterpolation.la linalg/libgsllinalg.la matrix/libgslmatrix.la min/libgslmin.la monte/libgslmonte.la multifit/libgslmultifit.la multimin/libgslmultimin.la multiroots/libgslmultiroots.la ntuple/libgslntuple.la ode-initval/libgslodeiv.la ode-initval2/libgslodeiv2.la permutation/libgslpermutation.la combination/libgslcombination.la multiset/libgslmultiset.la poly/libgslpoly.la qrng/libgslqrng.la randist/libgslrandist.la rng/libgslrng.la roots/libgslroots.la siman/libgslsiman.la sort/libgslsort.la specfunc/libgslspecfunc.la statistics/libgslstatistics.la sum/libgslsum.la sys/libgslsys.la test/libgsltest.la utils/libutils.la vector/libgslvector.la cdf/libgslcdf.la wavelet/libgslwavelet.la
+SUBLIBS = block/libgslblock.la blas/libgslblas.la bspline/libgslbspline.la complex/libgslcomplex.la cheb/libgslcheb.la dht/libgsldht.la diff/libgsldiff.la deriv/libgslderiv.la eigen/libgsleigen.la err/libgslerr.la fft/libgslfft.la fit/libgslfit.la histogram/libgslhistogram.la ieee-utils/libgslieeeutils.la integration/libgslintegration.la interpolation/libgslinterpolation.la linalg/libgsllinalg.la matrix/libgslmatrix.la min/libgslmin.la monte/libgslmonte.la multifit/libgslmultifit.la multifit_nlinear/libgslmultifit_nlinear.la multilarge/libgslmultilarge.la multilarge_nlinear/libgslmultilarge_nlinear.la multimin/libgslmultimin.la multiroots/libgslmultiroots.la ntuple/libgslntuple.la ode-initval/libgslodeiv.la ode-initval2/libgslodeiv2.la permutation/libgslpermutation.la combination/libgslcombination.la multiset/libgslmultiset.la poly/libgslpoly.la qrng/libgslqrng.la randist/libgslrandist.la rng/libgslrng.la roots/libgslroots.la siman/libgslsiman.la sort/libgslsort.la specfunc/libgslspecfunc.la rstat/libgslrstat.la statistics/libgslstatistics.la sum/libgslsum.la sys/libgslsys.la test/libgsltest.la utils/libutils.la vector/libgslvector.la cdf/libgslcdf.la wavelet/libgslwavelet.la spmatrix/libgslspmatrix.la spblas/libgslspblas.la splinalg/libgslsplinalg.la
 
 pkginclude_HEADERS = gsl_math.h gsl_pow_int.h gsl_nan.h gsl_machine.h gsl_mode.h gsl_precision.h gsl_types.h gsl_version.h gsl_minmax.h gsl_inline.h
 
@@ -19,16 +19,10 @@
 
 lib_LTLIBRARIES = libgsl.la
 libgsl_la_SOURCES = version.c
-libgsl_la_LIBADD = $(SUBLIBS)
-libgsl_la_LDFLAGS = -version-info $(GSL_LT_VERSION)
+libgsl_la_LIBADD = $(GSL_LIBADD) $(SUBLIBS)
+libgsl_la_LDFLAGS = $(GSL_LDFLAGS) -version-info $(GSL_LT_VERSION)
 noinst_HEADERS = templates_on.h templates_off.h build.h
 
-MINGW32_HOST = @MINGW32_HOST@
-if MINGW32_HOST
-libgsl_la_LIBADD += cblas/libgslcblas.la
-libgsl_la_LDFLAGS += -no-undefined
-endif
-
 m4datadir = $(datadir)/aclocal
 m4data_DATA = gsl.m4
 
diff -Nru gsl-doc-1.16/Makefile.in gsl-doc-2.3/Makefile.in
--- gsl-doc-1.16/Makefile.in	2013-07-19 15:14:52.000000000 +0000
+++ gsl-doc-2.3/Makefile.in	2016-12-09 00:04:20.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -84,8 +84,6 @@
 POST_UNINSTALL = :
 build_triplet = @build@
 host_triplet = @host@
-@MINGW32_HOST_TRUE@am__append_1 = cblas/libgslcblas.la
-@MINGW32_HOST_TRUE@am__append_2 = -no-undefined
 bin_PROGRAMS = gsl-randist$(EXEEXT) gsl-histogram$(EXEEXT)
 subdir = .
 DIST_COMMON = INSTALL NEWS README AUTHORS ChangeLog \
@@ -136,7 +134,8 @@
 	"$(DESTDIR)$(bindir)" "$(DESTDIR)$(m4datadir)" \
 	"$(DESTDIR)$(pkgconfigdir)" "$(DESTDIR)$(pkgincludedir)"
 LTLIBRARIES = $(lib_LTLIBRARIES)
-libgsl_la_DEPENDENCIES = $(SUBLIBS) $(am__append_1)
+am__DEPENDENCIES_1 =
+libgsl_la_DEPENDENCIES = $(am__DEPENDENCIES_1) $(SUBLIBS)
 am_libgsl_la_OBJECTS = version.lo
 libgsl_la_OBJECTS = $(am_libgsl_la_OBJECTS)
 AM_V_lt = $(am__v_lt_@AM_V@)
@@ -459,6 +458,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -481,7 +481,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -595,7 +598,7 @@
 top_build_prefix = @top_build_prefix@
 top_builddir = @top_builddir@
 top_srcdir = @top_srcdir@
-SUBDIRS = gsl utils sys test err const complex cheb block vector matrix permutation combination multiset sort ieee-utils cblas blas linalg eigen specfunc dht qrng rng randist fft poly fit multifit statistics siman sum integration interpolation histogram ode-initval ode-initval2 roots multiroots min multimin monte ntuple diff deriv cdf wavelet bspline doc
+SUBDIRS = gsl utils sys test err const complex cheb block vector matrix permutation combination multiset sort ieee-utils cblas blas linalg eigen specfunc dht qrng rng randist fft poly fit multifit multifit_nlinear multilarge multilarge_nlinear rstat statistics siman sum integration interpolation histogram ode-initval ode-initval2 roots multiroots min multimin monte ntuple diff deriv cdf wavelet bspline spblas spmatrix splinalg doc
 SUBLIBS = block/libgslblock.la blas/libgslblas.la \
 	bspline/libgslbspline.la complex/libgslcomplex.la \
 	cheb/libgslcheb.la dht/libgsldht.la diff/libgsldiff.la \
@@ -604,18 +607,22 @@
 	ieee-utils/libgslieeeutils.la integration/libgslintegration.la \
 	interpolation/libgslinterpolation.la linalg/libgsllinalg.la \
 	matrix/libgslmatrix.la min/libgslmin.la monte/libgslmonte.la \
-	multifit/libgslmultifit.la multimin/libgslmultimin.la \
-	multiroots/libgslmultiroots.la ntuple/libgslntuple.la \
-	ode-initval/libgslodeiv.la ode-initval2/libgslodeiv2.la \
-	permutation/libgslpermutation.la \
+	multifit/libgslmultifit.la \
+	multifit_nlinear/libgslmultifit_nlinear.la \
+	multilarge/libgslmultilarge.la \
+	multilarge_nlinear/libgslmultilarge_nlinear.la \
+	multimin/libgslmultimin.la multiroots/libgslmultiroots.la \
+	ntuple/libgslntuple.la ode-initval/libgslodeiv.la \
+	ode-initval2/libgslodeiv2.la permutation/libgslpermutation.la \
 	combination/libgslcombination.la multiset/libgslmultiset.la \
 	poly/libgslpoly.la qrng/libgslqrng.la randist/libgslrandist.la \
 	rng/libgslrng.la roots/libgslroots.la siman/libgslsiman.la \
 	sort/libgslsort.la specfunc/libgslspecfunc.la \
-	statistics/libgslstatistics.la sum/libgslsum.la \
-	sys/libgslsys.la test/libgsltest.la utils/libutils.la \
-	vector/libgslvector.la cdf/libgslcdf.la \
-	wavelet/libgslwavelet.la
+	rstat/libgslrstat.la statistics/libgslstatistics.la \
+	sum/libgslsum.la sys/libgslsys.la test/libgsltest.la \
+	utils/libutils.la vector/libgslvector.la cdf/libgslcdf.la \
+	wavelet/libgslwavelet.la spmatrix/libgslspmatrix.la \
+	spblas/libgslspblas.la splinalg/libgslsplinalg.la
 pkginclude_HEADERS = gsl_math.h gsl_pow_int.h gsl_nan.h gsl_machine.h gsl_mode.h gsl_precision.h gsl_types.h gsl_version.h gsl_minmax.h gsl_inline.h
 bin_SCRIPTS = gsl-config
 pkgconfigdir = $(libdir)/pkgconfig
@@ -624,10 +631,9 @@
 EXTRA_DIST = autogen.sh gsl-config.in gsl.pc.in configure.ac THANKS BUGS gsl.spec.in gsl.m4 test_gsl_histogram.sh pkgconfig.test
 lib_LTLIBRARIES = libgsl.la
 libgsl_la_SOURCES = version.c
-libgsl_la_LIBADD = $(SUBLIBS) $(am__append_1)
-libgsl_la_LDFLAGS = -version-info $(GSL_LT_VERSION) $(am__append_2)
+libgsl_la_LIBADD = $(GSL_LIBADD) $(SUBLIBS)
+libgsl_la_LDFLAGS = $(GSL_LDFLAGS) -version-info $(GSL_LT_VERSION)
 noinst_HEADERS = templates_on.h templates_off.h build.h
-MINGW32_HOST = @MINGW32_HOST@
 m4datadir = $(datadir)/aclocal
 m4data_DATA = gsl.m4
 gsl_randist_SOURCES = gsl-randist.c
diff -Nru gsl-doc-1.16/matrix/copy_source.c gsl-doc-2.3/matrix/copy_source.c
--- gsl-doc-1.16/matrix/copy_source.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/copy_source.c	2016-07-07 20:36:10.000000000 +0000
@@ -84,5 +84,76 @@
 }
 
 
+int
+FUNCTION (gsl_matrix, tricpy) (const char uplo_src,
+                               const int copy_diag, TYPE (gsl_matrix) * dest,
+                               const TYPE (gsl_matrix) * src)
+{
+  const size_t src_size1 = src->size1;
+  const size_t src_size2 = src->size2;
+  const size_t dest_size1 = dest->size1;
+  const size_t dest_size2 = dest->size2;
+
+  if (src_size1 != dest_size1 || src_size2 != dest_size2)
+    {
+      GSL_ERROR ("matrix sizes are different", GSL_EBADLEN);
+    }
+
+  {
+    const size_t src_tda = src->tda ;
+    const size_t dest_tda = dest->tda ;
+    size_t i, j, k;
+
+    if (uplo_src == 'L')
+      {
+        for (i = 0; i < src_size1 ; i++)
+          {
+            for (j = 0; j < i; j++)
+              {
+                for (k = 0; k < MULTIPLICITY; k++)
+                  {
+                    size_t e1 = (i *  dest_tda + j) * MULTIPLICITY + k ;
+                    size_t e2 = (i *  src_tda + j) * MULTIPLICITY + k ;
+                    dest->data[e1] = src->data[e2];
+                  }
+              }
+          }
+      }
+    else if (uplo_src == 'U')
+      {
+        for (i = 0; i < src_size1 ; i++)
+          {
+            for (j = i + 1; j < src_size2; j++)
+              {
+                for (k = 0; k < MULTIPLICITY; k++)
+                  {
+                    size_t e1 = (i *  dest_tda + j) * MULTIPLICITY + k ;
+                    size_t e2 = (i *  src_tda + j) * MULTIPLICITY + k ;
+                    dest->data[e1] = src->data[e2];
+                  }
+              }
+          }
+      }
+    else
+      {
+        GSL_ERROR ("invalid uplo parameters", GSL_EINVAL);
+      }
+
+    if (copy_diag)
+      {
+        for (i = 0; i < src_size1 ; i++)
+          {
+            for (k = 0; k < MULTIPLICITY; k++)
+              {
+                size_t e1 = (i *  dest_tda + i) * MULTIPLICITY + k ;
+                size_t e2 = (i *  src_tda + i) * MULTIPLICITY + k ;
+                dest->data[e1] = src->data[e2];
+              }
+          }
+      }
+  }
+
+  return GSL_SUCCESS;
+}
 
 
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_char.h gsl-doc-2.3/matrix/gsl_matrix_char.h
--- gsl-doc-1.16/matrix/gsl_matrix_char.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_char.h	2016-07-07 20:36:10.000000000 +0000
@@ -216,12 +216,14 @@
  
 int gsl_matrix_char_memcpy(gsl_matrix_char * dest, const gsl_matrix_char * src);
 int gsl_matrix_char_swap(gsl_matrix_char * m1, gsl_matrix_char * m2);
+int gsl_matrix_char_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_char * dest, const gsl_matrix_char * src);
 
 int gsl_matrix_char_swap_rows(gsl_matrix_char * m, const size_t i, const size_t j);
 int gsl_matrix_char_swap_columns(gsl_matrix_char * m, const size_t i, const size_t j);
 int gsl_matrix_char_swap_rowcol(gsl_matrix_char * m, const size_t i, const size_t j);
 int gsl_matrix_char_transpose (gsl_matrix_char * m);
 int gsl_matrix_char_transpose_memcpy (gsl_matrix_char * dest, const gsl_matrix_char * src);
+int gsl_matrix_char_transpose_tricpy (const char uplo_src, const int copy_diag, gsl_matrix_char * dest, const gsl_matrix_char * src);
 
 char gsl_matrix_char_max (const gsl_matrix_char * m);
 char gsl_matrix_char_min (const gsl_matrix_char * m);
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_complex_double.h gsl-doc-2.3/matrix/gsl_matrix_complex_double.h
--- gsl-doc-1.16/matrix/gsl_matrix_complex_double.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_complex_double.h	2016-08-23 14:27:35.000000000 +0000
@@ -216,6 +216,7 @@
 
 int gsl_matrix_complex_memcpy(gsl_matrix_complex * dest, const gsl_matrix_complex * src);
 int gsl_matrix_complex_swap(gsl_matrix_complex * m1, gsl_matrix_complex * m2);
+int gsl_matrix_complex_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_complex * dest, const gsl_matrix_complex * src);
 
 int gsl_matrix_complex_swap_rows(gsl_matrix_complex * m, const size_t i, const size_t j);
 int gsl_matrix_complex_swap_columns(gsl_matrix_complex * m, const size_t i, const size_t j);
@@ -223,6 +224,7 @@
 
 int gsl_matrix_complex_transpose (gsl_matrix_complex * m);
 int gsl_matrix_complex_transpose_memcpy (gsl_matrix_complex * dest, const gsl_matrix_complex * src);
+int gsl_matrix_complex_transpose_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_complex * dest, const gsl_matrix_complex * src);
 
 int gsl_matrix_complex_equal (const gsl_matrix_complex * a, const gsl_matrix_complex * b);
 
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_complex_float.h gsl-doc-2.3/matrix/gsl_matrix_complex_float.h
--- gsl-doc-1.16/matrix/gsl_matrix_complex_float.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_complex_float.h	2016-08-23 14:27:05.000000000 +0000
@@ -216,6 +216,7 @@
 
 int gsl_matrix_complex_float_memcpy(gsl_matrix_complex_float * dest, const gsl_matrix_complex_float * src);
 int gsl_matrix_complex_float_swap(gsl_matrix_complex_float * m1, gsl_matrix_complex_float * m2);
+int gsl_matrix_complex_float_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_complex_float * dest, const gsl_matrix_complex_float * src);
 
 int gsl_matrix_complex_float_swap_rows(gsl_matrix_complex_float * m, const size_t i, const size_t j);
 int gsl_matrix_complex_float_swap_columns(gsl_matrix_complex_float * m, const size_t i, const size_t j);
@@ -223,6 +224,7 @@
 
 int gsl_matrix_complex_float_transpose (gsl_matrix_complex_float * m);
 int gsl_matrix_complex_float_transpose_memcpy (gsl_matrix_complex_float * dest, const gsl_matrix_complex_float * src);
+int gsl_matrix_complex_float_transpose_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_complex_float * dest, const gsl_matrix_complex_float * src);
 
 int gsl_matrix_complex_float_equal (const gsl_matrix_complex_float * a, const gsl_matrix_complex_float * b);
 
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_complex_long_double.h gsl-doc-2.3/matrix/gsl_matrix_complex_long_double.h
--- gsl-doc-1.16/matrix/gsl_matrix_complex_long_double.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_complex_long_double.h	2016-08-23 14:27:35.000000000 +0000
@@ -216,6 +216,7 @@
 
 int gsl_matrix_complex_long_double_memcpy(gsl_matrix_complex_long_double * dest, const gsl_matrix_complex_long_double * src);
 int gsl_matrix_complex_long_double_swap(gsl_matrix_complex_long_double * m1, gsl_matrix_complex_long_double * m2);
+int gsl_matrix_complex_long_double_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_complex_long_double * dest, const gsl_matrix_complex_long_double * src);
 
 int gsl_matrix_complex_long_double_swap_rows(gsl_matrix_complex_long_double * m, const size_t i, const size_t j);
 int gsl_matrix_complex_long_double_swap_columns(gsl_matrix_complex_long_double * m, const size_t i, const size_t j);
@@ -223,6 +224,7 @@
 
 int gsl_matrix_complex_long_double_transpose (gsl_matrix_complex_long_double * m);
 int gsl_matrix_complex_long_double_transpose_memcpy (gsl_matrix_complex_long_double * dest, const gsl_matrix_complex_long_double * src);
+int gsl_matrix_complex_long_double_transpose_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_complex_long_double * dest, const gsl_matrix_complex_long_double * src);
 
 int gsl_matrix_complex_long_double_equal (const gsl_matrix_complex_long_double * a, const gsl_matrix_complex_long_double * b);
 
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_double.h gsl-doc-2.3/matrix/gsl_matrix_double.h
--- gsl-doc-1.16/matrix/gsl_matrix_double.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_double.h	2016-07-07 20:36:10.000000000 +0000
@@ -216,12 +216,14 @@
  
 int gsl_matrix_memcpy(gsl_matrix * dest, const gsl_matrix * src);
 int gsl_matrix_swap(gsl_matrix * m1, gsl_matrix * m2);
+int gsl_matrix_tricpy(const char uplo_src, const int copy_diag, gsl_matrix * dest, const gsl_matrix * src);
 
 int gsl_matrix_swap_rows(gsl_matrix * m, const size_t i, const size_t j);
 int gsl_matrix_swap_columns(gsl_matrix * m, const size_t i, const size_t j);
 int gsl_matrix_swap_rowcol(gsl_matrix * m, const size_t i, const size_t j);
 int gsl_matrix_transpose (gsl_matrix * m);
 int gsl_matrix_transpose_memcpy (gsl_matrix * dest, const gsl_matrix * src);
+int gsl_matrix_transpose_tricpy (const char uplo_src, const int copy_diag, gsl_matrix * dest, const gsl_matrix * src);
 
 double gsl_matrix_max (const gsl_matrix * m);
 double gsl_matrix_min (const gsl_matrix * m);
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_float.h gsl-doc-2.3/matrix/gsl_matrix_float.h
--- gsl-doc-1.16/matrix/gsl_matrix_float.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_float.h	2016-07-07 20:36:10.000000000 +0000
@@ -216,12 +216,14 @@
  
 int gsl_matrix_float_memcpy(gsl_matrix_float * dest, const gsl_matrix_float * src);
 int gsl_matrix_float_swap(gsl_matrix_float * m1, gsl_matrix_float * m2);
+int gsl_matrix_float_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_float * dest, const gsl_matrix_float * src);
 
 int gsl_matrix_float_swap_rows(gsl_matrix_float * m, const size_t i, const size_t j);
 int gsl_matrix_float_swap_columns(gsl_matrix_float * m, const size_t i, const size_t j);
 int gsl_matrix_float_swap_rowcol(gsl_matrix_float * m, const size_t i, const size_t j);
 int gsl_matrix_float_transpose (gsl_matrix_float * m);
 int gsl_matrix_float_transpose_memcpy (gsl_matrix_float * dest, const gsl_matrix_float * src);
+int gsl_matrix_float_transpose_tricpy (const char uplo_src, const int copy_diag, gsl_matrix_float * dest, const gsl_matrix_float * src);
 
 float gsl_matrix_float_max (const gsl_matrix_float * m);
 float gsl_matrix_float_min (const gsl_matrix_float * m);
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_int.h gsl-doc-2.3/matrix/gsl_matrix_int.h
--- gsl-doc-1.16/matrix/gsl_matrix_int.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_int.h	2016-07-07 20:36:10.000000000 +0000
@@ -216,12 +216,14 @@
  
 int gsl_matrix_int_memcpy(gsl_matrix_int * dest, const gsl_matrix_int * src);
 int gsl_matrix_int_swap(gsl_matrix_int * m1, gsl_matrix_int * m2);
+int gsl_matrix_int_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_int * dest, const gsl_matrix_int * src);
 
 int gsl_matrix_int_swap_rows(gsl_matrix_int * m, const size_t i, const size_t j);
 int gsl_matrix_int_swap_columns(gsl_matrix_int * m, const size_t i, const size_t j);
 int gsl_matrix_int_swap_rowcol(gsl_matrix_int * m, const size_t i, const size_t j);
 int gsl_matrix_int_transpose (gsl_matrix_int * m);
 int gsl_matrix_int_transpose_memcpy (gsl_matrix_int * dest, const gsl_matrix_int * src);
+int gsl_matrix_int_transpose_tricpy (const char uplo_src, const int copy_diag, gsl_matrix_int * dest, const gsl_matrix_int * src);
 
 int gsl_matrix_int_max (const gsl_matrix_int * m);
 int gsl_matrix_int_min (const gsl_matrix_int * m);
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_long_double.h gsl-doc-2.3/matrix/gsl_matrix_long_double.h
--- gsl-doc-1.16/matrix/gsl_matrix_long_double.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_long_double.h	2016-07-07 20:36:10.000000000 +0000
@@ -216,12 +216,14 @@
  
 int gsl_matrix_long_double_memcpy(gsl_matrix_long_double * dest, const gsl_matrix_long_double * src);
 int gsl_matrix_long_double_swap(gsl_matrix_long_double * m1, gsl_matrix_long_double * m2);
+int gsl_matrix_long_double_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_long_double * dest, const gsl_matrix_long_double * src);
 
 int gsl_matrix_long_double_swap_rows(gsl_matrix_long_double * m, const size_t i, const size_t j);
 int gsl_matrix_long_double_swap_columns(gsl_matrix_long_double * m, const size_t i, const size_t j);
 int gsl_matrix_long_double_swap_rowcol(gsl_matrix_long_double * m, const size_t i, const size_t j);
 int gsl_matrix_long_double_transpose (gsl_matrix_long_double * m);
 int gsl_matrix_long_double_transpose_memcpy (gsl_matrix_long_double * dest, const gsl_matrix_long_double * src);
+int gsl_matrix_long_double_transpose_tricpy (const char uplo_src, const int copy_diag, gsl_matrix_long_double * dest, const gsl_matrix_long_double * src);
 
 long double gsl_matrix_long_double_max (const gsl_matrix_long_double * m);
 long double gsl_matrix_long_double_min (const gsl_matrix_long_double * m);
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_long.h gsl-doc-2.3/matrix/gsl_matrix_long.h
--- gsl-doc-1.16/matrix/gsl_matrix_long.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_long.h	2016-07-07 20:36:10.000000000 +0000
@@ -216,12 +216,14 @@
  
 int gsl_matrix_long_memcpy(gsl_matrix_long * dest, const gsl_matrix_long * src);
 int gsl_matrix_long_swap(gsl_matrix_long * m1, gsl_matrix_long * m2);
+int gsl_matrix_long_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_long * dest, const gsl_matrix_long * src);
 
 int gsl_matrix_long_swap_rows(gsl_matrix_long * m, const size_t i, const size_t j);
 int gsl_matrix_long_swap_columns(gsl_matrix_long * m, const size_t i, const size_t j);
 int gsl_matrix_long_swap_rowcol(gsl_matrix_long * m, const size_t i, const size_t j);
 int gsl_matrix_long_transpose (gsl_matrix_long * m);
 int gsl_matrix_long_transpose_memcpy (gsl_matrix_long * dest, const gsl_matrix_long * src);
+int gsl_matrix_long_transpose_tricpy (const char uplo_src, const int copy_diag, gsl_matrix_long * dest, const gsl_matrix_long * src);
 
 long gsl_matrix_long_max (const gsl_matrix_long * m);
 long gsl_matrix_long_min (const gsl_matrix_long * m);
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_short.h gsl-doc-2.3/matrix/gsl_matrix_short.h
--- gsl-doc-1.16/matrix/gsl_matrix_short.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_short.h	2016-07-07 20:36:10.000000000 +0000
@@ -216,12 +216,14 @@
  
 int gsl_matrix_short_memcpy(gsl_matrix_short * dest, const gsl_matrix_short * src);
 int gsl_matrix_short_swap(gsl_matrix_short * m1, gsl_matrix_short * m2);
+int gsl_matrix_short_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_short * dest, const gsl_matrix_short * src);
 
 int gsl_matrix_short_swap_rows(gsl_matrix_short * m, const size_t i, const size_t j);
 int gsl_matrix_short_swap_columns(gsl_matrix_short * m, const size_t i, const size_t j);
 int gsl_matrix_short_swap_rowcol(gsl_matrix_short * m, const size_t i, const size_t j);
 int gsl_matrix_short_transpose (gsl_matrix_short * m);
 int gsl_matrix_short_transpose_memcpy (gsl_matrix_short * dest, const gsl_matrix_short * src);
+int gsl_matrix_short_transpose_tricpy (const char uplo_src, const int copy_diag, gsl_matrix_short * dest, const gsl_matrix_short * src);
 
 short gsl_matrix_short_max (const gsl_matrix_short * m);
 short gsl_matrix_short_min (const gsl_matrix_short * m);
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_uchar.h gsl-doc-2.3/matrix/gsl_matrix_uchar.h
--- gsl-doc-1.16/matrix/gsl_matrix_uchar.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_uchar.h	2016-07-07 20:36:10.000000000 +0000
@@ -216,12 +216,14 @@
  
 int gsl_matrix_uchar_memcpy(gsl_matrix_uchar * dest, const gsl_matrix_uchar * src);
 int gsl_matrix_uchar_swap(gsl_matrix_uchar * m1, gsl_matrix_uchar * m2);
+int gsl_matrix_uchar_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_uchar * dest, const gsl_matrix_uchar * src);
 
 int gsl_matrix_uchar_swap_rows(gsl_matrix_uchar * m, const size_t i, const size_t j);
 int gsl_matrix_uchar_swap_columns(gsl_matrix_uchar * m, const size_t i, const size_t j);
 int gsl_matrix_uchar_swap_rowcol(gsl_matrix_uchar * m, const size_t i, const size_t j);
 int gsl_matrix_uchar_transpose (gsl_matrix_uchar * m);
 int gsl_matrix_uchar_transpose_memcpy (gsl_matrix_uchar * dest, const gsl_matrix_uchar * src);
+int gsl_matrix_uchar_transpose_tricpy (const char uplo_src, const int copy_diag, gsl_matrix_uchar * dest, const gsl_matrix_uchar * src);
 
 unsigned char gsl_matrix_uchar_max (const gsl_matrix_uchar * m);
 unsigned char gsl_matrix_uchar_min (const gsl_matrix_uchar * m);
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_uint.h gsl-doc-2.3/matrix/gsl_matrix_uint.h
--- gsl-doc-1.16/matrix/gsl_matrix_uint.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_uint.h	2016-07-07 20:36:10.000000000 +0000
@@ -216,12 +216,14 @@
  
 int gsl_matrix_uint_memcpy(gsl_matrix_uint * dest, const gsl_matrix_uint * src);
 int gsl_matrix_uint_swap(gsl_matrix_uint * m1, gsl_matrix_uint * m2);
+int gsl_matrix_uint_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_uint * dest, const gsl_matrix_uint * src);
 
 int gsl_matrix_uint_swap_rows(gsl_matrix_uint * m, const size_t i, const size_t j);
 int gsl_matrix_uint_swap_columns(gsl_matrix_uint * m, const size_t i, const size_t j);
 int gsl_matrix_uint_swap_rowcol(gsl_matrix_uint * m, const size_t i, const size_t j);
 int gsl_matrix_uint_transpose (gsl_matrix_uint * m);
 int gsl_matrix_uint_transpose_memcpy (gsl_matrix_uint * dest, const gsl_matrix_uint * src);
+int gsl_matrix_uint_transpose_tricpy (const char uplo_src, const int copy_diag, gsl_matrix_uint * dest, const gsl_matrix_uint * src);
 
 unsigned int gsl_matrix_uint_max (const gsl_matrix_uint * m);
 unsigned int gsl_matrix_uint_min (const gsl_matrix_uint * m);
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_ulong.h gsl-doc-2.3/matrix/gsl_matrix_ulong.h
--- gsl-doc-1.16/matrix/gsl_matrix_ulong.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_ulong.h	2016-07-07 20:36:10.000000000 +0000
@@ -216,12 +216,14 @@
  
 int gsl_matrix_ulong_memcpy(gsl_matrix_ulong * dest, const gsl_matrix_ulong * src);
 int gsl_matrix_ulong_swap(gsl_matrix_ulong * m1, gsl_matrix_ulong * m2);
+int gsl_matrix_ulong_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_ulong * dest, const gsl_matrix_ulong * src);
 
 int gsl_matrix_ulong_swap_rows(gsl_matrix_ulong * m, const size_t i, const size_t j);
 int gsl_matrix_ulong_swap_columns(gsl_matrix_ulong * m, const size_t i, const size_t j);
 int gsl_matrix_ulong_swap_rowcol(gsl_matrix_ulong * m, const size_t i, const size_t j);
 int gsl_matrix_ulong_transpose (gsl_matrix_ulong * m);
 int gsl_matrix_ulong_transpose_memcpy (gsl_matrix_ulong * dest, const gsl_matrix_ulong * src);
+int gsl_matrix_ulong_transpose_tricpy (const char uplo_src, const int copy_diag, gsl_matrix_ulong * dest, const gsl_matrix_ulong * src);
 
 unsigned long gsl_matrix_ulong_max (const gsl_matrix_ulong * m);
 unsigned long gsl_matrix_ulong_min (const gsl_matrix_ulong * m);
diff -Nru gsl-doc-1.16/matrix/gsl_matrix_ushort.h gsl-doc-2.3/matrix/gsl_matrix_ushort.h
--- gsl-doc-1.16/matrix/gsl_matrix_ushort.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/gsl_matrix_ushort.h	2016-07-07 20:36:10.000000000 +0000
@@ -216,12 +216,14 @@
  
 int gsl_matrix_ushort_memcpy(gsl_matrix_ushort * dest, const gsl_matrix_ushort * src);
 int gsl_matrix_ushort_swap(gsl_matrix_ushort * m1, gsl_matrix_ushort * m2);
+int gsl_matrix_ushort_tricpy(const char uplo_src, const int copy_diag, gsl_matrix_ushort * dest, const gsl_matrix_ushort * src);
 
 int gsl_matrix_ushort_swap_rows(gsl_matrix_ushort * m, const size_t i, const size_t j);
 int gsl_matrix_ushort_swap_columns(gsl_matrix_ushort * m, const size_t i, const size_t j);
 int gsl_matrix_ushort_swap_rowcol(gsl_matrix_ushort * m, const size_t i, const size_t j);
 int gsl_matrix_ushort_transpose (gsl_matrix_ushort * m);
 int gsl_matrix_ushort_transpose_memcpy (gsl_matrix_ushort * dest, const gsl_matrix_ushort * src);
+int gsl_matrix_ushort_transpose_tricpy (const char uplo_src, const int copy_diag, gsl_matrix_ushort * dest, const gsl_matrix_ushort * src);
 
 unsigned short gsl_matrix_ushort_max (const gsl_matrix_ushort * m);
 unsigned short gsl_matrix_ushort_min (const gsl_matrix_ushort * m);
diff -Nru gsl-doc-1.16/matrix/init.c gsl-doc-2.3/matrix/init.c
--- gsl-doc-1.16/matrix/init.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/init.c	2015-11-03 16:21:55.000000000 +0000
@@ -1,4 +1,5 @@
 #include <config.h>
+#include <string.h>
 #include <gsl/gsl_errno.h>
 #include <gsl/gsl_matrix.h>
 
diff -Nru gsl-doc-1.16/matrix/init_source.c gsl-doc-2.3/matrix/init_source.c
--- gsl-doc-1.16/matrix/init_source.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/init_source.c	2015-11-03 16:21:55.000000000 +0000
@@ -73,6 +73,7 @@
     return 0;
 
   /* initialize matrix to zero */
+  memset(m->data, 0, MULTIPLICITY * n1 * n2 * sizeof(ATOMIC));
 
   for (i = 0; i < MULTIPLICITY * n1 * n2; i++)
     {
diff -Nru gsl-doc-1.16/matrix/Makefile.am gsl-doc-2.3/matrix/Makefile.am
--- gsl-doc-1.16/matrix/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -4,7 +4,7 @@
 
 pkginclude_HEADERS = gsl_matrix.h gsl_matrix_char.h gsl_matrix_complex_double.h gsl_matrix_complex_float.h gsl_matrix_complex_long_double.h gsl_matrix_double.h gsl_matrix_float.h gsl_matrix_int.h gsl_matrix_long.h gsl_matrix_long_double.h gsl_matrix_short.h gsl_matrix_uchar.h gsl_matrix_uint.h gsl_matrix_ulong.h gsl_matrix_ushort.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 TESTS = $(check_PROGRAMS) 
 
diff -Nru gsl-doc-1.16/matrix/Makefile.in gsl-doc-2.3/matrix/Makefile.in
--- gsl-doc-1.16/matrix/Makefile.in	2013-07-19 15:14:53.000000000 +0000
+++ gsl-doc-2.3/matrix/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -388,6 +388,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -410,7 +411,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -526,7 +530,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslmatrix.la 
 pkginclude_HEADERS = gsl_matrix.h gsl_matrix_char.h gsl_matrix_complex_double.h gsl_matrix_complex_float.h gsl_matrix_complex_long_double.h gsl_matrix_double.h gsl_matrix_float.h gsl_matrix_int.h gsl_matrix_long.h gsl_matrix_long_double.h gsl_matrix_short.h gsl_matrix_uchar.h gsl_matrix_uint.h gsl_matrix_ulong.h gsl_matrix_ushort.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 TESTS = $(check_PROGRAMS) 
 test_LDADD = libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la ../ieee-utils/libgslieeeutils.la  ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
 test_static_LDADD = libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la ../ieee-utils/libgslieeeutils.la  ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
diff -Nru gsl-doc-1.16/matrix/swap_source.c gsl-doc-2.3/matrix/swap_source.c
--- gsl-doc-1.16/matrix/swap_source.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/swap_source.c	2016-07-07 20:36:10.000000000 +0000
@@ -208,3 +208,77 @@
 
   return GSL_SUCCESS;
 }
+
+int
+FUNCTION (gsl_matrix, transpose_tricpy) (const char uplo_src,
+                                         const int copy_diag, TYPE (gsl_matrix) * dest,
+                                         const TYPE (gsl_matrix) * src)
+{
+  const size_t src_size1 = src->size1;
+  const size_t src_size2 = src->size2;
+  const size_t dest_size1 = dest->size1;
+  const size_t dest_size2 = dest->size2;
+
+  if (src_size1 != dest_size1 || src_size2 != dest_size2)
+    {
+      GSL_ERROR ("matrix sizes are different", GSL_EBADLEN);
+    }
+
+  {
+    const size_t src_tda = src->tda ;
+    const size_t dest_tda = dest->tda ;
+    size_t i, j, k;
+
+    if (uplo_src == 'L')
+      {
+        /* copy lower triangle of src to upper triangle of dest */
+        for (i = 0; i < src_size1 ; i++)
+          {
+            for (j = 0; j < i; j++)
+              {
+                for (k = 0; k < MULTIPLICITY; k++)
+                  {
+                    size_t e1 = (j *  dest_tda + i) * MULTIPLICITY + k ;
+                    size_t e2 = (i *  src_tda + j) * MULTIPLICITY + k ;
+                    dest->data[e1] = src->data[e2];
+                  }
+              }
+          }
+      }
+    else if (uplo_src == 'U')
+      {
+        /* copy upper triangle of src to lower triangle of dest */
+        for (i = 0; i < src_size1 ; i++)
+          {
+            for (j = i + 1; j < src_size2; j++)
+              {
+                for (k = 0; k < MULTIPLICITY; k++)
+                  {
+                    size_t e1 = (j *  dest_tda + i) * MULTIPLICITY + k ;
+                    size_t e2 = (i *  src_tda + j) * MULTIPLICITY + k ;
+                    dest->data[e1] = src->data[e2];
+                  }
+              }
+          }
+      }
+    else
+      {
+        GSL_ERROR ("invalid uplo_src parameter", GSL_EINVAL);
+      }
+
+    if (copy_diag)
+      {
+        for (i = 0; i < src_size1 ; i++)
+          {
+            for (k = 0; k < MULTIPLICITY; k++)
+              {
+                size_t e1 = (i * dest_tda + i) * MULTIPLICITY + k ;
+                size_t e2 = (i * src_tda + i) * MULTIPLICITY + k ;
+                dest->data[e1] = src->data[e2];
+              }
+          }
+      }
+  }
+
+  return GSL_SUCCESS;
+}
diff -Nru gsl-doc-1.16/matrix/test.c gsl-doc-2.3/matrix/test.c
--- gsl-doc-1.16/matrix/test.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/test.c	2015-11-03 16:21:55.000000000 +0000
@@ -19,6 +19,10 @@
 
 #include <config.h>
 
+#if defined( _MSC_VER ) && defined( GSL_DLL )
+#undef inline
+#define inline __forceinline 
+#endif
 #if (!GSL_RANGE_CHECK) && defined(HAVE_INLINE)
 #undef GSL_RANGE_CHECK
 #define GSL_RANGE_CHECK 1
@@ -26,6 +30,7 @@
 
 #include <stdlib.h>
 #include <stdio.h>
+#include <unistd.h>
 #include <math.h>
 #include <gsl/gsl_math.h>
 #include <gsl/gsl_matrix.h>
diff -Nru gsl-doc-1.16/matrix/test_complex_source.c gsl-doc-2.3/matrix/test_complex_source.c
--- gsl-doc-1.16/matrix/test_complex_source.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/test_complex_source.c	2015-11-03 16:21:55.000000000 +0000
@@ -249,8 +249,16 @@
   size_t i, j;
   int k = 0;
 
+  char filename[] = "test.XXXXXX";
+#if !defined( _WIN32 )
+  int fd = mkstemp(filename);
+#else
+  char * fd = _mktemp(filename);
+# define fdopen fopen
+#endif
+
   {
-    FILE *f = fopen ("test.txt", "w");
+    FILE *f = fdopen (fd, "w");
     k = 0;
     for (i = 0; i < M; i++)
       {
@@ -270,7 +278,7 @@
   }
 
   {
-    FILE *f = fopen ("test.txt", "r");
+    FILE *f = fopen (filename, "r");
     TYPE (gsl_matrix) * mm = FUNCTION (gsl_matrix, alloc) (M, N);
     status = 0;
 
@@ -293,6 +301,7 @@
     FUNCTION (gsl_matrix, free) (mm);
   }
 
+  unlink(filename);
   FUNCTION (gsl_matrix, free) (m);
 }
 #endif
@@ -305,8 +314,16 @@
   size_t i, j;
   int k = 0;
 
+  char filename[] = "test.XXXXXX";
+#if !defined( _WIN32 )
+  int fd = mkstemp(filename);
+#else
+  char * fd = _mktemp(filename);
+# define fdopen fopen
+#endif
+
   {
-    FILE *f = fopen ("test.dat", "wb");
+    FILE *f = fdopen (fd, "wb");
     k = 0;
     for (i = 0; i < M; i++)
       {
@@ -326,7 +343,7 @@
   }
 
   {
-    FILE *f = fopen ("test.dat", "rb");
+    FILE *f = fopen (filename, "rb");
     TYPE (gsl_matrix) * mm = FUNCTION (gsl_matrix, alloc) (M, N);
     status = 0;
 
@@ -349,20 +366,30 @@
     FUNCTION (gsl_matrix, free) (mm);
   }
 
+  unlink(filename);
+
   FUNCTION (gsl_matrix, free) (m);
 }
 
 void
 FUNCTION (test, binary_noncontiguous) (const size_t M, const size_t N)
 {
-  TYPE (gsl_matrix) * l = FUNCTION (gsl_matrix, alloc) (M+1, N+1);
+  TYPE (gsl_matrix) * l = FUNCTION (gsl_matrix, calloc) (M+1, N+1);
   VIEW (gsl_matrix, view) m = FUNCTION (gsl_matrix, submatrix) (l, 0, 0, M, N);
 
   size_t i, j;
   int k = 0;
 
+  char filename[] = "test.XXXXXX";
+#if !defined( _WIN32 )
+  int fd = mkstemp(filename);
+#else
+  char * fd = _mktemp(filename);
+# define fdopen fopen
+#endif
+
   {
-    FILE *f = fopen ("test.dat", "wb");
+    FILE *f = fdopen (fd, "wb");
     k = 0;
     for (i = 0; i < M; i++)
       {
@@ -382,7 +409,7 @@
   }
 
   {
-    FILE *f = fopen ("test.dat", "rb");
+    FILE *f = fopen (filename, "rb");
     TYPE (gsl_matrix) * ll = FUNCTION (gsl_matrix, alloc) (M+1, N+1);
     VIEW (gsl_matrix, view) mm = FUNCTION (gsl_matrix, submatrix) (ll, 0, 0, M, N);
     status = 0;
@@ -406,6 +433,7 @@
     FUNCTION (gsl_matrix, free) (ll);
   }
 
+  unlink(filename);
   FUNCTION (gsl_matrix, free) (l);
 }
 
@@ -577,7 +605,7 @@
             if (GSL_REAL (z) != (ATOMIC) (-5)
                 || GSL_IMAG (z) != (ATOMIC) (-10))
               status = 1;
-            k++;
+            k++; 
           }
       }
     gsl_test (status, NAME (gsl_matrix) "_sub matrix subtraction");
diff -Nru gsl-doc-1.16/matrix/test_source.c gsl-doc-2.3/matrix/test_source.c
--- gsl-doc-1.16/matrix/test_source.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/matrix/test_source.c	2015-11-03 16:21:55.000000000 +0000
@@ -418,7 +418,6 @@
 FUNCTION (test, ops) (const size_t M, const size_t N)
 {
   size_t i, j;
-  size_t k = 0;
   
   TYPE (gsl_matrix) * a = FUNCTION (gsl_matrix, calloc) (M, N);
   TYPE (gsl_matrix) * b = FUNCTION (gsl_matrix, calloc) (M, N);
@@ -581,7 +580,7 @@
           {
             BASE r = FUNCTION(gsl_matrix,get) (m,i,j);
             BASE x = FUNCTION(gsl_matrix,get) (a,i,j);
-            BASE y = (i == j) ? (x + 5.0) : x;
+            BASE y = (i == j) ? (x + (ATOMIC) 5.0) : x;
             if (fabs(r - y) > 2 * GSL_FLT_EPSILON * fabs(y))
               status = 1;
           }
@@ -623,8 +622,16 @@
   size_t i, j;
   int k = 0;
 
+  char filename[] = "test.XXXXXX";
+#if !defined( _WIN32 )
+  int fd = mkstemp(filename);
+#else
+  char * fd = _mktemp(filename);
+# define fdopen fopen
+#endif
+
   {
-    FILE *f = fopen ("test.txt", "w");
+    FILE *f = fdopen(fd, "w");
 
     for (i = 0; i < M; i++)
       {
@@ -640,7 +647,7 @@
   }
 
   {
-    FILE *f = fopen ("test.txt", "r");
+    FILE *f = fopen (filename, "r");
     TYPE (gsl_matrix) * mm = FUNCTION (gsl_matrix, alloc) (M, N);
     status = 0;
 
@@ -662,6 +669,8 @@
     FUNCTION (gsl_matrix, free) (mm);
   }
 
+  unlink(filename);
+
   FUNCTION (gsl_matrix, free) (m);
 }
 #endif
@@ -674,8 +683,16 @@
   size_t i, j;
   size_t k = 0;
 
+  char filename[] = "test.XXXXXX";
+#if !defined( _WIN32 )
+  int fd = mkstemp(filename);
+#else
+  char * fd = _mktemp(filename);
+# define fdopen fopen
+#endif
+
   {
-    FILE *f = fopen ("test.dat", "wb");
+    FILE *f = fdopen(fd, "wb");
     k = 0;
     for (i = 0; i < M; i++)
       {
@@ -691,7 +708,7 @@
   }
 
   {
-    FILE *f = fopen ("test.dat", "rb");
+    FILE *f = fopen (filename, "rb");
     TYPE (gsl_matrix) * mm = FUNCTION (gsl_matrix, alloc) (M, N);
     status = 0;
 
@@ -713,6 +730,8 @@
     FUNCTION (gsl_matrix, free) (mm);
   }
 
+  unlink(filename);
+
   FUNCTION (gsl_matrix, free) (m);
 }
 
@@ -725,8 +744,16 @@
   size_t i, j;
   size_t k = 0;
 
+  char filename[] = "test.XXXXXX";
+#if !defined( _WIN32 )
+  int fd = mkstemp(filename);
+#else
+  char * fd = _mktemp(filename);
+# define fdopen fopen
+#endif
+
   {
-    FILE *f = fopen ("test.dat", "wb");
+    FILE *f = fdopen(fd, "wb");
     k = 0;
     for (i = 0; i < M; i++)
       {
@@ -742,7 +769,7 @@
   }
 
   {
-    FILE *f = fopen ("test.dat", "rb");
+    FILE *f = fopen (filename, "rb");
     TYPE (gsl_matrix) * ll = FUNCTION (gsl_matrix, alloc) (M+1, N+1);
     VIEW (gsl_matrix, view) mm = FUNCTION (gsl_matrix, submatrix) (ll, 0, 0, M, N);
     status = 0;
@@ -765,6 +792,8 @@
     FUNCTION (gsl_matrix, free) (ll);
   }
 
+  unlink(filename);
+
   FUNCTION (gsl_matrix, free) (l);
 }
 
diff -Nru gsl-doc-1.16/min/Makefile.am gsl-doc-2.3/min/Makefile.am
--- gsl-doc-1.16/min/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/min/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -4,7 +4,7 @@
 
 noinst_HEADERS = min.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslmin_la_SOURCES = fsolver.c golden.c brent.c convergence.c bracketing.c quad_golden.c
 
diff -Nru gsl-doc-1.16/min/Makefile.in gsl-doc-2.3/min/Makefile.in
--- gsl-doc-1.16/min/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/min/Makefile.in	2016-12-09 00:04:21.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -378,6 +378,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -400,7 +401,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -517,7 +521,7 @@
 noinst_LTLIBRARIES = libgslmin.la 
 pkginclude_HEADERS = gsl_min.h
 noinst_HEADERS = min.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslmin_la_SOURCES = fsolver.c golden.c brent.c convergence.c bracketing.c quad_golden.c
 TESTS = $(check_PROGRAMS)
 test_SOURCES = test.c test_funcs.c test.h
diff -Nru gsl-doc-1.16/monte/Makefile.am gsl-doc-2.3/monte/Makefile.am
--- gsl-doc-1.16/monte/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/monte/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -4,7 +4,7 @@
 
 pkginclude_HEADERS = gsl_monte.h gsl_monte_vegas.h gsl_monte_miser.h gsl_monte_plain.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 TESTS = $(check_PROGRAMS)
 
diff -Nru gsl-doc-1.16/monte/Makefile.in gsl-doc-2.3/monte/Makefile.in
--- gsl-doc-1.16/monte/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/monte/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -377,6 +377,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -399,7 +400,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -516,7 +520,7 @@
 noinst_LTLIBRARIES = libgslmonte.la 
 libgslmonte_la_SOURCES = miser.c plain.c gsl_monte_vegas.h gsl_monte_miser.h gsl_monte_plain.h gsl_monte.h vegas.c
 pkginclude_HEADERS = gsl_monte.h gsl_monte_vegas.h gsl_monte_miser.h gsl_monte_plain.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 TESTS = $(check_PROGRAMS)
 test_SOURCES = test.c 
 test_LDADD = libgslmonte.la ../rng/libgslrng.la  ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
diff -Nru gsl-doc-1.16/multifit/convergence.c gsl-doc-2.3/multifit/convergence.c
--- gsl-doc-1.16/multifit/convergence.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/convergence.c	2015-11-03 16:21:55.000000000 +0000
@@ -21,6 +21,71 @@
 #include <gsl/gsl_math.h>
 #include <gsl/gsl_errno.h>
 #include <gsl/gsl_multifit_nlin.h>
+#include <gsl/gsl_blas.h>
+
+static double scaled_infnorm(const gsl_vector *x, const gsl_vector *g);
+
+/*
+gsl_multifit_fdfsolver_test()
+  Convergence tests for nonlinear minimization
+
+(1) |dx_i| <= xtol * (1 + |x_i|) for all i
+(2) || g .* x ||_inf <= gtol ||f||^2
+(3) ||f(x+dx) - f(x)|| <= ftol * max(||f(x)||, 1)
+
+Inputs: s - fdfsolver
+        xtol - tolerance for step size
+        gtol - tolerance for gradient vector
+        ftol - tolerance for residual vector
+        info - (output)
+          1 - stopped by small x step
+          2 - stopped by small gradient
+          3 - stopped by small residual vector change
+*/
+
+int
+gsl_multifit_fdfsolver_test (const gsl_multifit_fdfsolver * s,
+                             const double xtol, const double gtol,
+                             const double ftol, int *info)
+{
+  int status;
+  double gnorm, fnorm, phi;
+
+  *info = 0;
+
+  status = gsl_multifit_test_delta(s->dx, s->x, xtol*xtol, xtol);
+  if (status == GSL_SUCCESS)
+    {
+      *info = 1;
+      return GSL_SUCCESS;
+    }
+
+  /* compute gradient g = J^T f */
+  (s->type->gradient) (s->state, s->g);
+
+  /* compute gnorm = max_i( g_i * max(x_i, 1) ) */
+  gnorm = scaled_infnorm(s->x, s->g);
+
+  /* compute fnorm = ||f|| */
+  fnorm = gsl_blas_dnrm2(s->f);
+  phi = 0.5 * fnorm * fnorm;
+
+  if (gnorm <= gtol * GSL_MAX(phi, 1.0))
+    {
+      *info = 2;
+      return GSL_SUCCESS;
+    }
+
+#if 0
+  if (dfnorm <= ftol * GSL_MAX(fnorm, 1.0))
+    {
+      *info = 3;
+      return GSL_SUCCESS;
+    }
+#endif
+
+  return GSL_CONTINUE;
+} /* gsl_multifit_fdfsolver_test() */
 
 int
 gsl_multifit_test_delta (const gsl_vector * dx, const gsl_vector * x, 
@@ -87,3 +152,23 @@
   
   return GSL_CONTINUE ;
 }
+
+static double
+scaled_infnorm(const gsl_vector *x, const gsl_vector *g)
+{
+  const size_t n = x->size;
+  size_t i;
+  double norm = 0.0;
+
+  for (i = 0; i < n; ++i)
+    {
+      double xi = GSL_MAX(gsl_vector_get(x, i), 1.0);
+      double gi = gsl_vector_get(g, i);
+      double tmp = fabs(xi * gi);
+
+      if (tmp > norm)
+        norm = tmp;
+    }
+
+  return norm;
+}
diff -Nru gsl-doc-1.16/multifit/covar.c gsl-doc-2.3/multifit/covar.c
--- gsl-doc-1.16/multifit/covar.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/covar.c	2015-11-03 16:21:55.000000000 +0000
@@ -32,19 +32,15 @@
 */
 
 int
-gsl_multifit_covar (const gsl_matrix * J, double epsrel, gsl_matrix * covar)
+gsl_multifit_covar (const gsl_matrix * J, const double epsrel, gsl_matrix * covar)
 {
-  double tolr;
-
-  size_t i, j, k;
-  size_t kmax = 0;
-
+  int status;
   gsl_matrix * r;
   gsl_vector * tau;
   gsl_vector * norm;
   gsl_permutation * perm;
-
-  size_t m = J->size1, n = J->size2 ;
+  const size_t m = J->size1;
+  const size_t n = J->size2;
   
   if (m < n) 
     {
@@ -67,10 +63,26 @@
     gsl_linalg_QRPT_decomp (r, tau, perm, &signum, norm);
   }
   
-  
+  status = gsl_multifit_covar_QRPT(r, perm, epsrel, covar);
+
+  gsl_matrix_free (r);
+  gsl_permutation_free (perm);
+  gsl_vector_free (tau);
+  gsl_vector_free (norm);
+
+  return status;
+}
+
+int
+gsl_multifit_covar_QRPT (gsl_matrix * r, gsl_permutation * perm,
+                         const double epsrel, gsl_matrix * covar)
+{
   /* Form the inverse of R in the full upper triangle of R */
 
-  tolr = epsrel * fabs(gsl_matrix_get(r, 0, 0));
+  double tolr = epsrel * fabs(gsl_matrix_get(r, 0, 0));
+  const size_t n = r->size2;
+  size_t i, j, k;
+  size_t kmax = 0;
 
   for (k = 0 ; k < n ; k++)
     {
@@ -183,10 +195,5 @@
         }
     }
 
-  gsl_matrix_free (r);
-  gsl_permutation_free (perm);
-  gsl_vector_free (tau);
-  gsl_vector_free (norm);
-
   return GSL_SUCCESS;
-}
+} /* gsl_multifit_covar_QRPT() */
diff -Nru gsl-doc-1.16/multifit/fdfridge.c gsl-doc-2.3/multifit/fdfridge.c
--- gsl-doc-1.16/multifit/fdfridge.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/fdfridge.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,460 @@
+/* multifit/fdfridge.c
+ * 
+ * Copyright (C) 2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_multifit_nlin.h>
+#include <gsl/gsl_blas.h>
+
+static int fdfridge_f(const gsl_vector * x, void * params, gsl_vector * f);
+static int fdfridge_df(const gsl_vector * x, void * params, gsl_matrix * J);
+
+gsl_multifit_fdfridge *
+gsl_multifit_fdfridge_alloc (const gsl_multifit_fdfsolver_type * T,
+                             const size_t n, const size_t p)
+{
+  gsl_multifit_fdfridge * work;
+
+  work = calloc(1, sizeof(gsl_multifit_fdfridge));
+  if (work == NULL)
+    {
+      GSL_ERROR_VAL("failed to allocate workspace",
+                    GSL_ENOMEM, 0);
+    }
+
+  work->s = gsl_multifit_fdfsolver_alloc (T, n + p, p);
+  if (work->s == NULL)
+    {
+      gsl_multifit_fdfridge_free(work);
+      GSL_ERROR_VAL("failed to allocate space for fdfsolver",
+                    GSL_ENOMEM, 0);
+    }
+
+  work->wts = gsl_vector_alloc(n + p);
+  if (work->wts == NULL)
+    {
+      gsl_multifit_fdfridge_free(work);
+      GSL_ERROR_VAL("failed to allocate space for weight vector",
+                    GSL_ENOMEM, 0);
+    }
+
+  work->f = gsl_vector_alloc(n);
+  if (work->f == NULL)
+    {
+      gsl_multifit_fdfridge_free(work);
+      GSL_ERROR_VAL("failed to allocate space for f vector",
+                    GSL_ENOMEM, 0);
+    }
+
+  work->n = n;
+  work->p = p;
+  work->lambda = 0.0;
+
+  /* initialize weights to 1 (for augmented portion of vector) */
+  gsl_vector_set_all(work->wts, 1.0);
+
+  return work;
+} /* gsl_multifit_fdfridge_alloc() */
+
+void
+gsl_multifit_fdfridge_free(gsl_multifit_fdfridge *work)
+{
+  if (work->s)
+    gsl_multifit_fdfsolver_free(work->s);
+
+  if (work->wts)
+    gsl_vector_free(work->wts);
+    
+  if (work->f)
+    gsl_vector_free(work->f);
+
+  free(work);
+}
+
+const char *
+gsl_multifit_fdfridge_name(const gsl_multifit_fdfridge * w)
+{
+  return gsl_multifit_fdfsolver_name(w->s);
+}
+
+gsl_vector *
+gsl_multifit_fdfridge_position (const gsl_multifit_fdfridge * w)
+{
+  return gsl_multifit_fdfsolver_position(w->s);
+}
+
+gsl_vector *
+gsl_multifit_fdfridge_residual (const gsl_multifit_fdfridge * w)
+{
+  return gsl_multifit_fdfsolver_residual(w->s);
+}
+
+size_t
+gsl_multifit_fdfridge_niter (const gsl_multifit_fdfridge * w)
+{
+  return w->s->niter;
+}
+
+int
+gsl_multifit_fdfridge_set (gsl_multifit_fdfridge * w,
+                           gsl_multifit_function_fdf * f,
+                           const gsl_vector * x,
+                           const double lambda)
+{
+  return gsl_multifit_fdfridge_wset(w, f, x, lambda, NULL);
+} /* gsl_multifit_fdfridge_set() */
+
+int
+gsl_multifit_fdfridge_wset (gsl_multifit_fdfridge * w,
+                            gsl_multifit_function_fdf * f,
+                            const gsl_vector * x,
+                            const double lambda,
+                            const gsl_vector * wts)
+{
+  const size_t n = w->n;
+  const size_t p = w->p;
+
+  if (n != f->n || p != f->p)
+    {
+      GSL_ERROR ("function size does not match solver", GSL_EBADLEN);
+    }
+  else if (p != x->size)
+    {
+      GSL_ERROR ("vector length does not match solver", GSL_EBADLEN);
+    }
+  else if (wts != NULL && n != wts->size)
+    {
+      GSL_ERROR ("weight vector length does not match solver", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+      gsl_vector_view wv = gsl_vector_subvector(w->wts, 0, n);
+
+      /* save user defined fdf */
+      w->fdf = f;
+
+      /* build modified fdf for Tikhonov terms */
+      w->fdftik.f = &fdfridge_f;
+      w->fdftik.df = &fdfridge_df;
+      w->fdftik.n = n + p; /* add p for Tikhonov terms */
+      w->fdftik.p = p;
+      w->fdftik.params = (void *) w;
+
+      /* store damping parameter */
+      w->lambda = lambda;
+      w->L = NULL;
+
+      if (wts)
+        {
+          /* copy weight vector into user portion of w->wts */
+          gsl_vector_memcpy(&wv.vector, wts);
+          status = gsl_multifit_fdfsolver_wset(w->s, &(w->fdftik), x, w->wts);
+        }
+      else
+        {
+          status = gsl_multifit_fdfsolver_wset(w->s, &(w->fdftik), x, NULL);
+        }
+
+      /* update function/Jacobian evaluations */
+      f->nevalf = w->fdftik.nevalf;
+      f->nevaldf = w->fdftik.nevaldf;
+
+      return status;
+    }
+} /* gsl_multifit_fdfridge_wset() */
+
+int
+gsl_multifit_fdfridge_set2 (gsl_multifit_fdfridge * w,
+                            gsl_multifit_function_fdf * f,
+                            const gsl_vector * x,
+                            const gsl_vector * lambda)
+{
+  return gsl_multifit_fdfridge_wset2(w, f, x, lambda, NULL);
+} /* gsl_multifit_fdfridge_set2() */
+
+int
+gsl_multifit_fdfridge_wset2 (gsl_multifit_fdfridge * w,
+                             gsl_multifit_function_fdf * f,
+                             const gsl_vector * x,
+                             const gsl_vector * lambda,
+                             const gsl_vector * wts)
+{
+  const size_t n = w->n;
+  const size_t p = w->p;
+
+  if (n != f->n || p != f->p)
+    {
+      GSL_ERROR ("function size does not match solver", GSL_EBADLEN);
+    }
+  else if (p != x->size)
+    {
+      GSL_ERROR ("vector length does not match solver", GSL_EBADLEN);
+    }
+  else if (lambda->size != p)
+    {
+      GSL_ERROR ("lambda vector size does not match solver", GSL_EBADLEN);
+    }
+  else if (wts != NULL && n != wts->size)
+    {
+      GSL_ERROR ("weight vector length does not match solver", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+      gsl_vector_view wv = gsl_vector_subvector(w->wts, 0, n);
+
+      /* save user defined fdf */
+      w->fdf = f;
+      w->fdf->nevalf = 0;
+      w->fdf->nevaldf = 0;
+
+      /* build modified fdf for Tikhonov terms */
+      w->fdftik.f = &fdfridge_f;
+      w->fdftik.df = &fdfridge_df;
+      w->fdftik.n = n + p; /* add p for Tikhonov terms */
+      w->fdftik.p = p;
+      w->fdftik.params = (void *) w;
+
+      /* store damping matrix */
+      w->lambda = 0.0;
+      w->L_diag = lambda;
+      w->L = NULL;
+
+      if (wts)
+        {
+          /* copy weight vector into user portion */
+          gsl_vector_memcpy(&wv.vector, wts);
+          status = gsl_multifit_fdfsolver_wset(w->s, &(w->fdftik), x, w->wts);
+        }
+      else
+        {
+          status = gsl_multifit_fdfsolver_wset(w->s, &(w->fdftik), x, NULL);
+        }
+
+      /* update function/Jacobian evaluations */
+      f->nevalf = w->fdftik.nevalf;
+      f->nevaldf = w->fdftik.nevaldf;
+
+      return status;
+    }
+} /* gsl_multifit_fdfridge_wset2() */
+
+int
+gsl_multifit_fdfridge_set3 (gsl_multifit_fdfridge * w,
+                            gsl_multifit_function_fdf * f,
+                            const gsl_vector * x,
+                            const gsl_matrix * L)
+{
+  return gsl_multifit_fdfridge_wset3(w, f, x, L, NULL);
+} /* gsl_multifit_fdfridge_set3() */
+
+int
+gsl_multifit_fdfridge_wset3 (gsl_multifit_fdfridge * w,
+                             gsl_multifit_function_fdf * f,
+                             const gsl_vector * x,
+                             const gsl_matrix * L,
+                             const gsl_vector * wts)
+{
+  const size_t n = w->n;
+  const size_t p = w->p;
+
+  if (n != f->n || p != f->p)
+    {
+      GSL_ERROR ("function size does not match solver", GSL_EBADLEN);
+    }
+  else if (p != x->size)
+    {
+      GSL_ERROR ("vector length does not match solver", GSL_EBADLEN);
+    }
+  else if (L->size2 != p)
+    {
+      GSL_ERROR ("L matrix size2 does not match solver", GSL_EBADLEN);
+    }
+  else if (wts != NULL && n != wts->size)
+    {
+      GSL_ERROR ("weight vector length does not match solver", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+      gsl_vector_view wv = gsl_vector_subvector(w->wts, 0, n);
+
+      /* save user defined fdf */
+      w->fdf = f;
+      w->fdf->nevalf = 0;
+      w->fdf->nevaldf = 0;
+
+      /* build modified fdf for Tikhonov terms */
+      w->fdftik.f = &fdfridge_f;
+      w->fdftik.df = &fdfridge_df;
+      w->fdftik.n = n + p; /* add p for Tikhonov terms */
+      w->fdftik.p = p;
+      w->fdftik.params = (void *) w;
+
+      /* store damping matrix */
+      w->lambda = 0.0;
+      w->L_diag = NULL;
+      w->L = L;
+
+      if (wts)
+        {
+          /* copy weight vector into user portion */
+          gsl_vector_memcpy(&wv.vector, wts);
+          status = gsl_multifit_fdfsolver_wset(w->s, &(w->fdftik), x, w->wts);
+        }
+      else
+        {
+          status = gsl_multifit_fdfsolver_wset(w->s, &(w->fdftik), x, NULL);
+        }
+
+      /* update function/Jacobian evaluations */
+      f->nevalf = w->fdftik.nevalf;
+      f->nevaldf = w->fdftik.nevaldf;
+
+      return status;
+    }
+} /* gsl_multifit_fdfridge_wset3() */
+
+int
+gsl_multifit_fdfridge_iterate (gsl_multifit_fdfridge * w)
+{
+  int status = gsl_multifit_fdfsolver_iterate(w->s);
+
+  /* update function/Jacobian evaluations */
+  w->fdf->nevalf = w->fdftik.nevalf;
+  w->fdf->nevaldf = w->fdftik.nevaldf;
+
+  return status;
+}
+
+int
+gsl_multifit_fdfridge_driver (gsl_multifit_fdfridge * w,
+                              const size_t maxiter,
+                              const double xtol,
+                              const double gtol,
+                              const double ftol,
+                              int *info)
+{
+  int status = gsl_multifit_fdfsolver_driver(w->s, maxiter, xtol,
+                                             gtol, ftol, info);
+  return status;
+} /* gsl_multifit_fdfridge_driver() */
+
+/*
+fdfridge_f()
+  Callback function to provide residuals, including extra p
+Tikhonov terms. The residual vector will have the form:
+
+f~ = [     f     ]
+     [ \lambda x ]
+
+where f is the user supplied residuals, x are the model
+parameters, and \lambda is the Tikhonov damping parameter
+
+Inputs: x      - model parameters (size p)
+        params - pointer to fdfridge workspace
+        f      - (output) (n+p) vector to store f~
+*/
+
+static int
+fdfridge_f(const gsl_vector * x, void * params, gsl_vector * f)
+{
+  int status;
+  gsl_multifit_fdfridge *w = (gsl_multifit_fdfridge *) params;
+  const size_t n = w->n;
+  const size_t p = w->p;
+  gsl_vector_view f_user = gsl_vector_subvector(f, 0, n);
+  gsl_vector_view f_tik = gsl_vector_subvector(f, n, p);
+
+  /* call user callback function to get residual vector f */
+  status = gsl_multifit_eval_wf(w->fdf, x, NULL, &f_user.vector);
+  if (status)
+    return status;
+
+  if (w->L_diag)
+    {
+      /* store diag(L_diag) x in Tikhonov portion of f~ */
+      gsl_vector_memcpy(&f_tik.vector, x);
+      gsl_vector_mul(&f_tik.vector, w->L_diag);
+    }
+  else if (w->L)
+    {
+      /* store Lx in Tikhonov portion of f~ */
+      gsl_blas_dgemv(CblasNoTrans, 1.0, w->L, x, 0.0, &f_tik.vector);
+    }
+  else
+    {
+      /* store \lambda x in Tikhonov portion of f~ */
+      gsl_vector_memcpy(&f_tik.vector, x);
+      gsl_vector_scale(&f_tik.vector, w->lambda);
+    }
+
+  return GSL_SUCCESS;
+} /* fdfridge_f() */
+
+static int
+fdfridge_df(const gsl_vector * x, void * params, gsl_matrix * J)
+{
+  int status;
+  gsl_multifit_fdfridge *w = (gsl_multifit_fdfridge *) params;
+  const size_t n = w->n;
+  const size_t p = w->p;
+  gsl_matrix_view J_user = gsl_matrix_submatrix(J, 0, 0, n, p);
+  gsl_matrix_view J_tik = gsl_matrix_submatrix(J, n, 0, p, p);
+  gsl_vector_view diag = gsl_matrix_diagonal(&J_tik.matrix);
+
+  /* compute Jacobian */
+  if (w->fdf->df)
+    status = gsl_multifit_eval_wdf(w->fdf, x, NULL, &J_user.matrix);
+  else
+    {
+      /* compute f(x) and then finite difference Jacobian */
+      status = gsl_multifit_eval_wf(w->fdf, x, NULL, w->f);
+      status += gsl_multifit_fdfsolver_dif_df(x, NULL, w->fdf, w->f,
+                                              &J_user.matrix);
+    }
+
+  if (status)
+    return status;
+
+  if (w->L_diag)
+    {
+      /* store diag(L_diag) in Tikhonov portion of J */
+      gsl_matrix_set_zero(&J_tik.matrix);
+      gsl_vector_memcpy(&diag.vector, w->L_diag);
+    }
+  else if (w->L)
+    {
+      /* store L in Tikhonov portion of J */
+      gsl_matrix_memcpy(&J_tik.matrix, w->L);
+    }
+  else
+    {
+      /* store \lambda I_p in Tikhonov portion of J */
+      gsl_matrix_set_zero(&J_tik.matrix);
+      gsl_vector_set_all(&diag.vector, w->lambda);
+    }
+
+  return GSL_SUCCESS;
+} /* fdfridge_df() */
diff -Nru gsl-doc-1.16/multifit/fdfsolver.c gsl-doc-2.3/multifit/fdfsolver.c
--- gsl-doc-1.16/multifit/fdfsolver.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/fdfsolver.c	2015-11-03 16:21:55.000000000 +0000
@@ -20,6 +20,7 @@
 #include <config.h>
 #include <stdlib.h>
 #include <string.h>
+#include <gsl/gsl_math.h>
 #include <gsl/gsl_errno.h>
 #include <gsl/gsl_multifit_nlin.h>
 
@@ -36,8 +37,7 @@
       GSL_ERROR_VAL ("insufficient data points, n < p", GSL_EINVAL, 0);
     }
 
-  s = (gsl_multifit_fdfsolver *) malloc (sizeof (gsl_multifit_fdfsolver));
-
+  s = (gsl_multifit_fdfsolver *) calloc (1, sizeof (gsl_multifit_fdfsolver));
   if (s == 0)
     {
       GSL_ERROR_VAL ("failed to allocate space for multifit solver struct",
@@ -48,7 +48,7 @@
 
   if (s->x == 0) 
     {
-      free (s);
+      gsl_multifit_fdfsolver_free (s);
       GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
     }
 
@@ -56,44 +56,41 @@
 
   if (s->f == 0) 
     {
-      gsl_vector_free (s->x);
-      free (s);
+      gsl_multifit_fdfsolver_free (s);
       GSL_ERROR_VAL ("failed to allocate space for f", GSL_ENOMEM, 0);
     }
 
-  s->J = gsl_matrix_calloc (n,p);
+  s->dx = gsl_vector_calloc (p);
+
+  if (s->dx == 0) 
+    {
+      gsl_multifit_fdfsolver_free (s);
+      GSL_ERROR_VAL ("failed to allocate space for dx", GSL_ENOMEM, 0);
+    }
+
+  s->g = gsl_vector_alloc (p);
 
-  if (s->J == 0) 
+  if (s->g == 0) 
     {
-      gsl_vector_free (s->x);
-      gsl_vector_free (s->f);
-      free (s);
+      gsl_multifit_fdfsolver_free (s);
       GSL_ERROR_VAL ("failed to allocate space for g", GSL_ENOMEM, 0);
     }
 
-  s->dx = gsl_vector_calloc (p);
+  s->sqrt_wts = gsl_vector_calloc (n);
 
-  if (s->dx == 0) 
+  if (s->sqrt_wts == 0) 
     {
-      gsl_matrix_free (s->J);
-      gsl_vector_free (s->x);
-      gsl_vector_free (s->f);
-      free (s);
-      GSL_ERROR_VAL ("failed to allocate space for dx", GSL_ENOMEM, 0);
+      gsl_multifit_fdfsolver_free (s);
+      GSL_ERROR_VAL ("failed to allocate space for sqrt_wts", GSL_ENOMEM, 0);
     }
 
-  s->state = malloc (T->size);
+  s->state = calloc (1, T->size);
 
   if (s->state == 0)
     {
-      gsl_vector_free (s->dx);
-      gsl_vector_free (s->x);
-      gsl_vector_free (s->f);
-      gsl_matrix_free (s->J);
-      free (s);         /* exception in constructor, avoid memory leak */
-      
+      gsl_multifit_fdfsolver_free (s);
       GSL_ERROR_VAL ("failed to allocate space for multifit solver state",
-                        GSL_ENOMEM, 0);
+                     GSL_ENOMEM, 0);
     }
 
   s->type = T ;
@@ -102,17 +99,13 @@
 
   if (status != GSL_SUCCESS)
     {
-      free (s->state);
-      gsl_vector_free (s->dx);
-      gsl_vector_free (s->x);
-      gsl_vector_free (s->f);
-      gsl_matrix_free (s->J);
-      free (s);         /* exception in constructor, avoid memory leak */
-      
+      gsl_multifit_fdfsolver_free (s);
       GSL_ERROR_VAL ("failed to set solver", status, 0);
     }
 
   s->fdf = NULL;
+  
+  s->niter = 0;
 
   return s;
 }
@@ -122,61 +115,173 @@
                             gsl_multifit_function_fdf * f, 
                             const gsl_vector * x)
 {
-  if (s->f->size != f->n)
+  return gsl_multifit_fdfsolver_wset(s, f, x, NULL);
+}
+
+int
+gsl_multifit_fdfsolver_wset (gsl_multifit_fdfsolver * s, 
+                             gsl_multifit_function_fdf * f, 
+                             const gsl_vector * x,
+                             const gsl_vector * wts)
+{
+  const size_t n = s->f->size;
+
+  if (n != f->n)
     {
       GSL_ERROR ("function size does not match solver", GSL_EBADLEN);
     }
-
-  if (s->x->size != x->size)
+  else if (s->x->size != x->size)
     {
       GSL_ERROR ("vector length does not match solver", GSL_EBADLEN);
-    }  
+    }
+  else if (wts != NULL && n != wts->size)
+    {
+      GSL_ERROR ("weight vector length does not match solver", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i;
 
-  s->fdf = f;
-  gsl_vector_memcpy(s->x,x);
+      s->fdf = f;
+      gsl_vector_memcpy(s->x, x);
+      s->niter = 0;
+
+      if (wts)
+        {
+          for (i = 0; i < n; ++i)
+            {
+              double wi = gsl_vector_get(wts, i);
+              gsl_vector_set(s->sqrt_wts, i, sqrt(wi));
+            }
+        }
+      else
+        gsl_vector_set_all(s->sqrt_wts, 1.0);
   
-  return (s->type->set) (s->state, s->fdf, s->x, s->f, s->J, s->dx);
+      return (s->type->set) (s->state, s->sqrt_wts, s->fdf, s->x, s->f, s->dx);
+    }
 }
 
 int
 gsl_multifit_fdfsolver_iterate (gsl_multifit_fdfsolver * s)
 {
-  return (s->type->iterate) (s->state, s->fdf, s->x, s->f, s->J, s->dx);
+  int status =
+    (s->type->iterate) (s->state, s->sqrt_wts, s->fdf, s->x, s->f, s->dx);
+
+  s->niter++;
+
+  return status;
 }
 
+/*
+gsl_multifit_fdfsolver_driver()
+  Iterate the nonlinear least squares solver until completion
+
+Inputs: s - fdfsolver
+        maxiter - maximum iterations to allow
+        xtol    - tolerance in step x
+        gtol    - tolerance in gradient
+        ftol    - tolerance in ||f||
+        info    - (output) info flag on why iteration terminated
+                  1 = stopped due to small step size ||dx|
+                  2 = stopped due to small gradient
+                  3 = stopped due to small change in f
+                  GSL_ETOLX = ||dx|| has converged to within machine
+                              precision (and xtol is too small)
+                  GSL_ETOLG = ||g||_inf is smaller than machine
+                              precision (gtol is too small)
+                  GSL_ETOLF = change in ||f|| is smaller than machine
+                              precision (ftol is too small)
+
+Return: GSL_SUCCESS if converged, GSL_MAXITER if maxiter exceeded without
+converging
+*/
 int
 gsl_multifit_fdfsolver_driver (gsl_multifit_fdfsolver * s,
                                const size_t maxiter,
-                               const double epsabs,
-                               const double epsrel)
+                               const double xtol,
+                               const double gtol,
+                               const double ftol,
+                               int *info)
 {
   int status;
   size_t iter = 0;
 
-  do  
-    {   
+  do
+    {
       status = gsl_multifit_fdfsolver_iterate (s);
-      if (status) 
+
+      /*
+       * if status is GSL_ENOPROG or GSL_SUCCESS, continue iterating,
+       * otherwise the method has converged with a GSL_ETOLx flag
+       */
+      if (status != GSL_SUCCESS && status != GSL_ENOPROG)
         break;
 
       /* test for convergence */
-      status = gsl_multifit_test_delta (s->dx, s->x, epsabs, epsrel);
-    }   
+      status = gsl_multifit_fdfsolver_test(s, xtol, gtol, ftol, info);
+    }
   while (status == GSL_CONTINUE && ++iter < maxiter);
 
+  /*
+   * the following error codes mean that the solution has converged
+   * to within machine precision, so record the error code in info
+   * and return success
+   */
+  if (status == GSL_ETOLF || status == GSL_ETOLX || status == GSL_ETOLG)
+    {
+      *info = status;
+      status = GSL_SUCCESS;
+    }
+
+  /* check if max iterations reached */
+  if (iter >= maxiter && status != GSL_SUCCESS)
+    status = GSL_EMAXITER;
+
   return status;
 } /* gsl_multifit_fdfsolver_driver() */
 
+int
+gsl_multifit_fdfsolver_jac (gsl_multifit_fdfsolver * s, gsl_matrix * J)
+{
+  const size_t n = s->f->size;
+  const size_t p = s->x->size;
+
+  if (n != J->size1 || p != J->size2)
+    {
+      GSL_ERROR ("Jacobian dimensions do not match solver", GSL_EBADLEN);
+    }
+  else
+    {
+      return (s->type->jac) (s->state, J);
+    }
+} /* gsl_multifit_fdfsolver_jac() */
+
 void
 gsl_multifit_fdfsolver_free (gsl_multifit_fdfsolver * s)
 {
   RETURN_IF_NULL (s);
-  (s->type->free) (s->state);
-  free (s->state);
-  gsl_vector_free (s->dx);
-  gsl_vector_free (s->x);
-  gsl_vector_free (s->f);
-  gsl_matrix_free (s->J);
+
+  if (s->state)
+    {
+      (s->type->free) (s->state);
+      free (s->state);
+    }
+
+  if (s->dx)
+    gsl_vector_free (s->dx);
+
+  if (s->x)
+    gsl_vector_free (s->x);
+
+  if (s->f)
+    gsl_vector_free (s->f);
+
+  if (s->sqrt_wts)
+    gsl_vector_free (s->sqrt_wts);
+
+  if (s->g)
+    gsl_vector_free (s->g);
+
   free (s);
 }
 
@@ -192,3 +297,84 @@
   return s->x;
 }
 
+gsl_vector *
+gsl_multifit_fdfsolver_residual (const gsl_multifit_fdfsolver * s)
+{
+  return s->f;
+}
+
+size_t
+gsl_multifit_fdfsolver_niter (const gsl_multifit_fdfsolver * s)
+{
+  return s->niter;
+}
+
+/*
+gsl_multifit_eval_wf()
+  Compute residual vector y with user callback function, and apply
+weighting transform if given:
+
+y~ = sqrt(W) y
+
+Inputs: fdf  - callback function
+        x    - model parameters
+        swts - weight matrix sqrt(W) = sqrt(diag(w1,w2,...,wn))
+               set to NULL for unweighted fit
+        y    - (output) (weighted) residual vector
+               y_i = sqrt(w_i) f_i where f_i is unweighted residual
+*/
+
+int
+gsl_multifit_eval_wf(gsl_multifit_function_fdf *fdf, const gsl_vector *x,
+                     const gsl_vector *swts, gsl_vector *y)
+{
+  int s = ((*((fdf)->f)) (x, fdf->params, y));
+  ++(fdf->nevalf);
+
+  /* y <- sqrt(W) y */
+  if (swts)
+    gsl_vector_mul(y, swts);
+
+  return s;
+}
+
+/*
+gsl_multifit_eval_wdf()
+  Compute Jacobian matrix J with user callback function, and apply
+weighting transform if given:
+
+J~ = sqrt(W) J
+
+Inputs: fdf  - callback function
+        x    - model parameters
+        swts - weight matrix W = diag(w1,w2,...,wn)
+               set to NULL for unweighted fit
+        dy   - (output) (weighted) Jacobian matrix
+               dy = sqrt(W) dy where dy is unweighted Jacobian
+*/
+
+int
+gsl_multifit_eval_wdf(gsl_multifit_function_fdf *fdf, const gsl_vector *x,
+                      const gsl_vector *swts, gsl_matrix *dy)
+{
+  int status = ((*((fdf)->df)) (x, fdf->params, dy));
+
+  ++(fdf->nevaldf);
+
+  /* J <- sqrt(W) J */
+  if (swts)
+    {
+      const size_t n = swts->size;
+      size_t i;
+
+      for (i = 0; i < n; ++i)
+        {
+          double swi = gsl_vector_get(swts, i);
+          gsl_vector_view v = gsl_matrix_row(dy, i);
+
+          gsl_vector_scale(&v.vector, swi);
+        }
+    }
+
+  return status;
+}
diff -Nru gsl-doc-1.16/multifit/fdjac.c gsl-doc-2.3/multifit/fdjac.c
--- gsl-doc-1.16/multifit/fdjac.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/fdjac.c	2015-11-10 16:31:43.000000000 +0000
@@ -27,7 +27,8 @@
 #include <gsl/gsl_vector.h>
 #include <gsl/gsl_matrix.h>
 
-static int fdjac(const gsl_vector *x, gsl_multifit_function_fdf *fdf,
+static int fdjac(const gsl_vector *x, const gsl_vector *wts,
+                 gsl_multifit_function_fdf *fdf,
                  const gsl_vector *f, gsl_matrix *J);
 
 /*
@@ -35,6 +36,7 @@
   Compute approximate Jacobian using forward differences
 
 Inputs: x   - parameter vector
+        wts - data weights
         fdf - fdf struct
         f   - (input) vector of function values f_i(x)
         J   - (output) Jacobian matrix
@@ -43,8 +45,8 @@
 */
 
 static int
-fdjac(const gsl_vector *x, gsl_multifit_function_fdf *fdf,
-      const gsl_vector *f, gsl_matrix *J)
+fdjac(const gsl_vector *x, const gsl_vector *wts,
+      gsl_multifit_function_fdf *fdf, const gsl_vector *f, gsl_matrix *J)
 {
   int status = 0;
   size_t i, j;
@@ -66,7 +68,7 @@
       /* perturb x_j to compute forward difference */
       gsl_vector_set((gsl_vector *) x, j, xj + h);
 
-      status += GSL_MULTIFIT_FN_EVAL_F (fdf, x, &v.vector);
+      status += gsl_multifit_eval_wf (fdf, x, wts, &v.vector);
       if (status)
         return status;
 
@@ -91,6 +93,7 @@
   Compute approximate Jacobian using finite differences
 
 Inputs: x   - parameter vector
+        wts - data weights (set to NULL if not needed)
         fdf - fdf
         f   - (input) function values f_i(x)
         J   - (output) approximate Jacobian matrix
@@ -99,12 +102,15 @@
 */
 
 int
-gsl_multifit_fdfsolver_dif_df(const gsl_vector *x, gsl_multifit_function_fdf *fdf,
+gsl_multifit_fdfsolver_dif_df(const gsl_vector *x, const gsl_vector *wts,
+                              gsl_multifit_function_fdf *fdf,
                               const gsl_vector *f, gsl_matrix *J)
 {
-  return fdjac(x, fdf, f, J);
+  return fdjac(x, wts, fdf, f, J);
 } /* gsl_multifit_fdfsolver_dif_df() */
 
+#ifndef GSL_DISABLE_DEPRECATED
+
 /*
 gsl_multifit_fdfsolver_dif_fdf()
   Compute function values (analytic) and approximate Jacobian using finite
@@ -119,18 +125,21 @@
 */
 
 int
-gsl_multifit_fdfsolver_dif_fdf(const gsl_vector *x, gsl_multifit_function_fdf *fdf,
+gsl_multifit_fdfsolver_dif_fdf(const gsl_vector *x,
+                               gsl_multifit_function_fdf *fdf,
                                gsl_vector *f, gsl_matrix *J)
 {
   int status = 0;
 
-  status = GSL_MULTIFIT_FN_EVAL_F(fdf, x, f);
+  status = gsl_multifit_eval_wf(fdf, x, NULL, f);
   if (status)
     return status;
 
-  status = fdjac(x, fdf, f, J);
+  status = fdjac(x, NULL, fdf, f, J);
   if (status)
     return status;
 
   return status;
 } /* gsl_multifit_fdfsolver_dif_fdf() */
+
+#endif /* !GSL_DISABLE_DEPRECATED */
diff -Nru gsl-doc-1.16/multifit/gcv.c gsl-doc-2.3/multifit/gcv.c
--- gsl-doc-1.16/multifit/gcv.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/gcv.c	2016-11-21 17:55:13.000000000 +0000
@@ -0,0 +1,397 @@
+/* multifit/gcv.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/*
+ * References:
+ *
+ * [1] P. C. Hansen, "Discrete Inverse Problems: Insight and Algorithms,"
+ * SIAM Press, 2010.
+ */
+
+#include <config.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_multifit.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_min.h>
+
+typedef struct
+{
+  const gsl_vector * S;
+  const gsl_vector * UTy;
+  double delta0;
+  size_t np;
+  gsl_vector * workp;
+} gcv_params;
+
+static double gcv_func(double lambda, void * params);
+
+/*
+gsl_multifit_linear_gcv_init()
+  Initialize Generalized Cross Validation parameters
+
+Inputs: y         - right hand side vector
+        reg_param - (output) regularization parameters
+        UTy       - (output) U^T y
+        delta0    - (output) delta0
+        work      - workspace
+*/
+
+int
+gsl_multifit_linear_gcv_init(const gsl_vector * y,
+                             gsl_vector * reg_param,
+                             gsl_vector * UTy,
+                             double * delta0,
+                             gsl_multifit_linear_workspace * work)
+{
+  const size_t n = y->size;
+
+  if (n != work->n)
+    {
+      GSL_ERROR("y vector does not match workspace", GSL_EBADLEN);
+    }
+  else if (UTy->size != work->p)
+    {
+      GSL_ERROR ("UTy vector does not match workspace", GSL_EBADLEN);
+    }
+  else
+    {
+      const size_t p = work->p;
+
+      gsl_matrix_view U = gsl_matrix_submatrix(work->A, 0, 0, n, p);
+      gsl_vector_view S = gsl_vector_subvector(work->S, 0, p);
+
+      const double smax = gsl_vector_get(&S.vector, 0);
+      const double smin = gsl_vector_get(&S.vector, p - 1);
+
+      double dr; /* residual error from projection */
+
+      double normy = gsl_blas_dnrm2(y);
+      double normUTy;
+
+      /* compute projection UTy = U^T y */
+      gsl_blas_dgemv (CblasTrans, 1.0, &U.matrix, y, 0.0, UTy);
+      normUTy = gsl_blas_dnrm2(UTy);
+
+      /* dr = ||y||^2 - ||U^T y||^2 */
+      dr = (normy + normUTy) * (normy - normUTy);
+
+      /* calculate regularization parameters */
+      gsl_multifit_linear_lreg(smin, smax, reg_param);
+
+      if (n > p && dr > 0.0)
+        *delta0 = dr;
+      else
+        *delta0 = 0.0;
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+gsl_multifit_linear_gcv_curve()
+  Calculate Generalized Cross Validation curve for a set
+of regularization parameters
+
+Inputs: reg_param - regularization parameters
+        UTy       - U^T y vector, size p
+        delta0    - delta0
+        G         - (output) GCV curve values
+        work      - workspace
+*/
+
+int
+gsl_multifit_linear_gcv_curve(const gsl_vector * reg_param,
+                              const gsl_vector * UTy,
+                              const double delta0,
+                              gsl_vector * G,
+                              gsl_multifit_linear_workspace * work)
+{
+  const size_t n = work->n;
+  const size_t p = work->p;
+  const size_t N = reg_param->size; /* number of points on GCV curve */
+
+  if (UTy->size != p)
+    {
+      GSL_ERROR("UTy vector does not match workspace", GSL_EBADLEN);
+    }
+  else if (G->size != N)
+    {
+      GSL_ERROR ("size of reg_param and G vectors do not match",
+                 GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i;
+
+      gsl_vector_view S = gsl_vector_subvector(work->S, 0, p);
+      gsl_vector_view workp = gsl_matrix_subcolumn(work->QSI, 0, 0, p);
+
+      gcv_params params;
+
+      params.S = &S.vector;
+      params.UTy = UTy;
+      params.delta0 = delta0;
+      params.np = n - p;
+      params.workp = &workp.vector;
+
+      for (i = 0; i < N; ++i)
+        {
+          double lambdai = gsl_vector_get(reg_param, i);
+          double Gi = gcv_func(lambdai, &params);
+
+          gsl_vector_set(G, i, Gi);
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+gsl_multifit_linear_gcv_min()
+  Find regularization parameter which minimizes GCV curve
+
+Inputs: reg_param - regularization parameters
+        UTy       - U^T y vector, size p
+        G         - GCV curve values
+        delta0    - delta0
+        lambda    - (output) optimal regularization parameter
+        work      - workspace
+*/
+
+int
+gsl_multifit_linear_gcv_min(const gsl_vector * reg_param,
+                            const gsl_vector * UTy,
+                            const gsl_vector * G,
+                            const double delta0,
+                            double * lambda,
+                            gsl_multifit_linear_workspace * work)
+{
+  const size_t n = work->n;
+  const size_t p = work->p;
+  const size_t npts = reg_param->size; /* number of points on GCV curve */
+
+  if (UTy->size != p)
+    {
+      GSL_ERROR("UTy vector does not match workspace", GSL_EBADLEN);
+    }
+  else if (G->size != npts)
+    {
+      GSL_ERROR ("size of reg_param and G vectors do not match",
+                 GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+      const size_t max_iter = 500;
+      const double tol = 1.0e-4;
+      gsl_vector_view S = gsl_vector_subvector(work->S, 0, p);
+      gsl_vector_view workp = gsl_matrix_subcolumn(work->QSI, 0, 0, p);
+      gcv_params params;
+      int idxG = (int) gsl_vector_min_index(G);
+      double a = gsl_vector_get(reg_param, GSL_MIN(idxG + 1, (int) npts - 1));
+      double b = gsl_vector_get(reg_param, GSL_MAX(idxG - 1, 0));
+      double m = gsl_vector_get(reg_param, idxG);
+      size_t iter = 0;
+      gsl_function F;
+
+      /* XXX FIXME */
+      gsl_min_fminimizer *min_workspace_p;
+
+      if (idxG == 0 || idxG == ((int)npts - 1))
+        {
+          /* the minimum is an endpoint of the curve, no need to search */
+          *lambda = m;
+          return GSL_SUCCESS;
+        }
+
+      /* XXX FIXME */
+      min_workspace_p = gsl_min_fminimizer_alloc(gsl_min_fminimizer_brent);
+
+      params.S = &S.vector;
+      params.UTy = UTy;
+      params.delta0 = delta0;
+      params.np = n - p;
+      params.workp = &workp.vector;
+
+      F.function = gcv_func;
+      F.params = &params;
+
+      gsl_min_fminimizer_set(min_workspace_p, &F, m, a, b);
+
+      do
+        {
+          iter++;
+          status = gsl_min_fminimizer_iterate(min_workspace_p);
+
+          a = gsl_min_fminimizer_x_lower(min_workspace_p);
+          b = gsl_min_fminimizer_x_upper(min_workspace_p);
+
+          status = gsl_min_test_interval(a, b, 0.0, tol);
+        }
+      while (status == GSL_CONTINUE && iter < max_iter);
+
+      if (status == GSL_SUCCESS)
+        *lambda = gsl_min_fminimizer_minimum(min_workspace_p);
+      else
+        status = GSL_EMAXITER;
+
+      gsl_min_fminimizer_free(min_workspace_p);
+
+      return status;
+    }
+}
+
+/*
+gsl_multifit_linear_gcv_calc()
+  Calculate GCV function G(lambda) for given lambda
+
+Inputs: reg_param - regularization parameters
+        UTy       - U^T y vector, size p
+        delta0    - delta0
+        G         - (output) GCV curve values
+        work      - workspace
+*/
+
+double
+gsl_multifit_linear_gcv_calc(const double lambda,
+                             const gsl_vector * UTy,
+                             const double delta0,
+                             gsl_multifit_linear_workspace * work)
+{
+  const size_t n = work->n;
+  const size_t p = work->p;
+
+  if (UTy->size != p)
+    {
+      GSL_ERROR_VAL("UTy vector does not match workspace", GSL_EBADLEN, 0.0);
+    }
+  else
+    {
+      gsl_vector_view S = gsl_vector_subvector(work->S, 0, p);
+      gsl_vector_view workp = gsl_matrix_subcolumn(work->QSI, 0, 0, p);
+      gcv_params params;
+      double G;
+
+      params.S = &S.vector;
+      params.UTy = UTy;
+      params.delta0 = delta0;
+      params.np = n - p;
+      params.workp = &workp.vector;
+
+      G = gcv_func(lambda, &params);
+
+      return G;
+    }
+}
+
+/*
+gsl_multifit_linear_gcv()
+  Calculate Generalized Cross Validation curve for a set
+of regularization parameters
+
+Inputs: y         - right hand side vector
+        reg_param - (output) regularization parameters
+        G         - (output) GCV curve values
+        lambda    - (output) optimal regularization parameter which
+                    minimizes GCV curve
+        G_lambda  - (output) G(lambda) value at optimal parameter
+        work      - workspace
+*/
+
+int
+gsl_multifit_linear_gcv(const gsl_vector * y,
+                        gsl_vector * reg_param,
+                        gsl_vector * G,
+                        double * lambda,
+                        double * G_lambda,
+                        gsl_multifit_linear_workspace * work)
+{
+  const size_t n = y->size;
+  const size_t N = G->size; /* number of points on GCV curve */
+
+  if (n != work->n)
+    {
+      GSL_ERROR("y vector does not match workspace", GSL_EBADLEN);
+    }
+  else if (reg_param->size != N)
+    {
+      GSL_ERROR ("size of reg_param and G vectors do not match",
+                 GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+      const size_t p = work->p;
+      gsl_vector_view UTy = gsl_vector_subvector(work->xt, 0, p);
+      double delta0;
+
+      status = gsl_multifit_linear_gcv_init(y, reg_param, &UTy.vector, &delta0, work);
+      if (status)
+        return status;
+
+      status = gsl_multifit_linear_gcv_curve(reg_param, &UTy.vector, delta0, G, work);
+      if (status)
+        return status;
+
+      status = gsl_multifit_linear_gcv_min(reg_param, &UTy.vector, G, delta0, lambda, work);
+      if (status)
+        return status;
+
+      *G_lambda = gsl_multifit_linear_gcv_calc(*lambda, &UTy.vector, delta0, work);
+
+      return GSL_SUCCESS;
+    }
+}
+
+static double
+gcv_func(double lambda, void * params)
+{
+  gcv_params * par = (gcv_params *) params;
+  const gsl_vector *S = par->S;
+  const gsl_vector *UTy = par->UTy;
+  double delta0 = par->delta0;
+  size_t np = par->np;
+  gsl_vector *workp = par->workp;
+  const size_t p = S->size;
+  size_t i;
+  double lambda_sq = lambda * lambda;
+  double G, d, norm;
+  double sumf = 0.0;
+
+  /* compute workp = 1 - filter_factors */
+  for (i = 0; i < p; ++i)
+    {
+      double si = gsl_vector_get(S, i);
+      double fi = lambda_sq / (si * si + lambda_sq);
+      gsl_vector_set(workp, i, fi);
+      sumf += fi;
+    }
+
+  d = (double)np + sumf;
+
+  gsl_vector_mul(workp, UTy);
+  norm = gsl_blas_dnrm2(workp);
+
+  G = (norm*norm + delta0) / (d * d);
+
+  return G;
+}
diff -Nru gsl-doc-1.16/multifit/gradient.c gsl-doc-2.3/multifit/gradient.c
--- gsl-doc-1.16/multifit/gradient.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/gradient.c	2015-11-03 16:21:55.000000000 +0000
@@ -1,4 +1,4 @@
-/* multifit/covar.c
+/* multifit/gradient.c
  * 
  * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
  * 
diff -Nru gsl-doc-1.16/multifit/gsl_multifit.h gsl-doc-2.3/multifit/gsl_multifit.h
--- gsl-doc-1.16/multifit/gsl_multifit.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/gsl_multifit.h	2016-11-21 17:55:48.000000000 +0000
@@ -41,23 +41,26 @@
 
 typedef struct 
 {
-  size_t n; /* number of observations */
-  size_t p; /* number of parameters */
-  gsl_matrix * A;
+  size_t nmax;         /* maximum number of observations */
+  size_t pmax;         /* maximum number of parameters */
+  size_t n;            /* number of observations in current SVD decomposition */
+  size_t p;            /* number of parameters in current SVD decomposition */
+  gsl_matrix * A;      /* least squares matrix for SVD, n-by-p */
   gsl_matrix * Q;
   gsl_matrix * QSI;
   gsl_vector * S;
   gsl_vector * t;
   gsl_vector * xt;
   gsl_vector * D;
+  double rcond;        /* reciprocal condition number */
 } 
 gsl_multifit_linear_workspace;
 
 gsl_multifit_linear_workspace *
-gsl_multifit_linear_alloc (size_t n, size_t p);
+gsl_multifit_linear_alloc (const size_t n, const size_t p);
 
 void
-gsl_multifit_linear_free (gsl_multifit_linear_workspace * work);
+gsl_multifit_linear_free (gsl_multifit_linear_workspace * w);
 
 int
 gsl_multifit_linear (const gsl_matrix * X,
@@ -68,25 +71,138 @@
                      gsl_multifit_linear_workspace * work);
 
 int
+gsl_multifit_linear_tsvd (const gsl_matrix * X,
+                          const gsl_vector * y,
+                          const double tol,
+                          gsl_vector * c,
+                          gsl_matrix * cov,
+                          double * chisq,
+                          size_t * rank,
+                          gsl_multifit_linear_workspace * work);
+
+int
 gsl_multifit_linear_svd (const gsl_matrix * X,
-                         const gsl_vector * y,
-                         double tol,
-                         size_t * rank,
-                         gsl_vector * c,
-                         gsl_matrix * cov,
-                         double *chisq, 
                          gsl_multifit_linear_workspace * work);
 
 int
-gsl_multifit_linear_usvd (const gsl_matrix * X,
-                          const gsl_vector * y,
-                          double tol,
-                          size_t * rank,
-                          gsl_vector * c,
-                          gsl_matrix * cov,
-                          double *chisq, 
+gsl_multifit_linear_bsvd (const gsl_matrix * X,
                           gsl_multifit_linear_workspace * work);
 
+size_t
+gsl_multifit_linear_rank(const double tol, const gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_solve (const double lambda,
+                           const gsl_matrix * X,
+                           const gsl_vector * y,
+                           gsl_vector * c,
+                           double *rnorm,
+                           double *snorm,
+                           gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_applyW(const gsl_matrix * X,
+                           const gsl_vector * w,
+                           const gsl_vector * y,
+                           gsl_matrix * WX,
+                           gsl_vector * Wy);
+
+int
+gsl_multifit_linear_stdform1 (const gsl_vector * L,
+                              const gsl_matrix * X,
+                              const gsl_vector * y,
+                              gsl_matrix * Xs,
+                              gsl_vector * ys,
+                              gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_wstdform1 (const gsl_vector * L,
+                               const gsl_matrix * X,
+                               const gsl_vector * w,
+                               const gsl_vector * y,
+                               gsl_matrix * Xs,
+                               gsl_vector * ys,
+                               gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_L_decomp (gsl_matrix * L, gsl_vector * tau);
+
+int
+gsl_multifit_linear_stdform2 (const gsl_matrix * LQR,
+                              const gsl_vector * Ltau,
+                              const gsl_matrix * X,
+                              const gsl_vector * y,
+                              gsl_matrix * Xs,
+                              gsl_vector * ys,
+                              gsl_matrix * M,
+                              gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_wstdform2 (const gsl_matrix * LQR,
+                               const gsl_vector * Ltau,
+                               const gsl_matrix * X,
+                               const gsl_vector * w,
+                               const gsl_vector * y,
+                               gsl_matrix * Xs,
+                               gsl_vector * ys,
+                               gsl_matrix * M,
+                               gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_genform1 (const gsl_vector * L,
+                              const gsl_vector * cs,
+                              gsl_vector * c,
+                              gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_genform2 (const gsl_matrix * LQR,
+                              const gsl_vector * Ltau,
+                              const gsl_matrix * X,
+                              const gsl_vector * y,
+                              const gsl_vector * cs,
+                              const gsl_matrix * M,
+                              gsl_vector * c,
+                              gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_wgenform2 (const gsl_matrix * LQR,
+                               const gsl_vector * Ltau,
+                               const gsl_matrix * X,
+                               const gsl_vector * w,
+                               const gsl_vector * y,
+                               const gsl_vector * cs,
+                               const gsl_matrix * M,
+                               gsl_vector * c,
+                               gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_lreg (const double smin, const double smax,
+                          gsl_vector * reg_param);
+
+int
+gsl_multifit_linear_lcurve (const gsl_vector * y,
+                            gsl_vector * reg_param,
+                            gsl_vector * rho, gsl_vector * eta,
+                            gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_lcorner(const gsl_vector *rho,
+                            const gsl_vector *eta,
+                            size_t *idx);
+
+int
+gsl_multifit_linear_lcorner2(const gsl_vector *reg_param,
+                             const gsl_vector *eta,
+                             size_t *idx);
+
+int
+gsl_multifit_linear_Lk(const size_t p, const size_t k, gsl_matrix *L);
+
+int
+gsl_multifit_linear_Lsobolev(const size_t p, const size_t kmax,
+                             const gsl_vector *alpha, gsl_matrix *L,
+                             gsl_multifit_linear_workspace *work);
+
 int
 gsl_multifit_wlinear (const gsl_matrix * X,
                       const gsl_vector * w,
@@ -97,6 +213,17 @@
                       gsl_multifit_linear_workspace * work);
 
 int
+gsl_multifit_wlinear_tsvd (const gsl_matrix * X,
+                           const gsl_vector * w,
+                           const gsl_vector * y,
+                           const double tol,
+                           gsl_vector * c,
+                           gsl_matrix * cov,
+                           double * chisq,
+                           size_t * rank,
+                           gsl_multifit_linear_workspace * work);
+
+int
 gsl_multifit_wlinear_svd (const gsl_matrix * X,
                           const gsl_vector * w,
                           const gsl_vector * y,
@@ -123,10 +250,50 @@
                          const gsl_vector * c,
                          const gsl_matrix * cov, double *y, double *y_err);
 
+double
+gsl_multifit_linear_rcond (const gsl_multifit_linear_workspace * w);
+
 int
 gsl_multifit_linear_residuals (const gsl_matrix *X, const gsl_vector *y,
                                const gsl_vector *c, gsl_vector *r);
 
+/* gcv.c */
+int
+gsl_multifit_linear_gcv_init(const gsl_vector * y,
+                             gsl_vector * reg_param,
+                             gsl_vector * UTy,
+                             double * delta0,
+                             gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_gcv_curve(const gsl_vector * reg_param,
+                              const gsl_vector * UTy,
+                              const double delta0,
+                              gsl_vector * G,
+                              gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_gcv_min(const gsl_vector * reg_param,
+                            const gsl_vector * UTy,
+                            const gsl_vector * G,
+                            const double delta0,
+                            double * lambda,
+                            gsl_multifit_linear_workspace * work);
+
+double
+gsl_multifit_linear_gcv_calc(const double lambda,
+                             const gsl_vector * UTy,
+                             const double delta0,
+                             gsl_multifit_linear_workspace * work);
+
+int
+gsl_multifit_linear_gcv(const gsl_vector * y,
+                        gsl_vector * reg_param,
+                        gsl_vector * G,
+                        double * lambda,
+                        double * G_lambda,
+                        gsl_multifit_linear_workspace * work);
+
 typedef struct
 {
   const char * name;     /* method name */
@@ -190,14 +357,23 @@
 gsl_multifit_robust_workspace *gsl_multifit_robust_alloc(const gsl_multifit_robust_type *T,
                                                          const size_t n, const size_t p);
 void gsl_multifit_robust_free(gsl_multifit_robust_workspace *w);
-int gsl_multifit_robust_tune(const double tune, gsl_multifit_robust_workspace *w);
+int gsl_multifit_robust_tune(const double tune,
+                             gsl_multifit_robust_workspace *w);
+int gsl_multifit_robust_maxiter(const size_t maxiter,
+                                gsl_multifit_robust_workspace *w);
 const char *gsl_multifit_robust_name(const gsl_multifit_robust_workspace *w);
 gsl_multifit_robust_stats gsl_multifit_robust_statistics(const gsl_multifit_robust_workspace *w);
+int gsl_multifit_robust_weights(const gsl_vector *r, gsl_vector *wts,
+                                gsl_multifit_robust_workspace *w);
 int gsl_multifit_robust(const gsl_matrix * X, const gsl_vector * y,
                         gsl_vector * c, gsl_matrix *cov,
                         gsl_multifit_robust_workspace *w);
 int gsl_multifit_robust_est(const gsl_vector * x, const gsl_vector * c,
                             const gsl_matrix * cov, double *y, double *y_err);
+int gsl_multifit_robust_residuals(const gsl_matrix * X,
+                                  const gsl_vector * y,
+                                  const gsl_vector * c, gsl_vector * r,
+                                  gsl_multifit_robust_workspace * w);
 
 __END_DECLS
 
diff -Nru gsl-doc-1.16/multifit/gsl_multifit_nlin.h gsl-doc-2.3/multifit/gsl_multifit_nlin.h
--- gsl-doc-1.16/multifit/gsl_multifit_nlin.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/gsl_multifit_nlin.h	2015-11-03 16:21:55.000000000 +0000
@@ -25,6 +25,7 @@
 #include <gsl/gsl_math.h>
 #include <gsl/gsl_vector.h>
 #include <gsl/gsl_matrix.h>
+#include <gsl/gsl_permutation.h>
 
 #undef __BEGIN_DECLS
 #undef __END_DECLS
@@ -41,7 +42,9 @@
 int gsl_multifit_gradient (const gsl_matrix * J, const gsl_vector * f,
                            gsl_vector * g);
 
-int gsl_multifit_covar (const gsl_matrix * J, double epsrel, gsl_matrix * covar);
+int gsl_multifit_covar (const gsl_matrix * J, const double epsrel, gsl_matrix * covar);
+int gsl_multifit_covar_QRPT (gsl_matrix * r, gsl_permutation * perm,
+                             const double epsrel, gsl_matrix * covar);
 
 
 /* Definition of vector-valued functions with parameters based on gsl_vector */
@@ -87,8 +90,8 @@
 void gsl_multifit_fsolver_free (gsl_multifit_fsolver * s);
 
 int gsl_multifit_fsolver_set (gsl_multifit_fsolver * s, 
-                                   gsl_multifit_function * f, 
-                                   const gsl_vector * x);
+                              gsl_multifit_function * f, 
+                              const gsl_vector * x);
 
 int gsl_multifit_fsolver_iterate (gsl_multifit_fsolver * s);
 
@@ -107,24 +110,28 @@
   int (* f) (const gsl_vector * x, void * params, gsl_vector * f);
   int (* df) (const gsl_vector * x, void * params, gsl_matrix * df);
   int (* fdf) (const gsl_vector * x, void * params, gsl_vector * f, gsl_matrix *df);
-  size_t n;   /* number of functions */
-  size_t p;   /* number of independent variables */
-  void * params;
+  size_t n;       /* number of functions */
+  size_t p;       /* number of independent variables */
+  void * params;  /* user parameters */
+  size_t nevalf;  /* number of function evaluations */
+  size_t nevaldf; /* number of Jacobian evaluations */
 };
 
 typedef struct gsl_multifit_function_fdf_struct gsl_multifit_function_fdf ;
 
-#define GSL_MULTIFIT_FN_EVAL_F(F,x,y) ((*((F)->f))(x,(F)->params,(y)))
-#define GSL_MULTIFIT_FN_EVAL_DF(F,x,dy) ((*((F)->df))(x,(F)->params,(dy)))
-#define GSL_MULTIFIT_FN_EVAL_F_DF(F,x,y,dy) ((*((F)->fdf))(x,(F)->params,(y),(dy)))
-
 typedef struct
   {
     const char *name;
     size_t size;
     int (*alloc) (void *state, size_t n, size_t p);
-    int (*set) (void *state, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx);
-    int (*iterate) (void *state, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx);
+    int (*set) (void *state, const gsl_vector * wts,
+                gsl_multifit_function_fdf * fdf, gsl_vector * x,
+                gsl_vector * f, gsl_vector * dx);
+    int (*iterate) (void *state, const gsl_vector * wts,
+                    gsl_multifit_function_fdf * fdf, gsl_vector * x,
+                    gsl_vector * f, gsl_vector * dx);
+    int (*gradient) (void *state, gsl_vector * g);
+    int (*jac) (void *state, gsl_matrix * J);
     void (*free) (void *state);
   }
 gsl_multifit_fdfsolver_type;
@@ -133,10 +140,12 @@
   {
     const gsl_multifit_fdfsolver_type * type;
     gsl_multifit_function_fdf * fdf ;
-    gsl_vector * x;
-    gsl_vector * f;
-    gsl_matrix * J;
-    gsl_vector * dx;
+    gsl_vector * x;        /* parameter values x */
+    gsl_vector * f;        /* residual vector f(x) */
+    gsl_vector * dx;       /* step dx */
+    gsl_vector * g;        /* gradient J^T f */
+    gsl_vector * sqrt_wts; /* sqrt(wts) */
+    size_t niter;          /* number of iterations performed */
     void *state;
   }
 gsl_multifit_fdfsolver;
@@ -148,38 +157,118 @@
 
 int
 gsl_multifit_fdfsolver_set (gsl_multifit_fdfsolver * s, 
-                                 gsl_multifit_function_fdf * fdf,
-                                 const gsl_vector * x);
+                            gsl_multifit_function_fdf * fdf,
+                            const gsl_vector * x);
+int gsl_multifit_fdfsolver_wset (gsl_multifit_fdfsolver * s, 
+                                 gsl_multifit_function_fdf * f, 
+                                 const gsl_vector * x,
+                                 const gsl_vector * wts);
 
 int
 gsl_multifit_fdfsolver_iterate (gsl_multifit_fdfsolver * s);
 
-int
-gsl_multifit_fdfsolver_driver (gsl_multifit_fdfsolver * s,
-                               const size_t maxiter,
-                               const double epsabs, const double epsrel);
+int gsl_multifit_fdfsolver_driver (gsl_multifit_fdfsolver * s,
+                                   const size_t maxiter,
+                                   const double xtol,
+                                   const double gtol,
+                                   const double ftol,
+                                   int *info);
+
+int gsl_multifit_fdfsolver_jac (gsl_multifit_fdfsolver * s,
+                                gsl_matrix * J);
 
 void
 gsl_multifit_fdfsolver_free (gsl_multifit_fdfsolver * s);
 
 const char * gsl_multifit_fdfsolver_name (const gsl_multifit_fdfsolver * s);
 gsl_vector * gsl_multifit_fdfsolver_position (const gsl_multifit_fdfsolver * s);
-
+gsl_vector * gsl_multifit_fdfsolver_residual (const gsl_multifit_fdfsolver * s);
+size_t gsl_multifit_fdfsolver_niter (const gsl_multifit_fdfsolver * s);
+int gsl_multifit_eval_wf(gsl_multifit_function_fdf *fdf,
+                         const gsl_vector *x, const gsl_vector *wts,
+                         gsl_vector *y);
+int gsl_multifit_eval_wdf(gsl_multifit_function_fdf *fdf,
+                          const gsl_vector *x, const gsl_vector *wts,
+                          gsl_matrix *dy);
+
+int gsl_multifit_fdfsolver_test (const gsl_multifit_fdfsolver * s,
+                                 const double xtol,
+                                 const double gtol,
+                                 const double ftol, int *info);
 int gsl_multifit_test_delta (const gsl_vector * dx, const gsl_vector * x, 
                              double epsabs, double epsrel);
 
 int gsl_multifit_test_gradient (const gsl_vector * g, double epsabs);
 
-int gsl_multifit_fdfsolver_dif_df(const gsl_vector *x, gsl_multifit_function_fdf *fdf,
+int gsl_multifit_fdfsolver_dif_df(const gsl_vector *x,
+                                  const gsl_vector *wts,
+                                  gsl_multifit_function_fdf *fdf,
                                   const gsl_vector *f, gsl_matrix *J);
 int gsl_multifit_fdfsolver_dif_fdf(const gsl_vector *x, gsl_multifit_function_fdf *fdf,
                                    gsl_vector *f, gsl_matrix *J);
 
+typedef struct
+{
+  size_t n;                         /* number of (original) residuals */
+  size_t p;                         /* number of model parameters */
+  double lambda;                    /* damping parameter */
+  const gsl_vector *L_diag;         /* diagonal damping matrix or NULL */
+  const gsl_matrix *L;              /* general damping matrix or NULL */
+  gsl_vector *f;                    /* function values for finite diff J */
+  gsl_vector *wts;                  /* weight vector for augmented system */
+  gsl_multifit_fdfsolver * s;
+  gsl_multifit_function_fdf *fdf;   /* user defined fdf */
+  gsl_multifit_function_fdf fdftik; /* Tikhonov modified fdf */
+} gsl_multifit_fdfridge;
+
+gsl_multifit_fdfridge *
+gsl_multifit_fdfridge_alloc (const gsl_multifit_fdfsolver_type * T,
+                             const size_t n, const size_t p);
+void gsl_multifit_fdfridge_free(gsl_multifit_fdfridge *work);
+const char *gsl_multifit_fdfridge_name(const gsl_multifit_fdfridge * w);
+gsl_vector *gsl_multifit_fdfridge_position (const gsl_multifit_fdfridge * w);
+gsl_vector *gsl_multifit_fdfridge_residual (const gsl_multifit_fdfridge * w);
+size_t gsl_multifit_fdfridge_niter (const gsl_multifit_fdfridge * w);
+int gsl_multifit_fdfridge_set (gsl_multifit_fdfridge * w,
+                               gsl_multifit_function_fdf * f,
+                               const gsl_vector * x,
+                               const double lambda);
+int gsl_multifit_fdfridge_wset (gsl_multifit_fdfridge * w,
+                                gsl_multifit_function_fdf * f,
+                                const gsl_vector * x,
+                                const double lambda,
+                                const gsl_vector * wts);
+int gsl_multifit_fdfridge_set2 (gsl_multifit_fdfridge * w,
+                                gsl_multifit_function_fdf * f,
+                                const gsl_vector * x,
+                                const gsl_vector * lambda);
+int gsl_multifit_fdfridge_wset2 (gsl_multifit_fdfridge * w,
+                                 gsl_multifit_function_fdf * f,
+                                 const gsl_vector * x,
+                                 const gsl_vector * lambda,
+                                 const gsl_vector * wts);
+int gsl_multifit_fdfridge_set3 (gsl_multifit_fdfridge * w,
+                                gsl_multifit_function_fdf * f,
+                                const gsl_vector * x,
+                                const gsl_matrix * L);
+int gsl_multifit_fdfridge_wset3 (gsl_multifit_fdfridge * w,
+                                 gsl_multifit_function_fdf * f,
+                                 const gsl_vector * x,
+                                 const gsl_matrix * L,
+                                 const gsl_vector * wts);
+int gsl_multifit_fdfridge_iterate (gsl_multifit_fdfridge * w);
+int gsl_multifit_fdfridge_driver (gsl_multifit_fdfridge * w,
+                                  const size_t maxiter,
+                                  const double xtol,
+                                  const double gtol,
+                                  const double ftol,
+                                  int *info);
+
 /* extern const gsl_multifit_fsolver_type * gsl_multifit_fsolver_gradient; */
 
-GSL_VAR const gsl_multifit_fdfsolver_type * gsl_multifit_fdfsolver_lmder;
 GSL_VAR const gsl_multifit_fdfsolver_type * gsl_multifit_fdfsolver_lmsder;
-
+GSL_VAR const gsl_multifit_fdfsolver_type * gsl_multifit_fdfsolver_lmder;
+GSL_VAR const gsl_multifit_fdfsolver_type * gsl_multifit_fdfsolver_lmniel;
 
 __END_DECLS
 
diff -Nru gsl-doc-1.16/multifit/linear_common.c gsl-doc-2.3/multifit/linear_common.c
--- gsl-doc-1.16/multifit/linear_common.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/linear_common.c	2016-11-18 18:17:12.000000000 +0000
@@ -0,0 +1,197 @@
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_multifit.h>
+
+/* Fit
+ *
+ * y = X c
+ *
+ * where X is an n x p matrix of n observations for p variables.
+ *
+ * The solution includes a possible standard form Tikhonov regularization:
+ *
+ * c = (X^T X + lambda^2 I)^{-1} X^T y
+ *
+ * where lambda^2 is the Tikhonov regularization parameter.
+ *
+ * The function multifit_linear_svd() must first be called to
+ * compute the SVD decomposition of X
+ *
+ * Inputs: X        - least squares matrix
+ *         y        - right hand side vector
+ *         tol      - singular value tolerance
+ *         lambda   - Tikhonov regularization parameter lambda;
+ *                    ignored if <= 0
+ *         rank     - (output) effective rank
+ *         c        - (output) model coefficient vector
+ *         rnorm    - (output) residual norm ||y - X c||
+ *         snorm    - (output) solution norm ||c||
+ *         work     - workspace
+ *
+ * Notes:
+ * 1) The dimensions of X must match work->n and work->p which are set
+ *    by multifit_linear_svd()
+ * 2) On input:
+ *    work->A contains U
+ *    work->Q contains Q
+ *    work->S contains singular values
+ * 3) If this function is called from gsl_multifit_wlinear(), then
+ *    the input y points to work->t, which contains sqrt(W) y. Since
+ *    work->t is also used as scratch workspace by this function, we
+ *    do the necessary computations with y first to avoid problems.
+ * 4) When lambda <= 0, singular values are truncated when:
+ *    s_j <= tol * s_0
+ */
+
+static int
+multifit_linear_solve (const gsl_matrix * X,
+                       const gsl_vector * y,
+                       const double tol,
+                       const double lambda,
+                       size_t * rank,
+                       gsl_vector * c,
+                       double *rnorm,
+                       double *snorm,
+                       gsl_multifit_linear_workspace * work)
+{
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+
+  if (n != work->n || p != work->p)
+    {
+      GSL_ERROR("observation matrix does not match workspace", GSL_EBADLEN);
+    }
+  else if (n != y->size)
+    {
+      GSL_ERROR("number of observations in y does not match matrix",
+                GSL_EBADLEN);
+    }
+  else if (p != c->size)
+    {
+      GSL_ERROR ("number of parameters c does not match matrix",
+                 GSL_EBADLEN);
+    }
+  else if (tol <= 0)
+    {
+      GSL_ERROR ("tolerance must be positive", GSL_EINVAL);
+    }
+  else
+    {
+      const double lambda_sq = lambda * lambda;
+
+      double rho_ls = 0.0;     /* contribution to rnorm from OLS */
+
+      size_t j, p_eff;
+
+      /* these inputs are previously computed by multifit_linear_svd() */
+      gsl_matrix_view A = gsl_matrix_submatrix(work->A, 0, 0, n, p);
+      gsl_matrix_view Q = gsl_matrix_submatrix(work->Q, 0, 0, p, p);
+      gsl_vector_view S = gsl_vector_subvector(work->S, 0, p);
+
+      /* workspace */
+      gsl_matrix_view QSI = gsl_matrix_submatrix(work->QSI, 0, 0, p, p);
+      gsl_vector_view xt = gsl_vector_subvector(work->xt, 0, p);
+      gsl_vector_view D = gsl_vector_subvector(work->D, 0, p);
+      gsl_vector_view t = gsl_vector_subvector(work->t, 0, n);
+
+      /*
+       * Solve y = A c for c
+       * c = Q diag(s_i / (s_i^2 + lambda_i^2)) U^T y
+       */
+
+      /* compute xt = U^T y */
+      gsl_blas_dgemv (CblasTrans, 1.0, &A.matrix, y, 0.0, &xt.vector);
+
+      if (n > p)
+        {
+          /*
+           * compute OLS residual norm = || y - U U^T y ||;
+           * for n = p, U U^T = I, so no need to calculate norm
+           */
+          gsl_vector_memcpy(&t.vector, y);
+          gsl_blas_dgemv(CblasNoTrans, -1.0, &A.matrix, &xt.vector, 1.0, &t.vector);
+          rho_ls = gsl_blas_dnrm2(&t.vector);
+        }
+
+      if (lambda > 0.0)
+        {
+          /* xt <-- [ s(i) / (s(i)^2 + lambda^2) ] .* U^T y */
+          for (j = 0; j < p; ++j)
+            {
+              double sj = gsl_vector_get(&S.vector, j);
+              double f = (sj * sj) / (sj * sj + lambda_sq);
+              double *ptr = gsl_vector_ptr(&xt.vector, j);
+
+              /* use D as workspace for residual norm */
+              gsl_vector_set(&D.vector, j, (1.0 - f) * (*ptr));
+
+              *ptr *= sj / (sj*sj + lambda_sq);
+            }
+
+          /* compute regularized solution vector */
+          gsl_blas_dgemv (CblasNoTrans, 1.0, &Q.matrix, &xt.vector, 0.0, c);
+
+          /* compute solution norm */
+          *snorm = gsl_blas_dnrm2(c);
+
+          /* compute residual norm */
+          *rnorm = gsl_blas_dnrm2(&D.vector);
+
+          if (n > p)
+            {
+              /* add correction to residual norm (see eqs 6-7 of [1]) */
+              *rnorm = sqrt((*rnorm) * (*rnorm) + rho_ls * rho_ls);
+            }
+
+          /* reset D vector */
+          gsl_vector_set_all(&D.vector, 1.0);
+        }
+      else
+        {
+          /* Scale the matrix Q, QSI = Q S^{-1} */
+
+          gsl_matrix_memcpy (&QSI.matrix, &Q.matrix);
+
+          {
+            double s0 = gsl_vector_get (&S.vector, 0);
+            p_eff = 0;
+
+            for (j = 0; j < p; j++)
+              {
+                gsl_vector_view column = gsl_matrix_column (&QSI.matrix, j);
+                double sj = gsl_vector_get (&S.vector, j);
+                double alpha;
+
+                if (sj <= tol * s0)
+                  {
+                    alpha = 0.0;
+                  }
+                else
+                  {
+                    alpha = 1.0 / sj;
+                    p_eff++;
+                  }
+
+                gsl_vector_scale (&column.vector, alpha);
+              }
+
+            *rank = p_eff;
+          }
+
+          gsl_blas_dgemv (CblasNoTrans, 1.0, &QSI.matrix, &xt.vector, 0.0, c);
+
+          /* Unscale the balancing factors */
+          gsl_vector_div (c, &D.vector);
+
+          *snorm = gsl_blas_dnrm2(c);
+          *rnorm = rho_ls;
+        }
+
+      return GSL_SUCCESS;
+    }
+}
diff -Nru gsl-doc-1.16/multifit/lmder.c gsl-doc-2.3/multifit/lmder.c
--- gsl-doc-1.16/multifit/lmder.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/lmder.c	2015-11-03 16:21:55.000000000 +0000
@@ -40,17 +40,19 @@
     double fnorm;
     double delta;
     double par;
-    gsl_matrix *r;
+    gsl_matrix *J;             /* Jacobian matrix */
+    gsl_matrix *r;             /* R matrix in J = Q R P^T */
     gsl_vector *tau;
-    gsl_vector *diag;
-    gsl_vector *qtf;
+    gsl_vector *diag;          /* scaling matrix D = diag(d1,...,dp) */
+    gsl_vector *qtf;           /* Q^T f */
     gsl_vector *newton;
-    gsl_vector *gradient;
-    gsl_vector *x_trial;
-    gsl_vector *f_trial;
+    gsl_vector *gradient;      /* gradient g = J^T f */
+    gsl_vector *x_trial;       /* trial step x + dx */
+    gsl_vector *f_trial;       /* trial function f(x + dx) */
     gsl_vector *df;
     gsl_vector *sdiag;
     gsl_vector *rptdx;
+    const gsl_vector *weights; /* data weights */
     gsl_vector *w;
     gsl_vector *work1;
     gsl_permutation * perm;
@@ -58,12 +60,12 @@
 lmder_state_t;
 
 static int lmder_alloc (void *vstate, size_t n, size_t p);
-static int lmder_set (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx);
-static int lmsder_set (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx);
-static int set (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx, int scale);
-static int lmder_iterate (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx);
+static int lmder_set (void *vstate, const gsl_vector * swts, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_vector * dx);
+static int lmsder_set (void *vstate, const gsl_vector * swts, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_vector * dx);
+static int set (void *vstate, const gsl_vector * swts, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_vector * dx, int scale);
+static int lmder_iterate (void *vstate, const gsl_vector * swts, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_vector * dx);
 static void lmder_free (void *vstate);
-static int iterate (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx, int scale);
+static int iterate (void *vstate, const gsl_vector * swts, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_vector * dx, int scale);
 
 #include "lmutil.c"
 #include "lmpar.c"
@@ -75,12 +77,21 @@
 lmder_alloc (void *vstate, size_t n, size_t p)
 {
   lmder_state_t *state = (lmder_state_t *) vstate;
-  gsl_matrix *r;
+  gsl_matrix *r, *J;
   gsl_vector *tau, *diag, *qtf, *newton, *gradient, *x_trial, *f_trial,
    *df, *sdiag, *rptdx, *w, *work1;
   gsl_permutation *perm;
 
-  r = gsl_matrix_calloc (n, p);
+  J = gsl_matrix_alloc (n, p);
+
+  if (J == 0)
+    {
+      GSL_ERROR ("failed to allocate space for J", GSL_ENOMEM);
+    }
+
+  state->J = J;
+
+  r = gsl_matrix_alloc (n, p);
 
   if (r == 0)
     {
@@ -315,52 +326,107 @@
 }
 
 static int
-lmder_set (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx)
+lmder_set (void *vstate, const gsl_vector * swts,
+           gsl_multifit_function_fdf * fdf, gsl_vector * x,
+           gsl_vector * f, gsl_vector * dx)
 {
-  int status = set (vstate, fdf, x, f, J, dx, 0);
+  int status = set (vstate, swts, fdf, x, f, dx, 0);
   return status ;
 }
 
 static int
-lmsder_set (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx)
+lmsder_set (void *vstate, const gsl_vector * swts,
+            gsl_multifit_function_fdf * fdf, gsl_vector * x,
+            gsl_vector * f, gsl_vector * dx)
 {
-  int status = set (vstate, fdf, x, f, J, dx, 1);
+  int status = set (vstate, swts, fdf, x, f, dx, 1);
   return status ;
 }
 
 static int
-lmder_iterate (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx)
+lmder_iterate (void *vstate, const gsl_vector * swts,
+               gsl_multifit_function_fdf * fdf, gsl_vector * x,
+               gsl_vector * f, gsl_vector * dx)
 {
-  int status = iterate (vstate, fdf, x, f, J, dx, 0);
+  int status = iterate (vstate, swts, fdf, x, f, dx, 0);
   return status;
 }
 
 static int
-lmsder_iterate (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx)
+lmsder_iterate (void *vstate, const gsl_vector * swts,
+                gsl_multifit_function_fdf * fdf, gsl_vector * x,
+                gsl_vector * f, gsl_vector * dx)
 {
-  int status = iterate (vstate, fdf, x, f, J, dx, 1);
+  int status = iterate (vstate, swts, fdf, x, f, dx, 1);
   return status;
 }
 
+static int
+lmder_gradient (void *vstate, gsl_vector * g)
+{
+  lmder_state_t *state = (lmder_state_t *) vstate;
+  compute_gradient(state->r, state->qtf, g);
+  return GSL_SUCCESS;
+}
+
+static int
+lmder_jac (void *vstate, gsl_matrix * J)
+{
+  lmder_state_t *state = (lmder_state_t *) vstate;
+  int s = gsl_matrix_memcpy(J, state->J);
+
+  return s;
+}
+
 static void
 lmder_free (void *vstate)
 {
   lmder_state_t *state = (lmder_state_t *) vstate;
 
-  gsl_permutation_free (state->perm);
-  gsl_vector_free (state->work1);
-  gsl_vector_free (state->w);
-  gsl_vector_free (state->rptdx);
-  gsl_vector_free (state->sdiag);
-  gsl_vector_free (state->df);
-  gsl_vector_free (state->f_trial);
-  gsl_vector_free (state->x_trial);
-  gsl_vector_free (state->gradient);
-  gsl_vector_free (state->newton);
-  gsl_vector_free (state->qtf);
-  gsl_vector_free (state->diag);
-  gsl_vector_free (state->tau);
-  gsl_matrix_free (state->r);
+  if (state->perm)
+    gsl_permutation_free (state->perm);
+
+  if (state->work1)
+    gsl_vector_free (state->work1);
+
+  if (state->w)
+    gsl_vector_free (state->w);
+
+  if (state->rptdx)
+    gsl_vector_free (state->rptdx);
+
+  if (state->sdiag)
+    gsl_vector_free (state->sdiag);
+
+  if (state->df)
+    gsl_vector_free (state->df);
+
+  if (state->f_trial)
+    gsl_vector_free (state->f_trial);
+
+  if (state->x_trial)
+    gsl_vector_free (state->x_trial);
+
+  if (state->gradient)
+    gsl_vector_free (state->gradient);
+
+  if (state->newton)
+    gsl_vector_free (state->newton);
+
+  if (state->qtf)
+    gsl_vector_free (state->qtf);
+
+  if (state->diag)
+    gsl_vector_free (state->diag);
+
+  if (state->tau)
+    gsl_vector_free (state->tau);
+
+  if (state->r)
+    gsl_matrix_free (state->r);
+
+  if (state->J)
+    gsl_matrix_free (state->J);
 }
 
 static const gsl_multifit_fdfsolver_type lmder_type =
@@ -370,6 +436,8 @@
   &lmder_alloc,
   &lmder_set,
   &lmder_iterate,
+  &lmder_gradient,
+  &lmder_jac,
   &lmder_free
 };
 
@@ -380,6 +448,8 @@
   &lmder_alloc,
   &lmsder_set,
   &lmsder_iterate,
+  &lmder_gradient,
+  &lmder_jac,
   &lmder_free
 };
 
diff -Nru gsl-doc-1.16/multifit/lmiterate.c gsl-doc-2.3/multifit/lmiterate.c
--- gsl-doc-1.16/multifit/lmiterate.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/lmiterate.c	2015-11-03 16:21:55.000000000 +0000
@@ -1,5 +1,7 @@
 static int
-iterate (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx, int scale)
+iterate (void *vstate, const gsl_vector * swts,
+         gsl_multifit_function_fdf * fdf, gsl_vector * x,
+         gsl_vector * f, gsl_vector * dx, int scale)
 {
   lmder_state_t *state = (lmder_state_t *) vstate;
 
@@ -31,11 +33,6 @@
       return GSL_SUCCESS;
     }
 
-  /* Compute qtf = Q^T f */
-
-  gsl_vector_memcpy (qtf, f);
-  gsl_linalg_QR_QTvec (r, tau, qtf);
-
   /* Compute norm of scaled gradient */
 
   compute_gradient_direction (r, perm, qtf, diag, gradient);
@@ -80,7 +77,7 @@
   /* Evaluate function at x + p */
   /* return immediately if evaluation raised error */
   {
-    int status = GSL_MULTIFIT_FN_EVAL_F (fdf, x_trial, f_trial);
+    int status = gsl_multifit_eval_wf (fdf, x_trial, swts, f_trial);
     if (status)
       return status;
   }
@@ -182,11 +179,12 @@
       /* return immediately if evaluation raised error */
       {
         int status;
-        
+
+        /* compute Jacobian at new x and store in state->r */
         if (fdf->df)
-          status = GSL_MULTIFIT_FN_EVAL_DF (fdf, x_trial, J);
+          status = gsl_multifit_eval_wdf (fdf, x_trial, swts, r);
         else
-          status = gsl_multifit_fdfsolver_dif_df(x_trial, fdf, f_trial, J);
+          status = gsl_multifit_fdfsolver_dif_df(x_trial, swts, fdf, f_trial, r);
 
         if (status)
           return status;
@@ -201,13 +199,17 @@
 
       if (scale)
         {
-          update_diag (J, diag);
+          update_diag (r, diag);
         }
 
+      /* compute J = Q R P^T and qtf = Q^T f */
       {
         int signum;
-        gsl_matrix_memcpy (r, J);
+
+        gsl_matrix_memcpy(state->J, r);
         gsl_linalg_QRPT_decomp (r, tau, perm, &signum, work1);
+        gsl_vector_memcpy (qtf, f);
+        gsl_linalg_QR_QTvec (r, tau, qtf);
       }
       
       return GSL_SUCCESS;
diff -Nru gsl-doc-1.16/multifit/lmmisc.c gsl-doc-2.3/multifit/lmmisc.c
--- gsl-doc-1.16/multifit/lmmisc.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/lmmisc.c	2015-11-03 18:35:15.000000000 +0000
@@ -0,0 +1,111 @@
+/* multifit/lmmisc.c
+ * 
+ * Copyright (C) 2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/* compute step dx by solving (J^T J + mu*I) dx = -J^T f */
+static int
+lmniel_calc_dx(const double mu, const gsl_matrix *A, const gsl_vector *rhs,
+               gsl_vector *dx, lmniel_state_t *state)
+{
+  int status;
+  gsl_matrix *A_copy = state->A_copy;
+  gsl_vector_view diag = gsl_matrix_diagonal(A_copy);
+
+  /* make a copy of J^T J matrix */
+  gsl_matrix_memcpy(A_copy, A);
+
+  /* augment normal equations with LM parameter: A -> A + mu*I */
+  gsl_vector_add_constant(&diag.vector, mu);
+
+  status = gsl_linalg_QR_decomp(A_copy, state->work);
+  if (status)
+    return status;
+
+  status = gsl_linalg_QR_solve(A_copy, state->work, rhs, dx);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+} /* lmniel_calc_dx() */
+
+/* compute x_trial = x + dx */
+static void
+lmniel_trial_step(const gsl_vector * x, const gsl_vector * dx,
+                  gsl_vector * x_trial)
+{
+  size_t i, N = x->size;
+
+  for (i = 0; i < N; i++)
+    {
+      double dxi = gsl_vector_get (dx, i);
+      double xi = gsl_vector_get (x, i);
+      gsl_vector_set (x_trial, i, xi + dxi);
+    }
+} /* lmniel_trial_step() */
+
+/*
+lmniel_calc_dF()
+  Compute dF = F(x) - F(x + dx) = 1/2 (f - f_new)^T (f + f_new)
+*/
+static double
+lmniel_calc_dF(const gsl_vector *f, const gsl_vector *f_new)
+{
+  const size_t N = f->size;
+  size_t i;
+  double dF = 0.0;
+
+  for (i = 0; i < N; ++i)
+    {
+      double fi = gsl_vector_get(f, i);
+      double fnewi = gsl_vector_get(f_new, i);
+
+      dF += (fi - fnewi) * (fi + fnewi);
+    }
+
+  dF *= 0.5;
+
+  return dF;
+} /* lmniel_calc_dF() */
+
+/*
+lmniel_calc_dL()
+  Compute dL = L(0) - L(dx) = 1/2 dx^T (mu * D^T D dx - g)
+Here, the mg input is -g
+*/
+
+static double
+lmniel_calc_dL(const double mu, const gsl_vector *diag,
+               const gsl_vector *dx, const gsl_vector *mg)
+{
+  const size_t p = dx->size;
+  size_t i;
+  double dL = 0.0;
+
+  for (i = 0; i < p; ++i)
+    {
+      double dxi = gsl_vector_get(dx, i);
+      double di = gsl_vector_get(diag, i);
+      double mgi = gsl_vector_get(mg, i); /* -g_i */
+
+      dL += dxi * (mu * di * di * dxi + mgi);
+    }
+
+  dL *= 0.5;
+
+  return dL;
+} /* lmniel_calc_dL() */
diff -Nru gsl-doc-1.16/multifit/lmniel.c gsl-doc-2.3/multifit/lmniel.c
--- gsl-doc-1.16/multifit/lmniel.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/lmniel.c	2016-07-07 20:36:10.000000000 +0000
@@ -0,0 +1,382 @@
+/* multifit/lmniel.c
+ * 
+ * Copyright (C) 2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multifit_nlin.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+
+#define SCALE 0
+
+/*
+ * This module contains an implementation of the Levenberg-Marquardt
+ * algorithm for nonlinear optimization problems. This implementation
+ * closely follows the following works:
+ *
+ * [1] H. B. Nielsen, K. Madsen, Introduction to Optimization and
+ *     Data Fitting, Informatics and Mathematical Modeling,
+ *     Technical University of Denmark (DTU), 2010.
+ */
+
+typedef struct
+{
+  gsl_matrix *A;             /* J^T J */
+  gsl_matrix *A_copy;        /* copy of J^T J */
+  gsl_matrix *J;             /* Jacobian J(x) */
+  gsl_vector *diag;          /* D = diag(J^T J) */
+  gsl_vector *rhs;           /* rhs vector = -g = -J^T f */
+  gsl_vector *x_trial;       /* trial parameter vector */
+  gsl_vector *f_trial;       /* trial function vector */
+  gsl_vector *work;          /* workspace length p */
+  long nu;                   /* nu */
+  double mu;                 /* LM damping parameter mu */
+  double tau;                /* initial scale factor for mu */
+} lmniel_state_t;
+
+#include "lmmisc.c"
+
+#define LM_ONE_THIRD         (0.333333333333333)
+
+static int lmniel_alloc (void *vstate, const size_t n, const size_t p);
+static void lmniel_free(void *vstate);
+static int lmniel_set(void *vstate, const gsl_vector * swts,
+                      gsl_multifit_function_fdf *fdf,
+                      gsl_vector *x, gsl_vector *f, gsl_vector *dx);
+static int lmniel_iterate(void *vstate, const gsl_vector *swts,
+                          gsl_multifit_function_fdf *fdf,
+                          gsl_vector *x, gsl_vector *f, gsl_vector *dx);
+
+static int
+lmniel_alloc (void *vstate, const size_t n, const size_t p)
+{
+  lmniel_state_t *state = (lmniel_state_t *) vstate;
+
+  state->A = gsl_matrix_alloc(p, p);
+  if (state->A == NULL)
+    {
+      GSL_ERROR ("failed to allocate space for A", GSL_ENOMEM);
+    }
+
+  state->J = gsl_matrix_alloc(n, p);
+  if (state->J == NULL)
+    {
+      GSL_ERROR ("failed to allocate space for J", GSL_ENOMEM);
+    }
+
+  state->diag = gsl_vector_alloc(p);
+  if (state->diag == NULL)
+    {
+      GSL_ERROR ("failed to allocate space for diag", GSL_ENOMEM);
+    }
+
+  state->rhs = gsl_vector_alloc(p);
+  if (state->rhs == NULL)
+    {
+      GSL_ERROR ("failed to allocate space for rhs", GSL_ENOMEM);
+    }
+
+  state->work = gsl_vector_alloc(p);
+  if (state->work == NULL)
+    {
+      GSL_ERROR ("failed to allocate space for work", GSL_ENOMEM);
+    }
+
+  state->A_copy = gsl_matrix_alloc(p, p);
+  if (state->A_copy == NULL)
+    {
+      GSL_ERROR ("failed to allocate space for A_copy", GSL_ENOMEM);
+    }
+
+  state->x_trial = gsl_vector_alloc(p);
+  if (state->x_trial == NULL)
+    {
+      GSL_ERROR ("failed to allocate space for x_trial", GSL_ENOMEM);
+    }
+
+  state->f_trial = gsl_vector_alloc(n);
+  if (state->f_trial == NULL)
+    {
+      GSL_ERROR ("failed to allocate space for f_trial", GSL_ENOMEM);
+    }
+
+  state->tau = 1.0e-3;
+
+  return GSL_SUCCESS;
+} /* lmniel_alloc() */
+
+static void
+lmniel_free(void *vstate)
+{
+  lmniel_state_t *state = (lmniel_state_t *) vstate;
+
+  if (state->A)
+    gsl_matrix_free(state->A);
+
+  if (state->J)
+    gsl_matrix_free(state->J);
+
+  if (state->diag)
+    gsl_vector_free(state->diag);
+
+  if (state->rhs)
+    gsl_vector_free(state->rhs);
+
+  if (state->work)
+    gsl_vector_free(state->work);
+
+  if (state->A_copy)
+    gsl_matrix_free(state->A_copy);
+
+  if (state->x_trial)
+    gsl_vector_free(state->x_trial);
+
+  if (state->f_trial)
+    gsl_vector_free(state->f_trial);
+} /* lmniel_free() */
+
+static int
+lmniel_set(void *vstate, const gsl_vector *swts,
+           gsl_multifit_function_fdf *fdf, gsl_vector *x,
+           gsl_vector *f, gsl_vector *dx)
+{
+  int status;
+  lmniel_state_t *state = (lmniel_state_t *) vstate;
+  const size_t p = x->size;
+  size_t i;
+
+  /* initialize counters for function and Jacobian evaluations */
+  fdf->nevalf = 0;
+  fdf->nevaldf = 0;
+
+  /* evaluate function and Jacobian at x and apply weight transform */
+  status = gsl_multifit_eval_wf(fdf, x, swts, f);
+  if (status)
+   return status;
+
+  if (fdf->df)
+    status = gsl_multifit_eval_wdf(fdf, x, swts, state->J);
+  else
+    status = gsl_multifit_fdfsolver_dif_df(x, swts, fdf, f, state->J);
+  if (status)
+    return status;
+
+  /* compute rhs = -J^T f */
+  gsl_blas_dgemv(CblasTrans, -1.0, state->J, f, 0.0, state->rhs);
+
+#if SCALE
+  gsl_vector_set_zero(state->diag);
+#else
+  gsl_vector_set_all(state->diag, 1.0);
+#endif
+
+  /* set default parameters */
+  state->nu = 2;
+
+#if SCALE
+  state->mu = state->tau;
+#else
+  /* compute mu_0 = tau * max(diag(J^T J)) */
+  state->mu = -1.0;
+  for (i = 0; i < p; ++i)
+    {
+      gsl_vector_view c = gsl_matrix_column(state->J, i);
+      double result; /* (J^T J)_{ii} */
+
+      gsl_blas_ddot(&c.vector, &c.vector, &result);
+      state->mu = GSL_MAX(state->mu, result);
+    }
+
+  state->mu *= state->tau;
+#endif
+
+  return GSL_SUCCESS;
+} /* lmniel_set() */
+
+/*
+lmniel_iterate()
+  This function performs 1 iteration of the LM algorithm 6.18
+from [1]. The algorithm is slightly modified to loop until we
+find an acceptable step dx, in order to guarantee that each
+function call contains a new input vector x.
+
+Args: vstate - lm workspace
+      swts   - data weights (NULL if unweighted)
+      fdf    - function and Jacobian pointers
+      x      - on input, current parameter vector
+               on output, new parameter vector x + dx
+      f      - on input, f(x)
+               on output, f(x + dx)
+      dx     - (output only) parameter step vector
+
+Notes:
+1) On input, the following must be initialized in state:
+nu, mu, rhs, J
+
+2) On output, the following are updated with the current iterates:
+nu, mu, rhs, J
+
+rhs needs to be set on each output, so that lmniel_gradient supplies
+the correct g = J^T f
+*/
+
+static int
+lmniel_iterate(void *vstate, const gsl_vector *swts,
+               gsl_multifit_function_fdf *fdf, gsl_vector *x,
+               gsl_vector *f, gsl_vector *dx)
+{
+  int status;
+  lmniel_state_t *state = (lmniel_state_t *) vstate;
+  gsl_matrix *J = state->J;                   /* Jacobian J(x) */
+  gsl_matrix *A = state->A;                   /* J^T J */
+  gsl_vector *rhs = state->rhs;               /* -g = -J^T f */
+  gsl_vector *x_trial = state->x_trial;       /* trial x + dx */
+  gsl_vector *f_trial = state->f_trial;       /* trial f(x + dx) */
+  gsl_vector *diag = state->diag;             /* diag(D) */
+  double dF;                                  /* F(x) - F(x + dx) */
+  double dL;                                  /* L(0) - L(dx) */
+  int foundstep = 0;                          /* found step dx */
+
+  /* compute A = J^T J */
+  status = gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, J, 0.0, A);
+  if (status)
+    return status;
+
+  /* copy lower triangle to upper */
+  gsl_matrix_transpose_tricpy('L', 0, A, A);
+
+#if SCALE
+  lmniel_update_diag(J, diag);
+#endif
+
+  /* loop until we find an acceptable step dx */
+  while (!foundstep)
+    {
+      /* solve (A + mu*I) dx = g */
+      status = lmniel_calc_dx(state->mu, A, rhs, dx, state);
+      if (status)
+        return status;
+
+      /* compute x_trial = x + dx */
+      lmniel_trial_step(x, dx, x_trial);
+
+      /* compute f(x + dx) */
+      status = gsl_multifit_eval_wf(fdf, x_trial, swts, f_trial);
+      if (status)
+       return status;
+
+      /* compute dF = F(x) - F(x + dx) */
+      dF = lmniel_calc_dF(f, f_trial);
+
+      /* compute dL = L(0) - L(dx) = dx^T (mu*dx - g) */
+      dL = lmniel_calc_dL(state->mu, diag, dx, rhs);
+
+      /* check that rho = dF/dL > 0 */
+      if ((dL > 0.0) && (dF >= 0.0))
+        {
+          /* reduction in error, step acceptable */
+
+          double tmp;
+
+          /* update LM parameter mu */
+          tmp = 2.0 * (dF / dL) - 1.0;
+          tmp = 1.0 - tmp*tmp*tmp;
+          state->mu *= GSL_MAX(LM_ONE_THIRD, tmp);
+          state->nu = 2;
+
+          /* compute J <- J(x + dx) */
+          if (fdf->df)
+            status = gsl_multifit_eval_wdf(fdf, x_trial, swts, J);
+          else
+            status = gsl_multifit_fdfsolver_dif_df(x_trial, swts, fdf, f_trial, J);
+          if (status)
+            return status;
+
+          /* update x <- x + dx */
+          gsl_vector_memcpy(x, x_trial);
+
+          /* update f <- f(x + dx) */
+          gsl_vector_memcpy(f, f_trial);
+
+          /* compute new rhs = -J^T f */
+          gsl_blas_dgemv(CblasTrans, -1.0, J, f, 0.0, rhs);
+
+          foundstep = 1;
+        }
+      else
+        {
+          long nu2;
+
+          /* step did not reduce error, reject step */
+          state->mu *= (double) state->nu;
+          nu2 = state->nu << 1; /* 2*nu */
+          if (nu2 <= state->nu)
+            {
+              gsl_vector_view d = gsl_matrix_diagonal(A);
+
+              /*
+               * nu has wrapped around / overflown, reset mu and nu
+               * to original values and break to force another iteration
+               */
+              /*GSL_ERROR("nu parameter has overflown", GSL_EOVRFLW);*/
+              state->nu = 2;
+              state->mu = state->tau * gsl_vector_max(&d.vector);
+              break;
+            }
+          state->nu = nu2;
+        }
+    } /* while (!foundstep) */
+
+  return GSL_SUCCESS;
+} /* lmniel_iterate() */
+
+static int
+lmniel_gradient(void *vstate, gsl_vector * g)
+{
+  lmniel_state_t *state = (lmniel_state_t *) vstate;
+  gsl_vector_memcpy(g, state->rhs);
+  gsl_vector_scale(g, -1.0);
+  return GSL_SUCCESS;
+}
+
+static int
+lmniel_jac(void *vstate, gsl_matrix * J)
+{
+  lmniel_state_t *state = (lmniel_state_t *) vstate;
+  int s = gsl_matrix_memcpy(J, state->J);
+
+  return s;
+}
+
+static const gsl_multifit_fdfsolver_type lmniel_type =
+{
+  "lmniel",
+  sizeof(lmniel_state_t),
+  &lmniel_alloc,
+  &lmniel_set,
+  &lmniel_iterate,
+  &lmniel_gradient,
+  &lmniel_jac,
+  &lmniel_free
+};
+
+const gsl_multifit_fdfsolver_type *gsl_multifit_fdfsolver_lmniel = &lmniel_type;
diff -Nru gsl-doc-1.16/multifit/lmpar.c gsl-doc-2.3/multifit/lmpar.c
--- gsl-doc-1.16/multifit/lmpar.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/lmpar.c	2015-11-03 16:21:55.000000000 +0000
@@ -183,6 +183,7 @@
     }
 }
 
+/* compute scaled gradient g = D^{-1} J^T f (see More' eq 7.2) */
 static void
 compute_gradient_direction (const gsl_matrix * r, const gsl_permutation * p,
                             const gsl_vector * qtf, const gsl_vector * diag,
@@ -210,6 +211,28 @@
     }
 }
 
+/* compute gradient g = J^T f */
+static void
+compute_gradient (const gsl_matrix * r, const gsl_vector * qtf,
+                  gsl_vector * g)
+{
+  const size_t n = r->size2;
+
+  size_t i, j;
+
+  for (j = 0; j < n; j++)
+    {
+      double sum = 0;
+
+      for (i = 0; i <= j; i++)
+        {
+          sum += gsl_matrix_get (r, i, j) * gsl_vector_get (qtf, i);
+        }
+
+      gsl_vector_set (g, j, sum);
+    }
+}
+
 static int
 lmpar (gsl_matrix * r, const gsl_permutation * perm, const gsl_vector * qtf,
        const gsl_vector * diag, double delta, double * par_inout,
diff -Nru gsl-doc-1.16/multifit/lmset.c gsl-doc-2.3/multifit/lmset.c
--- gsl-doc-1.16/multifit/lmset.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/lmset.c	2015-11-03 16:21:55.000000000 +0000
@@ -1,25 +1,38 @@
 static int
-set (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx, int scale)
+set (void *vstate, const gsl_vector * swts, gsl_multifit_function_fdf * fdf,
+     gsl_vector * x, gsl_vector * f, gsl_vector * dx, int scale)
 {
   lmder_state_t *state = (lmder_state_t *) vstate;
 
   gsl_matrix *r = state->r;
   gsl_vector *tau = state->tau;
+  gsl_vector *qtf = state->qtf;
   gsl_vector *diag = state->diag;
   gsl_vector *work1 = state->work1;
   gsl_permutation *perm = state->perm;
 
   int signum;
 
-  /* Evaluate function at x */
+  /* start counting function and Jacobian evaluations */
+  fdf->nevalf = 0;
+  fdf->nevaldf = 0;
+
   /* return immediately if evaluation raised error */
   {
     int status;
-    
-    if (fdf->fdf)
-      status = GSL_MULTIFIT_FN_EVAL_F_DF (fdf, x, f, J);
+
+    /* Evaluate function at x */
+    status = gsl_multifit_eval_wf (fdf, x, swts, f);
+    if (status)
+      return status;
+
+    /* Evaluate Jacobian at x and store in state->r */
+    if (fdf->df)
+      status = gsl_multifit_eval_wdf (fdf, x, swts, r);
     else /* finite difference approximation */
-      status = gsl_multifit_fdfsolver_dif_fdf(x, fdf, f, J);
+      status = gsl_multifit_fdfsolver_dif_df(x, swts, fdf, f, r);
+
+    gsl_matrix_memcpy(state->J, r);
 
     if (status)
       return status;
@@ -35,7 +48,7 @@
 
   if (scale)
     {
-      compute_diag (J, diag);
+      compute_diag (r, diag);
     }
   else
     {
@@ -47,11 +60,13 @@
   state->xnorm = scaled_enorm (diag, x);
   state->delta = compute_delta (diag, x);
 
-  /* Factorize J into QR decomposition */
-
-  gsl_matrix_memcpy (r, J);
+  /* Factorize J = Q R P^T */
   gsl_linalg_QRPT_decomp (r, tau, perm, &signum, work1);
 
+  /* compute qtf = Q^T f */
+  gsl_vector_memcpy (qtf, f);
+  gsl_linalg_QR_QTvec (r, tau, qtf);
+
   gsl_vector_set_zero (state->rptdx);
   gsl_vector_set_zero (state->w);
 
diff -Nru gsl-doc-1.16/multifit/lmutil.c gsl-doc-2.3/multifit/lmutil.c
--- gsl-doc-1.16/multifit/lmutil.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/lmutil.c	2015-11-03 16:21:55.000000000 +0000
@@ -55,45 +55,35 @@
 static void
 compute_diag (const gsl_matrix * J, gsl_vector * diag)
 {
-  size_t i, j, n = J->size1, p = J->size2;
+  size_t j, p = J->size2;
 
   for (j = 0; j < p; j++)
     {
-      double sum = 0;
+      gsl_vector_const_view v = gsl_matrix_const_column(J, j);
+      double norm = gsl_blas_dnrm2(&v.vector);
 
-      for (i = 0; i < n; i++)
-        {
-          double Jij = gsl_matrix_get (J, i, j);
-          sum += Jij * Jij;
-        }
-      if (sum == 0)
-        sum = 1.0;
+      if (norm == 0)
+        norm = 1.0;
 
-      gsl_vector_set (diag, j, sqrt (sum));
+      gsl_vector_set (diag, j, norm);
     }
 }
 
 static void
 update_diag (const gsl_matrix * J, gsl_vector * diag)
 {
-  size_t i, j, n = diag->size;
+  size_t j, p = J->size2;
 
-  for (j = 0; j < n; j++)
+  for (j = 0; j < p; j++)
     {
-      double cnorm, diagj, sum = 0;
-      for (i = 0; i < n; i++)
-        {
-          double Jij = gsl_matrix_get (J, i, j);
-          sum += Jij * Jij;
-        }
-      if (sum == 0)
-        sum = 1.0;
+      gsl_vector_const_view v = gsl_matrix_const_column(J, j);
+      double norm = gsl_blas_dnrm2(&v.vector);
+      double *diagj = gsl_vector_ptr(diag, j);
 
-      cnorm = sqrt (sum);
-      diagj = gsl_vector_get (diag, j);
+      if (norm == 0)
+        norm = 1.0;
 
-      if (cnorm > diagj)
-        gsl_vector_set (diag, j, cnorm);
+      *diagj = GSL_MAX(*diagj, norm);
     }
 }
 
diff -Nru gsl-doc-1.16/multifit/Makefile.am gsl-doc-2.3/multifit/Makefile.am
--- gsl-doc-1.16/multifit/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/Makefile.am	2016-10-27 11:20:46.000000000 +0000
@@ -2,18 +2,72 @@
 
 pkginclude_HEADERS = gsl_multifit.h gsl_multifit_nlin.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
-libgslmultifit_la_SOURCES = multilinear.c work.c lmder.c fsolver.c fdfsolver.c fdjac.c convergence.c gradient.c covar.c multirobust.c robust_wfun.c
+libgslmultifit_la_SOURCES = gcv.c multilinear.c multiwlinear.c work.c lmniel.c lmder.c fsolver.c fdfsolver.c fdfridge.c fdjac.c convergence.c gradient.c covar.c multirobust.c robust_wfun.c multireg.c
 
-noinst_HEADERS = lmutil.c lmpar.c lmset.c lmiterate.c qrsolv.c test_brown.c test_enso.c test_filip.c test_fn.c test_hahn1.c test_kirby2.c test_longley.c test_nelson.c test_pontius.c test_estimator.c
+noinst_HEADERS =        \
+linear_common.c         \
+lmutil.c                \
+lmpar.c                 \
+lmset.c                 \
+lmiterate.c             \
+lmmisc.c                \
+qrsolv.c                \
+test_bard.c             \
+test_beale.c            \
+test_biggs.c            \
+test_box.c              \
+test_boxbod.c           \
+test_brown1.c           \
+test_brown2.c           \
+test_brown3.c           \
+test_eckerle.c          \
+test_enso.c             \
+test_estimator.c        \
+test_exp1.c             \
+test_filip.c            \
+test_gaussian.c         \
+test_hahn1.c            \
+test_helical.c          \
+test_jennrich.c         \
+test_kirby2.c           \
+test_kowalik.c          \
+test_lin1.c             \
+test_lin2.c             \
+test_lin3.c             \
+test_linear.c           \
+test_longley.c          \
+test_meyer.c            \
+test_meyerscal.c        \
+test_nelson.c           \
+test_nonlinear.c        \
+test_osborne.c          \
+test_penalty1.c         \
+test_penalty2.c         \
+test_pontius.c          \
+test_powell1.c          \
+test_powell2.c          \
+test_powell3.c          \
+test_rat42.c            \
+test_rat43.c            \
+test_reg.c              \
+test_rosenbrock.c       \
+test_rosenbrocke.c      \
+test_roth.c             \
+test_shaw.c             \
+test_thurber.c          \
+test_vardim.c           \
+test_watson.c           \
+test_wnlin.c            \
+test_wood.c
 
 check_PROGRAMS = test #demo
 
 TESTS = $(check_PROGRAMS)
 
 test_SOURCES = test.c
-test_LDADD = libgslmultifit.la ../linalg/libgsllinalg.la ../permutation/libgslpermutation.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../sort/libgslsort.la ../statistics/libgslstatistics.la ../vector/libgslvector.la ../block/libgslblock.la  ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../utils/libutils.la ../sys/libgslsys.la
+test_LDADD = libgslmultifit.la ../linalg/libgsllinalg.la ../permutation/libgslpermutation.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../sort/libgslsort.la ../statistics/libgslstatistics.la ../vector/libgslvector.la ../block/libgslblock.la  ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../utils/libutils.la ../sys/libgslsys.la ../rng/libgslrng.la ../specfunc/libgslspecfunc.la ../min/libgslmin.la
 
 #demo_SOURCES = demo.c
 #demo_LDADD = libgslmultifit.la ../linalg/libgsllinalg.la ../permutation/libgslpermutation.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la ../randist/libgslrandist.la ../rng/libgslrng.la ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../utils/libutils.la ../sys/libgslsys.la
diff -Nru gsl-doc-1.16/multifit/Makefile.in gsl-doc-2.3/multifit/Makefile.in
--- gsl-doc-1.16/multifit/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/multifit/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -95,9 +95,10 @@
 CONFIG_CLEAN_VPATH_FILES =
 LTLIBRARIES = $(noinst_LTLIBRARIES)
 libgslmultifit_la_LIBADD =
-am_libgslmultifit_la_OBJECTS = multilinear.lo work.lo lmder.lo \
-	fsolver.lo fdfsolver.lo fdjac.lo convergence.lo gradient.lo \
-	covar.lo multirobust.lo robust_wfun.lo
+am_libgslmultifit_la_OBJECTS = gcv.lo multilinear.lo multiwlinear.lo \
+	work.lo lmniel.lo lmder.lo fsolver.lo fdfsolver.lo fdfridge.lo \
+	fdjac.lo convergence.lo gradient.lo covar.lo multirobust.lo \
+	robust_wfun.lo multireg.lo
 libgslmultifit_la_OBJECTS = $(am_libgslmultifit_la_OBJECTS)
 AM_V_lt = $(am__v_lt_@AM_V@)
 am__v_lt_ = $(am__v_lt_@AM_DEFAULT_V@)
@@ -112,7 +113,8 @@
 	../vector/libgslvector.la ../block/libgslblock.la \
 	../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la \
 	../err/libgslerr.la ../test/libgsltest.la ../utils/libutils.la \
-	../sys/libgslsys.la
+	../sys/libgslsys.la ../rng/libgslrng.la \
+	../specfunc/libgslspecfunc.la ../min/libgslmin.la
 AM_V_P = $(am__v_P_@AM_V@)
 am__v_P_ = $(am__v_P_@AM_DEFAULT_V@)
 am__v_P_0 = false
@@ -384,6 +386,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -406,7 +409,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -522,12 +528,67 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslmultifit.la 
 pkginclude_HEADERS = gsl_multifit.h gsl_multifit_nlin.h
-INCLUDES = -I$(top_srcdir)
-libgslmultifit_la_SOURCES = multilinear.c work.c lmder.c fsolver.c fdfsolver.c fdjac.c convergence.c gradient.c covar.c multirobust.c robust_wfun.c
-noinst_HEADERS = lmutil.c lmpar.c lmset.c lmiterate.c qrsolv.c test_brown.c test_enso.c test_filip.c test_fn.c test_hahn1.c test_kirby2.c test_longley.c test_nelson.c test_pontius.c test_estimator.c
+AM_CPPFLAGS = -I$(top_srcdir)
+libgslmultifit_la_SOURCES = gcv.c multilinear.c multiwlinear.c work.c lmniel.c lmder.c fsolver.c fdfsolver.c fdfridge.c fdjac.c convergence.c gradient.c covar.c multirobust.c robust_wfun.c multireg.c
+noinst_HEADERS = \
+linear_common.c         \
+lmutil.c                \
+lmpar.c                 \
+lmset.c                 \
+lmiterate.c             \
+lmmisc.c                \
+qrsolv.c                \
+test_bard.c             \
+test_beale.c            \
+test_biggs.c            \
+test_box.c              \
+test_boxbod.c           \
+test_brown1.c           \
+test_brown2.c           \
+test_brown3.c           \
+test_eckerle.c          \
+test_enso.c             \
+test_estimator.c        \
+test_exp1.c             \
+test_filip.c            \
+test_gaussian.c         \
+test_hahn1.c            \
+test_helical.c          \
+test_jennrich.c         \
+test_kirby2.c           \
+test_kowalik.c          \
+test_lin1.c             \
+test_lin2.c             \
+test_lin3.c             \
+test_linear.c           \
+test_longley.c          \
+test_meyer.c            \
+test_meyerscal.c        \
+test_nelson.c           \
+test_nonlinear.c        \
+test_osborne.c          \
+test_penalty1.c         \
+test_penalty2.c         \
+test_pontius.c          \
+test_powell1.c          \
+test_powell2.c          \
+test_powell3.c          \
+test_rat42.c            \
+test_rat43.c            \
+test_reg.c              \
+test_rosenbrock.c       \
+test_rosenbrocke.c      \
+test_roth.c             \
+test_shaw.c             \
+test_thurber.c          \
+test_vardim.c           \
+test_watson.c           \
+test_wnlin.c            \
+test_wood.c
+
 TESTS = $(check_PROGRAMS)
 test_SOURCES = test.c
-test_LDADD = libgslmultifit.la ../linalg/libgsllinalg.la ../permutation/libgslpermutation.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../sort/libgslsort.la ../statistics/libgslstatistics.la ../vector/libgslvector.la ../block/libgslblock.la  ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../utils/libutils.la ../sys/libgslsys.la
+test_LDADD = libgslmultifit.la ../linalg/libgsllinalg.la ../permutation/libgslpermutation.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../sort/libgslsort.la ../statistics/libgslstatistics.la ../vector/libgslvector.la ../block/libgslblock.la  ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../utils/libutils.la ../sys/libgslsys.la ../rng/libgslrng.la ../specfunc/libgslspecfunc.la ../min/libgslmin.la
 all: all-am
 
 .SUFFIXES:
@@ -598,13 +659,18 @@
 
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/convergence.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/covar.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/fdfridge.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/fdfsolver.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/fdjac.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/fsolver.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/gcv.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/gradient.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/lmder.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/lmniel.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/multilinear.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/multireg.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/multirobust.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/multiwlinear.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/robust_wfun.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/test.Po@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/work.Plo@am__quote@
diff -Nru gsl-doc-1.16/multifit/multilinear.c gsl-doc-2.3/multifit/multilinear.c
--- gsl-doc-1.16/multifit/multilinear.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/multilinear.c	2016-11-18 19:07:56.000000000 +0000
@@ -1,7 +1,7 @@
 /* multifit/multilinear.c
  * 
  * Copyright (C) 2000, 2007, 2010 Brian Gough
- * Copyright (C) 2013 Patrick Alken
+ * Copyright (C) 2013, 2015 Patrick Alken
  * 
  * This program is free software; you can redistribute it and/or modify
  * it under the terms of the GNU General Public License as published by
@@ -26,170 +26,11 @@
 #include <gsl/gsl_matrix.h>
 #include <gsl/gsl_linalg.h>
 
-/* Fit
- *
- *  y = X c
- *
- *  where X is an M x N matrix of M observations for N variables.
- *
- */
+#include "linear_common.c"
 
-static int
-multifit_linear_svd (const gsl_matrix * X,
-                     const gsl_vector * y,
-                     double tol,
-                     int balance,
-                     size_t * rank,
-                     gsl_vector * c,
-                     gsl_matrix * cov,
-                     double *chisq, 
-                     gsl_multifit_linear_workspace * work)
-{
-  if (X->size1 != y->size)
-    {
-      GSL_ERROR
-        ("number of observations in y does not match rows of matrix X",
-         GSL_EBADLEN);
-    }
-  else if (X->size2 != c->size)
-    {
-      GSL_ERROR ("number of parameters c does not match columns of matrix X",
-                 GSL_EBADLEN);
-    }
-  else if (cov->size1 != cov->size2)
-    {
-      GSL_ERROR ("covariance matrix is not square", GSL_ENOTSQR);
-    }
-  else if (c->size != cov->size1)
-    {
-      GSL_ERROR
-        ("number of parameters does not match size of covariance matrix",
-         GSL_EBADLEN);
-    }
-  else if (X->size1 != work->n || X->size2 != work->p)
-    {
-      GSL_ERROR
-        ("size of workspace does not match size of observation matrix",
-         GSL_EBADLEN);
-    }
-  else if (tol <= 0)
-    {
-      GSL_ERROR ("tolerance must be positive", GSL_EINVAL);
-    }
-  else
-    {
-      const size_t n = X->size1;
-      const size_t p = X->size2;
-
-      size_t i, j, p_eff;
-
-      gsl_matrix *A = work->A;
-      gsl_matrix *Q = work->Q;
-      gsl_matrix *QSI = work->QSI;
-      gsl_vector *S = work->S;
-      gsl_vector *xt = work->xt;
-      gsl_vector *D = work->D;
-
-      /* Copy X to workspace,  A <= X */
-
-      gsl_matrix_memcpy (A, X);
-
-      /* Balance the columns of the matrix A if requested */
-
-      if (balance) 
-        {
-          gsl_linalg_balance_columns (A, D);
-        }
-      else
-        {
-          gsl_vector_set_all (D, 1.0);
-        }
-
-      /* Decompose A into U S Q^T */
-
-      gsl_linalg_SV_decomp_mod (A, QSI, Q, S, xt);
-
-      /* Solve y = A c for c */
-
-      gsl_blas_dgemv (CblasTrans, 1.0, A, y, 0.0, xt);
-
-      /* Scale the matrix Q,  Q' = Q S^-1 */
-
-      gsl_matrix_memcpy (QSI, Q);
-
-      {
-        double alpha0 = gsl_vector_get (S, 0);
-        p_eff = 0;
-
-        for (j = 0; j < p; j++)
-          {
-            gsl_vector_view column = gsl_matrix_column (QSI, j);
-            double alpha = gsl_vector_get (S, j);
-
-            if (alpha <= tol * alpha0) {
-              alpha = 0.0;
-            } else {
-              alpha = 1.0 / alpha;
-              p_eff++;
-            }
-
-            gsl_vector_scale (&column.vector, alpha);
-          }
-
-        *rank = p_eff;
-      }
-
-      gsl_vector_set_zero (c);
-
-      gsl_blas_dgemv (CblasNoTrans, 1.0, QSI, xt, 0.0, c);
-
-      /* Unscale the balancing factors */
-
-      gsl_vector_div (c, D);
-
-      /* Compute chisq, from residual r = y - X c */
-
-      {
-        double s2 = 0, r2 = 0;
-
-        for (i = 0; i < n; i++)
-          {
-            double yi = gsl_vector_get (y, i);
-            gsl_vector_const_view row = gsl_matrix_const_row (X, i);
-            double y_est, ri;
-            gsl_blas_ddot (&row.vector, c, &y_est);
-            ri = yi - y_est;
-            r2 += ri * ri;
-          }
-
-        s2 = r2 / (n - p_eff);   /* p_eff == rank */
-
-        *chisq = r2;
-
-        /* Form variance-covariance matrix cov = s2 * (Q S^-1) (Q S^-1)^T */
-
-        for (i = 0; i < p; i++)
-          {
-            gsl_vector_view row_i = gsl_matrix_row (QSI, i);
-            double d_i = gsl_vector_get (D, i);
-
-            for (j = i; j < p; j++)
-              {
-                gsl_vector_view row_j = gsl_matrix_row (QSI, j);
-                double d_j = gsl_vector_get (D, j);
-                double s;
-
-                gsl_blas_ddot (&row_i.vector, &row_j.vector, &s);
-
-                gsl_matrix_set (cov, i, j, s * s2 / (d_i * d_j));
-                gsl_matrix_set (cov, j, i, s * s2 / (d_i * d_j));
-              }
-          }
-      }
-
-      return GSL_SUCCESS;
-    }
-}
+static int multifit_linear_svd (const gsl_matrix * X,
+                                const int balance,
+                                gsl_multifit_linear_workspace * work);
 
 int
 gsl_multifit_linear (const gsl_matrix * X,
@@ -199,268 +40,148 @@
                      double *chisq, gsl_multifit_linear_workspace * work)
 {
   size_t rank;
-  int status  = multifit_linear_svd (X, y, GSL_DBL_EPSILON, 1, &rank, c,
-                                     cov, chisq, work);
+  int status = gsl_multifit_linear_tsvd(X, y, GSL_DBL_EPSILON, c, cov, chisq, &rank, work);
+
   return status;
 }
 
-/* Handle the general case of the SVD with tolerance and rank */
+/*
+gsl_multifit_linear_tsvd()
+  Solve linear least squares system with truncated SVD
 
-int
-gsl_multifit_linear_svd (const gsl_matrix * X,
-                         const gsl_vector * y,
-                         double tol,
-                         size_t * rank,
-                         gsl_vector * c,
-                         gsl_matrix * cov,
-                         double *chisq, gsl_multifit_linear_workspace * work)
-{
-  int status = multifit_linear_svd (X, y, tol, 1, rank, c, cov, chisq, work);
-  return status;
-}
+Inputs: X     - least squares matrix, n-by-p
+        y     - right hand side vector, n-by-1
+        tol   - tolerance for singular value truncation; if
+                s_j <= tol * s_0
+                then it is discarded from series expansion
+        c     - (output) solution vector, p-by-1
+        cov   - (output) covariance matrix, p-by-p
+        chisq - (output) cost function chi^2
+        rank  - (output) effective rank (number of singular values
+                used in solution)
+        work  - workspace
+*/
 
 int
-gsl_multifit_linear_usvd (const gsl_matrix * X,
+gsl_multifit_linear_tsvd (const gsl_matrix * X,
                           const gsl_vector * y,
-                          double tol,
-                          size_t * rank,
+                          const double tol,
                           gsl_vector * c,
                           gsl_matrix * cov,
-                          double *chisq, gsl_multifit_linear_workspace * work)
+                          double * chisq,
+                          size_t * rank,
+                          gsl_multifit_linear_workspace * work)
 {
-  int status = multifit_linear_svd (X, y, tol, 0, rank, c, cov, chisq, work);
-  return status;
-}
-
-/* General weighted case */ 
+  const size_t n = X->size1;
+  const size_t p = X->size2;
 
-static int
-multifit_wlinear_svd (const gsl_matrix * X,
-                      const gsl_vector * w,
-                      const gsl_vector * y,
-                      double tol,
-                      int balance,
-                      size_t * rank,
-                      gsl_vector * c,
-                      gsl_matrix * cov,
-                      double *chisq, gsl_multifit_linear_workspace * work)
-{
-  if (X->size1 != y->size)
-    {
-      GSL_ERROR
-        ("number of observations in y does not match rows of matrix X",
-         GSL_EBADLEN);
-    }
-  else if (X->size2 != c->size)
+  if (y->size != n)
     {
-      GSL_ERROR ("number of parameters c does not match columns of matrix X",
-                 GSL_EBADLEN);
+      GSL_ERROR("number of observations in y does not match matrix",
+                GSL_EBADLEN);
     }
-  else if (w->size != y->size)
+  else if (p != c->size)
     {
-      GSL_ERROR ("number of weights does not match number of observations",
+      GSL_ERROR ("number of parameters c does not match matrix",
                  GSL_EBADLEN);
     }
-  else if (cov->size1 != cov->size2)
-    {
-      GSL_ERROR ("covariance matrix is not square", GSL_ENOTSQR);
-    }
-  else if (c->size != cov->size1)
-    {
-      GSL_ERROR
-        ("number of parameters does not match size of covariance matrix",
-         GSL_EBADLEN);
-    }
-  else if (X->size1 != work->n || X->size2 != work->p)
+  else if (tol <= 0)
     {
-      GSL_ERROR
-        ("size of workspace does not match size of observation matrix",
-         GSL_EBADLEN);
+      GSL_ERROR ("tolerance must be positive", GSL_EINVAL);
     }
   else
     {
-      const size_t n = X->size1;
-      const size_t p = X->size2;
-
-      size_t i, j, p_eff;
+      int status;
+      double rnorm = 0.0, snorm;
 
-      gsl_matrix *A = work->A;
-      gsl_matrix *Q = work->Q;
-      gsl_matrix *QSI = work->QSI;
-      gsl_vector *S = work->S;
-      gsl_vector *t = work->t;
-      gsl_vector *xt = work->xt;
-      gsl_vector *D = work->D;
+      /* compute balanced SVD */
+      status = gsl_multifit_linear_bsvd (X, work);
+      if (status)
+        return status;
 
-      /* Scale X,  A = sqrt(w) X */
+      status = multifit_linear_solve (X, y, tol, -1.0, rank,
+                                      c, &rnorm, &snorm, work);
 
-      gsl_matrix_memcpy (A, X);
-
-      for (i = 0; i < n; i++)
-        {
-          double wi = gsl_vector_get (w, i);
-
-          if (wi < 0)
-            wi = 0;
-
-          {
-            gsl_vector_view row = gsl_matrix_row (A, i);
-            gsl_vector_scale (&row.vector, sqrt (wi));
-          }
-        }
-
-      /* Balance the columns of the matrix A if requested */
-
-      if (balance) 
-        {
-          gsl_linalg_balance_columns (A, D);
-        }
-      else
-        {
-          gsl_vector_set_all (D, 1.0);
-        }
-
-      /* Decompose A into U S Q^T */
-
-      gsl_linalg_SV_decomp_mod (A, QSI, Q, S, xt);
-
-      /* Solve sqrt(w) y = A c for c, by first computing t = sqrt(w) y */
-
-      for (i = 0; i < n; i++)
-        {
-          double wi = gsl_vector_get (w, i);
-          double yi = gsl_vector_get (y, i);
-          if (wi < 0)
-            wi = 0;
-          gsl_vector_set (t, i, sqrt (wi) * yi);
-        }
-
-      gsl_blas_dgemv (CblasTrans, 1.0, A, t, 0.0, xt);
-
-      /* Scale the matrix Q,  Q' = Q S^-1 */
-
-      gsl_matrix_memcpy (QSI, Q);
+      *chisq = rnorm * rnorm;
 
+      /* variance-covariance matrix cov = s2 * (Q S^-1) (Q S^-1)^T */
       {
-        double alpha0 = gsl_vector_get (S, 0);
-        p_eff = 0;
-        
-        for (j = 0; j < p; j++)
-          {
-            gsl_vector_view column = gsl_matrix_column (QSI, j);
-            double alpha = gsl_vector_get (S, j);
-
-            if (alpha <= tol * alpha0) {
-              alpha = 0.0;
-            } else {
-              alpha = 1.0 / alpha;
-              p_eff++;
-            }
-
-            gsl_vector_scale (&column.vector, alpha);
-          }
-
-        *rank = p_eff;
-      }
-
-      gsl_vector_set_zero (c);
-
-      /* Solution */
-
-      gsl_blas_dgemv (CblasNoTrans, 1.0, QSI, xt, 0.0, c);
-
-      /* Unscale the balancing factors */
-
-      gsl_vector_div (c, D);
-
-      /* Compute chisq, from residual r = y - X c */
-
-      {
-        double r2 = 0;
-
-        for (i = 0; i < n; i++)
-          {
-            double yi = gsl_vector_get (y, i);
-            double wi = gsl_vector_get (w, i);
-            gsl_vector_const_view row = gsl_matrix_const_row (X, i);
-            double y_est, ri;
-            gsl_blas_ddot (&row.vector, c, &y_est);
-            ri = yi - y_est;
-            r2 += wi * ri * ri;
-          }
-
-        *chisq = r2;
-
-        /* Form covariance matrix cov = (X^T W X)^-1 = (Q S^-1) (Q S^-1)^T */
+        double r2 = rnorm * rnorm;
+        double s2 = r2 / (double)(n - *rank);
+        size_t i, j;
+        gsl_matrix_view QSI = gsl_matrix_submatrix(work->QSI, 0, 0, p, p);
+        gsl_vector_view D = gsl_vector_subvector(work->D, 0, p);
 
         for (i = 0; i < p; i++)
           {
-            gsl_vector_view row_i = gsl_matrix_row (QSI, i);
-            double d_i = gsl_vector_get (D, i);
+            gsl_vector_view row_i = gsl_matrix_row (&QSI.matrix, i);
+            double d_i = gsl_vector_get (&D.vector, i);
 
             for (j = i; j < p; j++)
               {
-                gsl_vector_view row_j = gsl_matrix_row (QSI, j);
-                double d_j = gsl_vector_get (D, j);
+                gsl_vector_view row_j = gsl_matrix_row (&QSI.matrix, j);
+                double d_j = gsl_vector_get (&D.vector, j);
                 double s;
 
                 gsl_blas_ddot (&row_i.vector, &row_j.vector, &s);
 
-                gsl_matrix_set (cov, i, j, s / (d_i * d_j));
-                gsl_matrix_set (cov, j, i, s / (d_i * d_j));
+                gsl_matrix_set (cov, i, j, s * s2 / (d_i * d_j));
+                gsl_matrix_set (cov, j, i, s * s2 / (d_i * d_j));
               }
           }
       }
 
-      return GSL_SUCCESS;
+      return status;
     }
 }
 
+/*
+gsl_multifit_linear_svd()
+  Perform SVD decomposition of the matrix X and store in work without
+balancing
+*/
 
 int
-gsl_multifit_wlinear (const gsl_matrix * X,
-                      const gsl_vector * w,
-                      const gsl_vector * y,
-                      gsl_vector * c,
-                      gsl_matrix * cov,
-                      double *chisq, gsl_multifit_linear_workspace * work)
+gsl_multifit_linear_svd (const gsl_matrix * X,
+                         gsl_multifit_linear_workspace * work)
 {
-  size_t rank;
-  int status  = multifit_wlinear_svd (X, w, y, GSL_DBL_EPSILON, 1,  &rank, c,
-                                      cov, chisq, work);
+  /* do not balance by default */
+  int status = multifit_linear_svd(X, 0, work);
+
   return status;
 }
 
+/*
+gsl_multifit_linear_bsvd()
+  Perform SVD decomposition of the matrix X and store in work with
+balancing
+*/
+
 int
-gsl_multifit_wlinear_svd (const gsl_matrix * X,
-                          const gsl_vector * w,
-                          const gsl_vector * y,
-                          double tol,
-                          size_t * rank,
-                          gsl_vector * c,
-                          gsl_matrix * cov,
-                          double *chisq, gsl_multifit_linear_workspace * work)
+gsl_multifit_linear_bsvd (const gsl_matrix * X,
+                          gsl_multifit_linear_workspace * work)
 {
-  int status  = multifit_wlinear_svd (X, w, y, tol, 1, rank, c,
-                                      cov, chisq, work);
-  return status;
+  int status = multifit_linear_svd(X, 1, work);
 
+  return status;
 }
 
-int
-gsl_multifit_wlinear_usvd (const gsl_matrix * X,
-                           const gsl_vector * w,
-                           const gsl_vector * y,
-                           double tol,
-                           size_t * rank,
-                           gsl_vector * c,
-                           gsl_matrix * cov,
-                           double *chisq, gsl_multifit_linear_workspace * work)
+size_t
+gsl_multifit_linear_rank(const double tol, const gsl_multifit_linear_workspace * work)
 {
-  int status  = multifit_wlinear_svd (X, w, y, tol, 0, rank, c,
-                                      cov, chisq, work);
-  return status;
+  double s0 = gsl_vector_get (work->S, 0);
+  size_t rank = 0;
+  size_t j;
+
+  for (j = 0; j < work->p; j++)
+    {
+      double sj = gsl_vector_get (work->S, j);
+
+      if (sj > tol * s0)
+        ++rank;
+    }
 
+  return rank;
 }
 
 /* Estimation of values for given x */
@@ -513,6 +234,19 @@
 }
 
 /*
+gsl_multifit_linear_rcond()
+  Return reciprocal condition number of LS matrix;
+gsl_multifit_linear_svd() must first be called to
+compute the SVD of X and its reciprocal condition number
+*/
+
+double
+gsl_multifit_linear_rcond (const gsl_multifit_linear_workspace * w)
+{
+  return w->rcond;
+}
+
+/*
 gsl_multifit_linear_residuals()
   Compute vector of residuals from fit
 
@@ -551,3 +285,74 @@
       return GSL_SUCCESS;
     }
 } /* gsl_multifit_linear_residuals() */
+
+/* Perform a SVD decomposition on the least squares matrix X = U S Q^T
+ *
+ * Inputs: X       - least squares matrix
+ *         balance - 1 to perform column balancing
+ *         work    - workspace
+ *
+ * Notes:
+ * 1) On output,
+ *    work->A contains the matrix U
+ *    work->Q contains the matrix Q
+ *    work->S contains the vector of singular values
+ * 2) The matrix X may have smaller dimensions than the workspace
+ *    in the case of stdform2() - but the dimensions cannot be larger
+ * 3) On output, work->n and work->p are set to the dimensions of X
+ * 4) On output, work->rcond is set to the reciprocal condition number of X
+ */
+
+static int
+multifit_linear_svd (const gsl_matrix * X,
+                     const int balance,
+                     gsl_multifit_linear_workspace * work)
+{
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+
+  if (n > work->nmax || p > work->pmax)
+    {
+      GSL_ERROR("observation matrix larger than workspace", GSL_EBADLEN);
+    }
+  else
+    {
+      gsl_matrix_view A = gsl_matrix_submatrix(work->A, 0, 0, n, p);
+      gsl_matrix_view Q = gsl_matrix_submatrix(work->Q, 0, 0, p, p);
+      gsl_matrix_view QSI = gsl_matrix_submatrix(work->QSI, 0, 0, p, p);
+      gsl_vector_view S = gsl_vector_subvector(work->S, 0, p);
+      gsl_vector_view xt = gsl_vector_subvector(work->xt, 0, p);
+      gsl_vector_view D = gsl_vector_subvector(work->D, 0, p);
+
+      /* Copy X to workspace,  A <= X */
+
+      gsl_matrix_memcpy (&A.matrix, X);
+
+      /* Balance the columns of the matrix A if requested */
+
+      if (balance) 
+        {
+          gsl_linalg_balance_columns (&A.matrix, &D.vector);
+        }
+      else
+        {
+          gsl_vector_set_all (&D.vector, 1.0);
+        }
+
+      /* decompose A into U S Q^T */
+      gsl_linalg_SV_decomp_mod (&A.matrix, &QSI.matrix, &Q.matrix,
+                                &S.vector, &xt.vector);
+
+      /* compute reciprocal condition number rcond = smin / smax */
+      {
+        double smin, smax;
+        gsl_vector_minmax(&S.vector, &smin, &smax);
+        work->rcond = smin / smax;
+      }
+
+      work->n = n;
+      work->p = p;
+
+      return GSL_SUCCESS;
+    }
+}
diff -Nru gsl-doc-1.16/multifit/multireg.c gsl-doc-2.3/multifit/multireg.c
--- gsl-doc-1.16/multifit/multireg.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/multireg.c	2016-11-25 18:54:30.000000000 +0000
@@ -0,0 +1,1220 @@
+/* multifit/multireg.c
+ * 
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/*
+ * References:
+ *
+ * [1] P. C. Hansen & D. P. O'Leary, "The use of the L-curve in
+ * the regularization of discrete ill-posed problems",  SIAM J. Sci.
+ * Comput. 14 (1993), pp. 1487-1503.
+ *
+ * [2] P. C. Hansen, "Discrete Inverse Problems: Insight and Algorithms,"
+ * SIAM Press, 2010.
+ */
+
+#include <config.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_multifit.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+
+#include "linear_common.c"
+
+int
+gsl_multifit_linear_solve (const double lambda,
+                           const gsl_matrix * X,
+                           const gsl_vector * y,
+                           gsl_vector * c,
+                           double *rnorm,
+                           double *snorm,
+                           gsl_multifit_linear_workspace * work)
+{
+  size_t rank;
+  int status;
+
+  status = multifit_linear_solve(X, y, GSL_DBL_EPSILON, lambda, &rank, c,
+                                 rnorm, snorm, work);
+
+  return status;
+} /* gsl_multifit_linear_solve() */
+
+/*
+gsl_multifit_linear_applyW()
+  Apply weight matrix to (X,y) LS system
+
+Inputs: X    - least squares matrix n-by-p
+        w    - weight vector n-by-1 or NULL for W = I
+        y    - right hand side n-by-1
+        WX   - (output) sqrt(W) X, n-by-p
+        Wy   - (output) sqrt(W) y, n-by-1
+
+Notes:
+1) If w = NULL, on output WX = X and Wy = y
+2) It is allowed for WX = X and Wy = y for in-place transform
+*/
+
+int
+gsl_multifit_linear_applyW(const gsl_matrix * X,
+                           const gsl_vector * w,
+                           const gsl_vector * y,
+                           gsl_matrix * WX,
+                           gsl_vector * Wy)
+{
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+
+  if (n != y->size)
+    {
+      GSL_ERROR("y vector does not match X", GSL_EBADLEN);
+    }
+  else if (w != NULL && n != w->size)
+    {
+      GSL_ERROR("weight vector does not match X", GSL_EBADLEN);
+    }
+  else if (n != WX->size1 || p != WX->size2)
+    {
+      GSL_ERROR("WX matrix dimensions do not match X", GSL_EBADLEN);
+    }
+  else if (n != Wy->size)
+    {
+      GSL_ERROR("Wy vector must be length n", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i;
+
+      /* copy WX = X; Wy = y if distinct pointers */
+      if (WX != X)
+        gsl_matrix_memcpy(WX, X);
+      if (Wy != y)
+        gsl_vector_memcpy(Wy, y);
+
+      if (w != NULL)
+        {
+          /* construct WX = sqrt(W) X and Wy = sqrt(W) y */
+          for (i = 0; i < n; ++i)
+            {
+              double wi = gsl_vector_get(w, i);
+              double swi;
+              gsl_vector_view row = gsl_matrix_row(WX, i);
+              double *yi = gsl_vector_ptr(Wy, i);
+
+              if (wi < 0.0)
+                wi = 0.0;
+
+              swi = sqrt(wi);
+              gsl_vector_scale(&row.vector, swi);
+              *yi *= swi;
+            }
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+gsl_multifit_linear_wstdform1()
+  Using regularization matrix
+L = diag(l_1,l_2,...,l_p), transform to Tikhonov standard form:
+
+X~ = sqrt(W) X L^{-1}
+y~ = sqrt(W) y
+c~ = L c
+
+Inputs: L    - Tikhonov matrix as a vector of diagonal elements p-by-1;
+               or NULL for L = I
+        X    - least squares matrix n-by-p
+        y    - right hand side vector n-by-1
+        w    - weight vector n-by-1; or NULL for W = I
+        Xs   - least squares matrix in standard form X~ n-by-p
+        ys   - right hand side vector in standard form y~ n-by-1
+        work - workspace
+
+Return: success/error
+
+Notes:
+1) It is allowed for X = Xs and y = ys
+*/
+
+int
+gsl_multifit_linear_wstdform1 (const gsl_vector * L,
+                               const gsl_matrix * X,
+                               const gsl_vector * w,
+                               const gsl_vector * y,
+                               gsl_matrix * Xs,
+                               gsl_vector * ys,
+                               gsl_multifit_linear_workspace * work)
+{
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+
+  if (n > work->nmax || p > work->pmax)
+    {
+      GSL_ERROR("observation matrix larger than workspace", GSL_EBADLEN);
+    }
+  else if (L != NULL && p != L->size)
+    {
+      GSL_ERROR("L vector does not match X", GSL_EBADLEN);
+    }
+  else if (n != y->size)
+    {
+      GSL_ERROR("y vector does not match X", GSL_EBADLEN);
+    }
+  else if (w != NULL && n != w->size)
+    {
+      GSL_ERROR("weight vector does not match X", GSL_EBADLEN);
+    }
+  else if (n != Xs->size1 || p != Xs->size2)
+    {
+      GSL_ERROR("Xs matrix dimensions do not match X", GSL_EBADLEN);
+    }
+  else if (n != ys->size)
+    {
+      GSL_ERROR("ys vector must be length n", GSL_EBADLEN);
+    }
+  else
+    {
+      int status = GSL_SUCCESS;
+
+      /* compute Xs = sqrt(W) X and ys = sqrt(W) y */
+      status = gsl_multifit_linear_applyW(X, w, y, Xs, ys);
+      if (status)
+        return status;
+
+      if (L != NULL)
+        {
+          size_t j;
+
+          /* construct X~ = sqrt(W) X * L^{-1} matrix */
+          for (j = 0; j < p; ++j)
+            {
+              gsl_vector_view Xj = gsl_matrix_column(Xs, j);
+              double lj = gsl_vector_get(L, j);
+
+              if (lj == 0.0)
+                {
+                  GSL_ERROR("L matrix is singular", GSL_EDOM);
+                }
+
+              gsl_vector_scale(&Xj.vector, 1.0 / lj);
+            }
+        }
+
+      return status;
+    }
+}
+
+/*
+gsl_multifit_linear_stdform1()
+  Using regularization matrix L = diag(l_1,l_2,...,l_p),
+and W = I, transform to Tikhonov standard form:
+
+X~ = X L^{-1}
+y~ = y
+c~ = L c
+
+Inputs: L    - Tikhonov matrix as a vector of diagonal elements p-by-1
+        X    - least squares matrix n-by-p
+        y    - right hand side vector n-by-1
+        Xs   - least squares matrix in standard form X~ n-by-p
+        ys   - right hand side vector in standard form y~ n-by-1
+        work - workspace
+
+Return: success/error
+
+Notes:
+1) It is allowed for X = Xs
+*/
+
+int
+gsl_multifit_linear_stdform1 (const gsl_vector * L,
+                              const gsl_matrix * X,
+                              const gsl_vector * y,
+                              gsl_matrix * Xs,
+                              gsl_vector * ys,
+                              gsl_multifit_linear_workspace * work)
+{
+  int status;
+
+  status = gsl_multifit_linear_wstdform1(L, X, NULL, y, Xs, ys, work);
+
+  return status;
+}
+
+int
+gsl_multifit_linear_L_decomp (gsl_matrix * L, gsl_vector * tau)
+{
+  const size_t m = L->size1;
+  const size_t p = L->size2;
+  int status;
+
+  if (tau->size != GSL_MIN(m, p))
+    {
+      GSL_ERROR("tau vector must be min(m,p)", GSL_EBADLEN);
+    }
+  else if (m >= p)
+    {
+      /* square or tall L matrix */
+      status = gsl_linalg_QR_decomp(L, tau);
+      return status;
+    }
+  else
+    {
+      /* more columns than rows, compute qr(L^T) */
+      gsl_matrix_view LTQR = gsl_matrix_view_array(L->data, p, m);
+      gsl_matrix *LT = gsl_matrix_alloc(p, m);
+
+      /* XXX: use temporary storage due to difficulties in transforming
+       * a rectangular matrix in-place */
+      gsl_matrix_transpose_memcpy(LT, L);
+      gsl_matrix_memcpy(&LTQR.matrix, LT);
+      gsl_matrix_free(LT);
+
+      status = gsl_linalg_QR_decomp(&LTQR.matrix, tau);
+
+      return status;
+    }
+}
+
+/*
+gsl_multifit_linear_wstdform2()
+  Using regularization matrix L which is m-by-p, transform to Tikhonov
+standard form. This routine is separated into two cases:
+
+Case 1: m >= p, here we can use the QR decomposition of L = QR, and note
+that ||L c|| = ||R c|| where R is p-by-p. Therefore,
+
+X~ = X R^{-1} is n-by-p
+y~ = y is n-by-1
+c~ is p-by-1
+M is not used
+
+Case 2: m < p
+
+X~ is (n - p + m)-by-m
+y~ is (n - p + m)-by-1
+c~ is m-by-1
+M is n-by-p (workspace)
+
+Inputs: LQR  - output from gsl_multifit_linear_L_decomp()
+        Ltau - output from gsl_multifit_linear_L_decomp()
+        X    - least squares matrix n-by-p
+        w    - weight vector n-by-1; or NULL for W = I
+        y    - right hand side vector n-by-1
+        Xs   - (output) least squares matrix in standard form
+               case 1: n-by-p
+               case 2: (n - p + m)-by-m
+        ys   - (output) right hand side vector in standard form
+               case 1: n-by-1
+               case 2: (n - p + m)-by-1
+        M    - (output) workspace matrix needed to reconstruct solution vector
+               case 1: not used
+               case 2: n-by-p
+        work - workspace
+
+Return: success/error
+
+Notes:
+1) If m >= p, on output:
+   Xs = X R^{-1}
+   ys = y
+
+2) If m < p, on output:
+   M(:,1:pm) contains QR decomposition of A * K_o, needed to reconstruct
+   solution vector, where pm = p - m; M(:,p) contains Householder scalars
+*/
+
+int
+gsl_multifit_linear_wstdform2 (const gsl_matrix * LQR,
+                               const gsl_vector * Ltau,
+                               const gsl_matrix * X,
+                               const gsl_vector * w,
+                               const gsl_vector * y,
+                               gsl_matrix * Xs,
+                               gsl_vector * ys,
+                               gsl_matrix * M,
+                               gsl_multifit_linear_workspace * work)
+{
+  const size_t m = LQR->size1;
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+
+  if (n > work->nmax || p > work->pmax)
+    {
+      GSL_ERROR("observation matrix larger than workspace", GSL_EBADLEN);
+    }
+  else if (p != LQR->size2)
+    {
+      GSL_ERROR("LQR and X matrices have different numbers of columns", GSL_EBADLEN);
+    }
+  else if (n != y->size)
+    {
+      GSL_ERROR("y vector does not match X", GSL_EBADLEN);
+    }
+  else if (w != NULL && n != w->size)
+    {
+      GSL_ERROR("weights vector must be length n", GSL_EBADLEN);
+    }
+  else if (m >= p) /* square or tall L matrix */
+    {
+      /* the sizes of Xs and ys depend on whether m >= p or m < p */
+      if (n != Xs->size1 || p != Xs->size2)
+        {
+          GSL_ERROR("Xs matrix must be n-by-p", GSL_EBADLEN);
+        }
+      else if (n != ys->size)
+        {
+          GSL_ERROR("ys vector must have length n", GSL_EBADLEN);
+        }
+      else
+        {
+          int status;
+          size_t i;
+          gsl_matrix_const_view R = gsl_matrix_const_submatrix(LQR, 0, 0, p, p);
+
+          /* compute Xs = sqrt(W) X and ys = sqrt(W) y */
+          status = gsl_multifit_linear_applyW(X, w, y, Xs, ys);
+          if (status)
+            return status;
+
+          /* compute X~ = X R^{-1} using QR decomposition of L */
+          for (i = 0; i < n; ++i)
+            {
+              gsl_vector_view v = gsl_matrix_row(Xs, i);
+
+              /* solve: R^T y = X_i */
+              gsl_blas_dtrsv(CblasUpper, CblasTrans, CblasNonUnit, &R.matrix, &v.vector);
+            }
+
+          return GSL_SUCCESS;
+        }
+    }
+  else /* L matrix with m < p */
+    {
+      const size_t pm = p - m;
+      const size_t npm = n - pm;
+
+      /*
+       * This code closely follows section 2.6.1 of Hansen's
+       * "Regularization Tools" manual
+       */
+
+      if (npm != Xs->size1 || m != Xs->size2)
+        {
+          GSL_ERROR("Xs matrix must be (n-p+m)-by-m", GSL_EBADLEN);
+        }
+      else if (npm != ys->size)
+        {
+          GSL_ERROR("ys vector must be of length (n-p+m)", GSL_EBADLEN);
+        }
+      else if (n != M->size1 || p != M->size2)
+        {
+          GSL_ERROR("M matrix must be n-by-p", GSL_EBADLEN);
+        }
+      else
+        {
+          int status;
+          gsl_matrix_view A = gsl_matrix_submatrix(work->A, 0, 0, n, p);
+          gsl_vector_view b = gsl_vector_subvector(work->t, 0, n);
+
+          gsl_matrix_view LTQR = gsl_matrix_view_array(LQR->data, p, m);           /* qr(L^T) */
+          gsl_matrix_view Rp = gsl_matrix_view_array(LQR->data, m, m);             /* R factor of L^T */
+          gsl_vector_const_view LTtau = gsl_vector_const_subvector(Ltau, 0, m);
+
+          /*
+           * M(:,1:p-m) will hold QR decomposition of A K_o; M(:,p) will hold
+           * Householder scalars
+           */
+          gsl_matrix_view MQR = gsl_matrix_submatrix(M, 0, 0, n, pm);
+          gsl_vector_view Mtau = gsl_matrix_subcolumn(M, p - 1, 0, GSL_MIN(n, pm));
+
+          gsl_matrix_view AKo, AKp, HqTAKp;
+          gsl_vector_view v;
+          size_t i;
+
+          /* compute A = sqrt(W) X and b = sqrt(W) y */
+          status = gsl_multifit_linear_applyW(X, w, y, &A.matrix, &b.vector);
+          if (status)
+            return status;
+
+          /* compute: A <- A K = [ A K_p ; A K_o ] */
+          gsl_linalg_QR_matQ(&LTQR.matrix, &LTtau.vector, &A.matrix);
+          AKp = gsl_matrix_submatrix(&A.matrix, 0, 0, n, m); 
+          AKo = gsl_matrix_submatrix(&A.matrix, 0, m, n, pm); 
+
+          /* compute QR decomposition [H,T] = qr(A * K_o) and store in M */
+          gsl_matrix_memcpy(&MQR.matrix, &AKo.matrix);
+          gsl_linalg_QR_decomp(&MQR.matrix, &Mtau.vector);
+
+          /* AKp currently contains A K_p; apply H^T from the left to get H^T A K_p */
+          gsl_linalg_QR_QTmat(&MQR.matrix, &Mtau.vector, &AKp.matrix);
+
+          /* the last npm rows correspond to H_q^T A K_p */
+          HqTAKp = gsl_matrix_submatrix(&AKp.matrix, pm, 0, npm, m);
+
+          /* solve: Xs R_p^T = H_q^T A K_p for Xs */
+          gsl_matrix_memcpy(Xs, &HqTAKp.matrix);
+          for (i = 0; i < npm; ++i)
+            {
+              gsl_vector_view x = gsl_matrix_row(Xs, i);
+              gsl_blas_dtrsv(CblasUpper, CblasNoTrans, CblasNonUnit, &Rp.matrix, &x.vector);
+            }
+
+          /*
+           * compute: ys = H_q^T b; this is equivalent to computing
+           * the last q elements of H^T b (q = npm)
+           */
+          v = gsl_vector_subvector(&b.vector, pm, npm);
+          gsl_linalg_QR_QTvec(&MQR.matrix, &Mtau.vector, &b.vector);
+          gsl_vector_memcpy(ys, &v.vector);
+
+          return GSL_SUCCESS;
+        }
+    }
+}
+
+int
+gsl_multifit_linear_stdform2 (const gsl_matrix * LQR,
+                              const gsl_vector * Ltau,
+                              const gsl_matrix * X,
+                              const gsl_vector * y,
+                              gsl_matrix * Xs,
+                              gsl_vector * ys,
+                              gsl_matrix * M,
+                              gsl_multifit_linear_workspace * work)
+{
+  int status;
+
+  status = gsl_multifit_linear_wstdform2(LQR, Ltau, X, NULL, y, Xs, ys, M, work);
+
+  return status;
+}
+
+/*
+gsl_multifit_linear_genform1()
+  Backtransform regularized solution vector using matrix
+L = diag(L)
+*/
+
+int
+gsl_multifit_linear_genform1 (const gsl_vector * L,
+                              const gsl_vector * cs,
+                              gsl_vector * c,
+                              gsl_multifit_linear_workspace * work)
+{
+  if (L->size > work->pmax)
+    {
+      GSL_ERROR("L vector does not match workspace", GSL_EBADLEN);
+    }
+  else if (L->size != cs->size)
+    {
+      GSL_ERROR("cs vector does not match L", GSL_EBADLEN);
+    }
+  else if (L->size != c->size)
+    {
+      GSL_ERROR("c vector does not match L", GSL_EBADLEN);
+    }
+  else
+    {
+      /* compute true solution vector c = L^{-1} c~ */
+      gsl_vector_memcpy(c, cs);
+      gsl_vector_div(c, L);
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+gsl_multifit_linear_wgenform2()
+  Backtransform regularized solution vector in standard form to recover
+original vector
+
+Inputs: LQR  - output from gsl_multifit_linear_L_decomp()
+        Ltau - output from gsl_multifit_linear_L_decomp()
+        X    - original least squares matrix n-by-p
+        w    - original weight vector n-by-1 or NULL for W = I
+        y    - original rhs vector n-by-1
+        cs   - standard form solution vector
+        c    - (output) original solution vector p-by-1
+        M    - matrix computed by gsl_multifit_linear_wstdform2()
+        work - workspace
+*/
+
+int
+gsl_multifit_linear_wgenform2 (const gsl_matrix * LQR,
+                               const gsl_vector * Ltau,
+                               const gsl_matrix * X,
+                               const gsl_vector * w,
+                               const gsl_vector * y,
+                               const gsl_vector * cs,
+                               const gsl_matrix * M,
+                               gsl_vector * c,
+                               gsl_multifit_linear_workspace * work)
+{
+  const size_t m = LQR->size1;
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+
+  if (n > work->nmax || p > work->pmax)
+    {
+      GSL_ERROR("X matrix does not match workspace", GSL_EBADLEN);
+    }
+  else if (p != LQR->size2)
+    {
+      GSL_ERROR("LQR matrix does not match X", GSL_EBADLEN);
+    }
+  else if (p != c->size)
+    {
+      GSL_ERROR("c vector does not match X", GSL_EBADLEN);
+    }
+  else if (w != NULL && n != w->size)
+    {
+      GSL_ERROR("w vector does not match X", GSL_EBADLEN);
+    }
+  else if (n != y->size)
+    {
+      GSL_ERROR("y vector does not match X", GSL_EBADLEN);
+    }
+  else if (m >= p)                    /* square or tall L matrix */
+    {
+      if (p != cs->size)
+        {
+          GSL_ERROR("cs vector must be length p", GSL_EBADLEN);
+        }
+      else
+        {
+          int s;
+          gsl_matrix_const_view R = gsl_matrix_const_submatrix(LQR, 0, 0, p, p); /* R factor of L */
+
+          /* solve R c = cs for true solution c, using QR decomposition of L */
+          gsl_vector_memcpy(c, cs);
+          s = gsl_blas_dtrsv(CblasUpper, CblasNoTrans, CblasNonUnit, &R.matrix, c);
+
+          return s;
+        }
+    }
+  else                                /* rectangular L matrix with m < p */
+    {
+      if (m != cs->size)
+        {
+          GSL_ERROR("cs vector must be length m", GSL_EBADLEN);
+        }
+      else if (n != M->size1 || p != M->size2)
+        {
+          GSL_ERROR("M matrix must be size n-by-p", GSL_EBADLEN);
+        }
+      else
+        {
+          int status;
+          const size_t pm = p - m;
+          gsl_matrix_view A = gsl_matrix_submatrix(work->A, 0, 0, n, p);
+          gsl_vector_view b = gsl_vector_subvector(work->t, 0, n);
+          gsl_matrix_view Rp = gsl_matrix_view_array(LQR->data, m, m); /* R_p */
+          gsl_matrix_view LTQR = gsl_matrix_view_array(LQR->data, p, m);
+          gsl_vector_const_view LTtau = gsl_vector_const_subvector(Ltau, 0, m);
+          gsl_matrix_const_view MQR = gsl_matrix_const_submatrix(M, 0, 0, n, pm);
+          gsl_vector_const_view Mtau = gsl_matrix_const_subcolumn(M, p - 1, 0, GSL_MIN(n, pm));
+          gsl_matrix_const_view To = gsl_matrix_const_submatrix(&MQR.matrix, 0, 0, pm, pm);
+          gsl_vector_view workp = gsl_vector_subvector(work->xt, 0, p);
+          gsl_vector_view v1, v2;
+
+          /* compute A = sqrt(W) X and b = sqrt(W) y */
+          status = gsl_multifit_linear_applyW(X, w, y, &A.matrix, &b.vector);
+          if (status)
+            return status;
+
+          /* initialize c to zero */
+          gsl_vector_set_zero(c);
+
+          /* compute c = L_inv cs = K_p R_p^{-T} cs */
+
+          /* set c(1:m) = R_p^{-T} cs */
+          v1 = gsl_vector_subvector(c, 0, m);
+          gsl_vector_memcpy(&v1.vector, cs);
+          gsl_blas_dtrsv(CblasUpper, CblasTrans, CblasNonUnit, &Rp.matrix, &v1.vector);
+
+          /* c <- K R_p^{-T} cs = [ K_p R_p^{_T} cs ; 0 ] */
+          gsl_linalg_QR_Qvec(&LTQR.matrix, &LTtau.vector, c);
+
+          /* compute: b1 = b - A L_inv cs */
+          gsl_blas_dgemv(CblasNoTrans, -1.0, &A.matrix, c, 1.0, &b.vector);
+
+          /* compute: b2 = H^T b1 */
+          gsl_linalg_QR_QTvec(&MQR.matrix, &Mtau.vector, &b.vector);
+
+          /* compute: b3 = T_o^{-1} b2 */
+          v1 = gsl_vector_subvector(&b.vector, 0, pm);
+          gsl_blas_dtrsv(CblasUpper, CblasNoTrans, CblasNonUnit, &To.matrix, &v1.vector);
+
+          /* compute: b4 = K_o b3 */
+          gsl_vector_set_zero(&workp.vector);
+          v2 = gsl_vector_subvector(&workp.vector, m, pm);
+          gsl_vector_memcpy(&v2.vector, &v1.vector);
+          gsl_linalg_QR_Qvec(&LTQR.matrix, &LTtau.vector, &workp.vector);
+
+          /* final solution vector */
+          gsl_vector_add(c, &workp.vector);
+
+          return GSL_SUCCESS;
+        }
+    }
+}
+
+int
+gsl_multifit_linear_genform2 (const gsl_matrix * LQR,
+                              const gsl_vector * Ltau,
+                              const gsl_matrix * X,
+                              const gsl_vector * y,
+                              const gsl_vector * cs,
+                              const gsl_matrix * M,
+                              gsl_vector * c,
+                              gsl_multifit_linear_workspace * work)
+{
+  int status;
+
+  status = gsl_multifit_linear_wgenform2(LQR, Ltau, X, NULL, y, cs, M, c, work);
+
+  return status;
+}
+
+/*
+gsl_multifit_linear_lreg()
+  Calculate regularization parameters to use in L-curve
+analysis
+
+Inputs: smin      - smallest singular value of LS system
+        smax      - largest singular value of LS system > 0
+        reg_param - (output) vector of regularization parameters
+                    derived from singular values
+
+Return: success/error
+*/
+
+int
+gsl_multifit_linear_lreg (const double smin, const double smax,
+                          gsl_vector * reg_param)
+{
+  if (smax <= 0.0)
+    {
+      GSL_ERROR("smax must be positive", GSL_EINVAL);
+    }
+  else
+    {
+      const size_t N = reg_param->size;
+
+      /* smallest regularization parameter */
+      const double smin_ratio = 16.0 * GSL_DBL_EPSILON;
+      const double new_smin = GSL_MAX(smin, smax*smin_ratio);
+      double ratio;
+      size_t i;
+
+      gsl_vector_set(reg_param, N - 1, new_smin);
+
+      /* ratio so that reg_param(1) = s(1) */
+      ratio = pow(smax / new_smin, 1.0 / ((double)N - 1.0));
+
+      /* calculate the regularization parameters */
+      for (i = N - 1; i > 0 && i--; )
+        {
+          double rp1 = gsl_vector_get(reg_param, i + 1);
+          gsl_vector_set(reg_param, i, ratio * rp1);
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+gsl_multifit_linear_lcurve()
+  Calculate L-curve using regularization parameters estimated
+from singular values of least squares matrix
+
+Inputs: y         - right hand side vector
+        reg_param - (output) vector of regularization parameters
+                    derived from singular values
+        rho       - (output) vector of residual norms ||y - X c||
+        eta       - (output) vector of solution norms ||lambda c||
+        work      - workspace
+
+Return: success/error
+
+Notes:
+1) SVD of X must be computed first by calling multifit_linear_svd();
+   work->n and work->p are initialized by this function
+*/
+
+int
+gsl_multifit_linear_lcurve (const gsl_vector * y,
+                            gsl_vector * reg_param,
+                            gsl_vector * rho, gsl_vector * eta,
+                            gsl_multifit_linear_workspace * work)
+{
+  const size_t n = y->size;
+  const size_t N = rho->size; /* number of points on L-curve */
+
+  if (n != work->n)
+    {
+      GSL_ERROR("y vector does not match workspace", GSL_EBADLEN);
+    }
+  else if (N < 3)
+    {
+      GSL_ERROR ("at least 3 points are needed for L-curve analysis",
+                 GSL_EBADLEN);
+    }
+  else if (N != eta->size)
+    {
+      GSL_ERROR ("size of rho and eta vectors do not match",
+                 GSL_EBADLEN);
+    }
+  else if (reg_param->size != eta->size)
+    {
+      GSL_ERROR ("size of reg_param and eta vectors do not match",
+                 GSL_EBADLEN);
+    }
+  else
+    {
+      int status = GSL_SUCCESS;
+      const size_t p = work->p;
+
+      size_t i, j;
+
+      gsl_matrix_view A = gsl_matrix_submatrix(work->A, 0, 0, n, p);
+      gsl_vector_view S = gsl_vector_subvector(work->S, 0, p);
+      gsl_vector_view xt = gsl_vector_subvector(work->xt, 0, p);
+      gsl_vector_view workp = gsl_matrix_subcolumn(work->QSI, 0, 0, p);
+      gsl_vector_view workp2 = gsl_vector_subvector(work->D, 0, p); /* D isn't used for regularized problems */
+
+      const double smax = gsl_vector_get(&S.vector, 0);
+      const double smin = gsl_vector_get(&S.vector, p - 1);
+
+      double dr; /* residual error from projection */
+      double normy = gsl_blas_dnrm2(y);
+      double normUTy;
+
+      /* compute projection xt = U^T y */
+      gsl_blas_dgemv (CblasTrans, 1.0, &A.matrix, y, 0.0, &xt.vector);
+
+      normUTy = gsl_blas_dnrm2(&xt.vector);
+      dr = normy*normy - normUTy*normUTy;
+
+      /* calculate regularization parameters */
+      gsl_multifit_linear_lreg(smin, smax, reg_param);
+
+      for (i = 0; i < N; ++i)
+        {
+          double lambda = gsl_vector_get(reg_param, i);
+          double lambda_sq = lambda * lambda;
+
+          for (j = 0; j < p; ++j)
+            {
+              double sj = gsl_vector_get(&S.vector, j);
+              double xtj = gsl_vector_get(&xt.vector, j);
+              double f = sj / (sj*sj + lambda_sq);
+
+              gsl_vector_set(&workp.vector, j, f * xtj);
+              gsl_vector_set(&workp2.vector, j, (1.0 - sj*f) * xtj);
+            }
+
+          gsl_vector_set(eta, i, gsl_blas_dnrm2(&workp.vector));
+          gsl_vector_set(rho, i, gsl_blas_dnrm2(&workp2.vector));
+        }
+
+      if (n > p && dr > 0.0)
+        {
+          /* add correction to residual norm (see eqs 6-7 of [1]) */
+          for (i = 0; i < N; ++i)
+            {
+              double rhoi = gsl_vector_get(rho, i);
+              double *ptr = gsl_vector_ptr(rho, i);
+
+              *ptr = sqrt(rhoi*rhoi + dr);
+            }
+        }
+
+      /* restore D to identity matrix */
+      gsl_vector_set_all(work->D, 1.0);
+
+      return status;
+    }
+} /* gsl_multifit_linear_lcurve() */
+
+/*
+gsl_multifit_linear_lcorner()
+  Determine point on L-curve of maximum curvature. For each
+set of 3 points on the L-curve, the circle which passes through
+the 3 points is computed. The radius of the circle is then used
+as an estimate of the curvature at the middle point. The point
+with maximum curvature is then selected.
+
+Inputs: rho - vector of residual norms ||A x - b||
+        eta - vector of solution norms ||L x||
+        idx - (output) index i such that
+              (log(rho(i)),log(eta(i))) is the point of
+              maximum curvature
+
+Return: success/error
+*/
+
+int
+gsl_multifit_linear_lcorner(const gsl_vector *rho,
+                            const gsl_vector *eta,
+                            size_t *idx)
+{
+  const size_t n = rho->size;
+
+  if (n < 3)
+    {
+      GSL_ERROR ("at least 3 points are needed for L-curve analysis",
+                 GSL_EBADLEN);
+    }
+  else if (n != eta->size)
+    {
+      GSL_ERROR ("size of rho and eta vectors do not match",
+                 GSL_EBADLEN);
+    }
+  else
+    {
+      int s = GSL_SUCCESS;
+      size_t i;
+      double x1, y1;      /* first point of triangle on L-curve */
+      double x2, y2;      /* second point of triangle on L-curve */
+      double rmin = -1.0; /* minimum radius of curvature */
+
+      /* initial values */
+      x1 = log(gsl_vector_get(rho, 0));
+      y1 = log(gsl_vector_get(eta, 0));
+
+      x2 = log(gsl_vector_get(rho, 1));
+      y2 = log(gsl_vector_get(eta, 1));
+
+      for (i = 1; i < n - 1; ++i)
+        {
+          /*
+           * The points (x1,y1), (x2,y2), (x3,y3) are the previous,
+           * current, and next point on the L-curve. We will find
+           * the circle which fits these 3 points and take its radius
+           * as an estimate of the curvature at this point.
+           */
+          double x3 = log(gsl_vector_get(rho, i + 1));
+          double y3 = log(gsl_vector_get(eta, i + 1));
+
+          double x21 = x2 - x1;
+          double y21 = y2 - y1;
+          double x31 = x3 - x1;
+          double y31 = y3 - y1;
+          double h21 = x21*x21 + y21*y21;
+          double h31 = x31*x31 + y31*y31;
+          double d = fabs(2.0 * (x21*y31 - x31*y21));
+          double r = sqrt(h21*h31*((x3-x2)*(x3-x2)+(y3-y2)*(y3-y2))) / d;
+
+          /* if d =~ 0 then there are nearly colinear points */
+          if (gsl_finite(r))
+            {
+              /* check for smallest radius of curvature */
+              if (r < rmin || rmin < 0.0)
+                {
+                  rmin = r;
+                  *idx = i;
+                }
+            }
+
+          /* update previous/current L-curve values */
+          x1 = x2;
+          y1 = y2;
+          x2 = x3;
+          y2 = y3;
+        }
+
+      /* check if a minimum radius was found */
+      if (rmin < 0.0)
+        {
+          /* possibly co-linear points */
+          GSL_ERROR("failed to find minimum radius", GSL_EINVAL);
+        }
+
+      return s;
+    }
+} /* gsl_multifit_linear_lcorner() */
+
+/*
+gsl_multifit_linear_lcorner2()
+  Determine point on L-curve (lambda^2, ||c||^2) of maximum curvature.
+For each set of 3 points on the L-curve, the circle which passes through
+the 3 points is computed. The radius of the circle is then used
+as an estimate of the curvature at the middle point. The point
+with maximum curvature is then selected.
+
+This routine is based on the paper
+
+M. Rezghi and S. M. Hosseini, "A new variant of L-curve for Tikhonov
+regularization", J. Comp. App. Math., 231 (2009).
+
+Inputs: reg_param - vector of regularization parameters
+        eta       - vector of solution norms ||L x||
+        idx       - (output) index i such that
+                    (lambda(i)^2,eta(i)^2) is the point of
+                    maximum curvature
+
+Return: success/error
+*/
+
+int
+gsl_multifit_linear_lcorner2(const gsl_vector *reg_param,
+                             const gsl_vector *eta,
+                             size_t *idx)
+{
+  const size_t n = reg_param->size;
+
+  if (n < 3)
+    {
+      GSL_ERROR ("at least 3 points are needed for L-curve analysis",
+                 GSL_EBADLEN);
+    }
+  else if (n != eta->size)
+    {
+      GSL_ERROR ("size of reg_param and eta vectors do not match",
+                 GSL_EBADLEN);
+    }
+  else
+    {
+      int s = GSL_SUCCESS;
+      size_t i;
+      double x1, y1;      /* first point of triangle on L-curve */
+      double x2, y2;      /* second point of triangle on L-curve */
+      double rmin = -1.0; /* minimum radius of curvature */
+
+      /* initial values */
+      x1 = gsl_vector_get(reg_param, 0);
+      x1 *= x1;
+      y1 = gsl_vector_get(eta, 0);
+      y1 *= y1;
+
+      x2 = gsl_vector_get(reg_param, 1);
+      x2 *= x2;
+      y2 = gsl_vector_get(eta, 1);
+      y2 *= y2;
+
+      for (i = 1; i < n - 1; ++i)
+        {
+          /*
+           * The points (x1,y1), (x2,y2), (x3,y3) are the previous,
+           * current, and next point on the L-curve. We will find
+           * the circle which fits these 3 points and take its radius
+           * as an estimate of the curvature at this point.
+           */
+          double lamip1 = gsl_vector_get(reg_param, i + 1);
+          double etaip1 = gsl_vector_get(eta, i + 1);
+          double x3 = lamip1 * lamip1;
+          double y3 = etaip1 * etaip1;
+
+          double x21 = x2 - x1;
+          double y21 = y2 - y1;
+          double x31 = x3 - x1;
+          double y31 = y3 - y1;
+          double h21 = x21*x21 + y21*y21;
+          double h31 = x31*x31 + y31*y31;
+          double d = fabs(2.0 * (x21*y31 - x31*y21));
+          double r = sqrt(h21*h31*((x3-x2)*(x3-x2)+(y3-y2)*(y3-y2))) / d;
+
+          /* if d =~ 0 then there are nearly colinear points */
+          if (gsl_finite(r))
+            {
+              /* check for smallest radius of curvature */
+              if (r < rmin || rmin < 0.0)
+                {
+                  rmin = r;
+                  *idx = i;
+                }
+            }
+
+          /* update previous/current L-curve values */
+          x1 = x2;
+          y1 = y2;
+          x2 = x3;
+          y2 = y3;
+        }
+
+      /* check if a minimum radius was found */
+      if (rmin < 0.0)
+        {
+          /* possibly co-linear points */
+          GSL_ERROR("failed to find minimum radius", GSL_EINVAL);
+        }
+
+      return s;
+    }
+} /* gsl_multifit_linear_lcorner2() */
+
+#define GSL_MULTIFIT_MAXK      100
+
+/*
+gsl_multifit_linear_L()
+  Compute discrete approximation to derivative operator of order
+k on a regular grid of p points, ie: L is (p-k)-by-p
+*/
+
+int
+gsl_multifit_linear_Lk(const size_t p, const size_t k, gsl_matrix *L)
+{
+  if (p <= k)
+    {
+      GSL_ERROR("p must be larger than derivative order", GSL_EBADLEN);
+    }
+  else if (k >= GSL_MULTIFIT_MAXK - 1)
+    {
+      GSL_ERROR("derivative order k too large", GSL_EBADLEN);
+    }
+  else if (p - k != L->size1 || p != L->size2)
+    {
+      GSL_ERROR("L matrix must be (p-k)-by-p", GSL_EBADLEN);
+    }
+  else
+    {
+      double c_data[GSL_MULTIFIT_MAXK];
+      gsl_vector_view cv = gsl_vector_view_array(c_data, k + 1);
+      size_t i, j;
+
+      /* zeroth derivative */
+      if (k == 0)
+        {
+          gsl_matrix_set_identity(L);
+          return GSL_SUCCESS;
+        }
+
+      gsl_matrix_set_zero(L);
+  
+      gsl_vector_set_zero(&cv.vector);
+      gsl_vector_set(&cv.vector, 0, -1.0);
+      gsl_vector_set(&cv.vector, 1, 1.0);
+
+      for (i = 1; i < k; ++i)
+        {
+          double cjm1 = 0.0;
+
+          for (j = 0; j < k + 1; ++j)
+            {
+              double cj = gsl_vector_get(&cv.vector, j);
+
+              gsl_vector_set(&cv.vector, j, cjm1 - cj);
+              cjm1 = cj;
+            }
+        }
+
+      /* build L, the c_i are the entries on the diagonals */
+      for (i = 0; i < k + 1; ++i)
+        {
+          gsl_vector_view v = gsl_matrix_superdiagonal(L, i);
+          double ci = gsl_vector_get(&cv.vector, i);
+
+          gsl_vector_set_all(&v.vector, ci);
+        }
+
+      return GSL_SUCCESS;
+    }
+} /* gsl_multifit_linear_Lk() */
+
+/*
+gsl_multifit_linear_Lsobolev()
+  Construct Sobolev smoothing norm operator
+
+L = [ a_0 I; a_1 L_1; a_2 L_2; ...; a_k L_k ]
+
+by computing the Cholesky factor of L^T L
+
+Inputs: p     - number of columns of L
+        kmax  - maximum derivative order (< p)
+        alpha - vector of weights; alpha_k multiplies L_k, size kmax + 1
+        L     - (output) upper triangular Sobolev matrix p-by-p,
+                stored in upper triangle
+        work  - workspace
+
+Notes:
+1) work->Q is used to store intermediate L_k matrices
+*/
+
+int
+gsl_multifit_linear_Lsobolev(const size_t p, const size_t kmax,
+                             const gsl_vector *alpha, gsl_matrix *L,
+                             gsl_multifit_linear_workspace *work)
+{
+  if (p > work->pmax)
+    {
+      GSL_ERROR("p is larger than workspace", GSL_EBADLEN);
+    }
+  else if (p <= kmax)
+    {
+      GSL_ERROR("p must be larger than derivative order", GSL_EBADLEN);
+    }
+  else if (kmax + 1 != alpha->size)
+    {
+      GSL_ERROR("alpha must be size kmax + 1", GSL_EBADLEN);
+    }
+  else if (p != L->size1)
+    {
+      GSL_ERROR("L matrix is wrong size", GSL_EBADLEN);
+    }
+  else if (L->size1 != L->size2)
+    {
+      GSL_ERROR("L matrix is not square", GSL_ENOTSQR);
+    }
+  else
+    {
+      int s;
+      size_t j, k;
+      gsl_vector_view d = gsl_matrix_diagonal(L);
+      const double alpha0 = gsl_vector_get(alpha, 0);
+
+      /* initialize L to alpha0^2 I */
+      gsl_matrix_set_zero(L);
+      gsl_vector_add_constant(&d.vector, alpha0 * alpha0);
+
+      for (k = 1; k <= kmax; ++k)
+        {
+          gsl_matrix_view Lk = gsl_matrix_submatrix(work->Q, 0, 0, p - k, p);
+          double ak = gsl_vector_get(alpha, k);
+
+          /* compute a_k L_k */
+          s = gsl_multifit_linear_Lk(p, k, &Lk.matrix);
+          if (s)
+            return s;
+
+          gsl_matrix_scale(&Lk.matrix, ak);
+
+          /* LTL += L_k^T L_k */
+          gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &Lk.matrix, 1.0, L);
+        }
+
+      s = gsl_linalg_cholesky_decomp(L);
+      if (s)
+        return s;
+
+      /* copy Cholesky factor to upper triangle and zero out bottom */
+      gsl_matrix_transpose_tricpy('L', 1, L, L);
+
+      for (j = 0; j < p; ++j)
+        {
+          for (k = 0; k < j; ++k)
+            gsl_matrix_set(L, j, k, 0.0);
+        }
+
+      return GSL_SUCCESS;
+    }
+}
diff -Nru gsl-doc-1.16/multifit/multirobust.c gsl-doc-2.3/multifit/multirobust.c
--- gsl-doc-1.16/multifit/multirobust.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/multirobust.c	2016-08-19 15:37:27.000000000 +0000
@@ -43,7 +43,7 @@
 
 static int robust_test_convergence(const gsl_vector *c_prev, const gsl_vector *c,
                                    const double tol);
-static double robust_madsigma(const gsl_vector *x, gsl_multifit_robust_workspace *w);
+static double robust_madsigma(const gsl_vector *r, const size_t p, gsl_vector *workn);
 static double robust_robsigma(const gsl_vector *r, const double s,
                               const double tune, gsl_multifit_robust_workspace *w);
 static double robust_sigma(const double s_ols, const double s_rob,
@@ -89,6 +89,7 @@
   w->multifit_p = gsl_multifit_linear_alloc(n, p);
   if (w->multifit_p == 0)
     {
+      gsl_multifit_robust_free(w);
       GSL_ERROR_VAL("failed to allocate space for multifit_linear struct",
                     GSL_ENOMEM, 0);
     }
@@ -96,6 +97,7 @@
   w->r = gsl_vector_alloc(n);
   if (w->r == 0)
     {
+      gsl_multifit_robust_free(w);
       GSL_ERROR_VAL("failed to allocate space for residuals",
                     GSL_ENOMEM, 0);
     }
@@ -103,18 +105,21 @@
   w->weights = gsl_vector_alloc(n);
   if (w->weights == 0)
     {
+      gsl_multifit_robust_free(w);
       GSL_ERROR_VAL("failed to allocate space for weights", GSL_ENOMEM, 0);
     }
 
   w->c_prev = gsl_vector_alloc(p);
   if (w->c_prev == 0)
     {
+      gsl_multifit_robust_free(w);
       GSL_ERROR_VAL("failed to allocate space for c_prev", GSL_ENOMEM, 0);
     }
 
   w->resfac = gsl_vector_alloc(n);
   if (w->resfac == 0)
     {
+      gsl_multifit_robust_free(w);
       GSL_ERROR_VAL("failed to allocate space for residual factors",
                     GSL_ENOMEM, 0);
     }
@@ -122,30 +127,35 @@
   w->psi = gsl_vector_alloc(n);
   if (w->psi == 0)
     {
+      gsl_multifit_robust_free(w);
       GSL_ERROR_VAL("failed to allocate space for psi", GSL_ENOMEM, 0);
     }
 
   w->dpsi = gsl_vector_alloc(n);
   if (w->dpsi == 0)
     {
+      gsl_multifit_robust_free(w);
       GSL_ERROR_VAL("failed to allocate space for dpsi", GSL_ENOMEM, 0);
     }
 
   w->QSI = gsl_matrix_alloc(p, p);
   if (w->QSI == 0)
     {
+      gsl_multifit_robust_free(w);
       GSL_ERROR_VAL("failed to allocate space for QSI", GSL_ENOMEM, 0);
     }
 
   w->D = gsl_vector_alloc(p);
   if (w->D == 0)
     {
+      gsl_multifit_robust_free(w);
       GSL_ERROR_VAL("failed to allocate space for D", GSL_ENOMEM, 0);
     }
 
   w->workn = gsl_vector_alloc(n);
   if (w->workn == 0)
     {
+      gsl_multifit_robust_free(w);
       GSL_ERROR_VAL("failed to allocate space for workn", GSL_ENOMEM, 0);
     }
 
@@ -212,6 +222,21 @@
   return GSL_SUCCESS;
 }
 
+int
+gsl_multifit_robust_maxiter(const size_t maxiter,
+                            gsl_multifit_robust_workspace *w)
+{
+  if (w->maxiter == 0)
+    {
+      GSL_ERROR("maxiter must be greater than 0", GSL_EINVAL);
+    }
+  else
+    {
+      w->maxiter = maxiter;
+      return GSL_SUCCESS;
+    }
+}
+
 const char *
 gsl_multifit_robust_name(const gsl_multifit_robust_workspace *w)
 {
@@ -225,6 +250,49 @@
 }
 
 /*
+gsl_multifit_robust_weights()
+  Compute iterative weights for given residuals
+
+Inputs: r   - residuals
+        wts - (output) where to store weights
+              w_i = r_i / (sigma_mad * tune)
+        w   - workspace
+
+Return: success/error
+
+Notes:
+1) Sizes of r and wts must be equal
+2) Size of r/wts may be less than or equal to w->n, to allow
+for computing weights of a subset of data
+*/
+
+int
+gsl_multifit_robust_weights(const gsl_vector *r, gsl_vector *wts,
+                            gsl_multifit_robust_workspace *w)
+{
+  if (r->size != wts->size)
+    {
+      GSL_ERROR("residual vector does not match weight vector size", GSL_EBADLEN);
+    }
+  else
+    {
+      int s;
+      double sigma;
+
+      sigma = robust_madsigma(r, w->p, wts);
+
+      /* scale residuals by sigma and tuning factor */
+      gsl_vector_memcpy(wts, r);
+      gsl_vector_scale(wts, 1.0 / (sigma * w->tune));
+
+      /* compute weights in-place */
+      s = w->type->wfun(wts, wts);
+
+      return s;
+    }
+} /* gsl_multifit_robust_weights() */
+
+/*
 gsl_multifit_robust()
   Perform robust iteratively reweighted linear least squares
 fit
@@ -336,7 +404,7 @@
             return s;
 
           /* compute estimate of standard deviation using MAD */
-          sig = robust_madsigma(w->r, w);
+          sig = robust_madsigma(w->r, w->p, w->workn);
 
           /* scale residuals by standard deviation and tuning parameter */
           gsl_vector_scale(w->r, 1.0 / (GSL_MAX(sig, sig_lower) * w->tune));
@@ -362,7 +430,7 @@
         }
 
       /* compute final MAD sigma */
-      w->stats.sigma_mad = robust_madsigma(w->r, w);
+      w->stats.sigma_mad = robust_madsigma(w->r, w->p, w->workn);
 
       /* compute robust estimate of sigma */
       w->stats.sigma_rob = robust_robsigma(w->r, w->stats.sigma_mad, w->tune, w);
@@ -383,7 +451,7 @@
         w->stats.Rsq = 1.0 - ss_err / ss_tot;
 
         /* compute adjusted R^2 */
-        w->stats.adj_Rsq = 1.0 - (1.0 - w->stats.Rsq) * (n - 1.0) / dof;
+        w->stats.adj_Rsq = 1.0 - (1.0 - w->stats.Rsq) * ((double)n - 1.0) / dof;
 
         /* compute rmse */
         w->stats.rmse = sqrt(ss_err / dof);
@@ -417,6 +485,68 @@
   return s;
 }
 
+/*
+gsl_multifit_robust_residuals()
+  Compute robust / studentized residuals from fit
+
+r_i = (y_i - Y_i) / (sigma * sqrt(1 - h_i))
+
+Inputs: X - design matrix
+        y - rhs vector
+        c - fit coefficients
+        r - (output) studentized residuals
+        w - workspace
+
+Notes:
+1) gsl_multifit_robust() must first be called to compute the coefficients
+c, the leverage factors in w->resfac, and sigma in w->stats.sigma
+*/
+
+int
+gsl_multifit_robust_residuals(const gsl_matrix * X, const gsl_vector * y,
+                              const gsl_vector * c, gsl_vector * r,
+                              gsl_multifit_robust_workspace * w)
+{
+  if (X->size1 != y->size)
+    {
+      GSL_ERROR
+        ("number of observations in y does not match rows of matrix X",
+         GSL_EBADLEN);
+    }
+  else if (X->size2 != c->size)
+    {
+      GSL_ERROR ("number of parameters c does not match columns of matrix X",
+                 GSL_EBADLEN);
+    }
+  else if (y->size != r->size)
+    {
+      GSL_ERROR ("number of observations in y does not match number of residuals",
+                 GSL_EBADLEN);
+    }
+  else
+    {
+      const double sigma = w->stats.sigma; /* previously calculated sigma */
+      int s;
+      size_t i;
+
+      /* compute r = y - X c */
+      s = gsl_multifit_linear_residuals(X, y, c, r);
+      if (s)
+        return s;
+
+      for (i = 0; i < r->size; ++i)
+        {
+          double hfac = gsl_vector_get(w->resfac, i); /* 1/sqrt(1 - h_i) */
+          double *ri = gsl_vector_ptr(r, i);
+
+          /* multiply residual by 1 / (sigma * sqrt(1 - h_i)) */
+          *ri *= hfac / sigma;
+        }
+
+      return s;
+    }
+} /* gsl_multifit_robust_residuals() */
+
 /***********************************
  * INTERNAL ROUTINES               *
  ***********************************/
@@ -466,33 +596,37 @@
 
 See: Street et al, 1988
 
-Inputs: r - vector of residuals
-        w - workspace
+Inputs: r     - vector of residuals
+        p     - number of model coefficients (smallest p residuals are
+                ignored)
+        workn - workspace of size n = length(r)
 */
 
 static double
-robust_madsigma(const gsl_vector *r, gsl_multifit_robust_workspace *w)
+robust_madsigma(const gsl_vector *r, const size_t p, gsl_vector *workn)
 {
-  gsl_vector_view v;
-  double sigma;
   size_t n = r->size;
-  const size_t p = w->p;
+  double sigma;
   size_t i;
 
+  /* allow for the possibility that r->size < w->n */
+  gsl_vector_view v1 = gsl_vector_subvector(workn, 0, n);
+  gsl_vector_view v2;
+
   /* copy |r| into workn */
   for (i = 0; i < n; ++i)
     {
-      gsl_vector_set(w->workn, i, fabs(gsl_vector_get(r, i)));
+      gsl_vector_set(&v1.vector, i, fabs(gsl_vector_get(r, i)));
     }
 
-  gsl_sort_vector(w->workn);
+  gsl_sort_vector(&v1.vector);
 
   /*
    * ignore the smallest p residuals when computing the median
    * (see Street et al 1988)
    */
-  v = gsl_vector_subvector(w->workn, p - 1, n - p + 1);
-  sigma = gsl_stats_median_from_sorted_data(v.vector.data, v.vector.stride, v.vector.size) / 0.6745;
+  v2 = gsl_vector_subvector(&v1.vector, p - 1, n - p + 1);
+  sigma = gsl_stats_median_from_sorted_data(v2.vector.data, v2.vector.stride, v2.vector.size) / 0.6745;
 
   return sigma;
 } /* robust_madsigma() */
@@ -576,8 +710,8 @@
              gsl_multifit_robust_workspace *w)
 {
   double sigma;
-  const size_t p = w->p;
-  const size_t n = w->n;
+  const double p = (double) w->p;
+  const double n = (double) w->n;
 
   /* see DuMouchel and O'Brien, sec 4.1 */
   sigma = GSL_MAX(s_rob,
@@ -602,7 +736,7 @@
 robust_covariance(const double sigma, gsl_matrix *cov,
                   gsl_multifit_robust_workspace *w)
 {
-  int s = 0;
+  int status = 0;
   const size_t p = w->p;
   const double s2 = sigma * sigma;
   size_t i, j;
@@ -629,5 +763,5 @@
         }
     }
 
-  return s;
+  return status;
 } /* robust_covariance() */
diff -Nru gsl-doc-1.16/multifit/multiwlinear.c gsl-doc-2.3/multifit/multiwlinear.c
--- gsl-doc-1.16/multifit/multiwlinear.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/multiwlinear.c	2016-11-18 19:09:31.000000000 +0000
@@ -0,0 +1,346 @@
+/* multifit/multiwlinear.c
+ * 
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_multifit.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+
+#include "linear_common.c"
+
+/* General weighted case */ 
+
+static int
+multifit_wlinear_svd (const gsl_matrix * X,
+                      const gsl_vector * w,
+                      const gsl_vector * y,
+                      double tol,
+                      int balance,
+                      size_t * rank,
+                      gsl_vector * c,
+                      gsl_matrix * cov,
+                      double *chisq, gsl_multifit_linear_workspace * work)
+{
+  if (X->size1 != y->size)
+    {
+      GSL_ERROR
+        ("number of observations in y does not match rows of matrix X",
+         GSL_EBADLEN);
+    }
+  else if (X->size2 != c->size)
+    {
+      GSL_ERROR ("number of parameters c does not match columns of matrix X",
+                 GSL_EBADLEN);
+    }
+  else if (w->size != y->size)
+    {
+      GSL_ERROR ("number of weights does not match number of observations",
+                 GSL_EBADLEN);
+    }
+  else if (cov->size1 != cov->size2)
+    {
+      GSL_ERROR ("covariance matrix is not square", GSL_ENOTSQR);
+    }
+  else if (c->size != cov->size1)
+    {
+      GSL_ERROR
+        ("number of parameters does not match size of covariance matrix",
+         GSL_EBADLEN);
+    }
+  else if (X->size1 != work->n || X->size2 != work->p)
+    {
+      GSL_ERROR
+        ("size of workspace does not match size of observation matrix",
+         GSL_EBADLEN);
+    }
+  else
+    {
+      const size_t n = X->size1;
+      const size_t p = X->size2;
+
+      size_t i, j, p_eff;
+
+      gsl_matrix *A = work->A;
+      gsl_matrix *Q = work->Q;
+      gsl_matrix *QSI = work->QSI;
+      gsl_vector *S = work->S;
+      gsl_vector *t = work->t;
+      gsl_vector *xt = work->xt;
+      gsl_vector *D = work->D;
+
+      /* Scale X,  A = sqrt(w) X */
+
+      gsl_matrix_memcpy (A, X);
+
+      for (i = 0; i < n; i++)
+        {
+          double wi = gsl_vector_get (w, i);
+
+          if (wi < 0)
+            wi = 0;
+
+          {
+            gsl_vector_view row = gsl_matrix_row (A, i);
+            gsl_vector_scale (&row.vector, sqrt (wi));
+          }
+        }
+
+      /* Balance the columns of the matrix A if requested */
+
+      if (balance) 
+        {
+          gsl_linalg_balance_columns (A, D);
+        }
+      else
+        {
+          gsl_vector_set_all (D, 1.0);
+        }
+
+      /* Decompose A into U S Q^T */
+
+      gsl_linalg_SV_decomp_mod (A, QSI, Q, S, xt);
+
+      /* Solve sqrt(w) y = A c for c, by first computing t = sqrt(w) y */
+
+      for (i = 0; i < n; i++)
+        {
+          double wi = gsl_vector_get (w, i);
+          double yi = gsl_vector_get (y, i);
+          if (wi < 0)
+            wi = 0;
+          gsl_vector_set (t, i, sqrt (wi) * yi);
+        }
+
+      gsl_blas_dgemv (CblasTrans, 1.0, A, t, 0.0, xt);
+
+      /* Scale the matrix Q,  Q' = Q S^-1 */
+
+      gsl_matrix_memcpy (QSI, Q);
+
+      {
+        double s0 = gsl_vector_get (S, 0);
+        p_eff = 0;
+        
+        for (j = 0; j < p; j++)
+          {
+            gsl_vector_view column = gsl_matrix_column (QSI, j);
+            double sj = gsl_vector_get (S, j);
+            double alpha;
+
+            if (sj <= tol * s0)
+              {
+                alpha = 0.0;
+              }
+            else
+              {
+                alpha = 1.0 / sj;
+                p_eff++;
+              }
+
+            gsl_vector_scale (&column.vector, alpha);
+          }
+
+        *rank = p_eff;
+      }
+
+      gsl_vector_set_zero (c);
+
+      /* solution */
+      gsl_blas_dgemv (CblasNoTrans, 1.0, QSI, xt, 0.0, c);
+
+      /* unscale the balancing factors */
+      gsl_vector_div (c, D);
+
+      /* compute chisq, from residual r = y - X c */
+      {
+        double r2 = 0;
+
+        for (i = 0; i < n; i++)
+          {
+            double yi = gsl_vector_get (y, i);
+            double wi = gsl_vector_get (w, i);
+            gsl_vector_const_view row = gsl_matrix_const_row (X, i);
+            double y_est, ri;
+            gsl_blas_ddot (&row.vector, c, &y_est);
+            ri = yi - y_est;
+            r2 += wi * ri * ri;
+          }
+
+        *chisq = r2;
+
+        /* Form covariance matrix cov = (X^T W X)^-1 = (Q S^-1) (Q S^-1)^T */
+
+        for (i = 0; i < p; i++)
+          {
+            gsl_vector_view row_i = gsl_matrix_row (QSI, i);
+            double d_i = gsl_vector_get (D, i);
+
+            for (j = i; j < p; j++)
+              {
+                gsl_vector_view row_j = gsl_matrix_row (QSI, j);
+                double d_j = gsl_vector_get (D, j);
+                double s;
+
+                gsl_blas_ddot (&row_i.vector, &row_j.vector, &s);
+
+                gsl_matrix_set (cov, i, j, s / (d_i * d_j));
+                gsl_matrix_set (cov, j, i, s / (d_i * d_j));
+              }
+          }
+      }
+
+      return GSL_SUCCESS;
+    }
+}
+
+int
+gsl_multifit_wlinear (const gsl_matrix * X,
+                      const gsl_vector * w,
+                      const gsl_vector * y,
+                      gsl_vector * c,
+                      gsl_matrix * cov,
+                      double *chisq, gsl_multifit_linear_workspace * work)
+{
+  size_t rank;
+  int status = gsl_multifit_wlinear_tsvd(X, w, y, GSL_DBL_EPSILON, c, cov, chisq, &rank, work);
+
+  return status;
+}
+
+int
+gsl_multifit_wlinear_tsvd (const gsl_matrix * X,
+                           const gsl_vector * w,
+                           const gsl_vector * y,
+                           const double tol,
+                           gsl_vector * c,
+                           gsl_matrix * cov,
+                           double * chisq,
+                           size_t * rank,
+                           gsl_multifit_linear_workspace * work)
+{
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+
+  if (y->size != n)
+    {
+      GSL_ERROR("number of observations in y does not match matrix",
+                GSL_EBADLEN);
+    }
+  else if (w->size != n)
+    {
+      GSL_ERROR("number of weights in w does not match matrix",
+                GSL_EBADLEN);
+    }
+  else if (p != c->size)
+    {
+      GSL_ERROR ("number of parameters c does not match matrix",
+                 GSL_EBADLEN);
+    }
+  else if (tol <= 0)
+    {
+      GSL_ERROR ("tolerance must be positive", GSL_EINVAL);
+    }
+  else
+    {
+      int status;
+      double rnorm, snorm;
+      gsl_matrix_view A = gsl_matrix_submatrix(work->A, 0, 0, n, p);
+      gsl_vector_view b = gsl_vector_subvector(work->t, 0, n);
+
+      /* compute A = sqrt(W) X, b = sqrt(W) y */
+      status = gsl_multifit_linear_applyW(X, w, y, &A.matrix, &b.vector);
+      if (status)
+        return status;
+
+      /* compute SVD of A */
+      status = gsl_multifit_linear_bsvd(&A.matrix, work);
+      if (status)
+        return status;
+
+      status = multifit_linear_solve(X, &b.vector, tol, 0.0, rank,
+                                     c, &rnorm, &snorm, work);
+      if (status)
+        return status;
+
+      *chisq = rnorm * rnorm;
+
+      /* variance-covariance matrix cov = s2 * (Q S^-1) (Q S^-1)^T */
+      {
+        const size_t p = X->size2;
+        size_t i, j;
+        gsl_matrix_view QSI = gsl_matrix_submatrix(work->QSI, 0, 0, p, p);
+        gsl_vector_view D = gsl_vector_subvector(work->D, 0, p);
+
+        for (i = 0; i < p; i++)
+          {
+            gsl_vector_view row_i = gsl_matrix_row (&QSI.matrix, i);
+            double d_i = gsl_vector_get (&D.vector, i);
+
+            for (j = i; j < p; j++)
+              {
+                gsl_vector_view row_j = gsl_matrix_row (&QSI.matrix, j);
+                double d_j = gsl_vector_get (&D.vector, j);
+                double s;
+
+                gsl_blas_ddot (&row_i.vector, &row_j.vector, &s);
+
+                gsl_matrix_set (cov, i, j, s / (d_i * d_j));
+                gsl_matrix_set (cov, j, i, s / (d_i * d_j));
+              }
+          }
+      }
+    }
+
+  return GSL_SUCCESS;
+}
+
+int
+gsl_multifit_wlinear_svd (const gsl_matrix * X,
+                          const gsl_vector * w,
+                          const gsl_vector * y,
+                          double tol,
+                          size_t * rank,
+                          gsl_vector * c,
+                          gsl_matrix * cov,
+                          double *chisq, gsl_multifit_linear_workspace * work)
+{
+  int status  = multifit_wlinear_svd (X, w, y, tol, 1, rank, c,
+                                      cov, chisq, work);
+  return status;
+
+}
+
+int
+gsl_multifit_wlinear_usvd (const gsl_matrix * X,
+                           const gsl_vector * w,
+                           const gsl_vector * y,
+                           double tol,
+                           size_t * rank,
+                           gsl_vector * c,
+                           gsl_matrix * cov,
+                           double *chisq, gsl_multifit_linear_workspace * work)
+{
+  int status  = multifit_wlinear_svd (X, w, y, tol, 0, rank, c,
+                                      cov, chisq, work);
+  return status;
+
+}
diff -Nru gsl-doc-1.16/multifit/robust_wfun.c gsl-doc-2.3/multifit/robust_wfun.c
--- gsl-doc-1.16/multifit/robust_wfun.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/robust_wfun.c	2015-11-03 16:21:55.000000000 +0000
@@ -30,6 +30,12 @@
 #define TUNING_OLS            (1.0)
 #define TUNING_WELSCH         (2.985)
 
+/*
+ * Note: for each of the weighting functions below, it
+ * is safe to call them with in-place parameters, so that
+ * input/output vectors are the same
+ */
+
 static int
 bisquare(const gsl_vector *r, gsl_vector *w)
 {
diff -Nru gsl-doc-1.16/multifit/test_bard.c gsl-doc-2.3/multifit/test_bard.c
--- gsl-doc-1.16/multifit/test_bard.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_bard.c	2016-11-30 21:30:22.000000000 +0000
@@ -0,0 +1,121 @@
+#define bard_N         15
+#define bard_P         3
+
+#define bard_NTRIES    3
+
+static double bard_x0[bard_P] = { 1.0, 1.0, 1.0 };
+
+static double bard_epsrel = 1.0e-8;
+
+static double bard_Y[bard_N] = {
+0.14, 0.18, 0.22, 0.25, 0.29, 0.32, 0.35, 0.39, 0.37,
+0.58, 0.73, 0.96, 1.34, 2.10, 4.39
+};
+
+static void
+bard_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact1 = 8.214877306578963e-03;
+  const double bard_x1[bard_P] = { 8.241055975623580e-02,
+                                   1.133036092245175,
+                                   2.343695178435405 };
+  const double sumsq_exact2 = 17.42869333333333;
+  const double bard_x2[bard_P] = {  8.406666666666666e-01,
+                                   -99999.9,    /* -inf */
+                                   -99999.9 };  /* -inf */
+  const double *bard_x;
+  double sumsq_exact;
+
+  if (fabs(x[1]) < 10.0 && fabs(x[2]) < 10.0)
+    {
+      bard_x = bard_x1;
+      sumsq_exact = sumsq_exact1;
+    }
+  else
+    {
+      bard_x = bard_x2;
+      sumsq_exact = sumsq_exact2;
+    }
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < bard_P; ++i)
+    {
+      if (bard_x[i] < -90000.0)
+        continue;
+
+      gsl_test_rel(x[i], bard_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+bard_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < bard_N; ++i)
+    {
+      double ui = i + 1.0;
+      double vi = 16.0 - i - 1.0;
+      double wi = GSL_MIN(ui, vi);
+      double yi = bard_Y[i];
+      double fi = yi - (x1 + (ui / (x2*vi + x3*wi)));
+
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+bard_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < bard_N; ++i)
+    {
+      double ui = i + 1.0;
+      double vi = 16.0 - i - 1.0;
+      double wi = GSL_MIN(ui, vi);
+      double term = x2 * vi + x3 * wi;
+
+      gsl_matrix_set(J, i, 0, -1.0);
+      gsl_matrix_set(J, i, 1, ui * vi / (term * term));
+      gsl_matrix_set(J, i, 2, ui * wi / (term * term));
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf bard_func =
+{
+  &bard_f,
+  &bard_df,
+  NULL,
+  bard_N,
+  bard_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem bard_problem =
+{
+  "bard",
+  bard_x0,
+  NULL,
+  &bard_epsrel,
+  bard_NTRIES,
+  &bard_checksol,
+  &bard_func
+};
diff -Nru gsl-doc-1.16/multifit/test_beale.c gsl-doc-2.3/multifit/test_beale.c
--- gsl-doc-1.16/multifit/test_beale.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_beale.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,87 @@
+#define beale_N         3
+#define beale_P         2
+
+#define beale_NTRIES    1
+
+static double beale_x0[beale_P] = { 1.0, 1.0 };
+static double beale_epsrel = 1.0e-12;
+
+static double beale_Y[beale_N] = { 1.5, 2.25, 2.625 };
+
+static void
+beale_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double beale_x[beale_P] = { 3.0, 0.5 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < beale_P; ++i)
+    {
+      gsl_test_rel(x[i], beale_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+beale_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < beale_N; ++i)
+    {
+      double yi = beale_Y[i];
+      double term = pow(x2, i + 1.0);
+      double fi = yi - x1*(1.0 - term);
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+beale_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < beale_N; ++i)
+    {
+      double term = pow(x2, (double) i);
+
+      gsl_matrix_set(J, i, 0, term*x2 - 1.0);
+      gsl_matrix_set(J, i, 1, (i + 1.0) * x1 * term);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf beale_func =
+{
+  &beale_f,
+  &beale_df,
+  NULL,
+  beale_N,
+  beale_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem beale_problem =
+{
+  "beale",
+  beale_x0,
+  NULL,
+  &beale_epsrel,
+  beale_NTRIES,
+  &beale_checksol,
+  &beale_func
+};
diff -Nru gsl-doc-1.16/multifit/test_biggs.c gsl-doc-2.3/multifit/test_biggs.c
--- gsl-doc-1.16/multifit/test_biggs.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_biggs.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,101 @@
+#define biggs_N         6  /* >= p */
+#define biggs_P         6
+
+#define biggs_NTRIES    2
+
+static double biggs_x0[biggs_P] = { 1.0, 2.0, 1.0, 1.0, 1.0, 1.0 };
+static double biggs_epsrel = 1.0e-9;
+
+static void
+biggs_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  const double sumsq_exact = 0.0;
+  const double biggs_x[biggs_P] = { 1.0, 10.0, 1.0, 5.0, 4.0, 3.0 };
+  const double norm_exact = 12.3288280059380;
+  gsl_vector_const_view v = gsl_vector_const_view_array(biggs_x, biggs_P);
+  double norm = gsl_blas_dnrm2(&v.vector);
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  /*
+   * the solution vector is not unique due to permutations, so test
+   * the norm instead of individual elements
+   */
+  gsl_test_rel(norm, norm_exact, epsrel, "%s/%s norm",
+               sname, pname);
+}
+
+static int
+biggs_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  double x6 = gsl_vector_get(x, 5);
+  size_t i;
+
+  for (i = 0; i < biggs_N; ++i)
+    {
+      double ti = 0.1 * (i + 1.0);
+      double yi = exp(-ti) - 5*exp(-10*ti) + 3*exp(-4*ti);
+      double fi = x3*exp(-ti*x1) - x4*exp(-ti*x2) + x6*exp(-ti*x5) - yi;
+
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+biggs_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  double x6 = gsl_vector_get(x, 5);
+  size_t i;
+
+  for (i = 0; i < biggs_N; ++i)
+    {
+      double ti = 0.1 * (i + 1.0);
+
+      gsl_matrix_set(J, i, 0, -ti*x3*exp(-ti*x1));
+      gsl_matrix_set(J, i, 1, ti*x4*exp(-ti*x2));
+      gsl_matrix_set(J, i, 2, exp(-ti*x1));
+      gsl_matrix_set(J, i, 3, -exp(-ti*x2));
+      gsl_matrix_set(J, i, 4, -ti*x6*exp(-ti*x5));
+      gsl_matrix_set(J, i, 5, exp(-ti*x5));
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf biggs_func =
+{
+  &biggs_f,
+  &biggs_df,
+  NULL,
+  biggs_N,
+  biggs_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem biggs_problem =
+{
+  "biggs",
+  biggs_x0,
+  NULL,
+  &biggs_epsrel,
+  biggs_NTRIES,
+  &biggs_checksol,
+  &biggs_func
+};
diff -Nru gsl-doc-1.16/multifit/test_boxbod.c gsl-doc-2.3/multifit/test_boxbod.c
--- gsl-doc-1.16/multifit/test_boxbod.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_boxbod.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,106 @@
+#define boxbod_N       6
+#define boxbod_P       2
+
+#define boxbod_NTRIES  1
+
+static double boxbod_x0[boxbod_P] = { 100.0, 0.75 };
+static double boxbod_epsrel = 1.0e-7;
+
+static double boxbod_sigma[boxbod_P] = {
+  1.2354515176E+01, 1.0455993237E-01
+};
+
+static double boxbod_X[boxbod_N] = { 1.0, 2.0, 3.0, 5.0, 7.0, 10.0 };
+
+static double boxbod_F[boxbod_N] = { 109.0, 149.0, 149.0, 191.0,
+                                     213.0, 224.0 };
+
+static void
+boxbod_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.1680088766E+03;
+  const double boxbod_x[boxbod_P] = { 2.1380940889E+02,
+                                      5.4723748542E-01 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < boxbod_P; ++i)
+    {
+      gsl_test_rel(x[i], boxbod_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+boxbod_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[boxbod_P];
+  size_t i;
+
+  for (i = 0; i < boxbod_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < boxbod_N; i++)
+    {
+      double xi = boxbod_X[i];
+      double yi;
+
+      yi = b[0] * (1.0 - exp(-b[1] * xi));
+      gsl_vector_set (f, i, yi - boxbod_F[i]);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+boxbod_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[boxbod_P];
+  size_t i;
+
+  for (i = 0; i < boxbod_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < boxbod_N; i++)
+    {
+      double xi = boxbod_X[i];
+      double term = exp(-b[1] * xi);
+
+      gsl_matrix_set (df, i, 0, 1.0 - term);
+      gsl_matrix_set (df, i, 1, b[0] * term * xi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf boxbod_func =
+{
+  &boxbod_f,
+  &boxbod_df,
+  NULL,
+  boxbod_N,
+  boxbod_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem boxbod_problem =
+{
+  "nist-boxbod",
+  boxbod_x0,
+  boxbod_sigma,
+  &boxbod_epsrel,
+  boxbod_NTRIES,
+  &boxbod_checksol,
+  &boxbod_func
+};
diff -Nru gsl-doc-1.16/multifit/test_box.c gsl-doc-2.3/multifit/test_box.c
--- gsl-doc-1.16/multifit/test_box.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_box.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,89 @@
+#define box_N         10 /* can be >= p */
+#define box_P         3
+
+#define box_NTRIES    1
+
+static double box_x0[box_P] = { 0.0, 10.0, 20.0 };
+static double box_epsrel = 1.0e-12;
+
+static void
+box_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double box_x[box_P] = { 1.0, 10.0, 1.0 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < box_P; ++i)
+    {
+      gsl_test_rel(x[i], box_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+box_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < box_N; ++i)
+    {
+      double ti = (i + 1.0) / 10.0;
+      double fi = exp(-x1*ti) - exp(-x2*ti) - x3*(exp(-ti) - exp(-10.0*ti));
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+box_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < box_N; ++i)
+    {
+      double ti = (i + 1.0) / 10.0;
+      double term1 = exp(-x1*ti);
+      double term2 = exp(-x2*ti);
+      double term3 = exp(-10.0*ti) - exp(-ti);
+
+      gsl_matrix_set(J, i, 0, -ti*term1);
+      gsl_matrix_set(J, i, 1, ti*term2);
+      gsl_matrix_set(J, i, 2, term3);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf box_func =
+{
+  &box_f,
+  &box_df,
+  NULL,
+  box_N,
+  box_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem box_problem =
+{
+  "box3d",
+  box_x0,
+  NULL,
+  &box_epsrel,
+  box_NTRIES,
+  &box_checksol,
+  &box_func
+};
diff -Nru gsl-doc-1.16/multifit/test_brown1.c gsl-doc-2.3/multifit/test_brown1.c
--- gsl-doc-1.16/multifit/test_brown1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_brown1.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,96 @@
+#define brown1_N         20
+#define brown1_P         4
+
+#define brown1_NTRIES    3
+
+static double brown1_x0[brown1_P] = { 25, 5, -5, -1 };
+static double brown1_epsrel = 1.0e-6;
+
+static void
+brown1_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.582220162635628e+04;
+  const double brown1_x[brown1_P] = {
+    -1.159443990239263e+01, 1.320363005221244e+01,
+    -4.034395456782477e-01, 2.367789088597534e-01 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < brown1_P; ++i)
+    {
+      gsl_test_rel(x[i], brown1_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+brown1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x0 = gsl_vector_get (x, 0);
+  double x1 = gsl_vector_get (x, 1);
+  double x2 = gsl_vector_get (x, 2);
+  double x3 = gsl_vector_get (x, 3);
+  size_t i;
+
+  for (i = 0; i < brown1_N; i++)
+    {
+      double ti = 0.2 * (i + 1);
+      double ui = x0 + x1 * ti - exp (ti);
+      double vi = x2 + x3 * sin (ti) - cos (ti);
+
+      gsl_vector_set (f, i, ui * ui + vi * vi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown1_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double x0 = gsl_vector_get (x, 0);
+  double x1 = gsl_vector_get (x, 1);
+  double x2 = gsl_vector_get (x, 2);
+  double x3 = gsl_vector_get (x, 3);
+  size_t i;
+
+  for (i = 0; i < brown1_N; i++)
+    {
+      double ti = 0.2 * (i + 1);
+      double ui = x0 + x1 * ti - exp (ti);
+      double vi = x2 + x3 * sin (ti) - cos (ti);
+
+      gsl_matrix_set (df, i, 0, 2 * ui);
+      gsl_matrix_set (df, i, 1, 2 * ui * ti);
+      gsl_matrix_set (df, i, 2, 2 * vi);
+      gsl_matrix_set (df, i, 3, 2 * vi * sin (ti));
+
+    }
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf brown1_func =
+{
+  &brown1_f,
+  &brown1_df,
+  NULL,
+  brown1_N,
+  brown1_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem brown1_problem =
+{
+  "brown_dennis",
+  brown1_x0,
+  NULL,
+  &brown1_epsrel,
+  brown1_NTRIES,
+  &brown1_checksol,
+  &brown1_func
+};
diff -Nru gsl-doc-1.16/multifit/test_brown2.c gsl-doc-2.3/multifit/test_brown2.c
--- gsl-doc-1.16/multifit/test_brown2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_brown2.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,128 @@
+#define brown2_N        5
+#define brown2_P        5
+
+#define brown2_NTRIES   3
+
+static double brown2_x0[brown2_P] = { 0.5, 0.5, 0.5, 0.5, 0.5 };
+static double brown2_epsrel = 1.0e-12;
+
+static void
+brown2_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  double sumsq_exact;
+  double alpha;
+  const double p = (double) brown2_P;
+  double alpha1mp, lhs, lastel;
+
+  if (sumsq < 0.5)
+    {
+      /* sumsq = 0 case */
+
+      sumsq_exact = 0.0;
+      alpha = x[0];
+      alpha1mp = pow(alpha, 1.0 - p);
+      lhs = p*pow(alpha, p) - (p + 1)/alpha1mp;
+      lastel = alpha1mp;
+
+      gsl_test_rel(lhs, -1.0, epsrel, "%s/%s alpha lhs",
+                   sname, pname);
+    }
+  else
+    {
+      /* sumsq = 1 case */
+
+      sumsq_exact = 1.0;
+      alpha = 0.0;
+      lastel = p + 1.0;
+    }
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 1; i < brown2_P - 1; ++i)
+    {
+      gsl_test_rel(x[i], alpha, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+
+  gsl_test_rel(x[brown2_P - 1], lastel, epsrel, "%s/%s last element",
+               sname, pname);
+}
+
+static int
+brown2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i;
+  double sum = -(brown2_N + 1.0);
+  double prod = 1.0;
+
+  for (i = 0; i < brown2_N; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      sum += xi;
+      prod *= xi;
+    }
+
+  for (i = 0; i < brown2_N - 1; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      gsl_vector_set(f, i, xi + sum);
+    }
+
+  gsl_vector_set(f, brown2_N - 1, prod - 1.0);
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown2_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  size_t i, j;
+
+  for (j = 0; j < brown2_P; ++j)
+    {
+      double prod = 1.0;
+
+      for (i = 0; i < brown2_N - 1; i++)
+        {
+          double Jij = (i == j) ? 2.0 : 1.0;
+          gsl_matrix_set(J, i, j, Jij);
+        }
+
+      for (i = 0; i < brown2_N; i++)
+        {
+          if (i != j)
+            prod *= gsl_vector_get(x, i);
+        }
+
+      gsl_matrix_set(J, brown2_N - 1, j, prod);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf brown2_func =
+{
+  &brown2_f,
+  &brown2_df,
+  NULL,
+  brown2_N,
+  brown2_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem brown2_problem =
+{
+  "brown_almost_linear",
+  brown2_x0,
+  NULL,
+  &brown2_epsrel,
+  brown2_NTRIES,
+  &brown2_checksol,
+  &brown2_func
+};
diff -Nru gsl-doc-1.16/multifit/test_brown3.c gsl-doc-2.3/multifit/test_brown3.c
--- gsl-doc-1.16/multifit/test_brown3.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_brown3.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,78 @@
+#define brown3_N         3
+#define brown3_P         2
+
+#define brown3_NTRIES    3
+
+static double brown3_x0[brown3_P] = { 1.0, 1.0 };
+static double brown3_epsrel = 1.0e-12;
+
+static void
+brown3_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double brown3_x[brown3_P] = { 1.0e6, 2.0e-6 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < brown3_P; ++i)
+    {
+      gsl_test_rel(x[i], brown3_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+brown3_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, x1 - 1.0e6);
+  gsl_vector_set(f, 1, x2 - 2.0e-6);
+  gsl_vector_set(f, 2, x1*x2 - 2.0);
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown3_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_matrix_set_zero(J);
+
+  gsl_matrix_set(J, 0, 0, 1.0);
+  gsl_matrix_set(J, 1, 1, 1.0);
+  gsl_matrix_set(J, 2, 0, x2);
+  gsl_matrix_set(J, 2, 1, x1);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf brown3_func =
+{
+  &brown3_f,
+  &brown3_df,
+  NULL,
+  brown3_N,
+  brown3_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem brown3_problem =
+{
+  "brown_badly_scaled",
+  brown3_x0,
+  NULL,
+  &brown3_epsrel,
+  brown3_NTRIES,
+  &brown3_checksol,
+  &brown3_func
+};
diff -Nru gsl-doc-1.16/multifit/test_brown.c gsl-doc-2.3/multifit/test_brown.c
--- gsl-doc-1.16/multifit/test_brown.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/test_brown.c	1970-01-01 00:00:00.000000000 +0000
@@ -1,113 +0,0 @@
-const size_t brown_N = 20;
-const size_t brown_P = 4;
-
-double brown_X[20][4] = {
-  {24.3485677, 4.71448798, -2.19486633, 2.69405755},
-  {22.4116222, 3.93075538, -1.42344852, 2.5233557},
-  {17.88886, 2.9290853, .125174936, -3.96823353},
-  {17.3237176, 2.99606803, 2.03285653, 2.28992327},
-  {17.0906508, 3.02485425, .296995153, .0876226126},
-  {16.578006, 3.1036312, -.18617941, .103262914},
-  {15.692993, 3.33088442, .0706406887, 1.05923955},
-  {14.3232177, 3.85604218, -2.3762839, -3.09486813},
-  {14.1279266, 3.97896121, .446109351, 1.40023753},
-  {13.6081961, 4.16435075, -1.51250057, -1.52510626},
-  {13.4295245, 4.22697223, -.196985195, .532009293},
-  {13.0176117, 4.3579261, -.353131208, .301377627},
-  {12.2713535, 4.62398535, -.00183585584, .894170703},
-  {11.0316144, 5.13967727, -2.38978772, -2.89510064},
-  {10.8807981, 5.24558004, .230495952, 1.27315117},
-  {10.4029264, 5.41141257, -1.5116632, -1.47615921},
-  {10.2574435, 5.46211045, -.299855732, .451893162},
-  {9.87863876, 5.57914292, -.368885288, .358086545},
-  {9.1894983, 5.82082741, -.230157969, .621476534},
-  {8.00589008, 6.27788753, -1.46022815, -1.33468082}
-};
-
-double brown_F[20] = {
-  2474.05541,
-  1924.69004,
-  1280.63194,
-  1244.81867,
-  1190.53739,
-  1159.34935,
-  1108.44426,
-  1090.11073,
-  1015.92942,
-  1002.43533,
-  971.221084,
-  949.589435,
-  911.359899,
-  906.522994,
-  840.525729,
-  833.950164,
-  807.557511,
-  791.00924,
-  761.09598,
-  726.787783,
-};
-
-double brown_cov[4][4] = {
-  { 1.8893186910e-01, -4.7099989571e-02,  5.2154168404e-01,  1.6608168209e-02},
-  {-4.7099989571e-02,  1.1761534388e-02, -1.2987843074e-01, -4.1615942391e-03},
-  { 5.2154168404e-01, -1.2987843074e-01,  1.4653936514e+00,  1.5738321686e-02},
-  { 1.6608168209e-02, -4.1615942391e-03,  1.5738321686e-02,  4.2348042340e-02},
-};
-
-double brown_x0[4] = { 25, 5, -5, -1 };
-
-int
-brown_f (const gsl_vector * x, void *params, gsl_vector * f)
-{
-  double x0 = gsl_vector_get (x, 0);
-  double x1 = gsl_vector_get (x, 1);
-  double x2 = gsl_vector_get (x, 2);
-  double x3 = gsl_vector_get (x, 3);
-  size_t i;
-
-  for (i = 0; i < 20; i++)
-    {
-      double ti = 0.2 * (i + 1);
-      double ui = x0 + x1 * ti - exp (ti);
-      double vi = x2 + x3 * sin (ti) - cos (ti);
-
-      gsl_vector_set (f, i, ui * ui + vi * vi);
-    }
-
-  return GSL_SUCCESS;
-}
-
-int
-brown_df (const gsl_vector * x, void *params, gsl_matrix * df)
-{
-  double x0 = gsl_vector_get (x, 0);
-  double x1 = gsl_vector_get (x, 1);
-  double x2 = gsl_vector_get (x, 2);
-  double x3 = gsl_vector_get (x, 3);
-  size_t i;
-
-  for (i = 0; i < 20; i++)
-    {
-      double ti = 0.2 * (i + 1);
-      double ui = x0 + x1 * ti - exp (ti);
-      double vi = x2 + x3 * sin (ti) - cos (ti);
-
-      gsl_matrix_set (df, i, 0, 2 * ui);
-      gsl_matrix_set (df, i, 1, 2 * ui * ti);
-      gsl_matrix_set (df, i, 2, 2 * vi);
-      gsl_matrix_set (df, i, 3, 2 * vi * sin (ti));
-
-    }
-  return GSL_SUCCESS;
-}
-
-int
-brown_fdf (const gsl_vector * x, void *params,
-           gsl_vector * f, gsl_matrix * df)
-{
-  brown_f (x, params, f);
-  brown_df (x, params, df);
-
-  return GSL_SUCCESS;
-}
-
diff -Nru gsl-doc-1.16/multifit/test.c gsl-doc-2.3/multifit/test.c
--- gsl-doc-1.16/multifit/test.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/test.c	2016-12-07 17:55:14.000000000 +0000
@@ -28,278 +28,27 @@
 #include <gsl/gsl_multifit.h>
 #include <gsl/gsl_multifit_nlin.h>
 #include <gsl/gsl_blas.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_permutation.h>
 
 #include <gsl/gsl_ieee_utils.h>
 
-#include "test_longley.c"
-#include "test_filip.c"
-#include "test_pontius.c"
-#include "test_brown.c"
-#include "test_enso.c"
-#include "test_kirby2.c"
-#include "test_hahn1.c"
-#include "test_nelson.c"
-#include "test_fn.c"
-#include "test_estimator.c"
-
-void
-test_lmder (gsl_multifit_function_fdf * f, double x0[], 
-            double * X, double F[], double * cov);
-
-void
-test_fdf (const char * name, gsl_multifit_function_fdf * f, 
-          double x0[], double x[], double sumsq,
-          double sigma[], double epsrel, double epsrel_sigma);
+#include "test_linear.c"
+#include "test_nonlinear.c"
 
 int
 main (void)
 {
-  double epsrel = 1.0e-5;
-  double epsrel_sigma = 1.0e-4;
-  double epsrel_fd = 1.0e-2;
-  double epsrel_sigma_fd = 1.0e-2;
-  gsl_multifit_function_fdf f;
-
   gsl_ieee_env_setup();
 
   /* test linear regression */
-  test_longley();
-  test_filip();
-  test_pontius();
-  test_estimator();
-
-  {
-    f = make_fdf (&brown_f, &brown_df, &brown_fdf, brown_N, brown_P, 0);
-    test_lmder(&f, brown_x0, &brown_X[0][0], brown_F, &brown_cov[0][0]);
-  }
-
-  {
-    f = make_fdf (&enso_f, &enso_df, &enso_fdf, enso_N, enso_P, 0);
-    test_fdf("nist-ENSO", &f, enso_x0, enso_x, enso_sumsq, enso_sigma, epsrel, epsrel_sigma);
-
-    f = make_fdf (&enso_f, NULL, NULL, enso_N, enso_P, 0);
-    test_fdf("nist-ENSO", &f, enso_x0, enso_x, enso_sumsq, enso_sigma, epsrel_fd, epsrel_sigma_fd);
-
-  }
-
-  {
-    f = make_fdf (&kirby2_f, &kirby2_df, &kirby2_fdf, kirby2_N, kirby2_P, 0);
-    test_fdf("nist-kirby2", &f, kirby2_x0, kirby2_x, kirby2_sumsq, kirby2_sigma, epsrel, epsrel_sigma);
+  test_linear();
 
-    f = make_fdf (&kirby2_f, NULL, NULL, kirby2_N, kirby2_P, 0);
-    test_fdf("nist-kirby2", &f, kirby2_x0, kirby2_x, kirby2_sumsq, kirby2_sigma, epsrel_fd, epsrel_sigma_fd);
-  }
-
-  {
-    f = make_fdf (&hahn1_f, &hahn1_df, &hahn1_fdf, hahn1_N, hahn1_P, 0);
-    test_fdf("nist-hahn1", &f, hahn1_x0, hahn1_x, hahn1_sumsq, hahn1_sigma, epsrel, epsrel_sigma);
-
-    f = make_fdf (&hahn1_f, NULL, NULL, hahn1_N, hahn1_P, 0);
-    test_fdf("nist-hahn1", &f, hahn1_x0, hahn1_x, hahn1_sumsq, hahn1_sigma, epsrel_fd, epsrel_sigma_fd);
-  }
-
-#ifdef JUNK
-  {
-    f = make_fdf (&nelson_f, &nelson_df, &nelson_fdf, nelson_N, nelson_P, 0);
-    test_fdf("nist-nelson", &f, nelson_x0, nelson_x, nelson_sumsq, nelson_sigma, epsrel, epsrel_sigma);
-  }
+#if 0 /* fdfsolver interface now deprecated */
+  /* test nonlinear regression */
+  test_nonlinear();
 #endif
 
-  /* now summarize the results */
-
   exit (gsl_test_summary ());
 }
-
-
-void
-test_lmder (gsl_multifit_function_fdf * f, double x0[], 
-            double * X, double F[], double * cov)
-{
-  const gsl_multifit_fdfsolver_type *T;
-  gsl_multifit_fdfsolver *s;
-
-  const size_t n = f->n;
-  const size_t p = f->p;
-
-  int status;
-  size_t iter = 0, i;
-  
-  gsl_vector_view x = gsl_vector_view_array (x0, p);
-
-  T = gsl_multifit_fdfsolver_lmsder;
-  s = gsl_multifit_fdfsolver_alloc (T, n, p);
-  gsl_multifit_fdfsolver_set (s, f, &x.vector);
-
-  do
-    {
-      status = gsl_multifit_fdfsolver_iterate (s);
-
-      for (i = 0 ; i < p; i++)
-        {
-          gsl_test_rel (gsl_vector_get (s->x, i), X[p*iter+i], 1e-5, 
-                        "lmsder, iter=%u, x%u", iter, i);
-        }
-
-      gsl_test_rel (gsl_blas_dnrm2 (s->f), F[iter], 1e-5, 
-                    "lmsder, iter=%u, f", iter);
-
-      iter++;
-    }
-  while (iter < 20);
-  
-  {
-    size_t i, j;
-    gsl_matrix * covar = gsl_matrix_alloc (4, 4);
-    gsl_multifit_covar (s->J, 0.0, covar);
-
-    for (i = 0; i < 4; i++) 
-      {
-        for (j = 0; j < 4; j++)
-          {
-            gsl_test_rel (gsl_matrix_get(covar,i,j), cov[i*p + j], 1e-7, 
-                          "gsl_multifit_covar cov(%d,%d)", i, j) ;
-          }
-      }
-
-    gsl_matrix_free (covar);
-  }
-
-  gsl_multifit_fdfsolver_free (s);
-
-}
-
-void
-test_fdf (const char * name, gsl_multifit_function_fdf * f, 
-          double x0[], double x_final[], 
-          double f_sumsq, double sigma[], double epsrel,
-          double epsrel_sigma)
-{
-  const gsl_multifit_fdfsolver_type *T;
-  gsl_multifit_fdfsolver *s;
-  
-  const size_t n = f->n;
-  const size_t p = f->p;
-
-  int status;
-  size_t iter = 0;
-
-  gsl_vector_view x = gsl_vector_view_array (x0, p);
-
-  T = gsl_multifit_fdfsolver_lmsder;
-  s = gsl_multifit_fdfsolver_alloc (T, n, p);
-  gsl_multifit_fdfsolver_set (s, f, &x.vector);
-
-  do
-    {
-      status = gsl_multifit_fdfsolver_iterate (s);
-
-#ifdef DEBUG
-       printf("iter = %d  status = %d  |f| = %.18e x = \n", 
-         iter, status, gsl_blas_dnrm2 (s->f));
-         
-         gsl_vector_fprintf(stdout, s->x, "%.8e");
-#endif       
-      status = gsl_multifit_test_delta (s->dx, s->x, 0.0, 1e-7);
-
-      iter++;
-    }
-  while (status == GSL_CONTINUE && iter < 1000);
-  
-  {
-    size_t i;
-    gsl_matrix * covar = gsl_matrix_alloc (p, p);
-    gsl_multifit_covar (s->J, 0.0, covar);
-
-    for (i = 0 ; i < p; i++)
-      {
-        gsl_test_rel (gsl_vector_get (s->x, i), x_final[i], epsrel, 
-                      "%s, lmsder, x%u", name, i);
-      }
-
-
-    {
-      double s2 = pow(gsl_blas_dnrm2 (s->f), 2.0);
-
-      gsl_test_rel (s2, f_sumsq, epsrel, "%s, lmsder, |f|^2", name);
-
-      for (i = 0; i < p; i++) 
-        {
-          double ei = sqrt(s2/(n-p))*sqrt(gsl_matrix_get(covar,i,i));
-          gsl_test_rel (ei, sigma[i], epsrel_sigma, 
-                        "%s, sigma(%d)", name, i) ;
-        }
-    }
-
-    gsl_matrix_free (covar);
-  }
-
-  /* check higher level driver routine */
-  {
-    size_t i;
-
-    gsl_multifit_fdfsolver_set (s, f, &x.vector);
-    gsl_multifit_fdfsolver_driver (s, 1000, 0.0, 1.0e-7);
-
-    for (i = 0 ; i < p; i++)
-      {
-        gsl_test_rel (gsl_vector_get (s->x, i), x_final[i], epsrel, 
-                      "%s, lmsder, x%u", name, i);
-      }
-  }
-
-  /* Check that there is no hidden state, restarting should 
-     produce identical results. */
-
-  {
-    int status0, status1;
-    size_t i;
-    gsl_multifit_fdfsolver *t = gsl_multifit_fdfsolver_alloc (T, n, p);
-    gsl_multifit_fdfsolver_set (t, f, &x.vector);
-
-    /* do a few extra iterations to stir things up */
-
-    gsl_multifit_fdfsolver_set (s, f, &x.vector);
-
-    for (i = 0; i < 3; i++) 
-      {
-        gsl_multifit_fdfsolver_iterate (s);
-      }
-
-    gsl_multifit_fdfsolver_set (s, f, &x.vector);
-
-    do
-      {
-        status0 = gsl_multifit_fdfsolver_iterate (s);
-        status1 = gsl_multifit_fdfsolver_iterate (t);
-
-        gsl_test_int(status0, status1, "%s, lmsder status after set iter=%u", name, iter);
-        
-        for (i = 0; i < p; i++) {
-          double sxi = gsl_vector_get(s->x,i);
-          double txi = gsl_vector_get(t->x,i);
-#ifdef DEBUG
-          printf("%d %g %g\n", i, sxi, txi);
-#endif
-          gsl_test_rel(sxi, txi, 1e-15, "%s, lmsder after set, %u/%u", name, iter, i);
-        }
-        
-#ifdef DEBUG
-        printf("iter = %d  status = %d  |f| = %.18e x = \n", 
-               iter, status, gsl_blas_dnrm2 (s->f));
-        
-        gsl_vector_fprintf(stdout, s->x, "%.8e");
-#endif       
-        status0 = gsl_multifit_test_delta (s->dx, s->x, 0.0, 1e-7);
-        status1 = gsl_multifit_test_delta (t->dx, s->x, 0.0, 1e-7);
-        
-        gsl_test_int(status0, status1, "%s, lmsder test delta status after set iter=%u", name, iter);
-
-        iter++;
-      }
-    while (status1 == GSL_CONTINUE && iter < 1000);
-
-    gsl_multifit_fdfsolver_free (t);
-  }
-
-  gsl_multifit_fdfsolver_free (s);
-}
diff -Nru gsl-doc-1.16/multifit/test_eckerle.c gsl-doc-2.3/multifit/test_eckerle.c
--- gsl-doc-1.16/multifit/test_eckerle.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_eckerle.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,124 @@
+#define eckerle_N       35
+#define eckerle_P       3
+
+#define eckerle_NTRIES  1
+
+static double eckerle_x0[eckerle_P] = { 1.0, 10.0, 500.0 };
+static double eckerle_epsrel = 1.0e-7;
+
+static double eckerle_sigma[eckerle_P] = {
+  1.5408051163E-02, 4.6803020753E-02, 4.6800518816E-02
+};
+
+static double eckerle_X[eckerle_N] = {
+  400.000000, 405.000000, 410.000000, 415.000000, 420.000000,
+  425.000000, 430.000000, 435.000000, 436.500000, 438.000000,
+  439.500000, 441.000000, 442.500000, 444.000000, 445.500000,
+  447.000000, 448.500000, 450.000000, 451.500000, 453.000000,
+  454.500000, 456.000000, 457.500000, 459.000000, 460.500000,
+  462.000000, 463.500000, 465.000000, 470.000000, 475.000000,
+  480.000000, 485.000000, 490.000000, 495.000000, 500.000000 };
+
+static double eckerle_F[eckerle_N] = {
+  0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917,
+  0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302,
+  0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458,
+  0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534,
+  0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200,
+  0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800,
+  0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710 };
+
+static void
+eckerle_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.4635887487E-03;
+  const double eckerle_x[eckerle_P] = { 1.5543827178E+00,
+                                        4.0888321754E+00,
+                                        4.5154121844E+02 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < eckerle_P; ++i)
+    {
+      gsl_test_rel(x[i], eckerle_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+eckerle_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[eckerle_P];
+  size_t i;
+
+  for (i = 0; i < eckerle_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < eckerle_N; i++)
+    {
+      double xi = eckerle_X[i];
+      double term = xi - b[2];
+      double yi;
+
+      yi = b[0] / b[1] * exp(-0.5 * term * term / b[1] / b[1]);
+      gsl_vector_set (f, i, yi - eckerle_F[i]);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+eckerle_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[eckerle_P];
+  size_t i;
+
+  for (i = 0; i < eckerle_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < eckerle_N; i++)
+    {
+      double xi = eckerle_X[i];
+      double term1 = xi - b[2];
+      double term2 = exp(-0.5 * term1 * term1 / (b[1] * b[1]));
+
+      gsl_matrix_set (df, i, 0, term2 / b[1]);
+      gsl_matrix_set (df, i, 1,
+        -b[0] * term2 / (b[1] * b[1]) + b[0] / pow(b[1], 4.0) * term2 * term1 * term1);
+      gsl_matrix_set (df, i, 2, b[0] / pow(b[1], 3.0) * term1 * term2);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf eckerle_func =
+{
+  &eckerle_f,
+  &eckerle_df,
+  NULL,
+  eckerle_N,
+  eckerle_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem eckerle_problem =
+{
+  "nist-eckerle",
+  eckerle_x0,
+  eckerle_sigma,
+  &eckerle_epsrel,
+  eckerle_NTRIES,
+  &eckerle_checksol,
+  &eckerle_func
+};
diff -Nru gsl-doc-1.16/multifit/test_enso.c gsl-doc-2.3/multifit/test_enso.c
--- gsl-doc-1.16/multifit/test_enso.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/test_enso.c	2015-11-03 16:21:55.000000000 +0000
@@ -1,23 +1,14 @@
-const size_t enso_N = 168;
-const size_t enso_P = 9;
+#define enso_N       168
+#define enso_P       9
 
-double enso_x0[9] = { 10.0, 3.0, 0.5, 44.0, -1.5, 0.5, 26.0, 0.1, 1.5 };
+#define enso_NTRIES  1
+
+static double enso_x0[enso_P] = { 10.0, 3.0, 0.5, 44.0, -1.5, 0.5, 26.0, 0.1, 1.5 };
 
-double enso_x[9] = {
-  1.0510749193E+01, 
-  3.0762128085E+00,
-  5.3280138227E-01,
-  4.4311088700E+01,
- -1.6231428586E+00,
-  5.2554493756E-01,
-  2.6887614440E+01,
-  2.1232288488E-01,
-  1.4966870418E+00
-};
 
-double enso_sumsq = 7.8853978668E+02;
+static double enso_epsrel = 1.0e-3;
 
-double enso_sigma[9] = {
+static double enso_sigma[enso_P] = {
  1.7488832467E-01,
  2.4310052139E-01,
  2.4354686618E-01,
@@ -29,7 +20,7 @@
  2.5434468893E-01
 };
 
-double enso_F[168] = {
+static double enso_F[enso_N] = {
     12.90000, 
     11.30000, 
     10.60000, 
@@ -200,19 +191,41 @@
     14.80000
 };
 
+static void
+enso_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 7.8853978668E+02;
+  const double enso_x[enso_P] = {
+    1.0510749193E+01, 3.0762128085E+00, 5.3280138227E-01,
+    4.4311088700E+01, -1.6231428586E+00, 5.2554493756E-01,
+    2.6887614440E+01, 2.1232288488E-01, 1.4966870418E+00 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < enso_P; ++i)
+    {
+      gsl_test_rel(x[i], enso_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
 
-int
+static int
 enso_f (const gsl_vector * x, void *params, gsl_vector * f)
 {
-  double b[9];
+  double b[enso_P];
   size_t i;
 
-  for (i = 0; i < 9; i++)
+  for (i = 0; i < enso_P; i++)
     {
       b[i] = gsl_vector_get(x, i);
     }
 
-  for (i = 0; i < 168; i++)
+  for (i = 0; i < enso_N; i++)
     {
       double t = (i + 1.0);
       double y;
@@ -230,18 +243,18 @@
   return GSL_SUCCESS;
 }
 
-int
+static int
 enso_df (const gsl_vector * x, void *params, gsl_matrix * df)
 {
-  double b[9];
+  double b[enso_P];
   size_t i;
 
-  for (i = 0; i < 9; i++)
+  for (i = 0; i < enso_P; i++)
     {
       b[i] = gsl_vector_get(x, i);
     }
 
-  for (i = 0; i < 168; i++)
+  for (i = 0; i < enso_N; i++)
     {
       double t = (i + 1.0);
 
@@ -263,17 +276,25 @@
   return GSL_SUCCESS;
 }
 
-int
-enso_fdf (const gsl_vector * x, void *params,
-           gsl_vector * f, gsl_matrix * df)
+static gsl_multifit_function_fdf enso_func =
 {
-  enso_f (x, params, f);
-  enso_df (x, params, df);
-
-  return GSL_SUCCESS;
-}
-
-
-
-
+  &enso_f,
+  &enso_df,
+  NULL,
+  enso_N,
+  enso_P,
+  NULL,
+  0,
+  0
+};
 
+static test_fdf_problem enso_problem =
+{
+  "nist-ENSO",
+  enso_x0,
+  enso_sigma,
+  &enso_epsrel,
+  enso_NTRIES,
+  &enso_checksol,
+  &enso_func
+};
diff -Nru gsl-doc-1.16/multifit/test_exp1.c gsl-doc-2.3/multifit/test_exp1.c
--- gsl-doc-1.16/multifit/test_exp1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_exp1.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,105 @@
+#define exp1_N         45
+#define exp1_P         4
+
+#define exp1_NTRIES    3
+
+static double exp1_x0[exp1_P] = { -1.0, -2.0, 1.0, -1.0 };
+static double exp1_epsrel = 1.0e-4;
+
+static double exp1_Y[exp1_N] = {
+0.090542, 0.124569, 0.179367, 0.195654, 0.269707,
+0.286027, 0.289892, 0.317475, 0.308191, 0.336995,
+0.348371, 0.321337, 0.299423, 0.338972, 0.304763,
+0.288903, 0.300820, 0.303974, 0.283987, 0.262078,
+0.281593, 0.267531, 0.218926, 0.225572, 0.200594,
+0.197375, 0.182440, 0.183892, 0.152285, 0.174028,
+0.150874, 0.126220, 0.126266, 0.106384, 0.118923,
+0.091868, 0.128926, 0.119273, 0.115997, 0.105831,
+0.075261, 0.068387, 0.090823, 0.085205, 0.067203
+};
+
+static void
+exp1_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.0e-2;
+  const double exp1_x[exp1_P] = { -4.0, -5.0, 4.0, -4.0 }; /* approx */
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < exp1_P; ++i)
+    {
+      gsl_test_rel(x[i], exp1_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+exp1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  size_t i;
+
+  for (i = 0; i < exp1_N; ++i)
+    {
+      double ti = 0.02*(i + 1.0);
+      double yi = exp1_Y[i];
+      double fi = yi - (x3*exp(x1*ti) + x4*exp(x2*ti));
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+exp1_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  size_t i;
+
+  for (i = 0; i < exp1_N; ++i)
+    {
+      double ti = 0.02*(i + 1.0);
+      double term1 = exp(x1*ti);
+      double term2 = exp(x2*ti);
+
+      gsl_matrix_set(J, i, 0, -x3*ti*term1);
+      gsl_matrix_set(J, i, 1, -x4*ti*term2);
+      gsl_matrix_set(J, i, 2, -term1);
+      gsl_matrix_set(J, i, 3, -term2);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf exp1_func =
+{
+  &exp1_f,
+  &exp1_df,
+  NULL,
+  exp1_N,
+  exp1_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem exp1_problem =
+{
+  "expfit1",
+  exp1_x0,
+  NULL,
+  &exp1_epsrel,
+  exp1_NTRIES,
+  &exp1_checksol,
+  &exp1_func
+};
diff -Nru gsl-doc-1.16/multifit/test_fn.c gsl-doc-2.3/multifit/test_fn.c
--- gsl-doc-1.16/multifit/test_fn.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/test_fn.c	1970-01-01 00:00:00.000000000 +0000
@@ -1,25 +0,0 @@
-gsl_multifit_function_fdf
-make_fdf (int (* f) (const gsl_vector *, void *, gsl_vector *),
-          int (* df) (const gsl_vector *, void *, gsl_matrix *),
-          int (* fdf) (const gsl_vector *, void *, gsl_vector *, gsl_matrix *),
-          size_t n,
-          size_t p,
-          void * params);
-
-gsl_multifit_function_fdf
-make_fdf (int (* f) (const gsl_vector *, void *, gsl_vector *),
-          int (* df) (const gsl_vector *, void *, gsl_matrix *),
-          int (* fdf) (const gsl_vector *, void *, gsl_vector *, gsl_matrix *),
-          size_t n,
-          size_t p,
-          void * params)
-{
-  gsl_multifit_function_fdf F_new;
-  F_new.f = f;
-  F_new.df = df;
-  F_new.fdf = fdf;
-  F_new.n = n;
-  F_new.p = p;
-  F_new.params = params;
-  return F_new;
-}
diff -Nru gsl-doc-1.16/multifit/test_gaussian.c gsl-doc-2.3/multifit/test_gaussian.c
--- gsl-doc-1.16/multifit/test_gaussian.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_gaussian.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,99 @@
+#define gaussian_N         15
+#define gaussian_P         3
+
+#define gaussian_NTRIES    2
+
+static double gaussian_x0[gaussian_P] = { 0.4, 1.0, 0.0 };
+
+static double gaussian_epsrel = 1.0e-10;
+
+static double gaussian_Y[gaussian_N] = {
+0.0009, 0.0044, 0.0175, 0.0540, 0.1295, 0.2420, 0.3521, 0.3989,
+0.3521, 0.2420, 0.1295, 0.0540, 0.0175, 0.0044, 0.0009
+};
+
+static void
+gaussian_checksol(const double x[], const double sumsq,
+                  const double epsrel, const char *sname,
+                  const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.12793276961871985e-08;
+  const double gaussian_x[gaussian_P] = { 0.398956137838762825,
+                                          1.00001908448786647,
+                                          0.0 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < gaussian_P; ++i)
+    {
+      gsl_test_rel(x[i], gaussian_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+gaussian_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < gaussian_N; ++i)
+    {
+      double ti = (7.0 - i) / 2.0;
+      double yi = gaussian_Y[i];
+      double term = ti - x3;
+      double fi = x1 * exp(-x2*term*term/2.0) - yi;
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+gaussian_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < gaussian_N; ++i)
+    {
+      double ti = (7.0 - i) / 2.0;
+      double term1 = ti - x3;
+      double term2 = exp(-x2*term1*term1/2.0);
+
+      gsl_matrix_set(J, i, 0, term2);
+      gsl_matrix_set(J, i, 1, -0.5*x1*term2*term1*term1);
+      gsl_matrix_set(J, i, 2, x1*x2*term1*term2);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf gaussian_func =
+{
+  &gaussian_f,
+  &gaussian_df,
+  NULL,
+  gaussian_N,
+  gaussian_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem gaussian_problem =
+{
+  "gaussian",
+  gaussian_x0,
+  NULL,
+  &gaussian_epsrel,
+  gaussian_NTRIES,
+  &gaussian_checksol,
+  &gaussian_func
+};
diff -Nru gsl-doc-1.16/multifit/test_hahn1.c gsl-doc-2.3/multifit/test_hahn1.c
--- gsl-doc-1.16/multifit/test_hahn1.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/test_hahn1.c	2015-11-03 16:21:55.000000000 +0000
@@ -1,23 +1,16 @@
-const size_t hahn1_N = 236;
-const size_t hahn1_P = 7;
+#define hahn1_N      236
+#define hahn1_P      7
+
+#define hahn1_NTRIES 1
 
 /* double hahn1_x0[7] = { 10, -1, 0.05, -0.00001, -0.05, 0.001, -0.000001 }; */
 
-double hahn1_x0[7] = { 1, -0.1, 0.005, -0.000001, -0.005, 0.0001, -0.0000001}; 
+static double hahn1_x0[hahn1_P] = { 1, -0.1, 0.005, -0.000001, -0.005, 0.0001, -0.0000001}; 
 
-double hahn1_x[7] = {
-1.0776351733E+00,
--1.2269296921E-01,
-4.0863750610E-03,
--1.4262662514E-06,
--5.7609940901E-03,
-2.4053735503E-04,
--1.2314450199E-07
-};
 
-double hahn1_sumsq = 1.5324382854E+00;
+static double hahn1_epsrel = 1.0e-5;
 
-double hahn1_sigma[7] = {
+static double hahn1_sigma[hahn1_P] = {
   1.7070154742E-01,
   1.2000289189E-02,
   2.2508314937E-04,
@@ -27,7 +20,7 @@
   1.3027335327E-08
 };
 
-double hahn1_F1[236] = {
+static double hahn1_F1[hahn1_N] = {
         .591E0,
        1.547E0,
        2.902E0,
@@ -267,7 +260,7 @@
 };
 
 
-double hahn1_F0[236] = {
+static double hahn1_F0[hahn1_N] = {
     24.41E0,
     34.82E0,
     44.09E0,
@@ -506,19 +499,40 @@
    848.23E0
 };
 
+static void
+hahn1_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.5324382854E+00;
+  const double hahn1_x[hahn1_P] = {
+     1.0776351733E+00, -1.2269296921E-01, 4.0863750610E-03,
+    -1.4262662514E-06, -5.7609940901E-03, 2.4053735503E-04,
+    -1.2314450199E-07 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < hahn1_P; ++i)
+    {
+      gsl_test_rel(x[i], hahn1_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
 
-int
+static int
 hahn1_f (const gsl_vector * x, void *params, gsl_vector * f)
 {
-  double b[7];
+  double b[hahn1_P];
   size_t i;
 
-  for (i = 0; i < 7; i++)
+  for (i = 0; i < hahn1_P; i++)
     {
       b[i] = gsl_vector_get(x, i);
     }
 
-  for (i = 0; i < 236; i++)
+  for (i = 0; i < hahn1_N; i++)
     {
       double x = hahn1_F0[i];
       double y = ((b[0] + x* (b[1]  + x * (b[2] + x * b[3])))
@@ -529,18 +543,18 @@
   return GSL_SUCCESS;
 }
 
-int
+static int
 hahn1_df (const gsl_vector * x, void *params, gsl_matrix * df)
 {
-  double b[7];
+  double b[hahn1_P];
   size_t i;
 
-  for (i = 0; i < 7; i++)
+  for (i = 0; i < hahn1_P; i++)
     {
       b[i] = gsl_vector_get(x, i);
     }
 
-  for (i = 0; i < 236; i++)
+  for (i = 0; i < hahn1_N; i++)
     {
       double x = hahn1_F0[i];
       double u = (b[0] + x*(b[1] + x*(b[2] + x * b[3])));
@@ -557,12 +571,25 @@
   return GSL_SUCCESS;
 }
 
-int
-hahn1_fdf (const gsl_vector * x, void *params,
-           gsl_vector * f, gsl_matrix * df)
+static gsl_multifit_function_fdf hahn1_func =
 {
-  hahn1_f (x, params, f);
-  hahn1_df (x, params, df);
+  &hahn1_f,
+  &hahn1_df,
+  NULL,
+  hahn1_N,
+  hahn1_P,
+  NULL,
+  0,
+  0
+};
 
-  return GSL_SUCCESS;
-}
+static test_fdf_problem hahn1_problem =
+{
+  "nist-hahn1",
+  hahn1_x0,
+  hahn1_sigma,
+  &hahn1_epsrel,
+  hahn1_NTRIES,
+  &hahn1_checksol,
+  &hahn1_func
+};
diff -Nru gsl-doc-1.16/multifit/test_helical.c gsl-doc-2.3/multifit/test_helical.c
--- gsl-doc-1.16/multifit/test_helical.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_helical.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,91 @@
+#define helical_N         3
+#define helical_P         3
+
+#define helical_NTRIES    4
+
+static double helical_x0[helical_P] = { -1.0, 0.0, 0.0 };
+static double helical_x[helical_P] = { 1.0, 0.0, 0.0 };
+
+static double helical_epsrel = 1.0e-12;
+
+static void
+helical_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < helical_P; ++i)
+    {
+      gsl_test_rel(x[i], helical_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+helical_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double theta = (x1 >= 0.0) ? 0.0 : 5.0;
+  double nx = gsl_hypot(x1, x2);
+
+  gsl_vector_set(f, 0, 10.0 * (x3 - 5.0/M_PI*atan(x2 / x1) - theta));
+  gsl_vector_set(f, 1, 10.0*(nx - 1.0));
+  gsl_vector_set(f, 2, x3);
+
+  return GSL_SUCCESS;
+}
+
+static int
+helical_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double nx = gsl_hypot(x1, x2);
+  double nx_sq = nx * nx;
+  double term1 = 50.0 / (M_PI * nx_sq);
+  double term2 = 10.0 / nx;
+
+  gsl_matrix_set(J, 0, 0, term1*x2);
+  gsl_matrix_set(J, 0, 1, -term1*x1);
+  gsl_matrix_set(J, 0, 2, 10.0);
+
+  gsl_matrix_set(J, 1, 0, term2*x1);
+  gsl_matrix_set(J, 1, 1, term2*x2);
+  gsl_matrix_set(J, 1, 2, 0.0);
+
+  gsl_matrix_set(J, 2, 0, 0.0);
+  gsl_matrix_set(J, 2, 1, 0.0);
+  gsl_matrix_set(J, 2, 2, 1.0);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf helical_func =
+{
+  &helical_f,
+  &helical_df,
+  NULL,
+  helical_N,
+  helical_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem helical_problem =
+{
+  "helical",
+  helical_x0,
+  NULL,
+  &helical_epsrel,
+  helical_NTRIES,
+  &helical_checksol,
+  &helical_func
+};
diff -Nru gsl-doc-1.16/multifit/test_jennrich.c gsl-doc-2.3/multifit/test_jennrich.c
--- gsl-doc-1.16/multifit/test_jennrich.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_jennrich.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,85 @@
+#define jennrich_N         10
+#define jennrich_P         2
+
+#define jennrich_NTRIES    1
+
+static double jennrich_x0[jennrich_P] = { 0.3, 0.4 };
+static double jennrich_epsrel = 1.0e-8;
+
+static void
+jennrich_checksol(const double x[], const double sumsq,
+                  const double epsrel, const char *sname,
+                  const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.243621823556148e+02;
+  const double jennrich_x[jennrich_P] = { 2.578252139935855e-01,
+                                          2.578252133471426e-01 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < jennrich_P; ++i)
+    {
+      gsl_test_rel(x[i], jennrich_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+jennrich_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < jennrich_N; ++i)
+    {
+      double ip1 = i + 1.0;
+      double fi = 2.0*(i + 2.0) - (exp(x1*ip1) + exp(x2*ip1));
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+jennrich_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < jennrich_N; ++i)
+    {
+      double ip1 = i + 1.0;
+
+      gsl_matrix_set(J, i, 0, -ip1*exp(ip1*x1));
+      gsl_matrix_set(J, i, 1, -ip1*exp(ip1*x2));
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf jennrich_func =
+{
+  &jennrich_f,
+  &jennrich_df,
+  NULL,
+  jennrich_N,
+  jennrich_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem jennrich_problem =
+{
+  "jennrich",
+  jennrich_x0,
+  NULL,
+  &jennrich_epsrel,
+  jennrich_NTRIES,
+  &jennrich_checksol,
+  &jennrich_func
+};
diff -Nru gsl-doc-1.16/multifit/test_kirby2.c gsl-doc-2.3/multifit/test_kirby2.c
--- gsl-doc-1.16/multifit/test_kirby2.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/test_kirby2.c	2015-11-03 16:21:55.000000000 +0000
@@ -1,21 +1,15 @@
-const size_t kirby2_N = 151;
-const size_t kirby2_P = 5;
+#define kirby2_N       151
+#define kirby2_P       5
 
-/* double kirby2_x0[5] = { 2, -0.1, 0.003, -0.001, 0.00001 }; */
+#define kirby2_NTRIES  1
 
-double kirby2_x0[5] = { 1.5, -0.15, 0.0025, -0.0015, 0.00002 }; 
+/* double kirby2_x0[kirby2_P] = { 2, -0.1, 0.003, -0.001, 0.00001 }; */
 
-double kirby2_x[5] = {
-  1.6745063063E+00,
-  -1.3927397867E-01,
-  2.5961181191E-03,
-  -1.7241811870E-03,
-  2.1664802578E-05
-};
+static double kirby2_x0[kirby2_P] = { 1.5, -0.15, 0.0025, -0.0015, 0.00002 }; 
 
-double kirby2_sumsq = 3.9050739624E+00;
+static double kirby2_epsrel = 1.0e-5;
 
-double kirby2_sigma[5] = {
+static double kirby2_sigma[kirby2_P] = {
   8.7989634338E-02,
   4.1182041386E-03,
   4.1856520458E-05,
@@ -23,7 +17,7 @@
   2.0129761919E-07
 };
 
-double kirby2_F1[151] = {
+static double kirby2_F1[kirby2_N] = {
        0.0082E0,
        0.0112E0,
        0.0149E0,
@@ -178,7 +172,7 @@
 };
 
 
-double kirby2_F0[151] = {
+static double kirby2_F0[kirby2_N] = {
     9.65E0,
    10.74E0,
    11.81E0,
@@ -332,19 +326,39 @@
   371.30E0
 };
 
+static void
+kirby2_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 3.9050739624E+00;
+  const double kirby2_x[kirby2_P] = {
+    1.6745063063E+00, -1.3927397867E-01, 2.5961181191E-03,
+   -1.7241811870E-03, 2.1664802578E-05 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
 
-int
+  for (i = 0; i < kirby2_P; ++i)
+    {
+      gsl_test_rel(x[i], kirby2_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
 kirby2_f (const gsl_vector * x, void *params, gsl_vector * f)
 {
-  double b[5];
+  double b[kirby2_P];
   size_t i;
 
-  for (i = 0; i < 5; i++)
+  for (i = 0; i < kirby2_P; i++)
     {
       b[i] = gsl_vector_get(x, i);
     }
 
-  for (i = 0; i < 151; i++)
+  for (i = 0; i < kirby2_N; i++)
     {
       double x = kirby2_F0[i];
       double y = ((b[0] + x* (b[1]  + x * b[2]))
@@ -355,18 +369,18 @@
   return GSL_SUCCESS;
 }
 
-int
+static int
 kirby2_df (const gsl_vector * x, void *params, gsl_matrix * df)
 {
-  double b[5];
+  double b[kirby2_P];
   size_t i;
 
-  for (i = 0; i < 5; i++)
+  for (i = 0; i < kirby2_P; i++)
     {
       b[i] = gsl_vector_get(x, i);
     }
 
-  for (i = 0; i < 151; i++)
+  for (i = 0; i < kirby2_N; i++)
     {
       double x = kirby2_F0[i];
       double u = (b[0] + x*(b[1] + x*b[2]));
@@ -381,12 +395,25 @@
   return GSL_SUCCESS;
 }
 
-int
-kirby2_fdf (const gsl_vector * x, void *params,
-           gsl_vector * f, gsl_matrix * df)
+static gsl_multifit_function_fdf kirby2_func =
 {
-  kirby2_f (x, params, f);
-  kirby2_df (x, params, df);
+  &kirby2_f,
+  &kirby2_df,
+  NULL,
+  kirby2_N,
+  kirby2_P,
+  NULL,
+  0,
+  0
+};
 
-  return GSL_SUCCESS;
-}
+static test_fdf_problem kirby2_problem =
+{
+  "nist-kirby2",
+  kirby2_x0,
+  kirby2_sigma,
+  &kirby2_epsrel,
+  kirby2_NTRIES,
+  &kirby2_checksol,
+  &kirby2_func
+};
diff -Nru gsl-doc-1.16/multifit/test_kowalik.c gsl-doc-2.3/multifit/test_kowalik.c
--- gsl-doc-1.16/multifit/test_kowalik.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_kowalik.c	2016-11-30 21:28:37.000000000 +0000
@@ -0,0 +1,130 @@
+#define kowalik_N         11
+#define kowalik_P         4
+
+#define kowalik_NTRIES    4
+
+static double kowalik_x0[kowalik_P] = { 0.25, 0.39, 0.415, 0.39 };
+
+static double kowalik_epsrel = 1.0e-7;
+
+static double kowalik_Y[kowalik_N] = {
+0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627,
+0.0456, 0.0342, 0.0323, 0.0235, 0.0246
+};
+
+static double kowalik_U[kowalik_N] = {
+4.0000, 2.0000, 1.0000, 0.5000, 0.2500, 0.1670,
+0.1250, 0.1000, 0.0833, 0.0714, 0.0625
+};
+
+static void
+kowalik_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  gsl_vector_const_view v = gsl_vector_const_view_array(x, kowalik_P);
+  const double norm = gsl_blas_dnrm2(&v.vector);
+  const double sumsq_exact1 = 3.075056038492370e-04;
+  const double kowalik_x1[kowalik_P] = { 1.928069345723978e-01,
+                                         1.912823290344599e-01,
+                                         1.230565070690708e-01,
+                                         1.360623308065148e-01 };
+  const double sumsq_exact2 = 0.00102734304869549252;
+  const double kowalik_x2[kowalik_P] = { -99999.9,   /* inf */
+                                         -14.0758834005984603,
+                                         -99999.9,   /* -inf */
+                                         -99999.9 }; /* -inf */
+  const double *kowalik_x;
+  double sumsq_exact;
+
+  if (norm < 10.0)
+    {
+      kowalik_x = kowalik_x1;
+      sumsq_exact = sumsq_exact1;
+    }
+  else
+    {
+      kowalik_x = kowalik_x2;
+      sumsq_exact = sumsq_exact2;
+    }
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < kowalik_P; ++i)
+    {
+      if (kowalik_x[i] < -90000.0)
+        continue;
+
+      gsl_test_rel(x[i], kowalik_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+kowalik_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  size_t i;
+
+  for (i = 0; i < kowalik_N; ++i)
+    {
+      double yi = kowalik_Y[i];
+      double ui = kowalik_U[i];
+      double fi = yi - (x1*ui*(ui+x2)) / (x4 + ui*(ui + x3));
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+kowalik_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  size_t i;
+
+  for (i = 0; i < kowalik_N; ++i)
+    {
+      double ui = kowalik_U[i];
+      double term1 = ui*(ui + x2);
+      double term2 = ui*(ui + x3) + x4;
+
+      gsl_matrix_set(J, i, 0, -term1 / term2);
+      gsl_matrix_set(J, i, 1, -ui*x1/term2);
+      gsl_matrix_set(J, i, 2, ui*term1*x1 / (term2*term2));
+      gsl_matrix_set(J, i, 3, term1*x1 / (term2*term2));
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf kowalik_func =
+{
+  &kowalik_f,
+  &kowalik_df,
+  NULL,
+  kowalik_N,
+  kowalik_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem kowalik_problem =
+{
+  "kowalik",
+  kowalik_x0,
+  NULL,
+  &kowalik_epsrel,
+  kowalik_NTRIES,
+  &kowalik_checksol,
+  &kowalik_func
+};
diff -Nru gsl-doc-1.16/multifit/test_lin1.c gsl-doc-2.3/multifit/test_lin1.c
--- gsl-doc-1.16/multifit/test_lin1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_lin1.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,90 @@
+#define lin1_N         11  /* can be anything >= p */
+#define lin1_P         5
+
+#define lin1_NTRIES    3
+
+static double lin1_x0[lin1_P] = { 1.0, 1.0, 1.0, 1.0, 1.0 };
+static double lin1_epsrel = 1.0e-10;
+
+static void
+lin1_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = (double) (lin1_N - lin1_P);
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < lin1_P; ++i)
+    {
+      gsl_test_rel(x[i], -1.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+lin1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i, j;
+
+  for (i = 0; i < lin1_N; ++i)
+    {
+      double fi = 0.0;
+
+      for (j = 0; j < lin1_P; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+          double Aij = (i == j) ? 1.0 : 0.0;
+          Aij -= 2.0 / lin1_N;
+          fi += Aij * xj;
+        }
+
+      fi -= 1.0;
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin1_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  size_t i, j;
+
+  for (i = 0; i < lin1_N; ++i)
+    {
+      for (j = 0; j < lin1_P; ++j)
+        {
+          double Jij = (i == j) ? 1.0 : 0.0;
+          Jij -= 2.0 / lin1_N;
+          gsl_matrix_set(J, i, j, Jij);
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf lin1_func =
+{
+  &lin1_f,
+  &lin1_df,
+  NULL,
+  lin1_N,
+  lin1_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem lin1_problem =
+{
+  "linear_full",
+  lin1_x0,
+  NULL,
+  &lin1_epsrel,
+  lin1_NTRIES,
+  &lin1_checksol,
+  &lin1_func
+};
diff -Nru gsl-doc-1.16/multifit/test_lin2.c gsl-doc-2.3/multifit/test_lin2.c
--- gsl-doc-1.16/multifit/test_lin2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_lin2.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,89 @@
+#define lin2_N         20  /* can be anything >= p */
+#define lin2_P         5
+
+#define lin2_NTRIES    3
+
+static double lin2_x0[lin2_P] = { 1.0, 1.0, 1.0, 1.0, 1.0 };
+static double lin2_epsrel = 1.0e-11;
+
+static void
+lin2_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double n = (double) lin2_N;
+  const double sumsq_exact = 0.5 * (n*(n - 1.0)) / (2.0*n + 1.0);
+  const double sum_exact = 3.0 / (2.0*n + 1.0);
+  double sum = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < lin2_P; ++i)
+    sum += (i + 1.0) * x[i];
+
+  gsl_test_rel(sum, sum_exact, epsrel, "%s/%s coeff sum",
+               sname, pname);
+}
+
+static int
+lin2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i, j;
+
+  for (i = 0; i < lin2_N; ++i)
+    {
+      double fi = 0.0;
+
+      for (j = 0; j < lin2_P; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+          fi += (j + 1) * xj;
+        }
+
+      fi = (i + 1) * fi - 1.0;
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin2_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  size_t i, j;
+
+  for (i = 0; i < lin2_N; ++i)
+    {
+      for (j = 0; j < lin2_P; ++j)
+        {
+          gsl_matrix_set(J, i, j, (i + 1.0) * (j + 1.0));
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf lin2_func =
+{
+  &lin2_f,
+  &lin2_df,
+  NULL,
+  lin2_N,
+  lin2_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem lin2_problem =
+{
+  "linear_rank1",
+  lin2_x0,
+  NULL,
+  &lin2_epsrel,
+  lin2_NTRIES,
+  &lin2_checksol,
+  &lin2_func
+};
diff -Nru gsl-doc-1.16/multifit/test_lin3.c gsl-doc-2.3/multifit/test_lin3.c
--- gsl-doc-1.16/multifit/test_lin3.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_lin3.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,94 @@
+#define lin3_N         50  /* can be anything >= p */
+#define lin3_P         10  /* >= 3 */
+
+#define lin3_NTRIES    3
+
+static double lin3_x0[lin3_P] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
+static double lin3_epsrel = 1.0e-10;
+
+static void
+lin3_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double n = (double) lin3_N;
+  const double sumsq_exact = 0.5 * (n*n + 3*n - 6.0) / (2*n - 3.0);
+  const double sum_exact = 3.0 / (2.0*n - 3.0);
+  double sum = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 1; i < lin3_P - 1; ++i)
+    sum += (i + 1.0) * x[i];
+
+  gsl_test_rel(sum, sum_exact, epsrel, "%s/%s coeff sum",
+               sname, pname);
+}
+
+static int
+lin3_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i, j;
+
+  gsl_vector_set(f, 0, -1.0);
+  gsl_vector_set(f, lin3_N - 1, -1.0);
+
+  for (i = 1; i < lin3_N - 1; ++i)
+    {
+      double fi = 0.0;
+
+      for (j = 1; j < lin3_P - 1; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+          fi += (j + 1) * xj;
+        }
+
+      fi = i * fi - 1.0;
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin3_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  size_t i, j;
+
+  gsl_matrix_set_zero(J);
+
+  for (i = 1; i < lin3_N - 1; ++i)
+    {
+      for (j = 1; j < lin3_P - 1; ++j)
+        {
+          gsl_matrix_set(J, i, j, i * (j + 1.0));
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf lin3_func =
+{
+  &lin3_f,
+  &lin3_df,
+  NULL,
+  lin3_N,
+  lin3_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem lin3_problem =
+{
+  "linear_rank1zeros",
+  lin3_x0,
+  NULL,
+  &lin3_epsrel,
+  lin3_NTRIES,
+  &lin3_checksol,
+  &lin3_func
+};
diff -Nru gsl-doc-1.16/multifit/test_linear.c gsl-doc-2.3/multifit/test_linear.c
--- gsl-doc-1.16/multifit/test_linear.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_linear.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,82 @@
+/* multifit/test_linear.c
+ * 
+ * Copyright (C) 2007, 2013 Brian Gough, Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+static void
+test_random_vector(gsl_vector *v, const gsl_rng *r,
+                   const double lower, const double upper)
+{
+  size_t i;
+  size_t N = v->size;
+
+  for (i = 0; i < N; ++i)
+    {
+      gsl_vector_set(v, i,
+                     gsl_rng_uniform(r) * (upper - lower) + lower);
+    }
+}
+
+static void
+test_random_matrix(gsl_matrix *m, const gsl_rng *r,
+                   const double lower, const double upper)
+{
+  size_t i, j;
+  size_t M = m->size1;
+  size_t N = m->size2;
+
+  for (i = 0; i < M; ++i)
+    {
+      for (j = 0; j < N; ++j)
+      {
+        gsl_matrix_set(m, i, j,
+                       gsl_rng_uniform(r) * (upper - lower) + lower);
+      }
+    }
+}
+
+static void
+test_random_vector_noise(const gsl_rng *r, gsl_vector *y)
+{
+  size_t i;
+
+  for (i = 0; i < y->size; ++i)
+    {
+      double *ptr = gsl_vector_ptr(y, i);
+      *ptr += 1.0e-3 * gsl_rng_uniform(r);
+    }
+}
+
+#include "test_longley.c"
+#include "test_filip.c"
+#include "test_pontius.c"
+#include "test_estimator.c"
+#include "test_reg.c"
+#include "test_shaw.c"
+
+/* test linear regression */
+
+void
+test_linear(void)
+{
+  test_longley();
+  test_filip();
+  test_pontius();
+  test_estimator();
+  test_reg();
+  test_shaw();
+}
diff -Nru gsl-doc-1.16/multifit/test_longley.c gsl-doc-2.3/multifit/test_longley.c
--- gsl-doc-1.16/multifit/test_longley.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/test_longley.c	2015-11-03 16:21:55.000000000 +0000
@@ -111,7 +111,6 @@
                        &diag.vector, &exp_sd.vector,
                        1.0, 1.0, 1.0);
 
-
   /* test weighted least squares */
   {
     size_t i, j;
diff -Nru gsl-doc-1.16/multifit/test_meyer.c gsl-doc-2.3/multifit/test_meyer.c
--- gsl-doc-1.16/multifit/test_meyer.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_meyer.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,98 @@
+#define meyer_N         16
+#define meyer_P         3
+
+#define meyer_NTRIES    1
+
+static double meyer_x0[meyer_P] = { 0.02, 4000.0, 250.0 };
+static double meyer_epsrel = 1.0e-8;
+
+static double meyer_Y[meyer_N] = {
+34780., 28610., 23650., 19630., 16370., 13720., 11540.,
+9744.,  8261.,  7030.,  6005., 5147., 4427., 3820.,
+3307.,  2872.
+};
+
+static void
+meyer_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.794585517053883e+01;
+  const double meyer_x[meyer_P] = { 5.609636471049458e-03,
+                                    6.181346346283188e+03,
+                                    3.452236346240292e+02 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < meyer_P; ++i)
+    {
+      gsl_test_rel(x[i], meyer_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+meyer_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < meyer_N; ++i)
+    {
+      double ti = 45.0 + 5.0*(i + 1.0);
+      double yi = meyer_Y[i];
+      double fi = x1 * exp(x2 / (ti + x3)) - yi;
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+meyer_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < meyer_N; ++i)
+    {
+      double ti = 45.0 + 5.0*(i + 1.0);
+      double term1 = ti + x3;
+      double term2 = exp(x2 / term1);
+
+      gsl_matrix_set(J, i, 0, term2);
+      gsl_matrix_set(J, i, 1, x1*term2/term1);
+      gsl_matrix_set(J, i, 2, -x1*x2*term2/(term1*term1));
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf meyer_func =
+{
+  &meyer_f,
+  &meyer_df,
+  NULL,
+  meyer_N,
+  meyer_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem meyer_problem =
+{
+  "meyer",
+  meyer_x0,
+  NULL,
+  &meyer_epsrel,
+  meyer_NTRIES,
+  &meyer_checksol,
+  &meyer_func
+};
diff -Nru gsl-doc-1.16/multifit/test_meyerscal.c gsl-doc-2.3/multifit/test_meyerscal.c
--- gsl-doc-1.16/multifit/test_meyerscal.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_meyerscal.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,98 @@
+#define meyerscal_N         16
+#define meyerscal_P         3
+
+#define meyerscal_NTRIES    1
+
+static double meyerscal_x0[meyerscal_P] = { 8.85, 4.0, 2.5 };
+static double meyerscal_epsrel = 1.0e-8;
+
+static double meyerscal_Y[meyerscal_N] = {
+34780., 28610., 23650., 19630., 16370., 13720., 11540.,
+9744.,  8261.,  7030.,  6005., 5147., 4427., 3820.,
+3307.,  2872.
+};
+
+static void
+meyerscal_checksol(const double x[], const double sumsq,
+                   const double epsrel, const char *sname,
+                   const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.794585517003888e-05;
+  const double meyerscal_x[meyerscal_P] = { 2.481778312286695e+00,
+                                            6.181346341853554e+00,
+                                            3.452236344749865e+00 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < meyerscal_P; ++i)
+    {
+      gsl_test_rel(x[i], meyerscal_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+meyerscal_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < meyerscal_N; ++i)
+    {
+      double ti = 0.45 + 0.05*(i + 1.0);
+      double yi = meyerscal_Y[i];
+      double fi = x1 * exp(10.0*x2 / (ti + x3) - 13.0) - 1.0e-3*yi;
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+meyerscal_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < meyerscal_N; ++i)
+    {
+      double ti = 0.45 + 0.05*(i + 1.0);
+      double term1 = ti + x3;
+      double term2 = exp(10.0*x2/term1 - 13.0);
+
+      gsl_matrix_set(J, i, 0, term2);
+      gsl_matrix_set(J, i, 1, 10.0*x1*term2/term1);
+      gsl_matrix_set(J, i, 2, -10.0*x1*x2*term2/(term1*term1));
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf meyerscal_func =
+{
+  &meyerscal_f,
+  &meyerscal_df,
+  NULL,
+  meyerscal_N,
+  meyerscal_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem meyerscal_problem =
+{
+  "meyerscal",
+  meyerscal_x0,
+  NULL,
+  &meyerscal_epsrel,
+  meyerscal_NTRIES,
+  &meyerscal_checksol,
+  &meyerscal_func
+};
diff -Nru gsl-doc-1.16/multifit/test_nelson.c gsl-doc-2.3/multifit/test_nelson.c
--- gsl-doc-1.16/multifit/test_nelson.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/test_nelson.c	2015-11-03 16:21:55.000000000 +0000
@@ -200,18 +200,3 @@
 
   return GSL_SUCCESS;
 }
-
-int
-nelson_fdf (const gsl_vector * x, void *params,
-           gsl_vector * f, gsl_matrix * df)
-{
-  nelson_f (x, params, f);
-  nelson_df (x, params, df);
-
-  return GSL_SUCCESS;
-}
-
-
-
-
-
diff -Nru gsl-doc-1.16/multifit/test_nonlinear.c gsl-doc-2.3/multifit/test_nonlinear.c
--- gsl-doc-1.16/multifit/test_nonlinear.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_nonlinear.c	2016-07-07 20:36:10.000000000 +0000
@@ -0,0 +1,580 @@
+/* multifit/test_nonlinear.c
+ * 
+ * Copyright (C) 2007, 2013, 2014 Brian Gough, Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+typedef struct
+{
+  const char *name;
+  double *x0;       /* initial parameters (size p) */
+  double *sigma;
+  double *epsrel;   /* relative tolerance for solution checking */
+  size_t ntries;
+  void (*checksol) (const double x[], const double sumsq,
+                    const double epsrel, const char *sname,
+                    const char *pname);
+  gsl_multifit_function_fdf *fdf;
+} test_fdf_problem;
+
+#include "test_bard.c"
+#include "test_beale.c"
+#include "test_biggs.c"
+#include "test_box.c"
+#include "test_boxbod.c"
+#include "test_brown1.c"
+#include "test_brown2.c"
+#include "test_brown3.c"
+#include "test_eckerle.c"
+#include "test_enso.c"
+#include "test_exp1.c"
+#include "test_gaussian.c"
+#include "test_hahn1.c"
+#include "test_helical.c"
+#include "test_jennrich.c"
+#include "test_kirby2.c"
+#include "test_kowalik.c"
+#include "test_lin1.c"
+#include "test_lin2.c"
+#include "test_lin3.c"
+#include "test_meyer.c"
+#include "test_meyerscal.c"
+#include "test_osborne.c"
+#include "test_penalty1.c"
+#include "test_penalty2.c"
+#include "test_powell1.c"
+#include "test_powell2.c"
+#include "test_powell3.c"
+#include "test_rat42.c"
+#include "test_rat43.c"
+#include "test_rosenbrock.c"
+#include "test_rosenbrocke.c"
+#include "test_roth.c"
+#include "test_thurber.c"
+#include "test_vardim.c"
+#include "test_watson.c"
+#include "test_wood.c"
+
+#include "test_wnlin.c"
+
+static void test_fdf(const gsl_multifit_fdfsolver_type * T,
+                     const double xtol, const double gtol,
+                     const double ftol, const double epsrel,
+                     const double x0_scale, test_fdf_problem *problem,
+                     const double *wts);
+static void test_fdfridge(const gsl_multifit_fdfsolver_type * T,
+                          const double xtol, const double gtol,
+                          const double ftol, const double epsrel,
+                          const double x0_scale, test_fdf_problem *problem,
+                          const double *wts);
+static void test_fdf_checksol(const char *sname, const char *pname,
+                              const double epsrel,
+                              gsl_multifit_fdfsolver *s,
+                              test_fdf_problem *problem);
+static void test_scale_x0(gsl_vector *x0, const double scale);
+
+/*
+ * These test problems are taken from
+ *
+ * H. B. Nielsen, UCTP test problems for unconstrained optimization,
+ * IMM Department of Mathematical Modeling, Tech. Report IMM-REP-2000-17,
+ * 2000.
+ */
+static test_fdf_problem *test_fdf_nielsen[] = {
+  &lin1_problem,       /* 1 */
+  &lin2_problem,       /* 2 */
+  &lin3_problem,       /* 3 */
+  &rosenbrock_problem, /* 4 */
+  &helical_problem,    /* 5 */
+  &powell1_problem,    /* 6 */
+  &roth_problem,       /* 7 */
+  &bard_problem,       /* 8 */
+  &kowalik_problem,    /* 9 */
+  &meyer_problem,      /* 10 */
+  &watson_problem,     /* 11 */
+  &box_problem,        /* 12 */
+  &jennrich_problem,   /* 13 */
+  &brown1_problem,     /* 14 */
+  &brown2_problem,     /* 16 */
+  &osborne_problem,    /* 17 */
+  &exp1_problem,       /* 18 */
+  &meyerscal_problem,  /* 20 */
+
+  &powell2_problem,
+
+  NULL
+};
+
+/*
+ * These tests are from
+ *
+ * J. J. More, B. S. Garbow and K. E. Hillstrom, Testing
+ * Unconstrained Optimization Software, ACM Trans. Math. Soft.
+ * Vol 7, No 1, 1981.
+ *
+ * Many of these overlap with the Nielsen tests
+ */
+static test_fdf_problem *test_fdf_more[] = {
+  &rosenbrock_problem,   /* 1 */
+  &roth_problem,         /* 2 */
+  &powell3_problem,      /* 3 */
+  &brown3_problem,       /* 4 */
+  &beale_problem,        /* 5 */
+  &jennrich_problem,     /* 6 */
+  &helical_problem,      /* 7 */
+  &bard_problem,         /* 8 */
+  &gaussian_problem,     /* 9 */
+  &meyer_problem,        /* 10 */
+  &box_problem,          /* 12 */
+  &powell1_problem,      /* 13 */
+  &wood_problem,         /* 14 */
+  &kowalik_problem,      /* 15 */
+  &brown1_problem,       /* 16 */
+  &osborne_problem,      /* 17 */
+  &biggs_problem,        /* 18 */
+  &watson_problem,       /* 20 */
+  &rosenbrocke_problem,  /* 21 */
+  &penalty1_problem,     /* 23 */
+  &penalty2_problem,     /* 24 */
+  &vardim_problem,       /* 25 */
+  &brown2_problem,       /* 27 */
+  &lin1_problem,         /* 32 */
+  &lin2_problem,         /* 33 */
+  &lin3_problem,         /* 34 */
+
+  NULL
+};
+
+/* NIST test cases */
+static test_fdf_problem *test_fdf_nist[] = {
+  &kirby2_problem,
+  &hahn1_problem,
+  &enso_problem,
+  &thurber_problem,
+  &boxbod_problem,
+  &rat42_problem,
+  &eckerle_problem,
+  &rat43_problem,
+
+  NULL
+};
+
+static void
+test_nonlinear(void)
+{
+  const double xtol = pow(GSL_DBL_EPSILON, 0.9);
+  const double gtol = pow(GSL_DBL_EPSILON, 0.9);
+  const double ftol = 0.0;
+  size_t i, j;
+
+  /* Nielsen tests */
+  for (i = 0; test_fdf_nielsen[i] != NULL; ++i)
+    {
+      test_fdf_problem *problem = test_fdf_nielsen[i];
+      double epsrel = *(problem->epsrel);
+      double scale = 1.0;
+
+      for (j = 0; j < problem->ntries; ++j)
+        {
+          double eps_scale = epsrel * scale;
+
+          test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+                   eps_scale, scale, problem, NULL);
+          test_fdfridge(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+                        eps_scale, scale, problem, NULL);
+
+          /* test finite difference Jacobian */
+          {
+            gsl_multifit_function_fdf fdf;
+            fdf.df = problem->fdf->df;
+            problem->fdf->df = NULL;
+            test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+                     1.0e5 * eps_scale, 1.0, problem, NULL);
+            test_fdfridge(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+                          1.0e5 * eps_scale, 1.0, problem, NULL);
+            problem->fdf->df = fdf.df;
+          }
+
+          scale *= 10.0;
+        }
+
+      test_fdf(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,
+               10.0 * epsrel, 1.0, problem, NULL);
+    }
+
+  /* More tests */
+  for (i = 0; test_fdf_more[i] != NULL; ++i)
+    {
+      test_fdf_problem *problem = test_fdf_more[i];
+      double epsrel = *(problem->epsrel);
+      double scale = 1.0;
+
+      for (j = 0; j < problem->ntries; ++j)
+        {
+          double eps_scale = epsrel * scale;
+
+          test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+                   eps_scale, scale, problem, NULL);
+          test_fdfridge(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+                        eps_scale, scale, problem, NULL);
+
+          /* test finite difference Jacobian */
+          {
+            gsl_multifit_function_fdf fdf;
+            fdf.df = problem->fdf->df;
+            problem->fdf->df = NULL;
+            test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+                     1.0e5 * eps_scale, 1.0, problem, NULL);
+            test_fdfridge(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+                          1.0e5 * eps_scale, 1.0, problem, NULL);
+            problem->fdf->df = fdf.df;
+          }
+
+          scale *= 10.0;
+        }
+
+      test_fdf(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,
+               10.0 * epsrel, 1.0, problem, NULL);
+    }
+
+  /* NIST tests */
+  for (i = 0; test_fdf_nist[i] != NULL; ++i)
+    {
+      test_fdf_problem *problem = test_fdf_nist[i];
+      double epsrel = *(problem->epsrel);
+      double scale = 1.0;
+
+      for (j = 0; j < problem->ntries; ++j)
+        {
+          double eps_scale = epsrel * scale;
+
+          test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+                   eps_scale, scale, problem, NULL);
+          test_fdf(gsl_multifit_fdfsolver_lmder, xtol, gtol, ftol,
+                   eps_scale, scale, problem, NULL);
+
+          /* test finite difference Jacobian */
+          {
+            gsl_multifit_function_fdf fdf;
+            fdf.df = problem->fdf->df;
+            problem->fdf->df = NULL;
+            test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+                     eps_scale, 1.0, problem, NULL);
+            test_fdf(gsl_multifit_fdfsolver_lmder, xtol, gtol, ftol,
+                     eps_scale, scale, problem, NULL);
+            problem->fdf->df = fdf.df;
+          }
+
+          scale *= 10.0;
+        }
+
+      test_fdf(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,
+               epsrel, 1.0, problem, NULL);
+    }
+
+  /* test weighted nonlinear least squares */
+
+  /* internal weighting in _f and _df functions */
+  test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+           wnlin_epsrel, 1.0, &wnlin_problem1, NULL);
+  test_fdf(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,
+           wnlin_epsrel, 1.0, &wnlin_problem1, NULL);
+  test_fdfridge(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+                wnlin_epsrel, 1.0, &wnlin_problem1, NULL);
+  test_fdfridge(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,
+                wnlin_epsrel, 1.0, &wnlin_problem1, NULL);
+
+  /* weighting through fdfsolver_wset */
+  test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+           wnlin_epsrel, 1.0, &wnlin_problem2, wnlin_W);
+  test_fdf(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,
+           wnlin_epsrel, 1.0, &wnlin_problem2, wnlin_W);
+  test_fdfridge(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,
+                wnlin_epsrel, 1.0, &wnlin_problem2, wnlin_W);
+  test_fdfridge(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,
+                wnlin_epsrel, 1.0, &wnlin_problem2, wnlin_W);
+}
+
+/*
+test_fdf()
+  Test a weighted nonlinear least squares problem
+
+Inputs: T        - solver to use
+        xtol     - tolerance in x
+        gtol     - tolerance in gradient
+        ftol     - tolerance in residual vector
+        epsrel   - relative error tolerance in solution
+        x0_scale - to test robustness against starting points,
+                   the standard starting point in 'problem' is
+                   multiplied by this scale factor:
+                   x0 <- x0 * x0_scale
+                   If x0 = 0, then all components of x0 are set to
+                   x0_scale
+        problem  - contains the nonlinear problem and solution point
+        wts      - weight vector (NULL for unweighted)
+*/
+
+static void
+test_fdf(const gsl_multifit_fdfsolver_type * T, const double xtol,
+         const double gtol, const double ftol,
+         const double epsrel, const double x0_scale,
+         test_fdf_problem *problem,
+         const double *wts)
+{
+  gsl_multifit_function_fdf *fdf = problem->fdf;
+  const size_t n = fdf->n;
+  const size_t p = fdf->p;
+  const size_t max_iter = 1500;
+  gsl_vector *x0 = gsl_vector_alloc(p);
+  gsl_vector_view x0v = gsl_vector_view_array(problem->x0, p);
+  gsl_multifit_fdfsolver *s = gsl_multifit_fdfsolver_alloc (T, n, p);
+  const char *pname = problem->name;
+  char sname[2048];
+  int status, info;
+
+  sprintf(sname, "%s/scale=%g%s",
+    gsl_multifit_fdfsolver_name(s), x0_scale,
+    problem->fdf->df ? "" : "/fdiff");
+
+  /* scale starting point x0 */
+  gsl_vector_memcpy(x0, &x0v.vector);
+  test_scale_x0(x0, x0_scale);
+
+  if (wts)
+    {
+      gsl_vector_const_view wv = gsl_vector_const_view_array(wts, n);
+      gsl_multifit_fdfsolver_wset(s, fdf, x0, &wv.vector);
+    }
+  else
+    gsl_multifit_fdfsolver_set(s, fdf, x0);
+
+  status = gsl_multifit_fdfsolver_driver(s, max_iter, xtol, gtol,
+                                         ftol, &info);
+  gsl_test(status, "%s/%s did not converge, status=%s",
+           sname, pname, gsl_strerror(status));
+
+  /* check solution */
+  test_fdf_checksol(sname, pname, epsrel, s, problem);
+
+  if (wts == NULL)
+    {
+      /* test again with weighting matrix W = I */
+      gsl_vector *wv = gsl_vector_alloc(n);
+
+      sprintf(sname, "%s/scale=%g%s/weights",
+        gsl_multifit_fdfsolver_name(s), x0_scale,
+        problem->fdf->df ? "" : "/fdiff");
+
+      gsl_vector_memcpy(x0, &x0v.vector);
+      test_scale_x0(x0, x0_scale);
+
+      gsl_vector_set_all(wv, 1.0);
+      gsl_multifit_fdfsolver_wset(s, fdf, x0, wv);
+  
+      status = gsl_multifit_fdfsolver_driver(s, max_iter, xtol, gtol,
+                                             ftol, &info);
+      gsl_test(status, "%s/%s did not converge, status=%s",
+               sname, pname, gsl_strerror(status));
+
+      test_fdf_checksol(sname, pname, epsrel, s, problem);
+
+      gsl_vector_free(wv);
+    }
+
+  gsl_multifit_fdfsolver_free(s);
+  gsl_vector_free(x0);
+}
+
+/*
+test_fdfridge()
+  Test a nonlinear least squares problem
+
+Inputs: T        - solver to use
+        xtol     - tolerance in x
+        gtol     - tolerance in gradient
+        ftol     - tolerance in residual vector
+        epsrel   - relative error tolerance in solution
+        x0_scale - to test robustness against starting points,
+                   the standard starting point in 'problem' is
+                   multiplied by this scale factor:
+                   x0 <- x0 * x0_scale
+                   If x0 = 0, then all components of x0 are set to
+                   x0_scale
+        problem  - contains the nonlinear problem and solution point
+        wts      - weight vector
+*/
+
+static void
+test_fdfridge(const gsl_multifit_fdfsolver_type * T, const double xtol,
+              const double gtol, const double ftol,
+              const double epsrel, const double x0_scale,
+              test_fdf_problem *problem, const double *wts)
+{
+  gsl_multifit_function_fdf *fdf = problem->fdf;
+  const size_t n = fdf->n;
+  const size_t p = fdf->p;
+  const size_t max_iter = 1500;
+  gsl_vector *x0 = gsl_vector_alloc(p);
+  gsl_vector_view x0v = gsl_vector_view_array(problem->x0, p);
+  gsl_multifit_fdfridge *w = gsl_multifit_fdfridge_alloc (T, n, p);
+  const char *pname = problem->name;
+  char sname[2048];
+  int status, info;
+  double lambda = 0.0;
+
+  sprintf(sname, "ridge/%s", gsl_multifit_fdfridge_name(w));
+
+  /* scale starting point x0 */
+  gsl_vector_memcpy(x0, &x0v.vector);
+  test_scale_x0(x0, x0_scale);
+
+  /* test undamped case with lambda = 0 */
+  if (wts)
+    {
+      gsl_vector_const_view wv = gsl_vector_const_view_array(wts, n);
+      gsl_multifit_fdfridge_wset(w, fdf, x0, lambda, &wv.vector);
+    }
+  else
+    gsl_multifit_fdfridge_set(w, fdf, x0, lambda);
+
+  status = gsl_multifit_fdfridge_driver(w, max_iter, xtol, gtol,
+                                        ftol, &info);
+  gsl_test(status, "%s/%s did not converge, status=%s",
+           sname, pname, gsl_strerror(status));
+
+  /* check solution */
+  test_fdf_checksol(sname, pname, epsrel, w->s, problem);
+
+  /* test for self consisent solution with L = \lambda I */
+  {
+    const double eps = 1.0e-10;
+    gsl_matrix *L = gsl_matrix_calloc(p, p);
+    gsl_vector_view diag = gsl_matrix_diagonal(L);
+    gsl_multifit_fdfridge *w2 = gsl_multifit_fdfridge_alloc (T, n, p);
+    gsl_vector *y0 = gsl_vector_alloc(p);
+    size_t i;
+
+    /* pick some value for lambda and set L = \lambda I */
+    lambda = 5.0;
+    gsl_vector_set_all(&diag.vector, lambda);
+
+    /* scale initial vector */
+    gsl_vector_memcpy(x0, &x0v.vector);
+    test_scale_x0(x0, x0_scale);
+    gsl_vector_memcpy(y0, x0);
+
+    if (wts)
+      {
+        gsl_vector_const_view wv = gsl_vector_const_view_array(wts, n);
+        gsl_multifit_fdfridge_wset(w, fdf, x0, lambda, &wv.vector);
+        gsl_multifit_fdfridge_wset3(w2, fdf, y0, L, &wv.vector);
+      }
+    else
+      {
+        gsl_multifit_fdfridge_set(w, fdf, x0, lambda);
+        gsl_multifit_fdfridge_set3(w2, fdf, y0, L);
+      }
+
+    /* solve with scalar lambda routine */
+    status = gsl_multifit_fdfridge_driver(w, max_iter, xtol, gtol,
+                                          ftol, &info);
+    gsl_test(status, "%s/lambda/%s did not converge, status=%s",
+             sname, pname, gsl_strerror(status));
+
+    /* solve with general matrix routine */
+    status = gsl_multifit_fdfridge_driver(w2, max_iter, xtol, gtol,
+                                          ftol, &info);
+    gsl_test(status, "%s/L/%s did not converge, status=%s",
+             sname, pname, gsl_strerror(status));
+
+    /* test x = y */
+    for (i = 0; i < p; ++i)
+      {
+        double xi = gsl_vector_get(w->s->x, i);
+        double yi = gsl_vector_get(w2->s->x, i);
+
+        if (fabs(xi) < eps)
+          {
+            gsl_test_abs(yi, xi, eps, "%s/%s ridge lambda=%g i=%zu",
+                         sname, pname, lambda, i);
+          }
+        else
+          {
+            gsl_test_rel(yi, xi, eps, "%s/%s ridge lambda=%g i=%zu",
+                         sname, pname, lambda, i);
+          }
+      }
+
+    gsl_matrix_free(L);
+    gsl_vector_free(y0);
+    gsl_multifit_fdfridge_free(w2);
+  }
+
+  gsl_multifit_fdfridge_free(w);
+  gsl_vector_free(x0);
+}
+
+static void
+test_fdf_checksol(const char *sname, const char *pname,
+                  const double epsrel, gsl_multifit_fdfsolver *s,
+                  test_fdf_problem *problem)
+{
+  gsl_multifit_function_fdf *fdf = problem->fdf;
+  const double *sigma = problem->sigma;
+  gsl_vector *f = gsl_multifit_fdfsolver_residual(s);
+  gsl_vector *x = gsl_multifit_fdfsolver_position(s);
+  double sumsq;
+
+  /* check solution vector x and sumsq = ||f||^2 */
+  gsl_blas_ddot(f, f, &sumsq);
+  (problem->checksol)(x->data, sumsq, epsrel, sname, pname);
+
+#if 1
+  /* check variances */
+  if (sigma)
+    {
+      const size_t n = fdf->n;
+      const size_t p = fdf->p;
+      size_t i;
+      gsl_matrix * J = gsl_matrix_alloc(n, p);
+      gsl_matrix * covar = gsl_matrix_alloc (p, p);
+
+      gsl_multifit_fdfsolver_jac (s, J);
+      gsl_multifit_covar(J, 0.0, covar);
+
+      for (i = 0; i < p; i++) 
+        {
+          double ei = sqrt(sumsq/(n-p))*sqrt(gsl_matrix_get(covar,i,i));
+          gsl_test_rel (ei, sigma[i], epsrel, 
+                        "%s/%s, sigma(%d)", sname, pname, i) ;
+        }
+
+      gsl_matrix_free (J);
+      gsl_matrix_free (covar);
+    }
+#endif
+}
+
+static void
+test_scale_x0(gsl_vector *x0, const double scale)
+{
+  double nx = gsl_blas_dnrm2(x0);
+
+  if (nx == 0.0)
+    gsl_vector_set_all(x0, scale);
+  else
+    gsl_vector_scale(x0, scale);
+} /* test_scale_x0() */
diff -Nru gsl-doc-1.16/multifit/test_osborne.c gsl-doc-2.3/multifit/test_osborne.c
--- gsl-doc-1.16/multifit/test_osborne.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_osborne.c	2016-11-30 21:29:39.000000000 +0000
@@ -0,0 +1,105 @@
+#define osborne_N         33
+#define osborne_P         5
+
+#define osborne_NTRIES    3
+
+static double osborne_x0[osborne_P] = { 0.5, 1.5, -1.0, 0.01, 0.02 };
+static double osborne_epsrel = 1.0e-8;
+
+static double osborne_Y[osborne_N] = {
+0.844, 0.908, 0.932, 0.936, 0.925, 0.908, 0.881,
+0.850, 0.818, 0.784, 0.751, 0.718, 0.685, 0.658,
+0.628, 0.603, 0.580, 0.558, 0.538, 0.522, 0.506,
+0.490, 0.478, 0.467, 0.457, 0.448, 0.438, 0.431,
+0.424, 0.420, 0.414, 0.411, 0.406
+};
+
+static void
+osborne_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  const double sumsq_exact = 5.464894697482687e-05;
+  const double osborne_x[osborne_P] = {
+    3.754100521058740e-01,
+   -99999.0,
+   -99999.0,
+   -99999.0,
+   -99999.0 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  /* only the first model parameter is uniquely constrained */
+  gsl_test_rel(x[0], osborne_x[0], epsrel, "%s/%s i=0",
+               sname, pname);
+}
+
+static int
+osborne_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  size_t i;
+
+  for (i = 0; i < osborne_N; ++i)
+    {
+      double ti = 10.0*i;
+      double yi = osborne_Y[i];
+      double fi = yi - (x1 + x2*exp(-x4*ti) + x3*exp(-x5*ti));
+      gsl_vector_set(f, i, fi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+osborne_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  size_t i;
+
+  for (i = 0; i < osborne_N; ++i)
+    {
+      double ti = 10.0*i;
+      double term1 = exp(-x4*ti);
+      double term2 = exp(-x5*ti);
+
+      gsl_matrix_set(J, i, 0, -1.0);
+      gsl_matrix_set(J, i, 1, -term1);
+      gsl_matrix_set(J, i, 2, -term2);
+      gsl_matrix_set(J, i, 3, ti*x2*term1);
+      gsl_matrix_set(J, i, 4, ti*x3*term2);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf osborne_func =
+{
+  &osborne_f,
+  &osborne_df,
+  NULL,
+  osborne_N,
+  osborne_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem osborne_problem =
+{
+  "osborne",
+  osborne_x0,
+  NULL,
+  &osborne_epsrel,
+  osborne_NTRIES,
+  &osborne_checksol,
+  &osborne_func
+};
diff -Nru gsl-doc-1.16/multifit/test_penalty1.c gsl-doc-2.3/multifit/test_penalty1.c
--- gsl-doc-1.16/multifit/test_penalty1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_penalty1.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,86 @@
+#define penalty1_N         11 /* p + 1 */
+#define penalty1_P         10
+
+#define penalty1_NTRIES    4
+
+static double penalty1_x0[penalty1_P] = { 1.0, 2.0, 3.0, 4.0, 5.0,
+                                          6.0, 7.0, 8.0, 9.0, 10.0 };
+
+static double penalty1_epsrel = 1.0e-12;
+
+static void
+penalty1_checksol(const double x[], const double sumsq,
+                  const double epsrel, const char *sname,
+                  const char *pname)
+{
+  const double sumsq_exact = 7.08765146709037993e-05;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+}
+
+static int
+penalty1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  size_t i;
+  double sum = 0.0;
+
+  for (i = 0; i < penalty1_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+
+      gsl_vector_set(f, i, sqrt_alpha*(xi - 1.0));
+
+      sum += xi * xi;
+    }
+
+  gsl_vector_set(f, penalty1_P, sum - 0.25);
+
+  return GSL_SUCCESS;
+}
+
+static int
+penalty1_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  size_t i;
+  gsl_matrix_view m = gsl_matrix_submatrix(J, 0, 0, penalty1_P, penalty1_P);
+  gsl_vector_view diag = gsl_matrix_diagonal(&m.matrix);
+
+  gsl_matrix_set_zero(&m.matrix);
+  gsl_vector_set_all(&diag.vector, sqrt_alpha);
+
+  for (i = 0; i < penalty1_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      gsl_matrix_set(J, penalty1_P, i, 2.0 * xi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf penalty1_func =
+{
+  &penalty1_f,
+  &penalty1_df,
+  NULL,
+  penalty1_N,
+  penalty1_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem penalty1_problem =
+{
+  "penalty1",
+  penalty1_x0,
+  NULL,
+  &penalty1_epsrel,
+  penalty1_NTRIES,
+  &penalty1_checksol,
+  &penalty1_func
+};
diff -Nru gsl-doc-1.16/multifit/test_penalty2.c gsl-doc-2.3/multifit/test_penalty2.c
--- gsl-doc-1.16/multifit/test_penalty2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_penalty2.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,128 @@
+#define penalty2_N         8 /* 2*p */
+#define penalty2_P         4
+
+#define penalty2_NTRIES    3
+
+static double penalty2_x0[penalty2_P] = { 0.5, 0.5, 0.5, 0.5 };
+static double penalty2_epsrel = 1.0e-12;
+
+static void
+penalty2_checksol(const double x[], const double sumsq,
+                  const double epsrel, const char *sname,
+                  const char *pname)
+{
+  const double sumsq_exact = 9.37629300735544219e-06;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+}
+
+static int
+penalty2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  double x1 = gsl_vector_get(x, 0);
+  size_t i;
+  double sum = penalty2_P * x1 * x1;
+
+  gsl_vector_set(f, 0, x1 - 0.2);
+
+  /* rows [2:p] */
+  for (i = 1; i < penalty2_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      double xim1 = gsl_vector_get(x, i - 1);
+      double yi = exp(0.1*(i + 1.0)) + exp(0.1*i);
+
+      gsl_vector_set(f, i, sqrt_alpha*(exp(0.1*xi) + exp(0.1*xim1) - yi));
+
+      sum += (penalty2_P - i) * xi * xi;
+    }
+
+  /* rows [p+1:2p-1] */
+  for (i = penalty2_P; i < penalty2_N - 1; ++i)
+    {
+      double xi = gsl_vector_get(x, i - penalty2_P + 1);
+
+      gsl_vector_set(f, i, sqrt_alpha*(exp(0.1*xi) - exp(-0.1)));
+    }
+
+  /* row 2p */
+  gsl_vector_set(f, penalty2_N - 1, sum - 1.0);
+
+  return GSL_SUCCESS;
+}
+
+static int
+penalty2_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  size_t i, j;
+
+  for (j = 0; j < penalty2_P; ++j)
+    {
+      double xj = gsl_vector_get(x, j);
+      double delta1j = (j == 0) ? 1.0 : 0.0;
+
+      /* first and last rows */
+      gsl_matrix_set(J, 0, j, delta1j);
+      gsl_matrix_set(J, penalty2_N - 1, j, 2.0 * (penalty2_P - j) * xj);
+
+      /* rows [2:p] */
+      for (i = 1; i < penalty2_P; ++i)
+        {
+          double xi = gsl_vector_get(x, i);
+          double xim1 = gsl_vector_get(x, i - 1);
+          double Jij;
+
+          if (i == j)
+            Jij = exp(0.1 * xi);
+          else if (i - 1 == j)
+            Jij = exp(0.1 * xim1);
+          else
+            Jij = 0.0;
+
+          Jij *= 0.1 * sqrt_alpha;
+
+          gsl_matrix_set(J, i, j, Jij);
+        }
+
+      /* rows [p+1:2p-1] */
+      for (i = penalty2_P; i < penalty2_N - 1; ++i)
+        {
+          double xi = gsl_vector_get(x, i - penalty2_P + 1);
+
+          if (i - penalty2_P + 1 == j)
+            gsl_matrix_set(J, i, j, 0.1 * sqrt_alpha * exp(0.1*xi));
+          else
+            gsl_matrix_set(J, i, j, 0.0);
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf penalty2_func =
+{
+  &penalty2_f,
+  &penalty2_df,
+  NULL,
+  penalty2_N,
+  penalty2_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem penalty2_problem =
+{
+  "penalty2",
+  penalty2_x0,
+  NULL,
+  &penalty2_epsrel,
+  penalty2_NTRIES,
+  &penalty2_checksol,
+  &penalty2_func
+};
diff -Nru gsl-doc-1.16/multifit/test_powell1.c gsl-doc-2.3/multifit/test_powell1.c
--- gsl-doc-1.16/multifit/test_powell1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_powell1.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,97 @@
+#define powell1_N        4
+#define powell1_P        4
+
+#define powell1_NTRIES   4
+
+static double powell1_x0[powell1_P] = { 3.0, -1.0, 0.0, 1.0 };
+static double powell1_epsrel = 1.0e-5;
+
+static void
+powell1_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < powell1_P; ++i)
+    {
+      gsl_test_rel(x[i], 0.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+powell1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get (x, 0);
+  double x2 = gsl_vector_get (x, 1);
+  double x3 = gsl_vector_get (x, 2);
+  double x4 = gsl_vector_get (x, 3);
+
+  gsl_vector_set(f, 0, x1 + 10.0*x2);
+  gsl_vector_set(f, 1, sqrt(5.0) * (x3 - x4));
+  gsl_vector_set(f, 2, pow(x2 - 2.0*x3, 2.0));
+  gsl_vector_set(f, 3, sqrt(10.0) * pow((x1 - x4), 2.0));
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell1_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get (x, 0);
+  double x2 = gsl_vector_get (x, 1);
+  double x3 = gsl_vector_get (x, 2);
+  double x4 = gsl_vector_get (x, 3);
+  double term1 = x2 - 2.0*x3;
+  double term2 = x1 - x4;
+
+  gsl_matrix_set(J, 0, 0, 1.0);
+  gsl_matrix_set(J, 0, 1, 10.0);
+  gsl_matrix_set(J, 0, 2, 0.0);
+  gsl_matrix_set(J, 0, 3, 0.0);
+
+  gsl_matrix_set(J, 1, 0, 0.0);
+  gsl_matrix_set(J, 1, 1, 0.0);
+  gsl_matrix_set(J, 1, 2, sqrt(5.0));
+  gsl_matrix_set(J, 1, 3, -sqrt(5.0));
+
+  gsl_matrix_set(J, 2, 0, 0.0);
+  gsl_matrix_set(J, 2, 1, 2.0*term1);
+  gsl_matrix_set(J, 2, 2, -4.0*term1);
+  gsl_matrix_set(J, 2, 3, 0.0);
+
+  gsl_matrix_set(J, 3, 0, 2.0*sqrt(10.0)*term2);
+  gsl_matrix_set(J, 3, 1, 0.0);
+  gsl_matrix_set(J, 3, 2, 0.0);
+  gsl_matrix_set(J, 3, 3, -2.0*sqrt(10.0)*term2);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf powell1_func =
+{
+  &powell1_f,
+  &powell1_df,
+  NULL,
+  powell1_N,
+  powell1_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem powell1_problem =
+{
+  "powell_singular",
+  powell1_x0,
+  NULL,
+  &powell1_epsrel,
+  powell1_NTRIES,
+  &powell1_checksol,
+  &powell1_func
+};
diff -Nru gsl-doc-1.16/multifit/test_powell2.c gsl-doc-2.3/multifit/test_powell2.c
--- gsl-doc-1.16/multifit/test_powell2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_powell2.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,75 @@
+#define powell2_N        2
+#define powell2_P        2
+
+#define powell2_NTRIES   3
+
+static double powell2_x0[powell2_P] = { 3.0, 1.0 };
+static double powell2_epsrel = 1.0e-7;
+
+static void
+powell2_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < powell2_P; ++i)
+    {
+      gsl_test_rel(x[i], 0.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+powell2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x0 = gsl_vector_get (x, 0);
+  double x1 = gsl_vector_get (x, 1);
+
+  gsl_vector_set(f, 0, x0);
+  gsl_vector_set(f, 1, 10.0*x0/(x0 + 0.1) + 2.0*x1*x1);
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell2_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double x0 = gsl_vector_get (x, 0);
+  double x1 = gsl_vector_get (x, 1);
+  double term = x0 + 0.1;
+
+  gsl_matrix_set(df, 0, 0, 1.0);
+  gsl_matrix_set(df, 0, 1, 0.0);
+  gsl_matrix_set(df, 1, 0, 1.0 / (term * term));
+  gsl_matrix_set(df, 1, 1, 4.0 * x1);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf powell2_func =
+{
+  &powell2_f,
+  &powell2_df,
+  NULL,
+  powell2_N,
+  powell2_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem powell2_problem =
+{
+  "powell2",
+  powell2_x0,
+  NULL,
+  &powell2_epsrel,
+  powell2_NTRIES,
+  &powell2_checksol,
+  &powell2_func
+};
diff -Nru gsl-doc-1.16/multifit/test_powell3.c gsl-doc-2.3/multifit/test_powell3.c
--- gsl-doc-1.16/multifit/test_powell3.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_powell3.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,77 @@
+#define powell3_N         2
+#define powell3_P         2
+
+#define powell3_NTRIES    1
+
+static double powell3_x0[powell3_P] = { 0.0, 1.0 };
+static double powell3_epsrel = 1.0e-12;
+
+static void
+powell3_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double powell3_x[powell3_P] = { 1.09815932969975976e-05,
+                                        9.10614673986700218 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < powell3_P; ++i)
+    {
+      gsl_test_rel(x[i], powell3_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+powell3_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, 1.0e4*x1*x2 - 1.0);
+  gsl_vector_set(f, 1, exp(-x1) + exp(-x2) - 1.0001);
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell3_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_matrix_set(J, 0, 0, 1.0e4*x2);
+  gsl_matrix_set(J, 0, 1, 1.0e4*x1);
+
+  gsl_matrix_set(J, 1, 0, -exp(-x1));
+  gsl_matrix_set(J, 1, 1, -exp(-x2));
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf powell3_func =
+{
+  &powell3_f,
+  &powell3_df,
+  NULL,
+  powell3_N,
+  powell3_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem powell3_problem =
+{
+  "powell_badly_scaled",
+  powell3_x0,
+  NULL,
+  &powell3_epsrel,
+  powell3_NTRIES,
+  &powell3_checksol,
+  &powell3_func
+};
diff -Nru gsl-doc-1.16/multifit/test_rat42.c gsl-doc-2.3/multifit/test_rat42.c
--- gsl-doc-1.16/multifit/test_rat42.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_rat42.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,109 @@
+#define rat42_N       9
+#define rat42_P       3
+
+#define rat42_NTRIES  1
+
+static double rat42_x0[rat42_P] = { 100.0, 1.0, 0.1 };
+static double rat42_epsrel = 1.0e-7;
+
+static double rat42_sigma[rat42_P] = {
+  1.7340283401E+00, 8.8295217536E-02, 3.4465663377E-03
+};
+
+static double rat42_X[rat42_N] = { 9.0, 14.0, 21.0, 28.0, 42.0,
+                                   57.0, 63.0, 70.0, 79.0 };
+
+static double rat42_F[rat42_N] = { 8.930, 10.800, 18.590, 22.330,
+                                   39.350, 56.110, 61.730, 64.620,
+                                   67.080 };
+
+static void
+rat42_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.0565229338E+00;
+  const double rat42_x[rat42_P] = { 7.2462237576E+01,
+                                    2.6180768402E+00,
+                                    6.7359200066E-02 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < rat42_P; ++i)
+    {
+      gsl_test_rel(x[i], rat42_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+rat42_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[rat42_P];
+  size_t i;
+
+  for (i = 0; i < rat42_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < rat42_N; i++)
+    {
+      double xi = rat42_X[i];
+      double yi = b[0] / (1.0 + exp(b[1] - b[2]*xi));
+      gsl_vector_set (f, i, yi - rat42_F[i]);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+rat42_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[rat42_P];
+  size_t i;
+
+  for (i = 0; i < rat42_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < rat42_N; i++)
+    {
+      double xi = rat42_X[i];
+      double term1 = exp(b[1] - b[2]*xi);
+      double term2 = 1.0 + term1;
+
+      gsl_matrix_set (df, i, 0, 1.0 / term2);
+      gsl_matrix_set (df, i, 1, -b[0] * term1 / (term2 * term2));
+      gsl_matrix_set (df, i, 2, b[0] * term1 * xi / (term2 * term2));
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf rat42_func =
+{
+  &rat42_f,
+  &rat42_df,
+  NULL,
+  rat42_N,
+  rat42_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem rat42_problem =
+{
+  "nist-rat42",
+  rat42_x0,
+  rat42_sigma,
+  &rat42_epsrel,
+  rat42_NTRIES,
+  &rat42_checksol,
+  &rat42_func
+};
diff -Nru gsl-doc-1.16/multifit/test_rat43.c gsl-doc-2.3/multifit/test_rat43.c
--- gsl-doc-1.16/multifit/test_rat43.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_rat43.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,112 @@
+#define rat43_N       15
+#define rat43_P       4
+
+#define rat43_NTRIES  1
+
+static double rat43_x0[rat43_P] = { 100.0, 10.0, 1.0, 1.0 };
+static double rat43_epsrel = 1.0e-6;
+
+static double rat43_sigma[rat43_P] = {
+  1.6302297817E+01, 2.0828735829E+00,
+  1.9566123451E-01, 6.8761936385E-01
+};
+
+static double rat43_F[rat43_N] = { 16.08, 33.83, 65.80, 97.20, 191.55,
+                                   326.20, 386.87, 520.53, 590.03,
+                                   651.92, 724.93, 699.56, 689.96,
+                                   637.56, 717.41 };
+
+static void
+rat43_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.7864049080E+03;
+  const double rat43_x[rat43_P] = { 6.9964151270E+02,
+                                    5.2771253025E+00,
+                                    7.5962938329E-01,
+                                    1.2792483859E+00 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < rat43_P; ++i)
+    {
+      gsl_test_rel(x[i], rat43_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+rat43_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[rat43_P];
+  size_t i;
+
+  for (i = 0; i < rat43_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < rat43_N; i++)
+    {
+      double xi = i + 1.0;
+      double e = exp(b[1] - b[2]*xi);
+      double yi = b[0] / pow(1.0 + e, 1.0 / b[3]);
+      gsl_vector_set (f, i, yi - rat43_F[i]);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+rat43_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[rat43_P];
+  size_t i;
+
+  for (i = 0; i < rat43_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < rat43_N; i++)
+    {
+      double xi = i + 1.0;
+      double e = exp(b[1] - b[2]*xi);
+      double term1 = 1.0 + e;
+      double term2 = pow(term1, -1.0 / b[3]);
+
+      gsl_matrix_set (df, i, 0, term2);
+      gsl_matrix_set (df, i, 1, -b[0] / b[3] * e * term2 / term1);
+      gsl_matrix_set (df, i, 2, b[0] / b[3] * xi * e * term2 / term1);
+      gsl_matrix_set (df, i, 3, b[0] / b[3] / b[3] * log(term1) * term2);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf rat43_func =
+{
+  &rat43_f,
+  &rat43_df,
+  NULL,
+  rat43_N,
+  rat43_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem rat43_problem =
+{
+  "nist-rat43",
+  rat43_x0,
+  rat43_sigma,
+  &rat43_epsrel,
+  rat43_NTRIES,
+  &rat43_checksol,
+  &rat43_func
+};
diff -Nru gsl-doc-1.16/multifit/test_reg.c gsl-doc-2.3/multifit/test_reg.c
--- gsl-doc-1.16/multifit/test_reg.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_reg.c	2016-08-10 21:03:42.000000000 +0000
@@ -0,0 +1,548 @@
+/* generate random square orthogonal matrix via QR decomposition */
+static void
+test_random_matrix_orth(gsl_matrix *m, const gsl_rng *r)
+{
+  const size_t M = m->size1;
+  gsl_matrix *A = gsl_matrix_alloc(M, M);
+  gsl_vector *tau = gsl_vector_alloc(M);
+  gsl_matrix *R = gsl_matrix_alloc(M, M);
+
+  test_random_matrix(A, r, -1.0, 1.0);
+  gsl_linalg_QR_decomp(A, tau);
+  gsl_linalg_QR_unpack(A, tau, m, R);
+
+  gsl_matrix_free(A);
+  gsl_matrix_free(R);
+  gsl_vector_free(tau);
+}
+
+/* construct ill-conditioned matrix via SVD */
+static void
+test_random_matrix_ill(gsl_matrix *m, const gsl_rng *r)
+{
+  const size_t M = m->size1;
+  const size_t N = m->size2;
+  gsl_matrix *U = gsl_matrix_alloc(M, M);
+  gsl_matrix *V = gsl_matrix_alloc(N, N);
+  gsl_vector *S = gsl_vector_alloc(N);
+  gsl_matrix_view Uv = gsl_matrix_submatrix(U, 0, 0, M, N);
+  const double smin = 16.0 * GSL_DBL_EPSILON;
+  const double smax = 10.0;
+  const double ratio = pow(smin / smax, 1.0 / (N - 1.0));
+  double s;
+  size_t j;
+
+  test_random_matrix_orth(U, r);
+  test_random_matrix_orth(V, r);
+
+  /* compute U * S */
+
+  s = smax;
+  for (j = 0; j < N; ++j)
+    {
+      gsl_vector_view uj = gsl_matrix_column(U, j);
+
+      gsl_vector_scale(&uj.vector, s);
+      s *= ratio;
+    }
+
+  /* compute m = (U * S) * V' */
+  gsl_blas_dgemm(CblasNoTrans, CblasTrans, 1.0, &Uv.matrix, V, 0.0, m);
+
+  gsl_matrix_free(U);
+  gsl_matrix_free(V);
+  gsl_vector_free(S);
+}
+
+/* solve system with lambda = 0 and test against OLS solution */
+static void
+test_reg1(const gsl_matrix * X, const gsl_vector * y,
+          const gsl_vector * wts, const double tol,
+          gsl_multifit_linear_workspace * w, const char * desc)
+{
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+  double rnorm, snorm, chisq;
+  gsl_vector *c0 = gsl_vector_alloc(p);
+  gsl_vector *c1 = gsl_vector_alloc(p);
+  gsl_matrix *cov = gsl_matrix_alloc(p, p);
+  size_t j;
+
+  if (wts)
+    {
+      gsl_matrix *Xs = gsl_matrix_alloc(n, p);
+      gsl_vector *ys = gsl_vector_alloc(n);
+
+      gsl_multifit_wlinear(X, wts, y, c0, cov, &chisq, w);
+
+      gsl_multifit_linear_wstdform1(NULL, X, wts, y, Xs, ys, w);
+      gsl_multifit_linear_svd(Xs, w);
+      gsl_multifit_linear_solve(0.0, Xs, ys, c1, &rnorm, &snorm, w);
+
+      gsl_matrix_free(Xs);
+      gsl_vector_free(ys);
+    }
+  else
+    {
+      gsl_multifit_linear(X, y, c0, cov, &chisq, w);
+
+      gsl_multifit_linear_svd(X, w);
+      gsl_multifit_linear_solve(0.0, X, y, c1, &rnorm, &snorm, w);
+    }
+
+  gsl_test_rel(rnorm*rnorm, chisq, tol,
+               "test_reg1: %s, lambda = 0, n=%zu p=%zu chisq", desc, n, p);
+
+  /* test c0 = c1 */
+  for (j = 0; j < p; ++j)
+    {
+      double c0j = gsl_vector_get(c0, j);
+      double c1j = gsl_vector_get(c1, j);
+
+      gsl_test_rel(c1j, c0j, tol, "test_reg1: %s, lambda = 0, n=%zu p=%zu c0/c1",
+                   desc, n, p);
+    }
+
+  gsl_vector_free(c0);
+  gsl_vector_free(c1);
+  gsl_matrix_free(cov);
+}
+
+/* solve standard form system with given lambda and test against
+ * normal equations solution, L = I */
+static void
+test_reg2(const double lambda, const gsl_matrix * X, const gsl_vector * y,
+          const gsl_vector * wts, const double tol,
+          gsl_multifit_linear_workspace * w, const char * desc)
+{
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+  double rnorm0, snorm0;
+  double rnorm1, snorm1;
+  gsl_vector *c0 = gsl_vector_alloc(p);
+  gsl_vector *c1 = gsl_vector_alloc(p);
+  gsl_matrix *XTX = gsl_matrix_alloc(p, p); /* X^T W X + lambda^2 I */
+  gsl_vector *XTy = gsl_vector_alloc(p);    /* X^T W y */
+  gsl_matrix *Xs = gsl_matrix_alloc(n, p);
+  gsl_vector *ys = gsl_vector_alloc(n);
+  gsl_vector_view xtx_diag = gsl_matrix_diagonal(XTX);
+  gsl_permutation *perm = gsl_permutation_alloc(p);
+  gsl_vector *r = gsl_vector_alloc(n);
+  int signum;
+  size_t j;
+
+  /* compute Xs = sqrt(W) X and ys = sqrt(W) y */
+  gsl_multifit_linear_wstdform1(NULL, X, wts, y, Xs, ys, w);
+
+  /* construct XTy = X^T W y */
+  gsl_blas_dgemv(CblasTrans, 1.0, Xs, ys, 0.0, XTy);
+
+  /* construct XTX = X^T W X + lambda^2 I */
+  gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, Xs, Xs, 0.0, XTX);
+  gsl_vector_add_constant(&xtx_diag.vector, lambda*lambda);
+
+  /* solve XTX c = XTy with LU decomp */
+  gsl_linalg_LU_decomp(XTX, perm, &signum);
+  gsl_linalg_LU_solve(XTX, perm, XTy, c0);
+
+  /* compute SVD of X */
+  gsl_multifit_linear_svd(Xs, w);
+
+  /* solve regularized standard form system with lambda */
+  gsl_multifit_linear_solve(lambda, Xs, ys, c1, &rnorm0, &snorm0, w);
+
+  /* test snorm = ||c1|| */
+  snorm1 = gsl_blas_dnrm2(c1);
+  gsl_test_rel(snorm0, snorm1, tol, "test_reg2: %s, snorm lambda=%g n=%zu p=%zu",
+               desc, lambda, n, p);
+
+  /* test rnorm = ||y - X c1|| */
+  gsl_vector_memcpy(r, ys);
+  gsl_blas_dgemv(CblasNoTrans, -1.0, Xs, c1, 1.0, r);
+  rnorm1 = gsl_blas_dnrm2(r);
+  gsl_test_rel(rnorm0, rnorm1, tol, "test_reg2: %s, rnorm lambda=%g n=%zu p=%zu",
+               desc, lambda, n, p);
+
+  /* test c0 = c1 */
+  for (j = 0; j < p; ++j)
+    {
+      double c0j = gsl_vector_get(c0, j);
+      double c1j = gsl_vector_get(c1, j);
+
+      gsl_test_rel(c1j, c0j, tol, "test_reg2: %s, c0/c1 lambda=%g n=%zu p=%zu",
+                   desc, lambda, n, p);
+    }
+
+  gsl_matrix_free(XTX);
+  gsl_vector_free(XTy);
+  gsl_matrix_free(Xs);
+  gsl_vector_free(ys);
+  gsl_vector_free(c0);
+  gsl_vector_free(c1);
+  gsl_vector_free(r);
+  gsl_permutation_free(perm);
+}
+
+/* solve system with given lambda and L = diag(L) and test against
+ * normal equations solution */
+static void
+test_reg3(const double lambda, const gsl_vector * L, const gsl_matrix * X,
+          const gsl_vector * y, const gsl_vector * wts, const double tol,
+          gsl_multifit_linear_workspace * w, const char * desc)
+{
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+  double rnorm0, snorm0;
+  double rnorm1, snorm1;
+  gsl_vector *c0 = gsl_vector_alloc(p);
+  gsl_vector *c1 = gsl_vector_alloc(p);
+  gsl_matrix *XTX = gsl_matrix_alloc(p, p); /* X^T W X + lambda^2 L^T L */
+  gsl_vector *XTy = gsl_vector_alloc(p);    /* X^T W y */
+  gsl_matrix *Xs = gsl_matrix_alloc(n, p);  /* standard form X~ */
+  gsl_vector *ys = gsl_vector_alloc(n);     /* standard form y~ */
+  gsl_vector *Lc = gsl_vector_alloc(p);
+  gsl_vector *r = gsl_vector_alloc(n);
+  gsl_permutation *perm = gsl_permutation_alloc(p);
+  int signum;
+  size_t j;
+
+  /* compute Xs = sqrt(W) X, ys = sqrt(W) y */
+  gsl_multifit_linear_wstdform1(NULL, X, wts, y, Xs, ys, w);
+
+  /* construct XTy = X^T W y */
+  gsl_blas_dgemv(CblasTrans, 1.0, Xs, ys, 0.0, XTy);
+
+  /* construct XTX = X^T W X + lambda^2 L^T L */
+  gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, Xs, Xs, 0.0, XTX);
+
+  for (j = 0; j < p; ++j)
+    {
+      double lj = gsl_vector_get(L, j);
+      *gsl_matrix_ptr(XTX, j, j) += pow(lambda * lj, 2.0);
+    }
+
+  /* solve XTX c = XTy with LU decomp */
+  gsl_linalg_LU_decomp(XTX, perm, &signum);
+  gsl_linalg_LU_solve(XTX, perm, XTy, c0);
+
+  /* solve with reg routine */
+  gsl_multifit_linear_wstdform1(L, X, wts, y, Xs, ys, w);
+  gsl_multifit_linear_svd(Xs, w);
+  gsl_multifit_linear_solve(lambda, Xs, ys, c1, &rnorm0, &snorm0, w);
+  gsl_multifit_linear_genform1(L, c1, c1, w);
+
+  /* test snorm = ||L c1|| */
+  gsl_vector_memcpy(Lc, c1);
+  gsl_vector_mul(Lc, L);
+  snorm1 = gsl_blas_dnrm2(Lc);
+  gsl_test_rel(snorm0, snorm1, tol, "test_reg3: %s, snorm lambda=%g n=%zu p=%zu",
+               desc, lambda, n, p);
+
+  /* test rnorm = ||y - X c1||, compute again Xs = sqrt(W) X and ys = sqrt(W) y */
+  gsl_multifit_linear_wstdform1(NULL, X, wts, y, Xs, ys, w);
+  gsl_vector_memcpy(r, ys);
+  gsl_blas_dgemv(CblasNoTrans, -1.0, Xs, c1, 1.0, r);
+  rnorm1 = gsl_blas_dnrm2(r);
+  gsl_test_rel(rnorm0, rnorm1, tol, "test_reg3: %s, rnorm lambda=%g n=%zu p=%zu",
+               desc, lambda, n, p);
+
+  /* test c0 = c1 */
+  for (j = 0; j < p; ++j)
+    {
+      double c0j = gsl_vector_get(c0, j);
+      double c1j = gsl_vector_get(c1, j);
+
+      gsl_test_rel(c1j, c0j, tol, "test_reg3: %s, c0/c1 j=%zu lambda=%g n=%zu p=%zu",
+                   desc, j, lambda, n, p);
+    }
+
+  gsl_matrix_free(Xs);
+  gsl_matrix_free(XTX);
+  gsl_vector_free(XTy);
+  gsl_vector_free(c0);
+  gsl_vector_free(c1);
+  gsl_vector_free(Lc);
+  gsl_vector_free(ys);
+  gsl_vector_free(r);
+  gsl_permutation_free(perm);
+}
+
+/* solve system with given lambda and L and test against
+ * normal equations solution */
+static void
+test_reg4(const double lambda, const gsl_matrix * L, const gsl_matrix * X,
+          const gsl_vector * y, const gsl_vector * wts, const double tol,
+          gsl_multifit_linear_workspace * w, const char *desc)
+{
+  const size_t m = L->size1;
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+  double rnorm0, snorm0;
+  double rnorm1, snorm1;
+  gsl_vector *c0 = gsl_vector_alloc(p);
+  gsl_vector *c1 = gsl_vector_alloc(p);
+  gsl_matrix *LTL = gsl_matrix_alloc(p, p); /* L^T L */
+  gsl_matrix *XTX = gsl_matrix_alloc(p, p); /* X^T W X + lambda^2 L^T L */
+  gsl_vector *XTy = gsl_vector_alloc(p);    /* X^T W y */
+  gsl_permutation *perm = gsl_permutation_alloc(p);
+  gsl_matrix *Xs = (m < p) ? gsl_matrix_alloc(n - (p - m), m) : gsl_matrix_alloc(n, p);
+  gsl_vector *ys = (m < p) ? gsl_vector_alloc(n - (p - m)) : gsl_vector_alloc(n);
+  gsl_matrix *M = (m < p) ? gsl_matrix_alloc(n, p) : gsl_matrix_alloc(m, p);
+  gsl_vector *cs = (m < p) ? gsl_vector_alloc(m) : gsl_vector_alloc(p);
+  gsl_matrix *WX = gsl_matrix_alloc(n, p);
+  gsl_vector *Wy = gsl_vector_alloc(n);
+  gsl_vector *Lc = gsl_vector_alloc(m);
+  gsl_vector *r = gsl_vector_alloc(n);
+  gsl_matrix *LQR = gsl_matrix_alloc(m, p);
+  gsl_vector *Ltau = gsl_vector_alloc(GSL_MIN(m, p));
+  int signum;
+  size_t j;
+
+  /* compute WX = sqrt(W) X, Wy = sqrt(W) y */
+  gsl_multifit_linear_wstdform1(NULL, X, wts, y, WX, Wy, w);
+
+  /* construct XTy = X^T W y */
+  gsl_blas_dgemv(CblasTrans, 1.0, WX, Wy, 0.0, XTy);
+
+  /* construct XTX = X^T W X + lambda^2 L^T L */
+  gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, L, L, 0.0, LTL);
+  gsl_matrix_scale(LTL, lambda * lambda);
+
+  gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, WX, WX, 0.0, XTX);
+  gsl_matrix_add(XTX, LTL);
+
+  /* solve XTX c = XTy with LU decomp */
+  gsl_linalg_LU_decomp(XTX, perm, &signum);
+  gsl_linalg_LU_solve(XTX, perm, XTy, c0);
+
+  /* solve with reg routine */
+  gsl_matrix_memcpy(LQR, L);
+  gsl_multifit_linear_L_decomp(LQR, Ltau);
+  gsl_multifit_linear_wstdform2(LQR, Ltau, X, wts, y, Xs, ys, M, w);
+  gsl_multifit_linear_svd(Xs, w);
+  gsl_multifit_linear_solve(lambda, Xs, ys, cs, &rnorm0, &snorm0, w);
+  gsl_multifit_linear_wgenform2(LQR, Ltau, X, wts, y, cs, M, c1, w);
+
+  /* test snorm = ||L c1|| */
+  gsl_blas_dgemv(CblasNoTrans, 1.0, L, c1, 0.0, Lc);
+  snorm1 = gsl_blas_dnrm2(Lc);
+  gsl_test_rel(snorm0, snorm1, tol, "test_reg4: %s snorm lambda=%g", desc, lambda);
+
+  /* test rnorm = ||y - X c1||_W */
+  gsl_vector_memcpy(r, Wy);
+  gsl_blas_dgemv(CblasNoTrans, -1.0, WX, c1, 1.0, r);
+  rnorm1 = gsl_blas_dnrm2(r);
+  gsl_test_rel(rnorm0, rnorm1, tol, "test_reg4: %s rnorm lambda=%g", desc, lambda);
+
+  /* test c0 = c1 */
+  for (j = 0; j < p; ++j)
+    {
+      double c0j = gsl_vector_get(c0, j);
+      double c1j = gsl_vector_get(c1, j);
+
+      gsl_test_rel(c1j, c0j, tol, "test_reg4: %s lambda=%g n=%zu p=%zu j=%zu",
+                   desc, lambda, n, p, j);
+    }
+
+  gsl_matrix_free(LTL);
+  gsl_matrix_free(XTX);
+  gsl_vector_free(XTy);
+  gsl_vector_free(c0);
+  gsl_vector_free(c1);
+  gsl_permutation_free(perm);
+  gsl_matrix_free(Xs);
+  gsl_vector_free(ys);
+  gsl_vector_free(cs);
+  gsl_matrix_free(M);
+  gsl_vector_free(Lc);
+  gsl_matrix_free(WX);
+  gsl_vector_free(Wy);
+  gsl_vector_free(r);
+  gsl_matrix_free(LQR);
+  gsl_vector_free(Ltau);
+}
+
+static void
+test_reg_system(const size_t n, const size_t p, const gsl_rng *r)
+{
+  gsl_matrix *X = gsl_matrix_alloc(n, p);
+  gsl_vector *y = gsl_vector_alloc(n);
+  gsl_vector *c = gsl_vector_alloc(p);
+  gsl_vector *wts = gsl_vector_alloc(n);
+  gsl_multifit_linear_workspace *w = gsl_multifit_linear_alloc(n, p);
+  gsl_multifit_linear_workspace *wbig = gsl_multifit_linear_alloc(n + 10, p + 5);
+  gsl_vector *diagL = gsl_vector_alloc(p);
+  gsl_matrix *Lsqr = gsl_matrix_alloc(p, p);
+  gsl_matrix *Ltall = gsl_matrix_alloc(5*p, p);
+  gsl_matrix *L1 = gsl_matrix_alloc(p - 1, p);
+  gsl_matrix *L2 = gsl_matrix_alloc(p - 2, p);
+  gsl_matrix *L3 = gsl_matrix_alloc(p - 3, p);
+  gsl_matrix *L5 = gsl_matrix_alloc(p - 5, p);
+  size_t i;
+
+  /* generate random weights */
+  test_random_vector(wts, r, 0.0, 1.0);
+
+  /* generate well-conditioned system and test against OLS solution */
+  test_random_matrix(X, r, -1.0, 1.0);
+  test_random_vector(y, r, -1.0, 1.0);
+  test_reg1(X, y, NULL, 1.0e-10, w, "unweighted");
+  test_reg1(X, y, wts, 1.0e-10, w, "weighted");
+
+  /* generate ill-conditioned system */
+  test_random_matrix_ill(X, r);
+  test_random_vector(c, r, -1.0, 1.0);
+
+  /* compute y = X c + noise */
+  gsl_blas_dgemv(CblasNoTrans, 1.0, X, c, 0.0, y);
+  test_random_vector_noise(r, y);
+
+  /* random diag(L) vector */
+  test_random_vector(diagL, r, -2.0, 2.0);
+
+  /* random square and tall L matrices */
+  test_random_matrix(Lsqr, r, -2.0, 2.0);
+  test_random_matrix(Ltall, r, -2.0, 2.0);
+
+  gsl_multifit_linear_Lk(p, 1, L1);
+  gsl_multifit_linear_Lk(p, 2, L2);
+  gsl_multifit_linear_Lk(p, 3, L3);
+  gsl_multifit_linear_Lk(p, 5, L5);
+
+  for (i = 0; i < 3; ++i)
+    {
+      /*
+       * can't make lambda too small or normal equations
+       * approach won't work well
+       */
+      double lambda = pow(10.0, -(double) i);
+
+      /* test unweighted */
+      test_reg2(lambda, X, y, NULL, 1.0e-6, w, "unweighted");
+      test_reg3(lambda, diagL, X, y, NULL, 1.0e-6, w, "unweighted");
+      test_reg4(lambda, Lsqr, X, y, NULL, 1.0e-8, w, "Lsqr unweighted");
+      test_reg4(lambda, Ltall, X, y, NULL, 1.0e-8, w, "Ltall unweighted");
+      test_reg4(lambda, L1, X, y, NULL, 1.0e-6, w, "L1 unweighted");
+      test_reg4(lambda, L2, X, y, NULL, 1.0e-6, w, "L2 unweighted");
+      test_reg4(lambda, L3, X, y, NULL, 1.0e-5, w, "L3 unweighted");
+      test_reg4(lambda, L5, X, y, NULL, 1.0e-4, w, "L5 unweighted");
+
+      /* test weighted */
+      test_reg2(lambda, X, y, wts, 1.0e-6, w, "weighted");
+      test_reg3(lambda, diagL, X, y, wts, 1.0e-6, w, "weighted");
+      test_reg4(lambda, Lsqr, X, y, wts, 1.0e-8, w, "Lsqr weighted");
+      test_reg4(lambda, L1, X, y, wts, 1.0e-6, w, "L1 weighted");
+      test_reg4(lambda, L2, X, y, wts, 1.0e-6, w, "L2 weighted");
+      test_reg4(lambda, L3, X, y, wts, 1.0e-5, w, "L3 weighted");
+      test_reg4(lambda, L5, X, y, wts, 1.0e-4, w, "L5 weighted");
+
+      /* test again with larger workspace */
+      test_reg2(lambda, X, y, NULL, 1.0e-6, wbig, "unweighted big");
+      test_reg3(lambda, diagL, X, y, NULL, 1.0e-6, wbig, "unweighted big");
+      test_reg4(lambda, Lsqr, X, y, NULL, 1.0e-8, wbig, "Lsqr unweighted big");
+      test_reg4(lambda, L1, X, y, NULL, 1.0e-6, wbig, "L1 unweighted big");
+      test_reg4(lambda, L2, X, y, NULL, 1.0e-6, wbig, "L2 unweighted big");
+      test_reg4(lambda, L3, X, y, NULL, 1.0e-5, wbig, "L3 unweighted big");
+      test_reg4(lambda, L5, X, y, NULL, 1.0e-4, wbig, "L5 unweighted big");
+
+      test_reg2(lambda, X, y, wts, 1.0e-6, wbig, "weighted big");
+      test_reg3(lambda, diagL, X, y, wts, 1.0e-6, wbig, "weighted big");
+      test_reg4(lambda, Lsqr, X, y, wts, 1.0e-8, wbig, "Lsqr weighted big");
+      test_reg4(lambda, L1, X, y, wts, 1.0e-6, wbig, "L1 weighted big");
+      test_reg4(lambda, L2, X, y, wts, 1.0e-6, wbig, "L2 weighted big");
+      test_reg4(lambda, L3, X, y, wts, 1.0e-5, wbig, "L3 weighted big");
+      test_reg4(lambda, L5, X, y, wts, 1.0e-4, wbig, "L5 weighted big");
+    }
+
+  gsl_matrix_free(X);
+  gsl_vector_free(y);
+  gsl_vector_free(c);
+  gsl_vector_free(wts);
+  gsl_vector_free(diagL);
+  gsl_matrix_free(Lsqr);
+  gsl_matrix_free(Ltall);
+  gsl_matrix_free(L1);
+  gsl_matrix_free(L2);
+  gsl_matrix_free(L3);
+  gsl_matrix_free(L5);
+  gsl_multifit_linear_free(w);
+  gsl_multifit_linear_free(wbig);
+}
+
+static void
+test_reg_sobolev(const size_t p, const size_t kmax, const gsl_rng *r)
+{
+  const double tol = 1.0e-12;
+  size_t i, j, k;
+  gsl_matrix *L = gsl_matrix_calloc(p, p);
+  gsl_matrix *LTL = gsl_matrix_alloc(p, p);   /* Sobolov L^T L */
+  gsl_matrix *LTL2 = gsl_matrix_alloc(p, p);  /* alternate L^T L */
+  gsl_matrix *Li = gsl_matrix_alloc(p, p);
+  gsl_multifit_linear_workspace *w = gsl_multifit_linear_alloc(p, p);
+
+  for (k = 0; k <= kmax; ++k)
+    {
+      gsl_vector *alpha = gsl_vector_alloc(k + 1);
+
+      /* random weights */
+      test_random_vector(alpha, r, 0.0, 1.0);
+
+      /* compute Sobolev matrix */
+      gsl_multifit_linear_Lsobolev(p, k, alpha, L, w);
+
+      /* compute LTL = L^T L */
+      gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, L, L, 0.0, LTL);
+
+      /* now compute LTL2 = L^T L using individual L_i factors */
+      {
+        gsl_matrix_set_zero(LTL2);
+        for (i = 0; i <= k; ++i)
+          {
+            gsl_matrix_view Liv = gsl_matrix_submatrix(Li, 0, 0, p - i, p);
+            double ai = gsl_vector_get(alpha, i);
+
+            /* compute a_i L_i */
+            gsl_multifit_linear_Lk(p, i, &Liv.matrix);
+            gsl_matrix_scale(&Liv.matrix, ai);
+
+            /* LTL += L_i^T L_i */
+            gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, &Liv.matrix, &Liv.matrix, 1.0, LTL2);
+          }
+      }
+
+      /* test LTL = LTL2 */
+      for (i = 0; i < p; ++i)
+        {
+          for (j = 0; j < p; ++j)
+            {
+              double aij = gsl_matrix_get(LTL, i, j);
+              double bij = gsl_matrix_get(LTL2, i, j);
+
+              gsl_test_rel(aij, bij, tol, "sobolov k=%zu LTL(%zu,%zu)", k, i, j);
+            }
+        }
+
+      gsl_vector_free(alpha);
+    }
+
+  gsl_matrix_free(L);
+  gsl_matrix_free(Li);
+  gsl_matrix_free(LTL);
+  gsl_matrix_free(LTL2);
+  gsl_multifit_linear_free(w);
+}
+
+/* test linear regularized regression */
+static void
+test_reg(void)
+{
+  gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+
+  test_reg_system(100, 15, r);
+  test_reg_system(100, 50, r);
+  test_reg_system(100, 99, r);
+
+  test_reg_sobolev(20, 10, r);
+
+  gsl_rng_free(r);
+}
diff -Nru gsl-doc-1.16/multifit/test_rosenbrock.c gsl-doc-2.3/multifit/test_rosenbrock.c
--- gsl-doc-1.16/multifit/test_rosenbrock.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_rosenbrock.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,73 @@
+#define rosenbrock_N         2
+#define rosenbrock_P         2
+
+#define rosenbrock_NTRIES    4
+
+static double rosenbrock_x0[rosenbrock_P] = { -1.2, 1.0 };
+static double rosenbrock_epsrel = 1.0e-12;
+
+static void
+rosenbrock_checksol(const double x[], const double sumsq,
+                    const double epsrel, const char *sname,
+                    const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < rosenbrock_P; ++i)
+    {
+      gsl_test_rel(x[i], 1.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+rosenbrock_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, 10.0 * (x2 - x1*x1));
+  gsl_vector_set(f, 1, 1.0 - x1);
+
+  return GSL_SUCCESS;
+}
+
+static int
+rosenbrock_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+
+  gsl_matrix_set(J, 0, 0, -20.0*x1);
+  gsl_matrix_set(J, 0, 1, 10.0);
+  gsl_matrix_set(J, 1, 0, -1.0);
+  gsl_matrix_set(J, 1, 1, 0.0);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf rosenbrock_func =
+{
+  &rosenbrock_f,
+  &rosenbrock_df,
+  NULL,
+  rosenbrock_N,
+  rosenbrock_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem rosenbrock_problem =
+{
+  "rosenbrock",
+  rosenbrock_x0,
+  NULL,
+  &rosenbrock_epsrel,
+  rosenbrock_NTRIES,
+  &rosenbrock_checksol,
+  &rosenbrock_func
+};
diff -Nru gsl-doc-1.16/multifit/test_rosenbrocke.c gsl-doc-2.3/multifit/test_rosenbrocke.c
--- gsl-doc-1.16/multifit/test_rosenbrocke.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_rosenbrocke.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,88 @@
+#define rosenbrocke_N         8 /* = p */
+#define rosenbrocke_P         8 /* must be even */
+
+#define rosenbrocke_NTRIES    4
+
+static double rosenbrocke_x0[rosenbrocke_P] = { -1.2, 1.0, -1.2, 1.0,
+                                                -1.2, 1.0, -1.2, 1.0 };
+
+static double rosenbrocke_epsrel = 1.0e-12;
+
+static void
+rosenbrocke_checksol(const double x[], const double sumsq,
+                     const double epsrel, const char *sname,
+                     const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double rosenbrocke_x[rosenbrocke_P] = { 1.0, 1.0, 1.0, 1.0,
+                                                1.0, 1.0, 1.0, 1.0 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < rosenbrocke_P; ++i)
+    {
+      gsl_test_rel(x[i], rosenbrocke_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+rosenbrocke_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i;
+
+  for (i = 0; i < rosenbrocke_N / 2; ++i)
+    {
+      double x2i = gsl_vector_get(x, 2*i + 1);
+      double x2im1 = gsl_vector_get(x, 2*i);
+
+      gsl_vector_set(f, 2*i, 10.0 * (x2i - x2im1*x2im1));
+      gsl_vector_set(f, 2*i + 1, 1.0 - x2im1);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+rosenbrocke_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  size_t i;
+
+  gsl_matrix_set_zero(J);
+
+  for (i = 0; i < rosenbrocke_N / 2; ++i)
+    {
+      double x2im1 = gsl_vector_get(x, 2*i);
+
+      gsl_matrix_set(J, 2*i, 2*i, -20.0*x2im1);
+      gsl_matrix_set(J, 2*i, 2*i + 1, 10.0);
+      gsl_matrix_set(J, 2*i + 1, 2*i, -1.0);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf rosenbrocke_func =
+{
+  &rosenbrocke_f,
+  &rosenbrocke_df,
+  NULL,
+  rosenbrocke_N,
+  rosenbrocke_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem rosenbrocke_problem =
+{
+  "rosenbrock_extended",
+  rosenbrocke_x0,
+  NULL,
+  &rosenbrocke_epsrel,
+  rosenbrocke_NTRIES,
+  &rosenbrocke_checksol,
+  &rosenbrocke_func
+};
diff -Nru gsl-doc-1.16/multifit/test_roth.c gsl-doc-2.3/multifit/test_roth.c
--- gsl-doc-1.16/multifit/test_roth.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_roth.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,89 @@
+#define roth_N         2
+#define roth_P         2
+
+#define roth_NTRIES    3
+
+static double roth_x0[roth_P] = { 0.5, -2.0 };
+static double roth_epsrel = 1.0e-8;
+
+static void
+roth_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact1 = 0.0;
+  const double roth_x1[roth_P] = { 5.0, 4.0 };
+  const double sumsq_exact2 = 48.9842536792400;
+  const double roth_x2[roth_P] = { 11.4127789869021, -0.896805253274477 };
+  const double *roth_x;
+  double sumsq_exact;
+
+  if (fabs(sumsq) < 0.1)
+    {
+      sumsq_exact = sumsq_exact1;
+      roth_x = roth_x1;
+    }
+  else
+    {
+      sumsq_exact = sumsq_exact2;
+      roth_x = roth_x2;
+    }
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < roth_P; ++i)
+    {
+      gsl_test_rel(x[i], roth_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+roth_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, x1 - x2*(2.0 - x2*(5.0 - x2)) - 13.0);
+  gsl_vector_set(f, 1, x1 - x2*(14.0 - x2*(1.0 + x2)) - 29.0);
+
+  return GSL_SUCCESS;
+}
+
+static int
+roth_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_matrix_set(J, 0, 0, 1.0);
+  gsl_matrix_set(J, 0, 1, -2.0 + x2*(10.0 - 3.0*x2));
+  gsl_matrix_set(J, 1, 0, 1.0);
+  gsl_matrix_set(J, 1, 1, -14.0 + x2*(2.0 + 3.0*x2));
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf roth_func =
+{
+  &roth_f,
+  &roth_df,
+  NULL,
+  roth_N,
+  roth_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem roth_problem =
+{
+  "roth_freudenstein",
+  roth_x0,
+  NULL,
+  &roth_epsrel,
+  roth_NTRIES,
+  &roth_checksol,
+  &roth_func
+};
diff -Nru gsl-doc-1.16/multifit/test_shaw.c gsl-doc-2.3/multifit/test_shaw.c
--- gsl-doc-1.16/multifit/test_shaw.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_shaw.c	2016-11-30 21:31:39.000000000 +0000
@@ -0,0 +1,353 @@
+/*
+ * test_shaw.c
+ *
+ * Test L-curve (Tikhonov) regression routines using Shaw
+ * problem. See example 1.10 of
+ *
+ * [1] R.C. Aster, B. Borchers and C. H. Thurber,
+ *     Parameter Estimation and Inverse Problems (2nd ed), 2012.
+ */
+
+#include <gsl/gsl_sf_trig.h>
+
+/* alternate (and inefficient) method of computing G(lambda) */
+static double
+shaw_gcv_G(const double lambda, const gsl_matrix * X, const gsl_vector * y,
+           gsl_multifit_linear_workspace * work)
+{
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+  gsl_matrix * XTX = gsl_matrix_alloc(p, p);
+  gsl_matrix * XI = gsl_matrix_alloc(p, n);
+  gsl_matrix * XXI = gsl_matrix_alloc(n, n);
+  gsl_vector * c = gsl_vector_alloc(p);
+  gsl_vector_view d;
+  double rnorm, snorm;
+  double term1, term2, G;
+  size_t i;
+
+  /* compute regularized solution with this lambda */
+  gsl_multifit_linear_solve(lambda, X, y, c, &rnorm, &snorm, work);
+
+  /* compute X^T X */
+  gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, X, 0.0, XTX);
+
+  /* add lambda*I */
+  d = gsl_matrix_diagonal(XTX);
+  gsl_vector_add_constant(&d.vector, lambda * lambda);
+
+  /* invert (X^T X + lambda*I) */
+  gsl_linalg_cholesky_decomp1(XTX);
+  gsl_linalg_cholesky_invert(XTX);
+  gsl_matrix_transpose_tricpy('L', 0, XTX, XTX);
+
+  /* XI = (X^T X + lambda*I)^{-1} X^T */
+  gsl_blas_dgemm(CblasNoTrans, CblasTrans, 1.0, XTX, X, 0.0, XI);
+
+  /* XXI = X (X^T X + lambda*I)^{-1} X^T */
+  gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, X, XI, 0.0, XXI);
+
+  /* compute: term1 = Tr(I - X XI) */
+  term1 = 0.0;
+  for (i = 0; i < n; ++i)
+    {
+      double *Ai = gsl_matrix_ptr(XXI, i, i);
+      term1 += 1.0 - (*Ai);
+    }
+
+  gsl_matrix_free(XTX);
+  gsl_matrix_free(XI);
+  gsl_matrix_free(XXI);
+  gsl_vector_free(c);
+
+  term2 = rnorm / term1;
+
+  return term2 * term2;;
+}
+
+/* construct design matrix and rhs vector for Shaw problem */
+static int
+shaw_system(gsl_matrix * X, gsl_vector * y)
+{
+  int s = GSL_SUCCESS;
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+  const double dtheta = M_PI / (double) p;
+  size_t i, j;
+  gsl_vector *m = gsl_vector_alloc(p);
+
+  /* build the design matrix */
+  for (i = 0; i < n; ++i)
+    {
+      double si = (i + 0.5) * M_PI / n - M_PI / 2.0;
+      double csi = cos(si);
+      double sni = sin(si);
+
+      for (j = 0; j < p; ++j)
+        {
+          double thetaj = (j + 0.5) * M_PI / p - M_PI / 2.0;
+          double term1 = csi + cos(thetaj);
+          double term2 = gsl_sf_sinc(sni + sin(thetaj));
+          double Xij = term1 * term1 * term2 * term2 * dtheta;
+
+          gsl_matrix_set(X, i, j, Xij);
+        }
+    }
+
+  /* construct coefficient vector */
+  {
+    const double a1 = 2.0;
+    const double a2 = 1.0;
+    const double c1 = 6.0;
+    const double c2 = 2.0;
+    const double t1 = 0.8;
+    const double t2 = -0.5;
+
+    for (j = 0; j < p; ++j)
+      {
+        double tj = -M_PI / 2.0 + (j + 0.5) * dtheta;
+        double mj = a1 * exp(-c1 * (tj - t1) * (tj - t1)) +
+                    a2 * exp(-c2 * (tj - t2) * (tj - t2));
+        gsl_vector_set(m, j, mj);
+      }
+  }
+
+  /* construct rhs vector */
+  gsl_blas_dgemv(CblasNoTrans, 1.0, X, m, 0.0, y);
+
+  gsl_vector_free(m);
+
+  return s;
+}
+
+static int
+test_shaw_system_l(gsl_rng *rng_p, const size_t n, const size_t p,
+                   const double lambda_expected,
+                   gsl_vector *rhs)
+{
+  const size_t npoints = 1000; /* number of points on L-curve */
+  const double tol1 = 1.0e-12;
+  const double tol2 = 1.0e-10;
+  const double tol3 = 1.0e-5;
+  gsl_vector * reg_param = gsl_vector_alloc(npoints);
+  gsl_vector * rho = gsl_vector_alloc(npoints);
+  gsl_vector * eta = gsl_vector_alloc(npoints);
+
+  gsl_matrix * X = gsl_matrix_alloc(n, p);
+  gsl_matrix * cov = gsl_matrix_alloc(p, p);
+  gsl_vector * c = gsl_vector_alloc(p);
+  gsl_vector * ytmp = gsl_vector_alloc(n);
+  gsl_vector * y;
+  gsl_vector * r = gsl_vector_alloc(n);
+  gsl_multifit_linear_workspace * work = 
+    gsl_multifit_linear_alloc (n, p);
+
+  size_t reg_idx, i;
+  double lambda, rnorm, snorm;
+
+  /* build design matrix */
+  shaw_system(X, ytmp);
+
+  if (rhs)
+    y = rhs;
+  else
+    {
+      y = ytmp;
+
+      /* add random noise to exact rhs vector */
+      test_random_vector_noise(rng_p, y);
+    }
+
+  /* SVD decomposition */
+  gsl_multifit_linear_svd(X, work);
+
+  /* calculate L-curve */
+  gsl_multifit_linear_lcurve(y, reg_param, rho, eta, work);
+
+  /* test rho and eta vectors */
+  for (i = 0; i < npoints; ++i)
+    {
+      double rhoi = gsl_vector_get(rho, i);
+      double etai = gsl_vector_get(eta, i);
+      double lami = gsl_vector_get(reg_param, i);
+
+      /* solve regularized system and check for consistent rho/eta values */
+      gsl_multifit_linear_solve(lami, X, y, c, &rnorm, &snorm, work);
+      gsl_test_rel(rhoi, rnorm, tol3, "shaw rho n=%zu p=%zu lambda=%e",
+                   n, p, lami);
+      gsl_test_rel(etai, snorm, tol1, "shaw eta n=%zu p=%zu lambda=%e",
+                   n, p, lami);
+    }
+
+  /* calculate corner of L-curve */
+  gsl_multifit_linear_lcorner(rho, eta, &reg_idx);
+
+  lambda = gsl_vector_get(reg_param, reg_idx);
+
+  /* test against known lambda value if given */
+  if (lambda_expected > 0.0)
+    {
+      gsl_test_rel(lambda, lambda_expected, tol1,
+                   "shaw: n=%zu p=%zu L-curve corner lambda",
+                   n, p);
+    }
+
+  /* compute regularized solution with optimal lambda */
+  gsl_multifit_linear_solve(lambda, X, y, c, &rnorm, &snorm, work);
+
+  /* compute residual norm ||y - X c|| */
+  gsl_vector_memcpy(r, y);
+  gsl_blas_dgemv(CblasNoTrans, 1.0, X, c, -1.0, r);
+
+  /* test rnorm value */
+  gsl_test_rel(rnorm, gsl_blas_dnrm2(r), tol2,
+               "shaw: n=%zu p=%zu rnorm", n, p);
+
+  /* test snorm value */
+  gsl_test_rel(snorm, gsl_blas_dnrm2(c), tol2,
+               "shaw: n=%zu p=%zu snorm", n, p);
+
+  gsl_matrix_free(X);
+  gsl_matrix_free(cov);
+  gsl_vector_free(reg_param);
+  gsl_vector_free(rho);
+  gsl_vector_free(eta);
+  gsl_vector_free(r);
+  gsl_vector_free(c);
+  gsl_vector_free(ytmp);
+  gsl_multifit_linear_free(work);
+
+  return 0;
+} /* test_shaw_system_l() */
+
+static int
+test_shaw_system_gcv(gsl_rng *rng_p, const size_t n, const size_t p,
+                     const double lambda_expected,
+                     gsl_vector *rhs)
+{
+  const size_t npoints = 200; /* number of points on L-curve */
+  const double tol1 = 1.0e-12;
+  const double tol2 = 1.0e-10;
+  const double tol3 = 1.0e-5;
+  gsl_vector * reg_param = gsl_vector_alloc(npoints);
+  gsl_vector * G = gsl_vector_alloc(npoints);
+
+  gsl_matrix * X = gsl_matrix_alloc(n, p);
+  gsl_matrix * cov = gsl_matrix_alloc(p, p);
+  gsl_vector * c = gsl_vector_alloc(p);
+  gsl_vector * ytmp = gsl_vector_alloc(n);
+  gsl_vector * y;
+  gsl_vector * r = gsl_vector_alloc(n);
+  gsl_multifit_linear_workspace * work = 
+    gsl_multifit_linear_alloc (n, p);
+
+  size_t reg_idx, i;
+  double lambda, rnorm, snorm, G_lambda;
+
+  /* build design matrix */
+  shaw_system(X, ytmp);
+
+  if (rhs)
+    y = rhs;
+  else
+    {
+      y = ytmp;
+
+      /* add random noise to exact rhs vector */
+      test_random_vector_noise(rng_p, y);
+    }
+
+  /* SVD decomposition */
+  gsl_multifit_linear_svd(X, work);
+
+  /* calculate GCV curve */
+  gsl_multifit_linear_gcv(y, reg_param, G, &lambda, &G_lambda, work);
+
+  /* test G vector */
+  for (i = 0; i < npoints; ++i)
+    {
+      double lami = gsl_vector_get(reg_param, i);
+
+      if (lami > 1.0e-5)
+        {
+          /* test unreliable for small lambda */
+          double Gi = gsl_vector_get(G, i);
+          double Gi_expected = shaw_gcv_G(lami, X, y, work);
+
+          gsl_test_rel(Gi, Gi_expected, tol3, "shaw[%zu,%zu] gcv G i=%zu lambda=%e",
+                       n, p, i, lami);
+        }
+    }
+
+  /* test against known lambda value if given */
+  if (lambda_expected > 0.0)
+    {
+      gsl_test_rel(lambda, lambda_expected, tol2,
+                   "shaw gcv: n=%zu p=%zu lambda",
+                   n, p);
+    }
+
+  /* compute regularized solution with optimal lambda */
+  gsl_multifit_linear_solve(lambda, X, y, c, &rnorm, &snorm, work);
+
+  /* compute residual norm ||y - X c|| */
+  gsl_vector_memcpy(r, y);
+  gsl_blas_dgemv(CblasNoTrans, 1.0, X, c, -1.0, r);
+
+  /* test rnorm value */
+  gsl_test_rel(rnorm, gsl_blas_dnrm2(r), tol2,
+               "shaw gcv: n=%zu p=%zu rnorm", n, p);
+
+  /* test snorm value */
+  gsl_test_rel(snorm, gsl_blas_dnrm2(c), tol2,
+               "shaw gcv: n=%zu p=%zu snorm", n, p);
+
+  gsl_matrix_free(X);
+  gsl_matrix_free(cov);
+  gsl_vector_free(reg_param);
+  gsl_vector_free(G);
+  gsl_vector_free(r);
+  gsl_vector_free(c);
+  gsl_vector_free(ytmp);
+  gsl_multifit_linear_free(work);
+
+  return 0;
+} /* test_shaw_system_gcv() */
+
+void
+test_shaw(void)
+{
+  gsl_rng * r = gsl_rng_alloc(gsl_rng_default);
+
+  {
+    double shaw20_y[] = {
+      8.7547455124379323e-04, 5.4996835885761936e-04,
+      1.7527999407005367e-06, 1.9552372913117047e-03,
+      1.4411645433785081e-02, 5.2800013336393704e-02,
+      1.3609152023257112e-01, 2.7203484587635818e-01,
+      4.3752225136193390e-01, 5.7547667319875240e-01,
+      6.2445052213539942e-01, 5.6252658286441348e-01,
+      4.2322239923561566e-01, 2.6768469219560631e-01,
+      1.4337901162734543e-01, 6.5614569346074361e-02,
+      2.6013851831752945e-02, 9.2336933089481269e-03,
+      3.2269066658993694e-03, 1.3999201459261811e-03 };
+    gsl_vector_view rhs = gsl_vector_view_array(shaw20_y, 20);
+
+    /* lambda and rhs values from [1] */
+    test_shaw_system_l(r, 20, 20, 5.793190958069266e-06, &rhs.vector);
+
+    test_shaw_system_gcv(r, 20, 20, 1.24921780949051038e-05, &rhs.vector);
+  }
+
+  {
+    size_t n, p;
+
+    for (n = 10; n <= 50; n += 2)
+      {
+        for (p = n - 6; p <= n; p += 2)
+          test_shaw_system_l(r, n, p, -1.0, NULL);
+      }
+  }
+
+  gsl_rng_free(r);
+} /* test_shaw() */
diff -Nru gsl-doc-1.16/multifit/test_thurber.c gsl-doc-2.3/multifit/test_thurber.c
--- gsl-doc-1.16/multifit/test_thurber.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_thurber.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,136 @@
+#define thurber_N       37
+#define thurber_P       7
+
+#define thurber_NTRIES  1
+
+static double thurber_x0[thurber_P] = { 1000.0, 1000.0, 400.0, 40.0,
+                                        0.7, 0.3, 0.03 };
+
+static double thurber_epsrel = 1.0e-6;
+
+static double thurber_sigma[thurber_P] = {
+  4.6647963344E+00, 3.9571156086E+01, 2.8698696102E+01,
+  5.5675370270E+00, 3.1333340687E-02, 1.4984928198E-02,
+  6.5842344623E-03
+};
+
+static double thurber_X[thurber_N] = {
+  -3.067, -2.981, -2.921, -2.912, -2.840, -2.797, -2.702,
+  -2.699, -2.633, -2.481, -2.363, -2.322, -1.501, -1.460,
+  -1.274, -1.212, -1.100, -1.046, -0.915, -0.714, -0.566,
+  -0.545, -0.400, -0.309, -0.109, -0.103, 0.010, 0.119,
+  0.377, 0.790, 0.963, 1.006, 1.115, 1.572, 1.841,
+  2.047, 2.200
+};
+
+static double thurber_F[thurber_N] = {
+  80.574, 84.248, 87.264, 87.195, 89.076, 89.608, 89.868, 90.101,
+  92.405, 95.854, 100.696, 101.060, 401.672, 390.724, 567.534,
+  635.316, 733.054, 759.087, 894.206, 990.785, 1090.109, 1080.914,
+  1122.643, 1178.351, 1260.531, 1273.514, 1288.339, 1327.543, 1353.863,
+  1414.509, 1425.208, 1421.384, 1442.962, 1464.350, 1468.705,
+  1447.894, 1457.628
+};
+
+static void
+thurber_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 5.6427082397E+03;
+  const double thurber_x[thurber_P] = {
+    1.2881396800E+03, 1.4910792535E+03, 5.8323836877E+02,
+    7.5416644291E+01, 9.6629502864E-01, 3.9797285797E-01,
+    4.9727297349E-02 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < thurber_P; ++i)
+    {
+      gsl_test_rel(x[i], thurber_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+thurber_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[thurber_P];
+  size_t i;
+
+  for (i = 0; i < thurber_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < thurber_N; i++)
+    {
+      double xi = thurber_X[i];
+      double yi;
+
+      yi = b[0] + b[1]*xi + b[2]*xi*xi + b[3]*xi*xi*xi;
+      yi /= 1.0 + b[4]*xi + b[5]*xi*xi + b[6]*xi*xi*xi;
+
+      gsl_vector_set (f, i, yi - thurber_F[i]);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+thurber_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[thurber_P];
+  size_t i;
+
+  for (i = 0; i < thurber_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < thurber_N; i++)
+    {
+      double xi = thurber_X[i];
+      double d, n, d_sq;
+
+      n = b[0] + b[1]*xi + b[2]*xi*xi + b[3]*xi*xi*xi;
+      d = 1.0 + b[4]*xi + b[5]*xi*xi + b[6]*xi*xi*xi;
+      d_sq = d * d;
+
+      gsl_matrix_set (df, i, 0, 1.0 / d);
+      gsl_matrix_set (df, i, 1, xi / d);
+      gsl_matrix_set (df, i, 2, (xi * xi) / d);
+      gsl_matrix_set (df, i, 3, (xi * xi * xi) / d);
+      gsl_matrix_set (df, i, 4, -xi * n / d_sq);
+      gsl_matrix_set (df, i, 5, -xi * xi * n / d_sq);
+      gsl_matrix_set (df, i, 6, -xi * xi * xi * n / d_sq);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf thurber_func =
+{
+  &thurber_f,
+  &thurber_df,
+  NULL,
+  thurber_N,
+  thurber_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem thurber_problem =
+{
+  "nist-thurber",
+  thurber_x0,
+  thurber_sigma,
+  &thurber_epsrel,
+  thurber_NTRIES,
+  &thurber_checksol,
+  &thurber_func
+};
diff -Nru gsl-doc-1.16/multifit/test_vardim.c gsl-doc-2.3/multifit/test_vardim.c
--- gsl-doc-1.16/multifit/test_vardim.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_vardim.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,94 @@
+#define vardim_N         7 /* p + 2 */
+#define vardim_P         5
+
+#define vardim_NTRIES    4
+
+static double vardim_x0[vardim_P] = { 0.8, 0.6, 0.4, 0.2, 0.0 };
+
+static double vardim_epsrel = 1.0e-12;
+
+static void
+vardim_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      gsl_test_rel(x[i], 1.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+vardim_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i;
+  double sum = 0.0;
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+
+      gsl_vector_set(f, i, xi - 1.0);
+
+      sum += (i + 1.0) * (xi - 1.0);
+    }
+
+  gsl_vector_set(f, vardim_P, sum);
+  gsl_vector_set(f, vardim_P + 1, sum*sum);
+
+  return GSL_SUCCESS;
+}
+
+static int
+vardim_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  size_t i;
+  double sum = 0.0;
+  gsl_matrix_view m = gsl_matrix_submatrix(J, 0, 0, vardim_P, vardim_P);
+
+  gsl_matrix_set_identity(&m.matrix);
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      sum += (i + 1.0) * (xi - 1.0);
+    }
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      gsl_matrix_set(J, vardim_P, i, i + 1.0);
+      gsl_matrix_set(J, vardim_P + 1, i, 2*(i + 1.0)*sum);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf vardim_func =
+{
+  &vardim_f,
+  &vardim_df,
+  NULL,
+  vardim_N,
+  vardim_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem vardim_problem =
+{
+  "vardim",
+  vardim_x0,
+  NULL,
+  &vardim_epsrel,
+  vardim_NTRIES,
+  &vardim_checksol,
+  &vardim_func
+};
diff -Nru gsl-doc-1.16/multifit/test_watson.c gsl-doc-2.3/multifit/test_watson.c
--- gsl-doc-1.16/multifit/test_watson.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_watson.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,127 @@
+#define watson_N         31
+#define watson_P         6
+
+#define watson_NTRIES    4
+
+static double watson_x0[watson_P] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+static double watson_epsrel = 1.0e-6;
+
+static void
+watson_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 2.287670053552372e-03;
+  const double watson_x[watson_P] = {
+    -1.572508640629858e-02,  1.012434869366059e+00, -2.329916259263380e-01,
+     1.260430087686035e+00, -1.513728922580576e+00,  9.929964323646112e-01 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < watson_P; ++i)
+    {
+      gsl_test_rel(x[i], watson_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+watson_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  const double x1 = gsl_vector_get(x, 0);
+  const double x2 = gsl_vector_get(x, 1);
+  size_t i, j;
+
+  for (i = 0; i < watson_N - 2; ++i)
+    {
+      double ti = (i + 1) / 29.0;
+      double tjm1 = 1.0, tjm2 = 1.0;
+      double sum1 = 0.0, sum2 = 0.0;
+
+      for (j = 0; j < watson_P; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+
+          sum1 += xj * tjm1;
+          tjm1 *= ti;
+
+          if (j > 0)
+            {
+              sum2 += j * xj * tjm2;
+              tjm2 *= ti;
+            }
+        }
+
+      gsl_vector_set (f, i, sum2 - sum1*sum1 - 1.0);
+    }
+
+  gsl_vector_set(f, watson_N - 2, x1);
+  gsl_vector_set(f, watson_N - 1, x2 - x1*x1 - 1.0);
+
+  return GSL_SUCCESS;
+}
+
+static int
+watson_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get (x, 0);
+  size_t i, j;
+
+  gsl_matrix_set_zero(J);
+
+  for (i = 0; i < watson_N - 2; ++i)
+    {
+      double ti = (i + 1) / 29.0;
+      double tjm1 = 1.0, tjm2 = 1.0;
+      double sum1 = 0.0;
+
+      for (j = 0; j < watson_P; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+          sum1 += xj * tjm1;
+          tjm1 *= ti;
+        }
+
+      tjm1 = 1.0;
+      tjm2 = 1.0;
+      for (j = 0; j < watson_P; ++j)
+        {
+          gsl_matrix_set(J, i, j, j * tjm2 - 2.0*sum1*tjm1);
+          tjm1 *= ti;
+
+          if (j > 0)
+            tjm2 *= ti;
+        }
+    }
+
+  gsl_matrix_set(J, watson_N - 2, 0, 1.0);
+  gsl_matrix_set(J, watson_N - 1, 0, -2.0*x1);
+  gsl_matrix_set(J, watson_N - 1, 1, 1.0);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf watson_func =
+{
+  &watson_f,
+  &watson_df,
+  NULL,
+  watson_N,
+  watson_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem watson_problem =
+{
+  "watson",
+  watson_x0,
+  NULL,
+  &watson_epsrel,
+  watson_NTRIES,
+  &watson_checksol,
+  &watson_func
+};
diff -Nru gsl-doc-1.16/multifit/test_wnlin.c gsl-doc-2.3/multifit/test_wnlin.c
--- gsl-doc-1.16/multifit/test_wnlin.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_wnlin.c	2016-08-23 20:28:28.000000000 +0000
@@ -0,0 +1,154 @@
+#define wnlin_N         40
+#define wnlin_P         3
+
+#define wnlin_NTRIES    1
+
+static double wnlin_x0[wnlin_P] = { 1.0, 0.0, 0.0 };
+static double wnlin_epsrel = 1.0e-8;
+
+static int wnlin_internal_weight = 1;
+
+/* data */
+static double wnlin_Y[wnlin_N] = {
+  6.08035e+00, 5.47552e+00, 5.94654e+00, 5.04920e+00, 4.78568e+00,
+  3.51748e+00, 2.84671e+00, 3.24634e+00, 3.23395e+00, 3.30385e+00,
+  2.83439e+00, 2.31891e+00, 2.33858e+00, 2.40559e+00, 2.41856e+00,
+  1.99966e+00, 1.88127e+00, 1.91477e+00, 1.70415e+00, 1.60316e+00,
+  1.77937e+00, 1.55302e+00, 1.50903e+00, 1.36364e+00, 1.36873e+00,
+  1.41954e+00, 1.37778e+00, 1.23573e+00, 1.28524e+00, 1.46327e+00,
+  1.22315e+00, 1.19330e+00, 1.18717e+00, 8.83172e-01, 1.23424e+00,
+  1.14683e+00, 1.11091e+00, 1.20396e+00, 1.28722e+00, 1.05801e+00
+};
+
+/* weights */
+static double wnlin_W[wnlin_N] = {
+  2.77778e+00, 3.27690e+00, 3.85426e+00, 4.51906e+00, 5.28083e+00,
+  6.14919e+00, 7.13370e+00, 8.24349e+00, 9.48703e+00, 1.08717e+01,
+  1.24036e+01, 1.40869e+01, 1.59238e+01, 1.79142e+01, 2.00553e+01,
+  2.23415e+01, 2.47646e+01, 2.73137e+01, 2.99753e+01, 3.27337e+01,
+  3.55714e+01, 3.84696e+01, 4.14085e+01, 4.43678e+01, 4.73278e+01,
+  5.02690e+01, 5.31731e+01, 5.60234e+01, 5.88046e+01, 6.15036e+01,
+  6.41092e+01, 6.66121e+01, 6.90054e+01, 7.12839e+01, 7.34442e+01,
+  7.54848e+01, 7.74053e+01, 7.92069e+01, 8.08918e+01, 8.24632e+01
+};
+
+static void
+wnlin_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 29.7481259665713758;
+  const double wnlin_x[wnlin_P] = { 5.17378551196259195,
+                                    0.111041758006851149,
+                                    1.05282724070446099 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < wnlin_P; ++i)
+    {
+      gsl_test_rel(x[i], wnlin_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+wnlin_f (const gsl_vector *x, void *params, gsl_vector *f)
+{
+  int *iptr = (int *) params;
+  int doweight = iptr ? *iptr : 0;
+  double A = gsl_vector_get (x, 0);
+  double lambda = gsl_vector_get (x, 1);
+  double b = gsl_vector_get (x, 2);
+  size_t i;
+
+  /* model Yi = A * exp(-lambda * i) + b */
+  for (i = 0; i < wnlin_N; i++)
+    {
+      double ti = i;
+      double yi = wnlin_Y[i];
+      double swi = sqrt(wnlin_W[i]);
+      double Mi = A * exp (-lambda * ti) + b;
+
+      if (doweight)
+        gsl_vector_set (f, i, swi * (Mi - yi));
+      else
+        gsl_vector_set (f, i, Mi - yi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+wnlin_df (const gsl_vector *x, void *params, gsl_matrix *df)
+{
+  int *iptr = (int *) params;
+  int doweight = iptr ? *iptr : 0;
+  double A = gsl_vector_get (x, 0);
+  double lambda = gsl_vector_get (x, 1);
+  size_t i;
+
+  for (i = 0; i < wnlin_N; i++)
+    {
+      gsl_vector_view v = gsl_matrix_row(df, i);
+      double ti = i;
+      double swi = sqrt(wnlin_W[i]);
+      double e = exp(-lambda * ti);
+
+      gsl_vector_set(&v.vector, 0, e);
+      gsl_vector_set(&v.vector, 1, -ti * A * e);
+      gsl_vector_set(&v.vector, 2, 1.0);
+
+      if (doweight)
+        gsl_vector_scale(&v.vector, swi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf wnlin_func1 =
+{
+  &wnlin_f,
+  &wnlin_df,
+  NULL,
+  wnlin_N,
+  wnlin_P,
+  (void *) &wnlin_internal_weight,
+  0,
+  0
+};
+
+static gsl_multifit_function_fdf wnlin_func2 =
+{
+  &wnlin_f,
+  &wnlin_df,
+  NULL,
+  wnlin_N,
+  wnlin_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem wnlin_problem1 =
+{
+  "wnlin_internal_weights",
+  wnlin_x0,
+  NULL,
+  &wnlin_epsrel,
+  wnlin_NTRIES,
+  &wnlin_checksol,
+  &wnlin_func1
+};
+
+static test_fdf_problem wnlin_problem2 =
+{
+  "wnlin_external_weights",
+  wnlin_x0,
+  NULL,
+  &wnlin_epsrel,
+  wnlin_NTRIES,
+  &wnlin_checksol,
+  &wnlin_func2
+};
diff -Nru gsl-doc-1.16/multifit/test_wood.c gsl-doc-2.3/multifit/test_wood.c
--- gsl-doc-1.16/multifit/test_wood.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit/test_wood.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,91 @@
+#define wood_N         6
+#define wood_P         4
+
+#define wood_NTRIES    3
+
+static double wood_x0[wood_P] = { -3.0, -1.0, -3.0, -1.0 };
+static double wood_epsrel = 1.0e-12;
+
+static void
+wood_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double wood_x[wood_P] = { 1.0, 1.0, 1.0, 1.0 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < wood_P; ++i)
+    {
+      gsl_test_rel(x[i], wood_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+wood_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+
+  gsl_vector_set(f, 0, 10.0*(x2 - x1*x1));
+  gsl_vector_set(f, 1, 1.0 - x1);
+  gsl_vector_set(f, 2, sqrt(90.0)*(x4 - x3*x3));
+  gsl_vector_set(f, 3, 1.0 - x3);
+  gsl_vector_set(f, 4, sqrt(10.0)*(x2 + x4 - 2.0));
+  gsl_vector_set(f, 5, (x2 - x4) / sqrt(10.0));
+
+  return GSL_SUCCESS;
+}
+
+static int
+wood_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x3 = gsl_vector_get(x, 2);
+  double s90 = sqrt(90.0);
+  double s10 = sqrt(10.0);
+
+  gsl_matrix_set_zero(J);
+
+  gsl_matrix_set(J, 0, 0, -20.0*x1);
+  gsl_matrix_set(J, 0, 1, 10.0);
+  gsl_matrix_set(J, 1, 0, -1.0);
+  gsl_matrix_set(J, 2, 2, -2.0*s90*x3);
+  gsl_matrix_set(J, 2, 3, s90);
+  gsl_matrix_set(J, 3, 2, -1.0);
+  gsl_matrix_set(J, 4, 1, s10);
+  gsl_matrix_set(J, 4, 3, s10);
+  gsl_matrix_set(J, 5, 1, 1.0/s10);
+  gsl_matrix_set(J, 5, 3, -1.0/s10);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_function_fdf wood_func =
+{
+  &wood_f,
+  &wood_df,
+  NULL,
+  wood_N,
+  wood_P,
+  NULL,
+  0,
+  0
+};
+
+static test_fdf_problem wood_problem =
+{
+  "wood",
+  wood_x0,
+  NULL,
+  &wood_epsrel,
+  wood_NTRIES,
+  &wood_checksol,
+  &wood_func
+};
diff -Nru gsl-doc-1.16/multifit/TODO gsl-doc-2.3/multifit/TODO
--- gsl-doc-1.16/multifit/TODO	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/TODO	2016-11-21 17:57:37.000000000 +0000
@@ -10,10 +10,10 @@
 
 The following features should be added to the nonlinear least squares routines:
 
-1. More information reporting to the user (see levmar code for examples) such as:
-   - number of function evaluations
-   - number of Jacobian evaluations
+1. Support for constraints
 
-2. Support for constraints
+2. robust nonlinear least squares and robust ridge regression
 
-3. robust fitting
+3. covariance matrices for ridge regression
+
+4. min_workspace_p is dynamically allocated in gsl_multifit_linear_gcv_min - fix
diff -Nru gsl-doc-1.16/multifit/work.c gsl-doc-2.3/multifit/work.c
--- gsl-doc-1.16/multifit/work.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multifit/work.c	2016-11-21 17:56:02.000000000 +0000
@@ -22,12 +22,11 @@
 #include <gsl/gsl_multifit.h>
 
 gsl_multifit_linear_workspace *
-gsl_multifit_linear_alloc (size_t n, size_t p)
+gsl_multifit_linear_alloc (const size_t nmax, const size_t pmax)
 {
   gsl_multifit_linear_workspace *w;
 
-  w = (gsl_multifit_linear_workspace *)
-    malloc (sizeof (gsl_multifit_linear_workspace));
+  w = calloc (1, sizeof (gsl_multifit_linear_workspace));
 
   if (w == 0)
     {
@@ -35,100 +34,97 @@
                      GSL_ENOMEM, 0);
     }
 
-  w->n = n;                     /* number of observations */
-  w->p = p;                     /* number of parameters */
+  w->nmax = nmax;                     /* max number of observations */
+  w->pmax = pmax;                     /* max number of parameters */
+  w->n = 0;
+  w->p = 0;
+  w->rcond = 0.0;
 
-  w->A = gsl_matrix_alloc (n, p);
+  w->A = gsl_matrix_alloc (nmax, pmax);
 
   if (w->A == 0)
     {
-      free (w);
+      gsl_multifit_linear_free(w);
       GSL_ERROR_VAL ("failed to allocate space for A", GSL_ENOMEM, 0);
     }
 
-  w->Q = gsl_matrix_alloc (p, p);
+  w->Q = gsl_matrix_alloc (pmax, pmax);
 
   if (w->Q == 0)
     {
-      gsl_matrix_free (w->A);
-      free (w);
+      gsl_multifit_linear_free(w);
       GSL_ERROR_VAL ("failed to allocate space for Q", GSL_ENOMEM, 0);
     }
 
-  w->QSI = gsl_matrix_alloc (p, p);
+  w->QSI = gsl_matrix_alloc (pmax, pmax);
 
   if (w->QSI == 0)
     {
-      gsl_matrix_free (w->Q);
-      gsl_matrix_free (w->A);
-      free (w);
+      gsl_multifit_linear_free(w);
       GSL_ERROR_VAL ("failed to allocate space for QSI", GSL_ENOMEM, 0);
     }
 
-  w->S = gsl_vector_alloc (p);
+  w->S = gsl_vector_alloc (pmax);
 
   if (w->S == 0)
     {
-      gsl_matrix_free (w->QSI);
-      gsl_matrix_free (w->Q);
-      gsl_matrix_free (w->A);
-      free (w);
+      gsl_multifit_linear_free(w);
       GSL_ERROR_VAL ("failed to allocate space for S", GSL_ENOMEM, 0);
     }
 
-  w->t = gsl_vector_alloc (n);
+  w->t = gsl_vector_alloc (nmax);
 
   if (w->t == 0)
     {
-      gsl_vector_free (w->S);
-      gsl_matrix_free (w->QSI);
-      gsl_matrix_free (w->Q);
-      gsl_matrix_free (w->A);
-      free (w);
+      gsl_multifit_linear_free(w);
       GSL_ERROR_VAL ("failed to allocate space for t", GSL_ENOMEM, 0);
     }
 
-  w->xt = gsl_vector_calloc (p);
+  w->xt = gsl_vector_calloc (pmax);
 
   if (w->xt == 0)
     {
-      gsl_vector_free (w->t);
-      gsl_vector_free (w->S);
-      gsl_matrix_free (w->QSI);
-      gsl_matrix_free (w->Q);
-      gsl_matrix_free (w->A);
-      free (w);
+      gsl_multifit_linear_free(w);
       GSL_ERROR_VAL ("failed to allocate space for xt", GSL_ENOMEM, 0);
     }
 
-  w->D = gsl_vector_calloc (p);
+  w->D = gsl_vector_calloc (pmax);
 
   if (w->D == 0)
     {
-      gsl_vector_free (w->D);
-      gsl_vector_free (w->t);
-      gsl_vector_free (w->S);
-      gsl_matrix_free (w->QSI);
-      gsl_matrix_free (w->Q);
-      gsl_matrix_free (w->A);
-      free (w);
-      GSL_ERROR_VAL ("failed to allocate space for xt", GSL_ENOMEM, 0);
+      gsl_multifit_linear_free(w);
+      GSL_ERROR_VAL ("failed to allocate space for D", GSL_ENOMEM, 0);
     }
 
   return w;
 }
 
 void
-gsl_multifit_linear_free (gsl_multifit_linear_workspace * work)
+gsl_multifit_linear_free (gsl_multifit_linear_workspace * w)
 {
-  RETURN_IF_NULL (work);
-  gsl_matrix_free (work->A);
-  gsl_matrix_free (work->Q);
-  gsl_matrix_free (work->QSI);
-  gsl_vector_free (work->S);
-  gsl_vector_free (work->t);
-  gsl_vector_free (work->xt);
-  gsl_vector_free (work->D);
-  free (work);
+  RETURN_IF_NULL (w);
+
+  if (w->A)
+    gsl_matrix_free (w->A);
+
+  if (w->Q)
+    gsl_matrix_free (w->Q);
+
+  if (w->QSI)
+    gsl_matrix_free (w->QSI);
+
+  if (w->S)
+    gsl_vector_free (w->S);
+
+  if (w->t)
+    gsl_vector_free (w->t);
+
+  if (w->xt)
+    gsl_vector_free (w->xt);
+
+  if (w->D)
+    gsl_vector_free (w->D);
+
+  free (w);
 }
 
diff -Nru gsl-doc-1.16/multifit_nlinear/cholesky.c gsl-doc-2.3/multifit_nlinear/cholesky.c
--- gsl-doc-1.16/multifit_nlinear/cholesky.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/cholesky.c	2016-08-12 15:13:26.000000000 +0000
@@ -0,0 +1,301 @@
+/* multifit_nlinear/cholesky.c
+ * 
+ * Copyright (C) 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/*
+ * This module calculates the solution of the normal equations least squares
+ * system:
+ *
+ * [ J~^T J~ + mu D~^T D~ ] p~ = -J~^T f
+ *
+ * using the modified Cholesky decomposition. Quantities are scaled
+ * according to:
+ *
+ * J~ = J S
+ * D~ = D S
+ * p~ = S^{-1} p
+ *
+ * where S is a diagonal matrix and S_jj = || J_j || and J_j is column
+ * j of the Jacobian. This balancing transformation seems to be more
+ * numerically stable for some Jacobians.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_permutation.h>
+
+#include "common.c"
+
+typedef struct
+{
+  gsl_matrix *JTJ;           /* J^T J */
+  gsl_matrix *work_JTJ;      /* copy of J^T J */
+  gsl_vector *rhs;           /* -J^T f, size p */
+  gsl_permutation *perm;     /* permutation matrix for modified Cholesky */
+  gsl_vector *work3p;        /* workspace, size 3*p */
+  double mu;                 /* current regularization parameter */
+} cholesky_state_t;
+
+static void *cholesky_alloc (const size_t n, const size_t p);
+static int cholesky_init(const void * vtrust_state, void * vstate);
+static int cholesky_presolve(const double mu, const void * vtrust_state, void * vstate);
+static int cholesky_solve(const gsl_vector * f, gsl_vector *x,
+                          const  void * vtrust_state, void *vstate);
+static int cholesky_solve_rhs(const gsl_vector * b, gsl_vector *x, cholesky_state_t *state);
+static int cholesky_regularize(const double mu, const gsl_vector * diag, gsl_matrix * A,
+                               cholesky_state_t * state);
+
+static void *
+cholesky_alloc (const size_t n, const size_t p)
+{
+  cholesky_state_t *state;
+
+  (void)n;
+  
+  state = calloc(1, sizeof(cholesky_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate cholesky state", GSL_ENOMEM);
+    }
+
+  state->JTJ = gsl_matrix_alloc(p, p);
+  if (state->JTJ == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for JTJ", GSL_ENOMEM);
+    }
+
+  state->work_JTJ = gsl_matrix_alloc(p, p);
+  if (state->work_JTJ == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for JTJ workspace",
+                      GSL_ENOMEM);
+    }
+
+  state->rhs = gsl_vector_alloc(p);
+  if (state->rhs == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for rhs", GSL_ENOMEM);
+    }
+
+  state->perm = gsl_permutation_alloc(p);
+  if (state->perm == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for perm", GSL_ENOMEM);
+    }
+
+  state->work3p = gsl_vector_alloc(3 * p);
+  if (state->work3p == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for work3p", GSL_ENOMEM);
+    }
+
+  state->mu = -1.0;
+
+  return state;
+}
+
+static void
+cholesky_free(void *vstate)
+{
+  cholesky_state_t *state = (cholesky_state_t *) vstate;
+
+  if (state->JTJ)
+    gsl_matrix_free(state->JTJ);
+
+  if (state->work_JTJ)
+    gsl_matrix_free(state->work_JTJ);
+
+  if (state->rhs)
+    gsl_vector_free(state->rhs);
+
+  if (state->perm)
+    gsl_permutation_free(state->perm);
+
+  if (state->work3p)
+    gsl_vector_free(state->work3p);
+
+  free(state);
+}
+
+static int
+cholesky_init(const void * vtrust_state, void * vstate)
+{
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  cholesky_state_t *state = (cholesky_state_t *) vstate;
+
+  /* compute J^T J */
+  gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, trust_state->J, 0.0, state->JTJ);
+
+  return GSL_SUCCESS;
+}
+
+/*
+cholesky_presolve()
+  Compute the modified Cholesky decomposition of J^T J + mu D^T D.
+Modified Cholesky is used in case mu = 0 and there are rounding
+errors in forming J^T J which could lead to an indefinite matrix.
+
+Inputs: mu     - LM parameter
+        vstate - workspace
+
+Notes:
+1) On output, state->work_JTJ contains the Cholesky decomposition of
+J^T J + mu D^T D
+*/
+
+static int
+cholesky_presolve(const double mu, const void * vtrust_state, void * vstate)
+{
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  cholesky_state_t *state = (cholesky_state_t *) vstate;
+  gsl_matrix *JTJ = state->work_JTJ;
+  const gsl_vector *diag = trust_state->diag;
+  int status;
+
+  /* copy lower triangle of A to workspace */
+  gsl_matrix_tricpy('L', 1, JTJ, state->JTJ);
+
+  /* augment normal equations: A -> A + mu D^T D */
+  status = cholesky_regularize(mu, diag, JTJ, state);
+  if (status)
+    return status;
+
+  /* compute modified Cholesky decomposition */
+  status = gsl_linalg_mcholesky_decomp(JTJ, state->perm, NULL);
+  if (status)
+    return status;
+
+  state->mu = mu;
+
+  return GSL_SUCCESS;
+}
+
+/*
+cholesky_solve()
+  Compute (J^T J + mu D^T D) x = -J^T f
+
+Inputs: f      - right hand side vector f
+        x      - (output) solution vector
+        vstate - cholesky workspace
+*/
+
+static int
+cholesky_solve(const gsl_vector * f, gsl_vector *x,
+               const  void * vtrust_state, void *vstate)
+{
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  cholesky_state_t *state = (cholesky_state_t *) vstate;
+  int status;
+
+  /* compute rhs = -J^T f */
+  gsl_blas_dgemv(CblasTrans, -1.0, trust_state->J, f, 0.0, state->rhs);
+
+  status = cholesky_solve_rhs(state->rhs, x, state);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+}
+
+static int
+cholesky_rcond(double * rcond, void * vstate)
+{
+  int status;
+  cholesky_state_t *state = (cholesky_state_t *) vstate;
+  double rcond_JTJ;
+
+  if (state->mu != 0)
+    {
+      /*
+       * Cholesky decomposition hasn't been computed yet, or was computed
+       * with mu > 0 - recompute Cholesky decomposition of J^T J
+       */
+
+      /* copy lower triangle of JTJ to workspace */
+      gsl_matrix_tricpy('L', 1, state->work_JTJ, state->JTJ);
+
+      /* compute modified Cholesky decomposition */
+      status = gsl_linalg_mcholesky_decomp(state->work_JTJ, state->perm, NULL);
+      if (status)
+        return status;
+    }
+
+  status = gsl_linalg_mcholesky_rcond(state->work_JTJ, state->perm, &rcond_JTJ, state->work3p);
+  if (status == GSL_SUCCESS)
+    *rcond = sqrt(rcond_JTJ);
+
+  return status;
+}
+
+/* solve: (J^T J + mu D^T D) x = b */
+static int
+cholesky_solve_rhs(const gsl_vector * b, gsl_vector *x, cholesky_state_t *state)
+{
+  int status;
+  gsl_matrix *JTJ = state->work_JTJ;
+
+  status = gsl_linalg_mcholesky_solve(JTJ, state->perm, b, x);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+}
+
+/* A <- A + mu D^T D */
+static int
+cholesky_regularize(const double mu, const gsl_vector * diag, gsl_matrix * A,
+                    cholesky_state_t * state)
+{
+  (void) state;
+
+  if (mu != 0.0)
+    {
+      size_t i;
+
+      for (i = 0; i < diag->size; ++i)
+        {
+          double di = gsl_vector_get(diag, i);
+          double *Aii = gsl_matrix_ptr(A, i, i);
+          *Aii += mu * di * di;
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+static const gsl_multifit_nlinear_solver cholesky_type =
+{
+  "cholesky",
+  cholesky_alloc,
+  cholesky_init,
+  cholesky_presolve,
+  cholesky_solve,
+  cholesky_rcond,
+  cholesky_free
+};
+
+const gsl_multifit_nlinear_solver *gsl_multifit_nlinear_solver_cholesky = &cholesky_type;
diff -Nru gsl-doc-1.16/multifit_nlinear/common.c gsl-doc-2.3/multifit_nlinear/common.c
--- gsl-doc-1.16/multifit_nlinear/common.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/common.c	2016-08-10 21:03:42.000000000 +0000
@@ -0,0 +1,107 @@
+/* multifit_nlinear/common.c
+ * 
+ * Copyright (C) 2014, 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+static double scaled_enorm (const gsl_vector * d, const gsl_vector * f);
+static void scaled_addition (const double alpha, const gsl_vector * x,
+                             const double beta, const gsl_vector * y,
+                             gsl_vector * z);
+static double quadratic_preduction(const gsl_vector *f, const gsl_matrix * J,
+                                   const gsl_vector * dx, gsl_vector * work);
+
+/* compute || diag(d) f || */
+static double
+scaled_enorm (const gsl_vector * d, const gsl_vector * f)
+{
+  double e2 = 0;
+  size_t i, n = f->size;
+  for (i = 0; i < n; i++)
+    {
+      double fi = gsl_vector_get (f, i);
+      double di = gsl_vector_get (d, i);
+      double u = di * fi;
+      e2 += u * u;
+    }
+  return sqrt (e2);
+}
+
+/* compute z = alpha*x + beta*y */
+static void
+scaled_addition (const double alpha, const gsl_vector * x,
+                 const double beta, const gsl_vector * y, gsl_vector * z)
+{
+  const size_t N = z->size;
+  size_t i;
+
+  for (i = 0; i < N; i++)
+    {
+      double xi = gsl_vector_get (x, i);
+      double yi = gsl_vector_get (y, i);
+      gsl_vector_set (z, i, alpha * xi + beta * yi);
+    }
+}
+
+/*
+quadratic_preduction()
+  Calculate predicted reduction based on standard
+quadratic model:
+
+m_k(dx) = Phi(x_k) + dx' g + 1/2 dx' B_k dx
+
+predicted_reduction = m_k(0) - m_k(dx)
+                    = -2 g^T dx / ||f||^2 - ( ||J*dx|| / ||f|| )^2
+                    = -2 fhat . beta - ||beta||^2
+
+where: beta = J*dx / ||f||
+
+Inputs: f     - f(x), size n
+        J     - Jacobian J(x), n-by-p
+        dx    - proposed step, size p
+        work  - workspace, size n
+
+Return: predicted reduction
+*/
+
+static double
+quadratic_preduction(const gsl_vector * f, const gsl_matrix * J,
+                     const gsl_vector * dx, gsl_vector * work)
+{
+  const size_t n = f->size;
+  const double normf = gsl_blas_dnrm2(f);
+  double pred_reduction;
+  double norm_beta; /* ||J*dx|| / ||f|| */
+  size_t i;
+
+  /* compute beta = J*dx / ||f|| */
+  gsl_blas_dgemv(CblasNoTrans, 1.0 / normf, J, dx, 0.0, work);
+  norm_beta = gsl_blas_dnrm2(work);
+
+  /* initialize to ( ||J*dx|| / ||f|| )^2 */
+  pred_reduction = -norm_beta * norm_beta;
+
+  /* subtract 2*fhat.beta */
+  for (i = 0; i < n; ++i)
+    {
+      double fi = gsl_vector_get(f, i);
+      double betai = gsl_vector_get(work, i);
+
+      pred_reduction -= 2.0 * (fi / normf) * betai;
+    }
+
+  return pred_reduction;
+}
diff -Nru gsl-doc-1.16/multifit_nlinear/convergence.c gsl-doc-2.3/multifit_nlinear/convergence.c
--- gsl-doc-1.16/multifit_nlinear/convergence.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/convergence.c	2016-07-07 20:36:10.000000000 +0000
@@ -0,0 +1,146 @@
+/* multifit_nlinear/convergence.c
+ * 
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_blas.h>
+
+static int test_delta (const gsl_vector * dx, const gsl_vector * x, 
+                       double epsabs, double epsrel);
+static double scaled_infnorm(const gsl_vector *x, const gsl_vector *g);
+
+/*
+gsl_multifit_nlinear_test()
+  Convergence tests for nonlinear minimization
+
+(1) |dx_i| <= xtol * (1 + |x_i|) for all i
+(2) || g .* x ||_inf <= gtol ||f||^2
+(3) ||f(x+dx) - f(x)|| <= ftol * max(||f(x)||, 1)
+
+Inputs: xtol - tolerance for step size
+        gtol - tolerance for gradient vector
+        ftol - tolerance for residual vector
+        info - (output)
+          1 - stopped by small x step
+          2 - stopped by small gradient
+          3 - stopped by small residual vector change
+        w    - workspace
+*/
+
+int
+gsl_multifit_nlinear_test (const double xtol, const double gtol,
+                           const double ftol, int *info,
+                           const gsl_multifit_nlinear_workspace * w)
+{
+  int status;
+  double gnorm, fnorm, phi;
+
+  *info = 0;
+
+  status = test_delta(w->dx, w->x, xtol*xtol, xtol);
+  if (status == GSL_SUCCESS)
+    {
+      *info = 1;
+      return GSL_SUCCESS;
+    }
+
+  /* compute gnorm = max_i( g_i * max(x_i, 1) ) */
+  gnorm = scaled_infnorm(w->x, w->g);
+
+  /* compute fnorm = ||f|| */
+  fnorm = gsl_blas_dnrm2(w->f);
+  phi = 0.5 * fnorm * fnorm;
+
+  if (gnorm <= gtol * GSL_MAX(phi, 1.0))
+    {
+      *info = 2;
+      return GSL_SUCCESS;
+    }
+
+#if 0 /* XXX */
+  if (dfnorm <= ftol * GSL_MAX(fnorm, 1.0))
+    {
+      *info = 3;
+      return GSL_SUCCESS;
+    }
+#else
+  (void)ftol;
+#endif
+
+  return GSL_CONTINUE;
+}
+
+static int
+test_delta (const gsl_vector * dx, const gsl_vector * x, 
+            double epsabs, double epsrel)
+{
+  size_t i;
+  int ok = 1;
+  const size_t n = x->size ;
+
+  if (epsrel < 0.0)
+    {
+      GSL_ERROR ("relative tolerance is negative", GSL_EBADTOL);
+    }
+
+  for (i = 0 ; i < n ; i++)
+    {
+      double xi = gsl_vector_get(x,i);
+      double dxi = gsl_vector_get(dx,i);
+      double tolerance = epsabs + epsrel * fabs(xi)  ;
+
+      if (fabs(dxi) < tolerance)
+        {
+          ok = 1;
+        }
+      else
+        {
+          ok = 0;
+          break;
+        }
+    }
+
+  if (ok)
+    return GSL_SUCCESS ;
+
+  return GSL_CONTINUE;
+}
+
+static double
+scaled_infnorm(const gsl_vector *x, const gsl_vector *g)
+{
+  const size_t n = x->size;
+  size_t i;
+  double norm = 0.0;
+
+  for (i = 0; i < n; ++i)
+    {
+      double xi = GSL_MAX(gsl_vector_get(x, i), 1.0);
+      double gi = gsl_vector_get(g, i);
+      double tmp = fabs(xi * gi);
+
+      if (tmp > norm)
+        norm = tmp;
+    }
+
+  return norm;
+}
diff -Nru gsl-doc-1.16/multifit_nlinear/covar.c gsl-doc-2.3/multifit_nlinear/covar.c
--- gsl-doc-1.16/multifit_nlinear/covar.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/covar.c	2016-08-24 14:19:26.000000000 +0000
@@ -0,0 +1,203 @@
+/* multifit_nlinear/covar.c
+ * 
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004, 2007 Brian Gough
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multifit_nlinear.h>
+
+static int covar_QRPT (gsl_matrix * r, gsl_permutation * perm,
+                       const double epsrel, gsl_matrix * covar);
+
+/* Compute the covariance matrix
+
+   cov = inv (J^T J)
+
+   by QRP^T decomposition of J
+*/
+
+int
+gsl_multifit_nlinear_covar (const gsl_matrix * J, const double epsrel,
+                            gsl_matrix * covar)
+{
+  int status;
+  gsl_matrix * r;
+  gsl_vector * tau;
+  gsl_vector * norm;
+  gsl_permutation * perm;
+  const size_t m = J->size1;
+  const size_t n = J->size2;
+  
+  if (m < n) 
+    {
+      GSL_ERROR ("Jacobian be rectangular M x N with M >= N", GSL_EBADLEN);
+    }
+
+  if (covar->size1 != covar->size2 || covar->size1 != n)
+    {
+      GSL_ERROR ("covariance matrix must be square and match second dimension of jacobian", GSL_EBADLEN);
+    }
+
+  r = gsl_matrix_alloc (m, n);
+  tau = gsl_vector_alloc (n);
+  perm = gsl_permutation_alloc (n) ;
+  norm = gsl_vector_alloc (n) ;
+  
+  {
+    int signum = 0;
+    gsl_matrix_memcpy (r, J);
+    gsl_linalg_QRPT_decomp (r, tau, perm, &signum, norm);
+  }
+  
+  status = covar_QRPT(r, perm, epsrel, covar);
+
+  gsl_matrix_free (r);
+  gsl_permutation_free (perm);
+  gsl_vector_free (tau);
+  gsl_vector_free (norm);
+
+  return status;
+}
+
+static int
+covar_QRPT (gsl_matrix * r, gsl_permutation * perm,
+            const double epsrel, gsl_matrix * covar)
+{
+  /* Form the inverse of R in the full upper triangle of R */
+
+  double tolr = epsrel * fabs(gsl_matrix_get(r, 0, 0));
+  const size_t n = r->size2;
+  size_t i, j, k;
+  size_t kmax = 0;
+
+  for (k = 0 ; k < n ; k++)
+    {
+      double rkk = gsl_matrix_get(r, k, k);
+
+      if (fabs(rkk) <= tolr)
+        {
+          break;
+        }
+
+      gsl_matrix_set(r, k, k, 1.0/rkk);
+
+      for (j = 0; j < k ; j++)
+        {
+          double t = gsl_matrix_get(r, j, k) / rkk;
+          gsl_matrix_set (r, j, k, 0.0);
+
+          for (i = 0; i <= j; i++)
+            {
+              double rik = gsl_matrix_get (r, i, k);
+              double rij = gsl_matrix_get (r, i, j);
+              
+              gsl_matrix_set (r, i, k, rik - t * rij);
+            }
+        }
+      kmax = k;
+    }
+
+  /* Form the full upper triangle of the inverse of R^T R in the full
+     upper triangle of R */
+
+  for (k = 0; k <= kmax ; k++)
+    {
+      for (j = 0; j < k; j++)
+        {
+          double rjk = gsl_matrix_get (r, j, k);
+
+          for (i = 0; i <= j ; i++)
+            {
+              double rij = gsl_matrix_get (r, i, j);
+              double rik = gsl_matrix_get (r, i, k);
+
+              gsl_matrix_set (r, i, j, rij + rjk * rik);
+            }
+        }
+      
+      {
+        double t = gsl_matrix_get (r, k, k);
+
+        for (i = 0; i <= k; i++)
+          {
+            double rik = gsl_matrix_get (r, i, k);
+
+            gsl_matrix_set (r, i, k, t * rik);
+          };
+      }
+    }
+
+  /* Form the full lower triangle of the covariance matrix in the
+     strict lower triangle of R and in w */
+
+  for (j = 0 ; j < n ; j++)
+    {
+      size_t pj = gsl_permutation_get (perm, j);
+      
+      for (i = 0; i <= j; i++)
+        {
+          size_t pi = gsl_permutation_get (perm, i);
+
+          double rij;
+
+          if (j > kmax)
+            {
+              gsl_matrix_set (r, i, j, 0.0);
+              rij = 0.0 ;
+            }
+          else 
+            {
+              rij = gsl_matrix_get (r, i, j);
+            }
+
+          if (pi > pj)
+            {
+              gsl_matrix_set (r, pi, pj, rij); 
+            } 
+          else if (pi < pj)
+            {
+              gsl_matrix_set (r, pj, pi, rij);
+            }
+
+        }
+      
+      { 
+        double rjj = gsl_matrix_get (r, j, j);
+        gsl_matrix_set (covar, pj, pj, rjj);
+      }
+    }
+
+     
+  /* symmetrize the covariance matrix */
+
+  for (j = 0 ; j < n ; j++)
+    {
+      for (i = 0; i < j ; i++)
+        {
+          double rji = gsl_matrix_get (r, j, i);
+
+          gsl_matrix_set (covar, j, i, rji);
+          gsl_matrix_set (covar, i, j, rji);
+        }
+    }
+
+  return GSL_SUCCESS;
+}
diff -Nru gsl-doc-1.16/multifit_nlinear/dogleg.c gsl-doc-2.3/multifit_nlinear/dogleg.c
--- gsl-doc-1.16/multifit_nlinear/dogleg.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/dogleg.c	2016-09-05 16:59:19.000000000 +0000
@@ -0,0 +1,489 @@
+/* multifit_nlinear/dogleg.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+
+/*
+ * This module contains an implementation of the Powell dogleg
+ * algorithm for nonlinear optimization problems. This implementation
+ * closely follows the following works:
+ *
+ * [1] H. B. Nielsen, K. Madsen, Introduction to Optimization and
+ *     Data Fitting, Informatics and Mathematical Modeling,
+ *     Technical University of Denmark (DTU), 2010.
+ *
+ * [2] J. E. Dennis and H. H. W. Mei, Two new unconstrained optimization
+ *     algorithms which use function and gradient values, J. Opt. Theory and
+ *     Appl., 28(4), 1979.
+ */
+
+typedef struct
+{
+  size_t n;                  /* number of observations */
+  size_t p;                  /* number of parameters */
+  gsl_vector *dx_gn;         /* Gauss-Newton step, size p */
+  gsl_vector *dx_sd;         /* steepest descent step, size p */
+  double norm_Dgn;           /* || D dx_gn || */
+  double norm_Dsd;           /* || D dx_sd || */
+  double norm_Dinvg;         /* || D^{-1} g || */
+  double norm_JDinv2g;       /* || J D^{-2} g || */
+  gsl_vector *workp;         /* workspace, length p */
+  gsl_vector *workn;         /* workspace, length n */
+
+  /* tunable parameters */
+  gsl_multifit_nlinear_parameters params;
+} dogleg_state_t;
+
+#include "common.c"
+
+static void * dogleg_alloc (const void * params, const size_t n, const size_t p);
+static void dogleg_free(void *vstate);
+static int dogleg_init(const void *vtrust_state, void *vstate);
+static int dogleg_preloop(const void * vtrust_state, void * vstate);
+static int dogleg_step(const void * vtrust_state, const double delta,
+                       gsl_vector * dx, void * vstate);
+static int dogleg_double_step(const void * vtrust_state, const double delta,
+                              gsl_vector * dx, void * vstate);
+static int dogleg_preduction(const void * vtrust_state, const gsl_vector * dx,
+                             double * pred, void * vstate);
+static int dogleg_calc_gn(const gsl_multifit_nlinear_trust_state * trust_state, gsl_vector * dx);
+static double dogleg_beta(const double t, const double delta,
+                          const gsl_vector * diag, dogleg_state_t * state);
+
+static void *
+dogleg_alloc (const void * params, const size_t n, const size_t p)
+{
+  const gsl_multifit_nlinear_parameters *mparams = (const gsl_multifit_nlinear_parameters *) params;
+  dogleg_state_t *state;
+  
+  state = calloc(1, sizeof(dogleg_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate dogleg state", GSL_ENOMEM);
+    }
+
+  state->dx_gn = gsl_vector_alloc(p);
+  if (state->dx_gn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for dx_gn", GSL_ENOMEM);
+    }
+
+  state->dx_sd = gsl_vector_alloc(p);
+  if (state->dx_sd == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for dx_sd", GSL_ENOMEM);
+    }
+
+  state->workp = gsl_vector_alloc(p);
+  if (state->workp == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workp", GSL_ENOMEM);
+    }
+
+  state->workn = gsl_vector_alloc(n);
+  if (state->workn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workn", GSL_ENOMEM);
+    }
+
+  state->n = n;
+  state->p = p;
+  state->params = *mparams;
+
+  return state;
+}
+
+static void
+dogleg_free(void *vstate)
+{
+  dogleg_state_t *state = (dogleg_state_t *) vstate;
+
+  if (state->dx_gn)
+    gsl_vector_free(state->dx_gn);
+
+  if (state->dx_sd)
+    gsl_vector_free(state->dx_sd);
+
+  if (state->workp)
+    gsl_vector_free(state->workp);
+
+  if (state->workn)
+    gsl_vector_free(state->workn);
+
+  free(state);
+}
+
+/*
+dogleg_init()
+  Initialize dogleg solver
+
+Inputs: vtrust_state - trust state
+        vstate       - workspace
+
+Return: success/error
+*/
+
+static int
+dogleg_init(const void *vtrust_state, void *vstate)
+{
+  (void)vtrust_state;
+  (void)vstate;
+
+  return GSL_SUCCESS;
+}
+
+/*
+dogleg_preloop()
+  Initialize dogleg method prior to iteration loop.
+This involves computing the steepest descent step. The
+Gauss-Newton step is computed if needed in the _step()
+routines.
+
+Notes: on output,
+1) state->dx_sd contains steepest descent step
+2) state->norm_Dinvg contains || D^{-1} g ||
+3) state->norm_JDinv2g contains || J D^{-2} g ||
+*/
+
+static int
+dogleg_preloop(const void * vtrust_state, void * vstate)
+{
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  dogleg_state_t *state = (dogleg_state_t *) vstate;
+  double u;
+  double alpha; /* ||g||^2 / ||Jg||^2 */
+
+  /* calculate the steepest descent step */
+
+  /* compute workp = D^{-1} g and its norm */
+  gsl_vector_memcpy(state->workp, trust_state->g);
+  gsl_vector_div(state->workp, trust_state->diag);
+  state->norm_Dinvg = gsl_blas_dnrm2(state->workp);
+
+  /* compute workp = D^{-2} g */
+  gsl_vector_div(state->workp, trust_state->diag);
+
+  /* compute: workn = J D^{-2} g */
+  gsl_blas_dgemv(CblasNoTrans, 1.0, trust_state->J, state->workp, 0.0, state->workn);
+  state->norm_JDinv2g = gsl_blas_dnrm2(state->workn);
+
+  u = state->norm_Dinvg / state->norm_JDinv2g;
+  alpha = u * u;
+
+  /* dx_sd = -alpha D^{-2} g */
+  gsl_vector_memcpy(state->dx_sd, state->workp);
+  gsl_vector_scale(state->dx_sd, -alpha);
+
+  state->norm_Dsd = scaled_enorm(trust_state->diag, state->dx_sd);
+  state->norm_Dgn = -1.0; /* computed later if needed */
+
+  return GSL_SUCCESS;
+}
+
+/*
+dogleg_step()
+  Calculate a new step vector
+*/
+
+static int
+dogleg_step(const void * vtrust_state, const double delta,
+            gsl_vector * dx, void * vstate)
+{
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  dogleg_state_t *state = (dogleg_state_t *) vstate;
+
+  if (state->norm_Dsd >= delta)
+    {
+      /* steepest descent step is outside trust region;
+       * truncate steepest descent step to trust region boundary */
+      gsl_vector_memcpy(dx, state->dx_sd);
+      gsl_vector_scale(dx, delta / state->norm_Dsd);
+    }
+  else
+    {
+      /* compute Gauss-Newton step if needed */
+      if (state->norm_Dgn < 0.0)
+        {
+          int status = dogleg_calc_gn(trust_state, state->dx_gn);
+
+          if (status)
+            return status;
+
+          /* compute || D dx_gn || */
+          state->norm_Dgn = scaled_enorm(trust_state->diag, state->dx_gn);
+        }
+
+      if (state->norm_Dgn <= delta)
+        {
+          /* Gauss-Newton step is inside trust region, use it as final step
+           * since it is the global minimizer of the quadratic model function */
+          gsl_vector_memcpy(dx, state->dx_gn);
+        }
+      else
+        {
+          /* Gauss-Newton step is outside trust region, but steepest
+           * descent is inside; use dogleg step */
+
+          double beta = dogleg_beta(1.0, delta, trust_state->diag, state);
+
+          /* compute: workp = dx_gn - dx_sd */
+          scaled_addition(1.0, state->dx_gn, -1.0, state->dx_sd, state->workp);
+
+          /* dx = dx_sd + beta*(dx_gn - dx_sd) */
+          scaled_addition(beta, state->workp, 1.0, state->dx_sd, dx);
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+/*
+dogleg_double_step()
+  Calculate a new step with double dogleg method. Based on
+section 3 of [2]
+*/
+
+static int
+dogleg_double_step(const void * vtrust_state, const double delta,
+                   gsl_vector * dx, void * vstate)
+{
+  const double alpha_fac = 0.8; /* recommended value from Dennis and Mei */
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  dogleg_state_t *state = (dogleg_state_t *) vstate;
+
+  if (state->norm_Dsd >= delta)
+    {
+      /* steepest descent step is outside trust region;
+       * truncate steepest descent step to trust region boundary */
+      gsl_vector_memcpy(dx, state->dx_sd);
+      gsl_vector_scale(dx, delta / state->norm_Dsd);
+    }
+  else
+    {
+      /* compute Gauss-Newton step if needed */
+      if (state->norm_Dgn < 0.0)
+        {
+          int status = dogleg_calc_gn(trust_state, state->dx_gn);
+
+          if (status)
+            return status;
+
+          /* compute || D dx_gn || */
+          state->norm_Dgn = scaled_enorm(trust_state->diag, state->dx_gn);
+        }
+
+      if (state->norm_Dgn <= delta)
+        {
+          /* Gauss-Newton step is inside trust region, use it as final step
+           * since it is the global minimizer of the quadratic model function */
+          gsl_vector_memcpy(dx, state->dx_gn);
+        }
+      else
+        {
+          double t, u, v, c;
+
+          /* compute: u = ||D^{-1} g||^2 / ||J D^{-2} g||^2 */
+          v = state->norm_Dinvg / state->norm_JDinv2g;
+          u = v * v;
+
+          /* compute: v = g^T dx_gn */
+          gsl_blas_ddot(trust_state->g, state->dx_gn, &v);
+
+          /* compute: c = ||D^{-1} g||^4 / (||J D^{-2} g||^2 * |g^T dx_gn|) */
+          c = u * (state->norm_Dinvg / fabs(v)) * state->norm_Dinvg;
+
+          /* compute: t = 1 - alpha_fac*(1-c) */
+          t = 1.0 - alpha_fac*(1.0 - c);
+
+          if (t * state->norm_Dgn <= delta)
+            {
+              /* set dx = (delta / ||D dx_gn||) dx_gn */
+              gsl_vector_memcpy(dx, state->dx_gn);
+              gsl_vector_scale(dx, delta / state->norm_Dgn);
+            }
+          else
+            {
+              /* Cauchy point is inside, Gauss-Newton is outside trust region;
+               * use double dogleg step */
+
+              double beta = dogleg_beta(t, delta, trust_state->diag, state);
+
+              /* compute: workp = t*dx_gn - dx_sd */
+              scaled_addition(t, state->dx_gn, -1.0, state->dx_sd, state->workp);
+
+              /* dx = dx_sd + beta*(t*dx_gn - dx_sd) */
+              scaled_addition(beta, state->workp, 1.0, state->dx_sd, dx);
+            }
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+dogleg_preduction(const void * vtrust_state, const gsl_vector * dx,
+                  double * pred, void * vstate)
+{
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  dogleg_state_t *state = (dogleg_state_t *) vstate;
+
+  *pred = quadratic_preduction(trust_state->f, trust_state->J, dx, state->workn);
+
+  return GSL_SUCCESS;
+}
+
+/*
+dogleg_calc_gn()
+  Calculate Gauss-Newton step which satisfies:
+
+J dx_gn = -f
+
+Inputs: trust_state - trust state variables
+        dx          - (output) Gauss-Newton step
+
+Return: success/error
+*/
+
+static int
+dogleg_calc_gn(const gsl_multifit_nlinear_trust_state * trust_state, gsl_vector * dx)
+{
+  int status;
+  const gsl_multifit_nlinear_parameters *params = trust_state->params;
+
+  /* initialize linear least squares solver */
+  status = (params->solver->init)(trust_state, trust_state->solver_state);
+  if (status)
+    return status;
+
+  /* prepare the linear solver to compute Gauss-Newton step */
+  status = (params->solver->presolve)(0.0, trust_state, trust_state->solver_state);
+  if (status)
+    return status;
+
+  /* solve: J dx_gn = -f for Gauss-Newton step */
+  status = (params->solver->solve)(trust_state->f,
+                                   dx,
+                                   trust_state,
+                                   trust_state->solver_state);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+}
+
+/*
+dogleg_beta()
+  This function finds beta in [0,1] such that the step
+
+dx = dx_sd + beta*(t*dx_gn - dx_sd)
+
+has norm
+
+||D dx|| = delta
+
+beta is the positive root of the quadratic:
+
+a beta^2 + b beta + c = 0
+
+with
+
+a = ||D(t*dx_gn - dx_sd)||^2
+b = 2 dx_sd^T D^T D (t*dx_gn - dx_sd)
+c = ||D dx_sd||^2 - delta^2 
+
+Inputs: t     - amount of Gauss-Newton step to use for dogleg
+                (= 1 for classical dogleg, <= 1 for double dogleg)
+        delta - trust region radius
+        diag  - diag(D) scaling matrix
+        state - workspace
+*/
+
+static double
+dogleg_beta(const double t, const double delta,
+            const gsl_vector * diag, dogleg_state_t * state)
+{
+  double beta;
+  double a, b, c;
+
+  /* compute: workp = t*dx_gn - dx_sd */
+  scaled_addition(t, state->dx_gn, -1.0, state->dx_sd, state->workp);
+
+  /* a = || D (t*dx_gn - dx_sd) ||^2 */
+  a = scaled_enorm(diag, state->workp);
+  a *= a;
+
+  /* workp = D^T D (t*dx_gn - dx_sd) */
+  gsl_vector_mul(state->workp, diag);
+  gsl_vector_mul(state->workp, diag);
+
+  /* b = 2 dx_sd^T D^T D (t*dx_gn - dx-sd) */
+  gsl_blas_ddot(state->dx_sd, state->workp, &b);
+  b *= 2.0;
+
+  /* c = || D dx_sd ||^2 - delta^2 = (||D dx_sd|| + delta) (||D dx_sd|| - delta) */
+  c = (state->norm_Dsd + delta) * (state->norm_Dsd - delta);
+
+  if (b > 0.0)
+    {
+      beta = (-2.0 * c) / (b + sqrt(b*b - 4.0*a*c));
+    }
+  else
+    {
+      beta = (-b + sqrt(b*b - 4.0*a*c)) / (2.0 * a);
+    }
+
+  return beta;
+}
+
+static const gsl_multifit_nlinear_trs dogleg_type =
+{
+  "dogleg",
+  dogleg_alloc,
+  dogleg_init,
+  dogleg_preloop,
+  dogleg_step,
+  dogleg_preduction,
+  dogleg_free
+};
+
+const gsl_multifit_nlinear_trs *gsl_multifit_nlinear_trs_dogleg = &dogleg_type;
+
+static const gsl_multifit_nlinear_trs ddogleg_type =
+{
+  "double-dogleg",
+  dogleg_alloc,
+  dogleg_init,
+  dogleg_preloop,
+  dogleg_double_step,
+  dogleg_preduction,
+  dogleg_free
+};
+
+const gsl_multifit_nlinear_trs *gsl_multifit_nlinear_trs_ddogleg = &ddogleg_type;
diff -Nru gsl-doc-1.16/multifit_nlinear/fdf.c gsl-doc-2.3/multifit_nlinear/fdf.c
--- gsl-doc-1.16/multifit_nlinear/fdf.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/fdf.c	2016-09-24 15:46:41.000000000 +0000
@@ -0,0 +1,511 @@
+/* multifit_nlinear/fdf.c
+ * 
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
+ * Copyright (C) 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_multifit_nlinear.h>
+
+gsl_multifit_nlinear_workspace *
+gsl_multifit_nlinear_alloc (const gsl_multifit_nlinear_type * T, 
+                            const gsl_multifit_nlinear_parameters * params,
+                            const size_t n, const size_t p)
+{
+  gsl_multifit_nlinear_workspace * w;
+
+  if (n < p)
+    {
+      GSL_ERROR_VAL ("insufficient data points, n < p", GSL_EINVAL, 0);
+    }
+
+  w = calloc (1, sizeof (gsl_multifit_nlinear_workspace));
+  if (w == 0)
+    {
+      GSL_ERROR_VAL ("failed to allocate space for multifit workspace",
+                     GSL_ENOMEM, 0);
+    }
+
+  w->x = gsl_vector_calloc (p);
+  if (w->x == 0) 
+    {
+      gsl_multifit_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
+    }
+
+  w->f = gsl_vector_calloc (n);
+  if (w->f == 0) 
+    {
+      gsl_multifit_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for f", GSL_ENOMEM, 0);
+    }
+
+  w->dx = gsl_vector_calloc (p);
+  if (w->dx == 0) 
+    {
+      gsl_multifit_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for dx", GSL_ENOMEM, 0);
+    }
+
+  w->g = gsl_vector_alloc (p);
+  if (w->g == 0) 
+    {
+      gsl_multifit_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for g", GSL_ENOMEM, 0);
+    }
+
+  w->J = gsl_matrix_alloc(n, p);
+  if (w->J == 0) 
+    {
+      gsl_multifit_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for Jacobian", GSL_ENOMEM, 0);
+    }
+
+  w->sqrt_wts_work = gsl_vector_calloc (n);
+  if (w->sqrt_wts_work == 0)
+    {
+      gsl_multifit_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for weights", GSL_ENOMEM, 0);
+    }
+
+  w->state = (T->alloc)(params, n, p);
+  if (w->state == 0)
+    {
+      gsl_multifit_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for multifit state", GSL_ENOMEM, 0);
+    }
+
+  w->type = T;
+  w->fdf = NULL;
+  w->niter = 0;
+  w->params = *params;
+
+  return w;
+}
+
+void
+gsl_multifit_nlinear_free (gsl_multifit_nlinear_workspace * w)
+{
+  RETURN_IF_NULL (w);
+
+  if (w->state)
+    (w->type->free) (w->state);
+
+  if (w->dx)
+    gsl_vector_free (w->dx);
+
+  if (w->x)
+    gsl_vector_free (w->x);
+
+  if (w->f)
+    gsl_vector_free (w->f);
+
+  if (w->sqrt_wts_work)
+    gsl_vector_free (w->sqrt_wts_work);
+
+  if (w->g)
+    gsl_vector_free (w->g);
+
+  if (w->J)
+    gsl_matrix_free (w->J);
+
+  free (w);
+}
+
+gsl_multifit_nlinear_parameters
+gsl_multifit_nlinear_default_parameters(void)
+{
+  gsl_multifit_nlinear_parameters params;
+
+  params.trs = gsl_multifit_nlinear_trs_lm;
+  params.scale = gsl_multifit_nlinear_scale_more;
+  params.solver = gsl_multifit_nlinear_solver_qr;
+  params.fdtype = GSL_MULTIFIT_NLINEAR_FWDIFF;
+  params.factor_up = 3.0;
+  params.factor_down = 2.0;
+  params.avmax = 0.75;
+  params.h_df = GSL_SQRT_DBL_EPSILON;
+  params.h_fvv = 0.02;
+
+  return params;
+}
+
+int
+gsl_multifit_nlinear_init (const gsl_vector * x,
+                           gsl_multifit_nlinear_fdf * fdf,
+                           gsl_multifit_nlinear_workspace * w)
+{
+  return gsl_multifit_nlinear_winit(x, NULL, fdf, w);
+}
+
+int
+gsl_multifit_nlinear_winit (const gsl_vector * x,
+                            const gsl_vector * wts,
+                            gsl_multifit_nlinear_fdf * fdf, 
+                            gsl_multifit_nlinear_workspace * w)
+{
+  const size_t n = w->f->size;
+
+  if (n != fdf->n)
+    {
+      GSL_ERROR ("function size does not match workspace", GSL_EBADLEN);
+    }
+  else if (w->x->size != x->size)
+    {
+      GSL_ERROR ("vector length does not match workspace", GSL_EBADLEN);
+    }
+  else if (wts != NULL && n != wts->size)
+    {
+      GSL_ERROR ("weight vector length does not match workspace", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i;
+
+      /* initialize counters for function and Jacobian evaluations */
+      fdf->nevalf = 0;
+      fdf->nevaldf = 0;
+      fdf->nevalfvv = 0;
+
+      w->fdf = fdf;
+      gsl_vector_memcpy(w->x, x);
+      w->niter = 0;
+
+      if (wts)
+        {
+          w->sqrt_wts = w->sqrt_wts_work;
+
+          for (i = 0; i < n; ++i)
+            {
+              double wi = gsl_vector_get(wts, i);
+              gsl_vector_set(w->sqrt_wts, i, sqrt(wi));
+            }
+        }
+      else
+        {
+          w->sqrt_wts = NULL;
+        }
+  
+      return (w->type->init) (w->state, w->sqrt_wts, w->fdf,
+                              w->x, w->f, w->J, w->g);
+    }
+}
+
+int
+gsl_multifit_nlinear_iterate (gsl_multifit_nlinear_workspace * w)
+{
+  int status =
+    (w->type->iterate) (w->state, w->sqrt_wts, w->fdf,
+                        w->x, w->f, w->J, w->g, w->dx);
+
+  w->niter++;
+
+  return status;
+}
+
+double
+gsl_multifit_nlinear_avratio (const gsl_multifit_nlinear_workspace * w)
+{
+  return (w->type->avratio) (w->state);
+}
+
+/*
+gsl_multifit_nlinear_driver()
+  Iterate the nonlinear least squares solver until completion
+
+Inputs: maxiter  - maximum iterations to allow
+        xtol     - tolerance in step x
+        gtol     - tolerance in gradient
+        ftol     - tolerance in ||f||
+        callback - callback function to call each iteration
+        callback_params - parameters to pass to callback function
+        info     - (output) info flag on why iteration terminated
+                   1 = stopped due to small step size ||dx|
+                   2 = stopped due to small gradient
+                   3 = stopped due to small change in f
+                   GSL_ETOLX = ||dx|| has converged to within machine
+                               precision (and xtol is too small)
+                   GSL_ETOLG = ||g||_inf is smaller than machine
+                               precision (gtol is too small)
+                   GSL_ETOLF = change in ||f|| is smaller than machine
+                               precision (ftol is too small)
+        w        - workspace
+
+Return:
+GSL_SUCCESS if converged
+GSL_MAXITER if maxiter exceeded without converging
+GSL_ENOPROG if no accepted step found on first iteration
+*/
+
+int
+gsl_multifit_nlinear_driver (const size_t maxiter,
+                             const double xtol,
+                             const double gtol,
+                             const double ftol,
+                             void (*callback)(const size_t iter, void *params,
+                                              const gsl_multifit_nlinear_workspace *w),
+                             void *callback_params,
+                             int *info,
+                             gsl_multifit_nlinear_workspace * w)
+{
+  int status;
+  size_t iter = 0;
+
+  /* call user callback function prior to any iterations
+   * with initial system state */
+  if (callback)
+    callback(iter, callback_params, w);
+
+  do
+    {
+      status = gsl_multifit_nlinear_iterate (w);
+
+      /*
+       * If the solver reports no progress on the first iteration,
+       * then it didn't find a single step to reduce the
+       * cost function and more iterations won't help so return.
+       *
+       * If we get a no progress flag on subsequent iterations,
+       * it means we did find a good step in a previous iteration,
+       * so continue iterating since the solver has now reset
+       * mu to its initial value.
+       */
+      if (status == GSL_ENOPROG && iter == 0)
+        {
+          *info = status;
+          return GSL_EMAXITER;
+        }
+
+      ++iter;
+
+      if (callback)
+        callback(iter, callback_params, w);
+
+      /* test for convergence */
+      status = gsl_multifit_nlinear_test(xtol, gtol, ftol, info, w);
+    }
+  while (status == GSL_CONTINUE && iter < maxiter);
+
+  /*
+   * the following error codes mean that the solution has converged
+   * to within machine precision, so record the error code in info
+   * and return success
+   */
+  if (status == GSL_ETOLF || status == GSL_ETOLX || status == GSL_ETOLG)
+    {
+      *info = status;
+      status = GSL_SUCCESS;
+    }
+
+  /* check if max iterations reached */
+  if (iter >= maxiter && status != GSL_SUCCESS)
+    status = GSL_EMAXITER;
+
+  return status;
+} /* gsl_multifit_nlinear_driver() */
+
+gsl_matrix *
+gsl_multifit_nlinear_jac (const gsl_multifit_nlinear_workspace * w)
+{
+  return w->J;
+}
+
+const char *
+gsl_multifit_nlinear_name (const gsl_multifit_nlinear_workspace * w)
+{
+  return w->type->name;
+}
+
+gsl_vector *
+gsl_multifit_nlinear_position (const gsl_multifit_nlinear_workspace * w)
+{
+  return w->x;
+}
+
+gsl_vector *
+gsl_multifit_nlinear_residual (const gsl_multifit_nlinear_workspace * w)
+{
+  return w->f;
+}
+
+size_t
+gsl_multifit_nlinear_niter (const gsl_multifit_nlinear_workspace * w)
+{
+  return w->niter;
+}
+
+int
+gsl_multifit_nlinear_rcond (double *rcond, const gsl_multifit_nlinear_workspace * w)
+{
+  int status = (w->type->rcond) (rcond, w->state);
+  return status;
+}
+
+const char *
+gsl_multifit_nlinear_trs_name (const gsl_multifit_nlinear_workspace * w)
+{
+  return w->params.trs->name;
+}
+
+/*
+gsl_multifit_nlinear_eval_f()
+  Compute residual vector y with user callback function, and apply
+weighting transform if given:
+
+y~ = sqrt(W) y
+
+Inputs: fdf  - callback function
+        x    - model parameters
+        swts - weight matrix sqrt(W) = sqrt(diag(w1,w2,...,wn))
+               set to NULL for unweighted fit
+        y    - (output) (weighted) residual vector
+               y_i = sqrt(w_i) f_i where f_i is unweighted residual
+*/
+
+int
+gsl_multifit_nlinear_eval_f(gsl_multifit_nlinear_fdf *fdf,
+                            const gsl_vector *x,
+                            const gsl_vector *swts,
+                            gsl_vector *y)
+{
+  int s = ((*((fdf)->f)) (x, fdf->params, y));
+
+  ++(fdf->nevalf);
+
+  /* y <- sqrt(W) y */
+  if (swts)
+    gsl_vector_mul(y, swts);
+
+  return s;
+}
+
+/*
+gsl_multifit_nlinear_eval_df()
+  Compute Jacobian matrix J with user callback function, and apply
+weighting transform if given:
+
+J~ = sqrt(W) J
+
+Inputs: x      - model parameters
+        f      - residual vector f(x)
+        swts   - weight matrix W = diag(w1,w2,...,wn)
+                 set to NULL for unweighted fit
+        h      - finite difference step size
+        fdtype - finite difference method
+        fdf    - callback function
+        df     - (output) (weighted) Jacobian matrix
+                 df = sqrt(W) df where df is unweighted Jacobian
+        work   - workspace for finite difference, size n
+*/
+
+int
+gsl_multifit_nlinear_eval_df(const gsl_vector *x,
+                             const gsl_vector *f,
+                             const gsl_vector *swts,
+                             const double h,
+                             const gsl_multifit_nlinear_fdtype fdtype,
+                             gsl_multifit_nlinear_fdf *fdf,
+                             gsl_matrix *df,
+                             gsl_vector *work)
+{
+  int status;
+
+  if (fdf->df)
+    {
+      /* call user-supplied function */
+      status = ((*((fdf)->df)) (x, fdf->params, df));
+      ++(fdf->nevaldf);
+
+      /* J <- sqrt(W) J */
+      if (swts)
+        {
+          const size_t n = swts->size;
+          size_t i;
+
+          for (i = 0; i < n; ++i)
+            {
+              double swi = gsl_vector_get(swts, i);
+              gsl_vector_view v = gsl_matrix_row(df, i);
+
+              gsl_vector_scale(&v.vector, swi);
+            }
+        }
+    }
+  else
+    {
+      /* use finite difference Jacobian approximation */
+      status = gsl_multifit_nlinear_df(h, fdtype, x, swts, fdf, f, df, work);
+    }
+
+  return status;
+}
+
+/*
+gsl_multifit_nlinear_eval_fvv()
+  Compute second direction derivative vector yvv with user
+callback function, and apply weighting transform if given:
+
+yvv~ = sqrt(W) yvv
+
+Inputs: h    - step size for finite difference, if needed
+        x    - model parameters, size p
+        v    - unscaled geodesic velocity vector, size p
+        f    - residual vector f(x), size n
+        J    - Jacobian matrix J(x), n-by-p
+        swts - weight matrix sqrt(W) = sqrt(diag(w1,w2,...,wn))
+               set to NULL for unweighted fit
+        fdf  - callback function
+        yvv  - (output) (weighted) second directional derivative vector
+               yvv_i = sqrt(w_i) fvv_i where f_i is unweighted
+        work - workspace, size p
+*/
+
+int
+gsl_multifit_nlinear_eval_fvv(const double h,
+                              const gsl_vector *x,
+                              const gsl_vector *v,
+                              const gsl_vector *f,
+                              const gsl_matrix *J,
+                              const gsl_vector *swts,
+                              gsl_multifit_nlinear_fdf *fdf,
+                              gsl_vector *yvv, gsl_vector *work)
+{
+  int status;
+  
+  if (fdf->fvv != NULL)
+    {
+      /* call user-supplied function */
+      status = ((*((fdf)->fvv)) (x, v, fdf->params, yvv));
+      ++(fdf->nevalfvv);
+
+      /* yvv <- sqrt(W) yvv */
+      if (swts)
+        gsl_vector_mul(yvv, swts);
+    }
+  else
+    {
+      /* use finite difference approximation */
+      status = gsl_multifit_nlinear_fdfvv(h, x, v, f, J,
+                                          swts, fdf, yvv, work);
+    }
+
+  return status;
+}
diff -Nru gsl-doc-1.16/multifit_nlinear/fdfvv.c gsl-doc-2.3/multifit_nlinear/fdfvv.c
--- gsl-doc-1.16/multifit_nlinear/fdfvv.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/fdfvv.c	2016-09-24 10:55:01.000000000 +0000
@@ -0,0 +1,121 @@
+/* multifit_nlinear/fdfvv.c
+ * 
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_blas.h>
+
+/*
+fdfvv()
+  Compute approximate second directional derivative using
+finite differences.
+
+See Eq. 19 of:
+
+M. K. Transtrum, J. P. Sethna, Improvements to the Levenberg
+Marquardt algorithm for nonlinear least-squares minimization,
+arXiv:1201.5885, 2012.
+
+Inputs: h     - step size for finite difference
+        x     - parameter vector, size p
+        v     - geodesic velocity, size p
+        f     - vector of function values f_i(x), size n
+        J     - Jacobian matrix J(x), n-by-p
+        swts  - data weights
+        fdf   - fdf struct
+        fvv   - (output) approximate second directional derivative
+                vector D_v^2 f(x)
+        work  - workspace, size p
+
+Return: success or error
+*/
+
+static int
+fdfvv(const double h, const gsl_vector *x, const gsl_vector *v,
+      const gsl_vector *f, const gsl_matrix *J, const gsl_vector *swts,
+      gsl_multifit_nlinear_fdf *fdf, gsl_vector *fvv, gsl_vector *work)
+{
+  int status;
+  const size_t n = fdf->n;
+  const size_t p = fdf->p;
+  const double hinv = 1.0 / h;
+  size_t i;
+
+  /* compute work = x + h*v */
+  for (i = 0; i < p; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      double vi = gsl_vector_get(v, i);
+
+      gsl_vector_set(work, i, xi + h * vi);
+    }
+
+  /* compute f(x + h*v) */
+  status = gsl_multifit_nlinear_eval_f (fdf, work, swts, fvv);
+  if (status)
+    return status;
+
+  for (i = 0; i < n; ++i)
+    {
+      double fi = gsl_vector_get(f, i);    /* f_i(x) */
+      double fip = gsl_vector_get(fvv, i); /* f_i(x + h*v) */
+      gsl_vector_const_view row = gsl_matrix_const_row(J, i);
+      double u, fvvi;
+
+      /* compute u = sum_{ij} J_{ij} D v_j */
+      gsl_blas_ddot(&row.vector, v, &u);
+
+      fvvi = (2.0 * hinv) * ((fip - fi) * hinv - u);
+
+      gsl_vector_set(fvv, i, fvvi);
+    }
+
+  return status;
+}
+
+/*
+gsl_multifit_nlinear_fdfvv()
+  Compute approximate second directional derivative
+using finite differences
+
+Inputs: h    - step size for finite difference
+        x    - parameter vector, size p
+        v    - geodesic velocity, size p
+        f    - function values f_i(x), size n
+        J    - Jacobian matrix J(x), n-by-p
+        swts - sqrt data weights (set to NULL if not needed)
+        fdf  - fdf
+        fvv  - (output) approximate (weighted) second directional derivative
+               vector, size n, sqrt(W) fvv
+        work - workspace, size p
+
+Return: success or error
+*/
+
+int
+gsl_multifit_nlinear_fdfvv(const double h, const gsl_vector *x, const gsl_vector *v,
+                           const gsl_vector *f, const gsl_matrix *J,
+                           const gsl_vector *swts, gsl_multifit_nlinear_fdf *fdf,
+                           gsl_vector *fvv, gsl_vector *work)
+{
+  return fdfvv(h, x, v, f, J, swts, fdf, fvv, work);
+}
diff -Nru gsl-doc-1.16/multifit_nlinear/fdjac.c gsl-doc-2.3/multifit_nlinear/fdjac.c
--- gsl-doc-1.16/multifit_nlinear/fdjac.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/fdjac.c	2016-09-24 10:53:11.000000000 +0000
@@ -0,0 +1,194 @@
+/* multifit_nlinear/fdjac.c
+ * 
+ * Copyright (C) 2013, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ *
+ *
+ * This module contains routines for approximating the Jacobian with
+ * finite differences for nonlinear least-squares fitting.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+
+static int forward_jac(const double h, const gsl_vector *x,
+                       const gsl_vector *wts,
+                       gsl_multifit_nlinear_fdf *fdf,
+                       const gsl_vector *f, gsl_matrix *J);
+static int center_jac(const double h, const gsl_vector *x, const gsl_vector *wts,
+                      gsl_multifit_nlinear_fdf *fdf, gsl_matrix *J, gsl_vector *work);
+
+/*
+forward_jac()
+  Compute approximate Jacobian using forward differences
+
+Inputs: h   - finite difference step size
+        x   - parameter vector
+        wts - data weights
+        fdf - fdf struct
+        f   - (input) vector of function values f_i(x)
+        J   - (output) Jacobian matrix
+
+Return: success or error
+*/
+
+static int
+forward_jac(const double h, const gsl_vector *x, const gsl_vector *wts,
+            gsl_multifit_nlinear_fdf *fdf, const gsl_vector *f, gsl_matrix *J)
+{
+  int status = 0;
+  size_t i, j;
+  double delta;
+
+  for (j = 0; j < fdf->p; ++j)
+    {
+      double xj = gsl_vector_get(x, j);
+
+      /* use column j of J as temporary storage for f(x + dx) */
+      gsl_vector_view v = gsl_matrix_column(J, j);
+
+      delta = h * fabs(xj);
+      if (delta == 0.0)
+        delta = h;
+
+      /* perturb x_j to compute forward difference */
+      gsl_vector_set((gsl_vector *) x, j, xj + delta);
+
+      status += gsl_multifit_nlinear_eval_f (fdf, x, wts, &v.vector);
+      if (status)
+        return status;
+
+      /* restore x_j */
+      gsl_vector_set((gsl_vector *) x, j, xj);
+
+      delta = 1.0 / delta;
+      for (i = 0; i < fdf->n; ++i)
+        {
+          double fnext = gsl_vector_get(&v.vector, i);
+          double fi = gsl_vector_get(f, i);
+
+          gsl_matrix_set(J, i, j, (fnext - fi) * delta);
+        }
+    }
+
+  return status;
+}
+
+/*
+center_jac()
+  Compute approximate Jacobian using centered differences
+
+Inputs: h    - finite difference step size
+        x    - parameter vector
+        wts  - data weights
+        fdf  - fdf struct
+        J    - (output) Jacobian matrix
+        work - additional workspace, size n
+
+Return: success or error
+*/
+
+static int
+center_jac(const double h, const gsl_vector *x, const gsl_vector *wts,
+           gsl_multifit_nlinear_fdf *fdf, gsl_matrix *J, gsl_vector *work)
+{
+  int status = 0;
+  size_t i, j;
+  double delta;
+
+  for (j = 0; j < fdf->p; ++j)
+    {
+      double xj = gsl_vector_get(x, j);
+
+      /* use column j of J as temporary storage for f(x + dx) */
+      gsl_vector_view v = gsl_matrix_column(J, j);
+
+      delta = h * fabs(xj);
+      if (delta == 0.0)
+        delta = h;
+
+      /* perturb x_j to compute forward difference, f(x + 1/2 delta e_j) */
+      gsl_vector_set((gsl_vector *) x, j, xj + 0.5 * delta);
+
+      status += gsl_multifit_nlinear_eval_f (fdf, x, wts, &v.vector);
+      if (status)
+        return status;
+
+      /* perturb x_j to compute backward difference, f(x - 1/2 delta e_j) */
+      gsl_vector_set((gsl_vector *) x, j, xj - 0.5 * delta);
+
+      status += gsl_multifit_nlinear_eval_f (fdf, x, wts, work);
+      if (status)
+        return status;
+
+      /* restore x_j */
+      gsl_vector_set((gsl_vector *) x, j, xj);
+
+      delta = 1.0 / delta;
+      for (i = 0; i < fdf->n; ++i)
+        {
+          double fnext = gsl_vector_get(&v.vector, i);
+          double fprev = gsl_vector_get(work, i);
+
+          gsl_matrix_set(J, i, j, (fnext - fprev) * delta);
+        }
+    }
+
+  return status;
+}
+
+/*
+gsl_multifit_nlinear_df()
+  Compute approximate Jacobian using finite differences
+
+Inputs: h      - finite difference step size
+        fdtype - finite difference method
+        x      - parameter vector
+        wts    - data weights (set to NULL if not needed)
+        fdf    - fdf
+        f      - (input) function values f_i(x)
+        J      - (output) approximate (weighted) Jacobian matrix, sqrt(W) * J
+        work   - additional workspace for centered differences, size n
+
+Return: success or error
+*/
+
+int
+gsl_multifit_nlinear_df(const double h, const gsl_multifit_nlinear_fdtype fdtype,
+                        const gsl_vector *x, const gsl_vector *wts,
+                        gsl_multifit_nlinear_fdf *fdf,
+                        const gsl_vector *f, gsl_matrix *J, gsl_vector *work)
+{
+  int status;
+
+  if (fdtype == GSL_MULTIFIT_NLINEAR_FWDIFF)
+    {
+      status = forward_jac(h, x, wts, fdf, f, J);
+    }
+  else if (fdtype == GSL_MULTIFIT_NLINEAR_CTRDIFF)
+    {
+      status = center_jac(h, x, wts, fdf, J, work);
+    }
+  else
+    {
+      GSL_ERROR("invalid specified fdtype", GSL_EINVAL);
+    }
+
+  return status;
+}
diff -Nru gsl-doc-1.16/multifit_nlinear/gsl_multifit_nlinear.h gsl-doc-2.3/multifit_nlinear/gsl_multifit_nlinear.h
--- gsl-doc-1.16/multifit_nlinear/gsl_multifit_nlinear.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/gsl_multifit_nlinear.h	2016-08-12 19:46:44.000000000 +0000
@@ -0,0 +1,303 @@
+/* multifit_nlinear/gsl_multifit_nlinear.h
+ * 
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
+ * Copyright (C) 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_MULTIFIT_NLINEAR_H__
+#define __GSL_MULTIFIT_NLINEAR_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_types.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_permutation.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+typedef enum
+{
+  GSL_MULTIFIT_NLINEAR_FWDIFF,
+  GSL_MULTIFIT_NLINEAR_CTRDIFF
+} gsl_multifit_nlinear_fdtype;
+
+/* Definition of vector-valued functions and gradient with parameters
+   based on gsl_vector */
+
+typedef struct
+{
+  int (* f) (const gsl_vector * x, void * params, gsl_vector * f);
+  int (* df) (const gsl_vector * x, void * params, gsl_matrix * df);
+  int (* fvv) (const gsl_vector * x, const gsl_vector * v, void * params,
+               gsl_vector * fvv);
+  size_t n;        /* number of functions */
+  size_t p;        /* number of independent variables */
+  void * params;   /* user parameters */
+  size_t nevalf;   /* number of function evaluations */
+  size_t nevaldf;  /* number of Jacobian evaluations */
+  size_t nevalfvv; /* number of fvv evaluations */
+} gsl_multifit_nlinear_fdf;
+
+/* trust region subproblem method */
+typedef struct
+{
+  const char *name;
+  void * (*alloc) (const void * params, const size_t n, const size_t p);
+  int (*init) (const void * vtrust_state, void * vstate);
+  int (*preloop) (const void * vtrust_state, void * vstate);
+  int (*step) (const void * vtrust_state, const double delta,
+               gsl_vector * dx, void * vstate);
+  int (*preduction) (const void * vtrust_state, const gsl_vector * dx,
+                     double * pred, void * vstate);
+  void (*free) (void * vstate);
+} gsl_multifit_nlinear_trs;
+
+/* scaling matrix specification */
+typedef struct
+{
+  const char *name;
+  int (*init) (const gsl_matrix * J, gsl_vector * diag);
+  int (*update) (const gsl_matrix * J, gsl_vector * diag);
+} gsl_multifit_nlinear_scale;
+
+/*
+ * linear least squares solvers - there are three steps to
+ * solving a least squares problem using a trust region
+ * method:
+ *
+ * 1. init: called once per iteration when a new Jacobian matrix
+ *          is computed; perform factorization of Jacobian (qr,svd)
+ *          or form normal equations matrix (cholesky)
+ * 2. presolve: called each time a new LM parameter value mu is available;
+ *              used for cholesky method in order to factor
+ *              the (J^T J + mu D^T D) matrix
+ * 3. solve: solve the least square system for a given rhs
+ */
+typedef struct
+{
+  const char *name;
+  void * (*alloc) (const size_t n, const size_t p);
+  int (*init) (const void * vtrust_state, void * vstate);
+  int (*presolve) (const double mu, const void * vtrust_state, void * vstate);
+  int (*solve) (const gsl_vector * f, gsl_vector * x,
+                const void * vtrust_state, void * vstate);
+  int (*rcond) (double * rcond, void * vstate);
+  void (*free) (void * vstate);
+} gsl_multifit_nlinear_solver;
+
+/* tunable parameters */
+typedef struct
+{
+  const gsl_multifit_nlinear_trs *trs;        /* trust region subproblem method */
+  const gsl_multifit_nlinear_scale *scale;    /* scaling method */
+  const gsl_multifit_nlinear_solver *solver;  /* solver method */
+  gsl_multifit_nlinear_fdtype fdtype;         /* finite difference method */
+  double factor_up;                           /* factor for increasing trust radius */
+  double factor_down;                         /* factor for decreasing trust radius */
+  double avmax;                               /* max allowed |a|/|v| */
+  double h_df;                                /* step size for finite difference Jacobian */
+  double h_fvv;                               /* step size for finite difference fvv */
+} gsl_multifit_nlinear_parameters;
+
+typedef struct
+{
+  const char *name;
+  void * (*alloc) (const gsl_multifit_nlinear_parameters * params,
+                   const size_t n, const size_t p);
+  int (*init) (void * state, const gsl_vector * wts,
+               gsl_multifit_nlinear_fdf * fdf, const gsl_vector * x,
+               gsl_vector * f, gsl_matrix * J, gsl_vector * g);
+  int (*iterate) (void * state, const gsl_vector * wts,
+                  gsl_multifit_nlinear_fdf * fdf, gsl_vector * x,
+                  gsl_vector * f, gsl_matrix * J, gsl_vector * g,
+                  gsl_vector * dx);
+  int (*rcond) (double * rcond, void * state);
+  double (*avratio) (void * state);
+  void (*free) (void * state);
+} gsl_multifit_nlinear_type;
+
+/* current state passed to low-level trust region algorithms */
+typedef struct
+{
+  const gsl_vector * x;             /* parameter values x */
+  const gsl_vector * f;             /* residual vector f(x) */
+  const gsl_vector * g;             /* gradient J^T f */
+  const gsl_matrix * J;             /* Jacobian J(x) */
+  const gsl_vector * diag;          /* scaling matrix D */
+  const gsl_vector * sqrt_wts;      /* sqrt(diag(W)) or NULL for unweighted */
+  const double *mu;                 /* LM parameter */
+  const gsl_multifit_nlinear_parameters * params;
+  void *solver_state;               /* workspace for linear least squares solver */
+  gsl_multifit_nlinear_fdf * fdf;
+  double *avratio;                  /* |a| / |v| */
+} gsl_multifit_nlinear_trust_state;
+
+typedef struct
+{
+  const gsl_multifit_nlinear_type * type;
+  gsl_multifit_nlinear_fdf * fdf ;
+  gsl_vector * x;             /* parameter values x */
+  gsl_vector * f;             /* residual vector f(x) */
+  gsl_vector * dx;            /* step dx */
+  gsl_vector * g;             /* gradient J^T f */
+  gsl_matrix * J;             /* Jacobian J(x) */
+  gsl_vector * sqrt_wts_work; /* sqrt(W) */
+  gsl_vector * sqrt_wts;      /* ptr to sqrt_wts_work, or NULL if not using weights */
+  size_t niter;               /* number of iterations performed */
+  gsl_multifit_nlinear_parameters params;
+  void *state;
+} gsl_multifit_nlinear_workspace;
+
+gsl_multifit_nlinear_workspace *
+gsl_multifit_nlinear_alloc (const gsl_multifit_nlinear_type * T,
+                            const gsl_multifit_nlinear_parameters * params,
+                            size_t n, size_t p);
+
+void gsl_multifit_nlinear_free (gsl_multifit_nlinear_workspace * w);
+
+gsl_multifit_nlinear_parameters gsl_multifit_nlinear_default_parameters(void);
+
+int
+gsl_multifit_nlinear_init (const gsl_vector * x,
+                           gsl_multifit_nlinear_fdf * fdf,
+                           gsl_multifit_nlinear_workspace * w);
+
+int gsl_multifit_nlinear_winit (const gsl_vector * x,
+                                const gsl_vector * wts,
+                                gsl_multifit_nlinear_fdf * fdf,
+                                gsl_multifit_nlinear_workspace * w);
+
+int
+gsl_multifit_nlinear_iterate (gsl_multifit_nlinear_workspace * w);
+
+double
+gsl_multifit_nlinear_avratio (const gsl_multifit_nlinear_workspace * w);
+
+int
+gsl_multifit_nlinear_driver (const size_t maxiter,
+                             const double xtol,
+                             const double gtol,
+                             const double ftol,
+                             void (*callback)(const size_t iter, void *params,
+                                              const gsl_multifit_nlinear_workspace *w),
+                             void *callback_params,
+                             int *info,
+                             gsl_multifit_nlinear_workspace * w);
+
+gsl_matrix *
+gsl_multifit_nlinear_jac (const gsl_multifit_nlinear_workspace * w);
+
+const char *
+gsl_multifit_nlinear_name (const gsl_multifit_nlinear_workspace * w);
+
+gsl_vector *
+gsl_multifit_nlinear_position (const gsl_multifit_nlinear_workspace * w);
+
+gsl_vector *
+gsl_multifit_nlinear_residual (const gsl_multifit_nlinear_workspace * w);
+
+size_t
+gsl_multifit_nlinear_niter (const gsl_multifit_nlinear_workspace * w);
+
+int
+gsl_multifit_nlinear_rcond (double *rcond, const gsl_multifit_nlinear_workspace * w);
+
+const char *
+gsl_multifit_nlinear_trs_name (const gsl_multifit_nlinear_workspace * w);
+
+int gsl_multifit_nlinear_eval_f(gsl_multifit_nlinear_fdf *fdf,
+                                const gsl_vector *x,
+                                const gsl_vector *swts,
+                                gsl_vector *y);
+
+int gsl_multifit_nlinear_eval_df(const gsl_vector *x,
+                                 const gsl_vector *f,
+                                 const gsl_vector *swts,
+                                 const double h,
+                                 const gsl_multifit_nlinear_fdtype fdtype,
+                                 gsl_multifit_nlinear_fdf *fdf,
+                                 gsl_matrix *df, gsl_vector *work);
+
+int
+gsl_multifit_nlinear_eval_fvv(const double h,
+                              const gsl_vector *x,
+                              const gsl_vector *v,
+                              const gsl_vector *f,
+                              const gsl_matrix *J,
+                              const gsl_vector *swts,
+                              gsl_multifit_nlinear_fdf *fdf,
+                              gsl_vector *yvv, gsl_vector *work);
+
+/* covar.c */
+int
+gsl_multifit_nlinear_covar (const gsl_matrix * J, const double epsrel,
+                            gsl_matrix * covar);
+
+/* convergence.c */
+int
+gsl_multifit_nlinear_test (const double xtol, const double gtol,
+                           const double ftol, int *info,
+                           const gsl_multifit_nlinear_workspace * w);
+
+/* fdjac.c */
+int
+gsl_multifit_nlinear_df(const double h, const gsl_multifit_nlinear_fdtype fdtype,
+                        const gsl_vector *x, const gsl_vector *wts,
+                        gsl_multifit_nlinear_fdf *fdf,
+                        const gsl_vector *f, gsl_matrix *J, gsl_vector *work);
+
+/* fdfvv.c */
+int
+gsl_multifit_nlinear_fdfvv(const double h, const gsl_vector *x, const gsl_vector *v,
+                           const gsl_vector *f, const gsl_matrix *J,
+                           const gsl_vector *swts, gsl_multifit_nlinear_fdf *fdf,
+                           gsl_vector *fvv, gsl_vector *work);
+
+/* top-level algorithms */
+GSL_VAR const gsl_multifit_nlinear_type * gsl_multifit_nlinear_trust;
+
+/* trust region subproblem methods */
+GSL_VAR const gsl_multifit_nlinear_trs * gsl_multifit_nlinear_trs_lm;
+GSL_VAR const gsl_multifit_nlinear_trs * gsl_multifit_nlinear_trs_lmaccel;
+GSL_VAR const gsl_multifit_nlinear_trs * gsl_multifit_nlinear_trs_dogleg;
+GSL_VAR const gsl_multifit_nlinear_trs * gsl_multifit_nlinear_trs_ddogleg;
+GSL_VAR const gsl_multifit_nlinear_trs * gsl_multifit_nlinear_trs_subspace2D;
+
+/* scaling matrix strategies */
+GSL_VAR const gsl_multifit_nlinear_scale * gsl_multifit_nlinear_scale_levenberg;
+GSL_VAR const gsl_multifit_nlinear_scale * gsl_multifit_nlinear_scale_marquardt;
+GSL_VAR const gsl_multifit_nlinear_scale * gsl_multifit_nlinear_scale_more;
+
+/* linear solvers */
+GSL_VAR const gsl_multifit_nlinear_solver * gsl_multifit_nlinear_solver_cholesky;
+GSL_VAR const gsl_multifit_nlinear_solver * gsl_multifit_nlinear_solver_qr;
+GSL_VAR const gsl_multifit_nlinear_solver * gsl_multifit_nlinear_solver_svd;
+
+__END_DECLS
+
+#endif /* __GSL_MULTIFIT_NLINEAR_H__ */
diff -Nru gsl-doc-1.16/multifit_nlinear/lm.c gsl-doc-2.3/multifit_nlinear/lm.c
--- gsl-doc-1.16/multifit_nlinear/lm.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/lm.c	2016-09-09 17:23:39.000000000 +0000
@@ -0,0 +1,344 @@
+/* multifit_nlinear/lm.c
+ * 
+ * Copyright (C) 2014, 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_permutation.h>
+
+/*
+ * This module contains an implementation of the Levenberg-Marquardt
+ * algorithm for nonlinear optimization problems. This implementation
+ * closely follows the following works:
+ *
+ * [1] H. B. Nielsen, K. Madsen, Introduction to Optimization and
+ *     Data Fitting, Informatics and Mathematical Modeling,
+ *     Technical University of Denmark (DTU), 2010.
+ *
+ * [2] J. J. More, The Levenberg-Marquardt Algorithm: Implementation
+ *     and Theory, Lecture Notes in Mathematics, v630, 1978.
+ */
+
+typedef struct
+{
+  size_t n;           /* number of observations */
+  size_t p;           /* number of parameters */
+  gsl_vector *fvv;    /* D_v^2 f(x), size n */
+  gsl_vector *vel;    /* geodesic velocity (standard LM step), size p */
+  gsl_vector *acc;    /* geodesic acceleration, size p */
+  gsl_vector *workp;  /* workspace, length p */
+  gsl_vector *workn;  /* workspace, length n */
+
+  int accel;          /* use geodesic acceleration? */
+
+  /* tunable parameters */
+  gsl_multifit_nlinear_parameters params;
+} lm_state_t;
+
+#include "common.c"
+
+static void *lm_alloc (const int accel, const void * params, const size_t n, const size_t p);
+static void *lm_alloc_noaccel (const void * params, const size_t n, const size_t p);
+static void *lm_alloc_accel (const void * params, const size_t n, const size_t p);
+static void lm_free(void *vstate);
+static int lm_init(const void *vtrust_state, void *vstate);
+static int lm_preloop(const void * vtrust_state, void * vstate);
+static int lm_step(const void * vtrust_state, const double delta,
+                   gsl_vector * dx, void * vstate);
+static int lm_preduction(const void * vtrust_state, const gsl_vector * dx,
+                         double * pred, void * vstate);
+
+static void *
+lm_alloc (const int accel, const void * params, const size_t n, const size_t p)
+{
+  const gsl_multifit_nlinear_parameters *mparams = (const gsl_multifit_nlinear_parameters *) params;
+  lm_state_t *state;
+  
+  state = calloc(1, sizeof(lm_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate lm state", GSL_ENOMEM);
+    }
+
+  state->workp = gsl_vector_alloc(p);
+  if (state->workp == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workp", GSL_ENOMEM);
+    }
+
+  state->workn = gsl_vector_alloc(n);
+  if (state->workn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workn", GSL_ENOMEM);
+    }
+
+  state->fvv = gsl_vector_alloc(n);
+  if (state->fvv == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for fvv", GSL_ENOMEM);
+    }
+
+  state->vel = gsl_vector_alloc(p);
+  if (state->vel == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for vel", GSL_ENOMEM);
+    }
+
+  state->acc = gsl_vector_alloc(p);
+  if (state->acc == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for acc", GSL_ENOMEM);
+    }
+
+  state->n = n;
+  state->p = p;
+  state->params = *mparams;
+  state->accel = accel;
+
+  return state;
+}
+
+static void *
+lm_alloc_noaccel (const void * params, const size_t n, const size_t p)
+{
+  return lm_alloc(0, params, n, p);
+}
+
+static void *
+lm_alloc_accel (const void * params, const size_t n, const size_t p)
+{
+  return lm_alloc(1, params, n, p);
+}
+
+static void
+lm_free(void *vstate)
+{
+  lm_state_t *state = (lm_state_t *) vstate;
+
+  if (state->workp)
+    gsl_vector_free(state->workp);
+
+  if (state->workn)
+    gsl_vector_free(state->workn);
+
+  if (state->fvv)
+    gsl_vector_free(state->fvv);
+
+  if (state->vel)
+    gsl_vector_free(state->vel);
+
+  if (state->acc)
+    gsl_vector_free(state->acc);
+
+  free(state);
+}
+
+/*
+lm_init()
+  Initialize LM solver
+
+Inputs: vtrust_state - trust state
+        vstate       - workspace
+
+Return: success/error
+*/
+
+static int
+lm_init(const void *vtrust_state, void *vstate)
+{
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  lm_state_t *state = (lm_state_t *) vstate;
+
+  gsl_vector_set_zero(state->vel);
+  gsl_vector_set_zero(state->acc);
+
+  *(trust_state->avratio) = 0.0;
+
+  return GSL_SUCCESS;
+}
+
+/*
+lm_preloop()
+  Initialize LM method for new Jacobian matrix
+*/
+
+static int
+lm_preloop(const void * vtrust_state, void * vstate)
+{
+  int status;
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  const gsl_multifit_nlinear_parameters *params = trust_state->params;
+
+  (void)vstate;
+
+  /* initialize linear least squares solver */
+  status = (params->solver->init)(trust_state, trust_state->solver_state);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+}
+
+/*
+lm_step()
+  Calculate a new step vector by solving the linear
+least squares system:
+
+[      J     ] v = - [ f ]
+[ sqrt(mu) D ]       [ 0 ]
+*/
+
+static int
+lm_step(const void * vtrust_state, const double delta,
+        gsl_vector * dx, void * vstate)
+{
+  int status;
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  lm_state_t *state = (lm_state_t *) vstate;
+  const gsl_multifit_nlinear_parameters *params = trust_state->params;
+  const double mu = *(trust_state->mu);
+
+  (void)delta;
+
+  /* prepare the linear solver with current LM parameter mu */
+  status = (params->solver->presolve)(mu, trust_state, trust_state->solver_state);
+  if (status)
+    return status;
+
+  /*
+   * solve: [     J      ] v = - [ f ]
+   *        [ sqrt(mu)*D ]       [ 0 ]
+   */
+  status = (params->solver->solve)(trust_state->f,
+                                   state->vel,
+                                   trust_state,
+                                   trust_state->solver_state);
+  if (status)
+    return status;
+
+  if (state->accel)
+    {
+      double anorm, vnorm;
+
+      /* compute geodesic acceleration */
+      status = gsl_multifit_nlinear_eval_fvv(params->h_fvv,
+                                             trust_state->x,
+                                             state->vel,
+                                             trust_state->f,
+                                             trust_state->J,
+                                             trust_state->sqrt_wts,
+                                             trust_state->fdf,
+                                             state->fvv,
+                                             state->workp);
+      if (status)
+        return status;
+
+      /*
+       * solve: [     J      ] a = - [ fvv ]
+       *        [ sqrt(mu)*D ]       [  0  ]
+       */
+      status = (params->solver->solve)(state->fvv,
+                                       state->acc,
+                                       trust_state,
+                                       trust_state->solver_state);
+      if (status)
+        return status;
+
+      anorm = gsl_blas_dnrm2(state->acc);
+      vnorm = gsl_blas_dnrm2(state->vel);
+
+      /* store |a| / |v| */
+      *(trust_state->avratio) = anorm / vnorm;
+    }
+
+  /* compute step dx = v + 1/2 a */
+  scaled_addition(1.0, state->vel, 0.5, state->acc, dx);
+
+  return GSL_SUCCESS;
+}
+
+/*
+lm_preduction()
+  Compute predicted reduction using Eq 4.4 of More 1978
+*/
+
+static int
+lm_preduction(const void * vtrust_state, const gsl_vector * dx,
+              double * pred, void * vstate)
+{
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  lm_state_t *state = (lm_state_t *) vstate;
+  const gsl_vector *diag = trust_state->diag;
+  const gsl_vector *p = state->vel;
+  const double norm_Dp = scaled_enorm(diag, p);
+  const double normf = gsl_blas_dnrm2(trust_state->f);
+  const double mu = *(trust_state->mu);
+  double norm_Jp;
+  double u, v;
+
+  (void)dx;
+
+  /* compute work = J*p */
+  gsl_blas_dgemv(CblasNoTrans, 1.0, trust_state->J, p, 0.0, state->workn);
+
+  /* compute ||J*p|| */
+  norm_Jp = gsl_blas_dnrm2(state->workn);
+
+  u = norm_Jp / normf;
+  v = norm_Dp / normf;
+
+  *pred = u * u + 2.0 * mu * v * v;
+
+  return GSL_SUCCESS;
+}
+
+static const gsl_multifit_nlinear_trs lm_type =
+{
+  "levenberg-marquardt",
+  lm_alloc_noaccel,
+  lm_init,
+  lm_preloop,
+  lm_step,
+  lm_preduction,
+  lm_free
+};
+
+const gsl_multifit_nlinear_trs *gsl_multifit_nlinear_trs_lm = &lm_type;
+
+static const gsl_multifit_nlinear_trs lmaccel_type =
+{
+  "levenberg-marquardt+accel",
+  lm_alloc_accel,
+  lm_init,
+  lm_preloop,
+  lm_step,
+  lm_preduction,
+  lm_free
+};
+
+const gsl_multifit_nlinear_trs *gsl_multifit_nlinear_trs_lmaccel = &lmaccel_type;
diff -Nru gsl-doc-1.16/multifit_nlinear/Makefile.am gsl-doc-2.3/multifit_nlinear/Makefile.am
--- gsl-doc-1.16/multifit_nlinear/Makefile.am	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/Makefile.am	2016-08-12 15:35:44.000000000 +0000
@@ -0,0 +1,58 @@
+noinst_LTLIBRARIES = libgslmultifit_nlinear.la 
+
+pkginclude_HEADERS = gsl_multifit_nlinear.h
+
+AM_CPPFLAGS = -I$(top_srcdir)
+
+libgslmultifit_nlinear_la_SOURCES = cholesky.c convergence.c covar.c dogleg.c fdf.c fdfvv.c fdjac.c lm.c qr.c scaling.c subspace2D.c svd.c trust.c
+
+noinst_HEADERS =        \
+common.c                \
+nielsen.c               \
+qrsolv.c                \
+test_bard.c             \
+test_beale.c            \
+test_biggs.c            \
+test_box.c              \
+test_boxbod.c           \
+test_brown1.c           \
+test_brown2.c           \
+test_brown3.c           \
+test_eckerle.c          \
+test_enso.c             \
+test_exp1.c             \
+test_fdf.c              \
+test_gaussian.c         \
+test_hahn1.c            \
+test_helical.c          \
+test_jennrich.c         \
+test_kirby2.c           \
+test_kowalik.c          \
+test_lin1.c             \
+test_lin2.c             \
+test_lin3.c             \
+test_meyer.c            \
+test_meyerscal.c        \
+test_osborne.c          \
+test_penalty1.c         \
+test_penalty2.c         \
+test_powell1.c          \
+test_powell2.c          \
+test_powell3.c          \
+test_rat42.c            \
+test_rat43.c            \
+test_rosenbrock.c       \
+test_rosenbrocke.c      \
+test_roth.c             \
+test_thurber.c          \
+test_vardim.c           \
+test_watson.c           \
+test_wnlin.c            \
+test_wood.c
+
+check_PROGRAMS = test
+
+TESTS = $(check_PROGRAMS)
+
+test_SOURCES = test.c
+test_LDADD = libgslmultifit_nlinear.la ../eigen/libgsleigen.la ../linalg/libgsllinalg.la ../permutation/libgslpermutation.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../sort/libgslsort.la ../statistics/libgslstatistics.la ../vector/libgslvector.la ../block/libgslblock.la  ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../utils/libutils.la ../sys/libgslsys.la ../rng/libgslrng.la ../specfunc/libgslspecfunc.la ../poly/libgslpoly.la
diff -Nru gsl-doc-1.16/multifit_nlinear/Makefile.in gsl-doc-2.3/multifit_nlinear/Makefile.in
--- gsl-doc-1.16/multifit_nlinear/Makefile.in	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -0,0 +1,1091 @@
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diff -Nru gsl-doc-1.16/multifit_nlinear/nielsen.c gsl-doc-2.3/multifit_nlinear/nielsen.c
--- gsl-doc-1.16/multifit_nlinear/nielsen.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/nielsen.c	2016-08-12 15:39:42.000000000 +0000
@@ -0,0 +1,101 @@
+/* multifit_nlinear/nielsen.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/*
+ * This module contains routines for updating the Levenberg-Marquardt
+ * damping parameter on each iteration using Nielsen's method:
+ *
+ * [1] H. B. Nielsen, K. Madsen, Introduction to Optimization and
+ *     Data Fitting, Informatics and Mathematical Modeling,
+ *     Technical University of Denmark (DTU), 2010.
+ *
+ * 5 routines are needed to implement the update procedure:
+ *
+ * 1. accept - update parameter after a step has been accepted
+ * 2. reject - update parameter after a step has been rejected
+ * 3. free   - free workspace state
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+
+#define LM_ONE_THIRD         (0.333333333333333)
+
+static int nielsen_init(const gsl_matrix * J, const gsl_vector * diag,
+                        double * mu, long * nu);
+static int nielsen_accept(const double rho, double * mu, long * nu);
+static int nielsen_reject(double * mu, long * nu);
+
+static int
+nielsen_init(const gsl_matrix * J, const gsl_vector * diag,
+             double * mu, long * nu)
+{
+  const double mu0 = 1.0e-3;
+  const size_t p = J->size2;
+  size_t j;
+  double max = -1.0;
+
+  *nu = 2;
+
+  /* set mu = mu0 * max(diag(J~^T J~)), with J~ = J D^{-1} */
+
+  for (j = 0; j < p; ++j)
+    {
+      gsl_vector_const_view v = gsl_matrix_const_column(J, j);
+      double dj = gsl_vector_get(diag, j);
+      double norm = gsl_blas_dnrm2(&v.vector) / dj;
+      max = GSL_MAX(max, norm);
+    }
+
+  *mu = mu0 * max * max;
+
+  return GSL_SUCCESS;
+}
+
+static int
+nielsen_accept(const double rho, double * mu, long * nu)
+{
+  double  b;
+  
+  /* reset nu */
+  *nu = 2;
+
+  b = 2.0 * rho - 1.0;
+  b = 1.0 - b*b*b;
+  *mu *= GSL_MAX(LM_ONE_THIRD, b);
+
+  return GSL_SUCCESS;
+}
+
+static int
+nielsen_reject(double * mu, long * nu)
+{
+  *mu *= (double) *nu;
+
+  /* nu := 2*nu */
+  *nu <<= 1;
+
+  return GSL_SUCCESS;
+}
diff -Nru gsl-doc-1.16/multifit_nlinear/qr.c gsl-doc-2.3/multifit_nlinear/qr.c
--- gsl-doc-1.16/multifit_nlinear/qr.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/qr.c	2016-08-15 19:49:35.000000000 +0000
@@ -0,0 +1,286 @@
+/* multifit_nlinear/qr.c
+ * 
+ * Copyright (C) 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/*
+ * This module handles the solution of the linear least squares
+ * system:
+ *
+ * [     J~      ] p~ = - [ f ]
+ * [ sqrt(mu)*D~ ]        [ 0 ]
+ *
+ * using a QR approach. Quantities are scaled according to:
+ *
+ * J~ = J S
+ * D~ = D S
+ * p~ = S^{-1} p
+ *
+ * where S is a diagonal matrix and S_jj = || J_j || and J_j is column
+ * j of the Jacobian. This balancing transformation seems to be more
+ * numerically stable for some Jacobians.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+
+#include "common.c"
+#include "qrsolv.c"
+
+typedef struct
+{
+  size_t p;
+  gsl_matrix *QR;            /* QR factorization of J */
+  gsl_vector *tau_Q;         /* Householder scalars for Q */
+  gsl_matrix *T;             /* workspace matrix for qrsolv, p-by-p */
+  gsl_permutation *perm;     /* permutation matrix */
+  size_t rank;               /* rank of J */
+  gsl_vector *residual;      /* residual of LS problem [ J; sqrt(mu) D ] p = - [ f; 0 ] */
+  gsl_vector *qtf;           /* Q^T f */
+  gsl_vector *workn;         /* workspace, length n */
+  gsl_vector *workp;         /* workspace, length p */
+  gsl_vector *work3p;        /* workspace, length 3*p */
+  double mu;                 /* LM parameter */
+} qr_state_t;
+
+static int qr_init(const void * vtrust_state, void * vstate);
+static int qr_presolve(const double mu, const void * vtrust_state, void * vstate);
+static int qr_solve(const gsl_vector * f, gsl_vector *x,
+                    const void * vtrust_state, void *vstate);
+static int qr_rcond(double * rcond, void * vstate);
+
+static void *
+qr_alloc (const size_t n, const size_t p)
+{
+  qr_state_t *state;
+
+  (void)n;
+  
+  state = calloc(1, sizeof(qr_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate qr state", GSL_ENOMEM);
+    }
+
+  state->QR = gsl_matrix_alloc(n, p);
+  if (state->QR == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for QR", GSL_ENOMEM);
+    }
+
+  state->tau_Q = gsl_vector_alloc(p);
+  if (state->tau_Q == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for tau_Q",
+                      GSL_ENOMEM);
+    }
+
+  state->T = gsl_matrix_alloc(p, p);
+  if (state->T == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for T", GSL_ENOMEM);
+    }
+
+  state->qtf = gsl_vector_alloc(n);
+  if (state->qtf == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for qtf",
+                      GSL_ENOMEM);
+    }
+
+  state->residual = gsl_vector_alloc(n);
+  if (state->residual == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for residual",
+                      GSL_ENOMEM);
+    }
+
+  state->perm = gsl_permutation_calloc(p);
+  if (state->perm == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for perm",
+                      GSL_ENOMEM);
+    }
+
+  state->workn = gsl_vector_alloc(n);
+  if (state->workn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workn",
+                      GSL_ENOMEM);
+    }
+
+  state->workp = gsl_vector_alloc(p);
+  if (state->workp == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workp",
+                      GSL_ENOMEM);
+    }
+
+  state->work3p = gsl_vector_alloc(3 * p);
+  if (state->work3p == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for work3p",
+                      GSL_ENOMEM);
+    }
+
+  state->p = p;
+  state->mu = 0.0;
+  state->rank = 0;
+
+  return state;
+}
+
+static void
+qr_free(void *vstate)
+{
+  qr_state_t *state = (qr_state_t *) vstate;
+
+  if (state->QR)
+    gsl_matrix_free(state->QR);
+
+  if (state->tau_Q)
+    gsl_vector_free(state->tau_Q);
+
+  if (state->T)
+    gsl_matrix_free(state->T);
+
+  if (state->qtf)
+    gsl_vector_free(state->qtf);
+
+  if (state->residual)
+    gsl_vector_free(state->residual);
+
+  if (state->perm)
+    gsl_permutation_free(state->perm);
+
+  if (state->workn)
+    gsl_vector_free(state->workn);
+
+  if (state->workp)
+    gsl_vector_free(state->workp);
+
+  if (state->work3p)
+    gsl_vector_free(state->work3p);
+
+  free(state);
+}
+
+/* compute J = Q R PT */
+static int
+qr_init(const void * vtrust_state, void * vstate)
+{
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  qr_state_t *state = (qr_state_t *) vstate;
+  int signum;
+
+  /* perform QR decomposition of J */
+  gsl_matrix_memcpy(state->QR, trust_state->J);
+  gsl_linalg_QRPT_decomp(state->QR, state->tau_Q, state->perm,
+                         &signum, state->workp);
+
+  return GSL_SUCCESS;
+}
+
+static int
+qr_presolve(const double mu, const void * vtrust_state, void * vstate)
+{
+  qr_state_t *state = (qr_state_t *) vstate;
+
+  state->mu = mu;
+
+  (void) vtrust_state;
+
+  return GSL_SUCCESS;
+}
+
+static int
+qr_solve(const gsl_vector * f, gsl_vector *x,
+         const void * vtrust_state, void *vstate)
+{
+  qr_state_t *state = (qr_state_t *) vstate;
+  int status;
+
+  if (state->mu == 0.0)
+    {
+      /*
+       * compute Gauss-Newton direction by solving
+       * J x = f
+       * with an attempt to identify rank deficiency in J
+       */
+      size_t rank = gsl_linalg_QRPT_rank(state->QR, -1.0);
+      status = gsl_linalg_QRPT_lssolve2(state->QR, state->tau_Q, state->perm,
+                                        f, rank, x, state->residual);
+    }
+  else
+    {
+      /*
+       * solve:
+       *
+       * [     J      ] x = [ f ]
+       * [ sqrt(mu) D ]     [ 0 ]
+       *
+       * using QRPT factorization of J
+       */
+
+      const gsl_multifit_nlinear_trust_state *trust_state =
+        (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+      double sqrt_mu = sqrt(state->mu);
+
+      /* compute qtf = Q^T f */
+      gsl_vector_memcpy(state->qtf, f);
+      gsl_linalg_QR_QTvec(state->QR, state->tau_Q, state->qtf);
+
+      status = qrsolv(state->QR, state->perm, sqrt_mu, trust_state->diag,
+                      state->qtf, state->T, x, state->workn);
+    }
+
+  /* reverse step to go downhill */
+  gsl_vector_scale(x, -1.0);
+
+  return status;
+}
+
+static int
+qr_rcond(double * rcond, void * vstate)
+{
+  int status;
+  qr_state_t *state = (qr_state_t *) vstate;
+
+  status = gsl_linalg_QRPT_rcond(state->QR, rcond, state->work3p);
+
+  return status;
+}
+
+static const gsl_multifit_nlinear_solver qr_type =
+{
+  "qr",
+  qr_alloc,
+  qr_init,
+  qr_presolve,
+  qr_solve,
+  qr_rcond,
+  qr_free
+};
+
+const gsl_multifit_nlinear_solver *gsl_multifit_nlinear_solver_qr = &qr_type;
diff -Nru gsl-doc-1.16/multifit_nlinear/qrsolv.c gsl-doc-2.3/multifit_nlinear/qrsolv.c
--- gsl-doc-1.16/multifit_nlinear/qrsolv.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/qrsolv.c	2016-07-07 20:36:10.000000000 +0000
@@ -0,0 +1,217 @@
+/* This function computes the solution to the least squares system
+
+   phi = [ A x =  b , lambda D x = 0 ]^2
+    
+   where A is an M by N matrix, D is an N by N diagonal matrix, lambda
+   is a scalar parameter and b is a vector of length M.
+
+   The function requires the factorization of A into A = Q R P^T,
+   where Q is an orthogonal matrix, R is an upper triangular matrix
+   with diagonal elements of non-increasing magnitude and P is a
+   permuation matrix. The system above is then equivalent to
+
+   [ R z = Q^T b, P^T (lambda D) P z = 0 ]
+
+   where x = P z. If this system does not have full rank then a least
+   squares solution is obtained.  On output the function also provides
+   an upper triangular matrix S such that
+
+   P^T (A^T A + lambda^2 D^T D) P = S^T S
+
+   Parameters,
+   
+   r: On input, contains the full upper triangle of R. The diagonal
+   elements are modified but restored on output. The full
+   upper triangle of R is not modified.
+
+   p: the encoded form of the permutation matrix P. column j of P is
+   column p[j] of the identity matrix.
+
+   lambda, diag: contains the scalar lambda and the diagonal elements
+   of the matrix D
+
+   qtb: contains the product Q^T b
+
+   S: on output contains the matrix S, n-by-n
+
+   x: on output contains the least squares solution of the system
+
+   work: is a workspace of length N
+
+   */
+
+static int
+qrsolv (gsl_matrix * r, const gsl_permutation * p, const double lambda,
+        const gsl_vector * diag, const gsl_vector * qtb,
+        gsl_matrix * S, gsl_vector * x, gsl_vector * work)
+{
+  size_t n = r->size2;
+
+  size_t i, j, k, nsing;
+
+  /* Copy r and qtb to preserve input and initialise s. In particular,
+     save the diagonal elements of r in x */
+
+  for (j = 0; j < n; j++)
+    {
+      double rjj = gsl_matrix_get (r, j, j);
+      double qtbj = gsl_vector_get (qtb, j);
+
+      for (i = j + 1; i < n; i++)
+        {
+          double rji = gsl_matrix_get (r, j, i);
+          gsl_matrix_set (S, i, j, rji);
+        }
+
+      gsl_vector_set (x, j, rjj);
+      gsl_vector_set (work, j, qtbj);
+    }
+
+  /* Eliminate the diagonal matrix d using a Givens rotation */
+
+  for (j = 0; j < n; j++)
+    {
+      double qtbpj;
+
+      size_t pj = gsl_permutation_get (p, j);
+
+      double diagpj = lambda * gsl_vector_get (diag, pj);
+
+      if (diagpj == 0)
+        {
+          continue;
+        }
+
+      gsl_matrix_set (S, j, j, diagpj);
+
+      for (k = j + 1; k < n; k++)
+        {
+          gsl_matrix_set (S, k, k, 0.0);
+        }
+
+      /* The transformations to eliminate the row of d modify only a
+         single element of qtb beyond the first n, which is initially
+         zero */
+
+      qtbpj = 0;
+
+      for (k = j; k < n; k++)
+        {
+          /* Determine a Givens rotation which eliminates the
+             appropriate element in the current row of d */
+
+          double sine, cosine;
+
+          double wk = gsl_vector_get (work, k);
+          double rkk = gsl_matrix_get (r, k, k);
+          double skk = gsl_matrix_get (S, k, k);
+
+          if (skk == 0)
+            {
+              continue;
+            }
+
+          if (fabs (rkk) < fabs (skk))
+            {
+              double cotangent = rkk / skk;
+              sine = 0.5 / sqrt (0.25 + 0.25 * cotangent * cotangent);
+              cosine = sine * cotangent;
+            }
+          else
+            {
+              double tangent = skk / rkk;
+              cosine = 0.5 / sqrt (0.25 + 0.25 * tangent * tangent);
+              sine = cosine * tangent;
+            }
+
+          /* Compute the modified diagonal element of r and the
+             modified element of [qtb,0] */
+
+          {
+            double new_rkk = cosine * rkk + sine * skk;
+            double new_wk = cosine * wk + sine * qtbpj;
+            
+            qtbpj = -sine * wk + cosine * qtbpj;
+
+            gsl_matrix_set(r, k, k, new_rkk);
+            gsl_matrix_set(S, k, k, new_rkk);
+            gsl_vector_set(work, k, new_wk);
+          }
+
+          /* Accumulate the transformation in the row of s */
+
+          for (i = k + 1; i < n; i++)
+            {
+              double sik = gsl_matrix_get (S, i, k);
+              double sii = gsl_matrix_get (S, i, i);
+              
+              double new_sik = cosine * sik + sine * sii;
+              double new_sii = -sine * sik + cosine * sii;
+
+              gsl_matrix_set(S, i, k, new_sik);
+              gsl_matrix_set(S, i, i, new_sii);
+            }
+        }
+
+      /* Store the corresponding diagonal element of s and restore the
+         corresponding diagonal element of r */
+
+      {
+        double xj = gsl_vector_get(x, j);
+        gsl_matrix_set (r, j, j, xj);
+      }
+
+    }
+
+  /* Solve the triangular system for z. If the system is singular then
+     obtain a least squares solution */
+
+  nsing = n;
+
+  for (j = 0; j < n; j++)
+    {
+      double sjj = gsl_matrix_get (S, j, j);
+
+      if (sjj == 0)
+        {
+          nsing = j;
+          break;
+        }
+    }
+
+  for (j = nsing; j < n; j++)
+    {
+      gsl_vector_set (work, j, 0.0);
+    }
+
+  for (k = 0; k < nsing; k++)
+    {
+      double sum = 0;
+
+      j = (nsing - 1) - k;
+
+      for (i = j + 1; i < nsing; i++)
+        {
+          sum += gsl_matrix_get(S, i, j) * gsl_vector_get(work, i);
+        }
+
+      {
+        double wj = gsl_vector_get (work, j);
+        double sjj = gsl_matrix_get (S, j, j);
+
+        gsl_vector_set (work, j, (wj - sum) / sjj);
+      }
+    }
+
+  /* Permute the components of z back to the components of x */
+
+  for (j = 0; j < n; j++)
+    {
+      size_t pj = gsl_permutation_get (p, j);
+      double wj = gsl_vector_get (work, j);
+
+      gsl_vector_set (x, pj, wj);
+    }
+
+  return GSL_SUCCESS;
+}
diff -Nru gsl-doc-1.16/multifit_nlinear/scaling.c gsl-doc-2.3/multifit_nlinear/scaling.c
--- gsl-doc-1.16/multifit_nlinear/scaling.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/scaling.c	2016-07-07 20:36:10.000000000 +0000
@@ -0,0 +1,158 @@
+/* multifit_nlinear/scaling.c
+ * 
+ * Copyright (C) 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/*
+ * This module handles the updating of the scaling matrix D_k in the
+ * trust region subproblem:
+ *
+ * min m_k (dx), || D_k dx || <= Delta_k
+ *
+ * where m_k(dx) is a model which approximates the cost function
+ * F(x_k + dx) near the current iteration point x_k
+ *
+ * D_k can be updated according to several different strategies.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+
+static int init_diag_levenberg(const gsl_matrix * J, gsl_vector * diag);
+static int update_diag_levenberg(const gsl_matrix * J,
+                                 gsl_vector * diag);
+
+static int init_diag_marquardt(const gsl_matrix * J, gsl_vector * diag);
+static int update_diag_marquardt (const gsl_matrix * J,
+                                  gsl_vector * diag);
+
+static int init_diag_more(const gsl_matrix * J, gsl_vector * diag);
+static int update_diag_more(const gsl_matrix * J, gsl_vector * diag);
+
+/* Levenberg scaling, D = I */
+static int
+init_diag_levenberg(const gsl_matrix * J, gsl_vector * diag)
+{
+  (void)J; /* avoid unused parameter warning */
+  gsl_vector_set_all(diag, 1.0);
+  return GSL_SUCCESS;
+}
+
+static int
+update_diag_levenberg(const gsl_matrix * J, gsl_vector * diag)
+{
+  (void)J;    /* avoid unused parameter warning */
+  (void)diag; /* avoid unused parameter warning */
+
+  /* nothing to do */
+  return GSL_SUCCESS;
+}
+
+/* initialize diagonal scaling matrix D according to Marquardt method */
+static int
+init_diag_marquardt(const gsl_matrix * J, gsl_vector * diag)
+{
+  return update_diag_marquardt(J, diag);
+}
+
+/* update diagonal scaling matrix D according to Marquardt method */
+static int
+update_diag_marquardt (const gsl_matrix * J, gsl_vector * diag)
+{
+  const size_t p = J->size2;
+  size_t j;
+
+  for (j = 0; j < p; j++)
+    {
+      gsl_vector_const_view v = gsl_matrix_const_column(J, j);
+      double norm = gsl_blas_dnrm2(&v.vector);
+
+      if (norm == 0.0)
+        norm = 1.0;
+
+      gsl_vector_set(diag, j, norm);
+    }
+
+  return GSL_SUCCESS;
+}
+
+/* initialize diagonal scaling matrix D according to Eq 6.3 of
+ * More, 1978 */
+static int
+init_diag_more(const gsl_matrix * J, gsl_vector * diag)
+{
+  int status;
+
+  gsl_vector_set_zero(diag);
+  status = update_diag_more(J, diag);
+
+  return status;
+}
+
+/* update diagonal scaling matrix D according to Eq. 6.3 of
+ * More, 1978 */
+static int
+update_diag_more (const gsl_matrix * J, gsl_vector * diag)
+{
+  const size_t p = J->size2;
+  size_t j;
+
+  for (j = 0; j < p; j++)
+    {
+      gsl_vector_const_view v = gsl_matrix_const_column(J, j);
+      double norm = gsl_blas_dnrm2(&v.vector);
+      double *diagj = gsl_vector_ptr(diag, j);
+
+      if (norm == 0.0)
+        norm = 1.0;
+
+      *diagj = GSL_MAX(*diagj, norm);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static const gsl_multifit_nlinear_scale levenberg_type =
+{
+  "levenberg",
+  init_diag_levenberg,
+  update_diag_levenberg
+};
+
+static const gsl_multifit_nlinear_scale marquardt_type =
+{
+  "marquardt",
+  init_diag_marquardt,
+  update_diag_marquardt
+};
+
+static const gsl_multifit_nlinear_scale more_type =
+{
+  "more",
+  init_diag_more,
+  update_diag_more
+};
+
+const gsl_multifit_nlinear_scale *gsl_multifit_nlinear_scale_levenberg = &levenberg_type;
+const gsl_multifit_nlinear_scale *gsl_multifit_nlinear_scale_marquardt = &marquardt_type;
+const gsl_multifit_nlinear_scale *gsl_multifit_nlinear_scale_more = &more_type;
diff -Nru gsl-doc-1.16/multifit_nlinear/subspace2D.c gsl-doc-2.3/multifit_nlinear/subspace2D.c
--- gsl-doc-1.16/multifit_nlinear/subspace2D.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/subspace2D.c	2016-09-08 17:54:18.000000000 +0000
@@ -0,0 +1,711 @@
+/* multifit_nlinear/subspace2D.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_poly.h>
+
+/*
+ * This module implements a 2D subspace trust region subproblem method,
+ * as outlined in
+ *
+ * [1] G. A. Shultz, R. B. Schnabel, and R. H. Byrd
+ *     A Family of Trust-Region-Based Algorithms for Unconstrained
+ *     Minimization with Strong Global Convergence Properties,
+ *     SIAM Journal on Numerical Analysis 1985 22:1, 47-67 
+ *
+ * [2] R. H. Byrd, R. B. Schnabel, G. A. Shultz,
+ *     Approximate solution of the trust region problem by
+ *     minimization over two-dimensional subspaces,
+ *     Mathematical Programming, January 1988, Volume 40,
+ *     Issue 1, pp 247-263
+ *
+ * The idea is to solve:
+ *
+ * min_{dx} g^T dx + 1/2 dx^T B dx
+ * 
+ * with constraints:
+ *
+ * ||D dx|| <= delta
+ * dx \in span{dx_sd, dx_gn}
+ *
+ * where B is the Hessian matrix, B = J^T J
+ *
+ * The steps are as follows:
+ *
+ * 1. preloop:
+ *    a. Compute Gauss-Newton and steepest descent vectors,
+ *       dx_gn, dx_sd
+ *    b. Compute an orthonormal basis for span(D dx_sd, D dx_gn) by
+ *       constructing W = [ D dx_sd, D dx_gn ] and performing a QR
+ *       decomposition of W. The 2 columns of the Q matrix
+ *       will then span the column space of W. W should have rank 2
+ *       unless D*dx_sd and D*dx_gn are parallel, in which case it will
+ *       have rank 1.
+ *    c. Precompute various quantities needed for the step calculation
+ *
+ * 2. step:
+ *    a. If the Gauss-Newton step is inside the trust region, use it
+ *    b. if W has rank 1, we cannot form a 2D subspace, so in this case
+ *       follow the steepest descent direction to the trust region boundary
+ *       and use that as the step.
+ *    c. In the full rank 2 case, if the GN point is outside the trust region,
+ *       then the minimizer of the objective function lies on the trust
+ *       region boundary. Therefore the minimization problem becomes:
+ *
+ *       min_{dx} g^T dx + 1/2 dx^T B dx, with ||dx|| = delta, dx = Q * x
+ *
+ *       where x is a 2-vector to be determined and the columns of Q are
+ *       the orthonormal basis vectors of the subspace. Note the equality
+ *       constraint now instead of <=. In terms of the new variable x,
+ *       the minimization problem becomes:
+ *
+ *       min_x subg^T x + 1/2 x^T subB x, with ||Q*x|| = ||x|| = delta
+ *
+ *       where:
+ *         subg = Q^T g   (2-by-1)
+ *         subB = Q^T B Q (2-by-2)
+ *
+ *       This equality constrained 2D minimization problem can be solved
+ *       with a Lagrangian multiplier, which results in a 4th degree polynomial
+ *       equation to be solved. The equation is:
+ *
+ *         lambda^4  1
+ *       + lambda^3  2 tr(B)
+ *       + lambda^2  (tr(B)^2 + 2 det(B) - g^T g / delta^2)
+ *       + lambda^1  (2 det(B) tr(B) - 2 g^T adj(B)^T g / delta^2)
+ *       + lambda^0  (det(B)^2 - g^T adj(B)^T adj(B) g / delta^2)
+ *
+ *       where adj(B) is the adjugate matrix of B.
+ *
+ *       We then check each of the 4 solutions for lambda to determine which
+ *       lambda results in the smallest objective function value. This x
+ *       is then used to construct the final step: dx = Q*x
+ */
+
+typedef struct
+{
+  size_t n;                  /* number of observations */
+  size_t p;                  /* number of parameters */
+  gsl_vector *dx_gn;         /* Gauss-Newton step, size p */
+  gsl_vector *dx_sd;         /* steepest descent step, size p */
+  double norm_Dgn;           /* || D dx_gn || */
+  double norm_Dsd;           /* || D dx_sd || */
+  gsl_vector *workp;         /* workspace, length p */
+  gsl_vector *workn;         /* workspace, length n */
+  gsl_matrix *W;             /* orthonormal basis for 2D subspace, p-by-2 */
+  gsl_matrix *JQ;            /* J * Q, n-by-p */
+  gsl_vector *tau;           /* Householder scalars */
+  gsl_vector *subg;          /* subspace gradient = W^T g, 2-by-1 */
+  gsl_matrix *subB;          /* subspace Hessian = W^T B W, 2-by-2 */
+  gsl_permutation *perm;     /* permutation matrix */
+
+  double trB;                /* Tr(subB) */
+  double detB;               /* det(subB) */
+  double normg;              /* || subg || */
+  double term0;              /* g^T adj(B)^T adj(B) g */
+  double term1;              /* g^T adj(B)^T g */
+
+  size_t rank;               /* rank of [ dx_sd, dx_gn ] matrix */
+
+  gsl_poly_complex_workspace *poly_p;
+
+  /* tunable parameters */
+  gsl_multifit_nlinear_parameters params;
+} subspace2D_state_t;
+
+#include "common.c"
+
+static void * subspace2D_alloc (const void * params, const size_t n, const size_t p);
+static void subspace2D_free(void *vstate);
+static int subspace2D_init(const void *vtrust_state, void *vstate);
+static int subspace2D_preloop(const void * vtrust_state, void * vstate);
+static int subspace2D_step(const void * vtrust_state, const double delta,
+                           gsl_vector * dx, void * vstate);
+static int subspace2D_preduction(const void * vtrust_state, const gsl_vector * dx,
+                                 double * pred, void * vstate);
+static int subspace2D_solution(const double lambda, gsl_vector * x,
+                               subspace2D_state_t * state);
+static double subspace2D_objective(const gsl_vector * x, subspace2D_state_t * state);
+static int subspace2D_calc_gn(const gsl_multifit_nlinear_trust_state * trust_state, gsl_vector * dx);
+static int subspace2D_calc_sd(const gsl_multifit_nlinear_trust_state * trust_state, gsl_vector * dx,
+                              subspace2D_state_t * state);
+
+static void *
+subspace2D_alloc (const void * params, const size_t n, const size_t p)
+{
+  const gsl_multifit_nlinear_parameters *par = (const gsl_multifit_nlinear_parameters *) params;
+  subspace2D_state_t *state;
+  
+  state = calloc(1, sizeof(subspace2D_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate subspace2D state", GSL_ENOMEM);
+    }
+
+  state->dx_gn = gsl_vector_alloc(p);
+  if (state->dx_gn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for dx_gn", GSL_ENOMEM);
+    }
+
+  state->dx_sd = gsl_vector_alloc(p);
+  if (state->dx_sd == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for dx_sd", GSL_ENOMEM);
+    }
+
+  state->workp = gsl_vector_alloc(p);
+  if (state->workp == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workp", GSL_ENOMEM);
+    }
+
+  state->workn = gsl_vector_alloc(n);
+  if (state->workn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workn", GSL_ENOMEM);
+    }
+
+  state->W = gsl_matrix_alloc(p, 2);
+  if (state->W == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for W", GSL_ENOMEM);
+    }
+
+  state->JQ = gsl_matrix_alloc(n, p);
+  if (state->JQ == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for JQ", GSL_ENOMEM);
+    }
+
+  state->tau = gsl_vector_alloc(2);
+  if (state->tau == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for tau", GSL_ENOMEM);
+    }
+
+  state->subg = gsl_vector_alloc(2);
+  if (state->subg == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for subg", GSL_ENOMEM);
+    }
+
+  state->subB = gsl_matrix_alloc(2, 2);
+  if (state->subB == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for subB", GSL_ENOMEM);
+    }
+
+  state->perm = gsl_permutation_alloc(2);
+  if (state->perm == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for perm", GSL_ENOMEM);
+    }
+
+  state->poly_p = gsl_poly_complex_workspace_alloc(5);
+  if (state->poly_p == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for poly workspace", GSL_ENOMEM);
+    }
+
+  state->n = n;
+  state->p = p;
+  state->rank = 0;
+  state->params = *par;
+
+  return state;
+}
+
+static void
+subspace2D_free(void *vstate)
+{
+  subspace2D_state_t *state = (subspace2D_state_t *) vstate;
+
+  if (state->dx_gn)
+    gsl_vector_free(state->dx_gn);
+
+  if (state->dx_sd)
+    gsl_vector_free(state->dx_sd);
+
+  if (state->workp)
+    gsl_vector_free(state->workp);
+
+  if (state->workn)
+    gsl_vector_free(state->workn);
+
+  if (state->W)
+    gsl_matrix_free(state->W);
+
+  if (state->JQ)
+    gsl_matrix_free(state->JQ);
+
+  if (state->tau)
+    gsl_vector_free(state->tau);
+
+  if (state->subg)
+    gsl_vector_free(state->subg);
+
+  if (state->subB)
+    gsl_matrix_free(state->subB);
+
+  if (state->perm)
+    gsl_permutation_free(state->perm);
+
+  if (state->poly_p)
+    gsl_poly_complex_workspace_free(state->poly_p);
+
+  free(state);
+}
+
+/*
+subspace2D_init()
+  Initialize subspace2D solver
+
+Inputs: vtrust_state - trust state
+        vstate       - workspace
+
+Return: success/error
+*/
+
+static int
+subspace2D_init(const void *vtrust_state, void *vstate)
+{
+  (void)vtrust_state;
+  (void)vstate;
+
+  return GSL_SUCCESS;
+}
+
+/*
+subspace2D_preloop()
+  Initialize subspace2D method prior to iteration loop.
+This involves computing the Gauss-Newton step and
+steepest descent step
+
+Notes: on output,
+1) state->dx_gn contains Gauss-Newton step
+2) state->dx_sd contains steepest descent step
+3) state->rank contains the rank([dx_sd, dx_gn])
+4) if full rank subspace (rank = 2), then:
+   state->trB = Tr(subB)
+   state->detB = det(subB)
+   state->normg = || subg ||
+*/
+
+static int
+subspace2D_preloop(const void * vtrust_state, void * vstate)
+{
+  int status;
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  subspace2D_state_t *state = (subspace2D_state_t *) vstate;
+  gsl_vector_view v;
+  double work_data[2];
+  gsl_vector_view work = gsl_vector_view_array(work_data, 2);
+  int signum;
+
+  /* calculate Gauss-Newton step */
+  status = subspace2D_calc_gn(trust_state, state->dx_gn);
+  if (status)
+    return status;
+
+  /* now calculate the steepest descent step */
+  status = subspace2D_calc_sd(trust_state, state->dx_sd, state);
+  if (status)
+    return status;
+
+  /* store norms */
+  state->norm_Dgn = scaled_enorm(trust_state->diag, state->dx_gn);
+  state->norm_Dsd = scaled_enorm(trust_state->diag, state->dx_sd);
+
+  /*
+   * now compute orthonormal basis for span(D dx_sd, D dx_gn) using
+   * QR decomposition; set W = [ D dx_sd, D dx_gn ] and normalize each
+   * column to unit magnitude. Then the Q matrix will form a basis for Col(W)
+   */
+
+  v = gsl_matrix_column(state->W, 0);
+  gsl_vector_memcpy(&v.vector, state->dx_sd);
+  gsl_vector_mul(&v.vector, trust_state->diag);
+  if (state->norm_Dsd != 0)
+    gsl_vector_scale(&v.vector, 1.0 / state->norm_Dsd);
+
+  v = gsl_matrix_column(state->W, 1);
+  gsl_vector_memcpy(&v.vector, state->dx_gn);
+  gsl_vector_mul(&v.vector, trust_state->diag);
+  if (state->norm_Dgn != 0)
+    gsl_vector_scale(&v.vector, 1.0 / state->norm_Dgn);
+
+  /* use a rank revealing QR decomposition in case dx_sd and dx_gn
+   * are parallel */
+  gsl_linalg_QRPT_decomp(state->W, state->tau, state->perm, &signum, &work.vector);
+
+  /* check for parallel dx_sd, dx_gn, in which case rank will be 1 */
+  state->rank = gsl_linalg_QRPT_rank(state->W, -1.0);
+
+  if (state->rank == 2)
+    {
+      /*
+       * full rank subspace, compute:
+       * subg = Q^T D^{-1} g
+       * subB = Q^T D^{-1} B D^{-1} Q where B = J^T J
+       */
+      const size_t p = state->p;
+      size_t i;
+      gsl_matrix_view JQ = gsl_matrix_submatrix(state->JQ, 0, 0, state->n, GSL_MIN(2, p));
+      double B00, B10, B11, g0, g1;
+
+      /* compute subg */
+      gsl_vector_memcpy(state->workp, trust_state->g);
+      gsl_vector_div(state->workp, trust_state->diag);
+      gsl_linalg_QR_QTvec(state->W, state->tau, state->workp);
+
+      g0 = gsl_vector_get(state->workp, 0);
+      g1 = gsl_vector_get(state->workp, 1);
+
+      gsl_vector_set(state->subg, 0, g0);
+      gsl_vector_set(state->subg, 1, g1);
+
+      /* compute subB */
+
+      /* compute J D^{-1} */
+      gsl_matrix_memcpy(state->JQ, trust_state->J);
+
+      for (i = 0; i < p; ++i)
+        {
+          gsl_vector_view c = gsl_matrix_column(state->JQ, i);
+          double di = gsl_vector_get(trust_state->diag, i);
+          gsl_vector_scale(&c.vector, 1.0 / di);
+        }
+
+      /* compute J D^{-1} Q */
+      gsl_linalg_QR_matQ(state->W, state->tau, state->JQ);
+
+      /* compute subB = Q^T D^{-1} J^T J D^{-1} Q */
+      gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &JQ.matrix, 0.0, state->subB);
+
+      B00 = gsl_matrix_get(state->subB, 0, 0);
+      B10 = gsl_matrix_get(state->subB, 1, 0);
+      B11 = gsl_matrix_get(state->subB, 1, 1);
+
+      state->trB = B00 + B11;
+      state->detB = B00*B11 - B10*B10;
+      state->normg = gsl_blas_dnrm2(state->subg);
+
+      /* g^T adj(B)^T adj(B) g */
+      state->term0 = (B10*B10 + B11*B11)*g0*g0 -
+                     2*B10*(B00 + B11)*g0*g1 +
+                     (B00*B00 + B10*B10)*g1*g1;
+
+      /* g^T adj(B)^T g */
+      state->term1 = B11 * g0 * g0 + g1 * (B00*g1 - 2*B10*g0);
+
+    }
+
+  return GSL_SUCCESS;
+}
+
+
+/*
+subspace2D_step()
+  Calculate a new step with 2D subspace method. Based on [1]. We
+seek a vector dx in span{dx_gn, dx_sd} which minimizes the model
+function subject to ||dx|| <= delta
+*/
+
+static int
+subspace2D_step(const void * vtrust_state, const double delta,
+                gsl_vector * dx, void * vstate)
+{
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  subspace2D_state_t *state = (subspace2D_state_t *) vstate;
+
+  if (state->norm_Dgn <= delta)
+    {
+      /* Gauss-Newton step is inside trust region, use it as final step
+       * since it is the global minimizer of the quadratic model function */
+      gsl_vector_memcpy(dx, state->dx_gn);
+    }
+  else if (state->rank < 2)
+    {
+      /* rank of [dx_sd, dx_gn] is 1, meaning dx_sd and dx_gn
+       * are parallel so we can't form a 2D subspace. Follow the steepest
+       * descent direction to the trust region boundary as our step */
+      gsl_vector_memcpy(dx, state->dx_sd);
+      gsl_vector_scale(dx, delta / state->norm_Dsd);
+    }
+  else
+    {
+      int status;
+      const double delta_sq = delta * delta;
+      double u = state->normg / delta;
+      double a[5];
+      double z[8];
+
+#if 1
+      a[0] = state->detB * state->detB - state->term0 / delta_sq;
+      a[1] = 2 * state->detB * state->trB - 2 * state->term1 / delta_sq;
+      a[2] = state->trB * state->trB + 2 * state->detB - u * u;
+      a[3] = 2 * state->trB;
+      a[4] = 1.0;
+#else
+      double TrB_D = state->trB * delta;
+      double detB_D = state->detB * delta;
+      double normg_sq = state->normg * state->normg;
+
+      a[0] = detB_D * detB_D - state->term0;
+      a[1] = 2 * state->detB * state->trB * delta_sq - 2 * state->term1;
+      a[2] = TrB_D * TrB_D + 2 * state->detB * delta_sq - normg_sq;
+      a[3] = 2 * state->trB * delta_sq;
+      a[4] = delta_sq;
+#endif
+
+      status = gsl_poly_complex_solve(a, 5, state->poly_p, z);
+      if (status == GSL_SUCCESS)
+        {
+          size_t i;
+          double min = 0.0;
+          int mini = -1;
+          double x_data[2];
+          gsl_vector_view x = gsl_vector_view_array(x_data, 2);
+
+          /*
+           * loop through all four values of the Lagrange multiplier
+           * lambda. For each lambda, evaluate the objective function
+           * with Re(lambda) to determine which lambda minimizes the
+           * function
+           */
+          for (i = 0; i < 4; ++i)
+            {
+              double cost, normx;
+
+              /*fprintf(stderr, "root: %.12e + %.12e i\n",
+                      z[2*i], z[2*i+1]);*/
+
+              status = subspace2D_solution(z[2*i], &x.vector, state);
+              if (status != GSL_SUCCESS)
+                continue; /* singular matrix system */
+
+              /* ensure ||x|| = delta */
+
+              normx = gsl_blas_dnrm2(&x.vector);
+              if (normx == 0.0)
+                continue;
+
+              gsl_vector_scale(&x.vector, delta / normx);
+
+              /* evaluate objective function to determine minimizer */
+              cost = subspace2D_objective(&x.vector, state);
+              if (mini < 0 || cost < min)
+                {
+                  mini = (int) i;
+                  min = cost;
+                }
+            }
+
+          if (mini < 0)
+            {
+              /* did not find minimizer - should not get here */
+              return GSL_FAILURE;
+            }
+          else
+            {
+              /* compute x which minimizes objective function */
+              subspace2D_solution(z[2*mini], &x.vector, state);
+
+              /* dx = Q * x */
+              gsl_vector_set_zero(dx);
+              gsl_vector_set(dx, 0, gsl_vector_get(&x.vector, 0));
+              gsl_vector_set(dx, 1, gsl_vector_get(&x.vector, 1));
+              gsl_linalg_QR_Qvec(state->W, state->tau, dx);
+
+              /* compute final dx by multiplying by D^{-1} */
+              gsl_vector_div(dx, trust_state->diag);
+            }
+        }
+      else
+        {
+          GSL_ERROR ("gsl_poly_complex_solve failed", status);
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+subspace2D_preduction(const void * vtrust_state, const gsl_vector * dx,
+                  double * pred, void * vstate)
+{
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  subspace2D_state_t *state = (subspace2D_state_t *) vstate;
+
+  *pred = quadratic_preduction(trust_state->f, trust_state->J, dx, state->workn);
+
+  return GSL_SUCCESS;
+}
+
+/* solve 2D subspace problem: (B + lambda*I) x = -g */
+static int
+subspace2D_solution(const double lambda, gsl_vector * x,
+                    subspace2D_state_t * state)
+{
+  int status = GSL_SUCCESS;
+  double C_data[4];
+  gsl_matrix_view C = gsl_matrix_view_array(C_data, 2, 2);
+  double B00 = gsl_matrix_get(state->subB, 0, 0);
+  double B10 = gsl_matrix_get(state->subB, 1, 0);
+  double B11 = gsl_matrix_get(state->subB, 1, 1);
+
+  /* construct C = B + lambda*I */
+  gsl_matrix_set(&C.matrix, 0, 0, B00 + lambda);
+  gsl_matrix_set(&C.matrix, 1, 0, B10);
+  gsl_matrix_set(&C.matrix, 0, 1, B10);
+  gsl_matrix_set(&C.matrix, 1, 1, B11 + lambda);
+
+  /* use modified Cholesky in case C is not positive definite */
+  gsl_linalg_mcholesky_decomp(&C.matrix, state->perm, NULL);
+  gsl_linalg_mcholesky_solve(&C.matrix, state->perm, state->subg, x);
+
+  gsl_vector_scale(x, -1.0);
+
+  return status;
+}
+
+/* evaluate 2D objective function: f(x) = g^T x + 1/2 x^T B x */
+static double
+subspace2D_objective(const gsl_vector * x, subspace2D_state_t * state)
+{
+  double f;
+  double y_data[2];
+  gsl_vector_view y = gsl_vector_view_array(y_data, 2);
+
+  /* compute: y = g + 1/2 B x */
+  gsl_vector_memcpy(&y.vector, state->subg);
+  gsl_blas_dsymv(CblasLower, 0.5, state->subB, x, 1.0, &y.vector);
+
+  /* compute: f = x^T ( g + 1/2 B x ) */
+  gsl_blas_ddot(x, &y.vector, &f);
+
+  return f;
+}
+
+/*
+subspace2D_calc_gn()
+  Calculate Gauss-Newton step which satisfies:
+
+J dx_gn = -f
+
+Inputs: trust_state - trust state variables
+        dx          - (output) Gauss-Newton step
+
+Return: success/error
+*/
+
+static int
+subspace2D_calc_gn(const gsl_multifit_nlinear_trust_state * trust_state, gsl_vector * dx)
+{
+  int status;
+  const gsl_multifit_nlinear_parameters *params = trust_state->params;
+
+  /* initialize linear least squares solver */
+  status = (params->solver->init)(trust_state, trust_state->solver_state);
+  if (status)
+    return status;
+
+  /* prepare the linear solver to compute Gauss-Newton step */
+  status = (params->solver->presolve)(0.0, trust_state, trust_state->solver_state);
+  if (status)
+    return status;
+
+  /* solve: J dx_gn = -f for Gauss-Newton step */
+  status = (params->solver->solve)(trust_state->f,
+                                   dx,
+                                   trust_state,
+                                   trust_state->solver_state);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+}
+
+/*
+subspace2D_calc_sd()
+  Calculate steepest descent step,
+
+dx_sd = - || D^{-1} g ||^2 / || J D^{-2} g ||^2 D^{-2} g
+
+Inputs: trust_state - trust state variables
+        dx          - (output) steepest descent vector
+        state       - workspace
+
+Return: success/error
+*/
+
+static int
+subspace2D_calc_sd(const gsl_multifit_nlinear_trust_state * trust_state, gsl_vector * dx,
+                   subspace2D_state_t * state)
+{
+  double norm_Dinvg;   /* || D^{-1} g || */
+  double norm_JDinv2g; /* || J D^{-2} g || */
+  double alpha;        /* || D^{-1} g ||^2 / || J D^{-2} g ||^2 */
+  double u;
+
+  /* compute workp = D^{-1} g and its norm */
+  gsl_vector_memcpy(state->workp, trust_state->g);
+  gsl_vector_div(state->workp, trust_state->diag);
+  norm_Dinvg = gsl_blas_dnrm2(state->workp);
+
+  /* compute workp = D^{-2} g */
+  gsl_vector_div(state->workp, trust_state->diag);
+
+  /* compute: workn = J D^{-2} g */
+  gsl_blas_dgemv(CblasNoTrans, 1.0, trust_state->J, state->workp, 0.0, state->workn);
+  norm_JDinv2g = gsl_blas_dnrm2(state->workn);
+
+  u = norm_Dinvg / norm_JDinv2g;
+  alpha = u * u;
+
+  /* dx_sd = -alpha D^{-2} g */
+  gsl_vector_memcpy(dx, state->workp);
+  gsl_vector_scale(dx, -alpha);
+
+  return GSL_SUCCESS;
+}
+
+static const gsl_multifit_nlinear_trs subspace2D_type =
+{
+  "2D-subspace",
+  subspace2D_alloc,
+  subspace2D_init,
+  subspace2D_preloop,
+  subspace2D_step,
+  subspace2D_preduction,
+  subspace2D_free
+};
+
+const gsl_multifit_nlinear_trs *gsl_multifit_nlinear_trs_subspace2D = &subspace2D_type;
diff -Nru gsl-doc-1.16/multifit_nlinear/svd.c gsl-doc-2.3/multifit_nlinear/svd.c
--- gsl-doc-1.16/multifit_nlinear/svd.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/svd.c	2016-07-07 20:36:10.000000000 +0000
@@ -0,0 +1,269 @@
+/* multifit_nlinear/svd.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/*
+ * This module handles the solution of the linear least squares
+ * system:
+ *
+ * [     J      ] dx = - [ f ]
+ * [ sqrt(mu)*D ]        [ 0 ]
+ *
+ * using an SVD approach. The system above is transformed to "standard form"
+ * via:
+ *
+ * J~ = J D^{-1}
+ * dx~ = D dx
+ *
+ * so that
+ *
+ * [     J~     ] dx~ = - [ f ]
+ * [ sqrt(mu)*I ]         [ 0 ]
+ *
+ * can be solved with a standard SVD method, and then dx is recovered
+ * from dx~ via: dx = D^{-1} dx~
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+
+typedef struct
+{
+  size_t n;                  /* number of residuals */
+  size_t p;                  /* number of parameters */
+  gsl_matrix *U;             /* U factor of J, n-by-p */
+  gsl_matrix *V;             /* V factor of J, p-by-p */
+  gsl_vector *S;             /* singular values, size p */
+  gsl_vector *workp;         /* workspace, length p */
+  double mu;                 /* LM parameter */
+} svd_state_t;
+
+static int svd_init(const void * vtrust_state, void * vstate);
+static int svd_presolve(const double mu, const void * vtrust_state, void * vstate);
+static int svd_solve(const gsl_vector * f, gsl_vector *x,
+                     const void * vtrust_state, void *vstate);
+static int svd_rcond(double * rcond, void * vstate);
+
+static void *
+svd_alloc (const size_t n, const size_t p)
+{
+  svd_state_t *state;
+
+  (void)n;
+  
+  state = calloc(1, sizeof(svd_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate svd state", GSL_ENOMEM);
+    }
+
+  state->U = gsl_matrix_alloc(n, p);
+  if (state->U == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for U", GSL_ENOMEM);
+    }
+
+  state->V = gsl_matrix_alloc(p, p);
+  if (state->V == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for V", GSL_ENOMEM);
+    }
+
+  state->S = gsl_vector_alloc(p);
+  if (state->S == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for S",
+                      GSL_ENOMEM);
+    }
+
+  state->workp = gsl_vector_alloc(p);
+  if (state->workp == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workp",
+                      GSL_ENOMEM);
+    }
+
+  state->mu = 0.0;
+  state->n = n;
+  state->p = p;
+
+  return state;
+}
+
+static void
+svd_free(void *vstate)
+{
+  svd_state_t *state = (svd_state_t *) vstate;
+
+  if (state->U)
+    gsl_matrix_free(state->U);
+
+  if (state->V)
+    gsl_matrix_free(state->V);
+
+  if (state->S)
+    gsl_vector_free(state->S);
+
+  if (state->workp)
+    gsl_vector_free(state->workp);
+
+  free(state);
+}
+
+/* compute svd of J */
+static int
+svd_init(const void * vtrust_state, void * vstate)
+{
+  int status;
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  svd_state_t *state = (svd_state_t *) vstate;
+  size_t i;
+
+  gsl_matrix_set_zero(state->U);
+
+  /* compute U = J D^{-1} */
+  for (i = 0; i < state->p; ++i)
+    {
+      gsl_vector_const_view Ji = gsl_matrix_const_column(trust_state->J, i);
+      gsl_vector_view ui = gsl_matrix_column(state->U, i);
+      double di = gsl_vector_get(trust_state->diag, i);
+
+      gsl_blas_daxpy(1.0 / di, &Ji.vector, &ui.vector);
+    }
+
+  status = gsl_linalg_SV_decomp(state->U, state->V, state->S, state->workp);
+
+  return status;
+}
+
+static int
+svd_presolve(const double mu, const void * vtrust_state, void * vstate)
+{
+  svd_state_t *state = (svd_state_t *) vstate;
+
+  state->mu = mu;
+
+  (void)vtrust_state;
+
+  return GSL_SUCCESS;
+}
+
+static int
+svd_solve(const gsl_vector * f, gsl_vector *x,
+          const void * vtrust_state, void *vstate)
+{
+  int status = GSL_SUCCESS;
+  const gsl_multifit_nlinear_trust_state *trust_state =
+    (const gsl_multifit_nlinear_trust_state *) vtrust_state;
+  svd_state_t *state = (svd_state_t *) vstate;
+  const size_t p = state->p;
+  const double tol = GSL_DBL_EPSILON;
+  const double s0 = gsl_vector_get(state->S, 0);
+  size_t j;
+
+  /* compute workp = - U^T f */
+  gsl_blas_dgemv(CblasTrans, -1.0, state->U, f, 0.0, state->workp);
+
+  /*
+   * compute:
+   *
+   * workp = sum_i s_i / (s_i^2 + mu) (-u_i^T f)
+   */
+
+  if (state->mu == 0.0)
+    {
+      /*
+       * compute Gauss-Newton direction by solving
+       * J x = -f
+       */
+
+      for (j = 0; j < p; ++j)
+        {
+          double sj = gsl_vector_get(state->S, j);
+          double *ptr = gsl_vector_ptr(state->workp, j);
+          double alpha;
+
+          if (sj <= tol * s0)
+            alpha = 0.0;
+          else
+            alpha = 1.0 / sj;
+
+          *ptr *= alpha;
+        }
+    }
+  else
+    {
+      /*
+       * solve:
+       *
+       * [  J D^{-1}  ] (D x) = -[ f ]
+       * [ sqrt(mu) I ]          [ 0 ]
+       *
+       * using SVD factorization of J D^{-1}
+       */
+
+      for (j = 0; j < p; ++j)
+        {
+          double sj = gsl_vector_get(state->S, j);
+          double *ptr = gsl_vector_ptr(state->workp, j);
+
+          *ptr *= sj / (sj*sj + state->mu);
+        }
+    }
+
+  /* compute: x = V * workp */
+  gsl_blas_dgemv(CblasNoTrans, 1.0, state->V, state->workp, 0.0, x);
+
+  /* compute D^{-1} x */
+  gsl_vector_div(x, trust_state->diag);
+
+  return status;
+}
+
+static int
+svd_rcond(double * rcond, void * vstate)
+{
+  int status = GSL_SUCCESS;
+  svd_state_t *state = (svd_state_t *) vstate;
+  double smax = gsl_vector_get(state->S, 0);
+  double smin = gsl_vector_get(state->S, state->p - 1);
+
+  *rcond = smin / smax;
+
+  return status;
+}
+
+static const gsl_multifit_nlinear_solver svd_type =
+{
+  "svd",
+  svd_alloc,
+  svd_init,
+  svd_presolve,
+  svd_solve,
+  svd_rcond,
+  svd_free
+};
+
+const gsl_multifit_nlinear_solver *gsl_multifit_nlinear_solver_svd = &svd_type;
diff -Nru gsl-doc-1.16/multifit_nlinear/test_bard.c gsl-doc-2.3/multifit_nlinear/test_bard.c
--- gsl-doc-1.16/multifit_nlinear/test_bard.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_bard.c	2016-09-24 10:40:31.000000000 +0000
@@ -0,0 +1,153 @@
+#define bard_N         15
+#define bard_P         3
+
+static double bard_x0[bard_P] = { 1.0, 1.0, 1.0 };
+static double bard_epsrel = 1.0e-7;
+
+static double bard_Y[bard_N] = {
+0.14, 0.18, 0.22, 0.25, 0.29, 0.32, 0.35, 0.39, 0.37,
+0.58, 0.73, 0.96, 1.34, 2.10, 4.39
+};
+
+static void
+bard_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact1 = 8.214877306578963e-03;
+  double bard_x1[bard_P] = { 8.241055975623580e-02,
+                             1.133036092245175,
+                             2.343695178435405 };
+  const double sumsq_exact2 = 17.42869333333333;
+  double bard_x2[bard_P] = { 8.406666666666666e-01,
+                             0.0,    /* -inf */
+                             0.0 };  /* -inf */
+  double *bard_x;
+  double sumsq_exact;
+
+  bard_x2[1] = GSL_NAN;
+  bard_x2[2] = GSL_NAN;
+
+  if (fabs(x[1]) < 10.0 && fabs(x[2]) < 10.0)
+    {
+      bard_x = bard_x1;
+      sumsq_exact = sumsq_exact1;
+    }
+  else
+    {
+      bard_x = bard_x2;
+      sumsq_exact = sumsq_exact2;
+    }
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < bard_P; ++i)
+    {
+      if (!gsl_finite(bard_x[i]))
+        continue;
+
+      gsl_test_rel(x[i], bard_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+bard_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < bard_N; ++i)
+    {
+      double ui = i + 1.0;
+      double vi = 16.0 - i - 1.0;
+      double wi = GSL_MIN(ui, vi);
+      double yi = bard_Y[i];
+      double fi = yi - (x1 + (ui / (x2*vi + x3*wi)));
+
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+bard_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < bard_N; ++i)
+    {
+      double ui = i + 1.0;
+      double vi = 16.0 - i - 1.0;
+      double wi = GSL_MIN(ui, vi);
+      double term = x2 * vi + x3 * wi;
+
+      gsl_matrix_set(J, i, 0, -1.0);
+      gsl_matrix_set(J, i, 1, ui * vi / (term * term));
+      gsl_matrix_set(J, i, 2, ui * wi / (term * term));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+bard_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  size_t i;
+
+  for (i = 0; i < bard_N; ++i)
+    {
+      double ui = i + 1.0;
+      double vi = 16.0 - i - 1.0;
+      double wi = GSL_MIN(ui, vi);
+      double term1 = x2 * vi + x3 * wi;
+      double term2 = v2 * vi + v3 * wi;
+      double ratio = term2 / term1;
+
+      gsl_vector_set(fvv, i, -2.0 * ui * ratio * ratio / term1);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf bard_func =
+{
+  bard_f,
+  bard_df,
+  bard_fvv,
+  bard_N,
+  bard_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem bard_problem =
+{
+  "bard",
+  bard_x0,
+  NULL,
+  NULL,
+  &bard_epsrel,
+  &bard_checksol,
+  &bard_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_beale.c gsl-doc-2.3/multifit_nlinear/test_beale.c
--- gsl-doc-1.16/multifit_nlinear/test_beale.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_beale.c	2016-09-24 10:40:36.000000000 +0000
@@ -0,0 +1,113 @@
+#define beale_N         3
+#define beale_P         2
+
+static double beale_x0[beale_P] = { 1.0, 1.0 };
+static double beale_epsrel = 1.0e-12;
+
+static double beale_Y[beale_N] = { 1.5, 2.25, 2.625 };
+
+static void
+beale_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double beale_x[beale_P] = { 3.0, 0.5 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < beale_P; ++i)
+    {
+      gsl_test_rel(x[i], beale_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+beale_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < beale_N; ++i)
+    {
+      double yi = beale_Y[i];
+      double term = pow(x2, i + 1.0);
+      double fi = yi - x1*(1.0 - term);
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+beale_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < beale_N; ++i)
+    {
+      double term = pow(x2, (double) i);
+
+      gsl_matrix_set(J, i, 0, term*x2 - 1.0);
+      gsl_matrix_set(J, i, 1, (i + 1.0) * x1 * term);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+beale_fvv (const gsl_vector * x, const gsl_vector * v,
+           void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  size_t i;
+
+  for (i = 0; i < beale_N; ++i)
+    {
+      double term = pow(x2, (double)i - 1.0);
+
+      gsl_vector_set(fvv, i, (i + 1.0) * v2 * term *
+                             (i * v2 * x1 + 2.0 * v1 * x2));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf beale_func =
+{
+  beale_f,
+  beale_df,
+  beale_fvv,
+  beale_N,
+  beale_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem beale_problem =
+{
+  "beale",
+  beale_x0,
+  NULL,
+  NULL,
+  &beale_epsrel,
+  &beale_checksol,
+  &beale_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_biggs.c gsl-doc-2.3/multifit_nlinear/test_biggs.c
--- gsl-doc-1.16/multifit_nlinear/test_biggs.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_biggs.c	2016-09-24 10:40:42.000000000 +0000
@@ -0,0 +1,140 @@
+#define biggs_N         20 /* >= p */
+#define biggs_P         6
+
+/* dogleg method has trouble converging from recommended starting point,
+ * so we use an x0 which is a little closer to the true solution */
+/*static double biggs_x0[biggs_P] = { 1.0, 2.0, 1.0, 1.0, 1.0, 1.0 };*/
+static double biggs_x0[biggs_P] = { 1.0, 5.0, 1.0, 2.0, 3.0, 2.0 };
+static double biggs_epsrel = 1.0e-9;
+
+static void
+biggs_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  const double sumsq_exact = 0.0;
+  const double biggs_x[biggs_P] = { 1.0, 10.0, 1.0, 5.0, 4.0, 3.0 };
+  size_t i;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < biggs_P; ++i)
+    {
+      gsl_test_rel(x[i], biggs_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+biggs_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  double x6 = gsl_vector_get(x, 5);
+  size_t i;
+
+  for (i = 0; i < biggs_N; ++i)
+    {
+      double ti = 0.1 * (i + 1.0);
+      double yi = exp(-ti) - 5*exp(-10*ti) + 3*exp(-4*ti);
+      double fi = x3*exp(-ti*x1) - x4*exp(-ti*x2) + x6*exp(-ti*x5) - yi;
+
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+biggs_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  double x6 = gsl_vector_get(x, 5);
+  size_t i;
+
+  for (i = 0; i < biggs_N; ++i)
+    {
+      double ti = 0.1 * (i + 1.0);
+
+      gsl_matrix_set(J, i, 0, -ti*x3*exp(-ti*x1));
+      gsl_matrix_set(J, i, 1, ti*x4*exp(-ti*x2));
+      gsl_matrix_set(J, i, 2, exp(-ti*x1));
+      gsl_matrix_set(J, i, 3, -exp(-ti*x2));
+      gsl_matrix_set(J, i, 4, -ti*x6*exp(-ti*x5));
+      gsl_matrix_set(J, i, 5, exp(-ti*x5));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+biggs_fvv (const gsl_vector * x, const gsl_vector * v,
+           void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  double x6 = gsl_vector_get(x, 5);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  double v4 = gsl_vector_get(v, 3);
+  double v5 = gsl_vector_get(v, 4);
+  double v6 = gsl_vector_get(v, 5);
+  size_t i;
+
+  for (i = 0; i < biggs_N; ++i)
+    {
+      double ti = 0.1 * (i + 1.0);
+      double term1 = exp(-ti * x1);
+      double term2 = exp(-ti * x2);
+      double term3 = exp(-ti * x5);
+
+      gsl_vector_set(fvv, i, ti * term1 * term2 * term3 *
+                             (v1/(term2*term3)*(-2*v3 + ti*v1*x3) -
+                              v2/(term1*term3)*(-2*v4 + ti*v2*x4) +
+                              v5/(term1*term2)*(-2*v6 + ti*v5*x6)));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf biggs_func =
+{
+  biggs_f,
+  biggs_df,
+  biggs_fvv,
+  biggs_N,
+  biggs_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem biggs_problem =
+{
+  "biggs",
+  biggs_x0,
+  NULL,
+  NULL,
+  &biggs_epsrel,
+  &biggs_checksol,
+  &biggs_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_boxbod.c gsl-doc-2.3/multifit_nlinear/test_boxbod.c
--- gsl-doc-1.16/multifit_nlinear/test_boxbod.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_boxbod.c	2016-09-24 10:41:03.000000000 +0000
@@ -0,0 +1,144 @@
+#define boxbod_N       6
+#define boxbod_P       2
+
+static double boxbod_x0a[boxbod_P] = { 1.0, 1.0 };
+static double boxbod_x0b[boxbod_P] = { 100.0, 0.75 };
+static double boxbod_epsrel = 1.0e-7;
+
+static double boxbod_sigma[boxbod_P] = {
+  1.2354515176E+01, 1.0455993237E-01
+};
+
+static double boxbod_X[boxbod_N] = { 1.0, 2.0, 3.0, 5.0, 7.0, 10.0 };
+
+static double boxbod_F[boxbod_N] = { 109.0, 149.0, 149.0, 191.0,
+                                     213.0, 224.0 };
+
+static void
+boxbod_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.1680088766E+03;
+  const double boxbod_x[boxbod_P] = { 2.1380940889E+02,
+                                      5.4723748542E-01 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < boxbod_P; ++i)
+    {
+      gsl_test_rel(x[i], boxbod_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+boxbod_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[boxbod_P];
+  size_t i;
+
+  for (i = 0; i < boxbod_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < boxbod_N; i++)
+    {
+      double xi = boxbod_X[i];
+      double yi;
+
+      yi = b[0] * (1.0 - exp(-b[1] * xi));
+      gsl_vector_set (f, i, yi - boxbod_F[i]);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+boxbod_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[boxbod_P];
+  size_t i;
+
+  for (i = 0; i < boxbod_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < boxbod_N; i++)
+    {
+      double xi = boxbod_X[i];
+      double term = exp(-b[1] * xi);
+
+      gsl_matrix_set (df, i, 0, 1.0 - term);
+      gsl_matrix_set (df, i, 1, b[0] * term * xi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+boxbod_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  size_t i;
+
+  for (i = 0; i < boxbod_N; i++)
+    {
+      double ti = boxbod_X[i];
+      double term = exp(-x2 * ti);
+
+      gsl_vector_set(fvv, i, term * ti * v2 * (2*v1 - ti*v2*x1));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf boxbod_func =
+{
+  boxbod_f,
+  boxbod_df,
+  boxbod_fvv,
+  boxbod_N,
+  boxbod_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem boxboda_problem =
+{
+  "nist-boxboda",
+  boxbod_x0a,
+  NULL,
+  boxbod_sigma,
+  &boxbod_epsrel,
+  &boxbod_checksol,
+  &boxbod_func
+};
+
+static test_fdf_problem boxbodb_problem =
+{
+  "nist-boxbodb",
+  boxbod_x0b,
+  NULL,
+  boxbod_sigma,
+  &boxbod_epsrel,
+  &boxbod_checksol,
+  &boxbod_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_box.c gsl-doc-2.3/multifit_nlinear/test_box.c
--- gsl-doc-1.16/multifit_nlinear/test_box.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_box.c	2016-09-24 10:41:09.000000000 +0000
@@ -0,0 +1,143 @@
+#define box_N         10 /* can be >= p */
+#define box_P         3
+
+/* dogleg method fails with recommended starting point, so use
+ * a slightly easier x0 */
+/*static double box_x0[box_P] = { 0.0, 10.0, 20.0 };*/
+static double box_x0[box_P] = { 5.0, 10.0, 2.0 };
+static double box_epsrel = 1.0e-12;
+
+static void
+box_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  const double sumsq_exact = 0.0;
+  const double eps = 1.0e-6;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  /* there are 3 possible solution vectors */
+
+  if (fabs(x[2] - 1.0) < eps)
+    {
+      /* case 1: x* = [ 1; 10; 1 ] */
+      gsl_test_rel(x[0], 1.0, epsrel, "%s/%s i=0",
+                   sname, pname);
+      gsl_test_rel(x[1], 10.0, epsrel, "%s/%s i=1",
+                   sname, pname);
+      gsl_test_rel(x[2], 1.0, epsrel, "%s/%s i=2",
+                   sname, pname);
+    }
+  else if (fabs(x[2] + 1.0) < eps)
+    {
+      /* case 2: x* = [ 10; 1; -1 ] */
+      gsl_test_rel(x[0], 10.0, epsrel, "%s/%s i=0",
+                   sname, pname);
+      gsl_test_rel(x[1], 1.0, epsrel, "%s/%s i=1",
+                   sname, pname);
+      gsl_test_rel(x[2], -1.0, epsrel, "%s/%s i=2",
+                   sname, pname);
+    }
+  else
+    {
+      /* case 3: x* = [ a; a; 0 ] for any a */
+      gsl_test_rel(x[0], x[1], epsrel, "%s/%s i=0,1",
+                   sname, pname);
+      gsl_test_rel(x[2], 0.0, epsrel, "%s/%s i=2",
+                   sname, pname);
+    }
+}
+
+static int
+box_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < box_N; ++i)
+    {
+      double ti = (i + 1.0) / 10.0;
+      double fi = exp(-x1*ti) - exp(-x2*ti) - x3*(exp(-ti) - exp(-10.0*ti));
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+box_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < box_N; ++i)
+    {
+      double ti = (i + 1.0) / 10.0;
+      double term1 = exp(-x1*ti);
+      double term2 = exp(-x2*ti);
+      double term3 = exp(-10.0*ti) - exp(-ti);
+
+      gsl_matrix_set(J, i, 0, -ti*term1);
+      gsl_matrix_set(J, i, 1, ti*term2);
+      gsl_matrix_set(J, i, 2, term3);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+box_fvv (const gsl_vector * x, const gsl_vector * v,
+         void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  size_t i;
+
+  for (i = 0; i < box_N; ++i)
+    {
+      double ti = (i + 1.0) / 10.0;
+      double term1 = exp(-x1*ti);
+      double term2 = exp(-x2*ti);
+
+      gsl_vector_set(fvv, i, ti * ti * (v1*v1*term1 - v2*v2*term2));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf box_func =
+{
+  box_f,
+  box_df,
+  box_fvv,
+  box_N,
+  box_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem box_problem =
+{
+  "box3d",
+  box_x0,
+  NULL,
+  NULL,
+  &box_epsrel,
+  &box_checksol,
+  &box_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_brown1.c gsl-doc-2.3/multifit_nlinear/test_brown1.c
--- gsl-doc-1.16/multifit_nlinear/test_brown1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_brown1.c	2016-09-24 10:41:15.000000000 +0000
@@ -0,0 +1,126 @@
+#define brown1_N         20
+#define brown1_P         4
+
+static double brown1_x0[brown1_P] = { 25, 5, -5, -1 };
+static double brown1_epsrel = 1.0e-5;
+
+static void
+brown1_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.582220162635628e+04;
+  const double brown1_x[brown1_P] = {
+    -1.159443990239263e+01, 1.320363005221244e+01,
+    -4.034395456782477e-01, 2.367789088597534e-01 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < brown1_P; ++i)
+    {
+      gsl_test_rel(x[i], brown1_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+brown1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x0 = gsl_vector_get (x, 0);
+  double x1 = gsl_vector_get (x, 1);
+  double x2 = gsl_vector_get (x, 2);
+  double x3 = gsl_vector_get (x, 3);
+  size_t i;
+
+  for (i = 0; i < brown1_N; i++)
+    {
+      double ti = 0.2 * (i + 1);
+      double ui = x0 + x1 * ti - exp (ti);
+      double vi = x2 + x3 * sin (ti) - cos (ti);
+
+      gsl_vector_set (f, i, ui * ui + vi * vi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown1_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double x0 = gsl_vector_get (x, 0);
+  double x1 = gsl_vector_get (x, 1);
+  double x2 = gsl_vector_get (x, 2);
+  double x3 = gsl_vector_get (x, 3);
+  size_t i;
+
+  for (i = 0; i < brown1_N; i++)
+    {
+      double ti = 0.2 * (i + 1);
+      double ui = x0 + x1 * ti - exp (ti);
+      double vi = x2 + x3 * sin (ti) - cos (ti);
+
+      gsl_matrix_set (df, i, 0, 2 * ui);
+      gsl_matrix_set (df, i, 1, 2 * ui * ti);
+      gsl_matrix_set (df, i, 2, 2 * vi);
+      gsl_matrix_set (df, i, 3, 2 * vi * sin (ti));
+
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown1_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  double v0 = gsl_vector_get (v, 0);
+  double v1 = gsl_vector_get (v, 1);
+  double v2 = gsl_vector_get (v, 2);
+  double v3 = gsl_vector_get (v, 3);
+  size_t i;
+
+  for (i = 0; i < brown1_N; i++)
+    {
+      double ti = 0.2 * (i + 1);
+      double term1 = v0 + ti*v1;
+      double term2 = v3*sin(ti);
+
+      gsl_vector_set (fvv, i, 2.0 * (term1*term1 + v2*v2 +
+                                     term2 * (2*v2 + term2)));
+    }
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf brown1_func =
+{
+  brown1_f,
+  brown1_df,
+  brown1_fvv,
+  brown1_N,
+  brown1_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem brown1_problem =
+{
+  "brown_dennis",
+  brown1_x0,
+  NULL,
+  NULL,
+  &brown1_epsrel,
+  &brown1_checksol,
+  &brown1_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_brown2.c gsl-doc-2.3/multifit_nlinear/test_brown2.c
--- gsl-doc-1.16/multifit_nlinear/test_brown2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_brown2.c	2016-09-24 10:41:21.000000000 +0000
@@ -0,0 +1,170 @@
+#define brown2_N        5
+#define brown2_P        5
+
+static double brown2_x0[brown2_P] = { 0.5, 0.5, 0.5, 0.5, 0.5 };
+static double brown2_epsrel = 1.0e-12;
+
+static void
+brown2_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  double sumsq_exact;
+  double alpha;
+  const double p = (double) brown2_P;
+  double alpha1mp, lhs, lastel;
+
+  if (sumsq < 0.5)
+    {
+      /* sumsq = 0 case */
+
+      sumsq_exact = 0.0;
+      alpha = x[0];
+      alpha1mp = pow(alpha, 1.0 - p);
+      lhs = p*pow(alpha, p) - (p + 1)/alpha1mp;
+      lastel = alpha1mp;
+
+      gsl_test_rel(lhs, -1.0, epsrel, "%s/%s alpha lhs",
+                   sname, pname);
+    }
+  else
+    {
+      /* sumsq = 1 case */
+
+      sumsq_exact = 1.0;
+      alpha = 0.0;
+      lastel = p + 1.0;
+    }
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 1; i < brown2_P - 1; ++i)
+    {
+      gsl_test_rel(x[i], alpha, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+
+  gsl_test_rel(x[brown2_P - 1], lastel, epsrel, "%s/%s last element",
+               sname, pname);
+}
+
+static int
+brown2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i;
+  double sum = -(brown2_N + 1.0);
+  double prod = 1.0;
+
+  for (i = 0; i < brown2_N; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      sum += xi;
+      prod *= xi;
+    }
+
+  for (i = 0; i < brown2_N - 1; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      gsl_vector_set(f, i, xi + sum);
+    }
+
+  gsl_vector_set(f, brown2_N - 1, prod - 1.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown2_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  size_t i, j;
+
+  for (j = 0; j < brown2_P; ++j)
+    {
+      double prod = 1.0;
+
+      for (i = 0; i < brown2_N - 1; i++)
+        {
+          double Jij = (i == j) ? 2.0 : 1.0;
+          gsl_matrix_set(J, i, j, Jij);
+        }
+
+      for (i = 0; i < brown2_N; i++)
+        {
+          if (i != j)
+            prod *= gsl_vector_get(x, i);
+        }
+
+      gsl_matrix_set(J, brown2_N - 1, j, prod);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown2_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  size_t i, j, k;
+  double sum = 0.0;
+
+  gsl_vector_set_zero(fvv);
+
+  for (k = 0; k < brown2_P; ++k)
+    {
+      double vk = gsl_vector_get(v, k);
+
+      for (i = 0; i < brown2_P; ++i)
+        {
+          double vi = gsl_vector_get(v, i);
+          double delta = (i == k) ? 1.0 : 0.0;
+          double prod = 1.0;
+
+          for (j = 0; j < brown2_N; ++j)
+            {
+              if (j != i && j != k)
+                {
+                  double xj = gsl_vector_get(x, j);
+                  prod *= xj;
+                }
+            }
+
+          sum += vk * vi * (1.0 - delta) * prod;
+        }
+    }
+
+  gsl_vector_set(fvv, brown2_N - 1, sum);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf brown2_func =
+{
+  brown2_f,
+  brown2_df,
+  brown2_fvv,
+  brown2_N,
+  brown2_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem brown2_problem =
+{
+  "brown_almost_linear",
+  brown2_x0,
+  NULL,
+  NULL,
+  &brown2_epsrel,
+  &brown2_checksol,
+  &brown2_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_brown3.c gsl-doc-2.3/multifit_nlinear/test_brown3.c
--- gsl-doc-1.16/multifit_nlinear/test_brown3.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_brown3.c	2016-09-24 10:41:30.000000000 +0000
@@ -0,0 +1,98 @@
+#define brown3_N         3
+#define brown3_P         2
+
+static double brown3_x0[brown3_P] = { 1.0, 1.0 };
+static double brown3_epsrel = 1.0e-12;
+
+static void
+brown3_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double brown3_x[brown3_P] = { 1.0e6, 2.0e-6 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < brown3_P; ++i)
+    {
+      gsl_test_rel(x[i], brown3_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+brown3_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, x1 - 1.0e6);
+  gsl_vector_set(f, 1, x2 - 2.0e-6);
+  gsl_vector_set(f, 2, x1*x2 - 2.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown3_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_matrix_set_zero(J);
+
+  gsl_matrix_set(J, 0, 0, 1.0);
+  gsl_matrix_set(J, 1, 1, 1.0);
+  gsl_matrix_set(J, 2, 0, x2);
+  gsl_matrix_set(J, 2, 1, x1);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown3_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+
+  gsl_vector_set(fvv, 0, 0.0);
+  gsl_vector_set(fvv, 1, 0.0);
+  gsl_vector_set(fvv, 2, 2.0 * v1 * v2);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf brown3_func =
+{
+  brown3_f,
+  brown3_df,
+  brown3_fvv,
+  brown3_N,
+  brown3_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem brown3_problem =
+{
+  "brown_badly_scaled",
+  brown3_x0,
+  NULL,
+  NULL,
+  &brown3_epsrel,
+  &brown3_checksol,
+  &brown3_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test.c gsl-doc-2.3/multifit_nlinear/test.c
--- gsl-doc-1.16/multifit_nlinear/test.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test.c	2016-09-16 22:53:28.000000000 +0000
@@ -0,0 +1,105 @@
+/* multifit_nlinear/test.c
+ * 
+ * Copyright (C) 2007, 2013, 2015, 2016 Brian Gough, Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/* These tests are based on the NIST Statistical Reference Datasets
+   See http://www.nist.gov/itl/div898/strd/index.html for more
+   information. */
+
+#include <config.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_test.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_ieee_utils.h>
+
+#include "test_fdf.c"
+
+static void
+test_proc(const gsl_multifit_nlinear_trs *trs,
+          const gsl_multifit_nlinear_scale *scale,
+          const gsl_multifit_nlinear_solver *solver,
+          const int fdtype)
+{
+  gsl_multifit_nlinear_parameters fdf_params =
+    gsl_multifit_nlinear_default_parameters();
+
+  fdf_params.trs = trs;
+  fdf_params.scale = scale;
+  fdf_params.solver = solver;
+  fdf_params.fdtype = fdtype;
+
+  test_fdf_main(&fdf_params);
+}
+
+int
+main (void)
+{
+  const gsl_multifit_nlinear_trs **nlinear_trs[6];
+  const gsl_multifit_nlinear_solver **nlinear_solvers[4];
+  const gsl_multifit_nlinear_scale **nlinear_scales[3];
+  const gsl_multifit_nlinear_trs **trs;
+  const gsl_multifit_nlinear_solver **solver;
+  const gsl_multifit_nlinear_scale **scale;
+  size_t i = 0;
+
+  gsl_ieee_env_setup();
+
+  /* initialize arrays */
+
+  nlinear_trs[0] = &gsl_multifit_nlinear_trs_lm;
+  nlinear_trs[1] = &gsl_multifit_nlinear_trs_lmaccel;
+  nlinear_trs[2] = &gsl_multifit_nlinear_trs_dogleg;
+  nlinear_trs[3] = &gsl_multifit_nlinear_trs_ddogleg;
+  nlinear_trs[4] = &gsl_multifit_nlinear_trs_subspace2D;
+  nlinear_trs[5] = NULL;
+
+  nlinear_solvers[0] = &gsl_multifit_nlinear_solver_cholesky;
+  nlinear_solvers[1] = &gsl_multifit_nlinear_solver_qr;
+  nlinear_solvers[2] = &gsl_multifit_nlinear_solver_svd;
+  nlinear_solvers[3] = NULL;
+
+  /* skip Marquardt scaling since it won't pass */
+  nlinear_scales[0] = &gsl_multifit_nlinear_scale_levenberg;
+  nlinear_scales[1] = &gsl_multifit_nlinear_scale_more;
+  nlinear_scales[2] = NULL;
+
+  /* run testsuite over all parameter combinations */
+
+  for (trs = nlinear_trs[i]; trs != NULL; trs = nlinear_trs[++i])
+    {
+      size_t j = 0;
+
+      fprintf(stderr, "trs = %s\n", (*trs)->name);
+
+      for (solver = nlinear_solvers[j]; solver != NULL; solver = nlinear_solvers[++j])
+        {
+          size_t k = 0;
+          fprintf(stderr, "solver = %s\n", (*solver)->name);
+          for (scale = nlinear_scales[k]; scale != NULL; scale = nlinear_scales[++k])
+            {
+              test_proc(*trs, *scale, *solver, GSL_MULTIFIT_NLINEAR_FWDIFF);
+              test_proc(*trs, *scale, *solver, GSL_MULTIFIT_NLINEAR_CTRDIFF);
+            }
+        }
+    }
+
+  exit (gsl_test_summary ());
+}
diff -Nru gsl-doc-1.16/multifit_nlinear/test_eckerle.c gsl-doc-2.3/multifit_nlinear/test_eckerle.c
--- gsl-doc-1.16/multifit_nlinear/test_eckerle.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_eckerle.c	2016-09-24 15:45:10.000000000 +0000
@@ -0,0 +1,155 @@
+#define eckerle_N       35
+#define eckerle_P       3
+
+static double eckerle_x0a[eckerle_P] = { 1.0, 10.0, 500.0 };
+static double eckerle_x0b[eckerle_P] = { 1.5, 5.0, 450.0 };
+static double eckerle_epsrel = 1.0e-7;
+
+static double eckerle_sigma[eckerle_P] = {
+  1.5408051163E-02, 4.6803020753E-02, 4.6800518816E-02
+};
+
+static double eckerle_X[eckerle_N] = {
+  400.000000, 405.000000, 410.000000, 415.000000, 420.000000,
+  425.000000, 430.000000, 435.000000, 436.500000, 438.000000,
+  439.500000, 441.000000, 442.500000, 444.000000, 445.500000,
+  447.000000, 448.500000, 450.000000, 451.500000, 453.000000,
+  454.500000, 456.000000, 457.500000, 459.000000, 460.500000,
+  462.000000, 463.500000, 465.000000, 470.000000, 475.000000,
+  480.000000, 485.000000, 490.000000, 495.000000, 500.000000 };
+
+static double eckerle_F[eckerle_N] = {
+  0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917,
+  0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302,
+  0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458,
+  0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534,
+  0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200,
+  0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800,
+  0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710 };
+
+static void
+eckerle_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.4635887487E-03;
+  const double eckerle_x[eckerle_P] = { 1.5543827178E+00,
+                                        4.0888321754E+00,
+                                        4.5154121844E+02 };
+  double new_x[3];
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  /* x1 and x2 are unique up to a sign, but they must be
+   * the same sign */
+  if (x[0] < 0.0 && x[1] < 0.0)
+    {
+      new_x[0] = -x[0];
+      new_x[1] = -x[1];
+    }
+  else
+    {
+      new_x[0] = x[0];
+      new_x[1] = x[1];
+    }
+
+  new_x[2] = x[2];
+
+  for (i = 0; i < eckerle_P; ++i)
+    {
+      gsl_test_rel(new_x[i], eckerle_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+eckerle_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[eckerle_P];
+  size_t i;
+
+  for (i = 0; i < eckerle_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < eckerle_N; i++)
+    {
+      double xi = eckerle_X[i];
+      double term = xi - b[2];
+      double yi;
+
+      yi = b[0] / b[1] * exp(-0.5 * term * term / b[1] / b[1]);
+      gsl_vector_set (f, i, yi - eckerle_F[i]);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+eckerle_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[eckerle_P];
+  size_t i;
+
+  for (i = 0; i < eckerle_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < eckerle_N; i++)
+    {
+      double xi = eckerle_X[i];
+      double term1 = xi - b[2];
+      double term2 = exp(-0.5 * term1 * term1 / (b[1] * b[1]));
+
+      gsl_matrix_set (df, i, 0, term2 / b[1]);
+      gsl_matrix_set (df, i, 1,
+        -b[0] * term2 / (b[1] * b[1]) + b[0] / pow(b[1], 4.0) * term2 * term1 * term1);
+      gsl_matrix_set (df, i, 2, b[0] / pow(b[1], 3.0) * term1 * term2);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf eckerle_func =
+{
+  eckerle_f,
+  eckerle_df,
+  NULL, /* analytic expression too complex */
+  eckerle_N,
+  eckerle_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem eckerlea_problem =
+{
+  "nist-eckerlea",
+  eckerle_x0a,
+  NULL,
+  eckerle_sigma,
+  &eckerle_epsrel,
+  &eckerle_checksol,
+  &eckerle_func
+};
+
+static test_fdf_problem eckerleb_problem =
+{
+  "nist-eckerleb",
+  eckerle_x0b,
+  NULL,
+  eckerle_sigma,
+  &eckerle_epsrel,
+  &eckerle_checksol,
+  &eckerle_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_enso.c gsl-doc-2.3/multifit_nlinear/test_enso.c
--- gsl-doc-1.16/multifit_nlinear/test_enso.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_enso.c	2016-09-24 10:41:58.000000000 +0000
@@ -0,0 +1,173 @@
+#define enso_N       168
+#define enso_P       9
+
+static double enso_x0a[enso_P] = { 11.0, 3.0, 0.5, 40.0, -0.7, -1.3, 25.0, -0.3, 1.4 };
+static double enso_x0b[enso_P] = { 10.0, 3.0, 0.5, 44.0, -1.5, 0.5, 26.0, -0.1, 1.5 };
+
+static double enso_epsrel = 1.0e-3;
+
+static double enso_sigma[enso_P] = {
+ 1.7488832467E-01, 2.4310052139E-01, 2.4354686618E-01, 9.4408025976E-01, 2.8078369611E-01,
+ 4.8073701119E-01, 4.1612939130E-01, 5.1460022911E-01, 2.5434468893E-01
+};
+
+static double enso_F[enso_N] = {
+    12.90000, 11.30000, 10.60000, 11.20000, 10.90000, 
+    7.500000, 7.700000, 11.70000, 12.90000, 14.30000, 
+    10.90000, 13.70000, 17.10000, 14.00000, 15.30000, 
+    8.500000, 5.700000, 5.500000, 7.600000, 8.600000, 
+    7.300000, 7.600000, 12.70000, 11.00000, 12.70000, 
+    12.90000, 13.00000, 10.90000, 10.400000, 10.200000, 
+    8.000000, 10.90000, 13.60000, 10.500000, 9.200000, 
+    12.40000, 12.70000, 13.30000, 10.100000, 7.800000, 
+    4.800000, 3.000000, 2.500000, 6.300000, 9.700000, 
+    11.60000, 8.600000, 12.40000, 10.500000, 13.30000, 
+   10.400000, 8.100000, 3.700000, 10.70000, 5.100000, 
+   10.400000, 10.90000, 11.70000, 11.40000, 13.70000, 
+    14.10000, 14.00000, 12.50000, 6.300000, 9.600000, 
+    11.70000, 5.000000, 10.80000, 12.70000, 10.80000, 
+    11.80000, 12.60000, 15.70000, 12.60000, 14.80000, 
+    7.800000, 7.100000, 11.20000, 8.100000, 6.400000, 
+    5.200000, 12.00000, 10.200000, 12.70000, 10.200000, 
+    14.70000, 12.20000, 7.100000, 5.700000, 6.700000, 
+    3.900000, 8.500000, 8.300000, 10.80000, 16.70000, 
+    12.60000, 12.50000, 12.50000, 9.800000, 7.200000, 
+    4.100000, 10.60000, 10.100000, 10.100000, 11.90000, 
+    13.60000, 16.30000, 17.60000, 15.50000, 16.00000, 
+    15.20000, 11.20000, 14.30000, 14.50000, 8.500000, 
+    12.00000, 12.70000, 11.30000, 14.50000, 15.10000, 
+   10.400000, 11.50000, 13.40000, 7.500000, 0.6000000, 
+   0.3000000, 5.500000, 5.000000, 4.600000, 8.200000, 
+    9.900000, 9.200000, 12.50000, 10.90000, 9.900000, 
+    8.900000, 7.600000, 9.500000, 8.400000, 10.70000, 
+    13.60000, 13.70000, 13.70000, 16.50000, 16.80000, 
+    17.10000, 15.40000, 9.500000, 6.100000, 10.100000, 
+    9.300000, 5.300000, 11.20000, 16.60000, 15.60000, 
+    12.00000, 11.50000, 8.600000, 13.80000, 8.700000, 
+    8.600000, 8.600000, 8.700000, 12.80000, 13.20000, 
+    14.00000, 13.40000, 14.80000
+};
+
+static void
+enso_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 7.8853978668E+02;
+  const double enso_x[enso_P] = {
+    1.0510749193E+01, 3.0762128085E+00, 5.3280138227E-01,
+    4.4311088700E+01, -1.6231428586E+00, 5.2554493756E-01,
+    2.6887614440E+01, 2.1232288488E-01, 1.4966870418E+00 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < enso_P; ++i)
+    {
+      gsl_test_rel(x[i], enso_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+enso_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[enso_P];
+  size_t i;
+
+  for (i = 0; i < enso_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < enso_N; i++)
+    {
+      double t = (i + 1.0);
+      double y;
+      y = b[0];
+      y += b[1] * cos(2*M_PI*t/12);
+      y += b[2] * sin(2*M_PI*t/12);
+      y += b[4] * cos(2*M_PI*t/b[3]);
+      y += b[5] * sin(2*M_PI*t/b[3]);
+      y += b[7] * cos(2*M_PI*t/b[6]);
+      y += b[8] * sin(2*M_PI*t/b[6]);
+
+      gsl_vector_set (f, i, enso_F[i] - y);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+enso_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[enso_P];
+  size_t i;
+
+  for (i = 0; i < enso_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < enso_N; i++)
+    {
+      double t = (i + 1.0);
+
+      gsl_matrix_set (df, i, 0, -1.0);
+      gsl_matrix_set (df, i, 1, -cos(2*M_PI*t/12));
+      gsl_matrix_set (df, i, 2, -sin(2*M_PI*t/12));
+      gsl_matrix_set (df, i, 3, 
+                      -b[4]*(2*M_PI*t/(b[3]*b[3]))*sin(2*M_PI*t/b[3])
+                      +b[5]*(2*M_PI*t/(b[3]*b[3]))*cos(2*M_PI*t/b[3]));
+      gsl_matrix_set (df, i, 4, -cos(2*M_PI*t/b[3]));
+      gsl_matrix_set (df, i, 5, -sin(2*M_PI*t/b[3]));
+      gsl_matrix_set (df, i, 6, 
+                     -b[7] * (2*M_PI*t/(b[6]*b[6])) * sin(2*M_PI*t/b[6])
+                     +b[8] * (2*M_PI*t/(b[6]*b[6])) * cos(2*M_PI*t/b[6]));
+      gsl_matrix_set (df, i, 7, -cos(2*M_PI*t/b[6]));
+      gsl_matrix_set (df, i, 8, -sin(2*M_PI*t/b[6]));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf enso_func =
+{
+  enso_f,
+  enso_df,
+  NULL, /* analytic expression too complex */
+  enso_N,
+  enso_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem ensoa_problem =
+{
+  "nist-ENSOa",
+  enso_x0a,
+  NULL,
+  enso_sigma,
+  &enso_epsrel,
+  &enso_checksol,
+  &enso_func
+};
+
+static test_fdf_problem ensob_problem =
+{
+  "nist-ENSOb",
+  enso_x0b,
+  NULL,
+  enso_sigma,
+  &enso_epsrel,
+  &enso_checksol,
+  &enso_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_exp1.c gsl-doc-2.3/multifit_nlinear/test_exp1.c
--- gsl-doc-1.16/multifit_nlinear/test_exp1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_exp1.c	2016-09-24 10:42:04.000000000 +0000
@@ -0,0 +1,138 @@
+#define exp1_N         45
+#define exp1_P         4
+
+static double exp1_x0[exp1_P] = { -1.0, -2.0, 1.0, -1.0 };
+static double exp1_epsrel = 1.0e-4;
+
+static double exp1_Y[exp1_N] = {
+0.090542, 0.124569, 0.179367, 0.195654, 0.269707,
+0.286027, 0.289892, 0.317475, 0.308191, 0.336995,
+0.348371, 0.321337, 0.299423, 0.338972, 0.304763,
+0.288903, 0.300820, 0.303974, 0.283987, 0.262078,
+0.281593, 0.267531, 0.218926, 0.225572, 0.200594,
+0.197375, 0.182440, 0.183892, 0.152285, 0.174028,
+0.150874, 0.126220, 0.126266, 0.106384, 0.118923,
+0.091868, 0.128926, 0.119273, 0.115997, 0.105831,
+0.075261, 0.068387, 0.090823, 0.085205, 0.067203
+};
+
+static void
+exp1_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.0e-2;
+  const double exp1_x[exp1_P] = { -4.0, -5.0, 4.0, -4.0 }; /* approx */
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < exp1_P; ++i)
+    {
+      gsl_test_rel(x[i], exp1_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+exp1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  size_t i;
+
+  for (i = 0; i < exp1_N; ++i)
+    {
+      double ti = 0.02*(i + 1.0);
+      double yi = exp1_Y[i];
+      double fi = yi - (x3*exp(x1*ti) + x4*exp(x2*ti));
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+exp1_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  size_t i;
+
+  for (i = 0; i < exp1_N; ++i)
+    {
+      double ti = 0.02*(i + 1.0);
+      double term1 = exp(x1*ti);
+      double term2 = exp(x2*ti);
+
+      gsl_matrix_set(J, i, 0, -x3*ti*term1);
+      gsl_matrix_set(J, i, 1, -x4*ti*term2);
+      gsl_matrix_set(J, i, 2, -term1);
+      gsl_matrix_set(J, i, 3, -term2);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+exp1_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  double v4 = gsl_vector_get(v, 3);
+  size_t i;
+
+  for (i = 0; i < exp1_N; ++i)
+    {
+      double ti = 0.02*(i + 1.0);
+      double term1 = exp(x1*ti);
+      double term2 = exp(x2*ti);
+      double term3 = 2*v3 + ti*v1*x3;
+      double term4 = 2*v4 + ti*v2*x4;
+
+      gsl_vector_set(fvv, i, -ti*(v1*term1*term3 + v2*term2*term4));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf exp1_func =
+{
+  exp1_f,
+  exp1_df,
+  exp1_fvv,
+  exp1_N,
+  exp1_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem exp1_problem =
+{
+  "expfit1",
+  exp1_x0,
+  NULL,
+  NULL,
+  &exp1_epsrel,
+  &exp1_checksol,
+  &exp1_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_fdf.c gsl-doc-2.3/multifit_nlinear/test_fdf.c
--- gsl-doc-1.16/multifit_nlinear/test_fdf.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_fdf.c	2016-09-24 10:51:50.000000000 +0000
@@ -0,0 +1,365 @@
+/* multifit_nlinear/test_fdf.c
+ * 
+ * Copyright (C) 2007, 2013, 2014, 2015, 2016 Brian Gough, Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+typedef struct
+{
+  const char *name;
+  double *x0;       /* initial parameters (size p) */
+  double *weights;  /* data weights */
+  double *sigma;
+  double *epsrel;   /* relative tolerance for solution checking */
+  void (*checksol) (const double x[], const double sumsq,
+                    const double epsrel, const char *sname,
+                    const char *pname);
+  gsl_multifit_nlinear_fdf *fdf;
+} test_fdf_problem;
+
+#include "test_bard.c"
+#include "test_beale.c"
+#include "test_biggs.c"
+#include "test_box.c"
+#include "test_boxbod.c"
+#include "test_brown1.c"
+#include "test_brown2.c"
+#include "test_brown3.c"
+#include "test_eckerle.c"
+#include "test_enso.c"
+#include "test_exp1.c"
+#include "test_gaussian.c"
+#include "test_hahn1.c"
+#include "test_helical.c"
+#include "test_jennrich.c"
+#include "test_kirby2.c"
+#include "test_kowalik.c"
+#include "test_lin1.c"
+#include "test_lin2.c"
+#include "test_lin3.c"
+#include "test_meyer.c"
+#include "test_meyerscal.c"
+#include "test_osborne.c"
+#include "test_penalty1.c"
+#include "test_penalty2.c"
+#include "test_powell1.c"
+#include "test_powell2.c"
+#include "test_powell3.c"
+#include "test_rat42.c"
+#include "test_rat43.c"
+#include "test_rosenbrock.c"
+#include "test_rosenbrocke.c"
+#include "test_roth.c"
+#include "test_thurber.c"
+#include "test_vardim.c"
+#include "test_watson.c"
+#include "test_wood.c"
+
+#include "test_wnlin.c"
+
+static void test_fdf(const gsl_multifit_nlinear_type * T,
+                     const gsl_multifit_nlinear_parameters * params,
+                     const double xtol, const double gtol,
+                     const double ftol,
+                     const double epsrel,
+                     test_fdf_problem *problem);
+static void test_fdf_checksol(const char *sname, const char *pname,
+                              const double epsrel,
+                              gsl_multifit_nlinear_workspace *s,
+                              test_fdf_problem *problem);
+
+/*
+ * FIXME: some test problems are disabled since they fail on certain
+ * solvers. Known failures are:
+ *
+ * Method     test-problem
+ * ======     ============
+ * dogleg     thurbera
+ * dogleg     rat43a
+ * all        boxboda
+ */
+
+static test_fdf_problem *test_problems[] = {
+  /*
+   * These test problems are taken from
+   *
+   * H. B. Nielsen, UCTP test problems for unconstrained optimization,
+   * IMM Department of Mathematical Modeling, Tech. Report
+   * IMM-REP-2000-17, 2000.
+   */
+  &lin1_problem,       /* 1 */
+  &lin2_problem,       /* 2 */
+  &lin3_problem,       /* 3 */
+  &rosenbrock_problem, /* 4 */
+  &helical_problem,    /* 5 */
+  &powell1_problem,    /* 6 */
+  &roth_problem,       /* 7 */
+  &bard_problem,       /* 8 */
+  &kowalik_problem,    /* 9 */
+  &meyer_problem,      /* 10 */
+  &watson_problem,     /* 11 */
+  &box_problem,        /* 12 */
+  &jennrich_problem,   /* 13 */
+  &brown1_problem,     /* 14 */
+  &brown2_problem,     /* 16 */
+  &osborne_problem,    /* 17 */
+  &exp1_problem,       /* 18 */
+  &meyerscal_problem,  /* 20 */
+
+  &powell2_problem,
+
+  /*
+   * These tests are from
+   *
+   * J. J. More, B. S. Garbow and K. E. Hillstrom, Testing
+   * Unconstrained Optimization Software, ACM Trans. Math. Soft.
+   * Vol 7, No 1, 1981.
+   *
+   * Many of these overlap with the Nielsen tests
+   */
+  &rosenbrock_problem,   /* 1 */
+  &roth_problem,         /* 2 */
+  &powell3_problem,      /* 3 */
+  &brown3_problem,       /* 4 */
+  &beale_problem,        /* 5 */
+  &jennrich_problem,     /* 6 */
+  &helical_problem,      /* 7 */
+  &bard_problem,         /* 8 */
+  &gaussian_problem,     /* 9 */
+  &meyer_problem,        /* 10 */
+  &box_problem,          /* 12 */
+  &powell1_problem,      /* 13 */
+  &wood_problem,         /* 14 */
+  &kowalik_problem,      /* 15 */
+  &brown1_problem,       /* 16 */
+  &osborne_problem,      /* 17 */
+  &biggs_problem,        /* 18 */
+  &watson_problem,       /* 20 */
+  &rosenbrocke_problem,  /* 21 */
+  &penalty1_problem,     /* 23 */
+  &penalty2_problem,     /* 24 */
+  &vardim_problem,       /* 25 */
+  &brown2_problem,       /* 27 */
+  &lin1_problem,         /* 32 */
+  &lin2_problem,         /* 33 */
+  &lin3_problem,         /* 34 */
+
+  /* NIST test cases */
+  &kirby2a_problem,
+  &kirby2b_problem,
+  &hahn1a_problem,
+  &hahn1b_problem,
+  &ensoa_problem,
+  &ensob_problem,
+  /*&thurbera_problem,*/
+  &thurberb_problem,
+  /*&boxboda_problem,*/
+  &boxbodb_problem,
+  &rat42a_problem,
+  &rat42b_problem,
+  &eckerlea_problem,
+  &eckerleb_problem,
+  /*&rat43a_problem,*/
+  &rat43b_problem,
+
+  /* weighted test cases */
+  &wnlin_problem1,
+  &wnlin_problem2,
+
+  NULL
+};
+
+static void
+test_fdf_main(const gsl_multifit_nlinear_parameters * params)
+{
+  const double xtol = pow(GSL_DBL_EPSILON, 0.9);
+  const double gtol = pow(GSL_DBL_EPSILON, 0.9);
+  const double ftol = 0.0;
+  size_t i;
+
+  for (i = 0; test_problems[i] != NULL; ++i)
+    {
+      test_fdf_problem *problem = test_problems[i];
+      double epsrel = *(problem->epsrel);
+      gsl_multifit_nlinear_fdf fdf;
+
+      test_fdf(gsl_multifit_nlinear_trust, params, xtol, gtol, ftol,
+               epsrel, problem);
+
+      /* test finite difference Jacobian
+       * XXX: watson problem doesn't work with forward differences */
+      if (problem != &watson_problem)
+        {
+          fdf.df = problem->fdf->df;
+          problem->fdf->df = NULL;
+
+          test_fdf(gsl_multifit_nlinear_trust, params, xtol, gtol, ftol,
+                   1.0e3 * epsrel, problem);
+
+          problem->fdf->df = fdf.df;
+        }
+
+#if 1 /*XXX: box3d test fails on MacOS here */
+      if (params->trs == gsl_multifit_nlinear_trs_lmaccel && problem->fdf->fvv != NULL)
+        {
+          /* test finite difference second directional derivative */
+          fdf.fvv = problem->fdf->fvv;
+          problem->fdf->fvv = NULL;
+
+          test_fdf(gsl_multifit_nlinear_trust, params, xtol, gtol, ftol,
+                   epsrel / params->h_fvv, problem);
+
+          problem->fdf->fvv = fdf.fvv;
+        }
+#endif
+    }
+}
+
+/*
+test_fdf()
+  Test a weighted nonlinear least squares problem
+
+Inputs: T        - solver to use
+        params   - solver parameters
+        xtol     - tolerance in x
+        gtol     - tolerance in gradient
+        ftol     - tolerance in residual vector
+        epsrel   - relative error tolerance in solution
+        problem  - contains the nonlinear problem and solution point
+*/
+
+static void
+test_fdf(const gsl_multifit_nlinear_type * T,
+         const gsl_multifit_nlinear_parameters * params,
+         const double xtol, const double gtol, const double ftol,
+         const double epsrel,
+         test_fdf_problem *problem)
+{
+  gsl_multifit_nlinear_fdf *fdf = problem->fdf;
+  const size_t n = fdf->n;
+  const size_t p = fdf->p;
+  const size_t max_iter = 2500;
+  gsl_vector *x0 = gsl_vector_alloc(p);
+  gsl_vector_view x0v = gsl_vector_view_array(problem->x0, p);
+  gsl_multifit_nlinear_workspace *w =
+    gsl_multifit_nlinear_alloc (T, params, n, p);
+  const char *pname = problem->name;
+  char buf[2048];
+  char sname[2048];
+  int status, info;
+
+  sprintf(buf, "%s/%s/scale=%s/solver=%s",
+    gsl_multifit_nlinear_name(w),
+    params->trs->name,
+    params->scale->name,
+    params->solver->name);
+
+  if (problem->fdf->df == NULL)
+    {
+      if (params->fdtype == GSL_MULTIFIT_NLINEAR_FWDIFF)
+        strcat(buf, "/fdjac,forward");
+      else
+        strcat(buf, "/fdjac,center");
+    }
+
+  if (problem->fdf->fvv == NULL)
+    {
+      strcat(buf, "/fdfvv");
+    }
+
+  strcpy(sname, buf);
+
+  gsl_vector_memcpy(x0, &x0v.vector);
+
+  if (problem->weights != NULL)
+    {
+      gsl_vector_const_view wv = gsl_vector_const_view_array(problem->weights, n);
+      gsl_multifit_nlinear_winit(x0, &wv.vector, fdf, w);
+    }
+  else
+    gsl_multifit_nlinear_init(x0, fdf, w);
+
+  status = gsl_multifit_nlinear_driver(max_iter, xtol, gtol, ftol,
+                                       NULL, NULL, &info, w);
+  gsl_test(status, "%s/%s did not converge, status=%s",
+           sname, pname, gsl_strerror(status));
+
+  /* check solution */
+  test_fdf_checksol(sname, pname, epsrel, w, problem);
+
+  if (problem->weights == NULL)
+    {
+      /* test again with weighting matrix W = I */
+      gsl_vector *wv = gsl_vector_alloc(n);
+
+      sprintf(sname, "%s/weighted", buf);
+
+      gsl_vector_memcpy(x0, &x0v.vector);
+
+      gsl_vector_set_all(wv, 1.0);
+      gsl_multifit_nlinear_winit(x0, wv, fdf, w);
+  
+      status = gsl_multifit_nlinear_driver(max_iter, xtol, gtol, ftol,
+                                           NULL, NULL, &info, w);
+      gsl_test(status, "%s/%s did not converge, status=%s",
+               sname, pname, gsl_strerror(status));
+
+      test_fdf_checksol(sname, pname, epsrel, w, problem);
+
+      gsl_vector_free(wv);
+    }
+
+  gsl_multifit_nlinear_free(w);
+  gsl_vector_free(x0);
+}
+
+static void
+test_fdf_checksol(const char *sname, const char *pname,
+                  const double epsrel,
+                  gsl_multifit_nlinear_workspace *w,
+                  test_fdf_problem *problem)
+{
+  gsl_multifit_nlinear_fdf *fdf = problem->fdf;
+  const double *sigma = problem->sigma;
+  gsl_vector *f = gsl_multifit_nlinear_residual(w);
+  gsl_vector *x = gsl_multifit_nlinear_position(w);
+  double sumsq;
+
+  /* check solution vector x and sumsq = ||f||^2 */
+  gsl_blas_ddot(f, f, &sumsq);
+  (problem->checksol)(x->data, sumsq, epsrel, sname, pname);
+
+  /* check variances */
+  if (sigma)
+    {
+      const size_t n = fdf->n;
+      const size_t p = fdf->p;
+      size_t i;
+      gsl_matrix * covar = gsl_matrix_alloc (p, p);
+      gsl_matrix *J = gsl_multifit_nlinear_jac (w);
+
+      gsl_multifit_nlinear_covar (J, 0.0, covar);
+
+      for (i = 0; i < p; i++) 
+        {
+          double ei = sqrt(sumsq/(n-p))*sqrt(gsl_matrix_get(covar,i,i));
+          gsl_test_rel (ei, sigma[i], epsrel, 
+                        "%s/%s, sigma(%d)", sname, pname, i) ;
+        }
+
+      gsl_matrix_free (covar);
+    }
+}
diff -Nru gsl-doc-1.16/multifit_nlinear/test_gaussian.c gsl-doc-2.3/multifit_nlinear/test_gaussian.c
--- gsl-doc-1.16/multifit_nlinear/test_gaussian.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_gaussian.c	2016-09-24 10:42:15.000000000 +0000
@@ -0,0 +1,135 @@
+#define gaussian_N         15
+#define gaussian_P         3
+
+static double gaussian_x0[gaussian_P] = { 0.4, 1.0, 0.0 };
+static double gaussian_epsrel = 1.0e-10;
+
+static double gaussian_Y[gaussian_N] = {
+0.0009, 0.0044, 0.0175, 0.0540, 0.1295, 0.2420, 0.3521, 0.3989,
+0.3521, 0.2420, 0.1295, 0.0540, 0.0175, 0.0044, 0.0009
+};
+
+static void
+gaussian_checksol(const double x[], const double sumsq,
+                  const double epsrel, const char *sname,
+                  const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.12793276961871985e-08;
+  const double gaussian_x[gaussian_P] = { 0.398956137838762825,
+                                          1.00001908448786647,
+                                          0.0 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < gaussian_P; ++i)
+    {
+      gsl_test_rel(x[i], gaussian_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+gaussian_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < gaussian_N; ++i)
+    {
+      double ti = (7.0 - i) / 2.0;
+      double yi = gaussian_Y[i];
+      double term = ti - x3;
+      double fi = x1 * exp(-x2*term*term/2.0) - yi;
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+gaussian_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < gaussian_N; ++i)
+    {
+      double ti = (7.0 - i) / 2.0;
+      double term1 = ti - x3;
+      double term2 = exp(-x2*term1*term1/2.0);
+
+      gsl_matrix_set(J, i, 0, term2);
+      gsl_matrix_set(J, i, 1, -0.5*x1*term2*term1*term1);
+      gsl_matrix_set(J, i, 2, x1*x2*term1*term2);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+gaussian_fvv (const gsl_vector * x, const gsl_vector * v,
+              void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  size_t i;
+
+  for (i = 0; i < gaussian_N; ++i)
+    {
+      double ti = (7.0 - i) / 2.0;
+      double term1 = ti - x3;
+      double term2 = exp(-x2*term1*term1/2.0);
+
+      gsl_vector_set(fvv, i, 0.25 * term2 *
+                             (ti*ti*ti*ti*v2*v2*x1 -
+                              4*ti*ti*ti*v2*x1*(v3*x2 + v2*x3) +
+                              v2*x3*x3*(v2*x1*x3*x3 - 4*v1) +
+                              4*v3*v3*x1*x2*(x2*x3*x3 - 1.0) +
+                              4*v3*x3*(-2*v1*x2 + v2*x1*(x2*x3*x3 - 2.0)) +
+                              ti*ti*(4*v3*v3*x1*x2*x2 + 2*v2*(-2*v1 + 3*x1*x3*(2*v3*x2 + v2*x3))) -
+                              4*ti*(v2*v2*x1*x3*x3*x3 + 2*v3*x2*(-v1 + v3*x1*x2*x3) +
+                                    v2*(-2*v1*x3 + v3*x1*(-2.0 + 3*x2*x3*x3)))));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf gaussian_func =
+{
+  gaussian_f,
+  gaussian_df,
+  gaussian_fvv,
+  gaussian_N,
+  gaussian_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem gaussian_problem =
+{
+  "gaussian",
+  gaussian_x0,
+  NULL,
+  NULL,
+  &gaussian_epsrel,
+  &gaussian_checksol,
+  &gaussian_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_hahn1.c gsl-doc-2.3/multifit_nlinear/test_hahn1.c
--- gsl-doc-1.16/multifit_nlinear/test_hahn1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_hahn1.c	2016-09-24 10:42:27.000000000 +0000
@@ -0,0 +1,226 @@
+#define hahn1_N      236
+#define hahn1_P      7
+
+static double hahn1_x0a[hahn1_P] = { 10, -1, 0.05, -0.00001, -0.05, 0.001, -0.000001 };
+static double hahn1_x0b[hahn1_P] = { 1, -0.1, 0.005, -0.000001, -0.005, 0.0001, -0.0000001}; 
+
+static double hahn1_epsrel = 1.0e-5;
+
+static double hahn1_sigma[hahn1_P] = {
+  1.7070154742E-01, 1.2000289189E-02, 2.2508314937E-04, 2.7578037666E-07,
+  2.4712888219E-04, 1.0449373768E-05, 1.3027335327E-08
+};
+
+static double hahn1_F1[hahn1_N] = {
+        .591E0, 1.547E0, 2.902E0, 2.894E0, 4.703E0,
+       6.307E0, 7.03E0 , 7.898E0, 9.470E0, 9.484E0,
+      10.072E0, 10.163E0, 11.615E0, 12.005E0, 12.478E0,
+      12.982E0, 12.970E0, 13.926E0, 14.452E0, 14.404E0,
+      15.190E0, 15.550E0, 15.528E0, 15.499E0, 16.131E0,
+      16.438E0, 16.387E0, 16.549E0, 16.872E0, 16.830E0,
+      16.926E0, 16.907E0, 16.966E0, 17.060E0, 17.122E0,
+      17.311E0, 17.355E0, 17.668E0, 17.767E0, 17.803E0,
+      17.765E0, 17.768E0, 17.736E0, 17.858E0, 17.877E0,
+      17.912E0, 18.046E0, 18.085E0, 18.291E0, 18.357E0,
+      18.426E0, 18.584E0, 18.610E0, 18.870E0, 18.795E0,
+      19.111E0, .367E0, .796E0, 0.892E0, 1.903E0,
+       2.150E0, 3.697E0, 5.870E0, 6.421E0, 7.422E0,
+       9.944E0, 11.023E0, 11.87E0 , 12.786E0, 14.067E0,
+      13.974E0, 14.462E0, 14.464E0, 15.381E0, 15.483E0,
+      15.59E0 , 16.075E0, 16.347E0, 16.181E0, 16.915E0,
+      17.003E0, 16.978E0, 17.756E0, 17.808E0, 17.868E0,
+      18.481E0, 18.486E0, 19.090E0, 16.062E0, 16.337E0,
+      16.345E0, 16.388E0, 17.159E0, 17.116E0, 17.164E0,
+      17.123E0, 17.979E0, 17.974E0, 18.007E0, 17.993E0,
+      18.523E0, 18.669E0, 18.617E0, 19.371E0, 19.330E0,
+       0.080E0, 0.248E0, 1.089E0, 1.418E0, 2.278E0,
+       3.624E0, 4.574E0, 5.556E0, 7.267E0, 7.695E0,
+       9.136E0, 9.959E0, 9.957E0, 11.600E0, 13.138E0,
+      13.564E0, 13.871E0, 13.994E0, 14.947E0, 15.473E0,
+      15.379E0, 15.455E0, 15.908E0, 16.114E0, 17.071E0,
+      17.135E0, 17.282E0, 17.368E0, 17.483E0, 17.764E0,
+      18.185E0, 18.271E0, 18.236E0, 18.237E0, 18.523E0,
+      18.627E0, 18.665E0, 19.086E0, 0.214E0, 0.943E0,
+       1.429E0, 2.241E0, 2.951E0, 3.782E0, 4.757E0,
+       5.602E0, 7.169E0, 8.920E0, 10.055E0, 12.035E0,
+      12.861E0, 13.436E0, 14.167E0, 14.755E0, 15.168E0,
+      15.651E0, 15.746E0, 16.216E0, 16.445E0, 16.965E0,
+      17.121E0, 17.206E0, 17.250E0, 17.339E0, 17.793E0,
+      18.123E0, 18.49E0 , 18.566E0, 18.645E0, 18.706E0,
+      18.924E0, 19.1E0  , 0.375E0, 0.471E0, 1.504E0,
+       2.204E0, 2.813E0, 4.765E0, 9.835E0, 10.040E0,
+      11.946E0, 12.596E0, 13.303E0, 13.922E0, 14.440E0,
+      14.951E0, 15.627E0, 15.639E0, 15.814E0, 16.315E0,
+      16.334E0, 16.430E0, 16.423E0, 17.024E0, 17.009E0,
+      17.165E0, 17.134E0, 17.349E0, 17.576E0, 17.848E0,
+      18.090E0, 18.276E0, 18.404E0, 18.519E0, 19.133E0,
+      19.074E0, 19.239E0, 19.280E0, 19.101E0, 19.398E0,
+      19.252E0, 19.89E0 , 20.007E0, 19.929E0, 19.268E0,
+      19.324E0, 20.049E0, 20.107E0, 20.062E0, 20.065E0,
+      19.286E0, 19.972E0, 20.088E0, 20.743E0, 20.83E0 ,
+      20.935E0, 21.035E0, 20.93E0 , 21.074E0, 21.085E0,
+      20.935E0
+};
+
+
+static double hahn1_F0[hahn1_N] = {
+    24.41E0, 34.82E0, 44.09E0, 45.07E0, 54.98E0,
+    65.51E0, 70.53E0, 75.70E0, 89.57E0, 91.14E0,
+    96.40E0, 97.19E0, 114.26E0, 120.25E0, 127.08E0,
+   133.55E0, 133.61E0, 158.67E0, 172.74E0, 171.31E0,
+   202.14E0, 220.55E0, 221.05E0, 221.39E0, 250.99E0,
+   268.99E0, 271.80E0, 271.97E0, 321.31E0, 321.69E0,
+   330.14E0, 333.03E0, 333.47E0, 340.77E0, 345.65E0,
+   373.11E0, 373.79E0, 411.82E0, 419.51E0, 421.59E0,
+   422.02E0, 422.47E0, 422.61E0, 441.75E0, 447.41E0,
+   448.7E0 , 472.89E0, 476.69E0, 522.47E0, 522.62E0,
+   524.43E0, 546.75E0, 549.53E0, 575.29E0, 576.00E0,
+   625.55E0, 20.15E0, 28.78E0, 29.57E0, 37.41E0,
+    39.12E0, 50.24E0, 61.38E0, 66.25E0, 73.42E0,
+    95.52E0, 107.32E0, 122.04E0, 134.03E0, 163.19E0,
+   163.48E0, 175.70E0, 179.86E0, 211.27E0, 217.78E0,
+   219.14E0, 262.52E0, 268.01E0, 268.62E0, 336.25E0,
+   337.23E0, 339.33E0, 427.38E0, 428.58E0, 432.68E0,
+   528.99E0, 531.08E0, 628.34E0, 253.24E0, 273.13E0,
+   273.66E0, 282.10E0, 346.62E0, 347.19E0, 348.78E0,
+   351.18E0, 450.10E0, 450.35E0, 451.92E0, 455.56E0,
+   552.22E0, 553.56E0, 555.74E0, 652.59E0, 656.20E0,
+    14.13E0, 20.41E0, 31.30E0, 33.84E0, 39.70E0,
+    48.83E0, 54.50E0, 60.41E0, 72.77E0, 75.25E0,
+    86.84E0, 94.88E0, 96.40E0, 117.37E0, 139.08E0,
+   147.73E0, 158.63E0, 161.84E0, 192.11E0, 206.76E0,
+   209.07E0, 213.32E0, 226.44E0, 237.12E0, 330.90E0,
+   358.72E0, 370.77E0, 372.72E0, 396.24E0, 416.59E0,
+   484.02E0, 495.47E0, 514.78E0, 515.65E0, 519.47E0,
+   544.47E0, 560.11E0, 620.77E0, 18.97E0, 28.93E0,
+    33.91E0, 40.03E0, 44.66E0, 49.87E0, 55.16E0,
+    60.90E0, 72.08E0, 85.15E0, 97.06E0, 119.63E0,
+   133.27E0, 143.84E0, 161.91E0, 180.67E0, 198.44E0,
+   226.86E0, 229.65E0, 258.27E0, 273.77E0, 339.15E0,
+   350.13E0, 362.75E0, 371.03E0, 393.32E0, 448.53E0,
+   473.78E0, 511.12E0, 524.70E0, 548.75E0, 551.64E0,
+   574.02E0, 623.86E0, 21.46E0, 24.33E0, 33.43E0,
+    39.22E0, 44.18E0, 55.02E0, 94.33E0, 96.44E0,
+   118.82E0, 128.48E0, 141.94E0, 156.92E0, 171.65E0,
+   190.00E0, 223.26E0, 223.88E0, 231.50E0, 265.05E0,
+   269.44E0, 271.78E0, 273.46E0, 334.61E0, 339.79E0,
+   349.52E0, 358.18E0, 377.98E0, 394.77E0, 429.66E0,
+   468.22E0, 487.27E0, 519.54E0, 523.03E0, 612.99E0,
+   638.59E0, 641.36E0, 622.05E0, 631.50E0, 663.97E0,
+   646.9E0 , 748.29E0, 749.21E0, 750.14E0, 647.04E0,
+   646.89E0, 746.9E0 , 748.43E0, 747.35E0, 749.27E0,
+   647.61E0, 747.78E0, 750.51E0, 851.37E0, 845.97E0,
+   847.54E0, 849.93E0, 851.61E0, 849.75E0, 850.98E0,
+   848.23E0
+};
+
+static void
+hahn1_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.5324382854E+00;
+  const double hahn1_x[hahn1_P] = {
+     1.0776351733E+00, -1.2269296921E-01, 4.0863750610E-03,
+    -1.4262662514E-06, -5.7609940901E-03, 2.4053735503E-04,
+    -1.2314450199E-07 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < hahn1_P; ++i)
+    {
+      gsl_test_rel(x[i], hahn1_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+hahn1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[hahn1_P];
+  size_t i;
+
+  for (i = 0; i < hahn1_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < hahn1_N; i++)
+    {
+      double t = hahn1_F0[i];
+      double y = ((b[0] + t* (b[1]  + t * (b[2] + t * b[3])))
+                  / (1 + t*(b[4]  + t *(b[5] + t*b[6]))));
+      gsl_vector_set (f, i, hahn1_F1[i] - y);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+hahn1_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[hahn1_P];
+  size_t i;
+
+  for (i = 0; i < hahn1_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < hahn1_N; i++)
+    {
+      double t = hahn1_F0[i];
+      double u = (b[0] + t*(b[1] + t*(b[2] + t * b[3])));
+      double v = (1 + t*(b[4] + t*(b[5] + t*b[6])));
+      gsl_matrix_set (df, i, 0, -1/v);
+      gsl_matrix_set (df, i, 1, -t/v);
+      gsl_matrix_set (df, i, 2, -t*t/v);
+      gsl_matrix_set (df, i, 3, -t*t*t/v);
+      gsl_matrix_set (df, i, 4, t*u/(v*v));
+      gsl_matrix_set (df, i, 5, t*t*u/(v*v));
+      gsl_matrix_set (df, i, 6, t*t*t*u/(v*v));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf hahn1_func =
+{
+  hahn1_f,
+  hahn1_df,
+  NULL, /* analytic expression too complex */
+  hahn1_N,
+  hahn1_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem hahn1a_problem =
+{
+  "nist-hahn1a",
+  hahn1_x0a,
+  NULL,
+  hahn1_sigma,
+  &hahn1_epsrel,
+  &hahn1_checksol,
+  &hahn1_func
+};
+
+static test_fdf_problem hahn1b_problem =
+{
+  "nist-hahn1b",
+  hahn1_x0b,
+  NULL,
+  hahn1_sigma,
+  &hahn1_epsrel,
+  &hahn1_checksol,
+  &hahn1_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_helical.c gsl-doc-2.3/multifit_nlinear/test_helical.c
--- gsl-doc-1.16/multifit_nlinear/test_helical.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_helical.c	2016-09-24 10:42:32.000000000 +0000
@@ -0,0 +1,115 @@
+#define helical_N         3
+#define helical_P         3
+
+static double helical_x0[helical_P] = { -1.0, 0.0, 0.0 };
+static double helical_x[helical_P] = { 1.0, 0.0, 0.0 };
+
+static double helical_epsrel = 1.0e-12;
+
+static void
+helical_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < helical_P; ++i)
+    {
+      gsl_test_rel(x[i], helical_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+helical_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double theta = (x1 >= 0.0) ? 0.0 : 5.0;
+  double nx = gsl_hypot(x1, x2);
+
+  gsl_vector_set(f, 0, 10.0 * (x3 - 5.0/M_PI*atan(x2 / x1) - theta));
+  gsl_vector_set(f, 1, 10.0*(nx - 1.0));
+  gsl_vector_set(f, 2, x3);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+helical_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double nx = gsl_hypot(x1, x2);
+  double nx_sq = nx * nx;
+  double term1 = 50.0 / (M_PI * nx_sq);
+  double term2 = 10.0 / nx;
+
+  gsl_matrix_set(J, 0, 0, term1*x2);
+  gsl_matrix_set(J, 0, 1, -term1*x1);
+  gsl_matrix_set(J, 0, 2, 10.0);
+
+  gsl_matrix_set(J, 1, 0, term2*x1);
+  gsl_matrix_set(J, 1, 1, term2*x2);
+  gsl_matrix_set(J, 1, 2, 0.0);
+
+  gsl_matrix_set(J, 2, 0, 0.0);
+  gsl_matrix_set(J, 2, 1, 0.0);
+  gsl_matrix_set(J, 2, 2, 1.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+helical_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double term1 = v2*x1 - v1*x2;
+  double term2 = v1*x1 + v2*x2;
+  double term3 = x1*x1 + x2*x2;
+
+  gsl_vector_set(fvv, 0, 100.0 / M_PI * (term1 / term3) * (term2 / term3));
+  gsl_vector_set(fvv, 1, 10.0 * (term1 * term1) / pow(term3, 1.5));
+  gsl_vector_set(fvv, 2, 0.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf helical_func =
+{
+  helical_f,
+  helical_df,
+  helical_fvv,
+  helical_N,
+  helical_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem helical_problem =
+{
+  "helical",
+  helical_x0,
+  NULL,
+  NULL,
+  &helical_epsrel,
+  &helical_checksol,
+  &helical_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_jennrich.c gsl-doc-2.3/multifit_nlinear/test_jennrich.c
--- gsl-doc-1.16/multifit_nlinear/test_jennrich.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_jennrich.c	2016-09-24 10:42:38.000000000 +0000
@@ -0,0 +1,112 @@
+#define jennrich_N         10
+#define jennrich_P         2
+
+static double jennrich_x0[jennrich_P] = { 0.3, 0.4 };
+static double jennrich_epsrel = 1.0e-7;
+
+static void
+jennrich_checksol(const double x[], const double sumsq,
+                  const double epsrel, const char *sname,
+                  const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.243621823556148e+02;
+  const double jennrich_x[jennrich_P] = { 2.578252139935855e-01,
+                                          2.578252133471426e-01 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < jennrich_P; ++i)
+    {
+      gsl_test_rel(x[i], jennrich_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+jennrich_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < jennrich_N; ++i)
+    {
+      double ip1 = i + 1.0;
+      double fi = 2.0*(i + 2.0) - (exp(x1*ip1) + exp(x2*ip1));
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+jennrich_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < jennrich_N; ++i)
+    {
+      double ip1 = i + 1.0;
+
+      gsl_matrix_set(J, i, 0, -ip1*exp(ip1*x1));
+      gsl_matrix_set(J, i, 1, -ip1*exp(ip1*x2));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+jennrich_fvv (const gsl_vector * x, const gsl_vector * v,
+              void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  size_t i;
+
+  for (i = 0; i < jennrich_N; ++i)
+    {
+      double ip1 = i + 1.0;
+      double term1 = exp(ip1*x1);
+      double term2 = exp(ip1*x2);
+
+      gsl_vector_set(fvv, i, -ip1*ip1*(v1*v1*term1 + v2*v2*term2));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf jennrich_func =
+{
+  jennrich_f,
+  jennrich_df,
+  jennrich_fvv,
+  jennrich_N,
+  jennrich_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem jennrich_problem =
+{
+  "jennrich",
+  jennrich_x0,
+  NULL,
+  NULL,
+  &jennrich_epsrel,
+  &jennrich_checksol,
+  &jennrich_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_kirby2.c gsl-doc-2.3/multifit_nlinear/test_kirby2.c
--- gsl-doc-1.16/multifit_nlinear/test_kirby2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_kirby2.c	2016-09-24 10:42:49.000000000 +0000
@@ -0,0 +1,221 @@
+#define kirby2_N       151
+#define kirby2_P       5
+
+static double kirby2_x0a[kirby2_P] = { 2.0, -0.1, 0.003, -0.001, 0.00001 };
+static double kirby2_x0b[kirby2_P] = { 1.5, -0.15, 0.0025, -0.0015, 0.00002 }; 
+static double kirby2_x[kirby2_P] = { 1.6745063063E+00, -1.3927397867E-01, 2.5961181191E-03,
+                                    -1.7241811870E-03,  2.1664802578E-05 }; 
+
+static double kirby2_epsrel = 1.0e-5;
+
+static double kirby2_sigma[kirby2_P] = {
+  8.7989634338E-02, 4.1182041386E-03, 4.1856520458E-05,
+  5.8931897355E-05, 2.0129761919E-07
+};
+
+static double kirby2_F1[kirby2_N] = {
+       0.0082E0, 0.0112E0, 0.0149E0, 0.0198E0, 0.0248E0,
+       0.0324E0, 0.0420E0, 0.0549E0, 0.0719E0, 0.0963E0,
+       0.1291E0, 0.1710E0, 0.2314E0, 0.3227E0, 0.4809E0,
+       0.7084E0, 1.0220E0, 1.4580E0, 1.9520E0, 2.5410E0,
+       3.2230E0, 3.9990E0, 4.8520E0, 5.7320E0, 6.7270E0,
+       7.8350E0, 9.0250E0, 10.2670E0, 11.5780E0, 12.9440E0,
+      14.3770E0, 15.8560E0, 17.3310E0, 18.8850E0, 20.5750E0,
+      22.3200E0, 22.3030E0, 23.4600E0, 24.0600E0, 25.2720E0,
+      25.8530E0, 27.1100E0, 27.6580E0, 28.9240E0, 29.5110E0,
+      30.7100E0, 31.3500E0, 32.5200E0, 33.2300E0, 34.3300E0,
+      35.0600E0, 36.1700E0, 36.8400E0, 38.0100E0, 38.6700E0,
+      39.8700E0, 40.0300E0, 40.5000E0, 41.3700E0, 41.6700E0,
+      42.3100E0, 42.7300E0, 43.4600E0, 44.1400E0, 44.5500E0,
+      45.2200E0, 45.9200E0, 46.3000E0, 47.0000E0, 47.6800E0,
+      48.0600E0, 48.7400E0, 49.4100E0, 49.7600E0, 50.4300E0,
+      51.1100E0, 51.5000E0, 52.1200E0, 52.7600E0, 53.1800E0,
+      53.7800E0, 54.4600E0, 54.8300E0, 55.4000E0, 56.4300E0,
+      57.0300E0, 58.0000E0, 58.6100E0, 59.5800E0, 60.1100E0,
+      61.1000E0, 61.6500E0, 62.5900E0, 63.1200E0, 64.0300E0,
+      64.6200E0, 65.4900E0, 66.0300E0, 66.8900E0, 67.4200E0,
+      68.2300E0, 68.7700E0, 69.5900E0, 70.1100E0, 70.8600E0,
+      71.4300E0, 72.1600E0, 72.7000E0, 73.4000E0, 73.9300E0,
+      74.6000E0, 75.1600E0, 75.8200E0, 76.3400E0, 76.9800E0,
+      77.4800E0, 78.0800E0, 78.6000E0, 79.1700E0, 79.6200E0,
+      79.8800E0, 80.1900E0, 80.6600E0, 81.2200E0, 81.6600E0,
+      82.1600E0, 82.5900E0, 83.1400E0, 83.5000E0, 84.0000E0,
+      84.4000E0, 84.8900E0, 85.2600E0, 85.7400E0, 86.0700E0,
+      86.5400E0, 86.8900E0, 87.3200E0, 87.6500E0, 88.1000E0,
+      88.4300E0, 88.8300E0, 89.1200E0, 89.5400E0, 89.8500E0,
+      90.2500E0, 90.5500E0, 90.9300E0, 91.2000E0, 91.5500E0,
+      92.2000E0
+};
+
+
+static double kirby2_F0[kirby2_N] = {
+    9.65E0, 10.74E0, 11.81E0, 12.88E0, 14.06E0,
+   15.28E0, 16.63E0, 18.19E0, 19.88E0, 21.84E0,
+   24.00E0, 26.25E0, 28.86E0, 31.85E0, 35.79E0,
+   40.18E0, 44.74E0, 49.53E0, 53.94E0, 58.29E0,
+   62.63E0, 67.03E0, 71.25E0, 75.22E0, 79.33E0,
+   83.56E0, 87.75E0, 91.93E0, 96.10E0, 100.28E0,
+  104.46E0, 108.66E0, 112.71E0, 116.88E0, 121.33E0,
+  125.79E0, 125.79E0, 128.74E0, 130.27E0, 133.33E0,
+  134.79E0, 137.93E0, 139.33E0, 142.46E0, 143.90E0,
+  146.91E0, 148.51E0, 151.41E0, 153.17E0, 155.97E0,
+  157.76E0, 160.56E0, 162.30E0, 165.21E0, 166.90E0,
+  169.92E0, 170.32E0, 171.54E0, 173.79E0, 174.57E0,
+  176.25E0, 177.34E0, 179.19E0, 181.02E0, 182.08E0,
+  183.88E0, 185.75E0, 186.80E0, 188.63E0, 190.45E0,
+  191.48E0, 193.35E0, 195.22E0, 196.23E0, 198.05E0,
+  199.97E0, 201.06E0, 202.83E0, 204.69E0, 205.86E0,
+  207.58E0, 209.50E0, 210.65E0, 212.33E0, 215.43E0,
+  217.16E0, 220.21E0, 221.98E0, 225.06E0, 226.79E0,
+  229.92E0, 231.69E0, 234.77E0, 236.60E0, 239.63E0,
+  241.50E0, 244.48E0, 246.40E0, 249.35E0, 251.32E0,
+  254.22E0, 256.24E0, 259.11E0, 261.18E0, 264.02E0,
+  266.13E0, 268.94E0, 271.09E0, 273.87E0, 276.08E0,
+  278.83E0, 281.08E0, 283.81E0, 286.11E0, 288.81E0,
+  291.08E0, 293.75E0, 295.99E0, 298.64E0, 300.84E0,
+  302.02E0, 303.48E0, 305.65E0, 308.27E0, 310.41E0,
+  313.01E0, 315.12E0, 317.71E0, 319.79E0, 322.36E0,
+  324.42E0, 326.98E0, 329.01E0, 331.56E0, 333.56E0,
+  336.10E0, 338.08E0, 340.60E0, 342.57E0, 345.08E0,
+  347.02E0, 349.52E0, 351.44E0, 353.93E0, 355.83E0,
+  358.32E0, 360.20E0, 362.67E0, 364.53E0, 367.00E0,
+  371.30E0
+};
+
+static void
+kirby2_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 3.9050739624E+00;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < kirby2_P; ++i)
+    {
+      gsl_test_rel(x[i], kirby2_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+kirby2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[kirby2_P];
+  size_t i;
+
+  for (i = 0; i < kirby2_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < kirby2_N; i++)
+    {
+      double t = kirby2_F0[i];
+      double y = ((b[0] + t* (b[1]  + t * b[2]))
+                  / (1 + t*(b[3]  + t *b[4])));
+      gsl_vector_set (f, i, kirby2_F1[i] - y);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+kirby2_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[kirby2_P];
+  size_t i;
+
+  for (i = 0; i < kirby2_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < kirby2_N; i++)
+    {
+      double t = kirby2_F0[i];
+      double u = (b[0] + t*(b[1] + t*b[2]));
+      double v = (1 + t*(b[3] + t*b[4]));
+      gsl_matrix_set (df, i, 0, -1/v);
+      gsl_matrix_set (df, i, 1, -t/v);
+      gsl_matrix_set (df, i, 2, -t*t/v);
+      gsl_matrix_set (df, i, 3, t*u/(v*v));
+      gsl_matrix_set (df, i, 4, t*t*u/(v*v));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+kirby2_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  double v4 = gsl_vector_get(v, 3);
+  double v5 = gsl_vector_get(v, 4);
+  size_t i;
+
+  for (i = 0; i < kirby2_N; i++)
+    {
+      double t = kirby2_F0[i];
+      double term1 = 1.0 + t*(x4 + t*x5);
+
+      gsl_vector_set(fvv, i, -2*t/pow(term1, 3.0) *
+                             (v4 + t*v5) *
+                             (-t*(-v2 + v4*x1 +
+                                  t*(-v3 + v5*x1 + v4*x2 + t*v5*x2 + t*(v4+t*v5)*x3)) +
+                             t*t*(v2 + t*v3)*(x4 + t*x5) + v1*(1.0 + t*(x4 + t*x5))));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf kirby2_func =
+{
+  kirby2_f,
+  kirby2_df,
+  kirby2_fvv,
+  kirby2_N,
+  kirby2_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem kirby2a_problem =
+{
+  "nist-kirby2a",
+  kirby2_x0a,
+  NULL,
+  kirby2_sigma,
+  &kirby2_epsrel,
+  &kirby2_checksol,
+  &kirby2_func
+};
+
+static test_fdf_problem kirby2b_problem =
+{
+  "nist-kirby2b",
+  kirby2_x0b,
+  NULL,
+  kirby2_sigma,
+  &kirby2_epsrel,
+  &kirby2_checksol,
+  &kirby2_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_kowalik.c gsl-doc-2.3/multifit_nlinear/test_kowalik.c
--- gsl-doc-1.16/multifit_nlinear/test_kowalik.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_kowalik.c	2016-09-24 10:42:55.000000000 +0000
@@ -0,0 +1,167 @@
+#define kowalik_N         11
+#define kowalik_P         4
+
+static double kowalik_x0[kowalik_P] = { 0.25, 0.39, 0.415, 0.39 };
+static double kowalik_epsrel = 1.0e-6;
+
+static double kowalik_Y[kowalik_N] = {
+0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627,
+0.0456, 0.0342, 0.0323, 0.0235, 0.0246
+};
+
+static double kowalik_U[kowalik_N] = {
+4.0000, 2.0000, 1.0000, 0.5000, 0.2500, 0.1670,
+0.1250, 0.1000, 0.0833, 0.0714, 0.0625
+};
+
+static void
+kowalik_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  gsl_vector_const_view v = gsl_vector_const_view_array(x, kowalik_P);
+  const double norm = gsl_blas_dnrm2(&v.vector);
+  const double sumsq_exact1 = 3.075056038492370e-04;
+  double kowalik_x1[kowalik_P] = { 1.928069345723978e-01,
+                                   1.912823290344599e-01,
+                                   1.230565070690708e-01,
+                                   1.360623308065148e-01 };
+  const double sumsq_exact2 = 0.00102734304869549252;
+  double kowalik_x2[kowalik_P] = { 0.0,   /* inf */
+                                   -14.0758834005984603,
+                                   0.0,   /* -inf */
+                                   0.0 }; /* -inf */
+  const double *kowalik_x;
+  double sumsq_exact;
+
+  kowalik_x2[0] = GSL_NAN;
+  kowalik_x2[2] = GSL_NAN;
+  kowalik_x2[3] = GSL_NAN;
+
+  if (norm < 10.0)
+    {
+      kowalik_x = kowalik_x1;
+      sumsq_exact = sumsq_exact1;
+    }
+  else
+    {
+      kowalik_x = kowalik_x2;
+      sumsq_exact = sumsq_exact2;
+    }
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < kowalik_P; ++i)
+    {
+      if (!gsl_finite(kowalik_x[i]))
+        continue;
+
+      gsl_test_rel(x[i], kowalik_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+kowalik_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  size_t i;
+
+  for (i = 0; i < kowalik_N; ++i)
+    {
+      double yi = kowalik_Y[i];
+      double ui = kowalik_U[i];
+      double fi = yi - (x1*ui*(ui+x2)) / (x4 + ui*(ui + x3));
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+kowalik_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  size_t i;
+
+  for (i = 0; i < kowalik_N; ++i)
+    {
+      double ui = kowalik_U[i];
+      double term1 = ui*(ui + x2);
+      double term2 = ui*(ui + x3) + x4;
+
+      gsl_matrix_set(J, i, 0, -term1 / term2);
+      gsl_matrix_set(J, i, 1, -ui*x1/term2);
+      gsl_matrix_set(J, i, 2, ui*term1*x1 / (term2*term2));
+      gsl_matrix_set(J, i, 3, term1*x1 / (term2*term2));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+kowalik_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  double v4 = gsl_vector_get(v, 3);
+  size_t i;
+
+  for (i = 0; i < kowalik_N; ++i)
+    {
+      double ui = kowalik_U[i];
+      double term2 = ui*(ui + x3) + x4;
+      double term3 = ui*ui*v1 - ui*v3*x1 - v4*x1 +
+                     ui*v1*x3 + v1*x4;
+      double term4 = ui*ui*(v3-v2) + v4*x2 +
+                     ui*(v4 + v3*x2 - v2*x3) - v2*x4;
+
+      gsl_vector_set(fvv, i, 2.0*ui*term3*term4 / pow(term2, 3.0));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf kowalik_func =
+{
+  kowalik_f,
+  kowalik_df,
+  kowalik_fvv,
+  kowalik_N,
+  kowalik_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem kowalik_problem =
+{
+  "kowalik",
+  kowalik_x0,
+  NULL,
+  NULL,
+  &kowalik_epsrel,
+  &kowalik_checksol,
+  &kowalik_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_lin1.c gsl-doc-2.3/multifit_nlinear/test_lin1.c
--- gsl-doc-1.16/multifit_nlinear/test_lin1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_lin1.c	2016-09-24 10:43:00.000000000 +0000
@@ -0,0 +1,107 @@
+#define lin1_N         11  /* can be anything >= p */
+#define lin1_P         5
+
+static double lin1_x0[lin1_P] = { 1.0, 1.0, 1.0, 1.0, 1.0 };
+static double lin1_epsrel = 1.0e-10;
+
+static void
+lin1_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = (double) (lin1_N - lin1_P);
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < lin1_P; ++i)
+    {
+      gsl_test_rel(x[i], -1.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+lin1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i, j;
+
+  for (i = 0; i < lin1_N; ++i)
+    {
+      double fi = 0.0;
+
+      for (j = 0; j < lin1_P; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+          double Aij = (i == j) ? 1.0 : 0.0;
+          Aij -= 2.0 / lin1_N;
+          fi += Aij * xj;
+        }
+
+      fi -= 1.0;
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin1_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  size_t i, j;
+
+  for (i = 0; i < lin1_N; ++i)
+    {
+      for (j = 0; j < lin1_P; ++j)
+        {
+          double Jij = (i == j) ? 1.0 : 0.0;
+          Jij -= 2.0 / lin1_N;
+          gsl_matrix_set(J, i, j, Jij);
+        }
+    }
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin1_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  (void)x; /* avoid unused parameter warnings */
+  (void)v;
+  (void)params;
+
+  gsl_vector_set_zero(fvv);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf lin1_func =
+{
+  lin1_f,
+  lin1_df,
+  lin1_fvv,
+  lin1_N,
+  lin1_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem lin1_problem =
+{
+  "linear_full",
+  lin1_x0,
+  NULL,
+  NULL,
+  &lin1_epsrel,
+  &lin1_checksol,
+  &lin1_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_lin2.c gsl-doc-2.3/multifit_nlinear/test_lin2.c
--- gsl-doc-1.16/multifit_nlinear/test_lin2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_lin2.c	2016-09-24 10:43:05.000000000 +0000
@@ -0,0 +1,106 @@
+#define lin2_N         20  /* can be anything >= p */
+#define lin2_P         5
+
+static double lin2_x0[lin2_P] = { 1.0, 1.0, 1.0, 1.0, 1.0 };
+static double lin2_epsrel = 1.0e-9;
+
+static void
+lin2_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double n = (double) lin2_N;
+  const double sumsq_exact = 0.5 * (n*(n - 1.0)) / (2.0*n + 1.0);
+  const double sum_exact = 3.0 / (2.0*n + 1.0);
+  double sum = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < lin2_P; ++i)
+    sum += (i + 1.0) * x[i];
+
+  gsl_test_rel(sum, sum_exact, epsrel, "%s/%s coeff sum",
+               sname, pname);
+}
+
+static int
+lin2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i, j;
+
+  for (i = 0; i < lin2_N; ++i)
+    {
+      double fi = 0.0;
+
+      for (j = 0; j < lin2_P; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+          fi += (j + 1) * xj;
+        }
+
+      fi = (i + 1) * fi - 1.0;
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin2_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  size_t i, j;
+
+  for (i = 0; i < lin2_N; ++i)
+    {
+      for (j = 0; j < lin2_P; ++j)
+        {
+          gsl_matrix_set(J, i, j, (i + 1.0) * (j + 1.0));
+        }
+    }
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin2_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  (void)x; /* avoid unused parameter warnings */
+  (void)v;
+  (void)params;
+
+  gsl_vector_set_zero(fvv);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf lin2_func =
+{
+  lin2_f,
+  lin2_df,
+  lin2_fvv,
+  lin2_N,
+  lin2_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem lin2_problem =
+{
+  "linear_rank1",
+  lin2_x0,
+  NULL,
+  NULL,
+  &lin2_epsrel,
+  &lin2_checksol,
+  &lin2_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_lin3.c gsl-doc-2.3/multifit_nlinear/test_lin3.c
--- gsl-doc-1.16/multifit_nlinear/test_lin3.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_lin3.c	2016-09-24 10:43:10.000000000 +0000
@@ -0,0 +1,113 @@
+#define lin3_N         50  /* can be anything >= p */
+#define lin3_P         10  /* >= 3 */
+
+static double lin3_x0[lin3_P] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
+static double lin3_epsrel = 1.0e-8;
+
+static void
+lin3_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double n = (double) lin3_N;
+  const double sumsq_exact = 0.5 * (n*n + 3*n - 6.0) / (2*n - 3.0);
+  const double sum_exact = 3.0 / (2.0*n - 3.0);
+  double sum = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 1; i < lin3_P - 1; ++i)
+    sum += (i + 1.0) * x[i];
+
+  gsl_test_rel(sum, sum_exact, epsrel, "%s/%s coeff sum",
+               sname, pname);
+
+  (void)x; /* avoid unused parameter warning */
+}
+
+static int
+lin3_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i, j;
+
+  gsl_vector_set(f, 0, -1.0);
+  gsl_vector_set(f, lin3_N - 1, -1.0);
+
+  for (i = 1; i < lin3_N - 1; ++i)
+    {
+      double fi = 0.0;
+
+      for (j = 1; j < lin3_P - 1; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+          fi += (j + 1) * xj;
+        }
+
+      fi = i * fi - 1.0;
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin3_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  size_t i, j;
+
+  gsl_matrix_set_zero(J);
+
+  for (i = 1; i < lin3_N - 1; ++i)
+    {
+      for (j = 1; j < lin3_P - 1; ++j)
+        {
+          gsl_matrix_set(J, i, j, i * (j + 1.0));
+        }
+    }
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin3_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  (void)x; /* avoid unused parameter warnings */
+  (void)v;
+  (void)params;
+
+  gsl_vector_set_zero(fvv);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf lin3_func =
+{
+  lin3_f,
+  lin3_df,
+  lin3_fvv,
+  lin3_N,
+  lin3_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem lin3_problem =
+{
+  "linear_rank1zeros",
+  lin3_x0,
+  NULL,
+  NULL,
+  &lin3_epsrel,
+  &lin3_checksol,
+  &lin3_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_meyer.c gsl-doc-2.3/multifit_nlinear/test_meyer.c
--- gsl-doc-1.16/multifit_nlinear/test_meyer.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_meyer.c	2016-09-24 10:43:15.000000000 +0000
@@ -0,0 +1,131 @@
+#define meyer_N         16
+#define meyer_P         3
+
+static double meyer_x0[meyer_P] = { 0.02, 4000.0, 250.0 };
+static double meyer_epsrel = 1.0e-6;
+
+static double meyer_Y[meyer_N] = {
+34780., 28610., 23650., 19630., 16370., 13720., 11540.,
+9744.,  8261.,  7030.,  6005., 5147., 4427., 3820.,
+3307.,  2872.
+};
+
+static void
+meyer_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.794585517053883e+01;
+  const double meyer_x[meyer_P] = { 5.609636471049458e-03,
+                                    6.181346346283188e+03,
+                                    3.452236346240292e+02 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < meyer_P; ++i)
+    {
+      gsl_test_rel(x[i], meyer_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+meyer_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < meyer_N; ++i)
+    {
+      double ti = 45.0 + 5.0*(i + 1.0);
+      double yi = meyer_Y[i];
+      double fi = x1 * exp(x2 / (ti + x3)) - yi;
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+meyer_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < meyer_N; ++i)
+    {
+      double ti = 45.0 + 5.0*(i + 1.0);
+      double term1 = ti + x3;
+      double term2 = exp(x2 / term1);
+
+      gsl_matrix_set(J, i, 0, term2);
+      gsl_matrix_set(J, i, 1, x1*term2/term1);
+      gsl_matrix_set(J, i, 2, -x1*x2*term2/(term1*term1));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+meyer_fvv (const gsl_vector * x, const gsl_vector * v,
+           void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  size_t i;
+
+  for (i = 0; i < meyer_N; ++i)
+    {
+      double ti = 45.0 + 5.0*(i + 1.0);
+      double term1 = ti + x3;
+      double term2 = exp(x2 / term1);
+      double term3 = v2*term1 - v3*x2;
+      double term4 = 2*ti*ti*v1 - v3*x1*(x2 + 2*x3) +
+                     x3*(v2*x1 + 2*v1*x3) +
+                     ti*(v2*x1 - 2*v3*x1 + 4*v1*x3);
+
+      gsl_vector_set(fvv, i, term2 * term3 * term4 / pow(term1, 4.0));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf meyer_func =
+{
+  meyer_f,
+  meyer_df,
+  meyer_fvv,
+  meyer_N,
+  meyer_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem meyer_problem =
+{
+  "meyer",
+  meyer_x0,
+  NULL,
+  NULL,
+  &meyer_epsrel,
+  &meyer_checksol,
+  &meyer_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_meyerscal.c gsl-doc-2.3/multifit_nlinear/test_meyerscal.c
--- gsl-doc-1.16/multifit_nlinear/test_meyerscal.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_meyerscal.c	2016-09-24 10:43:22.000000000 +0000
@@ -0,0 +1,132 @@
+#define meyerscal_N         16
+#define meyerscal_P         3
+
+static double meyerscal_x0[meyerscal_P] = { 8.85, 4.0, 2.5 };
+static double meyerscal_epsrel = 1.0e-6;
+
+static double meyerscal_Y[meyerscal_N] = {
+34780., 28610., 23650., 19630., 16370., 13720., 11540.,
+9744.,  8261.,  7030.,  6005., 5147., 4427., 3820.,
+3307.,  2872.
+};
+
+static void
+meyerscal_checksol(const double x[], const double sumsq,
+                   const double epsrel, const char *sname,
+                   const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.794585517003888e-05;
+  const double meyerscal_x[meyerscal_P] = { 2.481778312286695e+00,
+                                            6.181346341853554e+00,
+                                            3.452236344749865e+00 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < meyerscal_P; ++i)
+    {
+      gsl_test_rel(x[i], meyerscal_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+meyerscal_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < meyerscal_N; ++i)
+    {
+      double ti = 0.45 + 0.05*(i + 1.0);
+      double yi = meyerscal_Y[i];
+      double fi = x1 * exp(10.0*x2 / (ti + x3) - 13.0) - 1.0e-3*yi;
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+meyerscal_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < meyerscal_N; ++i)
+    {
+      double ti = 0.45 + 0.05*(i + 1.0);
+      double term1 = ti + x3;
+      double term2 = exp(10.0*x2/term1 - 13.0);
+
+      gsl_matrix_set(J, i, 0, term2);
+      gsl_matrix_set(J, i, 1, 10.0*x1*term2/term1);
+      gsl_matrix_set(J, i, 2, -10.0*x1*x2*term2/(term1*term1));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+meyerscal_fvv (const gsl_vector * x, const gsl_vector * v,
+               void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  size_t i;
+
+  for (i = 0; i < meyerscal_N; ++i)
+    {
+      double ti = 0.45 + 0.05*(i + 1.0);
+      double term1 = ti + x3;
+      double term2 = exp(10.0*x2/term1 - 13.0);
+      double term3 = v2*term1 - v3*x2;
+      double term4 = ti*ti*v1 -
+                     v3*x1*(5*x2 + x3) +
+                     x3*(5*v2*x1 + v1*x3) +
+                     ti*(5*v2*x1 - v3*x1 + 2*v1*x3);
+
+      gsl_vector_set(fvv, i, 20*term2*term3*term4 / pow(term1, 4.0));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf meyerscal_func =
+{
+  meyerscal_f,
+  meyerscal_df,
+  meyerscal_fvv,
+  meyerscal_N,
+  meyerscal_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem meyerscal_problem =
+{
+  "meyerscal",
+  meyerscal_x0,
+  NULL,
+  NULL,
+  &meyerscal_epsrel,
+  &meyerscal_checksol,
+  &meyerscal_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_osborne.c gsl-doc-2.3/multifit_nlinear/test_osborne.c
--- gsl-doc-1.16/multifit_nlinear/test_osborne.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_osborne.c	2016-09-24 10:43:28.000000000 +0000
@@ -0,0 +1,140 @@
+#define osborne_N         33
+#define osborne_P         5
+
+static double osborne_x0[osborne_P] = { 0.5, 1.5, -1.0, 0.01, 0.02 };
+static double osborne_epsrel = 1.0e-8;
+
+static double osborne_Y[osborne_N] = {
+0.844, 0.908, 0.932, 0.936, 0.925, 0.908, 0.881,
+0.850, 0.818, 0.784, 0.751, 0.718, 0.685, 0.658,
+0.628, 0.603, 0.580, 0.558, 0.538, 0.522, 0.506,
+0.490, 0.478, 0.467, 0.457, 0.448, 0.438, 0.431,
+0.424, 0.420, 0.414, 0.411, 0.406
+};
+
+static void
+osborne_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  const double sumsq_exact = 5.464894697482687e-05;
+  double osborne_x[osborne_P];
+  
+  osborne_x[0] = 3.754100521058740e-01;
+  osborne_x[1] = GSL_NAN;
+  osborne_x[2] = GSL_NAN;
+  osborne_x[3] = GSL_NAN;
+  osborne_x[4] = GSL_NAN;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  /* only the first model parameter is uniquely constrained */
+  gsl_test_rel(x[0], osborne_x[0], epsrel, "%s/%s i=0",
+               sname, pname);
+}
+
+static int
+osborne_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  size_t i;
+
+  for (i = 0; i < osborne_N; ++i)
+    {
+      double ti = 10.0*i;
+      double yi = osborne_Y[i];
+      double fi = yi - (x1 + x2*exp(-x4*ti) + x3*exp(-x5*ti));
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+osborne_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  size_t i;
+
+  for (i = 0; i < osborne_N; ++i)
+    {
+      double ti = 10.0*i;
+      double term1 = exp(-x4*ti);
+      double term2 = exp(-x5*ti);
+
+      gsl_matrix_set(J, i, 0, -1.0);
+      gsl_matrix_set(J, i, 1, -term1);
+      gsl_matrix_set(J, i, 2, -term2);
+      gsl_matrix_set(J, i, 3, ti*x2*term1);
+      gsl_matrix_set(J, i, 4, ti*x3*term2);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+osborne_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  double v4 = gsl_vector_get(v, 3);
+  double v5 = gsl_vector_get(v, 4);
+  size_t i;
+
+  for (i = 0; i < osborne_N; ++i)
+    {
+      double ti = 10.0*i;
+      double term1 = exp(-x4*ti);
+      double term2 = exp(-x5*ti);
+      double term3 = -2*v2 + ti*v4*x2;
+      double term4 = -2*v3 + ti*v5*x3;
+
+      gsl_vector_set(fvv, i, -term1 * term2 * ti *
+                             (v4 / term2 * term3 + v5 / term1 * term4));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf osborne_func =
+{
+  osborne_f,
+  osborne_df,
+  osborne_fvv,
+  osborne_N,
+  osborne_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem osborne_problem =
+{
+  "osborne",
+  osborne_x0,
+  NULL,
+  NULL,
+  &osborne_epsrel,
+  &osborne_checksol,
+  &osborne_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_penalty1.c gsl-doc-2.3/multifit_nlinear/test_penalty1.c
--- gsl-doc-1.16/multifit_nlinear/test_penalty1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_penalty1.c	2016-09-24 10:43:33.000000000 +0000
@@ -0,0 +1,107 @@
+#define penalty1_P         10
+#define penalty1_N         (penalty1_P + 1)
+
+static double penalty1_x0[penalty1_P] = { 1.0, 2.0, 3.0, 4.0, 5.0,
+                                          6.0, 7.0, 8.0, 9.0, 10.0 };
+static double penalty1_epsrel = 1.0e-12;
+
+static void
+penalty1_checksol(const double x[], const double sumsq,
+                  const double epsrel, const char *sname,
+                  const char *pname)
+{
+  const double sumsq_exact = 7.08765146709037993e-05;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  (void)x; /* avoid unused parameter warning */
+}
+
+static int
+penalty1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  size_t i;
+  double sum = 0.0;
+
+  for (i = 0; i < penalty1_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+
+      gsl_vector_set(f, i, sqrt_alpha*(xi - 1.0));
+
+      sum += xi * xi;
+    }
+
+  gsl_vector_set(f, penalty1_N - 1, sum - 0.25);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+penalty1_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  size_t i;
+  gsl_matrix_view m = gsl_matrix_submatrix(J, 0, 0, penalty1_P, penalty1_P);
+  gsl_vector_view diag = gsl_matrix_diagonal(&m.matrix);
+
+  gsl_matrix_set_zero(&m.matrix);
+  gsl_vector_set_all(&diag.vector, sqrt_alpha);
+
+  for (i = 0; i < penalty1_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      gsl_matrix_set(J, penalty1_N - 1, i, 2.0 * xi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+penalty1_fvv (const gsl_vector * x, const gsl_vector * v,
+              void *params, gsl_vector * fvv)
+{
+  double u;
+
+  gsl_vector_set_zero(fvv);
+
+  gsl_blas_ddot(v, v, &u);
+  gsl_vector_set(fvv, penalty1_N - 1, 2.0 * u);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf penalty1_func =
+{
+  penalty1_f,
+  penalty1_df,
+  penalty1_fvv,
+  penalty1_N,
+  penalty1_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem penalty1_problem =
+{
+  "penalty1",
+  penalty1_x0,
+  NULL,
+  NULL,
+  &penalty1_epsrel,
+  &penalty1_checksol,
+  &penalty1_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_penalty2.c gsl-doc-2.3/multifit_nlinear/test_penalty2.c
--- gsl-doc-1.16/multifit_nlinear/test_penalty2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_penalty2.c	2016-09-24 10:43:38.000000000 +0000
@@ -0,0 +1,179 @@
+#define penalty2_N         8 /* 2*p */
+#define penalty2_P         4
+
+static double penalty2_x0[penalty2_P] = { 0.5, 0.5, 0.5, 0.5 };
+static double penalty2_epsrel = 1.0e-12;
+
+static void
+penalty2_checksol(const double x[], const double sumsq,
+                  const double epsrel, const char *sname,
+                  const char *pname)
+{
+  const double sumsq_exact = 9.37629300735544219e-06;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  (void)x; /* avoid unused parameter warning */
+}
+
+static int
+penalty2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  double x1 = gsl_vector_get(x, 0);
+  size_t i;
+  double sum = penalty2_P * x1 * x1;
+
+  gsl_vector_set(f, 0, x1 - 0.2);
+
+  /* rows [2:p] */
+  for (i = 1; i < penalty2_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      double xim1 = gsl_vector_get(x, i - 1);
+      double yi = exp(0.1*(i + 1.0)) + exp(0.1*i);
+
+      gsl_vector_set(f, i, sqrt_alpha*(exp(0.1*xi) + exp(0.1*xim1) - yi));
+
+      sum += (penalty2_P - i) * xi * xi;
+    }
+
+  /* rows [p+1:2p-1] */
+  for (i = penalty2_P; i < penalty2_N - 1; ++i)
+    {
+      double xi = gsl_vector_get(x, i - penalty2_P + 1);
+
+      gsl_vector_set(f, i, sqrt_alpha*(exp(0.1*xi) - exp(-0.1)));
+    }
+
+  /* row 2p */
+  gsl_vector_set(f, penalty2_N - 1, sum - 1.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+penalty2_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  size_t i, j;
+
+  for (j = 0; j < penalty2_P; ++j)
+    {
+      double xj = gsl_vector_get(x, j);
+      double delta1j = (j == 0) ? 1.0 : 0.0;
+
+      /* first and last rows */
+      gsl_matrix_set(J, 0, j, delta1j);
+      gsl_matrix_set(J, penalty2_N - 1, j, 2.0 * (penalty2_P - j) * xj);
+
+      /* rows [2:p] */
+      for (i = 1; i < penalty2_P; ++i)
+        {
+          double xi = gsl_vector_get(x, i);
+          double xim1 = gsl_vector_get(x, i - 1);
+          double Jij;
+
+          if (i == j)
+            Jij = exp(0.1 * xi);
+          else if (i - 1 == j)
+            Jij = exp(0.1 * xim1);
+          else
+            Jij = 0.0;
+
+          Jij *= 0.1 * sqrt_alpha;
+
+          gsl_matrix_set(J, i, j, Jij);
+        }
+
+      /* rows [p+1:2p-1] */
+      for (i = penalty2_P; i < penalty2_N - 1; ++i)
+        {
+          double xi = gsl_vector_get(x, i - penalty2_P + 1);
+
+          if (i - penalty2_P + 1 == j)
+            gsl_matrix_set(J, i, j, 0.1 * sqrt_alpha * exp(0.1*xi));
+          else
+            gsl_matrix_set(J, i, j, 0.0);
+        }
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+penalty2_fvv (const gsl_vector * x, const gsl_vector * v,
+              void *params, gsl_vector * fvv)
+{
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  double v1 = gsl_vector_get(v, 0);
+  double sum = penalty2_P * v1 * v1;
+  size_t i;
+
+  /* first row */
+  gsl_vector_set(fvv, 0, 0.0);
+
+  /* rows [2:p] */
+  for (i = 1; i < penalty2_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      double xim1 = gsl_vector_get(x, i - 1);
+      double vi = gsl_vector_get(v, i);
+      double vim1 = gsl_vector_get(v, i - 1);
+      double term1 = exp(xi / 10.0);
+      double term2 = exp(xim1 / 10.0);
+
+      gsl_vector_set(fvv, i,
+        sqrt_alpha / 100.0 * (term1 * vi * vi + term2 * vim1 * vim1));
+
+      sum += (penalty2_P - i) * vi * vi;
+    }
+
+  /* last row */
+  gsl_vector_set(fvv, penalty2_N - 1, 2.0 * sum);
+
+  /* rows [p+1:2p-1] */
+  for (i = penalty2_P; i < penalty2_N - 1; ++i)
+    {
+      double xi = gsl_vector_get(x, i - penalty2_P + 1);
+      double vi = gsl_vector_get(v, i - penalty2_P + 1);
+
+      gsl_vector_set(fvv, i, sqrt_alpha / 100.0 * exp(xi / 10.0) * vi * vi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf penalty2_func =
+{
+  penalty2_f,
+  penalty2_df,
+  penalty2_fvv,
+  penalty2_N,
+  penalty2_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem penalty2_problem =
+{
+  "penalty2",
+  penalty2_x0,
+  NULL,
+  NULL,
+  &penalty2_epsrel,
+  &penalty2_checksol,
+  &penalty2_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_powell1.c gsl-doc-2.3/multifit_nlinear/test_powell1.c
--- gsl-doc-1.16/multifit_nlinear/test_powell1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_powell1.c	2016-09-24 10:43:43.000000000 +0000
@@ -0,0 +1,120 @@
+#define powell1_N        4
+#define powell1_P        4
+
+static double powell1_x0[powell1_P] = { 3.0, -1.0, 0.0, 1.0 };
+static double powell1_epsrel = 1.0e-4;
+
+static void
+powell1_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < powell1_P; ++i)
+    {
+      gsl_test_rel(x[i], 0.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+powell1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get (x, 0);
+  double x2 = gsl_vector_get (x, 1);
+  double x3 = gsl_vector_get (x, 2);
+  double x4 = gsl_vector_get (x, 3);
+
+  gsl_vector_set(f, 0, x1 + 10.0*x2);
+  gsl_vector_set(f, 1, sqrt(5.0) * (x3 - x4));
+  gsl_vector_set(f, 2, pow(x2 - 2.0*x3, 2.0));
+  gsl_vector_set(f, 3, sqrt(10.0) * pow((x1 - x4), 2.0));
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell1_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get (x, 0);
+  double x2 = gsl_vector_get (x, 1);
+  double x3 = gsl_vector_get (x, 2);
+  double x4 = gsl_vector_get (x, 3);
+  double term1 = x2 - 2.0*x3;
+  double term2 = x1 - x4;
+
+  gsl_matrix_set(J, 0, 0, 1.0);
+  gsl_matrix_set(J, 0, 1, 10.0);
+  gsl_matrix_set(J, 0, 2, 0.0);
+  gsl_matrix_set(J, 0, 3, 0.0);
+
+  gsl_matrix_set(J, 1, 0, 0.0);
+  gsl_matrix_set(J, 1, 1, 0.0);
+  gsl_matrix_set(J, 1, 2, sqrt(5.0));
+  gsl_matrix_set(J, 1, 3, -sqrt(5.0));
+
+  gsl_matrix_set(J, 2, 0, 0.0);
+  gsl_matrix_set(J, 2, 1, 2.0*term1);
+  gsl_matrix_set(J, 2, 2, -4.0*term1);
+  gsl_matrix_set(J, 2, 3, 0.0);
+
+  gsl_matrix_set(J, 3, 0, 2.0*sqrt(10.0)*term2);
+  gsl_matrix_set(J, 3, 1, 0.0);
+  gsl_matrix_set(J, 3, 2, 0.0);
+  gsl_matrix_set(J, 3, 3, -2.0*sqrt(10.0)*term2);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell1_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  double v4 = gsl_vector_get(v, 3);
+
+  gsl_vector_set(fvv, 0, 0.0);
+  gsl_vector_set(fvv, 1, 0.0);
+  gsl_vector_set(fvv, 2, 2.0 * pow(v2 - 2.0*v3, 2.0));
+  gsl_vector_set(fvv, 3, 2.0 * sqrt(10.0) * pow(v1 - v4, 2.0));
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf powell1_func =
+{
+  powell1_f,
+  powell1_df,
+  powell1_fvv,
+  powell1_N,
+  powell1_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem powell1_problem =
+{
+  "powell_singular",
+  powell1_x0,
+  NULL,
+  NULL,
+  &powell1_epsrel,
+  &powell1_checksol,
+  &powell1_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_powell2.c gsl-doc-2.3/multifit_nlinear/test_powell2.c
--- gsl-doc-1.16/multifit_nlinear/test_powell2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_powell2.c	2016-09-24 10:43:47.000000000 +0000
@@ -0,0 +1,95 @@
+#define powell2_N        2
+#define powell2_P        2
+
+static double powell2_x0[powell2_P] = { 3.0, 1.0 };
+static double powell2_epsrel = 1.0e-3;
+
+static void
+powell2_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < powell2_P; ++i)
+    {
+      gsl_test_rel(x[i], 0.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+powell2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x0 = gsl_vector_get (x, 0);
+  double x1 = gsl_vector_get (x, 1);
+
+  gsl_vector_set(f, 0, x0);
+  gsl_vector_set(f, 1, 10.0*x0/(x0 + 0.1) + 2.0*x1*x1);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell2_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double x0 = gsl_vector_get (x, 0);
+  double x1 = gsl_vector_get (x, 1);
+  double term = x0 + 0.1;
+
+  gsl_matrix_set(df, 0, 0, 1.0);
+  gsl_matrix_set(df, 0, 1, 0.0);
+  gsl_matrix_set(df, 1, 0, 1.0 / (term * term));
+  gsl_matrix_set(df, 1, 1, 4.0 * x1);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell2_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  double x0 = gsl_vector_get (x, 0);
+  double v0 = gsl_vector_get (v, 0);
+  double v1 = gsl_vector_get (v, 1);
+  double term = x0 + 0.1;
+
+  gsl_vector_set(fvv, 0, 0.0);
+  gsl_vector_set(fvv, 1, 4*v1*v1 - (2*v0*v0)/pow(term, 3.0));
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf powell2_func =
+{
+  powell2_f,
+  powell2_df,
+  powell2_fvv,
+  powell2_N,
+  powell2_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem powell2_problem =
+{
+  "powell2",
+  powell2_x0,
+  NULL,
+  NULL,
+  &powell2_epsrel,
+  &powell2_checksol,
+  &powell2_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_powell3.c gsl-doc-2.3/multifit_nlinear/test_powell3.c
--- gsl-doc-1.16/multifit_nlinear/test_powell3.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_powell3.c	2016-09-24 10:43:52.000000000 +0000
@@ -0,0 +1,97 @@
+#define powell3_N         2
+#define powell3_P         2
+
+static double powell3_x0[powell3_P] = { 0.0, 1.0 };
+static double powell3_epsrel = 1.0e-10;
+
+static void
+powell3_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double powell3_x[powell3_P] = { 1.09815932969975976e-05,
+                                        9.10614673986700218 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < powell3_P; ++i)
+    {
+      gsl_test_rel(x[i], powell3_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+powell3_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, 1.0e4*x1*x2 - 1.0);
+  gsl_vector_set(f, 1, exp(-x1) + exp(-x2) - 1.0001);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell3_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_matrix_set(J, 0, 0, 1.0e4*x2);
+  gsl_matrix_set(J, 0, 1, 1.0e4*x1);
+
+  gsl_matrix_set(J, 1, 0, -exp(-x1));
+  gsl_matrix_set(J, 1, 1, -exp(-x2));
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell3_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+
+  gsl_vector_set(fvv, 0, 2.0e4 * v1 * v2);
+  gsl_vector_set(fvv, 1, v1*v1*exp(-x1) + v2*v2*exp(-x2));
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf powell3_func =
+{
+  powell3_f,
+  powell3_df,
+  powell3_fvv,
+  powell3_N,
+  powell3_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem powell3_problem =
+{
+  "powell_badly_scaled",
+  powell3_x0,
+  NULL,
+  NULL,
+  &powell3_epsrel,
+  &powell3_checksol,
+  &powell3_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_rat42.c gsl-doc-2.3/multifit_nlinear/test_rat42.c
--- gsl-doc-1.16/multifit_nlinear/test_rat42.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_rat42.c	2016-09-24 10:44:03.000000000 +0000
@@ -0,0 +1,153 @@
+#define rat42_N       9
+#define rat42_P       3
+
+static double rat42_x0a[rat42_P] = { 100.0, 1.0, 0.1 };
+static double rat42_x0b[rat42_P] = { 75.0, 2.5, 0.07 };
+static double rat42_epsrel = 1.0e-7;
+
+static double rat42_sigma[rat42_P] = {
+  1.7340283401E+00, 8.8295217536E-02, 3.4465663377E-03
+};
+
+static double rat42_X[rat42_N] = { 9.0, 14.0, 21.0, 28.0, 42.0,
+                                   57.0, 63.0, 70.0, 79.0 };
+
+static double rat42_F[rat42_N] = { 8.930, 10.800, 18.590, 22.330,
+                                   39.350, 56.110, 61.730, 64.620,
+                                   67.080 };
+
+static void
+rat42_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.0565229338E+00;
+  const double rat42_x[rat42_P] = { 7.2462237576E+01,
+                                    2.6180768402E+00,
+                                    6.7359200066E-02 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < rat42_P; ++i)
+    {
+      gsl_test_rel(x[i], rat42_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+rat42_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[rat42_P];
+  size_t i;
+
+  for (i = 0; i < rat42_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < rat42_N; i++)
+    {
+      double xi = rat42_X[i];
+      double yi = b[0] / (1.0 + exp(b[1] - b[2]*xi));
+      gsl_vector_set (f, i, yi - rat42_F[i]);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rat42_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[rat42_P];
+  size_t i;
+
+  for (i = 0; i < rat42_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < rat42_N; i++)
+    {
+      double xi = rat42_X[i];
+      double term1 = exp(b[1] - b[2]*xi);
+      double term2 = 1.0 + term1;
+
+      gsl_matrix_set (df, i, 0, 1.0 / term2);
+      gsl_matrix_set (df, i, 1, -b[0] * term1 / (term2 * term2));
+      gsl_matrix_set (df, i, 2, b[0] * term1 * xi / (term2 * term2));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rat42_fvv (const gsl_vector * x, const gsl_vector * v,
+           void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  size_t i;
+
+  for (i = 0; i < rat42_N; i++)
+    {
+      double ti = rat42_X[i];
+      double term1 = exp(x2);
+      double term2 = exp(ti * x3);
+
+      gsl_vector_set(fvv, i,
+        -pow(term1 + term2, -3.0) * term1 * term2 *
+         (v2 - ti*v3) * (term1*(2*v1 - v2*x1 + ti*v3*x1) +
+                         term2*(2*v1 + x1*(v2 - ti*v3))));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf rat42_func =
+{
+  rat42_f,
+  rat42_df,
+  rat42_fvv,
+  rat42_N,
+  rat42_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem rat42a_problem =
+{
+  "nist-rat42a",
+  rat42_x0a,
+  NULL,
+  rat42_sigma,
+  &rat42_epsrel,
+  &rat42_checksol,
+  &rat42_func
+};
+
+static test_fdf_problem rat42b_problem =
+{
+  "nist-rat42b",
+  rat42_x0b,
+  NULL,
+  rat42_sigma,
+  &rat42_epsrel,
+  &rat42_checksol,
+  &rat42_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_rat43.c gsl-doc-2.3/multifit_nlinear/test_rat43.c
--- gsl-doc-1.16/multifit_nlinear/test_rat43.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_rat43.c	2016-09-24 10:44:13.000000000 +0000
@@ -0,0 +1,127 @@
+#define rat43_N       15
+#define rat43_P       4
+
+static double rat43_x0a[rat43_P] = { 100.0, 10.0, 1.0, 1.0 };
+static double rat43_x0b[rat43_P] = { 700.0, 5.0, 0.75, 1.3 };
+static double rat43_epsrel = 1.0e-6;
+
+static double rat43_sigma[rat43_P] = {
+  1.6302297817E+01, 2.0828735829E+00,
+  1.9566123451E-01, 6.8761936385E-01
+};
+
+static double rat43_F[rat43_N] = { 16.08, 33.83, 65.80, 97.20, 191.55,
+                                   326.20, 386.87, 520.53, 590.03,
+                                   651.92, 724.93, 699.56, 689.96,
+                                   637.56, 717.41 };
+
+static void
+rat43_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.7864049080E+03;
+  const double rat43_x[rat43_P] = { 6.9964151270E+02,
+                                    5.2771253025E+00,
+                                    7.5962938329E-01,
+                                    1.2792483859E+00 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < rat43_P; ++i)
+    {
+      gsl_test_rel(x[i], rat43_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+rat43_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[rat43_P];
+  size_t i;
+
+  for (i = 0; i < rat43_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < rat43_N; i++)
+    {
+      double xi = i + 1.0;
+      double e = exp(b[1] - b[2]*xi);
+      double yi = b[0] / pow(1.0 + e, 1.0 / b[3]);
+      gsl_vector_set (f, i, yi - rat43_F[i]);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rat43_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[rat43_P];
+  size_t i;
+
+  for (i = 0; i < rat43_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < rat43_N; i++)
+    {
+      double xi = i + 1.0;
+      double e = exp(b[1] - b[2]*xi);
+      double term1 = 1.0 + e;
+      double term2 = pow(term1, -1.0 / b[3]);
+
+      gsl_matrix_set (df, i, 0, term2);
+      gsl_matrix_set (df, i, 1, -b[0] / b[3] * e * term2 / term1);
+      gsl_matrix_set (df, i, 2, b[0] / b[3] * xi * e * term2 / term1);
+      gsl_matrix_set (df, i, 3, b[0] / b[3] / b[3] * log(term1) * term2);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf rat43_func =
+{
+  rat43_f,
+  rat43_df,
+  NULL, /* analytic expression too complex */
+  rat43_N,
+  rat43_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem rat43a_problem =
+{
+  "nist-rat43a",
+  rat43_x0a,
+  NULL,
+  rat43_sigma,
+  &rat43_epsrel,
+  &rat43_checksol,
+  &rat43_func
+};
+
+static test_fdf_problem rat43b_problem =
+{
+  "nist-rat43b",
+  rat43_x0b,
+  NULL,
+  rat43_sigma,
+  &rat43_epsrel,
+  &rat43_checksol,
+  &rat43_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_rosenbrock.c gsl-doc-2.3/multifit_nlinear/test_rosenbrock.c
--- gsl-doc-1.16/multifit_nlinear/test_rosenbrock.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_rosenbrock.c	2016-09-24 10:44:18.000000000 +0000
@@ -0,0 +1,91 @@
+#define rosenbrock_N         2
+#define rosenbrock_P         2
+
+static double rosenbrock_x0[rosenbrock_P] = { -1.2, 1.0 };
+static double rosenbrock_epsrel = 1.0e-12;
+
+static void
+rosenbrock_checksol(const double x[], const double sumsq,
+                    const double epsrel, const char *sname,
+                    const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < rosenbrock_P; ++i)
+    {
+      gsl_test_rel(x[i], 1.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+rosenbrock_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, 10.0 * (x2 - x1*x1));
+  gsl_vector_set(f, 1, 1.0 - x1);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rosenbrock_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+
+  gsl_matrix_set(J, 0, 0, -20.0*x1);
+  gsl_matrix_set(J, 0, 1, 10.0);
+  gsl_matrix_set(J, 1, 0, -1.0);
+  gsl_matrix_set(J, 1, 1, 0.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rosenbrock_fvv (const gsl_vector * x, const gsl_vector * v,
+                void *params, gsl_vector * fvv)
+{
+  double v1 = gsl_vector_get(v, 0);
+
+  gsl_vector_set(fvv, 0, -20.0 * v1 * v1);
+  gsl_vector_set(fvv, 1, 0.0);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf rosenbrock_func =
+{
+  rosenbrock_f,
+  rosenbrock_df,
+  rosenbrock_fvv,
+  rosenbrock_N,
+  rosenbrock_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem rosenbrock_problem =
+{
+  "rosenbrock",
+  rosenbrock_x0,
+  NULL,
+  NULL,
+  &rosenbrock_epsrel,
+  &rosenbrock_checksol,
+  &rosenbrock_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_rosenbrocke.c gsl-doc-2.3/multifit_nlinear/test_rosenbrocke.c
--- gsl-doc-1.16/multifit_nlinear/test_rosenbrocke.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_rosenbrocke.c	2016-09-24 10:44:23.000000000 +0000
@@ -0,0 +1,110 @@
+#define rosenbrocke_N         8 /* = p */
+#define rosenbrocke_P         8 /* must be even */
+
+static double rosenbrocke_x0[rosenbrocke_P] = { -1.2, 1.0, -1.2, 1.0,
+                                                -1.2, 1.0, -1.2, 1.0 };
+static double rosenbrocke_epsrel = 1.0e-12;
+
+static void
+rosenbrocke_checksol(const double x[], const double sumsq,
+                     const double epsrel, const char *sname,
+                     const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double rosenbrocke_x[rosenbrocke_P] = { 1.0, 1.0, 1.0, 1.0,
+                                                1.0, 1.0, 1.0, 1.0 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < rosenbrocke_P; ++i)
+    {
+      gsl_test_rel(x[i], rosenbrocke_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+rosenbrocke_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i;
+
+  for (i = 0; i < rosenbrocke_N / 2; ++i)
+    {
+      double x2i = gsl_vector_get(x, 2*i + 1);
+      double x2im1 = gsl_vector_get(x, 2*i);
+
+      gsl_vector_set(f, 2*i, 10.0 * (x2i - x2im1*x2im1));
+      gsl_vector_set(f, 2*i + 1, 1.0 - x2im1);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rosenbrocke_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  size_t i;
+
+  gsl_matrix_set_zero(J);
+
+  for (i = 0; i < rosenbrocke_N / 2; ++i)
+    {
+      double x2im1 = gsl_vector_get(x, 2*i);
+
+      gsl_matrix_set(J, 2*i, 2*i, -20.0*x2im1);
+      gsl_matrix_set(J, 2*i, 2*i + 1, 10.0);
+      gsl_matrix_set(J, 2*i + 1, 2*i, -1.0);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rosenbrocke_fvv (const gsl_vector * x, const gsl_vector * v,
+                 void *params, gsl_vector * fvv)
+{
+  size_t i;
+
+  for (i = 0; i < rosenbrocke_N / 2; ++i)
+    {
+      double v2im1 = gsl_vector_get(v, 2*i);
+
+      gsl_vector_set(fvv, 2*i, -20.0 * v2im1 * v2im1);
+      gsl_vector_set(fvv, 2*i + 1, 0.0);
+    }
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf rosenbrocke_func =
+{
+  rosenbrocke_f,
+  rosenbrocke_df,
+  rosenbrocke_fvv,
+  rosenbrocke_N,
+  rosenbrocke_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem rosenbrocke_problem =
+{
+  "rosenbrock_extended",
+  rosenbrocke_x0,
+  NULL,
+  NULL,
+  &rosenbrocke_epsrel,
+  &rosenbrocke_checksol,
+  &rosenbrocke_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_roth.c gsl-doc-2.3/multifit_nlinear/test_roth.c
--- gsl-doc-1.16/multifit_nlinear/test_roth.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_roth.c	2016-09-24 10:44:27.000000000 +0000
@@ -0,0 +1,107 @@
+#define roth_N         2
+#define roth_P         2
+
+static double roth_x0[roth_P] = { 0.5, -2.0 };
+static double roth_epsrel = 1.0e-6;
+
+static void
+roth_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact1 = 0.0;
+  const double roth_x1[roth_P] = { 5.0, 4.0 };
+  const double sumsq_exact2 = 48.9842536792400;
+  const double roth_x2[roth_P] = { 11.4127789869021, -0.896805253274477 };
+  const double *roth_x;
+  double sumsq_exact;
+
+  if (fabs(sumsq) < 0.1)
+    {
+      sumsq_exact = sumsq_exact1;
+      roth_x = roth_x1;
+    }
+  else
+    {
+      sumsq_exact = sumsq_exact2;
+      roth_x = roth_x2;
+    }
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < roth_P; ++i)
+    {
+      gsl_test_rel(x[i], roth_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+roth_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, x1 - x2*(2.0 - x2*(5.0 - x2)) - 13.0);
+  gsl_vector_set(f, 1, x1 - x2*(14.0 - x2*(1.0 + x2)) - 29.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+roth_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_matrix_set(J, 0, 0, 1.0);
+  gsl_matrix_set(J, 0, 1, -2.0 + x2*(10.0 - 3.0*x2));
+  gsl_matrix_set(J, 1, 0, 1.0);
+  gsl_matrix_set(J, 1, 1, -14.0 + x2*(2.0 + 3.0*x2));
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+roth_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  double x2 = gsl_vector_get(x, 1);
+  double v2 = gsl_vector_get(v, 1);
+
+  gsl_vector_set(fvv, 0, (10.0 - 6.0*x2) * v2 * v2);
+  gsl_vector_set(fvv, 1, (2.0 + 6.0*x2) * v2 * v2);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf roth_func =
+{
+  roth_f,
+  roth_df,
+  roth_fvv,
+  roth_N,
+  roth_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem roth_problem =
+{
+  "roth_freudenstein",
+  roth_x0,
+  NULL,
+  NULL,
+  &roth_epsrel,
+  &roth_checksol,
+  &roth_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_thurber.c gsl-doc-2.3/multifit_nlinear/test_thurber.c
--- gsl-doc-1.16/multifit_nlinear/test_thurber.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_thurber.c	2016-09-24 10:44:40.000000000 +0000
@@ -0,0 +1,151 @@
+#define thurber_N       37
+#define thurber_P       7
+
+static double thurber_x0a[thurber_P] = { 1000.0, 1000.0, 400.0, 40.0,
+                                         0.7, 0.3, 0.03 };
+static double thurber_x0b[thurber_P] = { 1300.0, 1500.0, 500.0, 75.0,
+                                         1.0, 0.4, 0.05 };
+static double thurber_epsrel = 1.0e-6;
+
+static double thurber_sigma[thurber_P] = {
+  4.6647963344E+00, 3.9571156086E+01, 2.8698696102E+01,
+  5.5675370270E+00, 3.1333340687E-02, 1.4984928198E-02,
+  6.5842344623E-03
+};
+
+static double thurber_X[thurber_N] = {
+  -3.067, -2.981, -2.921, -2.912, -2.840, -2.797, -2.702,
+  -2.699, -2.633, -2.481, -2.363, -2.322, -1.501, -1.460,
+  -1.274, -1.212, -1.100, -1.046, -0.915, -0.714, -0.566,
+  -0.545, -0.400, -0.309, -0.109, -0.103, 0.010, 0.119,
+  0.377, 0.790, 0.963, 1.006, 1.115, 1.572, 1.841,
+  2.047, 2.200
+};
+
+static double thurber_F[thurber_N] = {
+  80.574, 84.248, 87.264, 87.195, 89.076, 89.608, 89.868, 90.101,
+  92.405, 95.854, 100.696, 101.060, 401.672, 390.724, 567.534,
+  635.316, 733.054, 759.087, 894.206, 990.785, 1090.109, 1080.914,
+  1122.643, 1178.351, 1260.531, 1273.514, 1288.339, 1327.543, 1353.863,
+  1414.509, 1425.208, 1421.384, 1442.962, 1464.350, 1468.705,
+  1447.894, 1457.628
+};
+
+static void
+thurber_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 5.6427082397E+03;
+  const double thurber_x[thurber_P] = {
+    1.2881396800E+03, 1.4910792535E+03, 5.8323836877E+02,
+    7.5416644291E+01, 9.6629502864E-01, 3.9797285797E-01,
+    4.9727297349E-02 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < thurber_P; ++i)
+    {
+      gsl_test_rel(x[i], thurber_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+thurber_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[thurber_P];
+  size_t i;
+
+  for (i = 0; i < thurber_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < thurber_N; i++)
+    {
+      double xi = thurber_X[i];
+      double yi;
+
+      yi = b[0] + b[1]*xi + b[2]*xi*xi + b[3]*xi*xi*xi;
+      yi /= 1.0 + b[4]*xi + b[5]*xi*xi + b[6]*xi*xi*xi;
+
+      gsl_vector_set (f, i, yi - thurber_F[i]);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+thurber_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+  double b[thurber_P];
+  size_t i;
+
+  for (i = 0; i < thurber_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < thurber_N; i++)
+    {
+      double xi = thurber_X[i];
+      double d, n, d_sq;
+
+      n = b[0] + b[1]*xi + b[2]*xi*xi + b[3]*xi*xi*xi;
+      d = 1.0 + b[4]*xi + b[5]*xi*xi + b[6]*xi*xi*xi;
+      d_sq = d * d;
+
+      gsl_matrix_set (df, i, 0, 1.0 / d);
+      gsl_matrix_set (df, i, 1, xi / d);
+      gsl_matrix_set (df, i, 2, (xi * xi) / d);
+      gsl_matrix_set (df, i, 3, (xi * xi * xi) / d);
+      gsl_matrix_set (df, i, 4, -xi * n / d_sq);
+      gsl_matrix_set (df, i, 5, -xi * xi * n / d_sq);
+      gsl_matrix_set (df, i, 6, -xi * xi * xi * n / d_sq);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf thurber_func =
+{
+  thurber_f,
+  thurber_df,
+  NULL, /* analytic expression too complex */
+  thurber_N,
+  thurber_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem thurbera_problem =
+{
+  "nist-thurbera",
+  thurber_x0a,
+  NULL,
+  thurber_sigma,
+  &thurber_epsrel,
+  &thurber_checksol,
+  &thurber_func
+};
+
+static test_fdf_problem thurberb_problem =
+{
+  "nist-thurberb",
+  thurber_x0b,
+  NULL,
+  thurber_sigma,
+  &thurber_epsrel,
+  &thurber_checksol,
+  &thurber_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_vardim.c gsl-doc-2.3/multifit_nlinear/test_vardim.c
--- gsl-doc-1.16/multifit_nlinear/test_vardim.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_vardim.c	2016-09-24 10:44:45.000000000 +0000
@@ -0,0 +1,119 @@
+#define vardim_N         7 /* p + 2 */
+#define vardim_P         5
+
+static double vardim_x0[vardim_P] = { 0.8, 0.6, 0.4, 0.2, 0.0 };
+static double vardim_epsrel = 1.0e-12;
+
+static void
+vardim_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      gsl_test_rel(x[i], 1.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+vardim_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i;
+  double sum = 0.0;
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+
+      gsl_vector_set(f, i, xi - 1.0);
+
+      sum += (i + 1.0) * (xi - 1.0);
+    }
+
+  gsl_vector_set(f, vardim_P, sum);
+  gsl_vector_set(f, vardim_P + 1, sum*sum);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+vardim_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  size_t i;
+  double sum = 0.0;
+  gsl_matrix_view m = gsl_matrix_submatrix(J, 0, 0, vardim_P, vardim_P);
+
+  gsl_matrix_set_identity(&m.matrix);
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      sum += (i + 1.0) * (xi - 1.0);
+    }
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      gsl_matrix_set(J, vardim_P, i, i + 1.0);
+      gsl_matrix_set(J, vardim_P + 1, i, 2*(i + 1.0)*sum);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+vardim_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  size_t i;
+  double sum = 0.0;
+
+  gsl_vector_set_zero(fvv);
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      double vi = gsl_vector_get(v, i);
+      sum += (i + 1.0) * vi;
+    }
+
+  gsl_vector_set(fvv, vardim_N - 1, 2.0 * sum * sum);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf vardim_func =
+{
+  vardim_f,
+  vardim_df,
+  vardim_fvv,
+  vardim_N,
+  vardim_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem vardim_problem =
+{
+  "vardim",
+  vardim_x0,
+  NULL,
+  NULL,
+  &vardim_epsrel,
+  &vardim_checksol,
+  &vardim_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_watson.c gsl-doc-2.3/multifit_nlinear/test_watson.c
--- gsl-doc-1.16/multifit_nlinear/test_watson.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_watson.c	2016-09-24 10:44:49.000000000 +0000
@@ -0,0 +1,162 @@
+#define watson_N         31
+#define watson_P         6
+
+static double watson_x0[watson_P] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+static double watson_epsrel = 1.0e-6;
+
+static void
+watson_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 2.287670053552372e-03;
+  const double watson_x[watson_P] = {
+    -1.572508640629858e-02,  1.012434869366059e+00, -2.329916259263380e-01,
+     1.260430087686035e+00, -1.513728922580576e+00,  9.929964323646112e-01 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < watson_P; ++i)
+    {
+      gsl_test_rel(x[i], watson_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+watson_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  const double x1 = gsl_vector_get(x, 0);
+  const double x2 = gsl_vector_get(x, 1);
+  size_t i, j;
+
+  for (i = 0; i < watson_N - 2; ++i)
+    {
+      double ti = (i + 1) / 29.0;
+      double tjm1 = 1.0, tjm2 = 1.0;
+      double sum1 = 0.0, sum2 = 0.0;
+
+      for (j = 0; j < watson_P; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+
+          sum1 += xj * tjm1;
+          tjm1 *= ti;
+
+          if (j > 0)
+            {
+              sum2 += j * xj * tjm2;
+              tjm2 *= ti;
+            }
+        }
+
+      gsl_vector_set (f, i, sum2 - sum1*sum1 - 1.0);
+    }
+
+  gsl_vector_set(f, watson_N - 2, x1);
+  gsl_vector_set(f, watson_N - 1, x2 - x1*x1 - 1.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+watson_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get (x, 0);
+  size_t i, j;
+
+  gsl_matrix_set_zero(J);
+
+  for (i = 0; i < watson_N - 2; ++i)
+    {
+      double ti = (i + 1) / 29.0;
+      double tjm1 = 1.0, tjm2 = 1.0;
+      double sum1 = 0.0;
+
+      for (j = 0; j < watson_P; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+          sum1 += xj * tjm1;
+          tjm1 *= ti;
+        }
+
+      tjm1 = 1.0;
+      tjm2 = 1.0;
+      for (j = 0; j < watson_P; ++j)
+        {
+          gsl_matrix_set(J, i, j, j * tjm2 - 2.0*sum1*tjm1);
+          tjm1 *= ti;
+
+          if (j > 0)
+            tjm2 *= ti;
+        }
+    }
+
+  gsl_matrix_set(J, watson_N - 2, 0, 1.0);
+  gsl_matrix_set(J, watson_N - 1, 0, -2.0*x1);
+  gsl_matrix_set(J, watson_N - 1, 1, 1.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+watson_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  double v1 = gsl_vector_get (v, 0);
+  size_t i, j;
+
+  for (i = 0; i < watson_N - 2; ++i)
+    {
+      double ti = (i + 1) / 29.0;
+      double sum = 0.0;
+      double tjm1 = 1.0;
+
+      for (j = 0; j < watson_P; ++j)
+        {
+          double vj = gsl_vector_get(v, j);
+          sum += vj * tjm1;
+          tjm1 *= ti;
+        }
+
+      gsl_vector_set(fvv, i, -2.0*sum*sum);
+    }
+
+  gsl_vector_set(fvv, watson_N - 2, 0.0);
+  gsl_vector_set(fvv, watson_N - 1, -2.0*v1*v1);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf watson_func =
+{
+  watson_f,
+  watson_df,
+  watson_fvv,
+  watson_N,
+  watson_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem watson_problem =
+{
+  "watson",
+  watson_x0,
+  NULL,
+  NULL,
+  &watson_epsrel,
+  &watson_checksol,
+  &watson_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_wnlin.c gsl-doc-2.3/multifit_nlinear/test_wnlin.c
--- gsl-doc-1.16/multifit_nlinear/test_wnlin.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_wnlin.c	2016-09-24 10:46:01.000000000 +0000
@@ -0,0 +1,185 @@
+#define wnlin_N         40
+#define wnlin_P         3
+
+/* initial guess should be chosen so that Jacobian has full rank,
+ * or some solvers will fail */
+static double wnlin_x0[wnlin_P] = { 1.0, 0.9, 0.0 };
+static double wnlin_epsrel = 1.0e-7;
+
+static int wnlin_internal_weight = 1;
+
+/* data */
+static double wnlin_Y[wnlin_N] = {
+  6.08035e+00, 5.47552e+00, 5.94654e+00, 5.04920e+00, 4.78568e+00,
+  3.51748e+00, 2.84671e+00, 3.24634e+00, 3.23395e+00, 3.30385e+00,
+  2.83439e+00, 2.31891e+00, 2.33858e+00, 2.40559e+00, 2.41856e+00,
+  1.99966e+00, 1.88127e+00, 1.91477e+00, 1.70415e+00, 1.60316e+00,
+  1.77937e+00, 1.55302e+00, 1.50903e+00, 1.36364e+00, 1.36873e+00,
+  1.41954e+00, 1.37778e+00, 1.23573e+00, 1.28524e+00, 1.46327e+00,
+  1.22315e+00, 1.19330e+00, 1.18717e+00, 8.83172e-01, 1.23424e+00,
+  1.14683e+00, 1.11091e+00, 1.20396e+00, 1.28722e+00, 1.05801e+00
+};
+
+/* weights */
+static double wnlin_W[wnlin_N] = {
+  2.77778e+00, 3.27690e+00, 3.85426e+00, 4.51906e+00, 5.28083e+00,
+  6.14919e+00, 7.13370e+00, 8.24349e+00, 9.48703e+00, 1.08717e+01,
+  1.24036e+01, 1.40869e+01, 1.59238e+01, 1.79142e+01, 2.00553e+01,
+  2.23415e+01, 2.47646e+01, 2.73137e+01, 2.99753e+01, 3.27337e+01,
+  3.55714e+01, 3.84696e+01, 4.14085e+01, 4.43678e+01, 4.73278e+01,
+  5.02690e+01, 5.31731e+01, 5.60234e+01, 5.88046e+01, 6.15036e+01,
+  6.41092e+01, 6.66121e+01, 6.90054e+01, 7.12839e+01, 7.34442e+01,
+  7.54848e+01, 7.74053e+01, 7.92069e+01, 8.08918e+01, 8.24632e+01
+};
+
+static void
+wnlin_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 29.7481259665713758;
+  const double wnlin_x[wnlin_P] = { 5.17378551196259195,
+                                    0.111041758006851149,
+                                    1.05282724070446099 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < wnlin_P; ++i)
+    {
+      gsl_test_rel(x[i], wnlin_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+wnlin_f (const gsl_vector *x, void *params, gsl_vector *f)
+{
+  int *iptr = (int *) params;
+  int doweight = iptr ? *iptr : 0;
+  double A = gsl_vector_get (x, 0);
+  double lambda = gsl_vector_get (x, 1);
+  double b = gsl_vector_get (x, 2);
+  size_t i;
+
+  /* model Yi = A * exp(-lambda * i) + b */
+  for (i = 0; i < wnlin_N; i++)
+    {
+      double ti = i;
+      double yi = wnlin_Y[i];
+      double swi = sqrt(wnlin_W[i]);
+      double Mi = A * exp (-lambda * ti) + b;
+
+      if (doweight)
+        gsl_vector_set (f, i, swi * (Mi - yi));
+      else
+        gsl_vector_set (f, i, Mi - yi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+wnlin_df (const gsl_vector *x, void *params, gsl_matrix *df)
+{
+  int *iptr = (int *) params;
+  int doweight = iptr ? *iptr : 0;
+  double A = gsl_vector_get (x, 0);
+  double lambda = gsl_vector_get (x, 1);
+  size_t i;
+
+  for (i = 0; i < wnlin_N; i++)
+    {
+      gsl_vector_view v = gsl_matrix_row(df, i);
+      double ti = i;
+      double swi = sqrt(wnlin_W[i]);
+      double e = exp(-lambda * ti);
+
+      gsl_vector_set(&v.vector, 0, e);
+      gsl_vector_set(&v.vector, 1, -ti * A * e);
+      gsl_vector_set(&v.vector, 2, 1.0);
+
+      if (doweight)
+        gsl_vector_scale(&v.vector, swi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+wnlin_fvv (const gsl_vector * x, const gsl_vector * v,
+           void *params, gsl_vector * fvv)
+{
+  int *iptr = (int *) params;
+  int doweight = iptr ? *iptr : 0;
+  double A = gsl_vector_get (x, 0);
+  double lambda = gsl_vector_get (x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  size_t i;
+
+  for (i = 0; i < wnlin_N; i++)
+    {
+      double ti = i;
+      double swi = sqrt(wnlin_W[i]);
+      double fvvi;
+
+      fvvi = exp(-ti*lambda)*ti*v2 * (-2*v1 + ti*v2*A);
+
+      if (doweight)
+        gsl_vector_set(fvv, i, swi * fvvi);
+      else
+        gsl_vector_set(fvv, i, fvvi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf wnlin_func1 =
+{
+  wnlin_f,
+  wnlin_df,
+  wnlin_fvv,
+  wnlin_N,
+  wnlin_P,
+  (void *) &wnlin_internal_weight,
+  0,
+  0,
+  0
+};
+
+static gsl_multifit_nlinear_fdf wnlin_func2 =
+{
+  wnlin_f,
+  wnlin_df,
+  wnlin_fvv,
+  wnlin_N,
+  wnlin_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem wnlin_problem1 =
+{
+  "wnlin_internal_weights",
+  wnlin_x0,
+  NULL,
+  NULL,
+  &wnlin_epsrel,
+  &wnlin_checksol,
+  &wnlin_func1
+};
+
+static test_fdf_problem wnlin_problem2 =
+{
+  "wnlin_external_weights",
+  wnlin_x0,
+  wnlin_W,
+  NULL,
+  &wnlin_epsrel,
+  &wnlin_checksol,
+  &wnlin_func2
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/test_wood.c gsl-doc-2.3/multifit_nlinear/test_wood.c
--- gsl-doc-1.16/multifit_nlinear/test_wood.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/test_wood.c	2016-09-24 10:46:07.000000000 +0000
@@ -0,0 +1,115 @@
+#define wood_N         6
+#define wood_P         4
+
+static double wood_x0[wood_P] = { -3.0, -1.0, -3.0, -1.0 };
+static double wood_epsrel = 1.0e-12;
+
+static void
+wood_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double wood_x[wood_P] = { 1.0, 1.0, 1.0, 1.0 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < wood_P; ++i)
+    {
+      gsl_test_rel(x[i], wood_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+wood_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+
+  gsl_vector_set(f, 0, 10.0*(x2 - x1*x1));
+  gsl_vector_set(f, 1, 1.0 - x1);
+  gsl_vector_set(f, 2, sqrt(90.0)*(x4 - x3*x3));
+  gsl_vector_set(f, 3, 1.0 - x3);
+  gsl_vector_set(f, 4, sqrt(10.0)*(x2 + x4 - 2.0));
+  gsl_vector_set(f, 5, (x2 - x4) / sqrt(10.0));
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+wood_df (const gsl_vector * x, void *params, gsl_matrix * J)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x3 = gsl_vector_get(x, 2);
+  double s90 = sqrt(90.0);
+  double s10 = sqrt(10.0);
+
+  gsl_matrix_set_zero(J);
+
+  gsl_matrix_set(J, 0, 0, -20.0*x1);
+  gsl_matrix_set(J, 0, 1, 10.0);
+  gsl_matrix_set(J, 1, 0, -1.0);
+  gsl_matrix_set(J, 2, 2, -2.0*s90*x3);
+  gsl_matrix_set(J, 2, 3, s90);
+  gsl_matrix_set(J, 3, 2, -1.0);
+  gsl_matrix_set(J, 4, 1, s10);
+  gsl_matrix_set(J, 4, 3, s10);
+  gsl_matrix_set(J, 5, 1, 1.0/s10);
+  gsl_matrix_set(J, 5, 3, -1.0/s10);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+wood_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  const double s10 = sqrt(10.0);
+  double v1 = gsl_vector_get(v, 0);
+  double v3 = gsl_vector_get(v, 2);
+
+  gsl_vector_set(fvv, 0, -20.0 * v1 * v1);
+  gsl_vector_set(fvv, 1, 0.0);
+  gsl_vector_set(fvv, 2, -6.0 * s10 * v3 * v3);
+  gsl_vector_set(fvv, 3, 0.0);
+  gsl_vector_set(fvv, 4, 0.0);
+  gsl_vector_set(fvv, 5, 0.0);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multifit_nlinear_fdf wood_func =
+{
+  wood_f,
+  wood_df,
+  wood_fvv,
+  wood_N,
+  wood_P,
+  NULL,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem wood_problem =
+{
+  "wood",
+  wood_x0,
+  NULL,
+  NULL,
+  &wood_epsrel,
+  &wood_checksol,
+  &wood_func
+};
diff -Nru gsl-doc-1.16/multifit_nlinear/TODO gsl-doc-2.3/multifit_nlinear/TODO
--- gsl-doc-1.16/multifit_nlinear/TODO	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/TODO	2016-10-03 09:30:38.000000000 +0000
@@ -0,0 +1,6 @@
+1. rewrite qrsolv (COD, test on lin2)
+2. More/Sorensen method for mu calculation
+3. better condition estimate for svd
+4. Revisit h_fvv = 0.01 vs 0.02 (originally 0.01)
+5. fdfvv test currently disabled in test_fdf.c - on MacOS, the lmaccel/box3d/fdfvv test fails
+6. Tikhonov regularization
diff -Nru gsl-doc-1.16/multifit_nlinear/trust.c gsl-doc-2.3/multifit_nlinear/trust.c
--- gsl-doc-1.16/multifit_nlinear/trust.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multifit_nlinear/trust.c	2016-09-08 18:00:52.000000000 +0000
@@ -0,0 +1,563 @@
+/* multifit_nlinear/trust.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multifit_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_permutation.h>
+
+#include "common.c"
+#include "nielsen.c"
+
+/*
+ * This module contains a high level driver for a general trust
+ * region nonlinear least squares solver. This container handles
+ * the computation of all of the quantities relevant to all trust
+ * region methods, including:
+ *
+ * residual vector: f_k = f(x_k)
+ * Jacobian matrix: J_k = J(x_k)
+ * gradient vector: g_k = J_k^T f_k
+ * scaling matrix:  D_k
+ */
+
+typedef struct
+{
+  size_t n;                  /* number of observations */
+  size_t p;                  /* number of parameters */
+  double delta;              /* trust region radius */
+  double mu;                 /* LM parameter */
+  long nu;                   /* for updating LM parameter */
+  gsl_vector *diag;          /* D = diag(J^T J) */
+  gsl_vector *x_trial;       /* trial parameter vector */
+  gsl_vector *f_trial;       /* trial function vector */
+  gsl_vector *workp;         /* workspace, length p */
+  gsl_vector *workn;         /* workspace, length n */
+
+  void *trs_state;           /* workspace for trust region subproblem */
+  void *solver_state;        /* workspace for linear least squares solver */
+
+  double avratio;            /* current |a| / |v| */
+
+  /* tunable parameters */
+  gsl_multifit_nlinear_parameters params;
+} trust_state_t;
+
+static void * trust_alloc (const gsl_multifit_nlinear_parameters * params,
+                           const size_t n, const size_t p);
+static void trust_free(void *vstate);
+static int trust_init(void *vstate, const gsl_vector * swts,
+                      gsl_multifit_nlinear_fdf *fdf, const gsl_vector *x,
+                      gsl_vector *f, gsl_matrix *J, gsl_vector *g);
+static int trust_iterate(void *vstate, const gsl_vector *swts,
+                         gsl_multifit_nlinear_fdf *fdf,
+                         gsl_vector *x, gsl_vector *f, gsl_matrix *J,
+                         gsl_vector *g, gsl_vector *dx);
+static int trust_rcond(double *rcond, void *vstate);
+static double trust_avratio(void *vstate);
+static void trust_trial_step(const gsl_vector * x, const gsl_vector * dx,
+                             gsl_vector * x_trial);
+static double trust_calc_rho(const gsl_vector * f, const gsl_vector * f_trial,
+                             const gsl_vector * g, const gsl_matrix * J,
+                             const gsl_vector * dx, trust_state_t * state);
+static int trust_eval_step(const gsl_vector * f, const gsl_vector * f_trial,
+                           const gsl_vector * g, const gsl_matrix * J,
+                           const gsl_vector * dx, double * rho, trust_state_t * state);
+static double trust_scaled_norm(const gsl_vector *D, const gsl_vector *a);
+
+static void *
+trust_alloc (const gsl_multifit_nlinear_parameters * params,
+             const size_t n, const size_t p)
+{
+  trust_state_t *state;
+  
+  state = calloc(1, sizeof(trust_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate lm state", GSL_ENOMEM);
+    }
+
+  state->diag = gsl_vector_alloc(p);
+  if (state->diag == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for diag", GSL_ENOMEM);
+    }
+
+  state->workp = gsl_vector_alloc(p);
+  if (state->workp == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workp", GSL_ENOMEM);
+    }
+
+  state->workn = gsl_vector_alloc(n);
+  if (state->workn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workn", GSL_ENOMEM);
+    }
+
+  state->x_trial = gsl_vector_alloc(p);
+  if (state->x_trial == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for x_trial", GSL_ENOMEM);
+    }
+
+  state->f_trial = gsl_vector_alloc(n);
+  if (state->f_trial == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for f_trial", GSL_ENOMEM);
+    }
+
+  state->trs_state = (params->trs->alloc)(params, n, p);
+  if (state->trs_state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for trs state", GSL_ENOMEM);
+    }
+
+  state->solver_state = (params->solver->alloc)(n, p);
+  if (state->solver_state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for solver state", GSL_ENOMEM);
+    }
+
+  state->n = n;
+  state->p = p;
+  state->delta = 0.0;
+  state->params = *params;
+
+  return state;
+}
+
+static void
+trust_free(void *vstate)
+{
+  trust_state_t *state = (trust_state_t *) vstate;
+  const gsl_multifit_nlinear_parameters *params = &(state->params);
+
+  if (state->diag)
+    gsl_vector_free(state->diag);
+
+  if (state->workp)
+    gsl_vector_free(state->workp);
+
+  if (state->workn)
+    gsl_vector_free(state->workn);
+
+  if (state->x_trial)
+    gsl_vector_free(state->x_trial);
+
+  if (state->f_trial)
+    gsl_vector_free(state->f_trial);
+
+  if (state->trs_state)
+    (params->trs->free)(state->trs_state);
+
+  if (state->solver_state)
+    (params->solver->free)(state->solver_state);
+
+  free(state);
+}
+
+/*
+trust_init()
+  Initialize trust region solver
+
+Inputs: vstate - workspace
+        swts   - sqrt(W) vector
+        fdf    - user callback functions
+        x      - initial parameter values
+        f      - (output) f(x) vector
+        J      - (output) J(x) matrix
+        g      - (output) J(x)' f(x) vector
+
+Return: success/error
+*/
+
+static int
+trust_init(void *vstate, const gsl_vector *swts,
+           gsl_multifit_nlinear_fdf *fdf, const gsl_vector *x,
+           gsl_vector *f, gsl_matrix *J, gsl_vector *g)
+{
+  int status;
+  trust_state_t *state = (trust_state_t *) vstate;
+  const gsl_multifit_nlinear_parameters *params = &(state->params);
+  double Dx;
+
+  /* evaluate function and Jacobian at x and apply weight transform */
+  status = gsl_multifit_nlinear_eval_f(fdf, x, swts, f);
+  if (status)
+   return status;
+
+  status = gsl_multifit_nlinear_eval_df(x, f, swts, params->h_df,
+                                        params->fdtype, fdf, J, state->workn);
+  if (status)
+    return status;
+
+  /* compute g = J^T f */
+  gsl_blas_dgemv(CblasTrans, 1.0, J, f, 0.0, g);
+
+  /* initialize diagonal scaling matrix D */
+  (params->scale->init)(J, state->diag);
+
+  /* compute initial trust region radius */
+  Dx = trust_scaled_norm(state->diag, x);
+  state->delta = 0.3 * GSL_MAX(1.0, Dx);
+
+  /* initialize LM parameter */
+  status = nielsen_init(J, state->diag, &(state->mu), &(state->nu));
+  if (status)
+    return status;
+
+  /* initialize trust region method solver */
+  {
+    const gsl_multifit_nlinear_trust_state trust_state = { x, f, g, J, state->diag,
+                                                           swts, &(state->mu), params,
+                                                           state->solver_state, fdf,
+                                                           &(state->avratio) };
+
+    status = (params->trs->init)(&trust_state, state->trs_state);
+
+    if (status)
+      return status;
+  }
+
+  /* set default parameters */
+
+  state->avratio = 0.0;
+
+  return GSL_SUCCESS;
+}
+
+/*
+trust_iterate()
+  This function performs 1 iteration of the trust region algorithm.
+It calls a user-specified method for computing the next step
+(LM or dogleg), then tests if the computed step is acceptable.
+
+Args: vstate - trust workspace
+      swts   - data weights (NULL if unweighted)
+      fdf    - function and Jacobian pointers
+      x      - on input, current parameter vector
+               on output, new parameter vector x + dx
+      f      - on input, f(x)
+               on output, f(x + dx)
+      J      - on input, J(x)
+               on output, J(x + dx)
+      g      - on input, g(x) = J(x)' f(x)
+               on output, g(x + dx) = J(x + dx)' f(x + dx)
+      dx     - (output only) parameter step vector
+
+Return:
+1) GSL_SUCCESS if we found a step which reduces the cost
+function
+
+2) GSL_ENOPROG if 15 successive attempts were to made to
+find a good step without success
+
+3) If a scaling matrix D is used, inputs and outputs are
+set to the unscaled quantities (ie: J and g)
+*/
+
+static int
+trust_iterate(void *vstate, const gsl_vector *swts,
+              gsl_multifit_nlinear_fdf *fdf, gsl_vector *x,
+              gsl_vector *f, gsl_matrix *J, gsl_vector *g,
+              gsl_vector *dx)
+{
+  int status;
+  trust_state_t *state = (trust_state_t *) vstate;
+  const gsl_multifit_nlinear_parameters *params = &(state->params);
+  const gsl_multifit_nlinear_trs *trs = params->trs;
+
+  /* collect all state parameters needed by low level methods */
+  const gsl_multifit_nlinear_trust_state trust_state = { x, f, g, J, state->diag,
+                                                         swts, &(state->mu), params,
+                                                         state->solver_state, fdf,
+                                                         &(state->avratio) };
+
+  gsl_vector *x_trial = state->x_trial;       /* trial x + dx */
+  gsl_vector *f_trial = state->f_trial;       /* trial f(x + dx) */
+  gsl_vector *diag = state->diag;             /* diag(D) */
+  double rho;                                 /* ratio actual_reduction/predicted_reduction */
+  int foundstep = 0;                          /* found step dx */
+  int bad_steps = 0;                          /* consecutive rejected steps */
+
+  /* initialize trust region subproblem with this Jacobian */
+  status = (trs->preloop)(&trust_state, state->trs_state);
+  if (status)
+    return status;
+
+  /* loop until we find an acceptable step dx */
+  while (!foundstep)
+    {
+      /* calculate new step */
+      status = (trs->step)(&trust_state, state->delta, dx, state->trs_state);
+
+      /* occasionally the iterative methods (ie: CG Steihaug) can fail to find a step,
+       * so in this case skip rho calculation and count it as a rejected step */
+
+      if (status == GSL_SUCCESS)
+        {
+          /* compute x_trial = x + dx */
+          trust_trial_step(x, dx, x_trial);
+
+          /* compute f_trial = f(x + dx) */
+          status = gsl_multifit_nlinear_eval_f(fdf, x_trial, swts, f_trial);
+          if (status)
+            return status;
+
+          /* check if step should be accepted or rejected */
+          status = trust_eval_step(f, f_trial, g, J, dx, &rho, state);
+          if (status == GSL_SUCCESS)
+            foundstep = 1;
+        }
+      else
+        {
+          /* an iterative TRS method failed to find a step vector */
+          rho = -1.0;
+        }
+
+      /*
+       * update trust region radius: if rho is large,
+       * then the quadratic model is a good approximation
+       * to the objective function, enlarge trust region.
+       * If rho is small (or negative), the model function
+       * is a poor approximation so decrease trust region. This
+       * can happen even if the step is accepted.
+       */
+      if (rho > 0.75)
+        state->delta *= params->factor_up;
+      else if (rho < 0.25)
+        state->delta /= params->factor_down;
+
+      if (foundstep)
+        {
+          /* step was accepted */
+
+          /* compute J <- J(x + dx) */
+          status = gsl_multifit_nlinear_eval_df(x_trial, f_trial, swts,
+                                                params->h_df, params->fdtype,
+                                                fdf, J, state->workn);
+          if (status)
+            return status;
+
+          /* update x <- x + dx */
+          gsl_vector_memcpy(x, x_trial);
+
+          /* update f <- f(x + dx) */
+          gsl_vector_memcpy(f, f_trial);
+
+          /* compute new g = J^T f */
+          gsl_blas_dgemv(CblasTrans, 1.0, J, f, 0.0, g);
+
+          /* update scaling matrix D */
+          (params->scale->update)(J, diag);
+
+          /* step accepted, decrease LM parameter */
+          status = nielsen_accept(rho, &(state->mu), &(state->nu));
+          if (status)
+            return status;
+
+          bad_steps = 0;
+        }
+      else
+        {
+          /* step rejected, increase LM parameter */
+          status = nielsen_reject(&(state->mu), &(state->nu));
+          if (status)
+            return status;
+
+          if (++bad_steps > 15)
+            {
+              /* if more than 15 consecutive rejected steps, report no progress */
+              return GSL_ENOPROG;
+            }
+        }
+    }
+
+  return GSL_SUCCESS;
+} /* trust_iterate() */
+
+static int
+trust_rcond(double *rcond, void *vstate)
+{
+  int status;
+  trust_state_t *state = (trust_state_t *) vstate;
+  const gsl_multifit_nlinear_parameters *params = &(state->params);
+  
+  status = (params->solver->rcond)(rcond, state->solver_state);
+
+  return status;
+}
+
+static double
+trust_avratio(void *vstate)
+{
+  trust_state_t *state = (trust_state_t *) vstate;
+  return state->avratio;
+}
+
+/* compute x_trial = x + dx */
+static void
+trust_trial_step(const gsl_vector * x, const gsl_vector * dx,
+                 gsl_vector * x_trial)
+{
+  size_t i, N = x->size;
+
+  for (i = 0; i < N; i++)
+    {
+      double dxi = gsl_vector_get (dx, i);
+      double xi = gsl_vector_get (x, i);
+      gsl_vector_set (x_trial, i, xi + dxi);
+    }
+}
+
+/*
+trust_calc_rho()
+  Calculate ratio of actual reduction to predicted
+reduction.
+
+rho = actual_reduction / predicted_reduction
+
+actual_reduction = 1 - ( ||f+|| / ||f|| )^2
+predicted_reduction = -2 g^T dx / ||f||^2 - ( ||J*dx|| / ||f|| )^2
+                    = -2 fhat . beta - ||beta||^2
+
+where: beta = J*dx / ||f||
+
+Inputs: f        - f(x)
+        f_trial  - f(x + dx)
+        g        - gradient J^T f
+        J        - Jacobian
+        dx       - proposed step, size p
+        state    - workspace
+
+Return: rho = actual_reduction / predicted_reduction
+If actual_reduction is < 0, return rho = -1
+*/
+
+static double
+trust_calc_rho(const gsl_vector * f, const gsl_vector * f_trial,
+               const gsl_vector * g, const gsl_matrix * J,
+               const gsl_vector * dx, trust_state_t * state)
+{
+  int status;
+  const gsl_multifit_nlinear_parameters *params = &(state->params);
+  const gsl_multifit_nlinear_trs *trs = params->trs;
+  const gsl_multifit_nlinear_trust_state trust_state = { NULL, f, g, J, state->diag,
+                                                         NULL, &(state->mu), params,
+                                                         state->solver_state, NULL,
+                                                         &(state->avratio) };
+  const double normf = gsl_blas_dnrm2(f);
+  const double normf_trial = gsl_blas_dnrm2(f_trial);
+  double rho;
+  double actual_reduction;
+  double pred_reduction;
+  double u;
+
+  /* if ||f(x+dx)|| > ||f(x)|| reject step immediately */
+  if (normf_trial >= normf)
+    return -1.0;
+
+  /* compute numerator of rho (actual reduction) */
+  u = normf_trial / normf;
+  actual_reduction = 1.0 - u*u;
+
+  /*
+   * compute denominator of rho (predicted reduction); this is calculated
+   * inside each trust region subproblem, since it depends on the local
+   * model used, which can vary according to each TRS
+   */
+  status = (trs->preduction)(&trust_state, dx, &pred_reduction, state->trs_state);
+  if (status)
+    return -1.0;
+
+  if (pred_reduction > 0.0)
+    rho = actual_reduction / pred_reduction;
+  else
+    rho = -1.0;
+
+  return rho;
+}
+
+/*
+trust_eval_step()
+  Evaluate proposed step to determine if it should be
+accepted or rejected
+*/
+
+static int
+trust_eval_step(const gsl_vector * f, const gsl_vector * f_trial,
+                const gsl_vector * g, const gsl_matrix * J,
+                const gsl_vector * dx, double * rho, trust_state_t * state)
+{
+  int status = GSL_SUCCESS;
+  const gsl_multifit_nlinear_parameters *params = &(state->params);
+
+  if (params->trs == gsl_multifit_nlinear_trs_lmaccel)
+    {
+      /* reject step if acceleration is too large compared to velocity */
+      if (state->avratio > params->avmax)
+        status = GSL_FAILURE;
+    }
+
+  /* compute rho */
+  *rho = trust_calc_rho(f, f_trial, g, J, dx, state);
+  if (*rho <= 0.0)
+    status = GSL_FAILURE;
+
+  return status;
+}
+
+/* compute || diag(D) a || */
+static double
+trust_scaled_norm(const gsl_vector *D, const gsl_vector *a)
+{
+  const size_t n = a->size;
+  double e2 = 0.0;
+  size_t i;
+
+  for (i = 0; i < n; ++i)
+    {
+      double Di = gsl_vector_get(D, i);
+      double ai = gsl_vector_get(a, i);
+      double u = Di * ai;
+
+      e2 += u * u;
+    }
+
+  return sqrt (e2);
+}
+
+static const gsl_multifit_nlinear_type trust_type =
+{
+  "trust-region",
+  trust_alloc,
+  trust_init,
+  trust_iterate,
+  trust_rcond,
+  trust_avratio,
+  trust_free
+};
+
+const gsl_multifit_nlinear_type *gsl_multifit_nlinear_trust = &trust_type;
diff -Nru gsl-doc-1.16/multilarge/gsl_multilarge.h gsl-doc-2.3/multilarge/gsl_multilarge.h
--- gsl-doc-1.16/multilarge/gsl_multilarge.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge/gsl_multilarge.h	2016-02-11 17:38:04.000000000 +0000
@@ -0,0 +1,141 @@
+/* gsl_multilarge.h
+ * 
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_MULTILARGE_H__
+#define __GSL_MULTILARGE_H__
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_types.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+/* iteration solver type */
+typedef struct
+{
+  const char *name;
+  void * (*alloc) (const size_t p);
+  int (*reset) (void *);
+  int (*accumulate) (gsl_matrix * X, gsl_vector * y,
+                     void *);
+  int (*solve) (const double lambda, gsl_vector * c,
+                double * rnorm, double * snorm, void *);
+  int (*rcond) (double * rcond, void *);
+  int (*lcurve) (gsl_vector * reg_param, gsl_vector * rho,
+                 gsl_vector * eta, void *);
+  void (*free) (void *);
+} gsl_multilarge_linear_type;
+
+typedef struct
+{
+  const gsl_multilarge_linear_type * type;
+  void * state;
+  size_t p;
+} gsl_multilarge_linear_workspace;
+
+/* available types */
+GSL_VAR const gsl_multilarge_linear_type * gsl_multilarge_linear_normal;
+GSL_VAR const gsl_multilarge_linear_type * gsl_multilarge_linear_tsqr;
+
+/*
+ * Prototypes
+ */
+gsl_multilarge_linear_workspace *
+gsl_multilarge_linear_alloc(const gsl_multilarge_linear_type * T,
+                            const size_t p);
+
+void gsl_multilarge_linear_free(gsl_multilarge_linear_workspace * w);
+
+const char *gsl_multilarge_linear_name(const gsl_multilarge_linear_workspace * w);
+
+int gsl_multilarge_linear_reset(gsl_multilarge_linear_workspace * w);
+
+int gsl_multilarge_linear_accumulate(gsl_matrix * X,
+                                     gsl_vector * y,
+                                     gsl_multilarge_linear_workspace * w);
+
+int gsl_multilarge_linear_solve(const double lambda, gsl_vector * c,
+                                double * rnorm, double * snorm,
+                                gsl_multilarge_linear_workspace * w);
+
+int gsl_multilarge_linear_rcond(double *rcond, gsl_multilarge_linear_workspace * w);
+
+int gsl_multilarge_linear_lcurve(gsl_vector * reg_param, gsl_vector * rho,
+                                 gsl_vector * eta,
+                                 gsl_multilarge_linear_workspace * w);
+
+int gsl_multilarge_linear_wstdform1 (const gsl_vector * L,
+                                     const gsl_matrix * X,
+                                     const gsl_vector * w,
+                                     const gsl_vector * y,
+                                     gsl_matrix * Xs,
+                                     gsl_vector * ys,
+                                     gsl_multilarge_linear_workspace * work);
+
+int gsl_multilarge_linear_stdform1 (const gsl_vector * L,
+                                    const gsl_matrix * X,
+                                    const gsl_vector * y,
+                                    gsl_matrix * Xs,
+                                    gsl_vector * ys,
+                                    gsl_multilarge_linear_workspace * work);
+
+int gsl_multilarge_linear_L_decomp (gsl_matrix * L, gsl_vector * tau);
+
+int gsl_multilarge_linear_wstdform2 (const gsl_matrix * LQR,
+                                     const gsl_vector * Ltau,
+                                     const gsl_matrix * X,
+                                     const gsl_vector * w,
+                                     const gsl_vector * y,
+                                     gsl_matrix * Xs,
+                                     gsl_vector * ys,
+                                     gsl_multilarge_linear_workspace * work);
+
+int gsl_multilarge_linear_stdform2 (const gsl_matrix * LQR,
+                                    const gsl_vector * Ltau,
+                                    const gsl_matrix * X,
+                                    const gsl_vector * y,
+                                    gsl_matrix * Xs,
+                                    gsl_vector * ys,
+                                    gsl_multilarge_linear_workspace * work);
+
+int gsl_multilarge_linear_genform1 (const gsl_vector * L,
+                                    const gsl_vector * cs,
+                                    gsl_vector * c,
+                                    gsl_multilarge_linear_workspace * work);
+
+int gsl_multilarge_linear_genform2 (const gsl_matrix * LQR,
+                                    const gsl_vector * Ltau,
+                                    const gsl_vector * cs,
+                                    gsl_vector * c,
+                                    gsl_multilarge_linear_workspace * work);
+
+__END_DECLS
+
+#endif /* __GSL_MULTILARGE_H__ */
diff -Nru gsl-doc-1.16/multilarge/Makefile.am gsl-doc-2.3/multilarge/Makefile.am
--- gsl-doc-1.16/multilarge/Makefile.am	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge/Makefile.am	2016-10-27 11:20:46.000000000 +0000
@@ -0,0 +1,14 @@
+noinst_LTLIBRARIES = libgslmultilarge.la 
+
+pkginclude_HEADERS = gsl_multilarge.h
+
+libgslmultilarge_la_SOURCES = multilarge.c normal.c tsqr.c
+
+AM_CPPFLAGS = -I$(top_srcdir)
+
+check_PROGRAMS = test
+
+TESTS = $(check_PROGRAMS)
+
+test_SOURCES = test.c
+test_LDADD = libgslmultilarge.la ../test/libgsltest.la ../multifit/libgslmultifit.la ../eigen/libgsleigen.la ../linalg/libgsllinalg.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../permutation/libgslpermutation.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la  ../sys/libgslsys.la ../utils/libutils.la ../rng/libgslrng.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../complex/libgslcomplex.la ../min/libgslmin.la
diff -Nru gsl-doc-1.16/multilarge/Makefile.in gsl-doc-2.3/multilarge/Makefile.in
--- gsl-doc-1.16/multilarge/Makefile.in	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -0,0 +1,1032 @@
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+# with or without modifications, as long as this notice is preserved.
+
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+	  success=false; \
+	fi; \
+	br='==================='; br=$$br$$br$$br$$br; \
+	result_count () \
+	{ \
+	    if test x"$$1" = x"--maybe-color"; then \
+	      maybe_colorize=yes; \
+	    elif test x"$$1" = x"--no-color"; then \
+	      maybe_colorize=no; \
+	    else \
+	      echo "$@: invalid 'result_count' usage" >&2; exit 4; \
+	    fi; \
+	    shift; \
+	    desc=$$1 count=$$2; \
+	    if test $$maybe_colorize = yes && test $$count -gt 0; then \
+	      color_start=$$3 color_end=$$std; \
+	    else \
+	      color_start= color_end=; \
+	    fi; \
+	    echo "$${color_start}# $$desc $$count$${color_end}"; \
+	}; \
+	create_testsuite_report () \
+	{ \
+	  result_count $$1 "TOTAL:" $$all   "$$brg"; \
+	  result_count $$1 "PASS: " $$pass  "$$grn"; \
+	  result_count $$1 "SKIP: " $$skip  "$$blu"; \
+	  result_count $$1 "XFAIL:" $$xfail "$$lgn"; \
+	  result_count $$1 "FAIL: " $$fail  "$$red"; \
+	  result_count $$1 "XPASS:" $$xpass "$$red"; \
+	  result_count $$1 "ERROR:" $$error "$$mgn"; \
+	}; \
+	{								\
+	  echo "$(PACKAGE_STRING): $(subdir)/$(TEST_SUITE_LOG)" |	\
+	    $(am__rst_title);						\
+	  create_testsuite_report --no-color;				\
+	  echo;								\
+	  echo ".. contents:: :depth: 2";				\
+	  echo;								\
+	  for b in $$bases; do echo $$b; done				\
+	    | $(am__create_global_log);					\
+	} >$(TEST_SUITE_LOG).tmp || exit 1;				\
+	mv $(TEST_SUITE_LOG).tmp $(TEST_SUITE_LOG);			\
+	if $$success; then						\
+	  col="$$grn";							\
+	 else								\
+	  col="$$red";							\
+	  test x"$$VERBOSE" = x || cat $(TEST_SUITE_LOG);		\
+	fi;								\
+	echo "$${col}$$br$${std}"; 					\
+	echo "$${col}Testsuite summary for $(PACKAGE_STRING)$${std}";	\
+	echo "$${col}$$br$${std}"; 					\
+	create_testsuite_report --maybe-color;				\
+	echo "$$col$$br$$std";						\
+	if $$success; then :; else					\
+	  echo "$${col}See $(subdir)/$(TEST_SUITE_LOG)$${std}";		\
+	  if test -n "$(PACKAGE_BUGREPORT)"; then			\
+	    echo "$${col}Please report to $(PACKAGE_BUGREPORT)$${std}";	\
+	  fi;								\
+	  echo "$$col$$br$$std";					\
+	fi;								\
+	$$success || exit 1
+
+check-TESTS:
+	@list='$(RECHECK_LOGS)';           test -z "$$list" || rm -f $$list
+	@list='$(RECHECK_LOGS:.log=.trs)'; test -z "$$list" || rm -f $$list
+	@test -z "$(TEST_SUITE_LOG)" || rm -f $(TEST_SUITE_LOG)
+	@set +e; $(am__set_TESTS_bases); \
+	log_list=`for i in $$bases; do echo $$i.log; done`; \
+	trs_list=`for i in $$bases; do echo $$i.trs; done`; \
+	log_list=`echo $$log_list`; trs_list=`echo $$trs_list`; \
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+	exit $$?;
+recheck: all $(check_PROGRAMS)
+	@test -z "$(TEST_SUITE_LOG)" || rm -f $(TEST_SUITE_LOG)
+	@set +e; $(am__set_TESTS_bases); \
+	bases=`for i in $$bases; do echo $$i; done \
+	         | $(am__list_recheck_tests)` || exit 1; \
+	log_list=`for i in $$bases; do echo $$i.log; done`; \
+	log_list=`echo $$log_list`; \
+	$(MAKE) $(AM_MAKEFLAGS) $(TEST_SUITE_LOG) \
+	        am__force_recheck=am--force-recheck \
+	        TEST_LOGS="$$log_list"; \
+	exit $$?
+test.log: test$(EXEEXT)
+	@p='test$(EXEEXT)'; \
+	b='test'; \
+	$(am__check_pre) $(LOG_DRIVER) --test-name "$$f" \
+	--log-file $$b.log --trs-file $$b.trs \
+	$(am__common_driver_flags) $(AM_LOG_DRIVER_FLAGS) $(LOG_DRIVER_FLAGS) -- $(LOG_COMPILE) \
+	"$$tst" $(AM_TESTS_FD_REDIRECT)
+.test.log:
+	@p='$<'; \
+	$(am__set_b); \
+	$(am__check_pre) $(TEST_LOG_DRIVER) --test-name "$$f" \
+	--log-file $$b.log --trs-file $$b.trs \
+	$(am__common_driver_flags) $(AM_TEST_LOG_DRIVER_FLAGS) $(TEST_LOG_DRIVER_FLAGS) -- $(TEST_LOG_COMPILE) \
+	"$$tst" $(AM_TESTS_FD_REDIRECT)
+@am__EXEEXT_TRUE@.test$(EXEEXT).log:
+@am__EXEEXT_TRUE@	@p='$<'; \
+@am__EXEEXT_TRUE@	$(am__set_b); \
+@am__EXEEXT_TRUE@	$(am__check_pre) $(TEST_LOG_DRIVER) --test-name "$$f" \
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+@am__EXEEXT_TRUE@	$(am__common_driver_flags) $(AM_TEST_LOG_DRIVER_FLAGS) $(TEST_LOG_DRIVER_FLAGS) -- $(TEST_LOG_COMPILE) \
+@am__EXEEXT_TRUE@	"$$tst" $(AM_TESTS_FD_REDIRECT)
+
+distdir: $(DISTFILES)
+	@srcdirstrip=`echo "$(srcdir)" | sed 's/[].[^$$\\*]/\\\\&/g'`; \
+	topsrcdirstrip=`echo "$(top_srcdir)" | sed 's/[].[^$$\\*]/\\\\&/g'`; \
+	list='$(DISTFILES)'; \
+	  dist_files=`for file in $$list; do echo $$file; done | \
+	  sed -e "s|^$$srcdirstrip/||;t" \
+	      -e "s|^$$topsrcdirstrip/|$(top_builddir)/|;t"`; \
+	case $$dist_files in \
+	  */*) $(MKDIR_P) `echo "$$dist_files" | \
+			   sed '/\//!d;s|^|$(distdir)/|;s,/[^/]*$$,,' | \
+			   sort -u` ;; \
+	esac; \
+	for file in $$dist_files; do \
+	  if test -f $$file || test -d $$file; then d=.; else d=$(srcdir); fi; \
+	  if test -d $$d/$$file; then \
+	    dir=`echo "/$$file" | sed -e 's,/[^/]*$$,,'`; \
+	    if test -d "$(distdir)/$$file"; then \
+	      find "$(distdir)/$$file" -type d ! -perm -700 -exec chmod u+rwx {} \;; \
+	    fi; \
+	    if test -d $(srcdir)/$$file && test $$d != $(srcdir); then \
+	      cp -fpR $(srcdir)/$$file "$(distdir)$$dir" || exit 1; \
+	      find "$(distdir)/$$file" -type d ! -perm -700 -exec chmod u+rwx {} \;; \
+	    fi; \
+	    cp -fpR $$d/$$file "$(distdir)$$dir" || exit 1; \
+	  else \
+	    test -f "$(distdir)/$$file" \
+	    || cp -p $$d/$$file "$(distdir)/$$file" \
+	    || exit 1; \
+	  fi; \
+	done
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+	$(MAKE) $(AM_MAKEFLAGS) $(check_PROGRAMS)
+	$(MAKE) $(AM_MAKEFLAGS) check-TESTS
+check: check-am
+all-am: Makefile $(LTLIBRARIES) $(HEADERS)
+installdirs:
+	for dir in "$(DESTDIR)$(pkgincludedir)"; do \
+	  test -z "$$dir" || $(MKDIR_P) "$$dir"; \
+	done
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+	  $(MAKE) $(AM_MAKEFLAGS) INSTALL_PROGRAM="$(INSTALL_STRIP_PROGRAM)" \
+	    install_sh_PROGRAM="$(INSTALL_STRIP_PROGRAM)" INSTALL_STRIP_FLAG=-s \
+	      install; \
+	else \
+	  $(MAKE) $(AM_MAKEFLAGS) INSTALL_PROGRAM="$(INSTALL_STRIP_PROGRAM)" \
+	    install_sh_PROGRAM="$(INSTALL_STRIP_PROGRAM)" INSTALL_STRIP_FLAG=-s \
+	    "INSTALL_PROGRAM_ENV=STRIPPROG='$(STRIP)'" install; \
+	fi
+mostlyclean-generic:
+	-test -z "$(TEST_LOGS)" || rm -f $(TEST_LOGS)
+	-test -z "$(TEST_LOGS:.log=.trs)" || rm -f $(TEST_LOGS:.log=.trs)
+	-test -z "$(TEST_SUITE_LOG)" || rm -f $(TEST_SUITE_LOG)
+
+clean-generic:
+
+distclean-generic:
+	-test -z "$(CONFIG_CLEAN_FILES)" || rm -f $(CONFIG_CLEAN_FILES)
+	-test . = "$(srcdir)" || test -z "$(CONFIG_CLEAN_VPATH_FILES)" || rm -f $(CONFIG_CLEAN_VPATH_FILES)
+
+maintainer-clean-generic:
+	@echo "This command is intended for maintainers to use"
+	@echo "it deletes files that may require special tools to rebuild."
+clean: clean-am
+
+clean-am: clean-checkPROGRAMS clean-generic clean-libtool \
+	clean-noinstLTLIBRARIES mostlyclean-am
+
+distclean: distclean-am
+	-rm -rf ./$(DEPDIR)
+	-rm -f Makefile
+distclean-am: clean-am distclean-compile distclean-generic \
+	distclean-tags
+
+dvi: dvi-am
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+install-dvi: install-dvi-am
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+	-rm -rf ./$(DEPDIR)
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+	mostlyclean-libtool
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+.MAKE: check-am install-am install-strip
+
+.PHONY: CTAGS GTAGS TAGS all all-am check check-TESTS check-am clean \
+	clean-checkPROGRAMS clean-generic clean-libtool \
+	clean-noinstLTLIBRARIES cscopelist-am ctags ctags-am distclean \
+	distclean-compile distclean-generic distclean-libtool \
+	distclean-tags distdir dvi dvi-am html html-am info info-am \
+	install install-am install-data install-data-am install-dvi \
+	install-dvi-am install-exec install-exec-am install-html \
+	install-html-am install-info install-info-am install-man \
+	install-pdf install-pdf-am install-pkgincludeHEADERS \
+	install-ps install-ps-am install-strip installcheck \
+	installcheck-am installdirs maintainer-clean \
+	maintainer-clean-generic mostlyclean mostlyclean-compile \
+	mostlyclean-generic mostlyclean-libtool pdf pdf-am ps ps-am \
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+	uninstall-pkgincludeHEADERS
+
+
+# Tell versions [3.59,3.63) of GNU make to not export all variables.
+# Otherwise a system limit (for SysV at least) may be exceeded.
+.NOEXPORT:
diff -Nru gsl-doc-1.16/multilarge/multilarge.c gsl-doc-2.3/multilarge/multilarge.c
--- gsl-doc-1.16/multilarge/multilarge.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge/multilarge.c	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,402 @@
+/* multilarge.c
+ * 
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_multifit.h>
+#include <gsl/gsl_multilarge.h>
+#include <gsl/gsl_blas.h>
+
+gsl_multilarge_linear_workspace *
+gsl_multilarge_linear_alloc(const gsl_multilarge_linear_type *T,
+                            const size_t p)
+{
+  gsl_multilarge_linear_workspace *w;
+
+  w = calloc(1, sizeof(gsl_multilarge_linear_workspace));
+  if (w == NULL)
+    {
+      GSL_ERROR_NULL("failed to allocate space for workspace",
+                     GSL_ENOMEM);
+    }
+
+  w->type = T;
+
+  w->state = w->type->alloc(p);
+  if (w->state == NULL)
+    {
+      gsl_multilarge_linear_free(w);
+      GSL_ERROR_NULL("failed to allocate space for multilarge state",
+                     GSL_ENOMEM);
+    }
+
+  w->p = p;
+
+  /* initialize newly allocated state */
+  gsl_multilarge_linear_reset(w);
+
+  return w;
+}
+
+void
+gsl_multilarge_linear_free(gsl_multilarge_linear_workspace *w)
+{
+  RETURN_IF_NULL(w);
+
+  if (w->state)
+    w->type->free(w->state);
+
+  free(w);
+}
+
+const char *
+gsl_multilarge_linear_name(const gsl_multilarge_linear_workspace *w)
+{
+  return w->type->name;
+}
+
+int
+gsl_multilarge_linear_reset(gsl_multilarge_linear_workspace *w)
+{
+  int status = w->type->reset(w->state);
+  return status;
+}
+
+int
+gsl_multilarge_linear_accumulate(gsl_matrix * X, gsl_vector * y,
+                                 gsl_multilarge_linear_workspace * w)
+{
+  int status = w->type->accumulate(X, y, w->state);
+  return status;
+}
+
+int
+gsl_multilarge_linear_solve(const double lambda, gsl_vector * c,
+                            double * rnorm, double * snorm,
+                            gsl_multilarge_linear_workspace * w)
+{
+  int status = w->type->solve(lambda, c, rnorm, snorm, w->state);
+  return status;
+}
+
+int
+gsl_multilarge_linear_rcond(double *rcond, gsl_multilarge_linear_workspace * w)
+{
+  int status = w->type->rcond(rcond, w->state);
+  return status;
+}
+
+int
+gsl_multilarge_linear_lcurve(gsl_vector * reg_param, gsl_vector * rho,
+                             gsl_vector * eta,
+                             gsl_multilarge_linear_workspace * w)
+{
+  const size_t len = reg_param->size;
+
+  if (len != rho->size)
+    {
+      GSL_ERROR ("reg_param and rho have different sizes", GSL_EBADLEN);
+    }
+  else if (len != eta->size)
+    {
+      GSL_ERROR ("reg_param and eta have different sizes", GSL_EBADLEN);
+    }
+  else
+    {
+      int status = w->type->lcurve(reg_param, rho, eta, w->state);
+      return status;
+    }
+}
+
+/*
+gsl_multilarge_linear_wstdform1()
+  Using regularization matrix
+L = diag(l_1,l_2,...,l_p), transform to Tikhonov standard form:
+
+X~ = sqrt(W) X L^{-1}
+y~ = sqrt(W) y
+c~ = L c
+
+Inputs: L    - Tikhonov matrix as a vector of diagonal elements p-by-1;
+               or NULL for L = I
+        X    - least squares matrix n-by-p
+        y    - right hand side vector n-by-1
+        w    - weight vector n-by-1; or NULL for W = I
+        Xs   - least squares matrix in standard form X~ n-by-p
+        ys   - right hand side vector in standard form y~ n-by-1
+        work - workspace
+
+Return: success/error
+
+Notes:
+1) It is allowed for X = Xs and y = ys
+*/
+
+int
+gsl_multilarge_linear_wstdform1 (const gsl_vector * L,
+                                 const gsl_matrix * X,
+                                 const gsl_vector * w,
+                                 const gsl_vector * y,
+                                 gsl_matrix * Xs,
+                                 gsl_vector * ys,
+                                 gsl_multilarge_linear_workspace * work)
+{
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+
+  if (L != NULL && p != L->size)
+    {
+      GSL_ERROR("L vector does not match X", GSL_EBADLEN);
+    }
+  else if (n != y->size)
+    {
+      GSL_ERROR("y vector does not match X", GSL_EBADLEN);
+    }
+  else if (w != NULL && n != w->size)
+    {
+      GSL_ERROR("weight vector does not match X", GSL_EBADLEN);
+    }
+  else if (n != Xs->size1 || p != Xs->size2)
+    {
+      GSL_ERROR("Xs matrix dimensions do not match X", GSL_EBADLEN);
+    }
+  else if (n != ys->size)
+    {
+      GSL_ERROR("ys vector must be length n", GSL_EBADLEN);
+    }
+  else
+    {
+      int status = GSL_SUCCESS;
+
+      /* compute Xs = sqrt(W) X and ys = sqrt(W) y */
+      status = gsl_multifit_linear_applyW(X, w, y, Xs, ys);
+      if (status)
+        return status;
+
+      if (L != NULL)
+        {
+          size_t j;
+
+          /* construct X~ = sqrt(W) X * L^{-1} matrix */
+          for (j = 0; j < p; ++j)
+            {
+              gsl_vector_view Xj = gsl_matrix_column(Xs, j);
+              double lj = gsl_vector_get(L, j);
+
+              if (lj == 0.0)
+                {
+                  GSL_ERROR("L matrix is singular", GSL_EDOM);
+                }
+
+              gsl_vector_scale(&Xj.vector, 1.0 / lj);
+            }
+        }
+
+      return status;
+    }
+}
+
+int
+gsl_multilarge_linear_stdform1 (const gsl_vector * L,
+                                const gsl_matrix * X,
+                                const gsl_vector * y,
+                                gsl_matrix * Xs,
+                                gsl_vector * ys,
+                                gsl_multilarge_linear_workspace * work)
+{
+  int status;
+
+  status = gsl_multilarge_linear_wstdform1(L, X, NULL, y, Xs, ys, work);
+
+  return status;
+}
+
+int
+gsl_multilarge_linear_L_decomp (gsl_matrix * L, gsl_vector * tau)
+{
+  const size_t m = L->size1;
+  const size_t p = L->size2;
+
+  if (m < p)
+    {
+      GSL_ERROR("m < p not yet supported", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+
+      status = gsl_multifit_linear_L_decomp(L, tau);
+
+      return status;
+    }
+}
+
+int
+gsl_multilarge_linear_wstdform2 (const gsl_matrix * LQR,
+                                 const gsl_vector * Ltau,
+                                 const gsl_matrix * X,
+                                 const gsl_vector * w,
+                                 const gsl_vector * y,
+                                 gsl_matrix * Xs,
+                                 gsl_vector * ys,
+                                 gsl_multilarge_linear_workspace * work)
+{
+  const size_t m = LQR->size1;
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+
+  if (p != work->p)
+    {
+      GSL_ERROR("X has wrong number of columns", GSL_EBADLEN);
+    }
+  else if (p != LQR->size2)
+    {
+      GSL_ERROR("LQR and X matrices have different numbers of columns", GSL_EBADLEN);
+    }
+  else if (n != y->size)
+    {
+      GSL_ERROR("y vector does not match X", GSL_EBADLEN);
+    }
+  else if (w != NULL && n != w->size)
+    {
+      GSL_ERROR("weights vector must be length n", GSL_EBADLEN);
+    }
+  else if (m < p)
+    {
+      GSL_ERROR("m < p not yet supported", GSL_EBADLEN);
+    }
+  else if (n != Xs->size1 || p != Xs->size2)
+    {
+      GSL_ERROR("Xs matrix must be n-by-p", GSL_EBADLEN);
+    }
+  else if (n != ys->size)
+    {
+      GSL_ERROR("ys vector must have length n", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+      size_t i;
+      gsl_matrix_const_view R = gsl_matrix_const_submatrix(LQR, 0, 0, p, p);
+
+      /* compute Xs = sqrt(W) X and ys = sqrt(W) y */
+      status = gsl_multifit_linear_applyW(X, w, y, Xs, ys);
+      if (status)
+        return status;
+
+      /* compute X~ = X R^{-1} using QR decomposition of L */
+      for (i = 0; i < n; ++i)
+        {
+          gsl_vector_view v = gsl_matrix_row(Xs, i);
+
+          /* solve: R^T y = X_i */
+          gsl_blas_dtrsv(CblasUpper, CblasTrans, CblasNonUnit, &R.matrix, &v.vector);
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+int
+gsl_multilarge_linear_stdform2 (const gsl_matrix * LQR,
+                                const gsl_vector * Ltau,
+                                const gsl_matrix * X,
+                                const gsl_vector * y,
+                                gsl_matrix * Xs,
+                                gsl_vector * ys,
+                                gsl_multilarge_linear_workspace * work)
+{
+  int status;
+
+  status = gsl_multilarge_linear_wstdform2(LQR, Ltau, X, NULL, y, Xs, ys, work);
+
+  return status;
+}
+
+/*
+gsl_multilarge_linear_genform1()
+  Backtransform regularized solution vector using matrix
+L = diag(L)
+*/
+
+int
+gsl_multilarge_linear_genform1 (const gsl_vector * L,
+                                const gsl_vector * cs,
+                                gsl_vector * c,
+                                gsl_multilarge_linear_workspace * work)
+{
+  if (L->size != work->p)
+    {
+      GSL_ERROR("L vector does not match workspace", GSL_EBADLEN);
+    }
+  else if (L->size != cs->size)
+    {
+      GSL_ERROR("cs vector does not match L", GSL_EBADLEN);
+    }
+  else if (L->size != c->size)
+    {
+      GSL_ERROR("c vector does not match L", GSL_EBADLEN);
+    }
+  else
+    {
+      /* compute true solution vector c = L^{-1} c~ */
+      gsl_vector_memcpy(c, cs);
+      gsl_vector_div(c, L);
+
+      return GSL_SUCCESS;
+    }
+}
+
+int
+gsl_multilarge_linear_genform2 (const gsl_matrix * LQR,
+                                const gsl_vector * Ltau,
+                                const gsl_vector * cs,
+                                gsl_vector * c,
+                                gsl_multilarge_linear_workspace * work)
+{
+  const size_t m = LQR->size1;
+  const size_t p = LQR->size2;
+
+  if (p != c->size)
+    {
+      GSL_ERROR("c vector does not match LQR", GSL_EBADLEN);
+    }
+  else if (m < p)
+    {
+      GSL_ERROR("m < p not yet supported", GSL_EBADLEN);
+    }
+  else if (p != cs->size)
+    {
+      GSL_ERROR("cs vector size does not match c", GSL_EBADLEN);
+    }
+  else
+    {
+      int s;
+      gsl_matrix_const_view R = gsl_matrix_const_submatrix(LQR, 0, 0, p, p); /* R factor of L */
+
+      /* solve R c = cs for true solution c, using QR decomposition of L */
+      gsl_vector_memcpy(c, cs);
+      s = gsl_blas_dtrsv(CblasUpper, CblasNoTrans, CblasNonUnit, &R.matrix, c);
+
+      return s;
+    }
+}
diff -Nru gsl-doc-1.16/multilarge/normal.c gsl-doc-2.3/multilarge/normal.c
--- gsl-doc-1.16/multilarge/normal.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge/normal.c	2016-08-12 17:50:06.000000000 +0000
@@ -0,0 +1,513 @@
+/* normal.c
+ * 
+ * Copyright (C) 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_eigen.h>
+#include <gsl/gsl_multifit.h>
+#include <gsl/gsl_multilarge.h>
+#include <gsl/gsl_permutation.h>
+
+typedef struct
+{
+  size_t p;              /* number of columns of LS matrix */
+  gsl_matrix *ATA;       /* A^T A, p-by-p */
+  gsl_vector *ATb;       /* A^T b, p-by-1 */
+  double normb;          /* || b || */
+  gsl_matrix *work_ATA;  /* workspace for chol(ATA), p-by-p */
+  gsl_permutation *perm; /* permutation vector */
+  gsl_vector *workp;     /* workspace size p */
+  gsl_vector *work3p;    /* workspace size 3*p */
+  gsl_vector *D;         /* scale factors for ATA, size p */
+  gsl_vector *c;         /* solution vector for L-curve */
+  int eigen;             /* 1 if eigenvalues computed */
+  double eval_min;       /* minimum eigenvalue */
+  double eval_max;       /* maximum eigenvalue */
+  gsl_eigen_symm_workspace *eigen_p;
+} normal_state_t;
+
+static void *normal_alloc(const size_t p);
+static void normal_free(void *vstate);
+static int normal_reset(void *vstate);
+static int normal_accumulate(gsl_matrix * A, gsl_vector * b,
+                             void * vstate);
+static int normal_solve(const double lambda, gsl_vector * x,
+                        double * rnorm, double * snorm,
+                        void * vstate);
+static int normal_rcond(double * rcond, void * vstate);
+static int normal_lcurve(gsl_vector * reg_param, gsl_vector * rho,
+                         gsl_vector * eta, void * vstate);
+static int normal_solve_system(const double lambda, gsl_vector * x,
+                               normal_state_t *state);
+static int normal_solve_cholesky(gsl_matrix * ATA, const gsl_vector * ATb,
+                                 gsl_vector * x, normal_state_t *state);
+static int normal_calc_norms(const gsl_vector *x, double *rnorm,
+                             double *snorm, normal_state_t *state);
+static int normal_eigen(normal_state_t *state);
+
+/*
+normal_alloc()
+  Allocate workspace for solving large linear least squares
+problems using the normal equations approach
+
+Inputs: p    - number of columns of LS matrix
+
+Return: pointer to workspace
+*/
+
+static void *
+normal_alloc(const size_t p)
+{
+  normal_state_t *state;
+
+  if (p == 0)
+    {
+      GSL_ERROR_NULL("p must be a positive integer",
+                     GSL_EINVAL);
+    }
+
+  state = calloc(1, sizeof(normal_state_t));
+  if (!state)
+    {
+      GSL_ERROR_NULL("failed to allocate normal state", GSL_ENOMEM);
+    }
+
+  state->p = p;
+
+  state->ATA = gsl_matrix_alloc(p, p);
+  if (state->ATA == NULL)
+    {
+      normal_free(state);
+      GSL_ERROR_NULL("failed to allocate ATA matrix", GSL_ENOMEM);
+    }
+
+  state->work_ATA = gsl_matrix_alloc(p, p);
+  if (state->work_ATA == NULL)
+    {
+      normal_free(state);
+      GSL_ERROR_NULL("failed to allocate temporary ATA matrix", GSL_ENOMEM);
+    }
+
+  state->ATb = gsl_vector_alloc(p);
+  if (state->ATb == NULL)
+    {
+      normal_free(state);
+      GSL_ERROR_NULL("failed to allocate ATb vector", GSL_ENOMEM);
+    }
+
+  state->perm = gsl_permutation_alloc(p);
+  if (state->perm == NULL)
+    {
+      normal_free(state);
+      GSL_ERROR_NULL("failed to allocate perm", GSL_ENOMEM);
+    }
+
+  state->D = gsl_vector_alloc(p);
+  if (state->D == NULL)
+    {
+      normal_free(state);
+      GSL_ERROR_NULL("failed to allocate D vector", GSL_ENOMEM);
+    }
+
+  state->workp = gsl_vector_alloc(p);
+  if (state->workp == NULL)
+    {
+      normal_free(state);
+      GSL_ERROR_NULL("failed to allocate temporary ATb vector", GSL_ENOMEM);
+    }
+
+  state->work3p = gsl_vector_alloc(3 * p);
+  if (state->work3p == NULL)
+    {
+      normal_free(state);
+      GSL_ERROR_NULL("failed to allocate work3p", GSL_ENOMEM);
+    }
+
+  state->c = gsl_vector_alloc(p);
+  if (state->c == NULL)
+    {
+      normal_free(state);
+      GSL_ERROR_NULL("failed to allocate c vector", GSL_ENOMEM);
+    }
+
+  state->eigen_p = gsl_eigen_symm_alloc(p);
+  if (state->eigen_p == NULL)
+    {
+      normal_free(state);
+      GSL_ERROR_NULL("failed to allocate eigen workspace", GSL_ENOMEM);
+    }
+
+  normal_reset(state);
+
+  return state;
+}
+
+static void
+normal_free(void *vstate)
+{
+  normal_state_t *state = (normal_state_t *) vstate;
+
+  if (state->ATA)
+    gsl_matrix_free(state->ATA);
+
+  if (state->work_ATA)
+    gsl_matrix_free(state->work_ATA);
+
+  if (state->ATb)
+    gsl_vector_free(state->ATb);
+
+  if (state->perm)
+    gsl_permutation_free(state->perm);
+
+  if (state->D)
+    gsl_vector_free(state->D);
+
+  if (state->workp)
+    gsl_vector_free(state->workp);
+
+  if (state->work3p)
+    gsl_vector_free(state->work3p);
+
+  if (state->c)
+    gsl_vector_free(state->c);
+
+  if (state->eigen_p)
+    gsl_eigen_symm_free(state->eigen_p);
+
+  free(state);
+}
+
+static int
+normal_reset(void *vstate)
+{
+  normal_state_t *state = (normal_state_t *) vstate;
+
+  gsl_matrix_set_zero(state->ATA);
+  gsl_vector_set_zero(state->ATb);
+  state->normb = 0.0;
+  state->eigen = 0;
+  state->eval_min = 0.0;
+  state->eval_max = 0.0;
+
+  return GSL_SUCCESS;
+}
+
+/*
+normal_accumulate()
+  Add a new block of rows to the normal equations system
+
+Inputs: A      - new block of rows, n-by-p
+        b      - new rhs vector n-by-1
+        vstate - workspace
+
+Return: success/error
+*/
+
+static int
+normal_accumulate(gsl_matrix * A, gsl_vector * b, void * vstate)
+{
+  normal_state_t *state = (normal_state_t *) vstate;
+  const size_t n = A->size1;
+
+  if (A->size2 != state->p)
+    {
+      GSL_ERROR("columns of A do not match workspace", GSL_EBADLEN);
+    }
+  else if (n != b->size)
+    {
+      GSL_ERROR("A and b have different numbers of rows", GSL_EBADLEN);
+    }
+  else
+    {
+      int s;
+
+      /* ATA += A^T A, using only the lower half of the matrix */
+      s = gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, A, 1.0, state->ATA);
+      if (s)
+        return s;
+
+      /* ATb += A^T b */
+      s = gsl_blas_dgemv(CblasTrans, 1.0, A, b, 1.0, state->ATb);
+      if (s)
+        return s;
+
+      /* update || b || */
+      state->normb = gsl_hypot(state->normb, gsl_blas_dnrm2(b));
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+normal_solve()
+  Solve normal equations system:
+
+(A^T A + \lambda^2 I) x = A^T b
+
+using Cholesky decomposition
+
+Inputs: lambda - regularization parameter
+        x      - (output) solution vector p-by-1
+        rnorm  - (output) residual norm ||b - A x||
+        snorm  - (output) solution norm ||x||
+        vstate - workspace
+
+Return: success/error
+*/
+
+static int
+normal_solve(const double lambda, gsl_vector * x,
+             double * rnorm, double * snorm,
+             void * vstate)
+{
+  normal_state_t *state = (normal_state_t *) vstate;
+
+  if (x->size != state->p)
+    {
+      GSL_ERROR("solution vector does not match workspace", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+
+      /* solve system (A^T A) x = A^T b */
+      status = normal_solve_system(lambda, x, state);
+      if (status)
+        {
+          GSL_ERROR("failed to solve normal equations", status);
+        }
+
+      /* compute residual norm ||y - X c|| and solution norm ||x|| */
+      normal_calc_norms(x, rnorm, snorm, state);
+
+      return GSL_SUCCESS;
+    }
+}
+
+static int
+normal_rcond(double * rcond, void * vstate)
+{
+  normal_state_t *state = (normal_state_t *) vstate;
+  int status = GSL_SUCCESS;
+  double rcond_ATA;
+
+  status = gsl_linalg_pcholesky_rcond(state->work_ATA, state->perm, &rcond_ATA, state->work3p);
+  if (status == GSL_SUCCESS)
+    *rcond = sqrt(rcond_ATA);
+
+  return status;
+}
+
+/*
+normal_lcurve()
+  Compute L-curve of least squares system
+
+Inputs: reg_param - (output) vector of regularization parameters
+        rho       - (output) vector of residual norms
+        eta       - (output) vector of solution norms
+        vstate    - workspace
+
+Return: success/error
+*/
+
+static int
+normal_lcurve(gsl_vector * reg_param, gsl_vector * rho,
+              gsl_vector * eta, void * vstate)
+{
+  normal_state_t *state = (normal_state_t *) vstate;
+  int status;
+  double smin, smax; /* minimum/maximum singular values */
+  size_t i;
+
+  if (state->eigen == 0)
+    {
+      status = normal_eigen(state);
+      if (status)
+        return status;
+    }
+
+  if (state->eval_max < 0.0)
+    {
+      GSL_ERROR("matrix is not positive definite", GSL_EDOM);
+    }
+
+  /* compute singular values which are sqrts of eigenvalues */
+  smax = sqrt(state->eval_max);
+  if (state->eval_min > 0.0)
+    smin = sqrt(state->eval_min);
+  else
+    smin = 0.0;
+
+  /* compute vector of regularization parameters */
+  gsl_multifit_linear_lreg(smin, smax, reg_param);
+
+  /* solve normal equations for each regularization parameter */
+  for (i = 0; i < reg_param->size; ++i)
+    {
+      double lambda = gsl_vector_get(reg_param, i);
+      double rnorm, snorm;
+
+      status = normal_solve_system(lambda, state->c, state);
+      if (status)
+        return status;
+
+      /* compute ||y - X c|| and ||c|| */
+      normal_calc_norms(state->c, &rnorm, &snorm, state);
+
+      gsl_vector_set(rho, i, rnorm);
+      gsl_vector_set(eta, i, snorm);
+    }
+
+  return GSL_SUCCESS;
+}
+
+/*
+normal_solve_system()
+  Compute solution to normal equations:
+
+(A^T A + lambda^2*I) x = A^T b
+
+using LDL decomposition.
+
+Inputs: x     - (output) solution vector
+        state - workspace
+
+Return: success/error
+*/
+
+static int
+normal_solve_system(const double lambda, gsl_vector * x, normal_state_t *state)
+{
+  int status;
+  const double lambda_sq = lambda * lambda;
+  gsl_vector_view d = gsl_matrix_diagonal(state->work_ATA);
+
+  /* copy ATA matrix to temporary workspace and regularize */
+  gsl_matrix_tricpy('L', 1, state->work_ATA, state->ATA);
+  gsl_vector_add_constant(&d.vector, lambda_sq);
+
+  /* solve with LDL decomposition */
+  status = normal_solve_cholesky(state->work_ATA, state->ATb, x, state);
+  if (status)
+    return status;
+
+  return status;
+}
+
+static int
+normal_solve_cholesky(gsl_matrix * ATA, const gsl_vector * ATb,
+                      gsl_vector * x, normal_state_t *state)
+{
+  int status;
+
+  status = gsl_linalg_pcholesky_decomp2(ATA, state->perm, state->D);
+  if (status)
+    return status;
+
+  status = gsl_linalg_pcholesky_solve2(ATA, state->perm, state->D, ATb, x);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+}
+
+/*
+normal_calc_norms()
+  Compute residual norm ||y - X c|| and solution
+norm ||c||
+
+Inputs: x     - solution vector
+        rnorm - (output) residual norm ||y - X c||
+        snorm - (output) solution norm ||c||
+        state - workspace
+*/
+
+static int
+normal_calc_norms(const gsl_vector *x, double *rnorm,
+                  double *snorm, normal_state_t *state)
+{
+  double r2;
+
+  /* compute solution norm ||x|| */
+  *snorm = gsl_blas_dnrm2(x);
+
+  /* compute residual norm ||b - Ax|| */
+
+  /* compute: A^T A x - 2 A^T b */
+  gsl_vector_memcpy(state->workp, state->ATb);
+  gsl_blas_dsymv(CblasLower, 1.0, state->ATA, x, -2.0, state->workp);
+
+  /* compute: x^T A^T A x - 2 x^T A^T b */
+  gsl_blas_ddot(x, state->workp, &r2);
+
+  /* add b^T b */
+  r2 += state->normb * state->normb;
+
+  *rnorm = sqrt(r2);
+
+  return GSL_SUCCESS;
+}
+
+/*
+normal_eigen()
+  Compute eigenvalues of A^T A matrix, which
+are stored in state->workp on output. Also,
+state->eval_min and state->eval_max are set
+to the minimum/maximum eigenvalues
+*/
+
+static int
+normal_eigen(normal_state_t *state)
+{
+  int status;
+
+  /* copy lower triangle of ATA to temporary workspace */
+  gsl_matrix_tricpy('L', 1, state->work_ATA, state->ATA);
+
+  /* compute eigenvalues of ATA */
+  status = gsl_eigen_symm(state->work_ATA, state->workp, state->eigen_p);
+  if (status)
+    return status;
+
+  gsl_vector_minmax(state->workp, &state->eval_min, &state->eval_max);
+
+  state->eigen = 1;
+
+  return GSL_SUCCESS;
+}
+
+static const gsl_multilarge_linear_type normal_type =
+{
+  "normal",
+  normal_alloc,
+  normal_reset,
+  normal_accumulate,
+  normal_solve,
+  normal_rcond,
+  normal_lcurve,
+  normal_free
+};
+
+const gsl_multilarge_linear_type * gsl_multilarge_linear_normal =
+  &normal_type;
diff -Nru gsl-doc-1.16/multilarge/test.c gsl-doc-2.3/multilarge/test.c
--- gsl-doc-1.16/multilarge/test.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge/test.c	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,515 @@
+/* multilarge/test.c
+ * 
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_test.h>
+#include <gsl/gsl_multifit.h>
+#include <gsl/gsl_multilarge.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_ieee_utils.h>
+
+static void test_random_matrix_orth(gsl_matrix *m, const gsl_rng *r);
+static void test_random_matrix_ill(gsl_matrix *m, const gsl_rng *r);
+static void test_random_vector(gsl_vector *v, const gsl_rng *r,
+                               const double lower, const double upper);
+static void test_random_matrix(gsl_matrix *m, const gsl_rng *r,
+                               const double lower, const double upper);
+static void test_random_vector_noise(const gsl_rng *r, gsl_vector *y);
+static void test_compare_vectors(const double tol, const gsl_vector * a,
+                                 const gsl_vector * b, const char * desc);
+static void test_multifit_solve(const double lambda, const gsl_matrix * X,
+                                const gsl_vector * y, const gsl_vector * wts,
+                                const gsl_vector * diagL, const gsl_matrix * L,
+                                double *rnorm, double *snorm, gsl_vector * c);
+static void test_multilarge_solve(const gsl_multilarge_linear_type * T, const double lambda,
+                                  const gsl_matrix * X, const gsl_vector * y, gsl_vector * wts,
+                                  const gsl_vector * diagL, const gsl_matrix * L,
+                                  double *rnorm, double *snorm, gsl_vector * c);
+
+/* generate random square orthogonal matrix via QR decomposition */
+static void
+test_random_matrix_orth(gsl_matrix *m, const gsl_rng *r)
+{
+  const size_t M = m->size1;
+  gsl_matrix *A = gsl_matrix_alloc(M, M);
+  gsl_vector *tau = gsl_vector_alloc(M);
+  gsl_matrix *R = gsl_matrix_alloc(M, M);
+
+  test_random_matrix(A, r, -1.0, 1.0);
+  gsl_linalg_QR_decomp(A, tau);
+  gsl_linalg_QR_unpack(A, tau, m, R);
+
+  gsl_matrix_free(A);
+  gsl_matrix_free(R);
+  gsl_vector_free(tau);
+}
+
+/* construct ill-conditioned matrix via SVD */
+static void
+test_random_matrix_ill(gsl_matrix *m, const gsl_rng *r)
+{
+  const size_t M = m->size1;
+  const size_t N = m->size2;
+  gsl_matrix *U = gsl_matrix_alloc(M, M);
+  gsl_matrix *V = gsl_matrix_alloc(N, N);
+  gsl_vector *S = gsl_vector_alloc(N);
+  gsl_matrix_view Uv = gsl_matrix_submatrix(U, 0, 0, M, N);
+  const double smin = 16.0 * GSL_DBL_EPSILON;
+  const double smax = 10.0;
+  const double ratio = pow(smin / smax, 1.0 / (N - 1.0));
+  double s;
+  size_t j;
+
+  test_random_matrix_orth(U, r);
+  test_random_matrix_orth(V, r);
+
+  /* compute U * S */
+
+  s = smax;
+  for (j = 0; j < N; ++j)
+    {
+      gsl_vector_view uj = gsl_matrix_column(U, j);
+
+      gsl_vector_scale(&uj.vector, s);
+      s *= ratio;
+    }
+
+  /* compute m = (U * S) * V' */
+  gsl_blas_dgemm(CblasNoTrans, CblasTrans, 1.0, &Uv.matrix, V, 0.0, m);
+
+  gsl_matrix_free(U);
+  gsl_matrix_free(V);
+  gsl_vector_free(S);
+}
+
+static void
+test_random_vector(gsl_vector *v, const gsl_rng *r,
+                   const double lower, const double upper)
+{
+  size_t i;
+  size_t N = v->size;
+
+  for (i = 0; i < N; ++i)
+    {
+      gsl_vector_set(v, i,
+                     gsl_rng_uniform(r) * (upper - lower) + lower);
+    }
+}
+
+static void
+test_random_matrix(gsl_matrix *m, const gsl_rng *r,
+                   const double lower, const double upper)
+{
+  size_t i, j;
+  size_t M = m->size1;
+  size_t N = m->size2;
+
+  for (i = 0; i < M; ++i)
+    {
+      for (j = 0; j < N; ++j)
+      {
+        gsl_matrix_set(m, i, j,
+                       gsl_rng_uniform(r) * (upper - lower) + lower);
+      }
+    }
+}
+
+/* generate Vandermonde matrix using equally spaced input points
+ * on [0,1] */
+static void
+test_vander_matrix(gsl_matrix * m)
+{
+  const size_t M = m->size1;
+  const size_t N = m->size2;
+  const double dt = 1.0 / (M - 1.0);
+  size_t i, j;
+
+  for (i = 0; i < M; ++i)
+    {
+      double ti = i * dt;
+      double mij = 1.0;
+
+      for (j = 0; j < N; ++j)
+        {
+          gsl_matrix_set(m, i, j, mij);
+          mij *= ti;
+        }
+    }
+}
+
+static void
+test_random_vector_noise(const gsl_rng *r, gsl_vector *y)
+{
+  size_t i;
+
+  for (i = 0; i < y->size; ++i)
+    {
+      double *ptr = gsl_vector_ptr(y, i);
+      *ptr += 1.0e-3 * gsl_rng_uniform(r);
+    }
+}
+
+static void
+test_compare_vectors(const double tol, const gsl_vector * a,
+                     const gsl_vector * b, const char * desc)
+{
+  size_t i;
+
+  for (i = 0; i < a->size; ++i)
+    {
+      double ai = gsl_vector_get(a, i);
+      double bi = gsl_vector_get(b, i);
+
+      gsl_test_rel(bi, ai, tol, "%s i=%zu", desc, i);
+    }
+}
+
+/* solve least squares system with multifit SVD */
+static void
+test_multifit_solve(const double lambda, const gsl_matrix * X,
+                    const gsl_vector * y, const gsl_vector * wts,
+                    const gsl_vector * diagL, const gsl_matrix * L,
+                    double *rnorm, double *snorm, gsl_vector * c)
+{
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+  gsl_multifit_linear_workspace *w =
+    gsl_multifit_linear_alloc(n, p);
+  gsl_matrix *Xs = gsl_matrix_alloc(n, p);
+  gsl_vector *ys = gsl_vector_alloc(n);
+  gsl_vector *cs = gsl_vector_alloc(p);
+  gsl_matrix *LQR = NULL;
+  gsl_vector *Ltau = NULL;
+  gsl_matrix *M = NULL;
+
+  /* convert to standard form */
+  if (diagL)
+    {
+      gsl_multifit_linear_wstdform1(diagL, X, wts, y, Xs, ys, w);
+    }
+  else if (L)
+    {
+      const size_t m = L->size1;
+
+      LQR = gsl_matrix_alloc(m, p);
+      Ltau = gsl_vector_alloc(GSL_MIN(m, p));
+      M = (m >= p) ? gsl_matrix_alloc(m, p) : gsl_matrix_alloc(n, p);
+
+      gsl_matrix_memcpy(LQR, L);
+      gsl_multifit_linear_L_decomp(LQR, Ltau);
+      gsl_multifit_linear_wstdform2(LQR, Ltau, X, wts, y, Xs, ys, M, w);
+    }
+  else
+    {
+      gsl_matrix_memcpy(Xs, X);
+      gsl_vector_memcpy(ys, y);
+    }
+
+  gsl_multifit_linear_svd(Xs, w);
+  gsl_multifit_linear_solve(lambda, Xs, ys, cs, rnorm, snorm, w);
+
+  /* convert to general form */
+  if (diagL)
+    gsl_multifit_linear_genform1(diagL, cs, c, w);
+  else if (L)
+    gsl_multifit_linear_wgenform2(LQR, Ltau, X, wts, y, cs, M, c, w);
+  else
+    gsl_vector_memcpy(c, cs);
+
+  gsl_multifit_linear_free(w);
+  gsl_matrix_free(Xs);
+  gsl_vector_free(ys);
+  gsl_vector_free(cs);
+
+  if (LQR)
+    gsl_matrix_free(LQR);
+  if (Ltau)
+    gsl_vector_free(Ltau);
+  if (M)
+    gsl_matrix_free(M);
+}
+
+/* solve least squares system with multilarge */
+static void
+test_multilarge_solve(const gsl_multilarge_linear_type * T, const double lambda,
+                      const gsl_matrix * X, const gsl_vector * y, gsl_vector * wts,
+                      const gsl_vector * diagL, const gsl_matrix * L,
+                      double *rnorm, double *snorm, gsl_vector * c)
+{
+  const size_t n = X->size1;
+  const size_t p = X->size2;
+  const size_t nblock = 5;
+  const size_t nrows = n / nblock; /* number of rows per block */
+  gsl_multilarge_linear_workspace *w =
+    gsl_multilarge_linear_alloc(T, p);
+  gsl_matrix *Xs = gsl_matrix_alloc(nrows, p);
+  gsl_vector *ys = gsl_vector_alloc(nrows);
+  gsl_vector *cs = gsl_vector_alloc(p);
+  gsl_matrix *LQR = NULL;
+  gsl_vector *Ltau = NULL;
+  size_t rowidx = 0;
+
+  if (L)
+    {
+      const size_t m = L->size1;
+
+      LQR = gsl_matrix_alloc(m, p);
+      Ltau = gsl_vector_alloc(p);
+
+      gsl_matrix_memcpy(LQR, L);
+      gsl_multilarge_linear_L_decomp(LQR, Ltau);
+    }
+
+  while (rowidx < n)
+    {
+      size_t nleft = n - rowidx;
+      size_t nr = GSL_MIN(nrows, nleft);
+      gsl_matrix_const_view Xv = gsl_matrix_const_submatrix(X, rowidx, 0, nr, p);
+      gsl_vector_const_view yv = gsl_vector_const_subvector(y, rowidx, nr);
+      gsl_vector_view wv;
+      gsl_matrix_view Xsv = gsl_matrix_submatrix(Xs, 0, 0, nr, p);
+      gsl_vector_view ysv = gsl_vector_subvector(ys, 0, nr);
+
+      if (wts)
+        wv = gsl_vector_subvector(wts, rowidx, nr);
+
+      /* convert to standard form */
+      if (diagL)
+        {
+          gsl_multilarge_linear_wstdform1(diagL, &Xv.matrix, wts ? &wv.vector : NULL,
+                                          &yv.vector, &Xsv.matrix, &ysv.vector, w);
+        }
+      else if (L)
+        {
+          gsl_multilarge_linear_wstdform2(LQR, Ltau, &Xv.matrix, wts ? &wv.vector : NULL,
+                                          &yv.vector, &Xsv.matrix, &ysv.vector, w);
+        }
+      else
+        {
+          gsl_matrix_memcpy(&Xsv.matrix, &Xv.matrix);
+          gsl_vector_memcpy(&ysv.vector, &yv.vector);
+        }
+
+      gsl_multilarge_linear_accumulate(&Xsv.matrix, &ysv.vector, w);
+
+      rowidx += nr;
+    }
+
+  gsl_multilarge_linear_solve(lambda, cs, rnorm, snorm, w);
+
+  if (diagL)
+    gsl_multilarge_linear_genform1(diagL, cs, c, w);
+  else if (L)
+    gsl_multilarge_linear_genform2(LQR, Ltau, cs, c, w);
+  else
+    gsl_vector_memcpy(c, cs);
+
+  gsl_multilarge_linear_free(w);
+  gsl_matrix_free(Xs);
+  gsl_vector_free(ys);
+  gsl_vector_free(cs);
+
+  if (LQR)
+    gsl_matrix_free(LQR);
+  if (Ltau)
+    gsl_vector_free(Ltau);
+}
+
+static void
+test_random(const gsl_multilarge_linear_type * T,
+            const size_t n, const size_t p,
+            const double tol,
+            const gsl_rng * r)
+{
+  const double tol1 = 1.0e3 * tol;
+  gsl_matrix *X = gsl_matrix_alloc(n, p);
+  gsl_vector *y = gsl_vector_alloc(n);
+  gsl_vector *c = gsl_vector_alloc(p);
+  gsl_vector *w = gsl_vector_alloc(n);
+  gsl_vector *diagL = gsl_vector_alloc(p);
+  gsl_matrix *Lsqr = gsl_matrix_alloc(p, p);
+  gsl_matrix *Ltall = gsl_matrix_alloc(5*p, p);
+  gsl_vector *c0 = gsl_vector_alloc(p);
+  gsl_vector *c1 = gsl_vector_alloc(p);
+  double rnorm0, snorm0;
+  double rnorm1, snorm1;
+  char str[2048];
+  size_t i;
+
+  /* generate LS system */
+  test_random_matrix_ill(X, r);
+  /*test_random_matrix(X, r, -1.0, 1.0);*/
+  test_random_vector(c, r, -1.0, 1.0);
+
+  /* compute y = X c + noise */
+  gsl_blas_dgemv(CblasNoTrans, 1.0, X, c, 0.0, y);
+  test_random_vector_noise(r, y);
+
+  /* random weights */
+  test_random_vector(w, r, 0.0, 1.0);
+
+  /* random diag(L) */
+  test_random_vector(diagL, r, 1.0, 5.0);
+
+  /* random square L */
+  test_random_matrix(Lsqr, r, -5.0, 5.0);
+
+  /* random tall L */
+  test_random_matrix(Ltall, r, -10.0, 10.0);
+
+  for (i = 0; i < 2; ++i)
+    {
+      double lambda = pow(10.0, -(double) i);
+
+      /* unweighted with L = I */
+      {
+        test_multifit_solve(lambda, X, y, NULL, NULL, NULL, &rnorm0, &snorm0, c0);
+        test_multilarge_solve(T, lambda, X, y, NULL, NULL, NULL, &rnorm1, &snorm1, c1);
+
+        sprintf(str, "random %s unweighted stdform n=%zu p=%zu lambda=%g",
+                T->name, n, p, lambda);
+        test_compare_vectors(tol, c0, c1, str);
+
+        gsl_test_rel(rnorm1, rnorm0, tol1, "rnorm %s", str);
+        gsl_test_rel(snorm1, snorm0, tol, "snorm %s", str);
+      }
+
+      /* weighted, L = diag(L) */
+      {
+        test_multifit_solve(lambda, X, y, w, diagL, NULL, &rnorm0, &snorm0, c0);
+        test_multilarge_solve(T, lambda, X, y, w, diagL, NULL, &rnorm1, &snorm1, c1);
+
+        sprintf(str, "random %s weighted diag(L) n=%zu p=%zu lambda=%g",
+                T->name, n, p, lambda);
+        test_compare_vectors(tol, c0, c1, str);
+
+        gsl_test_rel(rnorm1, rnorm0, tol1, "rnorm %s", str);
+        gsl_test_rel(snorm1, snorm0, tol, "snorm %s", str);
+      }
+
+      /* unweighted, L = diag(L) */
+      {
+        test_multifit_solve(lambda, X, y, NULL, diagL, NULL, &rnorm0, &snorm0, c0);
+        test_multilarge_solve(T, lambda, X, y, NULL, diagL, NULL, &rnorm1, &snorm1, c1);
+
+        sprintf(str, "random %s unweighted diag(L) n=%zu p=%zu lambda=%g",
+                T->name, n, p, lambda);
+        test_compare_vectors(tol, c0, c1, str);
+
+        gsl_test_rel(rnorm1, rnorm0, tol1, "rnorm %s", str);
+        gsl_test_rel(snorm1, snorm0, tol, "snorm %s", str);
+      }
+
+      /* weighted, L = square */
+      {
+        test_multifit_solve(lambda, X, y, w, NULL, Lsqr, &rnorm0, &snorm0, c0);
+        test_multilarge_solve(T, lambda, X, y, w, NULL, Lsqr, &rnorm1, &snorm1, c1);
+
+        sprintf(str, "random %s weighted Lsqr n=%zu p=%zu lambda=%g",
+                T->name, n, p, lambda);
+        test_compare_vectors(tol, c0, c1, str);
+
+        gsl_test_rel(rnorm1, rnorm0, tol1, "rnorm %s", str);
+        gsl_test_rel(snorm1, snorm0, tol, "snorm %s", str);
+      }
+
+      /* unweighted, L = square */
+      {
+        test_multifit_solve(lambda, X, y, NULL, NULL, Lsqr, &rnorm0, &snorm0, c0);
+        test_multilarge_solve(T, lambda, X, y, NULL, NULL, Lsqr, &rnorm1, &snorm1, c1);
+
+        sprintf(str, "random %s unweighted Lsqr n=%zu p=%zu lambda=%g",
+                T->name, n, p, lambda);
+        test_compare_vectors(tol, c0, c1, str);
+
+        gsl_test_rel(rnorm1, rnorm0, tol1, "rnorm %s", str);
+        gsl_test_rel(snorm1, snorm0, tol, "snorm %s", str);
+      }
+
+      /* weighted, L = tall */
+      {
+        test_multifit_solve(lambda, X, y, w, NULL, Ltall, &rnorm0, &snorm0, c0);
+        test_multilarge_solve(T, lambda, X, y, w, NULL, Ltall, &rnorm1, &snorm1, c1);
+
+        sprintf(str, "random %s weighted Ltall n=%zu p=%zu lambda=%g",
+                T->name, n, p, lambda);
+        test_compare_vectors(tol, c0, c1, str);
+
+        gsl_test_rel(rnorm1, rnorm0, tol1, "rnorm %s", str);
+        gsl_test_rel(snorm1, snorm0, tol, "snorm %s", str);
+      }
+
+      /* unweighted, L = tall */
+      {
+        test_multifit_solve(lambda, X, y, NULL, NULL, Ltall, &rnorm0, &snorm0, c0);
+        test_multilarge_solve(T, lambda, X, y, NULL, NULL, Ltall, &rnorm1, &snorm1, c1);
+
+        sprintf(str, "random %s unweighted Ltall n=%zu p=%zu lambda=%g",
+                T->name, n, p, lambda);
+        test_compare_vectors(tol, c0, c1, str);
+
+        gsl_test_rel(rnorm1, rnorm0, tol1, "rnorm %s", str);
+        gsl_test_rel(snorm1, snorm0, tol, "snorm %s", str);
+      }
+    }
+
+  gsl_matrix_free(X);
+  gsl_vector_free(y);
+  gsl_vector_free(c);
+  gsl_vector_free(w);
+  gsl_vector_free(diagL);
+  gsl_matrix_free(Lsqr);
+  gsl_matrix_free(Ltall);
+  gsl_vector_free(c0);
+  gsl_vector_free(c1);
+}
+
+int
+main (void)
+{
+  gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+
+  gsl_ieee_env_setup();
+
+  {
+    const double tol1 = 1.0e-8;
+    const double tol2 = 1.0e-11;
+    const size_t n_vals[] = { 40, 356, 501 };
+    const size_t p_vals[] = { 40, 213, 345 };
+    size_t i;
+
+    for (i = 0; i < 2; ++i)
+      {
+        size_t n = n_vals[i];
+        size_t p = p_vals[i];
+
+        /* generate random ill-conditioned LS system and test */
+        test_random(gsl_multilarge_linear_normal, n, p, tol1, r);
+        test_random(gsl_multilarge_linear_tsqr, n, p, tol2, r);
+      }
+  }
+
+  gsl_rng_free(r);
+
+  exit (gsl_test_summary ());
+}
diff -Nru gsl-doc-1.16/multilarge/tsqr.c gsl-doc-2.3/multilarge/tsqr.c
--- gsl-doc-1.16/multilarge/tsqr.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge/tsqr.c	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,705 @@
+/* tsqr.c
+ * 
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/*
+ * This module implements the sequential TSQR algorithm
+ * described in
+ *
+ * [1] Demmel, J., Grigori, L., Hoemmen, M. F., and Langou, J.
+ *     "Communication-optimal parallel and sequential QR and LU factorizations",
+ *     UCB Technical Report No. UCB/EECS-2008-89, 2008.
+ *
+ * The algorithm operates on a tall least squares system:
+ *
+ * [ A_1 ] x = [ b_1 ]
+ * [ A_2 ]     [ b_2 ]
+ * [ ... ]     [ ... ]
+ * [ A_k ]     [ b_k ]
+ *
+ * as follows:
+ *
+ * 1. Initialize
+ *    a. [Q_1,R_1] = qr(A_1)
+ *    b. z_1 = Q_1^T b_1
+ * 2. Loop i = 2:k
+ *    a. [Q_i,R_i] = qr( [ R_{i-1} ; A_i ] )
+ *    b. z_i = Q_i^T [ z_{i-1} ; b_i ]
+ * 3. Output:
+ *    a. R = R_k
+ *    b. Q^T b = z_k
+ *
+ * Step 2(a) is optimized to take advantage
+ * of the sparse structure of the matrix
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_multilarge.h>
+#include <gsl/gsl_multifit.h>
+
+typedef struct
+{
+  size_t p;             /* number of columns of LS matrix */
+  int init;             /* QR system has been initialized */
+  int svd;              /* SVD of R has been computed */
+  double normb;         /* || b || for computing residual norm */
+
+  gsl_vector *tau;      /* Householder scalars, p-by-1 */
+  gsl_matrix *R;        /* [ R ; A_i ], size p-by-p */
+  gsl_vector *QTb;      /* [ Q^T b ; b_i ], size p-by-1 */
+
+  gsl_multifit_linear_workspace *multifit_workspace_p;
+} tsqr_state_t;
+
+static void *tsqr_alloc(const size_t p);
+static void tsqr_free(void *vstate);
+static int tsqr_reset(void *vstate);
+static int tsqr_accumulate(gsl_matrix * A, gsl_vector * b,
+                           void * vstate);
+static int tsqr_solve(const double lambda, gsl_vector * x,
+                      double * rnorm, double * snorm,
+                      void * vstate);
+static int tsqr_rcond(double * rcond, void * vstate);
+static int tsqr_lcurve(gsl_vector * reg_param, gsl_vector * rho,
+                       gsl_vector * eta, void * vstate);
+static int tsqr_svd(tsqr_state_t * state);
+static double tsqr_householder_transform (double *v0, gsl_vector * v);
+static int tsqr_householder_hv (const double tau, const gsl_vector * v, double *w0,
+                                gsl_vector * w);
+static int tsqr_householder_hm (const double tau, const gsl_vector * v, gsl_matrix * R,
+                                gsl_matrix * A);
+static int tsqr_QR_decomp (gsl_matrix * R, gsl_matrix * A, gsl_vector * tau);
+
+/*
+tsqr_alloc()
+  Allocate workspace for solving large linear least squares
+problems using the TSQR approach
+
+Inputs: p    - number of columns of LS matrix
+
+Return: pointer to workspace
+*/
+
+static void *
+tsqr_alloc(const size_t p)
+{
+  tsqr_state_t *state;
+
+  if (p == 0)
+    {
+      GSL_ERROR_NULL("p must be a positive integer",
+                     GSL_EINVAL);
+    }
+
+  state = calloc(1, sizeof(tsqr_state_t));
+  if (!state)
+    {
+      GSL_ERROR_NULL("failed to allocate tsqr state", GSL_ENOMEM);
+    }
+
+  state->p = p;
+  state->init = 0;
+  state->svd = 0;
+  state->normb = 0.0;
+
+  state->R = gsl_matrix_alloc(p, p);
+  if (state->R == NULL)
+    {
+      tsqr_free(state);
+      GSL_ERROR_NULL("failed to allocate R matrix", GSL_ENOMEM);
+    }
+
+  state->QTb = gsl_vector_alloc(p);
+  if (state->QTb == NULL)
+    {
+      tsqr_free(state);
+      GSL_ERROR_NULL("failed to allocate QTb vector", GSL_ENOMEM);
+    }
+
+  state->tau = gsl_vector_alloc(p);
+  if (state->tau == NULL)
+    {
+      tsqr_free(state);
+      GSL_ERROR_NULL("failed to allocate tau vector", GSL_ENOMEM);
+    }
+
+  state->multifit_workspace_p = gsl_multifit_linear_alloc(p, p);
+  if (state->multifit_workspace_p == NULL)
+    {
+      tsqr_free(state);
+      GSL_ERROR_NULL("failed to allocate multifit workspace", GSL_ENOMEM);
+    }
+
+  return state;
+}
+
+static void
+tsqr_free(void *vstate)
+{
+  tsqr_state_t *state = (tsqr_state_t *) vstate;
+
+  if (state->R)
+    gsl_matrix_free(state->R);
+
+  if (state->QTb)
+    gsl_vector_free(state->QTb);
+
+  if (state->tau)
+    gsl_vector_free(state->tau);
+
+  if (state->multifit_workspace_p)
+    gsl_multifit_linear_free(state->multifit_workspace_p);
+
+  free(state);
+}
+
+static int
+tsqr_reset(void *vstate)
+{
+  tsqr_state_t *state = (tsqr_state_t *) vstate;
+
+  gsl_matrix_set_zero(state->R);
+  gsl_vector_set_zero(state->QTb);
+  state->init = 0;
+  state->svd = 0;
+  state->normb = 0.0;
+
+  return GSL_SUCCESS;
+}
+
+/*
+tsqr_accumulate()
+  Add a new block of rows to the QR system
+
+Inputs: A      - new block of rows, n-by-p
+        b      - new rhs vector n-by-1
+        vstate - workspace
+
+Return: success/error
+
+Notes:
+1) On output, the upper triangular portion of state->R(1:p,1:p)
+contains current R matrix
+
+2) state->QTb(1:p) contains current Q^T b vector
+
+3) A and b are destroyed
+*/
+
+static int
+tsqr_accumulate(gsl_matrix * A, gsl_vector * b, void * vstate)
+{
+  tsqr_state_t *state = (tsqr_state_t *) vstate;
+  const size_t n = A->size1;
+  const size_t p = A->size2;
+
+  if (p != state->p)
+    {
+      GSL_ERROR("columns of A do not match workspace", GSL_EBADLEN);
+    }
+  else if (n != b->size)
+    {
+      GSL_ERROR("A and b have different numbers of rows", GSL_EBADLEN);
+    }
+  else if (state->init == 0)
+    {
+      int status;
+      const size_t npmin = GSL_MIN(n, p);
+      gsl_vector_view tau = gsl_vector_subvector(state->tau, 0, npmin);
+      gsl_matrix_view R = gsl_matrix_submatrix(state->R, 0, 0, npmin, p);
+      gsl_matrix_view Av = gsl_matrix_submatrix(A, 0, 0, npmin, p);
+      gsl_vector_view QTb = gsl_vector_subvector(state->QTb, 0, npmin);
+      gsl_vector_view bv = gsl_vector_subvector(b, 0, npmin);
+
+      /* this is the first matrix block A_1, compute its (dense) QR decomposition */
+
+      /* compute QR decomposition of A */
+      status = gsl_linalg_QR_decomp(A, &tau.vector);
+      if (status)
+        return status;
+
+      /* store upper triangular R factor in state->R */
+      gsl_matrix_tricpy('U', 1, &R.matrix, &Av.matrix);
+
+      /* compute ||b|| */
+      state->normb = gsl_blas_dnrm2(b);
+
+      /* compute Q^T b and keep the first p elements */
+      gsl_linalg_QR_QTvec(A, &tau.vector, b);
+      gsl_vector_memcpy(&QTb.vector, &bv.vector);
+
+      state->init = 1;
+
+      return GSL_SUCCESS;
+    }
+  else
+    {
+      int status;
+
+      /* compute QR decomposition of [ R_{i-1} ; A_i ], accounting for
+       * sparse structure */
+      status = tsqr_QR_decomp(state->R, A, state->tau);
+      if (status)
+        return status;
+
+      /* update ||b|| */
+      state->normb = gsl_hypot(state->normb, gsl_blas_dnrm2(b));
+
+      /*
+       * compute Q^T [ QTb_{i - 1}; b_i ], accounting for the sparse
+       * structure of the Householder reflectors
+       */
+      {
+        size_t i;
+
+        for (i = 0; i < p; i++)
+          {
+            const double ti = gsl_vector_get (state->tau, i);
+            gsl_vector_const_view h = gsl_matrix_const_column (A, i);
+            double *wi = gsl_vector_ptr(state->QTb, i);
+            tsqr_householder_hv (ti, &(h.vector), wi, b);
+          }
+      }
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+tsqr_solve()
+  Solve the least squares system:
+
+chi^2 = || QTb - R x ||^2 + lambda^2 || x ||^2
+
+using the SVD of R
+
+Inputs: lambda - regularization parameter
+        x      - (output) solution vector p-by-1
+        rnorm  - (output) residual norm ||b - A x||
+        snorm  - (output) solution norm ||x||
+        vstate - workspace
+
+Return: success/error
+*/
+
+static int
+tsqr_solve(const double lambda, gsl_vector * x,
+           double * rnorm, double * snorm,
+           void * vstate)
+{
+  tsqr_state_t *state = (tsqr_state_t *) vstate;
+  const size_t p = x->size;
+
+  if (p != state->p)
+    {
+      GSL_ERROR("solution vector does not match workspace", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+
+      /* compute SVD of R if not already computed */
+      if (state->svd == 0)
+        {
+          status = tsqr_svd(state);
+          if (status)
+            return status;
+        }
+
+      status = gsl_multifit_linear_solve(lambda, state->R, state->QTb, x, rnorm, snorm,
+                                         state->multifit_workspace_p);
+      if (status)
+        return status;
+
+      /*
+       * Since we're solving a reduced square system above, we need
+       * to account for the full residual vector:
+       *
+       * rnorm = || [ Q1^T b - R x ; Q2^T b ] ||
+       *
+       * where Q1 is the thin Q factor of X, and Q2
+       * are the remaining columns of Q. But:
+       *
+       * || Q2^T b ||^2 = ||b||^2 - ||Q1^T b||^2
+       * 
+       * so add this into the rnorm calculation
+       */
+      {
+        double norm_Q1Tb = gsl_blas_dnrm2(state->QTb);
+        double ratio = norm_Q1Tb / state->normb;
+        double diff = 1.0 - ratio*ratio;
+
+        if (diff > GSL_DBL_EPSILON)
+          {
+            double norm_Q2Tb = state->normb * sqrt(diff);
+            *rnorm = gsl_hypot(*rnorm, norm_Q2Tb);
+          }
+      }
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+tsqr_lcurve()
+  Compute L-curve of least squares system
+
+Inputs: reg_param - (output) vector of regularization parameters
+        rho       - (output) vector of residual norms
+        eta       - (output) vector of solution norms
+        vstate    - workspace
+
+Return: success/error
+*/
+
+static int
+tsqr_lcurve(gsl_vector * reg_param, gsl_vector * rho,
+            gsl_vector * eta, void * vstate)
+{
+  tsqr_state_t *state = (tsqr_state_t *) vstate;
+  int status;
+
+  /* compute SVD of R if not already computed */
+  if (state->svd == 0)
+    {
+      status = tsqr_svd(state);
+      if (status)
+        return status;
+    }
+
+  status = gsl_multifit_linear_lcurve(state->QTb, reg_param, rho, eta,
+                                      state->multifit_workspace_p);
+
+  /* now add contribution to rnorm from Q2 factor */
+  {
+    double norm_Q1Tb = gsl_blas_dnrm2(state->QTb);
+    double ratio = norm_Q1Tb / state->normb;
+    double diff = 1.0 - ratio*ratio;
+    size_t i;
+
+    if (diff > GSL_DBL_EPSILON)
+      {
+        double norm_Q2Tb = state->normb * sqrt(diff);
+
+        for (i = 0; i < rho->size; ++i)
+          {
+            double *rhoi = gsl_vector_ptr(rho, i);
+            *rhoi = gsl_hypot(*rhoi, norm_Q2Tb);
+          }
+      }
+  }
+
+  return status;
+}
+
+static int
+tsqr_rcond(double * rcond, void * vstate)
+{
+  tsqr_state_t *state = (tsqr_state_t *) vstate;
+
+  /* compute SVD of R if not already computed */
+  if (state->svd == 0)
+    {
+      int status = tsqr_svd(state);
+      if (status)
+        return status;
+    }
+
+  *rcond = gsl_multifit_linear_rcond(state->multifit_workspace_p);
+
+  return GSL_SUCCESS;
+}
+
+/*
+tsqr_svd()
+  Compute the SVD of the upper triangular
+R factor. This allows us to compute the upper/lower
+bounds on the regularization parameter and compute
+the matrix reciprocal condition number.
+
+Inputs: state - workspace
+
+Return: success/error
+*/
+
+static int
+tsqr_svd(tsqr_state_t * state)
+{
+  int status;
+
+  status = gsl_multifit_linear_svd(state->R, state->multifit_workspace_p);
+  if (status)
+    {
+      GSL_ERROR("error computing SVD of R", status);
+    }
+
+  state->svd = 1;
+
+  return GSL_SUCCESS;
+}
+
+/*
+tsqr_householder_transform()
+  This routine is an optimized version of
+gsl_linalg_householder_transform(), designed for the QR
+decomposition of M-by-N matrices of the form:
+
+T = [ R ]
+    [ A ]
+
+where R is N-by-N upper triangular, and A is (M-N)-by-N dense.
+This routine computes a householder transformation (tau,v) of a 
+x so that P x = [ I - tau*v*v' ] x annihilates x(1:n-1). x will
+be a subcolumn of the matrix T, and so its structure will be:
+
+x = [ x0 ] <- 1 nonzero value for the diagonal element of R
+    [ 0  ] <- N - j - 1 zeros, where j is column of matrix in [0,N-1]
+    [ x  ] <- M-N nonzero values for the dense part A
+
+Inputs: v0 - pointer to diagonal element of R
+             on input, v0 = x0;
+        v  - on input, x vector
+             on output, householder vector v
+*/
+
+static double
+tsqr_householder_transform (double *v0, gsl_vector * v)
+{
+  /* replace v[0:M-1] with a householder vector (v[0:M-1]) and
+     coefficient tau that annihilate v[1:M-1] */
+
+  double alpha, beta, tau ;
+  
+  /* compute xnorm = || [ 0 ; v ] ||, ignoring zero part of vector */
+  double xnorm = gsl_blas_dnrm2(v);
+
+  if (xnorm == 0) 
+    {
+      return 0.0; /* tau = 0 */
+    }
+
+  alpha = *v0;
+  beta = - (alpha >= 0.0 ? +1.0 : -1.0) * hypot(alpha, xnorm) ;
+  tau = (beta - alpha) / beta ;
+  
+  {
+    double s = (alpha - beta);
+    
+    if (fabs(s) > GSL_DBL_MIN) 
+      {
+        gsl_blas_dscal (1.0 / s, v);
+        *v0 = beta;
+      }
+    else
+      {
+        gsl_blas_dscal (GSL_DBL_EPSILON / s, v);
+        gsl_blas_dscal (1.0 / GSL_DBL_EPSILON, v);
+        *v0 = beta;
+      }
+  }
+  
+  return tau;
+}
+
+/*
+tsqr_householder_hv()
+  Apply Householder reflector to a vector. The Householder
+reflectors are for the QR decomposition of the matrix
+
+  [ R ]
+  [ A ]
+
+where R is p-by-p upper triangular and A is n-by-p dense.
+Therefore all relevant components of the Householder
+vector are stored in the columns of A, while the components
+in R are 0, except for diag(R) which are 1.
+
+The vector w to be transformed is partitioned as
+
+  [ w1 ]
+  [ w2 ]
+
+where w1 is p-by-1 and w2 is n-by-1. The w2 portion
+of w is transformed by v, but most of w1 remains unchanged
+except for the first element, w0
+
+Inputs: tau - Householder scalar
+        v   - Householder vector, n-by-1
+        w0  - (input/output)
+              on input, w1(0);
+              on output, transformed w1(0)
+        w   - (input/output) n-by-1
+              on input, vector w2;
+              on output, P*w2
+*/
+
+static int
+tsqr_householder_hv (const double tau, const gsl_vector * v, double *w0, gsl_vector * w)
+{
+  /* applies a householder transformation v to vector w */
+ 
+  if (tau == 0)
+    return GSL_SUCCESS ;
+
+  {
+    double d1, d;
+
+    /* compute d1 = v(2:n)' w(2:n) */
+    gsl_blas_ddot (v, w, &d1);
+
+    /* compute d = v'w = w(1) + d1 since v(1) = 1 */
+    d = *w0 + d1;
+
+    /* compute w = w - tau (v) (v'w) */
+    *w0 -= tau * d;
+    gsl_blas_daxpy (-tau * d, v, w);
+  }
+  
+  return GSL_SUCCESS;
+}
+
+/*
+tsqr_householder_hm()
+  Apply Householder reflector to a submatrix of
+
+  [ R ]
+  [ A ]
+
+where R is p-by-p upper triangular and A is n-by-p dense.
+The diagonal terms of R are already transformed by
+tsqr_householder_transform(), so we just need to operate
+on the submatrix A(:,i:p) as well as the superdiagonal
+elements of R
+
+Inputs: tau - Householder scalar
+        v   - Householder vector
+        R   - upper triangular submatrix of R, (p-i)-by-(p-i-1)
+        A   - dense submatrix of A, n-by-(p-i)
+*/
+
+static int
+tsqr_householder_hm (const double tau, const gsl_vector * v, gsl_matrix * R,
+                     gsl_matrix * A)
+{
+  /* applies a householder transformation v,tau to matrix [ R ; A ] */
+
+  if (tau == 0.0)
+    {
+      return GSL_SUCCESS;
+    }
+  else
+    {
+      size_t j;
+
+      for (j = 0; j < A->size2; j++)
+        {
+          double R0j = gsl_matrix_get (R, 0, j);
+          double wj;
+          gsl_vector_view A1j = gsl_matrix_column(A, j);
+
+          gsl_blas_ddot (&A1j.vector, v, &wj);
+          wj += R0j;
+
+          gsl_matrix_set (R, 0, j, R0j - tau *  wj);
+
+          gsl_blas_daxpy (-tau * wj, v, &A1j.vector);
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+tsqr_QR_decomp()
+  Compute the QR decomposition of the matrix
+
+  [ R ]
+  [ A ]
+
+where R is p-by-p upper triangular and A is n-by-p dense.
+
+Inputs: R   - upper triangular p-by-p matrix
+        A   - dense n-by-p matrix
+        tau - Householder scalars
+*/
+
+static int
+tsqr_QR_decomp (gsl_matrix * R, gsl_matrix * A, gsl_vector * tau)
+{
+  const size_t n = A->size1;
+  const size_t p = R->size2;
+
+  if (R->size2 != A->size2)
+    {
+      GSL_ERROR ("R and A have different number of columns", GSL_EBADLEN);
+    }
+  else if (tau->size != p)
+    {
+      GSL_ERROR ("size of tau must be p", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i;
+
+      for (i = 0; i < p; i++)
+        {
+          /* Compute the Householder transformation to reduce the j-th
+             column of the matrix [ R ; A ] to a multiple of the j-th unit vector,
+             taking into account the sparse structure of R */
+
+          gsl_vector_view c = gsl_matrix_column(A, i);
+          double *Rii = gsl_matrix_ptr(R, i, i);
+          double tau_i = tsqr_householder_transform(Rii, &c.vector);
+
+          gsl_vector_set (tau, i, tau_i);
+
+          /* Apply the transformation to the remaining columns and
+             update the norms */
+
+          if (i + 1 < p)
+            {
+              gsl_matrix_view Rv = gsl_matrix_submatrix(R, i, i + 1, p - i, p - (i + 1));
+              gsl_matrix_view Av = gsl_matrix_submatrix(A, 0, i + 1, n, p - (i + 1));
+              tsqr_householder_hm (tau_i, &(c.vector), &(Rv.matrix), &(Av.matrix));
+            }
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+static const gsl_multilarge_linear_type tsqr_type =
+{
+  "tsqr",
+  tsqr_alloc,
+  tsqr_reset,
+  tsqr_accumulate,
+  tsqr_solve,
+  tsqr_rcond,
+  tsqr_lcurve,
+  tsqr_free
+};
+
+const gsl_multilarge_linear_type * gsl_multilarge_linear_tsqr =
+  &tsqr_type;
diff -Nru gsl-doc-1.16/multilarge_nlinear/cgst.c gsl-doc-2.3/multilarge_nlinear/cgst.c
--- gsl-doc-1.16/multilarge_nlinear/cgst.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/cgst.c	2016-08-10 21:03:42.000000000 +0000
@@ -0,0 +1,382 @@
+/* multilarge_nlinear/cgst.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multilarge_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+
+/*
+ * This module contains an implementation of the Steihaug-Toint
+ * conjugate gradient algorithm for nonlinear optimization problems.
+ * This implementation closely follows the following works:
+ *
+ * [1] T. Steihaug, The conjugate gradient method and trust regions
+ *     in large scale optimization, SIAM J. Num. Anal., 20(3) 1983.
+ *
+ * In the below algorithm, the Jacobian and gradient are scaled
+ * according to:
+ *
+ * J~ = J D^{-1}
+ * g~ = D^{-1}
+ *
+ * prior to any calculations which results in better numerical
+ * stability when solving for the Gauss-Newton step. The resulting
+ * step vector is then backtransformed as:
+ *
+ * dx = D^{-1} dx~
+ */
+
+typedef struct
+{
+  size_t n;                  /* number of observations */
+  size_t p;                  /* number of parameters */
+  gsl_vector *z;             /* Gauss-Newton step, size p */
+  gsl_vector *r;             /* steepest descent step, size p */
+  gsl_vector *d;             /* steepest descent step, size p */
+  gsl_vector *workp;         /* workspace, length p */
+  gsl_vector *workn;         /* workspace, length n */
+  double norm_g;             /* || g~ || */
+
+  double cgtol;              /* tolerance for CG solution */
+  size_t cgmaxit;            /* maximum CG iterations */
+} cgst_state_t;
+
+#include "common.c"
+
+static void * cgst_alloc (const void * params, const size_t n, const size_t p);
+static void cgst_free(void *vstate);
+static int cgst_init(const void *vtrust_state, void *vstate);
+static int cgst_preloop(const void * vtrust_state, void * vstate);
+static int cgst_step(const void * vtrust_state, const double delta,
+                     gsl_vector * dx, void * vstate);
+static int cgst_preduction(const void * vtrust_state, const gsl_vector * dx,
+                           double * pred, void * vstate);
+static double cgst_calc_tau(const gsl_vector * p, const gsl_vector * d,
+                            const double delta);
+
+static void *
+cgst_alloc (const void * params, const size_t n, const size_t p)
+{
+  const gsl_multilarge_nlinear_parameters *par = (const gsl_multilarge_nlinear_parameters *) params;
+  cgst_state_t *state;
+  
+  state = calloc(1, sizeof(cgst_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate st state", GSL_ENOMEM);
+    }
+
+  state->z = gsl_vector_alloc(p);
+  if (state->z == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for z", GSL_ENOMEM);
+    }
+
+  state->r = gsl_vector_alloc(p);
+  if (state->r == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for r", GSL_ENOMEM);
+    }
+
+  state->d = gsl_vector_alloc(p);
+  if (state->d == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for d", GSL_ENOMEM);
+    }
+
+  state->workp = gsl_vector_alloc(p);
+  if (state->workp == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workp", GSL_ENOMEM);
+    }
+
+  state->workn = gsl_vector_alloc(n);
+  if (state->workn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workn", GSL_ENOMEM);
+    }
+
+  state->n = n;
+  state->p = p;
+
+  state->cgmaxit = par->max_iter;
+  if (state->cgmaxit == 0)
+    state->cgmaxit = n;
+
+  state->cgtol = par->tol;
+
+  return state;
+}
+
+static void
+cgst_free(void *vstate)
+{
+  cgst_state_t *state = (cgst_state_t *) vstate;
+
+  if (state->z)
+    gsl_vector_free(state->z);
+
+  if (state->r)
+    gsl_vector_free(state->r);
+
+  if (state->d)
+    gsl_vector_free(state->d);
+
+  if (state->workp)
+    gsl_vector_free(state->workp);
+
+  if (state->workn)
+    gsl_vector_free(state->workn);
+
+  free(state);
+}
+
+/*
+cgst_init()
+  Initialize cgst solver
+
+Inputs: vtrust_state - trust state
+        vstate       - workspace
+
+Return: success/error
+*/
+
+static int
+cgst_init(const void *vtrust_state, void *vstate)
+{
+  /* nothing to do */
+
+  (void)vtrust_state;
+  (void)vstate;
+
+  return GSL_SUCCESS;
+}
+
+static int
+cgst_preloop(const void * vtrust_state, void * vstate)
+{
+  /* nothing to do */
+
+  (void)vtrust_state;
+  (void)vstate;
+
+  return GSL_SUCCESS;
+}
+
+/*
+cgst_step()
+  Calculate a new step vector
+
+Return:
+GSL_SUCCESS if CG solution found
+GSL_EMAXITER if no solution found
+*/
+
+static int
+cgst_step(const void * vtrust_state, const double delta,
+          gsl_vector * dx, void * vstate)
+{
+  int status;
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  cgst_state_t *state = (cgst_state_t *) vstate;
+  const gsl_vector * x = trust_state->x;
+  const gsl_vector * f = trust_state->f;
+  const gsl_vector * swts = trust_state->sqrt_wts;
+  const gsl_vector * diag = trust_state->diag;
+  const gsl_multilarge_nlinear_parameters * params = trust_state->params;
+  gsl_multilarge_nlinear_fdf * fdf = trust_state->fdf;
+  double alpha, beta, u;
+  double norm_Jd;   /* || J D^{-1} d_i || */
+  double norm_r;    /* || r_i || */
+  double norm_rp1;  /* || r_{i+1} || */
+  size_t i;
+
+  /* Step 1 of [1], section 2; scale gradient as
+   *
+   * g~ = D^{-1} g
+   *
+   * for better numerical stability
+   */
+
+  for (i = 0; i < state->p; ++i)
+    {
+      double gi = gsl_vector_get(trust_state->g, i);
+      double di = gsl_vector_get(trust_state->diag, i);
+
+      gsl_vector_set(state->z, i, 0.0);
+      gsl_vector_set(state->r, i, -gi / di);
+      gsl_vector_set(state->d, i, -gi / di);
+      gsl_vector_set(state->workp, i, gi / di);
+    }
+
+  /* compute || g~ || */
+  state->norm_g = gsl_blas_dnrm2(state->workp);
+
+  for (i = 0; i < state->cgmaxit; ++i)
+    {
+      /* workp := D^{-1} d_i */
+      gsl_vector_memcpy(state->workp, state->d);
+      gsl_vector_div(state->workp, trust_state->diag);
+
+      /* workn := J D^{-1} d_i */
+      status = gsl_multilarge_nlinear_eval_df(CblasNoTrans, x, f, state->workp,
+                                              swts, params->h_df, params->fdtype,
+                                              fdf, state->workn, NULL, NULL);
+      if (status)
+        return status;
+
+      /* compute || J D^{-1} d_i || */
+      norm_Jd = gsl_blas_dnrm2(state->workn);
+
+      /* Step 2 of [1], section 2 */
+      if (norm_Jd == 0.0)
+        {
+          double tau = cgst_calc_tau(state->z, state->d, delta);
+
+          /* dx = z_i + tau*d_i */
+          scaled_addition(1.0, state->z, tau, state->d, dx);
+          gsl_vector_div(dx, diag);
+
+          return GSL_SUCCESS;
+        }
+
+      /* Step 3 of [1], section 2 */
+
+      norm_r = gsl_blas_dnrm2(state->r);
+      u = norm_r / norm_Jd;
+      alpha = u * u;
+
+      /* workp <= z_{i+1} = z_i + alpha_i*d_i */
+      scaled_addition(1.0, state->z, alpha, state->d, state->workp);
+
+      u = gsl_blas_dnrm2(state->workp);
+      if (u >= delta)
+        {
+          double tau = cgst_calc_tau(state->z, state->d, delta);
+
+          /* dx = z_i + tau*d_i */
+          scaled_addition(1.0, state->z, tau, state->d, dx);
+          gsl_vector_div(dx, diag);
+
+          return GSL_SUCCESS;
+        }
+
+      /* store z_{i+1} */
+      gsl_vector_memcpy(state->z, state->workp);
+
+      /* Step 4 of [1], section 2 */
+
+      /* compute: workp := alpha B d_i = alpha D^{-1} J^T J D^{-1} d_i,
+       * where J D^{-1} d_i is already stored in workn */
+      status = gsl_multilarge_nlinear_eval_df(CblasTrans, x, f, state->workn,
+                                              swts, params->h_df, params->fdtype,
+                                              fdf, state->workp, NULL, NULL);
+      if (status)
+        return status;
+
+      gsl_vector_div(state->workp, trust_state->diag);
+      gsl_vector_scale(state->workp, alpha);
+
+      /* r_{i+1} = r_i - alpha*B*d_i */
+      gsl_vector_sub(state->r, state->workp);
+      norm_rp1 = gsl_blas_dnrm2(state->r);
+
+      u = norm_rp1 / state->norm_g;
+      if (u < state->cgtol)
+        {
+          gsl_vector_memcpy(dx, state->z);
+          gsl_vector_div(dx, diag);
+          return GSL_SUCCESS;
+        }
+
+      /* Step 5 of [1], section 2 */
+
+      /* compute u = ||r_{i+1}|| / || r_i|| */
+      u = norm_rp1 / norm_r;
+      beta = u * u;
+
+      /* compute: d_{i+1} = rt_{i+1} + beta*d_i */
+      scaled_addition(1.0, state->r, beta, state->d, state->d);
+    }
+
+  /* failed to converge, return current estimate */
+  gsl_vector_memcpy(dx, state->z);
+  gsl_vector_div(dx, diag);
+
+  return GSL_EMAXITER;
+}
+
+static int
+cgst_preduction(const void * vtrust_state, const gsl_vector * dx,
+                double * pred, void * vstate)
+{
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  cgst_state_t *state = (cgst_state_t *) vstate;
+
+  *pred = quadratic_preduction(trust_state, dx, state->workn);
+
+  return GSL_SUCCESS;
+}
+
+/*
+cgst_calc_tau()
+  Compute tau > 0 such that:
+
+|| p + tau*d || = delta
+*/
+
+static double
+cgst_calc_tau(const gsl_vector * p, const gsl_vector * d,
+              const double delta)
+{
+  double norm_p, norm_d, u;
+  double t1, t2, tau;
+
+  norm_p = gsl_blas_dnrm2(p);
+  norm_d = gsl_blas_dnrm2(d);
+
+  /* compute (p, d) */
+  gsl_blas_ddot(p, d, &u);
+
+  t1 = u / (norm_d * norm_d);
+  t2 = t1*u + (delta + norm_p) * (delta - norm_p);
+  tau = -t1 + sqrt(t2) / norm_d;
+
+  return tau;
+}
+
+static const gsl_multilarge_nlinear_trs cgst_type =
+{
+  "steihaug-toint",
+  cgst_alloc,
+  cgst_init,
+  cgst_preloop,
+  cgst_step,
+  cgst_preduction,
+  cgst_free
+};
+
+const gsl_multilarge_nlinear_trs *gsl_multilarge_nlinear_trs_cgst = &cgst_type;
diff -Nru gsl-doc-1.16/multilarge_nlinear/cholesky.c gsl-doc-2.3/multilarge_nlinear/cholesky.c
--- gsl-doc-1.16/multilarge_nlinear/cholesky.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/cholesky.c	2016-08-19 17:37:20.000000000 +0000
@@ -0,0 +1,324 @@
+/* multilarge_nlinear/cholesky.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/*
+ * This module calculates the solution of the normal equations least squares
+ * system:
+ *
+ * [ J^T J + mu D^T D ] p = -J^T f
+ *
+ * using the modified Cholesky decomposition.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multilarge_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_permutation.h>
+
+#include "common.c"
+
+typedef struct
+{
+  gsl_matrix *JTJ;           /* J^T J */
+  gsl_matrix *work_JTJ;      /* copy of J^T J */
+  gsl_vector *rhs;           /* -J^T f, size p */
+  gsl_permutation *perm;     /* permutation matrix for modified Cholesky */
+  gsl_vector *work3p;        /* workspace, size 3*p */
+  gsl_vector *workn;         /* workspace, size n */
+  double mu;                 /* current regularization parameter */
+} cholesky_state_t;
+
+static void *cholesky_alloc (const size_t n, const size_t p);
+static int cholesky_init(const void * vtrust_state, void * vstate);
+static int cholesky_presolve(const double mu, const void * vtrust_state, void * vstate);
+static int cholesky_solve(const gsl_vector * g, gsl_vector *x,
+                          const  void * vtrust_state, void *vstate);
+static int cholesky_rcond(double * rcond, const gsl_matrix * JTJ, void * vstate);
+static int cholesky_covar(const gsl_matrix * JTJ, gsl_matrix * covar, void * vstate);
+static int cholesky_solve_rhs(const gsl_vector * b, gsl_vector *x, cholesky_state_t *state);
+static int cholesky_regularize(const double mu, const gsl_vector * diag, gsl_matrix * A,
+                               cholesky_state_t * state);
+
+static void *
+cholesky_alloc (const size_t n, const size_t p)
+{
+  cholesky_state_t *state;
+
+  state = calloc(1, sizeof(cholesky_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate cholesky state", GSL_ENOMEM);
+    }
+
+  state->JTJ = gsl_matrix_alloc(p, p);
+  if (state->JTJ == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for JTJ", GSL_ENOMEM);
+    }
+
+  state->work_JTJ = gsl_matrix_alloc(p, p);
+  if (state->work_JTJ == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for JTJ workspace",
+                      GSL_ENOMEM);
+    }
+
+  state->rhs = gsl_vector_alloc(p);
+  if (state->rhs == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for rhs", GSL_ENOMEM);
+    }
+
+  state->perm = gsl_permutation_alloc(p);
+  if (state->perm == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for perm", GSL_ENOMEM);
+    }
+
+  state->work3p = gsl_vector_alloc(3 * p);
+  if (state->work3p == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for work3p", GSL_ENOMEM);
+    }
+
+  state->workn = gsl_vector_alloc(n);
+  if (state->workn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workn", GSL_ENOMEM);
+    }
+
+  state->mu = -1.0;
+
+  return state;
+}
+
+static void
+cholesky_free(void *vstate)
+{
+  cholesky_state_t *state = (cholesky_state_t *) vstate;
+
+  if (state->JTJ)
+    gsl_matrix_free(state->JTJ);
+
+  if (state->work_JTJ)
+    gsl_matrix_free(state->work_JTJ);
+
+  if (state->rhs)
+    gsl_vector_free(state->rhs);
+
+  if (state->perm)
+    gsl_permutation_free(state->perm);
+
+  if (state->work3p)
+    gsl_vector_free(state->work3p);
+
+  if (state->workn)
+    gsl_vector_free(state->workn);
+
+  free(state);
+}
+
+static int
+cholesky_init(const void * vtrust_state, void * vstate)
+{
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  cholesky_state_t *state = (cholesky_state_t *) vstate;
+
+  /* store J^T J normal equations matrix */
+  gsl_matrix_tricpy('L', 1, state->JTJ, trust_state->JTJ);
+
+  return GSL_SUCCESS;
+}
+
+/*
+cholesky_presolve()
+  Compute the modified Cholesky decomposition of J^T J + mu D^T D.
+Modified Cholesky is used in case mu = 0 and there are rounding
+errors in forming J^T J which could lead to an indefinite matrix.
+
+Inputs: mu     - LM parameter
+        vstate - workspace
+
+Notes:
+1) On output, state->work_JTJ contains the Cholesky decomposition of
+J^T J + mu D^T D
+*/
+
+static int
+cholesky_presolve(const double mu, const void * vtrust_state, void * vstate)
+{
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  cholesky_state_t *state = (cholesky_state_t *) vstate;
+  gsl_matrix *JTJ = state->work_JTJ;
+  const gsl_vector *diag = trust_state->diag;
+  int status;
+
+  /* copy lower triangle of A to workspace */
+  gsl_matrix_tricpy('L', 1, JTJ, state->JTJ);
+
+  /* augment normal equations: A -> A + mu D^T D */
+  status = cholesky_regularize(mu, diag, JTJ, state);
+  if (status)
+    return status;
+
+  /* compute modified Cholesky decomposition */
+  status = gsl_linalg_mcholesky_decomp(JTJ, state->perm, NULL);
+  if (status)
+    return status;
+
+  state->mu = mu;
+
+  return GSL_SUCCESS;
+}
+
+/*
+cholesky_solve()
+  Compute (J^T J + mu D^T D) x = -g
+
+where g = J^T f
+
+Inputs: g      - right hand side vector g, size p
+        x      - (output) solution vector
+        vstate - cholesky workspace
+*/
+
+static int
+cholesky_solve(const gsl_vector * g, gsl_vector *x,
+               const void * vtrust_state, void *vstate)
+{
+  cholesky_state_t *state = (cholesky_state_t *) vstate;
+  int status;
+
+  status = cholesky_solve_rhs(g, x, state);
+  if (status)
+    return status;
+
+  /* reverse direction to go downhill */
+  gsl_vector_scale(x, -1.0);
+
+  (void) vtrust_state;
+
+  return GSL_SUCCESS;
+}
+
+static int
+cholesky_rcond(double * rcond, const gsl_matrix * JTJ, void * vstate)
+{
+  int status;
+  cholesky_state_t *state = (cholesky_state_t *) vstate;
+  double rcond_JTJ;
+
+  /* its possible the current Cholesky decomposition is from the previous
+   * iteration so do a new one to be sure we use the right Jacobian */
+
+  /* copy lower triangle of JTJ to workspace */
+  gsl_matrix_tricpy('L', 1, state->work_JTJ, JTJ);
+
+  /* compute modified Cholesky decomposition */
+  status = gsl_linalg_mcholesky_decomp(state->work_JTJ, state->perm, NULL);
+  if (status)
+    return status;
+
+  status = gsl_linalg_mcholesky_rcond(state->work_JTJ, state->perm, &rcond_JTJ, state->work3p);
+  if (status == GSL_SUCCESS)
+    *rcond = sqrt(rcond_JTJ);
+
+  return status;
+}
+
+static int
+cholesky_covar(const gsl_matrix * JTJ, gsl_matrix * covar, void * vstate)
+{
+  int status;
+  cholesky_state_t *state = (cholesky_state_t *) vstate;
+
+  /* its possible the current Cholesky decomposition is from the previous
+   * iteration so do a new one to be sure we use the right Jacobian */
+
+  /* copy lower triangle of JTJ to workspace */
+  gsl_matrix_tricpy('L', 1, state->work_JTJ, JTJ);
+
+  /* compute modified Cholesky decomposition */
+  status = gsl_linalg_mcholesky_decomp(state->work_JTJ, state->perm, NULL);
+  if (status)
+    return status;
+
+  status = gsl_linalg_mcholesky_invert(state->work_JTJ, state->perm, covar);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+}
+
+/* solve: (J^T J + mu D^T D) x = b */
+static int
+cholesky_solve_rhs(const gsl_vector * b, gsl_vector *x, cholesky_state_t *state)
+{
+  int status;
+  gsl_matrix *JTJ = state->work_JTJ;
+
+  status = gsl_linalg_mcholesky_solve(JTJ, state->perm, b, x);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+}
+
+/* A <- A + mu D^T D */
+static int
+cholesky_regularize(const double mu, const gsl_vector * diag, gsl_matrix * A,
+                    cholesky_state_t * state)
+{
+  (void) state;
+
+  if (mu != 0.0)
+    {
+      size_t i;
+
+      for (i = 0; i < diag->size; ++i)
+        {
+          double di = gsl_vector_get(diag, i);
+          double *Aii = gsl_matrix_ptr(A, i, i);
+          *Aii += mu * di * di;
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+static const gsl_multilarge_nlinear_solver cholesky_type =
+{
+  "cholesky",
+  cholesky_alloc,
+  cholesky_init,
+  cholesky_presolve,
+  cholesky_solve,
+  cholesky_rcond,
+  cholesky_covar,
+  cholesky_free
+};
+
+const gsl_multilarge_nlinear_solver *gsl_multilarge_nlinear_solver_cholesky = &cholesky_type;
diff -Nru gsl-doc-1.16/multilarge_nlinear/common.c gsl-doc-2.3/multilarge_nlinear/common.c
--- gsl-doc-1.16/multilarge_nlinear/common.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/common.c	2016-08-10 21:03:42.000000000 +0000
@@ -0,0 +1,131 @@
+/* multilarge_nlinear/common.c
+ * 
+ * Copyright (C) 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+static double scaled_enorm (const gsl_vector * d, const gsl_vector * f);
+static void scaled_addition (const double alpha, const gsl_vector * x,
+                             const double beta, const gsl_vector * y,
+                             gsl_vector * z);
+static double quadratic_preduction(const gsl_multilarge_nlinear_trust_state * trust_state,
+                                   const gsl_vector * dx, gsl_vector * work);
+
+/* compute || diag(d) f || */
+static double
+scaled_enorm (const gsl_vector * d, const gsl_vector * f)
+{
+  double e2 = 0;
+  size_t i, n = f->size;
+  for (i = 0; i < n; i++)
+    {
+      double fi = gsl_vector_get (f, i);
+      double di = gsl_vector_get (d, i);
+      double u = di * fi;
+      e2 += u * u;
+    }
+  return sqrt (e2);
+}
+
+/* compute z = alpha*x + beta*y */
+static void
+scaled_addition (const double alpha, const gsl_vector * x,
+                 const double beta, const gsl_vector * y, gsl_vector * z)
+{
+  const size_t N = z->size;
+  size_t i;
+
+  for (i = 0; i < N; i++)
+    {
+      double xi = gsl_vector_get (x, i);
+      double yi = gsl_vector_get (y, i);
+      gsl_vector_set (z, i, alpha * xi + beta * yi);
+    }
+}
+
+/*
+quadratic_preduction()
+  Calculate predicted reduction based on standard
+quadratic model:
+
+m_k(dx) = Phi(x_k) + dx' g + 1/2 dx' B_k dx
+
+predicted_reduction = m_k(0) - m_k(dx)
+                    = -2 g^T dx / ||f||^2 - ( ||J*dx|| / ||f|| )^2
+                    = -2 fhat . beta - ||beta||^2
+
+where: beta = J*dx / ||f||
+
+Inputs: trust_state - trust state
+        dx          - proposed step, size p
+        work        - workspace, size n
+
+Return: predicted reduction
+*/
+
+static double
+quadratic_preduction(const gsl_multilarge_nlinear_trust_state * trust_state,
+                     const gsl_vector * dx, gsl_vector * work)
+{
+  const gsl_vector * f = trust_state->f;
+  const gsl_multilarge_nlinear_parameters * params = trust_state->params;
+  const double normf = gsl_blas_dnrm2(f);
+  double gTdx;      /* g^T dx */
+  gsl_multilarge_nlinear_fdf * fdf = trust_state->fdf;
+  double pred_reduction, u;
+
+  /* compute g^T dx */
+  gsl_blas_ddot(trust_state->g, dx, &gTdx);
+
+  /* first term: -2 g^T dx / ||f||^2 */
+  pred_reduction = -2.0 * gTdx / (normf * normf);
+
+  if (params->solver == gsl_multilarge_nlinear_solver_cholesky)
+    {
+      const size_t p = fdf->p;
+      gsl_vector_view workp = gsl_vector_subvector(work, 0, p);
+
+      /* compute workp = J^T J dx */
+      gsl_blas_dsymv(CblasLower, 1.0, trust_state->JTJ, dx, 0.0, &workp.vector);
+
+      /* compute u = dx^T J^T J dx = ||J dx||^2 */
+      gsl_blas_ddot(&workp.vector, dx, &u);
+
+      pred_reduction -= u / (normf * normf);
+    }
+  else
+    {
+      int status;
+      const gsl_vector * x = trust_state->x;
+      const gsl_vector * swts = trust_state->sqrt_wts;
+
+      /* compute work = J*dx */
+      status = gsl_multilarge_nlinear_eval_df(CblasNoTrans, x, f, dx,
+                                              swts, params->h_df, params->fdtype,
+                                              fdf, work, NULL, NULL);
+      if (status)
+        {
+          GSL_ERROR_VAL("error computing preduction", status, 0.0);
+        }
+
+      /* compute u = ||J*dx|| / ||f|| */
+      u = gsl_blas_dnrm2(work) / normf;
+
+      pred_reduction -= u * u;
+    }
+
+  return pred_reduction;
+}
diff -Nru gsl-doc-1.16/multilarge_nlinear/convergence.c gsl-doc-2.3/multilarge_nlinear/convergence.c
--- gsl-doc-1.16/multilarge_nlinear/convergence.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/convergence.c	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,111 @@
+/* multilargenlin/convergence.c
+ * 
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_multifit_nlin.h>
+#include <gsl/gsl_multilarge_nlinear.h>
+
+static double scaled_infnorm(const gsl_vector *x, const gsl_vector *g);
+
+/*
+gsl_multilarge_nlinear_test()
+  Convergence tests for nonlinear least squares minimization
+
+(1) |dx_i| <= xtol * (1 + |x_i|) for all i
+(2) || g .* x ||_inf <= gtol ||f||^2
+(3) ||f(x+dx) - f(x)|| <= ftol * max(||f(x)||, 1)
+
+Inputs: xtol - tolerance for step size
+        gtol - tolerance for gradient vector
+        ftol - tolerance for residual vector
+        info - (output)
+               1 - stopped by small x step
+               2 - stopped by small gradient
+               3 - stopped by small residual vector change
+        w    - workspace
+*/
+
+int
+gsl_multilarge_nlinear_test (const double xtol, const double gtol,
+                             const double ftol, int *info,
+                             const gsl_multilarge_nlinear_workspace * w)
+{
+  int status;
+  double gnorm, fnorm, phi;
+
+  *info = 0;
+
+  status = gsl_multifit_test_delta(w->dx, w->x, xtol*xtol, xtol);
+  if (status == GSL_SUCCESS)
+    {
+      *info = 1;
+      return GSL_SUCCESS;
+    }
+
+  /* compute gnorm = max_i( g_i * max(x_i, 1) ) */
+  gnorm = scaled_infnorm(w->x, w->g);
+
+  /* compute fnorm = ||f|| */
+  fnorm = gsl_blas_dnrm2(w->f);
+  phi = 0.5 * fnorm * fnorm;
+
+#if 0
+  fprintf(stderr, "gnorm = %.12e fnorm = %.12e gnorm/phi = %.12e\n", gnorm, fnorm, gnorm / phi);
+#endif
+
+  if (gnorm <= gtol * GSL_MAX(phi, 1.0))
+    {
+      *info = 2;
+      return GSL_SUCCESS;
+    }
+
+#if 0
+  if (dfnorm <= ftol * GSL_MAX(fnorm, 1.0))
+    {
+      *info = 3;
+      return GSL_SUCCESS;
+    }
+#endif
+
+  return GSL_CONTINUE;
+}
+
+static double
+scaled_infnorm(const gsl_vector *x, const gsl_vector *g)
+{
+  const size_t n = x->size;
+  size_t i;
+  double norm = 0.0;
+
+  for (i = 0; i < n; ++i)
+    {
+      double xi = GSL_MAX(gsl_vector_get(x, i), 1.0);
+      double gi = gsl_vector_get(g, i);
+      double tmp = fabs(xi * gi);
+
+      if (tmp > norm)
+        norm = tmp;
+    }
+
+  return norm;
+}
diff -Nru gsl-doc-1.16/multilarge_nlinear/dogleg.c gsl-doc-2.3/multilarge_nlinear/dogleg.c
--- gsl-doc-1.16/multilarge_nlinear/dogleg.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/dogleg.c	2016-09-05 17:11:27.000000000 +0000
@@ -0,0 +1,501 @@
+/* multilarge_nlinear/dogleg.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multilarge_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+
+/*
+ * This module contains an implementation of the Powell dogleg
+ * algorithm for nonlinear optimization problems. This implementation
+ * closely follows the following works:
+ *
+ * [1] H. B. Nielsen, K. Madsen, Introduction to Optimization and
+ *     Data Fitting, Informatics and Mathematical Modeling,
+ *     Technical University of Denmark (DTU), 2010.
+ *
+ * [2] J. E. Dennis and H. H. W. Mei, Two new unconstrained optimization
+ *     algorithms which use function and gradient values, J. Opt. Theory and
+ *     Appl., 28(4), 1979.
+ */
+
+typedef struct
+{
+  size_t n;                  /* number of observations */
+  size_t p;                  /* number of parameters */
+  gsl_vector *dx_gn;         /* Gauss-Newton step, size p */
+  gsl_vector *dx_sd;         /* steepest descent step, size p */
+  double norm_Dgn;           /* || D dx_gn || */
+  double norm_Dsd;           /* || D dx_sd || */
+  double norm_Dinvg;         /* || D^{-1} g || */
+  double norm_JDinv2g;       /* || J D^{-2} g || */
+  gsl_vector *workp1;        /* workspace, length p */
+  gsl_vector *workp2;        /* workspace, length p */
+  gsl_vector *workn;         /* workspace, length n */
+
+  /* tunable parameters */
+  gsl_multilarge_nlinear_parameters params;
+} dogleg_state_t;
+
+#include "common.c"
+
+static void * dogleg_alloc (const void * params, const size_t n, const size_t p);
+static void dogleg_free(void *vstate);
+static int dogleg_init(const void *vtrust_state, void *vstate);
+static int dogleg_preloop(const void * vtrust_state, void * vstate);
+static int dogleg_step(const void * vtrust_state, const double delta,
+                       gsl_vector * dx, void * vstate);
+static int dogleg_double_step(const void * vtrust_state, const double delta,
+                              gsl_vector * dx, void * vstate);
+static int dogleg_preduction(const void * vtrust_state, const gsl_vector * dx,
+                             double * pred, void * vstate);
+static int dogleg_calc_gn(const gsl_multilarge_nlinear_trust_state * trust_state, gsl_vector * dx);
+static double dogleg_beta(const double t, const double delta,
+                          const gsl_vector * diag, dogleg_state_t * state);
+
+static void *
+dogleg_alloc (const void * params, const size_t n, const size_t p)
+{
+  dogleg_state_t *state;
+  
+  state = calloc(1, sizeof(dogleg_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate dogleg state", GSL_ENOMEM);
+    }
+
+  state->dx_gn = gsl_vector_alloc(p);
+  if (state->dx_gn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for dx_gn", GSL_ENOMEM);
+    }
+
+  state->dx_sd = gsl_vector_alloc(p);
+  if (state->dx_sd == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for dx_sd", GSL_ENOMEM);
+    }
+
+  state->workp1 = gsl_vector_alloc(p);
+  if (state->workp1 == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workp1", GSL_ENOMEM);
+    }
+
+  state->workp2 = gsl_vector_alloc(p);
+  if (state->workp2 == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workp2", GSL_ENOMEM);
+    }
+
+  state->workn = gsl_vector_alloc(n);
+  if (state->workn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workn", GSL_ENOMEM);
+    }
+
+  state->n = n;
+  state->p = p;
+  state->params = *(const gsl_multilarge_nlinear_parameters *) params;
+
+  return state;
+}
+
+static void
+dogleg_free(void *vstate)
+{
+  dogleg_state_t *state = (dogleg_state_t *) vstate;
+
+  if (state->dx_gn)
+    gsl_vector_free(state->dx_gn);
+
+  if (state->dx_sd)
+    gsl_vector_free(state->dx_sd);
+
+  if (state->workp1)
+    gsl_vector_free(state->workp1);
+
+  if (state->workp2)
+    gsl_vector_free(state->workp2);
+
+  if (state->workn)
+    gsl_vector_free(state->workn);
+
+  free(state);
+}
+
+/*
+dogleg_init()
+  Initialize dogleg solver
+
+Inputs: vtrust_state - trust state
+        vstate       - workspace
+
+Return: success/error
+*/
+
+static int
+dogleg_init(const void *vtrust_state, void *vstate)
+{
+  (void)vtrust_state;
+  (void)vstate;
+
+  return GSL_SUCCESS;
+}
+
+/*
+dogleg_preloop()
+  Initialize dogleg method prior to iteration loop.
+This involves computing the steepest descent step. The
+Gauss-Newton step is computed later in the _step() functions
+if required.
+
+Notes: on output,
+1) state->dx_sd contains steepest descent step
+2) state->norm_Dinvg contains || D^{-1} g ||
+3) state->norm_JDinv2g contains || J D^{-2} g ||
+*/
+
+static int
+dogleg_preloop(const void * vtrust_state, void * vstate)
+{
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  dogleg_state_t *state = (dogleg_state_t *) vstate;
+  double u;
+  double alpha; /* ||g||^2 / ||Jg||^2 */
+
+  /* calculate the steepest descent step */
+
+  /* compute workp1 = D^{-1} g and its norm */
+  gsl_vector_memcpy(state->workp1, trust_state->g);
+  gsl_vector_div(state->workp1, trust_state->diag);
+  state->norm_Dinvg = gsl_blas_dnrm2(state->workp1);
+
+  /* compute workp1 = D^{-2} g */
+  gsl_vector_div(state->workp1, trust_state->diag);
+
+  /* compute workp2 = J^T J D^{-2} g */
+  gsl_blas_dsymv(CblasLower, 1.0, trust_state->JTJ, state->workp1, 0.0, state->workp2);
+
+  /* compute norm_JDinv2g = || J D^{-2} g || */
+  gsl_blas_ddot(state->workp1, state->workp2, &u);
+  state->norm_JDinv2g = sqrt(u);
+
+  u = state->norm_Dinvg / state->norm_JDinv2g;
+  alpha = u * u;
+
+  /* dx_sd = -alpha D^{-2} g */
+  gsl_vector_memcpy(state->dx_sd, state->workp1);
+  gsl_vector_scale(state->dx_sd, -alpha);
+
+  state->norm_Dsd = scaled_enorm(trust_state->diag, state->dx_sd);
+  state->norm_Dgn = -1.0; /* computed later if needed */
+
+  return GSL_SUCCESS;
+}
+
+/*
+dogleg_step()
+  Calculate a new step vector
+*/
+
+static int
+dogleg_step(const void * vtrust_state, const double delta,
+            gsl_vector * dx, void * vstate)
+{
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  dogleg_state_t *state = (dogleg_state_t *) vstate;
+
+  if (state->norm_Dsd >= delta)
+    {
+      /* steepest descent step is outside trust region;
+       * truncate steepest descent step to trust region boundary */
+      gsl_vector_memcpy(dx, state->dx_sd);
+      gsl_vector_scale(dx, delta / state->norm_Dsd);
+    }
+  else
+    {
+      /* compute Gauss-Newton step if needed */
+      if (state->norm_Dgn < 0.0)
+        {
+          int status = dogleg_calc_gn(trust_state, state->dx_gn);
+
+          if (status)
+            return status;
+
+          /* compute || D dx_gn || */
+          state->norm_Dgn = scaled_enorm(trust_state->diag, state->dx_gn);
+        }
+
+      if (state->norm_Dgn <= delta)
+        {
+          /* Gauss-Newton step is inside trust region, use it as final step
+           * since it is the global minimizer of the quadratic model function */
+          gsl_vector_memcpy(dx, state->dx_gn);
+        }
+      else
+        {
+          /* Gauss-Newton step is outside trust region, but steepest
+           * descent is inside; use dogleg step */
+
+          double beta = dogleg_beta(1.0, delta, trust_state->diag, state);
+
+          /* compute: workp1 = dx_gn - dx_sd */
+          scaled_addition(1.0, state->dx_gn, -1.0, state->dx_sd, state->workp1);
+
+          /* dx = dx_sd + beta*(dx_gn - dx_sd) */
+          scaled_addition(beta, state->workp1, 1.0, state->dx_sd, dx);
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+/*
+dogleg_double_step()
+  Calculate a new step with double dogleg method. Based on
+section 3 of [2]
+*/
+
+static int
+dogleg_double_step(const void * vtrust_state, const double delta,
+                   gsl_vector * dx, void * vstate)
+{
+  const double alpha_fac = 0.8; /* recommended value from Dennis and Mei */
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  dogleg_state_t *state = (dogleg_state_t *) vstate;
+
+  if (state->norm_Dsd >= delta)
+    {
+      /* steepest descent step is outside trust region;
+       * truncate steepest descent step to trust region boundary */
+      gsl_vector_memcpy(dx, state->dx_sd);
+      gsl_vector_scale(dx, delta / state->norm_Dsd);
+    }
+  else
+    {
+      /* compute Gauss-Newton step if needed */
+      if (state->norm_Dgn < 0.0)
+        {
+          int status = dogleg_calc_gn(trust_state, state->dx_gn);
+
+          if (status)
+            return status;
+
+          /* compute || D dx_gn || */
+          state->norm_Dgn = scaled_enorm(trust_state->diag, state->dx_gn);
+        }
+
+      if (state->norm_Dgn <= delta)
+        {
+          /* Gauss-Newton step is inside trust region, use it as final step
+           * since it is the global minimizer of the quadratic model function */
+          gsl_vector_memcpy(dx, state->dx_gn);
+        }
+      else
+        {
+          double t, u, v, c;
+
+          /* compute: u = ||D^{-1} g||^2 / ||J D^{-2} g||^2 */
+          v = state->norm_Dinvg / state->norm_JDinv2g;
+          u = v * v;
+
+          /* compute: v = g^T dx_gn */
+          gsl_blas_ddot(trust_state->g, state->dx_gn, &v);
+
+          /* compute: c = ||D^{-1} g||^4 / (||J D^{-2} g||^2 * |g^T dx_gn|) */
+          c = u * (state->norm_Dinvg / fabs(v)) * state->norm_Dinvg;
+
+          /* compute: t = 1 - alpha_fac*(1-c) */
+          t = 1.0 - alpha_fac*(1.0 - c);
+
+          if (t * state->norm_Dgn <= delta)
+            {
+              /* set dx = (delta / ||D dx_gn||) dx_gn */
+              gsl_vector_memcpy(dx, state->dx_gn);
+              gsl_vector_scale(dx, delta / state->norm_Dgn);
+            }
+          else
+            {
+              /* Cauchy point is inside, Gauss-Newton is outside trust region;
+               * use double dogleg step */
+
+              double beta = dogleg_beta(t, delta, trust_state->diag, state);
+
+              /* compute: workp1 = t*dx_gn - dx_sd */
+              scaled_addition(t, state->dx_gn, -1.0, state->dx_sd, state->workp1);
+
+              /* dx = dx_sd + beta*(t*dx_gn - dx_sd) */
+              scaled_addition(beta, state->workp1, 1.0, state->dx_sd, dx);
+            }
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+dogleg_preduction(const void * vtrust_state, const gsl_vector * dx,
+                  double * pred, void * vstate)
+{
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  dogleg_state_t *state = (dogleg_state_t *) vstate;
+
+  *pred = quadratic_preduction(trust_state, dx, state->workn);
+
+  return GSL_SUCCESS;
+}
+
+/*
+dogleg_calc_gn()
+  Calculate Gauss-Newton step by solving
+
+J^T J dx_gn = -J^T f
+
+Inputs: trust_state - trust state variables
+        dx          - (output) Gauss-Newton step vector
+
+Return: success/error
+*/
+
+static int
+dogleg_calc_gn(const gsl_multilarge_nlinear_trust_state * trust_state, gsl_vector * dx)
+{
+  int status;
+  const gsl_multilarge_nlinear_parameters *params = trust_state->params;
+
+  /* initialize linear least squares solver */
+  status = (params->solver->init)(trust_state, trust_state->solver_state);
+  if (status)
+    return status;
+
+  /* prepare the linear solver to compute Gauss-Newton step */
+  status = (params->solver->presolve)(0.0, trust_state, trust_state->solver_state);
+  if (status)
+    return status;
+
+  /* solve: J dx_gn = -f for Gauss-Newton step */
+  status = (params->solver->solve)(trust_state->g,
+                                   dx,
+                                   trust_state,
+                                   trust_state->solver_state);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+}
+
+/*
+dogleg_beta()
+  This function finds beta in [0,1] such that the step
+
+dx = dx_sd + beta*(t*dx_gn - dx_sd)
+
+has norm
+
+||D dx|| = delta
+
+beta is the positive root of the quadratic:
+
+a beta^2 + b beta + c = 0
+
+with
+
+a = ||D(t*dx_gn - dx_sd)||^2
+b = 2 dx_sd^T D^T D (t*dx_gn - dx_sd)
+c = ||D dx_sd||^2 - delta^2 
+
+Inputs: t     - amount of Gauss-Newton step to use for dogleg
+                (= 1 for classical dogleg, <= 1 for double dogleg)
+        delta - trust region radius
+        diag  - diag(D) scaling matrix
+        state - workspace
+*/
+
+static double
+dogleg_beta(const double t, const double delta,
+            const gsl_vector * diag, dogleg_state_t * state)
+{
+  double beta;
+  double a, b, c;
+
+  /* compute: workp1 = t*dx_gn - dx_sd */
+  scaled_addition(t, state->dx_gn, -1.0, state->dx_sd, state->workp1);
+
+  /* a = || D (t*dx_gn - dx_sd) ||^2 */
+  a = scaled_enorm(diag, state->workp1);
+  a *= a;
+
+  /* workp1 = D^T D (t*dx_gn - dx_sd) */
+  gsl_vector_mul(state->workp1, diag);
+  gsl_vector_mul(state->workp1, diag);
+
+  /* b = 2 dx_sd^T D^T D (t*dx_gn - dx-sd) */
+  gsl_blas_ddot(state->dx_sd, state->workp1, &b);
+  b *= 2.0;
+
+  /* c = || D dx_sd ||^2 - delta^2 = (||D dx_sd|| + delta) (||D dx_sd|| - delta) */
+  c = (state->norm_Dsd + delta) * (state->norm_Dsd - delta);
+
+  if (b > 0.0)
+    {
+      beta = (-2.0 * c) / (b + sqrt(b*b - 4.0*a*c));
+    }
+  else
+    {
+      beta = (-b + sqrt(b*b - 4.0*a*c)) / (2.0 * a);
+    }
+
+  return beta;
+}
+
+static const gsl_multilarge_nlinear_trs dogleg_type =
+{
+  "dogleg",
+  dogleg_alloc,
+  dogleg_init,
+  dogleg_preloop,
+  dogleg_step,
+  dogleg_preduction,
+  dogleg_free
+};
+
+const gsl_multilarge_nlinear_trs *gsl_multilarge_nlinear_trs_dogleg = &dogleg_type;
+
+static const gsl_multilarge_nlinear_trs ddogleg_type =
+{
+  "double-dogleg",
+  dogleg_alloc,
+  dogleg_init,
+  dogleg_preloop,
+  dogleg_double_step,
+  dogleg_preduction,
+  dogleg_free
+};
+
+const gsl_multilarge_nlinear_trs *gsl_multilarge_nlinear_trs_ddogleg = &ddogleg_type;
diff -Nru gsl-doc-1.16/multilarge_nlinear/dummy.c gsl-doc-2.3/multilarge_nlinear/dummy.c
--- gsl-doc-1.16/multilarge_nlinear/dummy.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/dummy.c	2016-08-19 17:08:56.000000000 +0000
@@ -0,0 +1,113 @@
+/* multilarge_nlinear/dummy.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/* dummy linear solver */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multilarge_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_permutation.h>
+
+static void *dummy_alloc (const size_t n, const size_t p);
+static int dummy_init(const void * vtrust_state, void * vstate);
+static int dummy_presolve(const double mu, const void * vtrust_state, void * vstate);
+static int dummy_solve(const gsl_vector * g, gsl_vector *x,
+                       const  void * vtrust_state, void *vstate);
+static int dummy_rcond(double * rcond, const gsl_matrix * JTJ, void * vstate);
+static int dummy_covar(const gsl_matrix * JTJ, gsl_matrix * covar, void * vstate);
+
+static void *
+dummy_alloc (const size_t n, const size_t p)
+{
+  (void) n;
+  (void) p;
+  return NULL;
+}
+
+static void
+dummy_free(void *vstate)
+{
+  (void) vstate;
+}
+
+static int
+dummy_init(const void * vtrust_state, void * vstate)
+{
+  (void) vtrust_state;
+  (void) vstate;
+  return GSL_SUCCESS;
+}
+
+static int
+dummy_presolve(const double mu, const void * vtrust_state, void * vstate)
+{
+  (void) mu;
+  (void) vtrust_state;
+  (void) vstate;
+  return GSL_SUCCESS;
+}
+
+static int
+dummy_solve(const gsl_vector * g, gsl_vector *x,
+            const void * vtrust_state, void *vstate)
+{
+  (void) g;
+  (void) x;
+  (void) vtrust_state;
+  (void) vstate;
+  return GSL_SUCCESS;
+}
+
+static int
+dummy_rcond(double * rcond, const gsl_matrix * JTJ, void * vstate)
+{
+  (void) vstate;
+  (void) rcond;
+  (void) JTJ;
+  *rcond = 0.0;
+  return GSL_SUCCESS;
+}
+
+static int
+dummy_covar(const gsl_matrix * JTJ, gsl_matrix * covar, void * vstate)
+{
+  (void) vstate;
+  (void) JTJ;
+  gsl_matrix_set_zero(covar);
+  return GSL_SUCCESS;
+}
+
+static const gsl_multilarge_nlinear_solver dummy_type =
+{
+  "dummy",
+  dummy_alloc,
+  dummy_init,
+  dummy_presolve,
+  dummy_solve,
+  dummy_rcond,
+  dummy_covar,
+  dummy_free
+};
+
+const gsl_multilarge_nlinear_solver *gsl_multilarge_nlinear_solver_none = &dummy_type;
diff -Nru gsl-doc-1.16/multilarge_nlinear/fdf.c gsl-doc-2.3/multilarge_nlinear/fdf.c
--- gsl-doc-1.16/multilarge_nlinear/fdf.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/fdf.c	2016-10-27 11:20:46.000000000 +0000
@@ -0,0 +1,564 @@
+/* multilarge_nlinear/fdf.c
+ * 
+ * Copyright (C) 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_multilarge_nlinear.h>
+
+gsl_multilarge_nlinear_workspace *
+gsl_multilarge_nlinear_alloc (const gsl_multilarge_nlinear_type * T, 
+                              const gsl_multilarge_nlinear_parameters * params,
+                              const size_t n, const size_t p)
+{
+  gsl_multilarge_nlinear_workspace * w;
+
+  if (n < p)
+    {
+      GSL_ERROR_VAL ("insufficient data points, n < p", GSL_EINVAL, 0);
+    }
+
+  w = calloc (1, sizeof (gsl_multilarge_nlinear_workspace));
+  if (w == 0)
+    {
+      GSL_ERROR_VAL ("failed to allocate space for workspace",
+                     GSL_ENOMEM, 0);
+    }
+
+  w->n = n;
+  w->p = p;
+  w->type = T;
+  w->fdf = NULL;
+  w->niter = 0;
+  w->params = *params;
+
+  /* the cgst method uses its own built-in linear solver */
+  if (w->params.trs == gsl_multilarge_nlinear_trs_cgst)
+    {
+      w->params.solver = gsl_multilarge_nlinear_solver_none;
+    }
+
+  w->x = gsl_vector_calloc (p);
+  if (w->x == 0) 
+    {
+      gsl_multilarge_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
+    }
+
+  w->f = gsl_vector_calloc (n);
+  if (w->f == 0) 
+    {
+      gsl_multilarge_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for f", GSL_ENOMEM, 0);
+    }
+
+  w->dx = gsl_vector_calloc (p);
+  if (w->dx == 0) 
+    {
+      gsl_multilarge_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for dx", GSL_ENOMEM, 0);
+    }
+
+  w->g = gsl_vector_alloc (p);
+  if (w->g == 0) 
+    {
+      gsl_multilarge_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for g", GSL_ENOMEM, 0);
+    }
+
+  if (w->params.solver == gsl_multilarge_nlinear_solver_cholesky)
+    {
+      w->JTJ = gsl_matrix_alloc (p, p);
+      if (w->JTJ == 0) 
+        {
+          gsl_multilarge_nlinear_free (w);
+          GSL_ERROR_VAL ("failed to allocate space for JTJ", GSL_ENOMEM, 0);
+        }
+    }
+
+  w->sqrt_wts_work = gsl_vector_calloc (n);
+  if (w->sqrt_wts_work == 0)
+    {
+      gsl_multilarge_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for weights", GSL_ENOMEM, 0);
+    }
+
+  w->state = (T->alloc)(&(w->params), n, p);
+  if (w->state == 0)
+    {
+      gsl_multilarge_nlinear_free (w);
+      GSL_ERROR_VAL ("failed to allocate space for state", GSL_ENOMEM, 0);
+    }
+
+  return w;
+}
+
+void
+gsl_multilarge_nlinear_free (gsl_multilarge_nlinear_workspace * w)
+{
+  RETURN_IF_NULL (w);
+
+  if (w->state)
+    (w->type->free) (w->state);
+
+  if (w->dx)
+    gsl_vector_free (w->dx);
+
+  if (w->x)
+    gsl_vector_free (w->x);
+
+  if (w->f)
+    gsl_vector_free (w->f);
+
+  if (w->sqrt_wts_work)
+    gsl_vector_free (w->sqrt_wts_work);
+
+  if (w->g)
+    gsl_vector_free (w->g);
+
+  if (w->JTJ)
+    gsl_matrix_free (w->JTJ);
+
+  free (w);
+}
+
+gsl_multilarge_nlinear_parameters
+gsl_multilarge_nlinear_default_parameters(void)
+{
+  gsl_multilarge_nlinear_parameters params;
+
+  params.trs = gsl_multilarge_nlinear_trs_lm;
+  params.scale = gsl_multilarge_nlinear_scale_more;
+  params.solver = gsl_multilarge_nlinear_solver_cholesky;
+  params.fdtype = GSL_MULTILARGE_NLINEAR_FWDIFF;
+  params.factor_up = 3.0;
+  params.factor_down = 2.0;
+  params.avmax = 0.75;
+  params.h_df = GSL_SQRT_DBL_EPSILON;
+  params.h_fvv = 0.01;
+  params.max_iter = 0;
+  params.tol = 1.0e-6;
+
+  return params;
+}
+
+int
+gsl_multilarge_nlinear_init (const gsl_vector * x,
+                             gsl_multilarge_nlinear_fdf * fdf,
+                             gsl_multilarge_nlinear_workspace * w)
+{
+  return gsl_multilarge_nlinear_winit(x, NULL, fdf, w);
+}
+
+int
+gsl_multilarge_nlinear_winit (const gsl_vector * x,
+                              const gsl_vector * wts,
+                              gsl_multilarge_nlinear_fdf * fdf, 
+                              gsl_multilarge_nlinear_workspace * w)
+{
+  const size_t n = w->f->size;
+
+  if (n != fdf->n)
+    {
+      GSL_ERROR ("function size does not match workspace", GSL_EBADLEN);
+    }
+  else if (w->x->size != x->size)
+    {
+      GSL_ERROR ("vector length does not match workspace", GSL_EBADLEN);
+    }
+  else if (wts != NULL && n != wts->size)
+    {
+      GSL_ERROR ("weight vector length does not match workspace", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i;
+
+      /* initialize counters for function and Jacobian evaluations */
+      fdf->nevalf = 0;
+      fdf->nevaldfu = 0;
+      fdf->nevaldf2 = 0;
+      fdf->nevalfvv = 0;
+
+      w->fdf = fdf;
+      gsl_vector_memcpy(w->x, x);
+      w->niter = 0;
+
+      if (wts)
+        {
+          w->sqrt_wts = w->sqrt_wts_work;
+
+          for (i = 0; i < n; ++i)
+            {
+              double wi = gsl_vector_get(wts, i);
+              gsl_vector_set(w->sqrt_wts, i, sqrt(wi));
+            }
+        }
+      else
+        {
+          w->sqrt_wts = NULL;
+        }
+  
+      return (w->type->init) (w->state, w->sqrt_wts, w->fdf,
+                              w->x, w->f, w->g, w->JTJ);
+    }
+}
+
+int
+gsl_multilarge_nlinear_iterate (gsl_multilarge_nlinear_workspace * w)
+{
+  int status =
+    (w->type->iterate) (w->state, w->sqrt_wts, w->fdf,
+                        w->x, w->f, w->g, w->JTJ, w->dx);
+
+  w->niter++;
+
+  return status;
+}
+
+double
+gsl_multilarge_nlinear_avratio (const gsl_multilarge_nlinear_workspace * w)
+{
+  return (w->type->avratio) (w->state);
+}
+
+int
+gsl_multilarge_nlinear_rcond (double * rcond, const gsl_multilarge_nlinear_workspace * w)
+{
+  int status = (w->type->rcond) (rcond, w->JTJ, w->state);
+  return status;
+}
+
+int
+gsl_multilarge_nlinear_covar (gsl_matrix * covar, gsl_multilarge_nlinear_workspace * w)
+{
+  if (covar->size1 != covar->size2)
+    {
+      GSL_ERROR ("covariance matrix must be square", GSL_ENOTSQR);
+    }
+  else if (covar->size1 != w->p)
+    {
+      GSL_ERROR ("covariance matrix does not match workspace", GSL_EBADLEN);
+    }
+  else
+    {
+      int status = (w->type->covar) (w->JTJ, covar, w->state);
+      return status;
+    }
+}
+
+/*
+gsl_multilarge_nlinear_driver()
+  Iterate the nonlinear least squares solver until completion
+
+Inputs: maxiter  - maximum iterations to allow
+        xtol     - tolerance in step x
+        gtol     - tolerance in gradient
+        ftol     - tolerance in ||f||
+        callback - callback function to call each iteration
+        callback_params - parameters to pass to callback function
+        info     - (output) info flag on why iteration terminated
+                   1 = stopped due to small step size ||dx|
+                   2 = stopped due to small gradient
+                   3 = stopped due to small change in f
+                   GSL_ETOLX = ||dx|| has converged to within machine
+                               precision (and xtol is too small)
+                   GSL_ETOLG = ||g||_inf is smaller than machine
+                               precision (gtol is too small)
+                   GSL_ETOLF = change in ||f|| is smaller than machine
+                               precision (ftol is too small)
+        w        - workspace
+
+Return:
+GSL_SUCCESS if converged
+GSL_MAXITER if maxiter exceeded without converging
+GSL_ENOPROG if no accepted step found on first iteration
+*/
+
+int
+gsl_multilarge_nlinear_driver (const size_t maxiter,
+                               const double xtol,
+                               const double gtol,
+                               const double ftol,
+                               void (*callback)(const size_t iter, void *params,
+                                                const gsl_multilarge_nlinear_workspace *w),
+                               void *callback_params,
+                               int *info,
+                               gsl_multilarge_nlinear_workspace * w)
+{
+  int status;
+  size_t iter = 0;
+
+  /* call user callback function prior to any iterations
+   * with initial system state */
+  if (callback)
+    callback(iter, callback_params, w);
+
+  do
+    {
+      status = gsl_multilarge_nlinear_iterate (w);
+
+      /*
+       * If the solver reports no progress on the first iteration,
+       * then it didn't find a single step to reduce the
+       * cost function and more iterations won't help so return.
+       *
+       * If we get a no progress flag on subsequent iterations,
+       * it means we did find a good step in a previous iteration,
+       * so continue iterating since the solver has now reset
+       * mu to its initial value.
+       */
+      if (status == GSL_ENOPROG && iter == 0)
+        {
+          *info = status;
+          return GSL_EMAXITER;
+        }
+
+      ++iter;
+
+      if (callback)
+        callback(iter, callback_params, w);
+
+      /* test for convergence */
+      status = gsl_multilarge_nlinear_test(xtol, gtol, ftol, info, w);
+    }
+  while (status == GSL_CONTINUE && iter < maxiter);
+
+  /*
+   * the following error codes mean that the solution has converged
+   * to within machine precision, so record the error code in info
+   * and return success
+   */
+  if (status == GSL_ETOLF || status == GSL_ETOLX || status == GSL_ETOLG)
+    {
+      *info = status;
+      status = GSL_SUCCESS;
+    }
+
+  /* check if max iterations reached */
+  if (iter >= maxiter && status != GSL_SUCCESS)
+    status = GSL_EMAXITER;
+
+  return status;
+} /* gsl_multilarge_nlinear_driver() */
+
+const char *
+gsl_multilarge_nlinear_name (const gsl_multilarge_nlinear_workspace * w)
+{
+  return w->type->name;
+}
+
+gsl_vector *
+gsl_multilarge_nlinear_position (const gsl_multilarge_nlinear_workspace * w)
+{
+  return w->x;
+}
+
+gsl_vector *
+gsl_multilarge_nlinear_residual (const gsl_multilarge_nlinear_workspace * w)
+{
+  return w->f;
+}
+
+gsl_vector *
+gsl_multilarge_nlinear_step (const gsl_multilarge_nlinear_workspace * w)
+{
+  return w->dx;
+}
+
+size_t
+gsl_multilarge_nlinear_niter (const gsl_multilarge_nlinear_workspace * w)
+{
+  return w->niter;
+}
+
+const char *
+gsl_multilarge_nlinear_trs_name (const gsl_multilarge_nlinear_workspace * w)
+{
+  return w->params.trs->name;
+}
+
+/*
+gsl_multilarge_nlinear_eval_f()
+  Compute residual vector y with user callback function, and apply
+weighting transform if given:
+
+y~ = sqrt(W) y
+
+Inputs: fdf  - callback function
+        x    - model parameters
+        swts - weight matrix sqrt(W) = sqrt(diag(w1,w2,...,wn))
+               set to NULL for unweighted fit
+        y    - (output) (weighted) residual vector
+               y_i = sqrt(w_i) f_i where f_i is unweighted residual
+*/
+
+int
+gsl_multilarge_nlinear_eval_f(gsl_multilarge_nlinear_fdf *fdf,
+                              const gsl_vector *x,
+                              const gsl_vector *swts,
+                              gsl_vector *y)
+{
+  int s = ((*((fdf)->f)) (x, fdf->params, y));
+
+  ++(fdf->nevalf);
+
+  /* y <- sqrt(W) y */
+  if (swts)
+    gsl_vector_mul(y, swts);
+
+  return s;
+}
+
+/*
+gsl_multilarge_nlinear_eval_df()
+  Compute Jacobian matrix-vector product:
+  
+v = J * u
+
+or
+
+v = J^T u
+
+Inputs: TransJ - use J or J^T
+        x      - model parameters
+        f      - residual vector f(x)
+        u      - input vector u
+        swts   - weight matrix W = diag(w1,w2,...,wn)
+                 set to NULL for unweighted fit
+        h      - finite difference step size
+        fdtype - finite difference method
+        fdf    - callback function
+        v      - (output) vector v
+        JTJ    - (output) matrix J^T J
+        work   - workspace for finite difference, size n
+*/
+
+int
+gsl_multilarge_nlinear_eval_df(const CBLAS_TRANSPOSE_t TransJ,
+                               const gsl_vector *x,
+                               const gsl_vector *f,
+                               const gsl_vector *u,
+                               const gsl_vector *swts,
+                               const double h,
+                               const gsl_multilarge_nlinear_fdtype fdtype,
+                               gsl_multilarge_nlinear_fdf *fdf,
+                               gsl_vector *v,
+                               gsl_matrix *JTJ,
+                               gsl_vector *work)
+{
+  const size_t n = fdf->n;
+  const size_t p = fdf->p;
+
+  if (u != NULL && ((TransJ == CblasNoTrans && u->size != p) ||
+                    (TransJ == CblasTrans && u->size != n)))
+    {
+      GSL_ERROR("u vector has wrong size", GSL_EBADLEN);
+    }
+  else if (v != NULL && ((TransJ == CblasNoTrans && v->size != n) ||
+                         (TransJ == CblasTrans && v->size != p)))
+    {
+      GSL_ERROR("v vector has wrong size", GSL_EBADLEN);
+    }
+  else if (JTJ != NULL && ((JTJ->size1 != p) || (JTJ->size2 != p)))
+    {
+      GSL_ERROR("JTJ matrix has wrong size", GSL_EBADLEN);
+    }
+  else
+    {
+      int status;
+
+      if (fdf->df)
+        {
+          /* call user-supplied function */
+          status = ((*((fdf)->df)) (TransJ, x, u, fdf->params, v, JTJ));
+
+          if (v)
+            ++(fdf->nevaldfu);
+
+          if (JTJ)
+            ++(fdf->nevaldf2);
+        }
+      else
+        {
+#if 0
+          /* use finite difference Jacobian approximation */
+          status = gsl_multilarge_nlinear_df(h, fdtype, x, swts, fdf, f, df, work);
+#endif
+        }
+
+      return status;
+    }
+}
+
+/*
+gsl_multilarge_nlinear_eval_fvv()
+  Compute second direction derivative vector yvv with user
+callback function, and apply weighting transform if given:
+
+yvv~ = sqrt(W) yvv
+
+Inputs: h    - step size for finite difference, if needed
+        x    - model parameters, size p
+        v    - unscaled geodesic velocity vector, size p
+        f    - residual vector f(x), size n
+        swts - weight matrix sqrt(W) = sqrt(diag(w1,w2,...,wn))
+               set to NULL for unweighted fit
+        fdf  - callback function
+        yvv  - (output) (weighted) second directional derivative vector
+               yvv_i = sqrt(w_i) fvv_i where f_i is unweighted
+        work - workspace, size p
+*/
+
+int
+gsl_multilarge_nlinear_eval_fvv(const double h,
+                                const gsl_vector *x,
+                                const gsl_vector *v,
+                                const gsl_vector *f,
+                                const gsl_vector *swts,
+                                gsl_multilarge_nlinear_fdf *fdf,
+                                gsl_vector *yvv,
+                                gsl_vector *work)
+{
+  int status;
+  
+  if (fdf->fvv != NULL)
+    {
+      /* call user-supplied function */
+      status = ((*((fdf)->fvv)) (x, v, fdf->params, yvv));
+      ++(fdf->nevalfvv);
+    }
+  else
+    {
+#if 0
+      /* use finite difference approximation */
+      status = gsl_multilarge_nlinear_fdfvv(h, x, v, f, J,
+                                          swts, fdf, yvv, work);
+#endif
+    }
+
+  /* yvv <- sqrt(W) yvv */
+  if (swts)
+    gsl_vector_mul(yvv, swts);
+
+  return status;
+}
diff -Nru gsl-doc-1.16/multilarge_nlinear/gsl_multilarge_nlinear.h gsl-doc-2.3/multilarge_nlinear/gsl_multilarge_nlinear.h
--- gsl-doc-1.16/multilarge_nlinear/gsl_multilarge_nlinear.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/gsl_multilarge_nlinear.h	2016-08-19 17:07:39.000000000 +0000
@@ -0,0 +1,313 @@
+/* multilarge_nlinear/gsl_multilarge_nlinear.h
+ * 
+ * Copyright (C) 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_MULTILARGE_NLINEAR_H__
+#define __GSL_MULTILARGE_NLINEAR_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_types.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_blas.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+typedef enum
+{
+  GSL_MULTILARGE_NLINEAR_FWDIFF,
+  GSL_MULTILARGE_NLINEAR_CTRDIFF
+} gsl_multilarge_nlinear_fdtype;
+
+/* Definition of vector-valued functions and gradient with parameters
+   based on gsl_vector */
+
+typedef struct
+{
+  int (* f) (const gsl_vector * x, void * params, gsl_vector * f);
+  int (* df) (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+              const gsl_vector * u, void * params, gsl_vector * v,
+              gsl_matrix * JTJ);
+  int (* fvv) (const gsl_vector * x, const gsl_vector * v, void * params,
+               gsl_vector * fvv);
+  size_t n;        /* number of functions */
+  size_t p;        /* number of independent variables */
+  void * params;   /* user parameters */
+  size_t nevalf;   /* number of function evaluations */
+  size_t nevaldfu; /* number of Jacobian matrix-vector evaluations */
+  size_t nevaldf2; /* number of Jacobian J^T J evaluations */
+  size_t nevalfvv; /* number of fvv evaluations */
+} gsl_multilarge_nlinear_fdf;
+
+/* trust region subproblem method */
+typedef struct
+{
+  const char *name;
+  void * (*alloc) (const void * params, const size_t n, const size_t p);
+  int (*init) (const void * vtrust_state, void * vstate);
+  int (*preloop) (const void * vtrust_state, void * vstate);
+  int (*step) (const void * vtrust_state, const double delta,
+               gsl_vector * dx, void * vstate);
+  int (*preduction) (const void * vtrust_state, const gsl_vector * dx,
+                     double * pred, void * vstate);
+  void (*free) (void * vstate);
+} gsl_multilarge_nlinear_trs;
+
+/* scaling matrix specification */
+typedef struct
+{
+  const char *name;
+  int (*init) (const gsl_matrix * JTJ, gsl_vector * diag);
+  int (*update) (const gsl_matrix * JTJ, gsl_vector * diag);
+} gsl_multilarge_nlinear_scale;
+
+/*
+ * linear least squares solvers - there are three steps to
+ * solving a least squares problem using a direct method:
+ *
+ * 1. init: called once per iteration when a new Jacobian matrix
+ *          is required; form normal equations matrix J^T J
+ * 2. presolve: called each time a new LM parameter value mu is available;
+ *              used for cholesky method in order to factor
+ *              the (J^T J + mu D^T D) matrix
+ * 3. solve: solve the least square system for a given rhs
+ */
+typedef struct
+{
+  const char *name;
+  void * (*alloc) (const size_t n, const size_t p);
+  int (*init) (const void * vtrust_state, void * vstate);
+  int (*presolve) (const double mu, const void * vtrust_state, void * vstate);
+  int (*solve) (const gsl_vector * g, gsl_vector * x,
+                const void * vtrust_state, void * vstate);
+  int (*rcond) (double * rcond, const gsl_matrix * JTJ, void * vstate);
+  int (*covar) (const gsl_matrix * JTJ, gsl_matrix * covar, void * vstate);
+  void (*free) (void * vstate);
+} gsl_multilarge_nlinear_solver;
+
+/* tunable parameters */
+typedef struct
+{
+  const gsl_multilarge_nlinear_trs *trs;       /* trust region subproblem method */
+  const gsl_multilarge_nlinear_scale *scale;   /* scaling method */
+  const gsl_multilarge_nlinear_solver *solver; /* solver method */
+  gsl_multilarge_nlinear_fdtype fdtype;        /* finite difference method */
+  double factor_up;                            /* factor for increasing trust radius */
+  double factor_down;                          /* factor for decreasing trust radius */
+  double avmax;                                /* max allowed |a|/|v| */
+  double h_df;                                 /* step size for finite difference Jacobian */
+  double h_fvv;                                /* step size for finite difference fvv */
+  size_t max_iter;                             /* maximum iterations for trs method */
+  double tol;                                  /* tolerance for solving trs */
+} gsl_multilarge_nlinear_parameters;
+
+typedef struct
+{
+  const char *name;
+  void * (*alloc) (const gsl_multilarge_nlinear_parameters * params,
+                   const size_t n, const size_t p);
+  int (*init) (void * state, const gsl_vector * wts,
+               gsl_multilarge_nlinear_fdf * fdf, const gsl_vector * x,
+               gsl_vector * f, gsl_vector * g, gsl_matrix * JTJ);
+  int (*iterate) (void * state, const gsl_vector * wts,
+                  gsl_multilarge_nlinear_fdf * fdf, gsl_vector * x,
+                  gsl_vector * f, gsl_vector * g, gsl_matrix * JTJ,
+                  gsl_vector * dx);
+  int (*rcond) (double * rcond, const gsl_matrix * JTJ, void * state);
+  int (*covar) (const gsl_matrix * JTJ, gsl_matrix * covar, void * state);
+  double (*avratio) (void * state);
+  void (*free) (void * state);
+} gsl_multilarge_nlinear_type;
+
+/* current state passed to low-level trust region algorithms */
+typedef struct
+{
+  const gsl_vector * x;             /* parameter values x */
+  const gsl_vector * f;             /* residual vector f(x) */
+  const gsl_vector * g;             /* gradient J^T f */
+  const gsl_matrix * JTJ;           /* matrix J^T J */
+  const gsl_vector * diag;          /* scaling matrix D */
+  const gsl_vector * sqrt_wts;      /* sqrt(diag(W)) or NULL for unweighted */
+  const double *mu;                 /* LM parameter */
+  const gsl_multilarge_nlinear_parameters * params;
+  void *solver_state;               /* workspace for direct least squares solver */
+  gsl_multilarge_nlinear_fdf * fdf;
+  double *avratio;                  /* |a| / |v| */
+} gsl_multilarge_nlinear_trust_state;
+
+typedef struct
+{
+  const gsl_multilarge_nlinear_type * type;
+  gsl_multilarge_nlinear_fdf * fdf ;
+  gsl_vector * x;             /* parameter values x */
+  gsl_vector * f;             /* residual vector f(x) */
+  gsl_vector * dx;            /* step dx */
+  gsl_vector * g;             /* gradient J^T f */
+  gsl_matrix * JTJ;           /* matrix J^T J */
+  gsl_vector * sqrt_wts_work; /* sqrt(W) */
+  gsl_vector * sqrt_wts;      /* ptr to sqrt_wts_work, or NULL if not using weights */
+  size_t n;                   /* number of residuals */
+  size_t p;                   /* number of parameters */
+  size_t niter;               /* number of iterations performed */
+  gsl_multilarge_nlinear_parameters params;
+  void *state;
+} gsl_multilarge_nlinear_workspace;
+
+gsl_multilarge_nlinear_workspace *
+gsl_multilarge_nlinear_alloc (const gsl_multilarge_nlinear_type * T,
+                              const gsl_multilarge_nlinear_parameters * params,
+                              size_t n, size_t p);
+
+void gsl_multilarge_nlinear_free (gsl_multilarge_nlinear_workspace * w);
+
+gsl_multilarge_nlinear_parameters gsl_multilarge_nlinear_default_parameters(void);
+
+int
+gsl_multilarge_nlinear_init (const gsl_vector * x,
+                             gsl_multilarge_nlinear_fdf * fdf,
+                             gsl_multilarge_nlinear_workspace * w);
+
+int gsl_multilarge_nlinear_winit (const gsl_vector * x,
+                                  const gsl_vector * wts,
+                                  gsl_multilarge_nlinear_fdf * fdf,
+                                  gsl_multilarge_nlinear_workspace * w);
+
+int
+gsl_multilarge_nlinear_iterate (gsl_multilarge_nlinear_workspace * w);
+
+double
+gsl_multilarge_nlinear_avratio (const gsl_multilarge_nlinear_workspace * w);
+
+int
+gsl_multilarge_nlinear_rcond (double * rcond, const gsl_multilarge_nlinear_workspace * w);
+
+int
+gsl_multilarge_nlinear_covar (gsl_matrix * covar, gsl_multilarge_nlinear_workspace * w);
+
+int
+gsl_multilarge_nlinear_driver (const size_t maxiter,
+                               const double xtol,
+                               const double gtol,
+                               const double ftol,
+                               void (*callback)(const size_t iter, void *params,
+                                                const gsl_multilarge_nlinear_workspace *w),
+                               void *callback_params,
+                               int *info,
+                               gsl_multilarge_nlinear_workspace * w);
+
+const char *
+gsl_multilarge_nlinear_name (const gsl_multilarge_nlinear_workspace * w);
+
+gsl_vector *
+gsl_multilarge_nlinear_position (const gsl_multilarge_nlinear_workspace * w);
+
+gsl_vector *
+gsl_multilarge_nlinear_residual (const gsl_multilarge_nlinear_workspace * w);
+
+gsl_vector *
+gsl_multilarge_nlinear_step (const gsl_multilarge_nlinear_workspace * w);
+
+size_t
+gsl_multilarge_nlinear_niter (const gsl_multilarge_nlinear_workspace * w);
+
+const char *
+gsl_multilarge_nlinear_trs_name (const gsl_multilarge_nlinear_workspace * w);
+
+int gsl_multilarge_nlinear_eval_f(gsl_multilarge_nlinear_fdf *fdf,
+                                  const gsl_vector *x,
+                                  const gsl_vector *swts,
+                                  gsl_vector *y);
+
+int
+gsl_multilarge_nlinear_eval_df(const CBLAS_TRANSPOSE_t TransJ,
+                               const gsl_vector *x,
+                               const gsl_vector *f,
+                               const gsl_vector *u,
+                               const gsl_vector *swts,
+                               const double h,
+                               const gsl_multilarge_nlinear_fdtype fdtype,
+                               gsl_multilarge_nlinear_fdf *fdf,
+                               gsl_vector *v,
+                               gsl_matrix *JTJ,
+                               gsl_vector *work);
+
+int
+gsl_multilarge_nlinear_eval_fvv(const double h,
+                                const gsl_vector *x,
+                                const gsl_vector *v,
+                                const gsl_vector *f,
+                                const gsl_vector *swts,
+                                gsl_multilarge_nlinear_fdf *fdf,
+                                gsl_vector *yvv,
+                                gsl_vector *work);
+
+/* convergence.c */
+int
+gsl_multilarge_nlinear_test (const double xtol, const double gtol,
+                             const double ftol, int *info,
+                             const gsl_multilarge_nlinear_workspace * w);
+
+/* fdjac.c */
+int
+gsl_multilarge_nlinear_df(const double h, const gsl_multilarge_nlinear_fdtype fdtype,
+                          const gsl_vector *x, const gsl_vector *wts,
+                          gsl_multilarge_nlinear_fdf *fdf,
+                          const gsl_vector *f, gsl_matrix *J, gsl_vector *work);
+
+/* fdfvv.c */
+int
+gsl_multilarge_nlinear_fdfvv(const double h, const gsl_vector *x, const gsl_vector *v,
+                             const gsl_vector *f, const gsl_matrix *J,
+                             const gsl_vector *swts, gsl_multilarge_nlinear_fdf *fdf,
+                             gsl_vector *fvv, gsl_vector *work);
+
+/* top-level algorithms */
+GSL_VAR const gsl_multilarge_nlinear_type * gsl_multilarge_nlinear_trust;
+
+/* trust region subproblem methods */
+GSL_VAR const gsl_multilarge_nlinear_trs * gsl_multilarge_nlinear_trs_lm;
+GSL_VAR const gsl_multilarge_nlinear_trs * gsl_multilarge_nlinear_trs_lmaccel;
+GSL_VAR const gsl_multilarge_nlinear_trs * gsl_multilarge_nlinear_trs_dogleg;
+GSL_VAR const gsl_multilarge_nlinear_trs * gsl_multilarge_nlinear_trs_ddogleg;
+GSL_VAR const gsl_multilarge_nlinear_trs * gsl_multilarge_nlinear_trs_subspace2D;
+GSL_VAR const gsl_multilarge_nlinear_trs * gsl_multilarge_nlinear_trs_cgst;
+
+/* scaling matrix strategies */
+GSL_VAR const gsl_multilarge_nlinear_scale * gsl_multilarge_nlinear_scale_levenberg;
+GSL_VAR const gsl_multilarge_nlinear_scale * gsl_multilarge_nlinear_scale_marquardt;
+GSL_VAR const gsl_multilarge_nlinear_scale * gsl_multilarge_nlinear_scale_more;
+
+/* linear solvers */
+GSL_VAR const gsl_multilarge_nlinear_solver * gsl_multilarge_nlinear_solver_cholesky;
+GSL_VAR const gsl_multilarge_nlinear_solver * gsl_multilarge_nlinear_solver_none;
+
+__END_DECLS
+
+#endif /* __GSL_MULTILARGE_NLINEAR_H__ */
diff -Nru gsl-doc-1.16/multilarge_nlinear/lm.c gsl-doc-2.3/multilarge_nlinear/lm.c
--- gsl-doc-1.16/multilarge_nlinear/lm.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/lm.c	2016-08-10 21:03:42.000000000 +0000
@@ -0,0 +1,364 @@
+/* multilarge_nlinear/lm.c
+ * 
+ * Copyright (C) 2014, 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multilarge_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_permutation.h>
+
+/*
+ * This module contains an implementation of the Levenberg-Marquardt
+ * algorithm for nonlinear optimization problems. This implementation
+ * closely follows the following works:
+ *
+ * [1] H. B. Nielsen, K. Madsen, Introduction to Optimization and
+ *     Data Fitting, Informatics and Mathematical Modeling,
+ *     Technical University of Denmark (DTU), 2010.
+ *
+ * [2] J. J. More, The Levenberg-Marquardt Algorithm: Implementation
+ *     and Theory, Lecture Notes in Mathematics, v630, 1978.
+ */
+
+typedef struct
+{
+  size_t n;                  /* number of observations */
+  size_t p;                  /* number of parameters */
+  gsl_vector *fvv;           /* D_v^2 f(x), size n */
+  gsl_vector *vel;           /* geodesic velocity (standard LM step), size p */
+  gsl_vector *acc;           /* geodesic acceleration, size p */
+  gsl_vector *JTfvv;         /* J^T fvv, size p */
+  gsl_vector *workp;         /* workspace, length p */
+  gsl_vector *workn;         /* workspace, length n */
+
+  int accel;                 /* use geodesic acceleration? */
+
+  /* tunable parameters */
+  gsl_multilarge_nlinear_parameters params;
+} lm_state_t;
+
+#include "common.c"
+
+static void *lm_alloc (const int accel, const void * params, const size_t n, const size_t p);
+static void *lm_alloc_noaccel (const void * params, const size_t n, const size_t p);
+static void *lm_alloc_accel (const void * params, const size_t n, const size_t p);
+static void lm_free(void *vstate);
+static int lm_init(const void *vtrust_state, void *vstate);
+static int lm_preloop(const void * vtrust_state, void * vstate);
+static int lm_step(const void * vtrust_state, const double delta,
+                   gsl_vector * dx, void * vstate);
+static int lm_preduction(const void * vtrust_state, const gsl_vector * dx,
+                         double * pred, void * vstate);
+
+static void *
+lm_alloc (const int accel, const void * params, const size_t n, const size_t p)
+{
+  const gsl_multilarge_nlinear_parameters *mparams = (const gsl_multilarge_nlinear_parameters *) params;
+  lm_state_t *state;
+  
+  state = calloc(1, sizeof(lm_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate lm state", GSL_ENOMEM);
+    }
+
+  state->workp = gsl_vector_alloc(p);
+  if (state->workp == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workp", GSL_ENOMEM);
+    }
+
+  state->workn = gsl_vector_alloc(n);
+  if (state->workn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workn", GSL_ENOMEM);
+    }
+
+  state->fvv = gsl_vector_alloc(n);
+  if (state->fvv == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for fvv", GSL_ENOMEM);
+    }
+
+  state->vel = gsl_vector_alloc(p);
+  if (state->vel == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for vel", GSL_ENOMEM);
+    }
+
+  state->acc = gsl_vector_alloc(p);
+  if (state->acc == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for acc", GSL_ENOMEM);
+    }
+
+  state->JTfvv = gsl_vector_alloc(p);
+  if (state->JTfvv == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for JTfvv", GSL_ENOMEM);
+    }
+
+  state->n = n;
+  state->p = p;
+  state->params = *mparams;
+  state->accel = accel;
+
+  return state;
+}
+
+static void *
+lm_alloc_noaccel (const void * params, const size_t n, const size_t p)
+{
+  return lm_alloc(0, params, n, p);
+}
+
+static void *
+lm_alloc_accel (const void * params, const size_t n, const size_t p)
+{
+  return lm_alloc(1, params, n, p);
+}
+
+static void
+lm_free(void *vstate)
+{
+  lm_state_t *state = (lm_state_t *) vstate;
+
+  if (state->workp)
+    gsl_vector_free(state->workp);
+
+  if (state->workn)
+    gsl_vector_free(state->workn);
+
+  if (state->fvv)
+    gsl_vector_free(state->fvv);
+
+  if (state->vel)
+    gsl_vector_free(state->vel);
+
+  if (state->acc)
+    gsl_vector_free(state->acc);
+
+  if (state->JTfvv)
+    gsl_vector_free(state->JTfvv);
+
+  free(state);
+}
+
+/*
+lm_init()
+  Initialize LM solver
+
+Inputs: vtrust_state - trust state
+        vstate       - workspace
+
+Return: success/error
+*/
+
+static int
+lm_init(const void *vtrust_state, void *vstate)
+{
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  lm_state_t *state = (lm_state_t *) vstate;
+
+  gsl_vector_set_zero(state->vel);
+  gsl_vector_set_zero(state->acc);
+
+  *(trust_state->avratio) = 0.0;
+
+  return GSL_SUCCESS;
+}
+
+/*
+lm_preloop()
+  Initialize LM method for new Jacobian matrix
+*/
+
+static int
+lm_preloop(const void * vtrust_state, void * vstate)
+{
+  int status;
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  const gsl_multilarge_nlinear_parameters *params = trust_state->params;
+
+  (void)vstate;
+
+  /* initialize linear least squares solver */
+  status = (params->solver->init)(trust_state, trust_state->solver_state);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+}
+
+/*
+lm_step()
+  Calculate a new step vector by solving the linear
+least squares system:
+
+[      J     ] v = - [ f ]
+[ sqrt(mu) D ]       [ 0 ]
+*/
+
+static int
+lm_step(const void * vtrust_state, const double delta,
+        gsl_vector * dx, void * vstate)
+{
+  int status;
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  lm_state_t *state = (lm_state_t *) vstate;
+  const gsl_multilarge_nlinear_parameters *params = trust_state->params;
+  const double mu = *(trust_state->mu);
+
+  (void)delta;
+
+  /* prepare the linear solver with current LM parameter mu */
+  status = (params->solver->presolve)(mu, trust_state, trust_state->solver_state);
+  if (status)
+    return status;
+
+  /* solve: (J^T J + mu D^T D) v = - J^T f */
+  status = (params->solver->solve)(trust_state->g,
+                                   state->vel,
+                                   trust_state,
+                                   trust_state->solver_state);
+  if (status)
+    return status;
+
+  if (state->accel)
+    {
+      double anorm, vnorm;
+
+      /* compute geodesic acceleration */
+      status = gsl_multilarge_nlinear_eval_fvv(params->h_fvv,
+                                               trust_state->x,
+                                               state->vel,
+                                               trust_state->f,
+                                               trust_state->sqrt_wts,
+                                               trust_state->fdf,
+                                               state->fvv,
+                                               state->workp);
+      if (status)
+        return status;
+
+      /* compute J^T fvv */
+      status = gsl_multilarge_nlinear_eval_df(CblasTrans,
+                                              trust_state->x,
+                                              trust_state->f,
+                                              state->fvv,
+                                              trust_state->sqrt_wts,
+                                              params->h_df,
+                                              params->fdtype,
+                                              trust_state->fdf,
+                                              state->JTfvv,
+                                              NULL,
+                                              state->workn);
+      if (status)
+        return status;
+
+      /* solve: (J^T J + mu D^T D) a = - J^T fvv */
+      status = (params->solver->solve)(state->JTfvv,
+                                       state->acc,
+                                       trust_state,
+                                       trust_state->solver_state);
+      if (status)
+        return status;
+
+      anorm = gsl_blas_dnrm2(state->acc);
+      vnorm = gsl_blas_dnrm2(state->vel);
+
+      /* store |a| / |v| */
+      *(trust_state->avratio) = anorm / vnorm;
+    }
+
+  /* compute step dx = v + 1/2 a */
+  scaled_addition(1.0, state->vel, 0.5, state->acc, dx);
+
+  return GSL_SUCCESS;
+}
+
+/*
+lm_preduction()
+  Compute predicted reduction using Eq 4.4 of More 1978
+*/
+
+static int
+lm_preduction(const void * vtrust_state, const gsl_vector * dx,
+              double * pred, void * vstate)
+{
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  lm_state_t *state = (lm_state_t *) vstate;
+  const gsl_vector *diag = trust_state->diag;
+  const gsl_vector *p = state->vel;
+  const double norm_Dp = scaled_enorm(diag, p);
+  const double normf = gsl_blas_dnrm2(trust_state->f);
+  const double mu = *(trust_state->mu);
+  double u, v;
+
+  (void)dx;
+
+  /* compute workp = J^T J p */
+  gsl_blas_dsymv(CblasLower, 1.0, trust_state->JTJ, p, 0.0, state->workp);
+
+  /* compute u = p^T J^T J p = ||J p||^2 */
+  gsl_blas_ddot(state->workp, p, &u);
+
+  /* compute u = ||J p||^2 / ||f||^2 */
+  u /= normf * normf;
+
+  /* v = ||D p|| / ||f|| */
+  v = norm_Dp / normf;
+
+  *pred = u + 2.0 * mu * v * v;
+
+  return GSL_SUCCESS;
+}
+
+static const gsl_multilarge_nlinear_trs lm_type =
+{
+  "levenberg-marquardt",
+  lm_alloc_noaccel,
+  lm_init,
+  lm_preloop,
+  lm_step,
+  lm_preduction,
+  lm_free
+};
+
+const gsl_multilarge_nlinear_trs *gsl_multilarge_nlinear_trs_lm = &lm_type;
+
+static const gsl_multilarge_nlinear_trs lmaccel_type =
+{
+  "levenberg-marquardt+accel",
+  lm_alloc_accel,
+  lm_init,
+  lm_preloop,
+  lm_step,
+  lm_preduction,
+  lm_free
+};
+
+const gsl_multilarge_nlinear_trs *gsl_multilarge_nlinear_trs_lmaccel = &lmaccel_type;
diff -Nru gsl-doc-1.16/multilarge_nlinear/Makefile.am gsl-doc-2.3/multilarge_nlinear/Makefile.am
--- gsl-doc-1.16/multilarge_nlinear/Makefile.am	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/Makefile.am	2016-09-16 14:55:19.000000000 +0000
@@ -0,0 +1,57 @@
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+
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+test_boxbod.c        \
+test_brown1.c        \
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+test_enso.c          \
+test_exp1.c          \
+test_hahn1.c         \
+test_helical.c       \
+test_gaussian.c      \
+test_jennrich.c      \
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+test_kowalik.c       \
+test_lin1.c          \
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+test_lin3.c          \
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+test_vardim.c        \
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+test_wnlin.c
+
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diff -Nru gsl-doc-1.16/multilarge_nlinear/Makefile.in gsl-doc-2.3/multilarge_nlinear/Makefile.in
--- gsl-doc-1.16/multilarge_nlinear/Makefile.in	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -0,0 +1,1087 @@
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diff -Nru gsl-doc-1.16/multilarge_nlinear/nielsen.c gsl-doc-2.3/multilarge_nlinear/nielsen.c
--- gsl-doc-1.16/multilarge_nlinear/nielsen.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/nielsen.c	2016-08-24 14:31:36.000000000 +0000
@@ -0,0 +1,106 @@
+/* multilarge_nlinear/nielsen.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/*
+ * This module contains routines for updating the Levenberg-Marquardt
+ * damping parameter on each iteration using Nielsen's method:
+ *
+ * [1] H. B. Nielsen, K. Madsen, Introduction to Optimization and
+ *     Data Fitting, Informatics and Mathematical Modeling,
+ *     Technical University of Denmark (DTU), 2010.
+ *
+ * 3 routines are needed to implement the update procedure:
+ *
+ * 1. init   - initialize parameter prior to iteration
+ * 2. accept - update parameter after a step has been accepted
+ * 3. reject - update parameter after a step has been rejected
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+
+#define LM_ONE_THIRD         (0.333333333333333)
+
+static int nielsen_init(const gsl_matrix * JTJ, const gsl_vector * diag,
+                        double * mu, long * nu);
+static int nielsen_accept(const double rho, double * mu, long * nu);
+static int nielsen_reject(double * mu, long * nu);
+
+static int
+nielsen_init(const gsl_matrix * JTJ, const gsl_vector * diag,
+             double * mu, long * nu)
+{
+  const double mu0 = 1.0e-3;
+  size_t i;
+  double max = -1.0;
+
+  *nu = 2;
+
+  if (JTJ == NULL)
+    {
+      /* not using cholesky solver */
+      *mu = mu0;
+      return GSL_SUCCESS;
+    }
+
+  /* set mu = mu0 * max(diag(J~^T J~)), with J~ = J D^{-1} */
+
+  for (i = 0; i < JTJ->size1; ++i)
+    {
+      double JTJi = gsl_matrix_get(JTJ, i, i);
+      double di = gsl_vector_get(diag, i);
+      double val = JTJi / (di * di);
+      max = GSL_MAX(max, val);
+    }
+
+  *mu = mu0 * max;
+
+  return GSL_SUCCESS;
+}
+
+static int
+nielsen_accept(const double rho, double * mu, long * nu)
+{
+  double b;
+  
+  /* reset nu */
+  *nu = 2;
+
+  b = 2.0 * rho - 1.0;
+  b = 1.0 - b*b*b;
+  *mu *= GSL_MAX(LM_ONE_THIRD, b);
+
+  return GSL_SUCCESS;
+}
+
+static int
+nielsen_reject(double * mu, long * nu)
+{
+  *mu *= (double) *nu;
+
+  /* nu := 2*nu */
+  *nu <<= 1;
+
+  return GSL_SUCCESS;
+}
diff -Nru gsl-doc-1.16/multilarge_nlinear/scaling.c gsl-doc-2.3/multilarge_nlinear/scaling.c
--- gsl-doc-1.16/multilarge_nlinear/scaling.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/scaling.c	2016-08-12 19:45:14.000000000 +0000
@@ -0,0 +1,160 @@
+/* multilarge_nlinear/scaling.c
+ * 
+ * Copyright (C) 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/*
+ * This module handles the updating of the scaling matrix D_k in the
+ * trust region subproblem:
+ *
+ * min m_k (dx), || D_k dx || <= Delta_k
+ *
+ * where m_k(dx) is a model which approximates the cost function
+ * F(x_k + dx) near the current iteration point x_k
+ *
+ * D_k can be updated according to several different strategies.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multilarge_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+
+static int init_diag_levenberg(const gsl_matrix * JTJ, gsl_vector * diag);
+static int update_diag_levenberg(const gsl_matrix * JTJ, gsl_vector * diag);
+
+static int init_diag_marquardt(const gsl_matrix * JTJ, gsl_vector * diag);
+static int update_diag_marquardt (const gsl_matrix * JTJ, gsl_vector * diag);
+
+static int init_diag_more(const gsl_matrix * JTJ, gsl_vector * diag);
+static int update_diag_more(const gsl_matrix * JTJ, gsl_vector * diag);
+
+/* Levenberg scaling, D = I */
+static int
+init_diag_levenberg(const gsl_matrix * JTJ, gsl_vector * diag)
+{
+  (void)JTJ; /* avoid unused parameter warning */
+  gsl_vector_set_all(diag, 1.0);
+  return GSL_SUCCESS;
+}
+
+static int
+update_diag_levenberg(const gsl_matrix * JTJ, gsl_vector * diag)
+{
+  (void)JTJ;  /* avoid unused parameter warning */
+  (void)diag; /* avoid unused parameter warning */
+
+  /* nothing to do */
+  return GSL_SUCCESS;
+}
+
+/* initialize diagonal scaling matrix D according to Marquardt method */
+static int
+init_diag_marquardt(const gsl_matrix * JTJ, gsl_vector * diag)
+{
+  return update_diag_marquardt(JTJ, diag);
+}
+
+/* update diagonal scaling matrix D according to Marquardt method */
+static int
+update_diag_marquardt (const gsl_matrix * JTJ, gsl_vector * diag)
+{
+  const size_t p = JTJ->size2;
+  size_t j;
+
+  for (j = 0; j < p; j++)
+    {
+      double Jjj = gsl_matrix_get(JTJ, j, j);
+      double norm;
+
+      if (Jjj <= 0.0)
+        norm = 1.0;
+      else
+        norm = sqrt(Jjj);
+
+      gsl_vector_set(diag, j, norm);
+    }
+
+  return GSL_SUCCESS;
+}
+
+/* initialize diagonal scaling matrix D according to Eq 6.3 of
+ * More, 1978 */
+static int
+init_diag_more(const gsl_matrix * JTJ, gsl_vector * diag)
+{
+  int status;
+
+  gsl_vector_set_zero(diag);
+  status = update_diag_more(JTJ, diag);
+
+  return status;
+}
+
+/* update diagonal scaling matrix D according to Eq. 6.3 of
+ * More, 1978 */
+static int
+update_diag_more (const gsl_matrix * JTJ, gsl_vector * diag)
+{
+  const size_t p = JTJ->size2;
+  size_t j;
+
+  for (j = 0; j < p; j++)
+    {
+      double Jjj = gsl_matrix_get(JTJ, j, j);
+      double *diagj = gsl_vector_ptr(diag, j);
+      double norm;
+
+      if (Jjj <= 0.0)
+        norm = 1.0;
+      else
+        norm = sqrt(Jjj);
+
+      *diagj = GSL_MAX(*diagj, norm);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static const gsl_multilarge_nlinear_scale levenberg_type =
+{
+  "levenberg",
+  init_diag_levenberg,
+  update_diag_levenberg
+};
+
+static const gsl_multilarge_nlinear_scale marquardt_type =
+{
+  "marquardt",
+  init_diag_marquardt,
+  update_diag_marquardt
+};
+
+static const gsl_multilarge_nlinear_scale more_type =
+{
+  "more",
+  init_diag_more,
+  update_diag_more
+};
+
+const gsl_multilarge_nlinear_scale *gsl_multilarge_nlinear_scale_levenberg = &levenberg_type;
+const gsl_multilarge_nlinear_scale *gsl_multilarge_nlinear_scale_marquardt = &marquardt_type;
+const gsl_multilarge_nlinear_scale *gsl_multilarge_nlinear_scale_more = &more_type;
diff -Nru gsl-doc-1.16/multilarge_nlinear/subspace2D.c gsl-doc-2.3/multilarge_nlinear/subspace2D.c
--- gsl-doc-1.16/multilarge_nlinear/subspace2D.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/subspace2D.c	2016-09-16 22:47:29.000000000 +0000
@@ -0,0 +1,736 @@
+/* multilarge_nlinear/subspace2D.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multilarge_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_poly.h>
+
+/*
+ * This module implements a 2D subspace trust region subproblem method,
+ * as outlined in
+ *
+ * [1] G. A. Shultz, R. B. Schnabel, and R. H. Byrd
+ *     A Family of Trust-Region-Based Algorithms for Unconstrained
+ *     Minimization with Strong Global Convergence Properties,
+ *     SIAM Journal on Numerical Analysis 1985 22:1, 47-67 
+ *
+ * [2] R. H. Byrd, R. B. Schnabel, G. A. Shultz,
+ *     Approximate solution of the trust region problem by
+ *     minimization over two-dimensional subspaces,
+ *     Mathematical Programming, January 1988, Volume 40,
+ *     Issue 1, pp 247-263
+ *
+ * The idea is to solve:
+ *
+ * min_{dx} g^T dx + 1/2 dx^T B dx
+ * 
+ * with constraints:
+ *
+ * ||D dx|| <= delta
+ * dx \in span{dx_sd, dx_gn}
+ *
+ * where B is the Hessian matrix, B = J^T J
+ *
+ * The steps are as follows:
+ *
+ * 1. preloop:
+ *    a. Compute Gauss-Newton and steepest descent vectors,
+ *       dx_gn, dx_sd
+ *    b. Compute an orthonormal basis for span(D dx_sd, D dx_gn) by
+ *       constructing W = [ D dx_sd, D dx_gn ] and performing a QR
+ *       decomposition of W. The 2 columns of the Q matrix
+ *       will then span the column space of W. W should have rank 2
+ *       unless D*dx_sd and D*dx_gn are parallel, in which case it will
+ *       have rank 1.
+ *    c. Precompute various quantities needed for the step calculation
+ *
+ * 2. step:
+ *    a. If the Gauss-Newton step is inside the trust region, use it
+ *    b. if W has rank 1, we cannot form a 2D subspace, so in this case
+ *       follow the steepest descent direction to the trust region boundary
+ *       and use that as the step.
+ *    c. In the full rank 2 case, if the GN point is outside the trust region,
+ *       then the minimizer of the objective function lies on the trust
+ *       region boundary. Therefore the minimization problem becomes:
+ *
+ *       min_{dx} g^T dx + 1/2 dx^T B dx, with ||dx|| = delta, dx = Q * x
+ *
+ *       where x is a 2-vector to be determined and the columns of Q are
+ *       the orthonormal basis vectors of the subspace. Note the equality
+ *       constraint now instead of <=. In terms of the new variable x,
+ *       the minimization problem becomes:
+ *
+ *       min_x subg^T x + 1/2 x^T subB x, with ||Q*x|| = ||x|| = delta
+ *
+ *       where:
+ *         subg = Q^T g   (2-by-1)
+ *         subB = Q^T B Q (2-by-2)
+ *
+ *       This equality constrained 2D minimization problem can be solved
+ *       with a Lagrangian multiplier, which results in a 4th degree polynomial
+ *       equation to be solved. The equation is:
+ *
+ *         lambda^4  1
+ *       + lambda^3  2 tr(B)
+ *       + lambda^2  (tr(B)^2 + 2 det(B) - g^T g / delta^2)
+ *       + lambda^1  (2 det(B) tr(B) - 2 g^T adj(B)^T g / delta^2)
+ *       + lambda^0  (det(B)^2 - g^T adj(B)^T adj(B) g / delta^2)
+ *
+ *       where adj(B) is the adjugate matrix of B.
+ *
+ *       We then check each of the 4 solutions for lambda to determine which
+ *       lambda results in the smallest objective function value. This x
+ *       is then used to construct the final step: dx = Q*x
+ */
+
+typedef struct
+{
+  size_t n;                  /* number of observations */
+  size_t p;                  /* number of parameters */
+  gsl_vector *dx_gn;         /* Gauss-Newton step, size p */
+  gsl_vector *dx_sd;         /* steepest descent step, size p */
+  double norm_Dgn;           /* || D dx_gn || */
+  double norm_Dsd;           /* || D dx_sd || */
+  gsl_vector *workp1;        /* workspace, length p */
+  gsl_vector *workp2;        /* workspace, length p */
+  gsl_vector *workn;         /* workspace, length n */
+  gsl_matrix *W;             /* orthonormal basis for 2D subspace, p-by-2 */
+  gsl_matrix *work_JTJ;      /* D^{-1} J^T J D^{-1}, p-by-p */
+  gsl_vector *tau;           /* Householder scalars */
+  gsl_vector *subg;          /* subspace gradient = W^T g, 2-by-1 */
+  gsl_matrix *subB;          /* subspace Hessian = W^T B W, 2-by-2 */
+  gsl_permutation *perm;     /* permutation matrix */
+
+  double trB;                /* Tr(subB) */
+  double detB;               /* det(subB) */
+  double normg;              /* || subg || */
+  double term0;              /* g^T adj(B)^T adj(B) g */
+  double term1;              /* g^T adj(B)^T g */
+
+  size_t rank;               /* rank of [ dx_sd, dx_gn ] matrix */
+
+  gsl_poly_complex_workspace *poly_p;
+
+  /* tunable parameters */
+  gsl_multilarge_nlinear_parameters params;
+} subspace2D_state_t;
+
+#include "common.c"
+
+static void * subspace2D_alloc (const void * params, const size_t n, const size_t p);
+static void subspace2D_free(void *vstate);
+static int subspace2D_init(const void *vtrust_state, void *vstate);
+static int subspace2D_preloop(const void * vtrust_state, void * vstate);
+static int subspace2D_step(const void * vtrust_state, const double delta,
+                           gsl_vector * dx, void * vstate);
+static int subspace2D_preduction(const void * vtrust_state, const gsl_vector * dx,
+                                 double * pred, void * vstate);
+static int subspace2D_solution(const double lambda, gsl_vector * x,
+                               subspace2D_state_t * state);
+static double subspace2D_objective(const gsl_vector * x, subspace2D_state_t * state);
+static int subspace2D_calc_gn(const gsl_multilarge_nlinear_trust_state * trust_state, gsl_vector * dx);
+static int subspace2D_calc_sd(const gsl_multilarge_nlinear_trust_state * trust_state, gsl_vector * dx,
+                              subspace2D_state_t * state);
+
+static void *
+subspace2D_alloc (const void * params, const size_t n, const size_t p)
+{
+  const gsl_multilarge_nlinear_parameters *par = (const gsl_multilarge_nlinear_parameters *) params;
+  subspace2D_state_t *state;
+  
+  state = calloc(1, sizeof(subspace2D_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate subspace2D state", GSL_ENOMEM);
+    }
+
+  state->dx_gn = gsl_vector_alloc(p);
+  if (state->dx_gn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for dx_gn", GSL_ENOMEM);
+    }
+
+  state->dx_sd = gsl_vector_alloc(p);
+  if (state->dx_sd == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for dx_sd", GSL_ENOMEM);
+    }
+
+  state->workp1 = gsl_vector_alloc(p);
+  if (state->workp1 == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workp1", GSL_ENOMEM);
+    }
+
+  state->workp2 = gsl_vector_alloc(p);
+  if (state->workp2 == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workp2", GSL_ENOMEM);
+    }
+
+  state->workn = gsl_vector_alloc(n);
+  if (state->workn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workn", GSL_ENOMEM);
+    }
+
+  state->W = gsl_matrix_alloc(p, 2);
+  if (state->W == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for W", GSL_ENOMEM);
+    }
+
+  state->work_JTJ = gsl_matrix_alloc(p, p);
+  if (state->work_JTJ == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for work_JTJ", GSL_ENOMEM);
+    }
+
+  state->tau = gsl_vector_alloc(2);
+  if (state->tau == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for tau", GSL_ENOMEM);
+    }
+
+  state->subg = gsl_vector_alloc(2);
+  if (state->subg == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for subg", GSL_ENOMEM);
+    }
+
+  state->subB = gsl_matrix_alloc(2, 2);
+  if (state->subB == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for subB", GSL_ENOMEM);
+    }
+
+  state->perm = gsl_permutation_alloc(2);
+  if (state->perm == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for perm", GSL_ENOMEM);
+    }
+
+  state->poly_p = gsl_poly_complex_workspace_alloc(5);
+  if (state->poly_p == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for poly workspace", GSL_ENOMEM);
+    }
+
+  state->n = n;
+  state->p = p;
+  state->rank = 0;
+  state->params = *par;
+
+  return state;
+}
+
+static void
+subspace2D_free(void *vstate)
+{
+  subspace2D_state_t *state = (subspace2D_state_t *) vstate;
+
+  if (state->dx_gn)
+    gsl_vector_free(state->dx_gn);
+
+  if (state->dx_sd)
+    gsl_vector_free(state->dx_sd);
+
+  if (state->workp1)
+    gsl_vector_free(state->workp1);
+
+  if (state->workp2)
+    gsl_vector_free(state->workp2);
+
+  if (state->workn)
+    gsl_vector_free(state->workn);
+
+  if (state->W)
+    gsl_matrix_free(state->W);
+
+  if (state->work_JTJ)
+    gsl_matrix_free(state->work_JTJ);
+
+  if (state->tau)
+    gsl_vector_free(state->tau);
+
+  if (state->subg)
+    gsl_vector_free(state->subg);
+
+  if (state->subB)
+    gsl_matrix_free(state->subB);
+
+  if (state->perm)
+    gsl_permutation_free(state->perm);
+
+  if (state->poly_p)
+    gsl_poly_complex_workspace_free(state->poly_p);
+
+  free(state);
+}
+
+/*
+subspace2D_init()
+  Initialize subspace2D solver
+
+Inputs: vtrust_state - trust state
+        vstate       - workspace
+
+Return: success/error
+*/
+
+static int
+subspace2D_init(const void *vtrust_state, void *vstate)
+{
+  (void)vtrust_state;
+  (void)vstate;
+
+  return GSL_SUCCESS;
+}
+
+/*
+subspace2D_preloop()
+  Initialize subspace2D method prior to iteration loop.
+This involves computing the Gauss-Newton step and
+steepest descent step
+
+Notes: on output,
+1) state->dx_gn contains Gauss-Newton step
+2) state->dx_sd contains steepest descent step
+3) state->rank contains the rank([dx_sd, dx_gn])
+4) if full rank subspace (rank = 2), then:
+   state->trB = Tr(subB)
+   state->detB = det(subB)
+   state->normg = || subg ||
+*/
+
+static int
+subspace2D_preloop(const void * vtrust_state, void * vstate)
+{
+  int status;
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  subspace2D_state_t *state = (subspace2D_state_t *) vstate;
+  gsl_vector_view v;
+  double work_data[2];
+  gsl_vector_view work = gsl_vector_view_array(work_data, 2);
+  int signum;
+
+  /* calculate Gauss-Newton step */
+  status = subspace2D_calc_gn(trust_state, state->dx_gn);
+  if (status)
+    return status;
+
+  /* now calculate the steepest descent step */
+  status = subspace2D_calc_sd(trust_state, state->dx_sd, state);
+  if (status)
+    return status;
+
+  /* store norms */
+  state->norm_Dgn = scaled_enorm(trust_state->diag, state->dx_gn);
+  state->norm_Dsd = scaled_enorm(trust_state->diag, state->dx_sd);
+
+  /*
+   * now compute orthonormal basis for span(D dx_sd, D dx_gn) using
+   * QR decomposition; set W = [ D dx_sd, D dx_gn ] and normalize each
+   * column to unit magnitude. Then the Q matrix will form a basis for Col(W)
+   */
+
+  v = gsl_matrix_column(state->W, 0);
+  gsl_vector_memcpy(&v.vector, state->dx_sd);
+  gsl_vector_mul(&v.vector, trust_state->diag);
+  if (state->norm_Dsd != 0)
+    gsl_vector_scale(&v.vector, 1.0 / state->norm_Dsd);
+
+  v = gsl_matrix_column(state->W, 1);
+  gsl_vector_memcpy(&v.vector, state->dx_gn);
+  gsl_vector_mul(&v.vector, trust_state->diag);
+  if (state->norm_Dgn != 0)
+    gsl_vector_scale(&v.vector, 1.0 / state->norm_Dgn);
+
+  /* use a rank revealing QR decomposition in case dx_sd and dx_gn
+   * are parallel */
+  gsl_linalg_QRPT_decomp(state->W, state->tau, state->perm, &signum, &work.vector);
+
+  /* check for parallel dx_sd, dx_gn, in which case rank will be 1 */
+  state->rank = gsl_linalg_QRPT_rank(state->W, -1.0);
+
+  if (state->rank == 2)
+    {
+      /*
+       * full rank subspace, compute:
+       * subg = Q^T D^{-1} g
+       * subB = Q^T D^{-1} B D^{-1} Q where B = J^T J
+       */
+      const size_t p = state->p;
+      size_t i, j;
+      double B00, B10, B11, g0, g1;
+
+      /* compute subg */
+      gsl_vector_memcpy(state->workp1, trust_state->g);
+      gsl_vector_div(state->workp1, trust_state->diag);
+      gsl_linalg_QR_QTvec(state->W, state->tau, state->workp1);
+
+      g0 = gsl_vector_get(state->workp1, 0);
+      g1 = gsl_vector_get(state->workp1, 1);
+
+      gsl_vector_set(state->subg, 0, g0);
+      gsl_vector_set(state->subg, 1, g1);
+
+      /* compute subB */
+
+      /* compute work_JTJ = D^{-1} J^T J D^{-1} using lower triangle */
+      for (j = 0; j < p; ++j)
+        {
+          double dj = gsl_vector_get(trust_state->diag, j);
+
+          for (i = j; i < p; ++i)
+            {
+              double di = gsl_vector_get(trust_state->diag, i);
+              double Aij = gsl_matrix_get(trust_state->JTJ, i, j);
+
+              gsl_matrix_set(state->work_JTJ, i, j, Aij / (di * dj));
+            }
+        }
+
+      gsl_matrix_transpose_tricpy('L', 0, state->work_JTJ, state->work_JTJ);
+
+      /* compute work_JTJ = Q^T D^{-1} J^T J D^{-1} Q */
+      gsl_linalg_QR_matQ(state->W, state->tau, state->work_JTJ);
+      gsl_linalg_QR_QTmat(state->W, state->tau, state->work_JTJ);
+
+#if 0
+      /* compute subB = Q^T D^{-1} J^T J D^{-1} Q */
+      gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &JQ.matrix, 0.0, state->subB);
+#endif
+
+      B00 = gsl_matrix_get(state->work_JTJ, 0, 0);
+      B10 = gsl_matrix_get(state->work_JTJ, 1, 0);
+      B11 = gsl_matrix_get(state->work_JTJ, 1, 1);
+
+      gsl_matrix_set(state->subB, 0, 0, B00);
+      gsl_matrix_set(state->subB, 1, 0, B10);
+      gsl_matrix_set(state->subB, 1, 1, B11);
+
+      state->trB = B00 + B11;
+      state->detB = B00*B11 - B10*B10;
+      state->normg = gsl_blas_dnrm2(state->subg);
+
+      /* g^T adj(B)^T adj(B) g */
+      state->term0 = (B10*B10 + B11*B11)*g0*g0 -
+                     2*B10*(B00 + B11)*g0*g1 +
+                     (B00*B00 + B10*B10)*g1*g1;
+
+      /* g^T adj(B)^T g */
+      state->term1 = B11 * g0 * g0 + g1 * (B00*g1 - 2*B10*g0);
+
+    }
+
+  return GSL_SUCCESS;
+}
+
+
+/*
+subspace2D_step()
+  Calculate a new step with 2D subspace method. Based on [1]. We
+seek a vector dx in span{dx_gn, dx_sd} which minimizes the model
+function subject to ||dx|| <= delta
+*/
+
+static int
+subspace2D_step(const void * vtrust_state, const double delta,
+                gsl_vector * dx, void * vstate)
+{
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  subspace2D_state_t *state = (subspace2D_state_t *) vstate;
+
+  if (state->norm_Dgn <= delta)
+    {
+      /* Gauss-Newton step is inside trust region, use it as final step
+       * since it is the global minimizer of the quadratic model function */
+      gsl_vector_memcpy(dx, state->dx_gn);
+    }
+  else if (state->rank < 2)
+    {
+      /* rank of [dx_sd, dx_gn] is 1, meaning dx_sd and dx_gn
+       * are parallel so we can't form a 2D subspace. Follow the steepest
+       * descent direction to the trust region boundary as our step */
+      gsl_vector_memcpy(dx, state->dx_sd);
+      gsl_vector_scale(dx, delta / state->norm_Dsd);
+    }
+  else
+    {
+      int status;
+      const double delta_sq = delta * delta;
+      double u = state->normg / delta;
+      double a[5];
+      double z[8];
+
+#if 1
+      a[0] = state->detB * state->detB - state->term0 / delta_sq;
+      a[1] = 2 * state->detB * state->trB - 2 * state->term1 / delta_sq;
+      a[2] = state->trB * state->trB + 2 * state->detB - u * u;
+      a[3] = 2 * state->trB;
+      a[4] = 1.0;
+#else
+      double TrB_D = state->trB * delta;
+      double detB_D = state->detB * delta;
+      double normg_sq = state->normg * state->normg;
+
+      a[0] = detB_D * detB_D - state->term0;
+      a[1] = 2 * state->detB * state->trB * delta_sq - 2 * state->term1;
+      a[2] = TrB_D * TrB_D + 2 * state->detB * delta_sq - normg_sq;
+      a[3] = 2 * state->trB * delta_sq;
+      a[4] = delta_sq;
+#endif
+
+      status = gsl_poly_complex_solve(a, 5, state->poly_p, z);
+      if (status == GSL_SUCCESS)
+        {
+          size_t i;
+          double min = 0.0;
+          int mini = -1;
+          double x_data[2];
+          gsl_vector_view x = gsl_vector_view_array(x_data, 2);
+
+          /*
+           * loop through all four values of the Lagrange multiplier
+           * lambda. For each lambda, evaluate the objective function
+           * with Re(lambda) to determine which lambda minimizes the
+           * function
+           */
+          for (i = 0; i < 4; ++i)
+            {
+              double cost, normx;
+
+              /*fprintf(stderr, "root: %.12e + %.12e i\n",
+                      z[2*i], z[2*i+1]);*/
+
+              status = subspace2D_solution(z[2*i], &x.vector, state);
+              if (status != GSL_SUCCESS)
+                continue; /* singular matrix system */
+
+              /* ensure ||x|| = delta */
+
+              normx = gsl_blas_dnrm2(&x.vector);
+              if (normx == 0.0)
+                continue;
+
+              gsl_vector_scale(&x.vector, delta / normx);
+
+              /* evaluate objective function to determine minimizer */
+              cost = subspace2D_objective(&x.vector, state);
+              if (mini < 0 || cost < min)
+                {
+                  mini = (int) i;
+                  min = cost;
+                }
+            }
+
+          if (mini < 0)
+            {
+              /* did not find minimizer - should not get here */
+              return GSL_FAILURE;
+            }
+          else
+            {
+              /* compute x which minimizes objective function */
+              subspace2D_solution(z[2*mini], &x.vector, state);
+
+              /* dx = Q * x */
+              gsl_vector_set_zero(dx);
+              gsl_vector_set(dx, 0, gsl_vector_get(&x.vector, 0));
+              gsl_vector_set(dx, 1, gsl_vector_get(&x.vector, 1));
+              gsl_linalg_QR_Qvec(state->W, state->tau, dx);
+
+              /* compute final dx by multiplying by D^{-1} */
+              gsl_vector_div(dx, trust_state->diag);
+            }
+        }
+      else
+        {
+          GSL_ERROR ("gsl_poly_complex_solve failed", status);
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+subspace2D_preduction(const void * vtrust_state, const gsl_vector * dx,
+                      double * pred, void * vstate)
+{
+  const gsl_multilarge_nlinear_trust_state *trust_state =
+    (const gsl_multilarge_nlinear_trust_state *) vtrust_state;
+  subspace2D_state_t *state = (subspace2D_state_t *) vstate;
+
+  *pred = quadratic_preduction(trust_state, dx, state->workn);
+
+  return GSL_SUCCESS;
+}
+
+/* solve 2D subspace problem: (B + lambda*I) x = -g */
+static int
+subspace2D_solution(const double lambda, gsl_vector * x,
+                    subspace2D_state_t * state)
+{
+  int status = GSL_SUCCESS;
+  double C_data[4];
+  gsl_matrix_view C = gsl_matrix_view_array(C_data, 2, 2);
+  double B00 = gsl_matrix_get(state->subB, 0, 0);
+  double B10 = gsl_matrix_get(state->subB, 1, 0);
+  double B11 = gsl_matrix_get(state->subB, 1, 1);
+
+  /* construct C = B + lambda*I */
+  gsl_matrix_set(&C.matrix, 0, 0, B00 + lambda);
+  gsl_matrix_set(&C.matrix, 1, 0, B10);
+  gsl_matrix_set(&C.matrix, 0, 1, B10);
+  gsl_matrix_set(&C.matrix, 1, 1, B11 + lambda);
+
+  /* use modified Cholesky in case C is not positive definite */
+  gsl_linalg_mcholesky_decomp(&C.matrix, state->perm, NULL);
+  gsl_linalg_mcholesky_solve(&C.matrix, state->perm, state->subg, x);
+
+  gsl_vector_scale(x, -1.0);
+
+  return status;
+}
+
+/* evaluate 2D objective function: f(x) = g^T x + 1/2 x^T B x */
+static double
+subspace2D_objective(const gsl_vector * x, subspace2D_state_t * state)
+{
+  double f;
+  double y_data[2];
+  gsl_vector_view y = gsl_vector_view_array(y_data, 2);
+
+  /* compute: y = g + 1/2 B x */
+  gsl_vector_memcpy(&y.vector, state->subg);
+  gsl_blas_dsymv(CblasLower, 0.5, state->subB, x, 1.0, &y.vector);
+
+  /* compute: f = x^T ( g + 1/2 B x ) */
+  gsl_blas_ddot(x, &y.vector, &f);
+
+  return f;
+}
+
+/*
+subspace2D_calc_gn()
+  Calculate Gauss-Newton step by solving
+
+J^T J dx_gn = -J^T f
+
+Inputs: trust_state - trust state variables
+        dx          - (output) Gauss-Newton step vector
+
+Return: success/error
+*/
+
+static int
+subspace2D_calc_gn(const gsl_multilarge_nlinear_trust_state * trust_state, gsl_vector * dx)
+{
+  int status;
+  const gsl_multilarge_nlinear_parameters *params = trust_state->params;
+
+  /* initialize linear least squares solver */
+  status = (params->solver->init)(trust_state, trust_state->solver_state);
+  if (status)
+    return status;
+
+  /* prepare the linear solver to compute Gauss-Newton step */
+  status = (params->solver->presolve)(0.0, trust_state, trust_state->solver_state);
+  if (status)
+    return status;
+
+  /* solve: J dx_gn = -f for Gauss-Newton step */
+  status = (params->solver->solve)(trust_state->g,
+                                   dx,
+                                   trust_state,
+                                   trust_state->solver_state);
+  if (status)
+    return status;
+
+  return GSL_SUCCESS;
+}
+
+/*
+subspace2D_calc_sd()
+  Calculate steepest descent step,
+
+dx_sd = - || D^{-1} g ||^2 / || J D^{-2} g ||^2 D^{-2} g
+
+Inputs: trust_state - trust state variables
+        dx          - (output) steepest descent vector
+        state       - workspace
+
+Return: success/error
+*/
+
+static int
+subspace2D_calc_sd(const gsl_multilarge_nlinear_trust_state * trust_state, gsl_vector * dx,
+                   subspace2D_state_t * state)
+{
+  double norm_Dinvg;   /* || D^{-1} g || */
+  double norm_JDinv2g; /* || J D^{-2} g || */
+  double alpha;        /* || D^{-1} g ||^2 / || J D^{-2} g ||^2 */
+  double u;
+
+  /* compute workp1 = D^{-1} g and its norm */
+  gsl_vector_memcpy(state->workp1, trust_state->g);
+  gsl_vector_div(state->workp1, trust_state->diag);
+  norm_Dinvg = gsl_blas_dnrm2(state->workp1);
+
+  /* compute workp1 = D^{-2} g */
+  gsl_vector_div(state->workp1, trust_state->diag);
+
+  /* compute workp2 = J^T J D^{-2} g */
+  gsl_blas_dsymv(CblasLower, 1.0, trust_state->JTJ, state->workp1, 0.0, state->workp2);
+
+  /* compute norm_JDinv2g = || J D^{-2} g || */
+  gsl_blas_ddot(state->workp1, state->workp2, &u);
+  norm_JDinv2g = sqrt(u);
+
+  u = norm_Dinvg / norm_JDinv2g;
+  alpha = u * u;
+
+  /* dx_sd = -alpha D^{-2} g */
+  gsl_vector_memcpy(dx, state->workp1);
+  gsl_vector_scale(dx, -alpha);
+
+  return GSL_SUCCESS;
+}
+
+static const gsl_multilarge_nlinear_trs subspace2D_type =
+{
+  "2D-subspace",
+  subspace2D_alloc,
+  subspace2D_init,
+  subspace2D_preloop,
+  subspace2D_step,
+  subspace2D_preduction,
+  subspace2D_free
+};
+
+const gsl_multilarge_nlinear_trs *gsl_multilarge_nlinear_trs_subspace2D = &subspace2D_type;
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_bard.c gsl-doc-2.3/multilarge_nlinear/test_bard.c
--- gsl-doc-1.16/multilarge_nlinear/test_bard.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_bard.c	2016-08-12 19:50:35.000000000 +0000
@@ -0,0 +1,161 @@
+#define bard_N         15
+#define bard_P         3
+
+static double bard_x0[bard_P] = { 1.0, 1.0, 1.0 };
+static double bard_epsrel = 1.0e-7;
+
+static double bard_J[bard_N * bard_P];
+
+static double bard_Y[bard_N] = {
+0.14, 0.18, 0.22, 0.25, 0.29, 0.32, 0.35, 0.39, 0.37,
+0.58, 0.73, 0.96, 1.34, 2.10, 4.39
+};
+
+static void
+bard_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact1 = 8.214877306578963e-03;
+  const double bard_x1[bard_P] = { 8.241055975623580e-02,
+                                   1.133036092245175,
+                                   2.343695178435405 };
+  const double sumsq_exact2 = 17.42869333333333;
+  const double bard_x2[bard_P] = { 8.406666666666666e-01,
+                                   GSL_NAN,    /* -inf */
+                                   GSL_NAN };  /* -inf */
+  const double *bard_x;
+  double sumsq_exact;
+
+  if (fabs(x[1]) < 10.0 && fabs(x[2]) < 10.0)
+    {
+      bard_x = bard_x1;
+      sumsq_exact = sumsq_exact1;
+    }
+  else
+    {
+      bard_x = bard_x2;
+      sumsq_exact = sumsq_exact2;
+    }
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < bard_P; ++i)
+    {
+      if (!gsl_finite(bard_x[i]))
+        continue;
+
+      gsl_test_rel(x[i], bard_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+bard_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < bard_N; ++i)
+    {
+      double ui = i + 1.0;
+      double vi = 16.0 - i - 1.0;
+      double wi = GSL_MIN(ui, vi);
+      double yi = bard_Y[i];
+      double fi = yi - (x1 + (ui / (x2*vi + x3*wi)));
+
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+bard_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+         const gsl_vector * u, void * params, gsl_vector * v,
+         gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(bard_J, bard_N, bard_P);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < bard_N; ++i)
+    {
+      double ui = i + 1.0;
+      double vi = 16.0 - i - 1.0;
+      double wi = GSL_MIN(ui, vi);
+      double term = x2 * vi + x3 * wi;
+
+      gsl_matrix_set(&J.matrix, i, 0, -1.0);
+      gsl_matrix_set(&J.matrix, i, 1, ui * vi / (term * term));
+      gsl_matrix_set(&J.matrix, i, 2, ui * wi / (term * term));
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+bard_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  size_t i;
+
+  for (i = 0; i < bard_N; ++i)
+    {
+      double ui = i + 1.0;
+      double vi = 16.0 - i - 1.0;
+      double wi = GSL_MIN(ui, vi);
+      double term1 = x2 * vi + x3 * wi;
+      double term2 = v2 * vi + v3 * wi;
+      double ratio = term2 / term1;
+
+      gsl_vector_set(fvv, i, -2.0 * ui * ratio * ratio / term1);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf bard_func =
+{
+  bard_f,
+  bard_df,
+  bard_fvv,
+  bard_N,
+  bard_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem bard_problem =
+{
+  "bard",
+  bard_x0,
+  NULL,
+  &bard_epsrel,
+  &bard_checksol,
+  &bard_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_beale.c gsl-doc-2.3/multilarge_nlinear/test_beale.c
--- gsl-doc-1.16/multilarge_nlinear/test_beale.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_beale.c	2016-08-12 19:50:40.000000000 +0000
@@ -0,0 +1,124 @@
+#define beale_N         3
+#define beale_P         2
+
+static double beale_x0[beale_P] = { 1.0, 1.0 };
+static double beale_epsrel = 1.0e-12;
+
+static double beale_J[beale_N * beale_P];
+
+static double beale_Y[beale_N] = { 1.5, 2.25, 2.625 };
+
+static void
+beale_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double beale_x[beale_P] = { 3.0, 0.5 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < beale_P; ++i)
+    {
+      gsl_test_rel(x[i], beale_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+beale_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < beale_N; ++i)
+    {
+      double yi = beale_Y[i];
+      double term = pow(x2, i + 1.0);
+      double fi = yi - x1*(1.0 - term);
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+beale_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+          const gsl_vector * u, void * params, gsl_vector * v,
+          gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(beale_J, beale_N, beale_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < beale_N; ++i)
+    {
+      double term = pow(x2, (double) i);
+
+      gsl_matrix_set(&J.matrix, i, 0, term*x2 - 1.0);
+      gsl_matrix_set(&J.matrix, i, 1, (i + 1.0) * x1 * term);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+beale_fvv (const gsl_vector * x, const gsl_vector * v,
+           void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  size_t i;
+
+  for (i = 0; i < beale_N; ++i)
+    {
+      double term = pow(x2, (double)i - 1.0);
+
+      gsl_vector_set(fvv, i, (i + 1.0) * v2 * term *
+                             (i * v2 * x1 + 2.0 * v1 * x2));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf beale_func =
+{
+  beale_f,
+  beale_df,
+  beale_fvv,
+  beale_N,
+  beale_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem beale_problem =
+{
+  "beale",
+  beale_x0,
+  NULL,
+  &beale_epsrel,
+  &beale_checksol,
+  &beale_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_biggs.c gsl-doc-2.3/multilarge_nlinear/test_biggs.c
--- gsl-doc-1.16/multilarge_nlinear/test_biggs.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_biggs.c	2016-08-25 16:29:42.000000000 +0000
@@ -0,0 +1,163 @@
+#define biggs_N         6  /* >= p */
+#define biggs_P         6
+
+/* dogleg method has trouble converging from recommended starting point,
+ * so we use an x0 which is a little closer to the true solution */
+/*static double biggs_x0[biggs_P] = { 1.0, 2.0, 1.0, 1.0, 1.0, 1.0 };*/
+static double biggs_x0[biggs_P] = { 1.0, 8.0, 1.0, 2.0, 3.0, 2.0 };
+static double biggs_epsrel = 1.0e-9;
+
+static double biggs_J[biggs_N * biggs_P];
+
+static void
+biggs_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+#if 0
+  const double sumsq_exact = 0.0;
+#endif
+  const double biggs_x[biggs_P] = { 1.0, 10.0, 1.0, 5.0, 4.0, 3.0 };
+  const double norm_exact = 12.3288280059380;
+  gsl_vector_const_view v = gsl_vector_const_view_array(biggs_x, biggs_P);
+  double norm = gsl_blas_dnrm2(&v.vector);
+
+#if 0
+  /* some solvers have difficulty reaching sumsq = 0 to sufficient
+   * decimal places */
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+#endif
+
+  /*
+   * the solution vector is not unique due to permutations, so test
+   * the norm instead of individual elements
+   */
+  gsl_test_rel(norm, norm_exact, epsrel, "%s/%s norm",
+               sname, pname);
+
+  (void)x;     /* avoid unused parameter warning */
+  (void)sumsq; /* avoid unused parameter warning */
+}
+
+static int
+biggs_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  double x6 = gsl_vector_get(x, 5);
+  size_t i;
+
+  for (i = 0; i < biggs_N; ++i)
+    {
+      double ti = 0.1 * (i + 1.0);
+      double yi = exp(-ti) - 5*exp(-10*ti) + 3*exp(-4*ti);
+      double fi = x3*exp(-ti*x1) - x4*exp(-ti*x2) + x6*exp(-ti*x5) - yi;
+
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+biggs_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+          const gsl_vector * u, void * params, gsl_vector * v,
+          gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(biggs_J, biggs_N, biggs_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  double x6 = gsl_vector_get(x, 5);
+  size_t i;
+
+  for (i = 0; i < biggs_N; ++i)
+    {
+      double ti = 0.1 * (i + 1.0);
+
+      gsl_matrix_set(&J.matrix, i, 0, -ti*x3*exp(-ti*x1));
+      gsl_matrix_set(&J.matrix, i, 1, ti*x4*exp(-ti*x2));
+      gsl_matrix_set(&J.matrix, i, 2, exp(-ti*x1));
+      gsl_matrix_set(&J.matrix, i, 3, -exp(-ti*x2));
+      gsl_matrix_set(&J.matrix, i, 4, -ti*x6*exp(-ti*x5));
+      gsl_matrix_set(&J.matrix, i, 5, exp(-ti*x5));
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+biggs_fvv (const gsl_vector * x, const gsl_vector * v,
+           void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  double x6 = gsl_vector_get(x, 5);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  double v4 = gsl_vector_get(v, 3);
+  double v5 = gsl_vector_get(v, 4);
+  double v6 = gsl_vector_get(v, 5);
+  size_t i;
+
+  for (i = 0; i < biggs_N; ++i)
+    {
+      double ti = 0.1 * (i + 1.0);
+      double term1 = exp(-ti * x1);
+      double term2 = exp(-ti * x2);
+      double term3 = exp(-ti * x5);
+
+      gsl_vector_set(fvv, i, ti * term1 * term2 * term3 *
+                             (v1/(term2*term3)*(-2*v3 + ti*v1*x3) -
+                              v2/(term1*term3)*(-2*v4 + ti*v2*x4) +
+                              v5/(term1*term2)*(-2*v6 + ti*v5*x6)));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf biggs_func =
+{
+  biggs_f,
+  biggs_df,
+  biggs_fvv,
+  biggs_N,
+  biggs_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem biggs_problem =
+{
+  "biggs",
+  biggs_x0,
+  NULL,
+  &biggs_epsrel,
+  &biggs_checksol,
+  &biggs_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_boxbod.c gsl-doc-2.3/multilarge_nlinear/test_boxbod.c
--- gsl-doc-1.16/multilarge_nlinear/test_boxbod.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_boxbod.c	2016-08-12 19:50:49.000000000 +0000
@@ -0,0 +1,154 @@
+#define boxbod_N       6
+#define boxbod_P       2
+
+static double boxbod_x0a[boxbod_P] = { 1.0, 1.0 };
+static double boxbod_x0b[boxbod_P] = { 100.0, 0.75 };
+static double boxbod_epsrel = 1.0e-7;
+
+static double boxbod_J[boxbod_N * boxbod_P];
+
+static double boxbod_sigma[boxbod_P] = {
+  1.2354515176E+01, 1.0455993237E-01
+};
+
+static double boxbod_X[boxbod_N] = { 1.0, 2.0, 3.0, 5.0, 7.0, 10.0 };
+
+static double boxbod_F[boxbod_N] = { 109.0, 149.0, 149.0, 191.0,
+                                     213.0, 224.0 };
+
+static void
+boxbod_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.1680088766E+03;
+  const double boxbod_x[boxbod_P] = { 2.1380940889E+02,
+                                      5.4723748542E-01 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < boxbod_P; ++i)
+    {
+      gsl_test_rel(x[i], boxbod_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+boxbod_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[boxbod_P];
+  size_t i;
+
+  for (i = 0; i < boxbod_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < boxbod_N; i++)
+    {
+      double xi = boxbod_X[i];
+      double yi;
+
+      yi = b[0] * (1.0 - exp(-b[1] * xi));
+      gsl_vector_set (f, i, yi - boxbod_F[i]);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+boxbod_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+           const gsl_vector * u, void * params, gsl_vector * v,
+           gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(boxbod_J, boxbod_N, boxbod_P);
+  double b[boxbod_P];
+  size_t i;
+
+  for (i = 0; i < boxbod_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < boxbod_N; i++)
+    {
+      double xi = boxbod_X[i];
+      double term = exp(-b[1] * xi);
+
+      gsl_matrix_set (&J.matrix, i, 0, 1.0 - term);
+      gsl_matrix_set (&J.matrix, i, 1, b[0] * term * xi);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+boxbod_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  size_t i;
+
+  for (i = 0; i < boxbod_N; i++)
+    {
+      double ti = boxbod_X[i];
+      double term = exp(-x2 * ti);
+
+      gsl_vector_set(fvv, i, term * ti * v2 * (2*v1 - ti*v2*x1));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf boxbod_func =
+{
+  boxbod_f,
+  boxbod_df,
+  boxbod_fvv,
+  boxbod_N,
+  boxbod_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem boxboda_problem =
+{
+  "nist-boxboda",
+  boxbod_x0a,
+  boxbod_sigma,
+  &boxbod_epsrel,
+  &boxbod_checksol,
+  &boxbod_func
+};
+
+static test_fdf_problem boxbodb_problem =
+{
+  "nist-boxbodb",
+  boxbod_x0b,
+  boxbod_sigma,
+  &boxbod_epsrel,
+  &boxbod_checksol,
+  &boxbod_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_box.c gsl-doc-2.3/multilarge_nlinear/test_box.c
--- gsl-doc-1.16/multilarge_nlinear/test_box.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_box.c	2016-08-12 19:50:53.000000000 +0000
@@ -0,0 +1,154 @@
+#define box_N         10 /* can be >= p */
+#define box_P         3
+
+/* dogleg method fails with recommended starting point, so use
+ * a slightly easier x0 */
+/*static double box_x0[box_P] = { 0.0, 10.0, 20.0 };*/
+static double box_x0[box_P] = { 5.0, 10.0, 2.0 };
+static double box_epsrel = 1.0e-12;
+
+static double box_J[box_N * box_P];
+
+static void
+box_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  const double sumsq_exact = 0.0;
+  const double eps = 1.0e-6;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  /* there are 3 possible solution vectors */
+
+  if (fabs(x[2] - 1.0) < eps)
+    {
+      /* case 1: x* = [ 1; 10; 1 ] */
+      gsl_test_rel(x[0], 1.0, epsrel, "%s/%s i=0",
+                   sname, pname);
+      gsl_test_rel(x[1], 10.0, epsrel, "%s/%s i=1",
+                   sname, pname);
+      gsl_test_rel(x[2], 1.0, epsrel, "%s/%s i=2",
+                   sname, pname);
+    }
+  else if (fabs(x[2] + 1.0) < eps)
+    {
+      /* case 2: x* = [ 10; 1; -1 ] */
+      gsl_test_rel(x[0], 10.0, epsrel, "%s/%s i=0",
+                   sname, pname);
+      gsl_test_rel(x[1], 1.0, epsrel, "%s/%s i=1",
+                   sname, pname);
+      gsl_test_rel(x[2], -1.0, epsrel, "%s/%s i=2",
+                   sname, pname);
+    }
+  else
+    {
+      /* case 3: x* = [ a; a; 0 ] for any a */
+      gsl_test_rel(x[0], x[1], epsrel, "%s/%s i=0,1",
+                   sname, pname);
+      gsl_test_rel(x[2], 0.0, epsrel, "%s/%s i=2",
+                   sname, pname);
+    }
+}
+
+static int
+box_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < box_N; ++i)
+    {
+      double ti = (i + 1.0) / 10.0;
+      double fi = exp(-x1*ti) - exp(-x2*ti) - x3*(exp(-ti) - exp(-10.0*ti));
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+box_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+        const gsl_vector * u, void * params, gsl_vector * v,
+        gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(box_J, box_N, box_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < box_N; ++i)
+    {
+      double ti = (i + 1.0) / 10.0;
+      double term1 = exp(-x1*ti);
+      double term2 = exp(-x2*ti);
+      double term3 = exp(-10.0*ti) - exp(-ti);
+
+      gsl_matrix_set(&J.matrix, i, 0, -ti*term1);
+      gsl_matrix_set(&J.matrix, i, 1, ti*term2);
+      gsl_matrix_set(&J.matrix, i, 2, term3);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+box_fvv (const gsl_vector * x, const gsl_vector * v,
+         void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  size_t i;
+
+  for (i = 0; i < box_N; ++i)
+    {
+      double ti = (i + 1.0) / 10.0;
+      double term1 = exp(-x1*ti);
+      double term2 = exp(-x2*ti);
+
+      gsl_vector_set(fvv, i, ti * ti * (v1*v1*term1 - v2*v2*term2));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf box_func =
+{
+  box_f,
+  box_df,
+  box_fvv,
+  box_N,
+  box_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem box_problem =
+{
+  "box3d",
+  box_x0,
+  NULL,
+  &box_epsrel,
+  &box_checksol,
+  &box_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_brown1.c gsl-doc-2.3/multilarge_nlinear/test_brown1.c
--- gsl-doc-1.16/multilarge_nlinear/test_brown1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_brown1.c	2016-08-12 19:50:56.000000000 +0000
@@ -0,0 +1,137 @@
+#define brown1_N         20
+#define brown1_P         4
+
+static double brown1_x0[brown1_P] = { 25, 5, -5, -1 };
+static double brown1_epsrel = 1.0e-5;
+
+static double brown1_J[brown1_N * brown1_P];
+
+static void
+brown1_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.582220162635628e+04;
+  const double brown1_x[brown1_P] = {
+    -1.159443990239263e+01, 1.320363005221244e+01,
+    -4.034395456782477e-01, 2.367789088597534e-01 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < brown1_P; ++i)
+    {
+      gsl_test_rel(x[i], brown1_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+brown1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x0 = gsl_vector_get (x, 0);
+  double x1 = gsl_vector_get (x, 1);
+  double x2 = gsl_vector_get (x, 2);
+  double x3 = gsl_vector_get (x, 3);
+  size_t i;
+
+  for (i = 0; i < brown1_N; i++)
+    {
+      double ti = 0.2 * (i + 1);
+      double ui = x0 + x1 * ti - exp (ti);
+      double vi = x2 + x3 * sin (ti) - cos (ti);
+
+      gsl_vector_set (f, i, ui * ui + vi * vi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown1_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+           const gsl_vector * u, void * params, gsl_vector * v,
+           gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(brown1_J, brown1_N, brown1_P);
+  double x0 = gsl_vector_get (x, 0);
+  double x1 = gsl_vector_get (x, 1);
+  double x2 = gsl_vector_get (x, 2);
+  double x3 = gsl_vector_get (x, 3);
+  size_t i;
+
+  for (i = 0; i < brown1_N; i++)
+    {
+      double ti = 0.2 * (i + 1);
+      double ui = x0 + x1 * ti - exp (ti);
+      double vi = x2 + x3 * sin (ti) - cos (ti);
+
+      gsl_matrix_set (&J.matrix, i, 0, 2 * ui);
+      gsl_matrix_set (&J.matrix, i, 1, 2 * ui * ti);
+      gsl_matrix_set (&J.matrix, i, 2, 2 * vi);
+      gsl_matrix_set (&J.matrix, i, 3, 2 * vi * sin (ti));
+
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown1_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  double v0 = gsl_vector_get (v, 0);
+  double v1 = gsl_vector_get (v, 1);
+  double v2 = gsl_vector_get (v, 2);
+  double v3 = gsl_vector_get (v, 3);
+  size_t i;
+
+  for (i = 0; i < brown1_N; i++)
+    {
+      double ti = 0.2 * (i + 1);
+      double term1 = v0 + ti*v1;
+      double term2 = v3*sin(ti);
+
+      gsl_vector_set (fvv, i, 2.0 * (term1*term1 + v2*v2 +
+                                     term2 * (2*v2 + term2)));
+    }
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf brown1_func =
+{
+  brown1_f,
+  brown1_df,
+  brown1_fvv,
+  brown1_N,
+  brown1_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem brown1_problem =
+{
+  "brown_dennis",
+  brown1_x0,
+  NULL,
+  &brown1_epsrel,
+  &brown1_checksol,
+  &brown1_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_brown2.c gsl-doc-2.3/multilarge_nlinear/test_brown2.c
--- gsl-doc-1.16/multilarge_nlinear/test_brown2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_brown2.c	2016-08-12 19:50:59.000000000 +0000
@@ -0,0 +1,181 @@
+#define brown2_N        5
+#define brown2_P        5
+
+static double brown2_x0[brown2_P] = { 0.5, 0.5, 0.5, 0.5, 0.5 };
+static double brown2_epsrel = 1.0e-12;
+
+static double brown2_J[brown2_N * brown2_P];
+
+static void
+brown2_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  double sumsq_exact;
+  double alpha;
+  const double p = (double) brown2_P;
+  double alpha1mp, lhs, lastel;
+
+  if (sumsq < 0.5)
+    {
+      /* sumsq = 0 case */
+
+      sumsq_exact = 0.0;
+      alpha = x[0];
+      alpha1mp = pow(alpha, 1.0 - p);
+      lhs = p*pow(alpha, p) - (p + 1)/alpha1mp;
+      lastel = alpha1mp;
+
+      gsl_test_rel(lhs, -1.0, epsrel, "%s/%s alpha lhs",
+                   sname, pname);
+    }
+  else
+    {
+      /* sumsq = 1 case */
+
+      sumsq_exact = 1.0;
+      alpha = 0.0;
+      lastel = p + 1.0;
+    }
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 1; i < brown2_P - 1; ++i)
+    {
+      gsl_test_rel(x[i], alpha, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+
+  gsl_test_rel(x[brown2_P - 1], lastel, epsrel, "%s/%s last element",
+               sname, pname);
+}
+
+static int
+brown2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i;
+  double sum = -(brown2_N + 1.0);
+  double prod = 1.0;
+
+  for (i = 0; i < brown2_N; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      sum += xi;
+      prod *= xi;
+    }
+
+  for (i = 0; i < brown2_N - 1; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      gsl_vector_set(f, i, xi + sum);
+    }
+
+  gsl_vector_set(f, brown2_N - 1, prod - 1.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown2_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+           const gsl_vector * u, void * params, gsl_vector * v,
+           gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(brown2_J, brown2_N, brown2_P);
+  size_t i, j;
+
+  for (j = 0; j < brown2_P; ++j)
+    {
+      double prod = 1.0;
+
+      for (i = 0; i < brown2_N - 1; i++)
+        {
+          double Jij = (i == j) ? 2.0 : 1.0;
+          gsl_matrix_set(&J.matrix, i, j, Jij);
+        }
+
+      for (i = 0; i < brown2_N; i++)
+        {
+          if (i != j)
+            prod *= gsl_vector_get(x, i);
+        }
+
+      gsl_matrix_set(&J.matrix, brown2_N - 1, j, prod);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown2_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  size_t i, j, k;
+  double sum = 0.0;
+
+  gsl_vector_set_zero(fvv);
+
+  for (k = 0; k < brown2_P; ++k)
+    {
+      double vk = gsl_vector_get(v, k);
+
+      for (i = 0; i < brown2_P; ++i)
+        {
+          double vi = gsl_vector_get(v, i);
+          double delta = (i == k) ? 1.0 : 0.0;
+          double prod = 1.0;
+
+          for (j = 0; j < brown2_N; ++j)
+            {
+              if (j != i && j != k)
+                {
+                  double xj = gsl_vector_get(x, j);
+                  prod *= xj;
+                }
+            }
+
+          sum += vk * vi * (1.0 - delta) * prod;
+        }
+    }
+
+  gsl_vector_set(fvv, brown2_N - 1, sum);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf brown2_func =
+{
+  brown2_f,
+  brown2_df,
+  brown2_fvv,
+  brown2_N,
+  brown2_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem brown2_problem =
+{
+  "brown_almost_linear",
+  brown2_x0,
+  NULL,
+  &brown2_epsrel,
+  &brown2_checksol,
+  &brown2_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_brown3.c gsl-doc-2.3/multilarge_nlinear/test_brown3.c
--- gsl-doc-1.16/multilarge_nlinear/test_brown3.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_brown3.c	2016-08-12 19:51:02.000000000 +0000
@@ -0,0 +1,109 @@
+#define brown3_N         3
+#define brown3_P         2
+
+static double brown3_x0[brown3_P] = { 1.0, 1.0 };
+static double brown3_epsrel = 1.0e-12;
+
+static double brown3_J[brown3_N * brown3_P];
+
+static void
+brown3_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double brown3_x[brown3_P] = { 1.0e6, 2.0e-6 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < brown3_P; ++i)
+    {
+      gsl_test_rel(x[i], brown3_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+brown3_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, x1 - 1.0e6);
+  gsl_vector_set(f, 1, x2 - 2.0e-6);
+  gsl_vector_set(f, 2, x1*x2 - 2.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown3_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+           const gsl_vector * u, void * params, gsl_vector * v,
+           gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(brown3_J, brown3_N, brown3_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_matrix_set_zero(&J.matrix);
+
+  gsl_matrix_set(&J.matrix, 0, 0, 1.0);
+  gsl_matrix_set(&J.matrix, 1, 1, 1.0);
+  gsl_matrix_set(&J.matrix, 2, 0, x2);
+  gsl_matrix_set(&J.matrix, 2, 1, x1);
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+brown3_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+
+  gsl_vector_set(fvv, 0, 0.0);
+  gsl_vector_set(fvv, 1, 0.0);
+  gsl_vector_set(fvv, 2, 2.0 * v1 * v2);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf brown3_func =
+{
+  brown3_f,
+  brown3_df,
+  brown3_fvv,
+  brown3_N,
+  brown3_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem brown3_problem =
+{
+  "brown_badly_scaled",
+  brown3_x0,
+  NULL,
+  &brown3_epsrel,
+  &brown3_checksol,
+  &brown3_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test.c gsl-doc-2.3/multilarge_nlinear/test.c
--- gsl-doc-1.16/multilarge_nlinear/test.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test.c	2016-09-16 22:52:14.000000000 +0000
@@ -0,0 +1,95 @@
+/* multilarge_nlinear/test.c
+ * 
+ * Copyright (C) 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/* These tests are based on the NIST Statistical Reference Datasets
+   See http://www.nist.gov/itl/div898/strd/index.html for more
+   information. */
+
+#include <config.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_test.h>
+#include <gsl/gsl_multilarge_nlinear.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_ieee_utils.h>
+
+#include "test_fdf.c"
+
+static void
+test_proc(const gsl_multilarge_nlinear_trs *trs,
+          const gsl_multilarge_nlinear_scale *scale,
+          const int fdtype)
+{
+  gsl_multilarge_nlinear_parameters fdf_params =
+    gsl_multilarge_nlinear_default_parameters();
+
+  fdf_params.trs = trs;
+  fdf_params.scale = scale;
+  fdf_params.fdtype = fdtype;
+
+  test_fdf_main(&fdf_params);
+}
+
+int
+main (void)
+{
+  const gsl_multilarge_nlinear_trs **nlinear_trs[7];
+  const gsl_multilarge_nlinear_scale **nlinear_scales[3];
+  const gsl_multilarge_nlinear_trs **trs;
+  const gsl_multilarge_nlinear_scale **scale;
+  int fdtype;
+  size_t i = 0;
+
+  gsl_ieee_env_setup();
+
+  /* initialize arrays */
+
+  nlinear_trs[0] = &gsl_multilarge_nlinear_trs_lm;
+  nlinear_trs[1] = &gsl_multilarge_nlinear_trs_lmaccel;
+  nlinear_trs[2] = &gsl_multilarge_nlinear_trs_dogleg;
+  nlinear_trs[3] = &gsl_multilarge_nlinear_trs_ddogleg;
+  nlinear_trs[4] = &gsl_multilarge_nlinear_trs_subspace2D;
+  nlinear_trs[5] = &gsl_multilarge_nlinear_trs_cgst;
+  nlinear_trs[6] = NULL;
+
+  nlinear_scales[0] = &gsl_multilarge_nlinear_scale_levenberg;
+  nlinear_scales[1] = &gsl_multilarge_nlinear_scale_more;
+  nlinear_scales[2] = NULL;
+
+  /* run testsuite over all parameter combinations */
+
+  for (trs = nlinear_trs[i]; trs != NULL; trs = nlinear_trs[++i])
+    {
+      size_t j = 0;
+
+      fprintf(stderr, "trs = %s\n", (*trs)->name);
+
+      for (scale = nlinear_scales[j]; scale != NULL; scale = nlinear_scales[++j])
+        {
+          for (fdtype = GSL_MULTILARGE_NLINEAR_FWDIFF;
+               fdtype <= GSL_MULTILARGE_NLINEAR_CTRDIFF; ++fdtype)
+            {
+              test_proc(*trs, *scale, fdtype);
+            }
+        }
+    }
+
+  exit (gsl_test_summary ());
+}
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_eckerle.c gsl-doc-2.3/multilarge_nlinear/test_eckerle.c
--- gsl-doc-1.16/multilarge_nlinear/test_eckerle.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_eckerle.c	2016-08-12 19:51:06.000000000 +0000
@@ -0,0 +1,164 @@
+#define eckerle_N       35
+#define eckerle_P       3
+
+static double eckerle_x0a[eckerle_P] = { 1.0, 10.0, 500.0 };
+static double eckerle_x0b[eckerle_P] = { 1.5, 5.0, 450.0 };
+static double eckerle_epsrel = 1.0e-7;
+
+static double eckerle_J[eckerle_N * eckerle_P];
+
+static double eckerle_sigma[eckerle_P] = {
+  1.5408051163E-02, 4.6803020753E-02, 4.6800518816E-02
+};
+
+static double eckerle_X[eckerle_N] = {
+  400.000000, 405.000000, 410.000000, 415.000000, 420.000000,
+  425.000000, 430.000000, 435.000000, 436.500000, 438.000000,
+  439.500000, 441.000000, 442.500000, 444.000000, 445.500000,
+  447.000000, 448.500000, 450.000000, 451.500000, 453.000000,
+  454.500000, 456.000000, 457.500000, 459.000000, 460.500000,
+  462.000000, 463.500000, 465.000000, 470.000000, 475.000000,
+  480.000000, 485.000000, 490.000000, 495.000000, 500.000000 };
+
+static double eckerle_F[eckerle_N] = {
+  0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917,
+  0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302,
+  0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458,
+  0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534,
+  0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200,
+  0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800,
+  0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710 };
+
+static void
+eckerle_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.4635887487E-03;
+  const double eckerle_x[eckerle_P] = { 1.5543827178E+00,
+                                        4.0888321754E+00,
+                                        4.5154121844E+02 };
+  double new_x[3];
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  /* x1 and x2 are unique up to a sign, but they must be
+   * the same sign */
+  if (x[0] < 0.0 && x[1] < 0.0)
+    {
+      new_x[0] = -x[0];
+      new_x[1] = -x[1];
+    }
+  else
+    {
+      new_x[0] = x[0];
+      new_x[1] = x[1];
+    }
+
+  new_x[2] = x[2];
+
+  for (i = 0; i < eckerle_P; ++i)
+    {
+      gsl_test_rel(new_x[i], eckerle_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+eckerle_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[eckerle_P];
+  size_t i;
+
+  for (i = 0; i < eckerle_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < eckerle_N; i++)
+    {
+      double xi = eckerle_X[i];
+      double term = xi - b[2];
+      double yi;
+
+      yi = b[0] / b[1] * exp(-0.5 * term * term / b[1] / b[1]);
+      gsl_vector_set (f, i, yi - eckerle_F[i]);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+eckerle_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+            const gsl_vector * u, void * params, gsl_vector * v,
+            gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(eckerle_J, eckerle_N, eckerle_P);
+  double b[eckerle_P];
+  size_t i;
+
+  for (i = 0; i < eckerle_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < eckerle_N; i++)
+    {
+      double xi = eckerle_X[i];
+      double term1 = xi - b[2];
+      double term2 = exp(-0.5 * term1 * term1 / (b[1] * b[1]));
+
+      gsl_matrix_set (&J.matrix, i, 0, term2 / b[1]);
+      gsl_matrix_set (&J.matrix, i, 1,
+        -b[0] * term2 / (b[1] * b[1]) + b[0] / pow(b[1], 4.0) * term2 * term1 * term1);
+      gsl_matrix_set (&J.matrix, i, 2, b[0] / pow(b[1], 3.0) * term1 * term2);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf eckerle_func =
+{
+  eckerle_f,
+  eckerle_df,
+  NULL, /* analytic expression too complex */
+  eckerle_N,
+  eckerle_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem eckerlea_problem =
+{
+  "nist-eckerlea",
+  eckerle_x0a,
+  eckerle_sigma,
+  &eckerle_epsrel,
+  &eckerle_checksol,
+  &eckerle_func
+};
+
+static test_fdf_problem eckerleb_problem =
+{
+  "nist-eckerleb",
+  eckerle_x0b,
+  eckerle_sigma,
+  &eckerle_epsrel,
+  &eckerle_checksol,
+  &eckerle_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_enso.c gsl-doc-2.3/multilarge_nlinear/test_enso.c
--- gsl-doc-1.16/multilarge_nlinear/test_enso.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_enso.c	2016-08-12 19:51:09.000000000 +0000
@@ -0,0 +1,182 @@
+#define enso_N       168
+#define enso_P       9
+
+static double enso_x0a[enso_P] = { 11.0, 3.0, 0.5, 40.0, -0.7, -1.3, 25.0, -0.3, 1.4 };
+static double enso_x0b[enso_P] = { 10.0, 3.0, 0.5, 44.0, -1.5, 0.5, 26.0, -0.1, 1.5 };
+static double enso_epsrel = 1.0e-3;
+
+static double enso_J[enso_N * enso_P];
+
+static double enso_sigma[enso_P] = {
+ 1.7488832467E-01, 2.4310052139E-01, 2.4354686618E-01, 9.4408025976E-01, 2.8078369611E-01,
+ 4.8073701119E-01, 4.1612939130E-01, 5.1460022911E-01, 2.5434468893E-01
+};
+
+static double enso_F[enso_N] = {
+    12.90000, 11.30000, 10.60000, 11.20000, 10.90000, 
+    7.500000, 7.700000, 11.70000, 12.90000, 14.30000, 
+    10.90000, 13.70000, 17.10000, 14.00000, 15.30000, 
+    8.500000, 5.700000, 5.500000, 7.600000, 8.600000, 
+    7.300000, 7.600000, 12.70000, 11.00000, 12.70000, 
+    12.90000, 13.00000, 10.90000, 10.400000, 10.200000, 
+    8.000000, 10.90000, 13.60000, 10.500000, 9.200000, 
+    12.40000, 12.70000, 13.30000, 10.100000, 7.800000, 
+    4.800000, 3.000000, 2.500000, 6.300000, 9.700000, 
+    11.60000, 8.600000, 12.40000, 10.500000, 13.30000, 
+   10.400000, 8.100000, 3.700000, 10.70000, 5.100000, 
+   10.400000, 10.90000, 11.70000, 11.40000, 13.70000, 
+    14.10000, 14.00000, 12.50000, 6.300000, 9.600000, 
+    11.70000, 5.000000, 10.80000, 12.70000, 10.80000, 
+    11.80000, 12.60000, 15.70000, 12.60000, 14.80000, 
+    7.800000, 7.100000, 11.20000, 8.100000, 6.400000, 
+    5.200000, 12.00000, 10.200000, 12.70000, 10.200000, 
+    14.70000, 12.20000, 7.100000, 5.700000, 6.700000, 
+    3.900000, 8.500000, 8.300000, 10.80000, 16.70000, 
+    12.60000, 12.50000, 12.50000, 9.800000, 7.200000, 
+    4.100000, 10.60000, 10.100000, 10.100000, 11.90000, 
+    13.60000, 16.30000, 17.60000, 15.50000, 16.00000, 
+    15.20000, 11.20000, 14.30000, 14.50000, 8.500000, 
+    12.00000, 12.70000, 11.30000, 14.50000, 15.10000, 
+   10.400000, 11.50000, 13.40000, 7.500000, 0.6000000, 
+   0.3000000, 5.500000, 5.000000, 4.600000, 8.200000, 
+    9.900000, 9.200000, 12.50000, 10.90000, 9.900000, 
+    8.900000, 7.600000, 9.500000, 8.400000, 10.70000, 
+    13.60000, 13.70000, 13.70000, 16.50000, 16.80000, 
+    17.10000, 15.40000, 9.500000, 6.100000, 10.100000, 
+    9.300000, 5.300000, 11.20000, 16.60000, 15.60000, 
+    12.00000, 11.50000, 8.600000, 13.80000, 8.700000, 
+    8.600000, 8.600000, 8.700000, 12.80000, 13.20000, 
+    14.00000, 13.40000, 14.80000
+};
+
+static void
+enso_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 7.8853978668E+02;
+  const double enso_x[enso_P] = {
+    1.0510749193E+01, 3.0762128085E+00, 5.3280138227E-01,
+    4.4311088700E+01, -1.6231428586E+00, 5.2554493756E-01,
+    2.6887614440E+01, 2.1232288488E-01, 1.4966870418E+00 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < enso_P; ++i)
+    {
+      gsl_test_rel(x[i], enso_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+enso_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[enso_P];
+  size_t i;
+
+  for (i = 0; i < enso_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < enso_N; i++)
+    {
+      double t = (i + 1.0);
+      double y;
+      y = b[0];
+      y += b[1] * cos(2*M_PI*t/12);
+      y += b[2] * sin(2*M_PI*t/12);
+      y += b[4] * cos(2*M_PI*t/b[3]);
+      y += b[5] * sin(2*M_PI*t/b[3]);
+      y += b[7] * cos(2*M_PI*t/b[6]);
+      y += b[8] * sin(2*M_PI*t/b[6]);
+
+      gsl_vector_set (f, i, enso_F[i] - y);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+enso_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+         const gsl_vector * u, void * params, gsl_vector * v,
+         gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(enso_J, enso_N, enso_P);
+  double b[enso_P];
+  size_t i;
+
+  for (i = 0; i < enso_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < enso_N; i++)
+    {
+      double t = (i + 1.0);
+
+      gsl_matrix_set (&J.matrix, i, 0, -1.0);
+      gsl_matrix_set (&J.matrix, i, 1, -cos(2*M_PI*t/12));
+      gsl_matrix_set (&J.matrix, i, 2, -sin(2*M_PI*t/12));
+      gsl_matrix_set (&J.matrix, i, 3, 
+                      -b[4]*(2*M_PI*t/(b[3]*b[3]))*sin(2*M_PI*t/b[3])
+                      +b[5]*(2*M_PI*t/(b[3]*b[3]))*cos(2*M_PI*t/b[3]));
+      gsl_matrix_set (&J.matrix, i, 4, -cos(2*M_PI*t/b[3]));
+      gsl_matrix_set (&J.matrix, i, 5, -sin(2*M_PI*t/b[3]));
+      gsl_matrix_set (&J.matrix, i, 6, 
+                     -b[7] * (2*M_PI*t/(b[6]*b[6])) * sin(2*M_PI*t/b[6])
+                     +b[8] * (2*M_PI*t/(b[6]*b[6])) * cos(2*M_PI*t/b[6]));
+      gsl_matrix_set (&J.matrix, i, 7, -cos(2*M_PI*t/b[6]));
+      gsl_matrix_set (&J.matrix, i, 8, -sin(2*M_PI*t/b[6]));
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf enso_func =
+{
+  enso_f,
+  enso_df,
+  NULL, /* analytic expression too complex */
+  enso_N,
+  enso_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem ensoa_problem =
+{
+  "nist-ENSOa",
+  enso_x0a,
+  enso_sigma,
+  &enso_epsrel,
+  &enso_checksol,
+  &enso_func
+};
+
+static test_fdf_problem ensob_problem =
+{
+  "nist-ENSOb",
+  enso_x0b,
+  enso_sigma,
+  &enso_epsrel,
+  &enso_checksol,
+  &enso_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_exp1.c gsl-doc-2.3/multilarge_nlinear/test_exp1.c
--- gsl-doc-1.16/multilarge_nlinear/test_exp1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_exp1.c	2016-08-12 19:51:13.000000000 +0000
@@ -0,0 +1,149 @@
+#define exp1_N         45
+#define exp1_P         4
+
+static double exp1_x0[exp1_P] = { -1.0, -2.0, 1.0, -1.0 };
+static double exp1_epsrel = 1.0e-4;
+
+static double exp1_J[exp1_N * exp1_P];
+
+static double exp1_Y[exp1_N] = {
+0.090542, 0.124569, 0.179367, 0.195654, 0.269707,
+0.286027, 0.289892, 0.317475, 0.308191, 0.336995,
+0.348371, 0.321337, 0.299423, 0.338972, 0.304763,
+0.288903, 0.300820, 0.303974, 0.283987, 0.262078,
+0.281593, 0.267531, 0.218926, 0.225572, 0.200594,
+0.197375, 0.182440, 0.183892, 0.152285, 0.174028,
+0.150874, 0.126220, 0.126266, 0.106384, 0.118923,
+0.091868, 0.128926, 0.119273, 0.115997, 0.105831,
+0.075261, 0.068387, 0.090823, 0.085205, 0.067203
+};
+
+static void
+exp1_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.0e-2;
+  const double exp1_x[exp1_P] = { -4.0, -5.0, 4.0, -4.0 }; /* approx */
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < exp1_P; ++i)
+    {
+      gsl_test_rel(x[i], exp1_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+exp1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  size_t i;
+
+  for (i = 0; i < exp1_N; ++i)
+    {
+      double ti = 0.02*(i + 1.0);
+      double yi = exp1_Y[i];
+      double fi = yi - (x3*exp(x1*ti) + x4*exp(x2*ti));
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+exp1_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+         const gsl_vector * u, void * params, gsl_vector * v,
+         gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(exp1_J, exp1_N, exp1_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  size_t i;
+
+  for (i = 0; i < exp1_N; ++i)
+    {
+      double ti = 0.02*(i + 1.0);
+      double term1 = exp(x1*ti);
+      double term2 = exp(x2*ti);
+
+      gsl_matrix_set(&J.matrix, i, 0, -x3*ti*term1);
+      gsl_matrix_set(&J.matrix, i, 1, -x4*ti*term2);
+      gsl_matrix_set(&J.matrix, i, 2, -term1);
+      gsl_matrix_set(&J.matrix, i, 3, -term2);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+exp1_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  double v4 = gsl_vector_get(v, 3);
+  size_t i;
+
+  for (i = 0; i < exp1_N; ++i)
+    {
+      double ti = 0.02*(i + 1.0);
+      double term1 = exp(x1*ti);
+      double term2 = exp(x2*ti);
+      double term3 = 2*v3 + ti*v1*x3;
+      double term4 = 2*v4 + ti*v2*x4;
+
+      gsl_vector_set(fvv, i, -ti*(v1*term1*term3 + v2*term2*term4));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf exp1_func =
+{
+  exp1_f,
+  exp1_df,
+  exp1_fvv,
+  exp1_N,
+  exp1_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem exp1_problem =
+{
+  "expfit1",
+  exp1_x0,
+  NULL,
+  &exp1_epsrel,
+  &exp1_checksol,
+  &exp1_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_fdf.c gsl-doc-2.3/multilarge_nlinear/test_fdf.c
--- gsl-doc-1.16/multilarge_nlinear/test_fdf.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_fdf.c	2016-09-16 22:48:29.000000000 +0000
@@ -0,0 +1,384 @@
+/* multilarge_nlinear/test_fdf.c
+ * 
+ * Copyright (C) 2015, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+typedef struct
+{
+  const char *name;
+  double *x0;       /* initial parameters (size p) */
+  double *sigma;
+  double *epsrel;   /* relative tolerance for solution checking */
+  void (*checksol) (const double x[], const double sumsq,
+                    const double epsrel, const char *sname,
+                    const char *pname);
+  gsl_multilarge_nlinear_fdf *fdf;
+} test_fdf_problem;
+
+#include "test_bard.c"
+#include "test_beale.c"
+#include "test_biggs.c"
+#include "test_box.c"
+#include "test_boxbod.c"
+#include "test_brown1.c"
+#include "test_brown2.c"
+#include "test_brown3.c"
+#include "test_eckerle.c"
+#include "test_enso.c"
+#include "test_exp1.c"
+#include "test_gaussian.c"
+#include "test_hahn1.c"
+#include "test_helical.c"
+#include "test_jennrich.c"
+#include "test_kirby2.c"
+#include "test_kowalik.c"
+#include "test_lin1.c"
+#include "test_lin2.c"
+#include "test_lin3.c"
+#include "test_meyer.c"
+#include "test_meyerscal.c"
+#include "test_osborne.c"
+#include "test_penalty1.c"
+#include "test_penalty2.c"
+#include "test_powell1.c"
+#include "test_powell2.c"
+#include "test_powell3.c"
+#include "test_rat42.c"
+#include "test_rat43.c"
+#include "test_rosenbrock.c"
+#include "test_rosenbrocke.c"
+#include "test_roth.c"
+#include "test_thurber.c"
+#include "test_vardim.c"
+#include "test_watson.c"
+#include "test_wood.c"
+
+#include "test_wnlin.c"
+
+static void test_fdf(const gsl_multilarge_nlinear_type * T,
+                     const gsl_multilarge_nlinear_parameters * params,
+                     const double xtol, const double gtol,
+                     const double ftol,
+                     const double epsrel, const double x0_scale,
+                     test_fdf_problem *problem,
+                     const double *wts);
+static void test_fdf_checksol(const char *sname, const char *pname,
+                              const double epsrel,
+                              gsl_multilarge_nlinear_workspace *s,
+                              test_fdf_problem *problem);
+static void test_scale_x0(gsl_vector *x0, const double scale);
+
+/*
+ * FIXME: some test problems are disabled since they fail on certain
+ * solvers. Known failures are:
+ *
+ * Method     test-problem
+ * ======     ============
+ * dogleg     thurbera
+ * dogleg     rat43a
+ * cgst       boxboda
+ */
+
+static test_fdf_problem *test_problems[] = {
+  /*
+   * These test problems are taken from
+   *
+   * H. B. Nielsen, UCTP test problems for unconstrained optimization,
+   * IMM Department of Mathematical Modeling, Tech. Report
+   * IMM-REP-2000-17, 2000.
+   */
+  &lin1_problem,       /* 1 */
+  &lin2_problem,       /* 2 */
+  &lin3_problem,       /* 3 */
+  &rosenbrock_problem, /* 4 */
+  &helical_problem,    /* 5 */
+  &powell1_problem,    /* 6 */
+  &roth_problem,       /* 7 */
+  &bard_problem,       /* 8 */
+  &kowalik_problem,    /* 9 */
+  &meyer_problem,      /* 10 */
+  &watson_problem,     /* 11 */
+  &box_problem,        /* 12 */
+  &jennrich_problem,   /* 13 */
+  &brown1_problem,     /* 14 */
+  &brown2_problem,     /* 16 */
+  &osborne_problem,    /* 17 */
+  &exp1_problem,       /* 18 */
+  &meyerscal_problem,  /* 20 */
+
+  &powell2_problem,
+
+  /*
+   * These tests are from
+   *
+   * J. J. More, B. S. Garbow and K. E. Hillstrom, Testing
+   * Unconstrained Optimization Software, ACM Trans. Math. Soft.
+   * Vol 7, No 1, 1981.
+   *
+   * Many of these overlap with the Nielsen tests
+   */
+  &rosenbrock_problem,   /* 1 */
+  &roth_problem,         /* 2 */
+  &powell3_problem,      /* 3 */
+  &brown3_problem,       /* 4 */
+  &beale_problem,        /* 5 */
+  &jennrich_problem,     /* 6 */
+  &helical_problem,      /* 7 */
+  &bard_problem,         /* 8 */
+  &gaussian_problem,     /* 9 */
+  &meyer_problem,        /* 10 */
+  &box_problem,          /* 12 */
+  &powell1_problem,      /* 13 */
+  &wood_problem,         /* 14 */
+  &kowalik_problem,      /* 15 */
+  &brown1_problem,       /* 16 */
+  &osborne_problem,      /* 17 */
+  &biggs_problem,        /* 18 */
+  &watson_problem,       /* 20 */
+  &rosenbrocke_problem,  /* 21 */
+  &penalty1_problem,     /* 23 */
+  &penalty2_problem,     /* 24 */
+  &vardim_problem,       /* 25 */
+  &brown2_problem,       /* 27 */
+  &lin1_problem,         /* 32 */
+  &lin2_problem,         /* 33 */
+  &lin3_problem,         /* 34 */
+
+  /* NIST test cases */
+  &kirby2a_problem,
+  &kirby2b_problem,
+  &hahn1a_problem,
+  &hahn1b_problem,
+  &ensoa_problem,
+  &ensob_problem,
+  /*&thurbera_problem,*/
+  &thurberb_problem,
+  /*&boxboda_problem,*/
+  &boxbodb_problem,
+  &rat42a_problem,
+  &rat42b_problem,
+  &eckerlea_problem,
+  &eckerleb_problem,
+  /*&rat43a_problem,*/
+  &rat43b_problem,
+
+  NULL
+};
+
+static void
+test_fdf_main(const gsl_multilarge_nlinear_parameters * params)
+{
+  const double xtol = pow(GSL_DBL_EPSILON, 0.9);
+  const double gtol = pow(GSL_DBL_EPSILON, 0.9);
+  const double ftol = 0.0;
+  size_t i;
+
+  for (i = 0; test_problems[i] != NULL; ++i)
+    {
+      test_fdf_problem *problem = test_problems[i];
+      double epsrel = *(problem->epsrel);
+      gsl_multilarge_nlinear_fdf fdf;
+
+      /*XXX: finite difference fvv not working yet */
+      if (problem->fdf->fvv == NULL)
+        continue;
+
+      test_fdf(gsl_multilarge_nlinear_trust, params, xtol, gtol, ftol,
+               epsrel, 1.0, problem, NULL);
+
+#if 0 /* XXX */
+      /* test finite difference Jacobian */
+      fdf.df = problem->fdf->df;
+      problem->fdf->df = NULL;
+
+      test_fdf(gsl_multilarge_nlinear_trust, params, xtol, gtol, ftol,
+               1.0e3 * epsrel, 1.0, problem, NULL);
+
+      problem->fdf->df = fdf.df;
+#endif
+
+#if 0
+      if (params->trs == gsl_multilarge_nlinear_trs_lmaccel && problem->fdf->fvv != NULL)
+        {
+          /* test finite difference second directional derivative */
+          fdf.fvv = problem->fdf->fvv;
+          problem->fdf->fvv = NULL;
+
+          test_fdf(gsl_multilarge_nlinear_trust, params, xtol, gtol, ftol,
+                   epsrel / params->h_fvv, 1.0, problem, NULL);
+
+          problem->fdf->fvv = fdf.fvv;
+        }
+#endif
+    }
+
+  /* test weighted nonlinear least squares */
+
+  /* internal weighting in _f and _df functions */
+  test_fdf(gsl_multilarge_nlinear_trust, params, xtol, gtol, ftol,
+           wnlin_epsrel, 1.0, &wnlin_problem1, NULL);
+}
+
+/*
+test_fdf()
+  Test a weighted nonlinear least squares problem
+
+Inputs: T        - solver to use
+        params   - solver parameters
+        xtol     - tolerance in x
+        gtol     - tolerance in gradient
+        ftol     - tolerance in residual vector
+        epsrel   - relative error tolerance in solution
+        x0_scale - to test robustness against starting points,
+                   the standard starting point in 'problem' is
+                   multiplied by this scale factor:
+                   x0 <- x0 * x0_scale
+                   If x0 = 0, then all components of x0 are set to
+                   x0_scale
+        problem  - contains the nonlinear problem and solution point
+        wts      - weight vector (NULL for unweighted)
+*/
+
+static void
+test_fdf(const gsl_multilarge_nlinear_type * T,
+         const gsl_multilarge_nlinear_parameters * params,
+         const double xtol, const double gtol, const double ftol,
+         const double epsrel, const double x0_scale,
+         test_fdf_problem *problem,
+         const double *wts)
+{
+  gsl_multilarge_nlinear_fdf *fdf = problem->fdf;
+  const size_t n = fdf->n;
+  const size_t p = fdf->p;
+  const size_t max_iter = 2500;
+  gsl_vector *x0 = gsl_vector_alloc(p);
+  gsl_vector_view x0v = gsl_vector_view_array(problem->x0, p);
+  gsl_multilarge_nlinear_workspace *w =
+    gsl_multilarge_nlinear_alloc (T, params, n, p);
+  const char *pname = problem->name;
+  char buf[2048];
+  char sname[2048];
+  int status, info;
+
+  sprintf(buf, "%s/%s/solver=%s/scale=%s%s%s",
+    gsl_multilarge_nlinear_name(w),
+    params->trs->name,
+    params->solver->name,
+    params->scale->name,
+    problem->fdf->df ? "" : "/fdjac",
+    problem->fdf->fvv ? "" : "/fdfvv");
+
+  strcpy(sname, buf);
+
+  /* scale starting point x0 */
+  gsl_vector_memcpy(x0, &x0v.vector);
+  test_scale_x0(x0, x0_scale);
+
+  if (wts)
+    {
+      gsl_vector_const_view wv = gsl_vector_const_view_array(wts, n);
+      gsl_multilarge_nlinear_winit(x0, &wv.vector, fdf, w);
+    }
+  else
+    gsl_multilarge_nlinear_init(x0, fdf, w);
+
+  status = gsl_multilarge_nlinear_driver(max_iter, xtol, gtol, ftol,
+                                       NULL, NULL, &info, w);
+  gsl_test(status, "%s/%s did not converge, status=%s",
+           sname, pname, gsl_strerror(status));
+
+  /* check solution */
+  test_fdf_checksol(sname, pname, epsrel, w, problem);
+
+  if (wts == NULL)
+    {
+      /* test again with weighting matrix W = I */
+      gsl_vector *wv = gsl_vector_alloc(n);
+
+      sprintf(sname, "%s/weighted", buf);
+
+      gsl_vector_memcpy(x0, &x0v.vector);
+      test_scale_x0(x0, x0_scale);
+
+      gsl_vector_set_all(wv, 1.0);
+      gsl_multilarge_nlinear_winit(x0, wv, fdf, w);
+  
+      status = gsl_multilarge_nlinear_driver(max_iter, xtol, gtol, ftol,
+                                           NULL, NULL, &info, w);
+      gsl_test(status, "%s/%s did not converge, status=%s",
+               sname, pname, gsl_strerror(status));
+
+      test_fdf_checksol(sname, pname, epsrel, w, problem);
+
+      gsl_vector_free(wv);
+    }
+
+  gsl_multilarge_nlinear_free(w);
+  gsl_vector_free(x0);
+}
+
+static void
+test_fdf_checksol(const char *sname, const char *pname,
+                  const double epsrel,
+                  gsl_multilarge_nlinear_workspace *w,
+                  test_fdf_problem *problem)
+{
+  gsl_multilarge_nlinear_fdf *fdf = problem->fdf;
+  const double *sigma = problem->sigma;
+  gsl_vector *f = gsl_multilarge_nlinear_residual(w);
+  gsl_vector *x = gsl_multilarge_nlinear_position(w);
+  double sumsq;
+
+  /* check solution vector x and sumsq = ||f||^2 */
+  gsl_blas_ddot(f, f, &sumsq);
+  (problem->checksol)(x->data, sumsq, epsrel, sname, pname);
+
+  /* XXX: covariance not implemented for cgst method */
+  if (w->params.trs == gsl_multilarge_nlinear_trs_cgst)
+    return;
+
+  /* check variances */
+  if (sigma)
+    {
+      const size_t n = fdf->n;
+      const size_t p = fdf->p;
+      size_t i;
+      gsl_matrix * covar = gsl_matrix_alloc (p, p);
+
+      gsl_multilarge_nlinear_covar (covar, w);
+
+      for (i = 0; i < p; i++) 
+        {
+          double ei = sqrt(sumsq/(n-p))*sqrt(gsl_matrix_get(covar,i,i));
+          gsl_test_rel (ei, sigma[i], epsrel, 
+                        "%s/%s, sigma(%d)", sname, pname, i) ;
+        }
+
+      gsl_matrix_free (covar);
+    }
+}
+
+static void
+test_scale_x0(gsl_vector *x0, const double scale)
+{
+  double nx = gsl_blas_dnrm2(x0);
+
+  if (nx == 0.0)
+    gsl_vector_set_all(x0, scale);
+  else
+    gsl_vector_scale(x0, scale);
+} /* test_scale_x0() */
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_gaussian.c gsl-doc-2.3/multilarge_nlinear/test_gaussian.c
--- gsl-doc-1.16/multilarge_nlinear/test_gaussian.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_gaussian.c	2016-08-12 19:51:19.000000000 +0000
@@ -0,0 +1,146 @@
+#define gaussian_N         15
+#define gaussian_P         3
+
+static double gaussian_x0[gaussian_P] = { 0.4, 1.0, 0.0 };
+static double gaussian_epsrel = 1.0e-10;
+
+static double gaussian_J[gaussian_N * gaussian_P];
+
+static double gaussian_Y[gaussian_N] = {
+0.0009, 0.0044, 0.0175, 0.0540, 0.1295, 0.2420, 0.3521, 0.3989,
+0.3521, 0.2420, 0.1295, 0.0540, 0.0175, 0.0044, 0.0009
+};
+
+static void
+gaussian_checksol(const double x[], const double sumsq,
+                  const double epsrel, const char *sname,
+                  const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.12793276961871985e-08;
+  const double gaussian_x[gaussian_P] = { 0.398956137838762825,
+                                          1.00001908448786647,
+                                          0.0 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < gaussian_P; ++i)
+    {
+      gsl_test_rel(x[i], gaussian_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+gaussian_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < gaussian_N; ++i)
+    {
+      double ti = (7.0 - i) / 2.0;
+      double yi = gaussian_Y[i];
+      double term = ti - x3;
+      double fi = x1 * exp(-x2*term*term/2.0) - yi;
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+gaussian_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+             const gsl_vector * u, void * params, gsl_vector * v,
+             gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(gaussian_J, gaussian_N, gaussian_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < gaussian_N; ++i)
+    {
+      double ti = (7.0 - i) / 2.0;
+      double term1 = ti - x3;
+      double term2 = exp(-x2*term1*term1/2.0);
+
+      gsl_matrix_set(&J.matrix, i, 0, term2);
+      gsl_matrix_set(&J.matrix, i, 1, -0.5*x1*term2*term1*term1);
+      gsl_matrix_set(&J.matrix, i, 2, x1*x2*term1*term2);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+gaussian_fvv (const gsl_vector * x, const gsl_vector * v,
+              void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  size_t i;
+
+  for (i = 0; i < gaussian_N; ++i)
+    {
+      double ti = (7.0 - i) / 2.0;
+      double term1 = ti - x3;
+      double term2 = exp(-x2*term1*term1/2.0);
+
+      gsl_vector_set(fvv, i, 0.25 * term2 *
+                             (ti*ti*ti*ti*v2*v2*x1 -
+                              4*ti*ti*ti*v2*x1*(v3*x2 + v2*x3) +
+                              v2*x3*x3*(v2*x1*x3*x3 - 4*v1) +
+                              4*v3*v3*x1*x2*(x2*x3*x3 - 1.0) +
+                              4*v3*x3*(-2*v1*x2 + v2*x1*(x2*x3*x3 - 2.0)) +
+                              ti*ti*(4*v3*v3*x1*x2*x2 + 2*v2*(-2*v1 + 3*x1*x3*(2*v3*x2 + v2*x3))) -
+                              4*ti*(v2*v2*x1*x3*x3*x3 + 2*v3*x2*(-v1 + v3*x1*x2*x3) +
+                                    v2*(-2*v1*x3 + v3*x1*(-2.0 + 3*x2*x3*x3)))));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf gaussian_func =
+{
+  gaussian_f,
+  gaussian_df,
+  gaussian_fvv,
+  gaussian_N,
+  gaussian_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem gaussian_problem =
+{
+  "gaussian",
+  gaussian_x0,
+  NULL,
+  &gaussian_epsrel,
+  &gaussian_checksol,
+  &gaussian_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_hahn1.c gsl-doc-2.3/multilarge_nlinear/test_hahn1.c
--- gsl-doc-1.16/multilarge_nlinear/test_hahn1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_hahn1.c	2016-08-12 19:51:23.000000000 +0000
@@ -0,0 +1,235 @@
+#define hahn1_N      236
+#define hahn1_P      7
+
+static double hahn1_x0a[hahn1_P] = { 10, -1, 0.05, -0.00001, -0.05, 0.001, -0.000001 };
+static double hahn1_x0b[hahn1_P] = { 1, -0.1, 0.005, -0.000001, -0.005, 0.0001, -0.0000001}; 
+static double hahn1_epsrel = 1.0e-5;
+
+static double hahn1_J[hahn1_N * hahn1_P];
+
+static double hahn1_sigma[hahn1_P] = {
+  1.7070154742E-01, 1.2000289189E-02, 2.2508314937E-04, 2.7578037666E-07,
+  2.4712888219E-04, 1.0449373768E-05, 1.3027335327E-08
+};
+
+static double hahn1_F1[hahn1_N] = {
+        .591E0, 1.547E0, 2.902E0, 2.894E0, 4.703E0,
+       6.307E0, 7.03E0 , 7.898E0, 9.470E0, 9.484E0,
+      10.072E0, 10.163E0, 11.615E0, 12.005E0, 12.478E0,
+      12.982E0, 12.970E0, 13.926E0, 14.452E0, 14.404E0,
+      15.190E0, 15.550E0, 15.528E0, 15.499E0, 16.131E0,
+      16.438E0, 16.387E0, 16.549E0, 16.872E0, 16.830E0,
+      16.926E0, 16.907E0, 16.966E0, 17.060E0, 17.122E0,
+      17.311E0, 17.355E0, 17.668E0, 17.767E0, 17.803E0,
+      17.765E0, 17.768E0, 17.736E0, 17.858E0, 17.877E0,
+      17.912E0, 18.046E0, 18.085E0, 18.291E0, 18.357E0,
+      18.426E0, 18.584E0, 18.610E0, 18.870E0, 18.795E0,
+      19.111E0, .367E0, .796E0, 0.892E0, 1.903E0,
+       2.150E0, 3.697E0, 5.870E0, 6.421E0, 7.422E0,
+       9.944E0, 11.023E0, 11.87E0 , 12.786E0, 14.067E0,
+      13.974E0, 14.462E0, 14.464E0, 15.381E0, 15.483E0,
+      15.59E0 , 16.075E0, 16.347E0, 16.181E0, 16.915E0,
+      17.003E0, 16.978E0, 17.756E0, 17.808E0, 17.868E0,
+      18.481E0, 18.486E0, 19.090E0, 16.062E0, 16.337E0,
+      16.345E0, 16.388E0, 17.159E0, 17.116E0, 17.164E0,
+      17.123E0, 17.979E0, 17.974E0, 18.007E0, 17.993E0,
+      18.523E0, 18.669E0, 18.617E0, 19.371E0, 19.330E0,
+       0.080E0, 0.248E0, 1.089E0, 1.418E0, 2.278E0,
+       3.624E0, 4.574E0, 5.556E0, 7.267E0, 7.695E0,
+       9.136E0, 9.959E0, 9.957E0, 11.600E0, 13.138E0,
+      13.564E0, 13.871E0, 13.994E0, 14.947E0, 15.473E0,
+      15.379E0, 15.455E0, 15.908E0, 16.114E0, 17.071E0,
+      17.135E0, 17.282E0, 17.368E0, 17.483E0, 17.764E0,
+      18.185E0, 18.271E0, 18.236E0, 18.237E0, 18.523E0,
+      18.627E0, 18.665E0, 19.086E0, 0.214E0, 0.943E0,
+       1.429E0, 2.241E0, 2.951E0, 3.782E0, 4.757E0,
+       5.602E0, 7.169E0, 8.920E0, 10.055E0, 12.035E0,
+      12.861E0, 13.436E0, 14.167E0, 14.755E0, 15.168E0,
+      15.651E0, 15.746E0, 16.216E0, 16.445E0, 16.965E0,
+      17.121E0, 17.206E0, 17.250E0, 17.339E0, 17.793E0,
+      18.123E0, 18.49E0 , 18.566E0, 18.645E0, 18.706E0,
+      18.924E0, 19.1E0  , 0.375E0, 0.471E0, 1.504E0,
+       2.204E0, 2.813E0, 4.765E0, 9.835E0, 10.040E0,
+      11.946E0, 12.596E0, 13.303E0, 13.922E0, 14.440E0,
+      14.951E0, 15.627E0, 15.639E0, 15.814E0, 16.315E0,
+      16.334E0, 16.430E0, 16.423E0, 17.024E0, 17.009E0,
+      17.165E0, 17.134E0, 17.349E0, 17.576E0, 17.848E0,
+      18.090E0, 18.276E0, 18.404E0, 18.519E0, 19.133E0,
+      19.074E0, 19.239E0, 19.280E0, 19.101E0, 19.398E0,
+      19.252E0, 19.89E0 , 20.007E0, 19.929E0, 19.268E0,
+      19.324E0, 20.049E0, 20.107E0, 20.062E0, 20.065E0,
+      19.286E0, 19.972E0, 20.088E0, 20.743E0, 20.83E0 ,
+      20.935E0, 21.035E0, 20.93E0 , 21.074E0, 21.085E0,
+      20.935E0
+};
+
+
+static double hahn1_F0[hahn1_N] = {
+    24.41E0, 34.82E0, 44.09E0, 45.07E0, 54.98E0,
+    65.51E0, 70.53E0, 75.70E0, 89.57E0, 91.14E0,
+    96.40E0, 97.19E0, 114.26E0, 120.25E0, 127.08E0,
+   133.55E0, 133.61E0, 158.67E0, 172.74E0, 171.31E0,
+   202.14E0, 220.55E0, 221.05E0, 221.39E0, 250.99E0,
+   268.99E0, 271.80E0, 271.97E0, 321.31E0, 321.69E0,
+   330.14E0, 333.03E0, 333.47E0, 340.77E0, 345.65E0,
+   373.11E0, 373.79E0, 411.82E0, 419.51E0, 421.59E0,
+   422.02E0, 422.47E0, 422.61E0, 441.75E0, 447.41E0,
+   448.7E0 , 472.89E0, 476.69E0, 522.47E0, 522.62E0,
+   524.43E0, 546.75E0, 549.53E0, 575.29E0, 576.00E0,
+   625.55E0, 20.15E0, 28.78E0, 29.57E0, 37.41E0,
+    39.12E0, 50.24E0, 61.38E0, 66.25E0, 73.42E0,
+    95.52E0, 107.32E0, 122.04E0, 134.03E0, 163.19E0,
+   163.48E0, 175.70E0, 179.86E0, 211.27E0, 217.78E0,
+   219.14E0, 262.52E0, 268.01E0, 268.62E0, 336.25E0,
+   337.23E0, 339.33E0, 427.38E0, 428.58E0, 432.68E0,
+   528.99E0, 531.08E0, 628.34E0, 253.24E0, 273.13E0,
+   273.66E0, 282.10E0, 346.62E0, 347.19E0, 348.78E0,
+   351.18E0, 450.10E0, 450.35E0, 451.92E0, 455.56E0,
+   552.22E0, 553.56E0, 555.74E0, 652.59E0, 656.20E0,
+    14.13E0, 20.41E0, 31.30E0, 33.84E0, 39.70E0,
+    48.83E0, 54.50E0, 60.41E0, 72.77E0, 75.25E0,
+    86.84E0, 94.88E0, 96.40E0, 117.37E0, 139.08E0,
+   147.73E0, 158.63E0, 161.84E0, 192.11E0, 206.76E0,
+   209.07E0, 213.32E0, 226.44E0, 237.12E0, 330.90E0,
+   358.72E0, 370.77E0, 372.72E0, 396.24E0, 416.59E0,
+   484.02E0, 495.47E0, 514.78E0, 515.65E0, 519.47E0,
+   544.47E0, 560.11E0, 620.77E0, 18.97E0, 28.93E0,
+    33.91E0, 40.03E0, 44.66E0, 49.87E0, 55.16E0,
+    60.90E0, 72.08E0, 85.15E0, 97.06E0, 119.63E0,
+   133.27E0, 143.84E0, 161.91E0, 180.67E0, 198.44E0,
+   226.86E0, 229.65E0, 258.27E0, 273.77E0, 339.15E0,
+   350.13E0, 362.75E0, 371.03E0, 393.32E0, 448.53E0,
+   473.78E0, 511.12E0, 524.70E0, 548.75E0, 551.64E0,
+   574.02E0, 623.86E0, 21.46E0, 24.33E0, 33.43E0,
+    39.22E0, 44.18E0, 55.02E0, 94.33E0, 96.44E0,
+   118.82E0, 128.48E0, 141.94E0, 156.92E0, 171.65E0,
+   190.00E0, 223.26E0, 223.88E0, 231.50E0, 265.05E0,
+   269.44E0, 271.78E0, 273.46E0, 334.61E0, 339.79E0,
+   349.52E0, 358.18E0, 377.98E0, 394.77E0, 429.66E0,
+   468.22E0, 487.27E0, 519.54E0, 523.03E0, 612.99E0,
+   638.59E0, 641.36E0, 622.05E0, 631.50E0, 663.97E0,
+   646.9E0 , 748.29E0, 749.21E0, 750.14E0, 647.04E0,
+   646.89E0, 746.9E0 , 748.43E0, 747.35E0, 749.27E0,
+   647.61E0, 747.78E0, 750.51E0, 851.37E0, 845.97E0,
+   847.54E0, 849.93E0, 851.61E0, 849.75E0, 850.98E0,
+   848.23E0
+};
+
+static void
+hahn1_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.5324382854E+00;
+  const double hahn1_x[hahn1_P] = {
+     1.0776351733E+00, -1.2269296921E-01, 4.0863750610E-03,
+    -1.4262662514E-06, -5.7609940901E-03, 2.4053735503E-04,
+    -1.2314450199E-07 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < hahn1_P; ++i)
+    {
+      gsl_test_rel(x[i], hahn1_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+hahn1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[hahn1_P];
+  size_t i;
+
+  for (i = 0; i < hahn1_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < hahn1_N; i++)
+    {
+      double t = hahn1_F0[i];
+      double y = ((b[0] + t* (b[1]  + t * (b[2] + t * b[3])))
+                  / (1 + t*(b[4]  + t *(b[5] + t*b[6]))));
+      gsl_vector_set (f, i, hahn1_F1[i] - y);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+hahn1_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+          const gsl_vector * u, void * params, gsl_vector * v,
+          gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(hahn1_J, hahn1_N, hahn1_P);
+  double b[hahn1_P];
+  size_t i;
+
+  for (i = 0; i < hahn1_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < hahn1_N; i++)
+    {
+      double t = hahn1_F0[i];
+      double u = (b[0] + t*(b[1] + t*(b[2] + t * b[3])));
+      double v = (1 + t*(b[4] + t*(b[5] + t*b[6])));
+      gsl_matrix_set (&J.matrix, i, 0, -1/v);
+      gsl_matrix_set (&J.matrix, i, 1, -t/v);
+      gsl_matrix_set (&J.matrix, i, 2, -t*t/v);
+      gsl_matrix_set (&J.matrix, i, 3, -t*t*t/v);
+      gsl_matrix_set (&J.matrix, i, 4, t*u/(v*v));
+      gsl_matrix_set (&J.matrix, i, 5, t*t*u/(v*v));
+      gsl_matrix_set (&J.matrix, i, 6, t*t*t*u/(v*v));
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf hahn1_func =
+{
+  hahn1_f,
+  hahn1_df,
+  NULL, /* analytic expression too complex */
+  hahn1_N,
+  hahn1_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem hahn1a_problem =
+{
+  "nist-hahn1a",
+  hahn1_x0a,
+  hahn1_sigma,
+  &hahn1_epsrel,
+  &hahn1_checksol,
+  &hahn1_func
+};
+
+static test_fdf_problem hahn1b_problem =
+{
+  "nist-hahn1b",
+  hahn1_x0b,
+  hahn1_sigma,
+  &hahn1_epsrel,
+  &hahn1_checksol,
+  &hahn1_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_helical.c gsl-doc-2.3/multilarge_nlinear/test_helical.c
--- gsl-doc-1.16/multilarge_nlinear/test_helical.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_helical.c	2016-08-12 19:51:26.000000000 +0000
@@ -0,0 +1,125 @@
+#define helical_N         3
+#define helical_P         3
+
+static double helical_x0[helical_P] = { -1.0, 0.0, 0.0 };
+static double helical_x[helical_P] = { 1.0, 0.0, 0.0 };
+static double helical_epsrel = 1.0e-12;
+
+static double helical_J[helical_N * helical_P];
+
+static void
+helical_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < helical_P; ++i)
+    {
+      gsl_test_rel(x[i], helical_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+helical_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double theta = (x1 >= 0.0) ? 0.0 : 5.0;
+  double nx = gsl_hypot(x1, x2);
+
+  gsl_vector_set(f, 0, 10.0 * (x3 - 5.0/M_PI*atan(x2 / x1) - theta));
+  gsl_vector_set(f, 1, 10.0*(nx - 1.0));
+  gsl_vector_set(f, 2, x3);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+helical_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+            const gsl_vector * u, void * params, gsl_vector * v,
+            gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(helical_J, helical_N, helical_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double nx = gsl_hypot(x1, x2);
+  double nx_sq = nx * nx;
+  double term1 = 50.0 / (M_PI * nx_sq);
+  double term2 = 10.0 / nx;
+
+  gsl_matrix_set(&J.matrix, 0, 0, term1*x2);
+  gsl_matrix_set(&J.matrix, 0, 1, -term1*x1);
+  gsl_matrix_set(&J.matrix, 0, 2, 10.0);
+
+  gsl_matrix_set(&J.matrix, 1, 0, term2*x1);
+  gsl_matrix_set(&J.matrix, 1, 1, term2*x2);
+  gsl_matrix_set(&J.matrix, 1, 2, 0.0);
+
+  gsl_matrix_set(&J.matrix, 2, 0, 0.0);
+  gsl_matrix_set(&J.matrix, 2, 1, 0.0);
+  gsl_matrix_set(&J.matrix, 2, 2, 1.0);
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+helical_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double term1 = v2*x1 - v1*x2;
+  double term2 = v1*x1 + v2*x2;
+  double term3 = x1*x1 + x2*x2;
+
+  gsl_vector_set(fvv, 0, 100.0 / M_PI * (term1 / term3) * (term2 / term3));
+  gsl_vector_set(fvv, 1, 10.0 * (term1 * term1) / pow(term3, 1.5));
+  gsl_vector_set(fvv, 2, 0.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf helical_func =
+{
+  helical_f,
+  helical_df,
+  helical_fvv,
+  helical_N,
+  helical_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem helical_problem =
+{
+  "helical",
+  helical_x0,
+  NULL,
+  &helical_epsrel,
+  &helical_checksol,
+  &helical_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_jennrich.c gsl-doc-2.3/multilarge_nlinear/test_jennrich.c
--- gsl-doc-1.16/multilarge_nlinear/test_jennrich.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_jennrich.c	2016-08-12 19:51:30.000000000 +0000
@@ -0,0 +1,123 @@
+#define jennrich_N         10
+#define jennrich_P         2
+
+static double jennrich_x0[jennrich_P] = { 0.3, 0.4 };
+static double jennrich_epsrel = 1.0e-7;
+
+static double jennrich_J[jennrich_N * jennrich_P];
+
+static void
+jennrich_checksol(const double x[], const double sumsq,
+                  const double epsrel, const char *sname,
+                  const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 1.243621823556148e+02;
+  const double jennrich_x[jennrich_P] = { 2.578252139935855e-01,
+                                          2.578252133471426e-01 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < jennrich_P; ++i)
+    {
+      gsl_test_rel(x[i], jennrich_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+jennrich_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < jennrich_N; ++i)
+    {
+      double ip1 = i + 1.0;
+      double fi = 2.0*(i + 2.0) - (exp(x1*ip1) + exp(x2*ip1));
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+jennrich_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+             const gsl_vector * u, void * params, gsl_vector * v,
+             gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(jennrich_J, jennrich_N, jennrich_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  size_t i;
+
+  for (i = 0; i < jennrich_N; ++i)
+    {
+      double ip1 = i + 1.0;
+
+      gsl_matrix_set(&J.matrix, i, 0, -ip1*exp(ip1*x1));
+      gsl_matrix_set(&J.matrix, i, 1, -ip1*exp(ip1*x2));
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+jennrich_fvv (const gsl_vector * x, const gsl_vector * v,
+              void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  size_t i;
+
+  for (i = 0; i < jennrich_N; ++i)
+    {
+      double ip1 = i + 1.0;
+      double term1 = exp(ip1*x1);
+      double term2 = exp(ip1*x2);
+
+      gsl_vector_set(fvv, i, -ip1*ip1*(v1*v1*term1 + v2*v2*term2));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf jennrich_func =
+{
+  jennrich_f,
+  jennrich_df,
+  jennrich_fvv,
+  jennrich_N,
+  jennrich_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem jennrich_problem =
+{
+  "jennrich",
+  jennrich_x0,
+  NULL,
+  &jennrich_epsrel,
+  &jennrich_checksol,
+  &jennrich_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_kirby2.c gsl-doc-2.3/multilarge_nlinear/test_kirby2.c
--- gsl-doc-1.16/multilarge_nlinear/test_kirby2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_kirby2.c	2016-08-12 19:51:33.000000000 +0000
@@ -0,0 +1,230 @@
+#define kirby2_N       151
+#define kirby2_P       5
+
+static double kirby2_x0a[kirby2_P] = { 2.0, -0.1, 0.003, -0.001, 0.00001 };
+static double kirby2_x0b[kirby2_P] = { 1.5, -0.15, 0.0025, -0.0015, 0.00002 }; 
+static double kirby2_x[kirby2_P] = { 1.6745063063E+00, -1.3927397867E-01, 2.5961181191E-03,
+                                    -1.7241811870E-03,  2.1664802578E-05 }; 
+static double kirby2_epsrel = 1.0e-5;
+
+static double kirby2_J[kirby2_N * kirby2_P];
+
+static double kirby2_sigma[kirby2_P] = {
+  8.7989634338E-02, 4.1182041386E-03, 4.1856520458E-05,
+  5.8931897355E-05, 2.0129761919E-07
+};
+
+static double kirby2_F1[kirby2_N] = {
+       0.0082E0, 0.0112E0, 0.0149E0, 0.0198E0, 0.0248E0,
+       0.0324E0, 0.0420E0, 0.0549E0, 0.0719E0, 0.0963E0,
+       0.1291E0, 0.1710E0, 0.2314E0, 0.3227E0, 0.4809E0,
+       0.7084E0, 1.0220E0, 1.4580E0, 1.9520E0, 2.5410E0,
+       3.2230E0, 3.9990E0, 4.8520E0, 5.7320E0, 6.7270E0,
+       7.8350E0, 9.0250E0, 10.2670E0, 11.5780E0, 12.9440E0,
+      14.3770E0, 15.8560E0, 17.3310E0, 18.8850E0, 20.5750E0,
+      22.3200E0, 22.3030E0, 23.4600E0, 24.0600E0, 25.2720E0,
+      25.8530E0, 27.1100E0, 27.6580E0, 28.9240E0, 29.5110E0,
+      30.7100E0, 31.3500E0, 32.5200E0, 33.2300E0, 34.3300E0,
+      35.0600E0, 36.1700E0, 36.8400E0, 38.0100E0, 38.6700E0,
+      39.8700E0, 40.0300E0, 40.5000E0, 41.3700E0, 41.6700E0,
+      42.3100E0, 42.7300E0, 43.4600E0, 44.1400E0, 44.5500E0,
+      45.2200E0, 45.9200E0, 46.3000E0, 47.0000E0, 47.6800E0,
+      48.0600E0, 48.7400E0, 49.4100E0, 49.7600E0, 50.4300E0,
+      51.1100E0, 51.5000E0, 52.1200E0, 52.7600E0, 53.1800E0,
+      53.7800E0, 54.4600E0, 54.8300E0, 55.4000E0, 56.4300E0,
+      57.0300E0, 58.0000E0, 58.6100E0, 59.5800E0, 60.1100E0,
+      61.1000E0, 61.6500E0, 62.5900E0, 63.1200E0, 64.0300E0,
+      64.6200E0, 65.4900E0, 66.0300E0, 66.8900E0, 67.4200E0,
+      68.2300E0, 68.7700E0, 69.5900E0, 70.1100E0, 70.8600E0,
+      71.4300E0, 72.1600E0, 72.7000E0, 73.4000E0, 73.9300E0,
+      74.6000E0, 75.1600E0, 75.8200E0, 76.3400E0, 76.9800E0,
+      77.4800E0, 78.0800E0, 78.6000E0, 79.1700E0, 79.6200E0,
+      79.8800E0, 80.1900E0, 80.6600E0, 81.2200E0, 81.6600E0,
+      82.1600E0, 82.5900E0, 83.1400E0, 83.5000E0, 84.0000E0,
+      84.4000E0, 84.8900E0, 85.2600E0, 85.7400E0, 86.0700E0,
+      86.5400E0, 86.8900E0, 87.3200E0, 87.6500E0, 88.1000E0,
+      88.4300E0, 88.8300E0, 89.1200E0, 89.5400E0, 89.8500E0,
+      90.2500E0, 90.5500E0, 90.9300E0, 91.2000E0, 91.5500E0,
+      92.2000E0
+};
+
+
+static double kirby2_F0[kirby2_N] = {
+    9.65E0, 10.74E0, 11.81E0, 12.88E0, 14.06E0,
+   15.28E0, 16.63E0, 18.19E0, 19.88E0, 21.84E0,
+   24.00E0, 26.25E0, 28.86E0, 31.85E0, 35.79E0,
+   40.18E0, 44.74E0, 49.53E0, 53.94E0, 58.29E0,
+   62.63E0, 67.03E0, 71.25E0, 75.22E0, 79.33E0,
+   83.56E0, 87.75E0, 91.93E0, 96.10E0, 100.28E0,
+  104.46E0, 108.66E0, 112.71E0, 116.88E0, 121.33E0,
+  125.79E0, 125.79E0, 128.74E0, 130.27E0, 133.33E0,
+  134.79E0, 137.93E0, 139.33E0, 142.46E0, 143.90E0,
+  146.91E0, 148.51E0, 151.41E0, 153.17E0, 155.97E0,
+  157.76E0, 160.56E0, 162.30E0, 165.21E0, 166.90E0,
+  169.92E0, 170.32E0, 171.54E0, 173.79E0, 174.57E0,
+  176.25E0, 177.34E0, 179.19E0, 181.02E0, 182.08E0,
+  183.88E0, 185.75E0, 186.80E0, 188.63E0, 190.45E0,
+  191.48E0, 193.35E0, 195.22E0, 196.23E0, 198.05E0,
+  199.97E0, 201.06E0, 202.83E0, 204.69E0, 205.86E0,
+  207.58E0, 209.50E0, 210.65E0, 212.33E0, 215.43E0,
+  217.16E0, 220.21E0, 221.98E0, 225.06E0, 226.79E0,
+  229.92E0, 231.69E0, 234.77E0, 236.60E0, 239.63E0,
+  241.50E0, 244.48E0, 246.40E0, 249.35E0, 251.32E0,
+  254.22E0, 256.24E0, 259.11E0, 261.18E0, 264.02E0,
+  266.13E0, 268.94E0, 271.09E0, 273.87E0, 276.08E0,
+  278.83E0, 281.08E0, 283.81E0, 286.11E0, 288.81E0,
+  291.08E0, 293.75E0, 295.99E0, 298.64E0, 300.84E0,
+  302.02E0, 303.48E0, 305.65E0, 308.27E0, 310.41E0,
+  313.01E0, 315.12E0, 317.71E0, 319.79E0, 322.36E0,
+  324.42E0, 326.98E0, 329.01E0, 331.56E0, 333.56E0,
+  336.10E0, 338.08E0, 340.60E0, 342.57E0, 345.08E0,
+  347.02E0, 349.52E0, 351.44E0, 353.93E0, 355.83E0,
+  358.32E0, 360.20E0, 362.67E0, 364.53E0, 367.00E0,
+  371.30E0
+};
+
+static void
+kirby2_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 3.9050739624E+00;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < kirby2_P; ++i)
+    {
+      gsl_test_rel(x[i], kirby2_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+kirby2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[kirby2_P];
+  size_t i;
+
+  for (i = 0; i < kirby2_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < kirby2_N; i++)
+    {
+      double t = kirby2_F0[i];
+      double y = ((b[0] + t* (b[1]  + t * b[2]))
+                  / (1 + t*(b[3]  + t *b[4])));
+      gsl_vector_set (f, i, kirby2_F1[i] - y);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+kirby2_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+           const gsl_vector * u, void * params, gsl_vector * v,
+           gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(kirby2_J, kirby2_N, kirby2_P);
+  double b[kirby2_P];
+  size_t i;
+
+  for (i = 0; i < kirby2_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < kirby2_N; i++)
+    {
+      double t = kirby2_F0[i];
+      double u = (b[0] + t*(b[1] + t*b[2]));
+      double v = (1 + t*(b[3] + t*b[4]));
+      gsl_matrix_set (&J.matrix, i, 0, -1/v);
+      gsl_matrix_set (&J.matrix, i, 1, -t/v);
+      gsl_matrix_set (&J.matrix, i, 2, -t*t/v);
+      gsl_matrix_set (&J.matrix, i, 3, t*u/(v*v));
+      gsl_matrix_set (&J.matrix, i, 4, t*t*u/(v*v));
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+kirby2_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  double v4 = gsl_vector_get(v, 3);
+  double v5 = gsl_vector_get(v, 4);
+  size_t i;
+
+  for (i = 0; i < kirby2_N; i++)
+    {
+      double t = kirby2_F0[i];
+      double term1 = 1.0 + t*(x4 + t*x5);
+
+      gsl_vector_set(fvv, i, -2*t/pow(term1, 3.0) *
+                             (v4 + t*v5) *
+                             (-t*(-v2 + v4*x1 +
+                                  t*(-v3 + v5*x1 + v4*x2 + t*v5*x2 + t*(v4+t*v5)*x3)) +
+                             t*t*(v2 + t*v3)*(x4 + t*x5) + v1*(1.0 + t*(x4 + t*x5))));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf kirby2_func =
+{
+  kirby2_f,
+  kirby2_df,
+  kirby2_fvv,
+  kirby2_N,
+  kirby2_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem kirby2a_problem =
+{
+  "nist-kirby2a",
+  kirby2_x0a,
+  kirby2_sigma,
+  &kirby2_epsrel,
+  &kirby2_checksol,
+  &kirby2_func
+};
+
+static test_fdf_problem kirby2b_problem =
+{
+  "nist-kirby2b",
+  kirby2_x0b,
+  kirby2_sigma,
+  &kirby2_epsrel,
+  &kirby2_checksol,
+  &kirby2_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_kowalik.c gsl-doc-2.3/multilarge_nlinear/test_kowalik.c
--- gsl-doc-1.16/multilarge_nlinear/test_kowalik.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_kowalik.c	2016-08-12 19:51:37.000000000 +0000
@@ -0,0 +1,174 @@
+#define kowalik_N         11
+#define kowalik_P         4
+
+static double kowalik_x0[kowalik_P] = { 0.25, 0.39, 0.415, 0.39 };
+static double kowalik_epsrel = 1.0e-7;
+
+static double kowalik_J[kowalik_N * kowalik_P];
+
+static double kowalik_Y[kowalik_N] = {
+0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627,
+0.0456, 0.0342, 0.0323, 0.0235, 0.0246
+};
+
+static double kowalik_U[kowalik_N] = {
+4.0000, 2.0000, 1.0000, 0.5000, 0.2500, 0.1670,
+0.1250, 0.1000, 0.0833, 0.0714, 0.0625
+};
+
+static void
+kowalik_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  gsl_vector_const_view v = gsl_vector_const_view_array(x, kowalik_P);
+  const double norm = gsl_blas_dnrm2(&v.vector);
+  const double sumsq_exact1 = 3.075056038492370e-04;
+  const double kowalik_x1[kowalik_P] = { 1.928069345723978e-01,
+                                         1.912823290344599e-01,
+                                         1.230565070690708e-01,
+                                         1.360623308065148e-01 };
+  const double sumsq_exact2 = 0.00102734304869549252;
+  const double kowalik_x2[kowalik_P] = { GSL_NAN,   /* inf */
+                                         -14.0758834005984603,
+                                         GSL_NAN,   /* -inf */
+                                         GSL_NAN }; /* -inf */
+  const double *kowalik_x;
+  double sumsq_exact;
+
+  if (norm < 10.0)
+    {
+      kowalik_x = kowalik_x1;
+      sumsq_exact = sumsq_exact1;
+    }
+  else
+    {
+      kowalik_x = kowalik_x2;
+      sumsq_exact = sumsq_exact2;
+    }
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < kowalik_P; ++i)
+    {
+      if (!gsl_finite(kowalik_x[i]))
+        continue;
+
+      gsl_test_rel(x[i], kowalik_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+kowalik_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  size_t i;
+
+  for (i = 0; i < kowalik_N; ++i)
+    {
+      double yi = kowalik_Y[i];
+      double ui = kowalik_U[i];
+      double fi = yi - (x1*ui*(ui+x2)) / (x4 + ui*(ui + x3));
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+kowalik_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+            const gsl_vector * u, void * params, gsl_vector * v,
+            gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(kowalik_J, kowalik_N, kowalik_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  size_t i;
+
+  for (i = 0; i < kowalik_N; ++i)
+    {
+      double ui = kowalik_U[i];
+      double term1 = ui*(ui + x2);
+      double term2 = ui*(ui + x3) + x4;
+
+      gsl_matrix_set(&J.matrix, i, 0, -term1 / term2);
+      gsl_matrix_set(&J.matrix, i, 1, -ui*x1/term2);
+      gsl_matrix_set(&J.matrix, i, 2, ui*term1*x1 / (term2*term2));
+      gsl_matrix_set(&J.matrix, i, 3, term1*x1 / (term2*term2));
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+kowalik_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  double v4 = gsl_vector_get(v, 3);
+  size_t i;
+
+  for (i = 0; i < kowalik_N; ++i)
+    {
+      double ui = kowalik_U[i];
+      double term2 = ui*(ui + x3) + x4;
+      double term3 = ui*ui*v1 - ui*v3*x1 - v4*x1 +
+                     ui*v1*x3 + v1*x4;
+      double term4 = ui*ui*(v3-v2) + v4*x2 +
+                     ui*(v4 + v3*x2 - v2*x3) - v2*x4;
+
+      gsl_vector_set(fvv, i, 2.0*ui*term3*term4 / pow(term2, 3.0));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf kowalik_func =
+{
+  kowalik_f,
+  kowalik_df,
+  kowalik_fvv,
+  kowalik_N,
+  kowalik_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem kowalik_problem =
+{
+  "kowalik",
+  kowalik_x0,
+  NULL,
+  &kowalik_epsrel,
+  &kowalik_checksol,
+  &kowalik_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_lin1.c gsl-doc-2.3/multilarge_nlinear/test_lin1.c
--- gsl-doc-1.16/multilarge_nlinear/test_lin1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_lin1.c	2016-08-12 19:51:40.000000000 +0000
@@ -0,0 +1,118 @@
+#define lin1_N         11  /* can be anything >= p */
+#define lin1_P         5
+
+static double lin1_x0[lin1_P] = { 1.0, 1.0, 1.0, 1.0, 1.0 };
+static double lin1_epsrel = 1.0e-10;
+
+static double lin1_J[lin1_N * lin1_P];
+
+static void
+lin1_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = (double) (lin1_N - lin1_P);
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < lin1_P; ++i)
+    {
+      gsl_test_rel(x[i], -1.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+lin1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i, j;
+
+  for (i = 0; i < lin1_N; ++i)
+    {
+      double fi = 0.0;
+
+      for (j = 0; j < lin1_P; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+          double Aij = (i == j) ? 1.0 : 0.0;
+          Aij -= 2.0 / lin1_N;
+          fi += Aij * xj;
+        }
+
+      fi -= 1.0;
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin1_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+         const gsl_vector * u, void * params, gsl_vector * v,
+         gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(lin1_J, lin1_N, lin1_P);
+  size_t i, j;
+
+  for (i = 0; i < lin1_N; ++i)
+    {
+      for (j = 0; j < lin1_P; ++j)
+        {
+          double Jij = (i == j) ? 1.0 : 0.0;
+          Jij -= 2.0 / lin1_N;
+          gsl_matrix_set(&J.matrix, i, j, Jij);
+        }
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin1_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  (void)x; /* avoid unused parameter warnings */
+  (void)v;
+  (void)params;
+
+  gsl_vector_set_zero(fvv);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf lin1_func =
+{
+  lin1_f,
+  lin1_df,
+  lin1_fvv,
+  lin1_N,
+  lin1_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem lin1_problem =
+{
+  "linear_full",
+  lin1_x0,
+  NULL,
+  &lin1_epsrel,
+  &lin1_checksol,
+  &lin1_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_lin2.c gsl-doc-2.3/multilarge_nlinear/test_lin2.c
--- gsl-doc-1.16/multilarge_nlinear/test_lin2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_lin2.c	2016-08-12 19:51:43.000000000 +0000
@@ -0,0 +1,117 @@
+#define lin2_N         20  /* can be anything >= p */
+#define lin2_P         5
+
+static double lin2_x0[lin2_P] = { 1.0, 1.0, 1.0, 1.0, 1.0 };
+static double lin2_epsrel = 1.0e-8;
+
+static double lin2_J[lin2_N * lin2_P];
+
+static void
+lin2_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double n = (double) lin2_N;
+  const double sumsq_exact = 0.5 * (n*(n - 1.0)) / (2.0*n + 1.0);
+  const double sum_exact = 3.0 / (2.0*n + 1.0);
+  double sum = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < lin2_P; ++i)
+    sum += (i + 1.0) * x[i];
+
+  gsl_test_rel(sum, sum_exact, epsrel, "%s/%s coeff sum",
+               sname, pname);
+}
+
+static int
+lin2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i, j;
+
+  for (i = 0; i < lin2_N; ++i)
+    {
+      double fi = 0.0;
+
+      for (j = 0; j < lin2_P; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+          fi += (j + 1) * xj;
+        }
+
+      fi = (i + 1) * fi - 1.0;
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin2_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+         const gsl_vector * u, void * params, gsl_vector * v,
+         gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(lin2_J, lin2_N, lin2_P);
+  size_t i, j;
+
+  for (i = 0; i < lin2_N; ++i)
+    {
+      for (j = 0; j < lin2_P; ++j)
+        {
+          gsl_matrix_set(&J.matrix, i, j, (i + 1.0) * (j + 1.0));
+        }
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin2_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  (void)x; /* avoid unused parameter warnings */
+  (void)v;
+  (void)params;
+
+  gsl_vector_set_zero(fvv);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf lin2_func =
+{
+  lin2_f,
+  lin2_df,
+  lin2_fvv,
+  lin2_N,
+  lin2_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem lin2_problem =
+{
+  "linear_rank1",
+  lin2_x0,
+  NULL,
+  &lin2_epsrel,
+  &lin2_checksol,
+  &lin2_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_lin3.c gsl-doc-2.3/multilarge_nlinear/test_lin3.c
--- gsl-doc-1.16/multilarge_nlinear/test_lin3.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_lin3.c	2016-08-12 19:51:46.000000000 +0000
@@ -0,0 +1,124 @@
+#define lin3_N         50  /* can be anything >= p */
+#define lin3_P         10  /* >= 3 */
+
+static double lin3_x0[lin3_P] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
+static double lin3_epsrel = 1.0e-8;
+
+static double lin3_J[lin3_N * lin3_P];
+
+static void
+lin3_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double n = (double) lin3_N;
+  const double sumsq_exact = 0.5 * (n*n + 3*n - 6.0) / (2*n - 3.0);
+  const double sum_exact = 3.0 / (2.0*n - 3.0);
+  double sum = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 1; i < lin3_P - 1; ++i)
+    sum += (i + 1.0) * x[i];
+
+  gsl_test_rel(sum, sum_exact, epsrel, "%s/%s coeff sum",
+               sname, pname);
+
+  (void)x; /* avoid unused parameter warning */
+}
+
+static int
+lin3_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i, j;
+
+  gsl_vector_set(f, 0, -1.0);
+  gsl_vector_set(f, lin3_N - 1, -1.0);
+
+  for (i = 1; i < lin3_N - 1; ++i)
+    {
+      double fi = 0.0;
+
+      for (j = 1; j < lin3_P - 1; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+          fi += (j + 1) * xj;
+        }
+
+      fi = i * fi - 1.0;
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin3_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+         const gsl_vector * u, void * params, gsl_vector * v,
+         gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(lin3_J, lin3_N, lin3_P);
+  size_t i, j;
+
+  gsl_matrix_set_zero(&J.matrix);
+
+  for (i = 1; i < lin3_N - 1; ++i)
+    {
+      for (j = 1; j < lin3_P - 1; ++j)
+        {
+          gsl_matrix_set(&J.matrix, i, j, i * (j + 1.0));
+        }
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+lin3_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  (void)x; /* avoid unused parameter warnings */
+  (void)v;
+  (void)params;
+
+  gsl_vector_set_zero(fvv);
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf lin3_func =
+{
+  lin3_f,
+  lin3_df,
+  lin3_fvv,
+  lin3_N,
+  lin3_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem lin3_problem =
+{
+  "linear_rank1zeros",
+  lin3_x0,
+  NULL,
+  &lin3_epsrel,
+  &lin3_checksol,
+  &lin3_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_meyer.c gsl-doc-2.3/multilarge_nlinear/test_meyer.c
--- gsl-doc-1.16/multilarge_nlinear/test_meyer.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_meyer.c	2016-08-23 20:27:03.000000000 +0000
@@ -0,0 +1,142 @@
+#define meyer_N         16
+#define meyer_P         3
+
+static double meyer_x0[meyer_P] = { 0.02, 4000.0, 250.0 };
+static double meyer_epsrel = 1.0e-7;
+
+static double meyer_J[meyer_N * meyer_P];
+
+static double meyer_Y[meyer_N] = {
+34780., 28610., 23650., 19630., 16370., 13720., 11540.,
+9744.,  8261.,  7030.,  6005., 5147., 4427., 3820.,
+3307.,  2872.
+};
+
+static void
+meyer_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.794585517053883e+01;
+  const double meyer_x[meyer_P] = { 5.609636471049458e-03,
+                                    6.181346346283188e+03,
+                                    3.452236346240292e+02 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < meyer_P; ++i)
+    {
+      gsl_test_rel(x[i], meyer_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+meyer_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < meyer_N; ++i)
+    {
+      double ti = 45.0 + 5.0*(i + 1.0);
+      double yi = meyer_Y[i];
+      double fi = x1 * exp(x2 / (ti + x3)) - yi;
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+meyer_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+          const gsl_vector * u, void * params, gsl_vector * v,
+          gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(meyer_J, meyer_N, meyer_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < meyer_N; ++i)
+    {
+      double ti = 45.0 + 5.0*(i + 1.0);
+      double term1 = ti + x3;
+      double term2 = exp(x2 / term1);
+
+      gsl_matrix_set(&J.matrix, i, 0, term2);
+      gsl_matrix_set(&J.matrix, i, 1, x1*term2/term1);
+      gsl_matrix_set(&J.matrix, i, 2, -x1*x2*term2/(term1*term1));
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+meyer_fvv (const gsl_vector * x, const gsl_vector * v,
+           void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  size_t i;
+
+  for (i = 0; i < meyer_N; ++i)
+    {
+      double ti = 45.0 + 5.0*(i + 1.0);
+      double term1 = ti + x3;
+      double term2 = exp(x2 / term1);
+      double term3 = v2*term1 - v3*x2;
+      double term4 = 2*ti*ti*v1 - v3*x1*(x2 + 2*x3) +
+                     x3*(v2*x1 + 2*v1*x3) +
+                     ti*(v2*x1 - 2*v3*x1 + 4*v1*x3);
+
+      gsl_vector_set(fvv, i, term2 * term3 * term4 / pow(term1, 4.0));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf meyer_func =
+{
+  meyer_f,
+  meyer_df,
+  meyer_fvv,
+  meyer_N,
+  meyer_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem meyer_problem =
+{
+  "meyer",
+  meyer_x0,
+  NULL,
+  &meyer_epsrel,
+  &meyer_checksol,
+  &meyer_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_meyerscal.c gsl-doc-2.3/multilarge_nlinear/test_meyerscal.c
--- gsl-doc-1.16/multilarge_nlinear/test_meyerscal.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_meyerscal.c	2016-08-25 15:11:40.000000000 +0000
@@ -0,0 +1,143 @@
+#define meyerscal_N         16
+#define meyerscal_P         3
+
+static double meyerscal_x0[meyerscal_P] = { 8.85, 4.0, 2.5 };
+static double meyerscal_epsrel = 1.0e-6;
+
+static double meyerscal_J[meyerscal_N * meyerscal_P];
+
+static double meyerscal_Y[meyerscal_N] = {
+34780., 28610., 23650., 19630., 16370., 13720., 11540.,
+9744.,  8261.,  7030.,  6005., 5147., 4427., 3820.,
+3307.,  2872.
+};
+
+static void
+meyerscal_checksol(const double x[], const double sumsq,
+                   const double epsrel, const char *sname,
+                   const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.794585517003888e-05;
+  const double meyerscal_x[meyerscal_P] = { 2.481778312286695e+00,
+                                            6.181346341853554e+00,
+                                            3.452236344749865e+00 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < meyerscal_P; ++i)
+    {
+      gsl_test_rel(x[i], meyerscal_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+meyerscal_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < meyerscal_N; ++i)
+    {
+      double ti = 0.45 + 0.05*(i + 1.0);
+      double yi = meyerscal_Y[i];
+      double fi = x1 * exp(10.0*x2 / (ti + x3) - 13.0) - 1.0e-3*yi;
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+meyerscal_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+              const gsl_vector * u, void * params, gsl_vector * v,
+              gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(meyerscal_J, meyerscal_N, meyerscal_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  size_t i;
+
+  for (i = 0; i < meyerscal_N; ++i)
+    {
+      double ti = 0.45 + 0.05*(i + 1.0);
+      double term1 = ti + x3;
+      double term2 = exp(10.0*x2/term1 - 13.0);
+
+      gsl_matrix_set(&J.matrix, i, 0, term2);
+      gsl_matrix_set(&J.matrix, i, 1, 10.0*x1*term2/term1);
+      gsl_matrix_set(&J.matrix, i, 2, -10.0*x1*x2*term2/(term1*term1));
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+meyerscal_fvv (const gsl_vector * x, const gsl_vector * v,
+               void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  size_t i;
+
+  for (i = 0; i < meyerscal_N; ++i)
+    {
+      double ti = 0.45 + 0.05*(i + 1.0);
+      double term1 = ti + x3;
+      double term2 = exp(10.0*x2/term1 - 13.0);
+      double term3 = v2*term1 - v3*x2;
+      double term4 = ti*ti*v1 -
+                     v3*x1*(5*x2 + x3) +
+                     x3*(5*v2*x1 + v1*x3) +
+                     ti*(5*v2*x1 - v3*x1 + 2*v1*x3);
+
+      gsl_vector_set(fvv, i, 20*term2*term3*term4 / pow(term1, 4.0));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf meyerscal_func =
+{
+  meyerscal_f,
+  meyerscal_df,
+  meyerscal_fvv,
+  meyerscal_N,
+  meyerscal_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem meyerscal_problem =
+{
+  "meyerscal",
+  meyerscal_x0,
+  NULL,
+  &meyerscal_epsrel,
+  &meyerscal_checksol,
+  &meyerscal_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_osborne.c gsl-doc-2.3/multilarge_nlinear/test_osborne.c
--- gsl-doc-1.16/multilarge_nlinear/test_osborne.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_osborne.c	2016-08-12 19:51:56.000000000 +0000
@@ -0,0 +1,146 @@
+#define osborne_N         33
+#define osborne_P         5
+
+static double osborne_x0[osborne_P] = { 0.5, 1.5, -1.0, 0.01, 0.02 };
+static double osborne_epsrel = 1.0e-8;
+
+static double osborne_J[osborne_N * osborne_P];
+
+static double osborne_Y[osborne_N] = {
+0.844, 0.908, 0.932, 0.936, 0.925, 0.908, 0.881,
+0.850, 0.818, 0.784, 0.751, 0.718, 0.685, 0.658,
+0.628, 0.603, 0.580, 0.558, 0.538, 0.522, 0.506,
+0.490, 0.478, 0.467, 0.457, 0.448, 0.438, 0.431,
+0.424, 0.420, 0.414, 0.411, 0.406
+};
+
+static void
+osborne_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  const double sumsq_exact = 5.464894697482687e-05;
+  const double osborne_x[osborne_P] = {
+    3.754100521058740e-01, GSL_NAN, GSL_NAN, GSL_NAN, GSL_NAN };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  /* only the first model parameter is uniquely constrained */
+  gsl_test_rel(x[0], osborne_x[0], epsrel, "%s/%s i=0",
+               sname, pname);
+}
+
+static int
+osborne_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  size_t i;
+
+  for (i = 0; i < osborne_N; ++i)
+    {
+      double ti = 10.0*i;
+      double yi = osborne_Y[i];
+      double fi = yi - (x1 + x2*exp(-x4*ti) + x3*exp(-x5*ti));
+      gsl_vector_set(f, i, fi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+osborne_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+            const gsl_vector * u, void * params, gsl_vector * v,
+            gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(osborne_J, osborne_N, osborne_P);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  size_t i;
+
+  for (i = 0; i < osborne_N; ++i)
+    {
+      double ti = 10.0*i;
+      double term1 = exp(-x4*ti);
+      double term2 = exp(-x5*ti);
+
+      gsl_matrix_set(&J.matrix, i, 0, -1.0);
+      gsl_matrix_set(&J.matrix, i, 1, -term1);
+      gsl_matrix_set(&J.matrix, i, 2, -term2);
+      gsl_matrix_set(&J.matrix, i, 3, ti*x2*term1);
+      gsl_matrix_set(&J.matrix, i, 4, ti*x3*term2);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+osborne_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+  double x5 = gsl_vector_get(x, 4);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  double v4 = gsl_vector_get(v, 3);
+  double v5 = gsl_vector_get(v, 4);
+  size_t i;
+
+  for (i = 0; i < osborne_N; ++i)
+    {
+      double ti = 10.0*i;
+      double term1 = exp(-x4*ti);
+      double term2 = exp(-x5*ti);
+      double term3 = -2*v2 + ti*v4*x2;
+      double term4 = -2*v3 + ti*v5*x3;
+
+      gsl_vector_set(fvv, i, -term1 * term2 * ti *
+                             (v4 / term2 * term3 + v5 / term1 * term4));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf osborne_func =
+{
+  osborne_f,
+  osborne_df,
+  osborne_fvv,
+  osborne_N,
+  osborne_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem osborne_problem =
+{
+  "osborne",
+  osborne_x0,
+  NULL,
+  &osborne_epsrel,
+  &osborne_checksol,
+  &osborne_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_penalty1.c gsl-doc-2.3/multilarge_nlinear/test_penalty1.c
--- gsl-doc-1.16/multilarge_nlinear/test_penalty1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_penalty1.c	2016-08-12 21:38:22.000000000 +0000
@@ -0,0 +1,118 @@
+#define penalty1_P         10
+#define penalty1_N         (penalty1_P + 1)
+
+static double penalty1_x0[penalty1_P] = { 1.0, 2.0, 3.0, 4.0, 5.0,
+                                          6.0, 7.0, 8.0, 9.0, 10.0 };
+static double penalty1_epsrel = 1.0e-12;
+
+static double penalty1_J[penalty1_N * penalty1_P];
+
+static void
+penalty1_checksol(const double x[], const double sumsq,
+                  const double epsrel, const char *sname,
+                  const char *pname)
+{
+  const double sumsq_exact = 7.08765146709037993e-05;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  (void)x; /* avoid unused parameter warning */
+}
+
+static int
+penalty1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  size_t i;
+  double sum = 0.0;
+
+  for (i = 0; i < penalty1_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+
+      gsl_vector_set(f, i, sqrt_alpha*(xi - 1.0));
+
+      sum += xi * xi;
+    }
+
+  gsl_vector_set(f, penalty1_N - 1, sum - 0.25);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+penalty1_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+             const gsl_vector * u, void * params, gsl_vector * v,
+             gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(penalty1_J, penalty1_N, penalty1_P);
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  size_t i;
+  gsl_matrix_view m = gsl_matrix_submatrix(&J.matrix, 0, 0, penalty1_P, penalty1_P);
+  gsl_vector_view diag = gsl_matrix_diagonal(&m.matrix);
+
+  gsl_matrix_set_zero(&m.matrix);
+  gsl_vector_set_all(&diag.vector, sqrt_alpha);
+
+  for (i = 0; i < penalty1_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      gsl_matrix_set(&J.matrix, penalty1_N - 1, i, 2.0 * xi);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+penalty1_fvv (const gsl_vector * x, const gsl_vector * v,
+              void *params, gsl_vector * fvv)
+{
+  double u;
+
+  gsl_vector_set_zero(fvv);
+
+  gsl_blas_ddot(v, v, &u);
+  gsl_vector_set(fvv, penalty1_N - 1, 2.0 * u);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf penalty1_func =
+{
+  penalty1_f,
+  penalty1_df,
+  penalty1_fvv,
+  penalty1_N,
+  penalty1_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem penalty1_problem =
+{
+  "penalty1",
+  penalty1_x0,
+  NULL,
+  &penalty1_epsrel,
+  &penalty1_checksol,
+  &penalty1_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_penalty2.c gsl-doc-2.3/multilarge_nlinear/test_penalty2.c
--- gsl-doc-1.16/multilarge_nlinear/test_penalty2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_penalty2.c	2016-08-12 19:52:02.000000000 +0000
@@ -0,0 +1,190 @@
+#define penalty2_N         8 /* 2*p */
+#define penalty2_P         4
+
+static double penalty2_x0[penalty2_P] = { 0.5, 0.5, 0.5, 0.5 };
+static double penalty2_epsrel = 1.0e-12;
+
+static double penalty2_J[penalty2_N * penalty2_P];
+
+static void
+penalty2_checksol(const double x[], const double sumsq,
+                  const double epsrel, const char *sname,
+                  const char *pname)
+{
+  const double sumsq_exact = 9.37629300735544219e-06;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  (void)x; /* avoid unused parameter warning */
+}
+
+static int
+penalty2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  double x1 = gsl_vector_get(x, 0);
+  size_t i;
+  double sum = penalty2_P * x1 * x1;
+
+  gsl_vector_set(f, 0, x1 - 0.2);
+
+  /* rows [2:p] */
+  for (i = 1; i < penalty2_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      double xim1 = gsl_vector_get(x, i - 1);
+      double yi = exp(0.1*(i + 1.0)) + exp(0.1*i);
+
+      gsl_vector_set(f, i, sqrt_alpha*(exp(0.1*xi) + exp(0.1*xim1) - yi));
+
+      sum += (penalty2_P - i) * xi * xi;
+    }
+
+  /* rows [p+1:2p-1] */
+  for (i = penalty2_P; i < penalty2_N - 1; ++i)
+    {
+      double xi = gsl_vector_get(x, i - penalty2_P + 1);
+
+      gsl_vector_set(f, i, sqrt_alpha*(exp(0.1*xi) - exp(-0.1)));
+    }
+
+  /* row 2p */
+  gsl_vector_set(f, penalty2_N - 1, sum - 1.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+penalty2_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+             const gsl_vector * u, void * params, gsl_vector * v,
+             gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(penalty2_J, penalty2_N, penalty2_P);
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  size_t i, j;
+
+  for (j = 0; j < penalty2_P; ++j)
+    {
+      double xj = gsl_vector_get(x, j);
+      double delta1j = (j == 0) ? 1.0 : 0.0;
+
+      /* first and last rows */
+      gsl_matrix_set(&J.matrix, 0, j, delta1j);
+      gsl_matrix_set(&J.matrix, penalty2_N - 1, j, 2.0 * (penalty2_P - j) * xj);
+
+      /* rows [2:p] */
+      for (i = 1; i < penalty2_P; ++i)
+        {
+          double xi = gsl_vector_get(x, i);
+          double xim1 = gsl_vector_get(x, i - 1);
+          double Jij;
+
+          if (i == j)
+            Jij = exp(0.1 * xi);
+          else if (i - 1 == j)
+            Jij = exp(0.1 * xim1);
+          else
+            Jij = 0.0;
+
+          Jij *= 0.1 * sqrt_alpha;
+
+          gsl_matrix_set(&J.matrix, i, j, Jij);
+        }
+
+      /* rows [p+1:2p-1] */
+      for (i = penalty2_P; i < penalty2_N - 1; ++i)
+        {
+          double xi = gsl_vector_get(x, i - penalty2_P + 1);
+
+          if (i - penalty2_P + 1 == j)
+            gsl_matrix_set(&J.matrix, i, j, 0.1 * sqrt_alpha * exp(0.1*xi));
+          else
+            gsl_matrix_set(&J.matrix, i, j, 0.0);
+        }
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+penalty2_fvv (const gsl_vector * x, const gsl_vector * v,
+              void *params, gsl_vector * fvv)
+{
+  const double alpha = 1.0e-5;
+  const double sqrt_alpha = sqrt(alpha);
+  double v1 = gsl_vector_get(v, 0);
+  double sum = penalty2_P * v1 * v1;
+  size_t i;
+
+  /* first row */
+  gsl_vector_set(fvv, 0, 0.0);
+
+  /* rows [2:p] */
+  for (i = 1; i < penalty2_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      double xim1 = gsl_vector_get(x, i - 1);
+      double vi = gsl_vector_get(v, i);
+      double vim1 = gsl_vector_get(v, i - 1);
+      double term1 = exp(xi / 10.0);
+      double term2 = exp(xim1 / 10.0);
+
+      gsl_vector_set(fvv, i,
+        sqrt_alpha / 100.0 * (term1 * vi * vi + term2 * vim1 * vim1));
+
+      sum += (penalty2_P - i) * vi * vi;
+    }
+
+  /* last row */
+  gsl_vector_set(fvv, penalty2_N - 1, 2.0 * sum);
+
+  /* rows [p+1:2p-1] */
+  for (i = penalty2_P; i < penalty2_N - 1; ++i)
+    {
+      double xi = gsl_vector_get(x, i - penalty2_P + 1);
+      double vi = gsl_vector_get(v, i - penalty2_P + 1);
+
+      gsl_vector_set(fvv, i, sqrt_alpha / 100.0 * exp(xi / 10.0) * vi * vi);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf penalty2_func =
+{
+  penalty2_f,
+  penalty2_df,
+  penalty2_fvv,
+  penalty2_N,
+  penalty2_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem penalty2_problem =
+{
+  "penalty2",
+  penalty2_x0,
+  NULL,
+  &penalty2_epsrel,
+  &penalty2_checksol,
+  &penalty2_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_powell1.c gsl-doc-2.3/multilarge_nlinear/test_powell1.c
--- gsl-doc-1.16/multilarge_nlinear/test_powell1.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_powell1.c	2016-08-12 19:52:05.000000000 +0000
@@ -0,0 +1,131 @@
+#define powell1_N        4
+#define powell1_P        4
+
+static double powell1_x0[powell1_P] = { 3.0, -1.0, 0.0, 1.0 };
+static double powell1_epsrel = 1.0e-4;
+
+static double powell1_J[powell1_N * powell1_P];
+
+static void
+powell1_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < powell1_P; ++i)
+    {
+      gsl_test_rel(x[i], 0.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+powell1_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get (x, 0);
+  double x2 = gsl_vector_get (x, 1);
+  double x3 = gsl_vector_get (x, 2);
+  double x4 = gsl_vector_get (x, 3);
+
+  gsl_vector_set(f, 0, x1 + 10.0*x2);
+  gsl_vector_set(f, 1, sqrt(5.0) * (x3 - x4));
+  gsl_vector_set(f, 2, pow(x2 - 2.0*x3, 2.0));
+  gsl_vector_set(f, 3, sqrt(10.0) * pow((x1 - x4), 2.0));
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell1_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+            const gsl_vector * u, void * params, gsl_vector * v,
+            gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(powell1_J, powell1_N, powell1_P);
+  double x1 = gsl_vector_get (x, 0);
+  double x2 = gsl_vector_get (x, 1);
+  double x3 = gsl_vector_get (x, 2);
+  double x4 = gsl_vector_get (x, 3);
+  double term1 = x2 - 2.0*x3;
+  double term2 = x1 - x4;
+
+  gsl_matrix_set(&J.matrix, 0, 0, 1.0);
+  gsl_matrix_set(&J.matrix, 0, 1, 10.0);
+  gsl_matrix_set(&J.matrix, 0, 2, 0.0);
+  gsl_matrix_set(&J.matrix, 0, 3, 0.0);
+
+  gsl_matrix_set(&J.matrix, 1, 0, 0.0);
+  gsl_matrix_set(&J.matrix, 1, 1, 0.0);
+  gsl_matrix_set(&J.matrix, 1, 2, sqrt(5.0));
+  gsl_matrix_set(&J.matrix, 1, 3, -sqrt(5.0));
+
+  gsl_matrix_set(&J.matrix, 2, 0, 0.0);
+  gsl_matrix_set(&J.matrix, 2, 1, 2.0*term1);
+  gsl_matrix_set(&J.matrix, 2, 2, -4.0*term1);
+  gsl_matrix_set(&J.matrix, 2, 3, 0.0);
+
+  gsl_matrix_set(&J.matrix, 3, 0, 2.0*sqrt(10.0)*term2);
+  gsl_matrix_set(&J.matrix, 3, 1, 0.0);
+  gsl_matrix_set(&J.matrix, 3, 2, 0.0);
+  gsl_matrix_set(&J.matrix, 3, 3, -2.0*sqrt(10.0)*term2);
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell1_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  double v4 = gsl_vector_get(v, 3);
+
+  gsl_vector_set(fvv, 0, 0.0);
+  gsl_vector_set(fvv, 1, 0.0);
+  gsl_vector_set(fvv, 2, 2.0 * pow(v2 - 2.0*v3, 2.0));
+  gsl_vector_set(fvv, 3, 2.0 * sqrt(10.0) * pow(v1 - v4, 2.0));
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf powell1_func =
+{
+  powell1_f,
+  powell1_df,
+  powell1_fvv,
+  powell1_N,
+  powell1_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem powell1_problem =
+{
+  "powell_singular",
+  powell1_x0,
+  NULL,
+  &powell1_epsrel,
+  &powell1_checksol,
+  &powell1_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_powell2.c gsl-doc-2.3/multilarge_nlinear/test_powell2.c
--- gsl-doc-1.16/multilarge_nlinear/test_powell2.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_powell2.c	2016-08-12 19:52:08.000000000 +0000
@@ -0,0 +1,106 @@
+#define powell2_N        2
+#define powell2_P        2
+
+static double powell2_x0[powell2_P] = { 3.0, 1.0 };
+static double powell2_epsrel = 1.0e-3;
+
+static double powell2_J[powell2_N * powell2_P];
+
+static void
+powell2_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < powell2_P; ++i)
+    {
+      gsl_test_rel(x[i], 0.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+powell2_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x0 = gsl_vector_get (x, 0);
+  double x1 = gsl_vector_get (x, 1);
+
+  gsl_vector_set(f, 0, x0);
+  gsl_vector_set(f, 1, 10.0*x0/(x0 + 0.1) + 2.0*x1*x1);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell2_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+            const gsl_vector * u, void * params, gsl_vector * v,
+            gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(powell2_J, powell2_N, powell2_P);
+  double x0 = gsl_vector_get (x, 0);
+  double x1 = gsl_vector_get (x, 1);
+  double term = x0 + 0.1;
+
+  gsl_matrix_set(&J.matrix, 0, 0, 1.0);
+  gsl_matrix_set(&J.matrix, 0, 1, 0.0);
+  gsl_matrix_set(&J.matrix, 1, 0, 1.0 / (term * term));
+  gsl_matrix_set(&J.matrix, 1, 1, 4.0 * x1);
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell2_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  double x0 = gsl_vector_get (x, 0);
+  double v0 = gsl_vector_get (v, 0);
+  double v1 = gsl_vector_get (v, 1);
+  double term = x0 + 0.1;
+
+  gsl_vector_set(fvv, 0, 0.0);
+  gsl_vector_set(fvv, 1, 4*v1*v1 - (2*v0*v0)/pow(term, 3.0));
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf powell2_func =
+{
+  powell2_f,
+  powell2_df,
+  powell2_fvv,
+  powell2_N,
+  powell2_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem powell2_problem =
+{
+  "powell2",
+  powell2_x0,
+  NULL,
+  &powell2_epsrel,
+  &powell2_checksol,
+  &powell2_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_powell3.c gsl-doc-2.3/multilarge_nlinear/test_powell3.c
--- gsl-doc-1.16/multilarge_nlinear/test_powell3.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_powell3.c	2016-08-12 19:52:11.000000000 +0000
@@ -0,0 +1,108 @@
+#define powell3_N         2
+#define powell3_P         2
+
+static double powell3_x0[powell3_P] = { 0.0, 1.0 };
+static double powell3_epsrel = 1.0e-10;
+
+static double powell3_J[powell3_N * powell3_P];
+
+static void
+powell3_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double powell3_x[powell3_P] = { 1.09815932969975976e-05,
+                                        9.10614673986700218 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < powell3_P; ++i)
+    {
+      gsl_test_rel(x[i], powell3_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+powell3_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, 1.0e4*x1*x2 - 1.0);
+  gsl_vector_set(f, 1, exp(-x1) + exp(-x2) - 1.0001);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell3_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+            const gsl_vector * u, void * params, gsl_vector * v,
+            gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(powell3_J, powell3_N, powell3_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_matrix_set(&J.matrix, 0, 0, 1.0e4*x2);
+  gsl_matrix_set(&J.matrix, 0, 1, 1.0e4*x1);
+
+  gsl_matrix_set(&J.matrix, 1, 0, -exp(-x1));
+  gsl_matrix_set(&J.matrix, 1, 1, -exp(-x2));
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+powell3_fvv (const gsl_vector * x, const gsl_vector * v,
+             void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+
+  gsl_vector_set(fvv, 0, 2.0e4 * v1 * v2);
+  gsl_vector_set(fvv, 1, v1*v1*exp(-x1) + v2*v2*exp(-x2));
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf powell3_func =
+{
+  powell3_f,
+  powell3_df,
+  powell3_fvv,
+  powell3_N,
+  powell3_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem powell3_problem =
+{
+  "powell_badly_scaled",
+  powell3_x0,
+  NULL,
+  &powell3_epsrel,
+  &powell3_checksol,
+  &powell3_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_rat42.c gsl-doc-2.3/multilarge_nlinear/test_rat42.c
--- gsl-doc-1.16/multilarge_nlinear/test_rat42.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_rat42.c	2016-08-12 19:52:14.000000000 +0000
@@ -0,0 +1,163 @@
+#define rat42_N       9
+#define rat42_P       3
+
+static double rat42_x0a[rat42_P] = { 100.0, 1.0, 0.1 };
+static double rat42_x0b[rat42_P] = { 75.0, 2.5, 0.07 };
+static double rat42_epsrel = 1.0e-7;
+
+static double rat42_J[rat42_N * rat42_P];
+
+static double rat42_sigma[rat42_P] = {
+  1.7340283401E+00, 8.8295217536E-02, 3.4465663377E-03
+};
+
+static double rat42_X[rat42_N] = { 9.0, 14.0, 21.0, 28.0, 42.0,
+                                   57.0, 63.0, 70.0, 79.0 };
+
+static double rat42_F[rat42_N] = { 8.930, 10.800, 18.590, 22.330,
+                                   39.350, 56.110, 61.730, 64.620,
+                                   67.080 };
+
+static void
+rat42_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.0565229338E+00;
+  const double rat42_x[rat42_P] = { 7.2462237576E+01,
+                                    2.6180768402E+00,
+                                    6.7359200066E-02 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < rat42_P; ++i)
+    {
+      gsl_test_rel(x[i], rat42_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+rat42_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[rat42_P];
+  size_t i;
+
+  for (i = 0; i < rat42_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < rat42_N; i++)
+    {
+      double xi = rat42_X[i];
+      double yi = b[0] / (1.0 + exp(b[1] - b[2]*xi));
+      gsl_vector_set (f, i, yi - rat42_F[i]);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rat42_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+          const gsl_vector * u, void * params, gsl_vector * v,
+          gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(rat42_J, rat42_N, rat42_P);
+  double b[rat42_P];
+  size_t i;
+
+  for (i = 0; i < rat42_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < rat42_N; i++)
+    {
+      double xi = rat42_X[i];
+      double term1 = exp(b[1] - b[2]*xi);
+      double term2 = 1.0 + term1;
+
+      gsl_matrix_set (&J.matrix, i, 0, 1.0 / term2);
+      gsl_matrix_set (&J.matrix, i, 1, -b[0] * term1 / (term2 * term2));
+      gsl_matrix_set (&J.matrix, i, 2, b[0] * term1 * xi / (term2 * term2));
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rat42_fvv (const gsl_vector * x, const gsl_vector * v,
+           void *params, gsl_vector * fvv)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  double v3 = gsl_vector_get(v, 2);
+  size_t i;
+
+  for (i = 0; i < rat42_N; i++)
+    {
+      double ti = rat42_X[i];
+      double term1 = exp(x2);
+      double term2 = exp(ti * x3);
+
+      gsl_vector_set(fvv, i,
+        -pow(term1 + term2, -3.0) * term1 * term2 *
+         (v2 - ti*v3) * (term1*(2*v1 - v2*x1 + ti*v3*x1) +
+                         term2*(2*v1 + x1*(v2 - ti*v3))));
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf rat42_func =
+{
+  rat42_f,
+  rat42_df,
+  rat42_fvv,
+  rat42_N,
+  rat42_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem rat42a_problem =
+{
+  "nist-rat42a",
+  rat42_x0a,
+  rat42_sigma,
+  &rat42_epsrel,
+  &rat42_checksol,
+  &rat42_func
+};
+
+static test_fdf_problem rat42b_problem =
+{
+  "nist-rat42b",
+  rat42_x0b,
+  rat42_sigma,
+  &rat42_epsrel,
+  &rat42_checksol,
+  &rat42_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_rat43.c gsl-doc-2.3/multilarge_nlinear/test_rat43.c
--- gsl-doc-1.16/multilarge_nlinear/test_rat43.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_rat43.c	2016-08-12 19:52:20.000000000 +0000
@@ -0,0 +1,137 @@
+#define rat43_N       15
+#define rat43_P       4
+
+static double rat43_x0a[rat43_P] = { 100.0, 10.0, 1.0, 1.0 };
+static double rat43_x0b[rat43_P] = { 700.0, 5.0, 0.75, 1.3 };
+static double rat43_epsrel = 1.0e-6;
+
+static double rat43_J[rat43_N * rat43_P];
+
+static double rat43_sigma[rat43_P] = {
+  1.6302297817E+01, 2.0828735829E+00,
+  1.9566123451E-01, 6.8761936385E-01
+};
+
+static double rat43_F[rat43_N] = { 16.08, 33.83, 65.80, 97.20, 191.55,
+                                   326.20, 386.87, 520.53, 590.03,
+                                   651.92, 724.93, 699.56, 689.96,
+                                   637.56, 717.41 };
+
+static void
+rat43_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 8.7864049080E+03;
+  const double rat43_x[rat43_P] = { 6.9964151270E+02,
+                                    5.2771253025E+00,
+                                    7.5962938329E-01,
+                                    1.2792483859E+00 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < rat43_P; ++i)
+    {
+      gsl_test_rel(x[i], rat43_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+rat43_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[rat43_P];
+  size_t i;
+
+  for (i = 0; i < rat43_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < rat43_N; i++)
+    {
+      double xi = i + 1.0;
+      double e = exp(b[1] - b[2]*xi);
+      double yi = b[0] / pow(1.0 + e, 1.0 / b[3]);
+      gsl_vector_set (f, i, yi - rat43_F[i]);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rat43_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+          const gsl_vector * u, void * params, gsl_vector * v,
+          gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(rat43_J, rat43_N, rat43_P);
+  double b[rat43_P];
+  size_t i;
+
+  for (i = 0; i < rat43_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < rat43_N; i++)
+    {
+      double xi = i + 1.0;
+      double e = exp(b[1] - b[2]*xi);
+      double term1 = 1.0 + e;
+      double term2 = pow(term1, -1.0 / b[3]);
+
+      gsl_matrix_set (&J.matrix, i, 0, term2);
+      gsl_matrix_set (&J.matrix, i, 1, -b[0] / b[3] * e * term2 / term1);
+      gsl_matrix_set (&J.matrix, i, 2, b[0] / b[3] * xi * e * term2 / term1);
+      gsl_matrix_set (&J.matrix, i, 3, b[0] / b[3] / b[3] * log(term1) * term2);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf rat43_func =
+{
+  rat43_f,
+  rat43_df,
+  NULL, /* analytic expression too complex */
+  rat43_N,
+  rat43_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem rat43a_problem =
+{
+  "nist-rat43a",
+  rat43_x0a,
+  rat43_sigma,
+  &rat43_epsrel,
+  &rat43_checksol,
+  &rat43_func
+};
+
+static test_fdf_problem rat43b_problem =
+{
+  "nist-rat43b",
+  rat43_x0b,
+  rat43_sigma,
+  &rat43_epsrel,
+  &rat43_checksol,
+  &rat43_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_rosenbrock.c gsl-doc-2.3/multilarge_nlinear/test_rosenbrock.c
--- gsl-doc-1.16/multilarge_nlinear/test_rosenbrock.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_rosenbrock.c	2016-08-12 19:52:24.000000000 +0000
@@ -0,0 +1,102 @@
+#define rosenbrock_N         2
+#define rosenbrock_P         2
+
+static double rosenbrock_x0[rosenbrock_P] = { -1.2, 1.0 };
+static double rosenbrock_epsrel = 1.0e-12;
+
+static double rosenbrock_J[rosenbrock_N * rosenbrock_P];
+
+static void
+rosenbrock_checksol(const double x[], const double sumsq,
+                    const double epsrel, const char *sname,
+                    const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < rosenbrock_P; ++i)
+    {
+      gsl_test_rel(x[i], 1.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+rosenbrock_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, 10.0 * (x2 - x1*x1));
+  gsl_vector_set(f, 1, 1.0 - x1);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rosenbrock_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+               const gsl_vector * u, void * params, gsl_vector * v,
+               gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(rosenbrock_J, rosenbrock_N, rosenbrock_P);
+  double x1 = gsl_vector_get(x, 0);
+
+  gsl_matrix_set(&J.matrix, 0, 0, -20.0*x1);
+  gsl_matrix_set(&J.matrix, 0, 1, 10.0);
+  gsl_matrix_set(&J.matrix, 1, 0, -1.0);
+  gsl_matrix_set(&J.matrix, 1, 1, 0.0);
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rosenbrock_fvv (const gsl_vector * x, const gsl_vector * v,
+                void *params, gsl_vector * fvv)
+{
+  double v1 = gsl_vector_get(v, 0);
+
+  gsl_vector_set(fvv, 0, -20.0 * v1 * v1);
+  gsl_vector_set(fvv, 1, 0.0);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf rosenbrock_func =
+{
+  rosenbrock_f,
+  rosenbrock_df,
+  rosenbrock_fvv,
+  rosenbrock_N,
+  rosenbrock_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem rosenbrock_problem =
+{
+  "rosenbrock",
+  rosenbrock_x0,
+  NULL,
+  &rosenbrock_epsrel,
+  &rosenbrock_checksol,
+  &rosenbrock_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_rosenbrocke.c gsl-doc-2.3/multilarge_nlinear/test_rosenbrocke.c
--- gsl-doc-1.16/multilarge_nlinear/test_rosenbrocke.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_rosenbrocke.c	2016-08-12 19:52:27.000000000 +0000
@@ -0,0 +1,121 @@
+#define rosenbrocke_N         8 /* = p */
+#define rosenbrocke_P         8 /* must be even */
+
+static double rosenbrocke_x0[rosenbrocke_P] = { -1.2, 1.0, -1.2, 1.0,
+                                                -1.2, 1.0, -1.2, 1.0 };
+static double rosenbrocke_epsrel = 1.0e-12;
+
+static double rosenbrocke_J[rosenbrocke_N * rosenbrocke_P];
+
+static void
+rosenbrocke_checksol(const double x[], const double sumsq,
+                     const double epsrel, const char *sname,
+                     const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double rosenbrocke_x[rosenbrocke_P] = { 1.0, 1.0, 1.0, 1.0,
+                                                1.0, 1.0, 1.0, 1.0 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < rosenbrocke_P; ++i)
+    {
+      gsl_test_rel(x[i], rosenbrocke_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+rosenbrocke_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i;
+
+  for (i = 0; i < rosenbrocke_N / 2; ++i)
+    {
+      double x2i = gsl_vector_get(x, 2*i + 1);
+      double x2im1 = gsl_vector_get(x, 2*i);
+
+      gsl_vector_set(f, 2*i, 10.0 * (x2i - x2im1*x2im1));
+      gsl_vector_set(f, 2*i + 1, 1.0 - x2im1);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rosenbrocke_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+                const gsl_vector * u, void * params, gsl_vector * v,
+                gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(rosenbrocke_J, rosenbrocke_N, rosenbrocke_P);
+  size_t i;
+
+  gsl_matrix_set_zero(&J.matrix);
+
+  for (i = 0; i < rosenbrocke_N / 2; ++i)
+    {
+      double x2im1 = gsl_vector_get(x, 2*i);
+
+      gsl_matrix_set(&J.matrix, 2*i, 2*i, -20.0*x2im1);
+      gsl_matrix_set(&J.matrix, 2*i, 2*i + 1, 10.0);
+      gsl_matrix_set(&J.matrix, 2*i + 1, 2*i, -1.0);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+rosenbrocke_fvv (const gsl_vector * x, const gsl_vector * v,
+                 void *params, gsl_vector * fvv)
+{
+  size_t i;
+
+  for (i = 0; i < rosenbrocke_N / 2; ++i)
+    {
+      double v2im1 = gsl_vector_get(v, 2*i);
+
+      gsl_vector_set(fvv, 2*i, -20.0 * v2im1 * v2im1);
+      gsl_vector_set(fvv, 2*i + 1, 0.0);
+    }
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf rosenbrocke_func =
+{
+  rosenbrocke_f,
+  rosenbrocke_df,
+  rosenbrocke_fvv,
+  rosenbrocke_N,
+  rosenbrocke_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem rosenbrocke_problem =
+{
+  "rosenbrock_extended",
+  rosenbrocke_x0,
+  NULL,
+  &rosenbrocke_epsrel,
+  &rosenbrocke_checksol,
+  &rosenbrocke_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_roth.c gsl-doc-2.3/multilarge_nlinear/test_roth.c
--- gsl-doc-1.16/multilarge_nlinear/test_roth.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_roth.c	2016-08-12 19:52:30.000000000 +0000
@@ -0,0 +1,118 @@
+#define roth_N         2
+#define roth_P         2
+
+static double roth_x0[roth_P] = { 0.5, -2.0 };
+static double roth_epsrel = 1.0e-7;
+
+static double roth_J[roth_N * roth_P];
+
+static void
+roth_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact1 = 0.0;
+  const double roth_x1[roth_P] = { 5.0, 4.0 };
+  const double sumsq_exact2 = 48.9842536792400;
+  const double roth_x2[roth_P] = { 11.4127789869021, -0.896805253274477 };
+  const double *roth_x;
+  double sumsq_exact;
+
+  if (fabs(sumsq) < 0.1)
+    {
+      sumsq_exact = sumsq_exact1;
+      roth_x = roth_x1;
+    }
+  else
+    {
+      sumsq_exact = sumsq_exact2;
+      roth_x = roth_x2;
+    }
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < roth_P; ++i)
+    {
+      gsl_test_rel(x[i], roth_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+roth_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_vector_set(f, 0, x1 - x2*(2.0 - x2*(5.0 - x2)) - 13.0);
+  gsl_vector_set(f, 1, x1 - x2*(14.0 - x2*(1.0 + x2)) - 29.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+roth_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+         const gsl_vector * u, void * params, gsl_vector * v,
+         gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(roth_J, roth_N, roth_P);
+  double x2 = gsl_vector_get(x, 1);
+
+  gsl_matrix_set(&J.matrix, 0, 0, 1.0);
+  gsl_matrix_set(&J.matrix, 0, 1, -2.0 + x2*(10.0 - 3.0*x2));
+  gsl_matrix_set(&J.matrix, 1, 0, 1.0);
+  gsl_matrix_set(&J.matrix, 1, 1, -14.0 + x2*(2.0 + 3.0*x2));
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+roth_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  double x2 = gsl_vector_get(x, 1);
+  double v2 = gsl_vector_get(v, 1);
+
+  gsl_vector_set(fvv, 0, (10.0 - 6.0*x2) * v2 * v2);
+  gsl_vector_set(fvv, 1, (2.0 + 6.0*x2) * v2 * v2);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf roth_func =
+{
+  roth_f,
+  roth_df,
+  roth_fvv,
+  roth_N,
+  roth_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem roth_problem =
+{
+  "roth_freudenstein",
+  roth_x0,
+  NULL,
+  &roth_epsrel,
+  &roth_checksol,
+  &roth_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_thurber.c gsl-doc-2.3/multilarge_nlinear/test_thurber.c
--- gsl-doc-1.16/multilarge_nlinear/test_thurber.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_thurber.c	2016-08-12 19:52:33.000000000 +0000
@@ -0,0 +1,161 @@
+#define thurber_N       37
+#define thurber_P       7
+
+static double thurber_x0a[thurber_P] = { 1000.0, 1000.0, 400.0, 40.0,
+                                         0.7, 0.3, 0.03 };
+static double thurber_x0b[thurber_P] = { 1300.0, 1500.0, 500.0, 75.0,
+                                         1.0, 0.4, 0.05 };
+static double thurber_epsrel = 1.0e-6;
+
+static double thurber_J[thurber_N * thurber_P];
+
+static double thurber_sigma[thurber_P] = {
+  4.6647963344E+00, 3.9571156086E+01, 2.8698696102E+01,
+  5.5675370270E+00, 3.1333340687E-02, 1.4984928198E-02,
+  6.5842344623E-03
+};
+
+static double thurber_X[thurber_N] = {
+  -3.067, -2.981, -2.921, -2.912, -2.840, -2.797, -2.702,
+  -2.699, -2.633, -2.481, -2.363, -2.322, -1.501, -1.460,
+  -1.274, -1.212, -1.100, -1.046, -0.915, -0.714, -0.566,
+  -0.545, -0.400, -0.309, -0.109, -0.103, 0.010, 0.119,
+  0.377, 0.790, 0.963, 1.006, 1.115, 1.572, 1.841,
+  2.047, 2.200
+};
+
+static double thurber_F[thurber_N] = {
+  80.574, 84.248, 87.264, 87.195, 89.076, 89.608, 89.868, 90.101,
+  92.405, 95.854, 100.696, 101.060, 401.672, 390.724, 567.534,
+  635.316, 733.054, 759.087, 894.206, 990.785, 1090.109, 1080.914,
+  1122.643, 1178.351, 1260.531, 1273.514, 1288.339, 1327.543, 1353.863,
+  1414.509, 1425.208, 1421.384, 1442.962, 1464.350, 1468.705,
+  1447.894, 1457.628
+};
+
+static void
+thurber_checksol(const double x[], const double sumsq,
+                 const double epsrel, const char *sname,
+                 const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 5.6427082397E+03;
+  const double thurber_x[thurber_P] = {
+    1.2881396800E+03, 1.4910792535E+03, 5.8323836877E+02,
+    7.5416644291E+01, 9.6629502864E-01, 3.9797285797E-01,
+    4.9727297349E-02 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < thurber_P; ++i)
+    {
+      gsl_test_rel(x[i], thurber_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+
+static int
+thurber_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double b[thurber_P];
+  size_t i;
+
+  for (i = 0; i < thurber_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < thurber_N; i++)
+    {
+      double xi = thurber_X[i];
+      double yi;
+
+      yi = b[0] + b[1]*xi + b[2]*xi*xi + b[3]*xi*xi*xi;
+      yi /= 1.0 + b[4]*xi + b[5]*xi*xi + b[6]*xi*xi*xi;
+
+      gsl_vector_set (f, i, yi - thurber_F[i]);
+    }
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+thurber_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+            const gsl_vector * u, void * params, gsl_vector * v,
+            gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(thurber_J, thurber_N, thurber_P);
+  double b[thurber_P];
+  size_t i;
+
+  for (i = 0; i < thurber_P; i++)
+    {
+      b[i] = gsl_vector_get(x, i);
+    }
+
+  for (i = 0; i < thurber_N; i++)
+    {
+      double xi = thurber_X[i];
+      double d, n, d_sq;
+
+      n = b[0] + b[1]*xi + b[2]*xi*xi + b[3]*xi*xi*xi;
+      d = 1.0 + b[4]*xi + b[5]*xi*xi + b[6]*xi*xi*xi;
+      d_sq = d * d;
+
+      gsl_matrix_set (&J.matrix, i, 0, 1.0 / d);
+      gsl_matrix_set (&J.matrix, i, 1, xi / d);
+      gsl_matrix_set (&J.matrix, i, 2, (xi * xi) / d);
+      gsl_matrix_set (&J.matrix, i, 3, (xi * xi * xi) / d);
+      gsl_matrix_set (&J.matrix, i, 4, -xi * n / d_sq);
+      gsl_matrix_set (&J.matrix, i, 5, -xi * xi * n / d_sq);
+      gsl_matrix_set (&J.matrix, i, 6, -xi * xi * xi * n / d_sq);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf thurber_func =
+{
+  thurber_f,
+  thurber_df,
+  NULL, /* analytic expression too complex */
+  thurber_N,
+  thurber_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem thurbera_problem =
+{
+  "nist-thurbera",
+  thurber_x0a,
+  thurber_sigma,
+  &thurber_epsrel,
+  &thurber_checksol,
+  &thurber_func
+};
+
+static test_fdf_problem thurberb_problem =
+{
+  "nist-thurberb",
+  thurber_x0b,
+  thurber_sigma,
+  &thurber_epsrel,
+  &thurber_checksol,
+  &thurber_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_vardim.c gsl-doc-2.3/multilarge_nlinear/test_vardim.c
--- gsl-doc-1.16/multilarge_nlinear/test_vardim.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_vardim.c	2016-08-12 19:52:36.000000000 +0000
@@ -0,0 +1,130 @@
+#define vardim_N         7 /* p + 2 */
+#define vardim_P         5
+
+static double vardim_x0[vardim_P] = { 0.8, 0.6, 0.4, 0.2, 0.0 };
+static double vardim_epsrel = 1.0e-12;
+
+static double vardim_J[vardim_N * vardim_P];
+
+static void
+vardim_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      gsl_test_rel(x[i], 1.0, epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+vardim_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  size_t i;
+  double sum = 0.0;
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+
+      gsl_vector_set(f, i, xi - 1.0);
+
+      sum += (i + 1.0) * (xi - 1.0);
+    }
+
+  gsl_vector_set(f, vardim_P, sum);
+  gsl_vector_set(f, vardim_P + 1, sum*sum);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+vardim_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+           const gsl_vector * u, void * params, gsl_vector * v,
+           gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(vardim_J, vardim_N, vardim_P);
+  size_t i;
+  double sum = 0.0;
+  gsl_matrix_view m = gsl_matrix_submatrix(&J.matrix, 0, 0, vardim_P, vardim_P);
+
+  gsl_matrix_set_identity(&m.matrix);
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      double xi = gsl_vector_get(x, i);
+      sum += (i + 1.0) * (xi - 1.0);
+    }
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      gsl_matrix_set(&J.matrix, vardim_P, i, i + 1.0);
+      gsl_matrix_set(&J.matrix, vardim_P + 1, i, 2*(i + 1.0)*sum);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+vardim_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  size_t i;
+  double sum = 0.0;
+
+  gsl_vector_set_zero(fvv);
+
+  for (i = 0; i < vardim_P; ++i)
+    {
+      double vi = gsl_vector_get(v, i);
+      sum += (i + 1.0) * vi;
+    }
+
+  gsl_vector_set(fvv, vardim_N - 1, 2.0 * sum * sum);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf vardim_func =
+{
+  vardim_f,
+  vardim_df,
+  vardim_fvv,
+  vardim_N,
+  vardim_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem vardim_problem =
+{
+  "vardim",
+  vardim_x0,
+  NULL,
+  &vardim_epsrel,
+  &vardim_checksol,
+  &vardim_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_watson.c gsl-doc-2.3/multilarge_nlinear/test_watson.c
--- gsl-doc-1.16/multilarge_nlinear/test_watson.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_watson.c	2016-08-12 19:52:40.000000000 +0000
@@ -0,0 +1,173 @@
+#define watson_N         31
+#define watson_P         6
+
+static double watson_x0[watson_P] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+static double watson_epsrel = 1.0e-6;
+
+static double watson_J[watson_N * watson_P];
+
+static void
+watson_checksol(const double x[], const double sumsq,
+                const double epsrel, const char *sname,
+                const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 2.287670053552372e-03;
+  const double watson_x[watson_P] = {
+    -1.572508640629858e-02,  1.012434869366059e+00, -2.329916259263380e-01,
+     1.260430087686035e+00, -1.513728922580576e+00,  9.929964323646112e-01 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < watson_P; ++i)
+    {
+      gsl_test_rel(x[i], watson_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+watson_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  const double x1 = gsl_vector_get(x, 0);
+  const double x2 = gsl_vector_get(x, 1);
+  size_t i, j;
+
+  for (i = 0; i < watson_N - 2; ++i)
+    {
+      double ti = (i + 1) / 29.0;
+      double tjm1 = 1.0, tjm2 = 1.0;
+      double sum1 = 0.0, sum2 = 0.0;
+
+      for (j = 0; j < watson_P; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+
+          sum1 += xj * tjm1;
+          tjm1 *= ti;
+
+          if (j > 0)
+            {
+              sum2 += j * xj * tjm2;
+              tjm2 *= ti;
+            }
+        }
+
+      gsl_vector_set (f, i, sum2 - sum1*sum1 - 1.0);
+    }
+
+  gsl_vector_set(f, watson_N - 2, x1);
+  gsl_vector_set(f, watson_N - 1, x2 - x1*x1 - 1.0);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+watson_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+           const gsl_vector * u, void * params, gsl_vector * v,
+           gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(watson_J, watson_N, watson_P);
+  double x1 = gsl_vector_get (x, 0);
+  size_t i, j;
+
+  gsl_matrix_set_zero(&J.matrix);
+
+  for (i = 0; i < watson_N - 2; ++i)
+    {
+      double ti = (i + 1) / 29.0;
+      double tjm1 = 1.0, tjm2 = 1.0;
+      double sum1 = 0.0;
+
+      for (j = 0; j < watson_P; ++j)
+        {
+          double xj = gsl_vector_get(x, j);
+          sum1 += xj * tjm1;
+          tjm1 *= ti;
+        }
+
+      tjm1 = 1.0;
+      tjm2 = 1.0;
+      for (j = 0; j < watson_P; ++j)
+        {
+          gsl_matrix_set(&J.matrix, i, j, j * tjm2 - 2.0*sum1*tjm1);
+          tjm1 *= ti;
+
+          if (j > 0)
+            tjm2 *= ti;
+        }
+    }
+
+  gsl_matrix_set(&J.matrix, watson_N - 2, 0, 1.0);
+  gsl_matrix_set(&J.matrix, watson_N - 1, 0, -2.0*x1);
+  gsl_matrix_set(&J.matrix, watson_N - 1, 1, 1.0);
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+watson_fvv (const gsl_vector * x, const gsl_vector * v,
+            void *params, gsl_vector * fvv)
+{
+  double v1 = gsl_vector_get (v, 0);
+  size_t i, j;
+
+  for (i = 0; i < watson_N - 2; ++i)
+    {
+      double ti = (i + 1) / 29.0;
+      double sum = 0.0;
+      double tjm1 = 1.0;
+
+      for (j = 0; j < watson_P; ++j)
+        {
+          double vj = gsl_vector_get(v, j);
+          sum += vj * tjm1;
+          tjm1 *= ti;
+        }
+
+      gsl_vector_set(fvv, i, -2.0*sum*sum);
+    }
+
+  gsl_vector_set(fvv, watson_N - 2, 0.0);
+  gsl_vector_set(fvv, watson_N - 1, -2.0*v1*v1);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf watson_func =
+{
+  watson_f,
+  watson_df,
+  watson_fvv,
+  watson_N,
+  watson_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem watson_problem =
+{
+  "watson",
+  watson_x0,
+  NULL,
+  &watson_epsrel,
+  &watson_checksol,
+  &watson_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_wnlin.c gsl-doc-2.3/multilarge_nlinear/test_wnlin.c
--- gsl-doc-1.16/multilarge_nlinear/test_wnlin.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_wnlin.c	2016-08-19 17:44:50.000000000 +0000
@@ -0,0 +1,155 @@
+#define wnlin_N         40
+#define wnlin_P         3
+
+static double wnlin_x0[wnlin_P] = { 1.0, 0.9, 0.0 };
+static double wnlin_epsrel = 1.0e-8;
+
+static double wnlin_J[wnlin_N * wnlin_P];
+
+/* data */
+static double wnlin_Y[wnlin_N] = {
+  6.08035e+00, 5.47552e+00, 5.94654e+00, 5.04920e+00, 4.78568e+00,
+  3.51748e+00, 2.84671e+00, 3.24634e+00, 3.23395e+00, 3.30385e+00,
+  2.83439e+00, 2.31891e+00, 2.33858e+00, 2.40559e+00, 2.41856e+00,
+  1.99966e+00, 1.88127e+00, 1.91477e+00, 1.70415e+00, 1.60316e+00,
+  1.77937e+00, 1.55302e+00, 1.50903e+00, 1.36364e+00, 1.36873e+00,
+  1.41954e+00, 1.37778e+00, 1.23573e+00, 1.28524e+00, 1.46327e+00,
+  1.22315e+00, 1.19330e+00, 1.18717e+00, 8.83172e-01, 1.23424e+00,
+  1.14683e+00, 1.11091e+00, 1.20396e+00, 1.28722e+00, 1.05801e+00
+};
+
+/* weights */
+static double wnlin_W[wnlin_N] = {
+  2.77778e+00, 3.27690e+00, 3.85426e+00, 4.51906e+00, 5.28083e+00,
+  6.14919e+00, 7.13370e+00, 8.24349e+00, 9.48703e+00, 1.08717e+01,
+  1.24036e+01, 1.40869e+01, 1.59238e+01, 1.79142e+01, 2.00553e+01,
+  2.23415e+01, 2.47646e+01, 2.73137e+01, 2.99753e+01, 3.27337e+01,
+  3.55714e+01, 3.84696e+01, 4.14085e+01, 4.43678e+01, 4.73278e+01,
+  5.02690e+01, 5.31731e+01, 5.60234e+01, 5.88046e+01, 6.15036e+01,
+  6.41092e+01, 6.66121e+01, 6.90054e+01, 7.12839e+01, 7.34442e+01,
+  7.54848e+01, 7.74053e+01, 7.92069e+01, 8.08918e+01, 8.24632e+01
+};
+
+static void
+wnlin_checksol(const double x[], const double sumsq,
+               const double epsrel, const char *sname,
+               const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 29.7481259665713758;
+  const double wnlin_x[wnlin_P] = { 5.17378551196259195,
+                                    0.111041758006851149,
+                                    1.05282724070446099 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < wnlin_P; ++i)
+    {
+      gsl_test_rel(x[i], wnlin_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+wnlin_f (const gsl_vector *x, void *params, gsl_vector *f)
+{
+  double A = gsl_vector_get (x, 0);
+  double lambda = gsl_vector_get (x, 1);
+  double b = gsl_vector_get (x, 2);
+  size_t i;
+
+  /* model Yi = A * exp(-lambda * i) + b */
+  for (i = 0; i < wnlin_N; i++)
+    {
+      double ti = i;
+      double yi = wnlin_Y[i];
+      double swi = sqrt(wnlin_W[i]);
+      double Mi = A * exp (-lambda * ti) + b;
+
+      gsl_vector_set (f, i, swi * (Mi - yi));
+    }
+
+  return GSL_SUCCESS;
+}
+
+static int
+wnlin_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+          const gsl_vector * u, void * params, gsl_vector * v,
+          gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(wnlin_J, wnlin_N, wnlin_P);
+  double A = gsl_vector_get (x, 0);
+  double lambda = gsl_vector_get (x, 1);
+  size_t i;
+
+  for (i = 0; i < wnlin_N; i++)
+    {
+      gsl_vector_view v = gsl_matrix_row(&J.matrix, i);
+      double ti = i;
+      double swi = sqrt(wnlin_W[i]);
+      double e = exp(-lambda * ti);
+
+      gsl_vector_set(&v.vector, 0, e);
+      gsl_vector_set(&v.vector, 1, -ti * A * e);
+      gsl_vector_set(&v.vector, 2, 1.0);
+
+      gsl_vector_scale(&v.vector, swi);
+    }
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  return GSL_SUCCESS;
+}
+
+static int
+wnlin_fvv (const gsl_vector * x, const gsl_vector * v,
+           void *params, gsl_vector * fvv)
+{
+  double A = gsl_vector_get (x, 0);
+  double lambda = gsl_vector_get (x, 1);
+  double v1 = gsl_vector_get(v, 0);
+  double v2 = gsl_vector_get(v, 1);
+  size_t i;
+
+  for (i = 0; i < wnlin_N; i++)
+    {
+      double ti = i;
+      double swi = sqrt(wnlin_W[i]);
+      double fvvi;
+
+      fvvi = exp(-ti*lambda)*ti*v2 * (-2*v1 + ti*v2*A);
+
+      gsl_vector_set(fvv, i, swi * fvvi);
+    }
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf wnlin_func1 =
+{
+  wnlin_f,
+  wnlin_df,
+  wnlin_fvv,
+  wnlin_N,
+  wnlin_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem wnlin_problem1 =
+{
+  "wnlin_internal_weights",
+  wnlin_x0,
+  NULL,
+  &wnlin_epsrel,
+  &wnlin_checksol,
+  &wnlin_func1
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/test_wood.c gsl-doc-2.3/multilarge_nlinear/test_wood.c
--- gsl-doc-1.16/multilarge_nlinear/test_wood.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/test_wood.c	2016-08-12 19:52:46.000000000 +0000
@@ -0,0 +1,126 @@
+#define wood_N         6
+#define wood_P         4
+
+static double wood_x0[wood_P] = { -3.0, -1.0, -3.0, -1.0 };
+static double wood_epsrel = 1.0e-12;
+
+static double wood_J[wood_N * wood_P];
+
+static void
+wood_checksol(const double x[], const double sumsq,
+              const double epsrel, const char *sname,
+              const char *pname)
+{
+  size_t i;
+  const double sumsq_exact = 0.0;
+  const double wood_x[wood_P] = { 1.0, 1.0, 1.0, 1.0 };
+
+  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
+               sname, pname);
+
+  for (i = 0; i < wood_P; ++i)
+    {
+      gsl_test_rel(x[i], wood_x[i], epsrel, "%s/%s i=%zu",
+                   sname, pname, i);
+    }
+}
+
+static int
+wood_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+  double x1 = gsl_vector_get(x, 0);
+  double x2 = gsl_vector_get(x, 1);
+  double x3 = gsl_vector_get(x, 2);
+  double x4 = gsl_vector_get(x, 3);
+
+  gsl_vector_set(f, 0, 10.0*(x2 - x1*x1));
+  gsl_vector_set(f, 1, 1.0 - x1);
+  gsl_vector_set(f, 2, sqrt(90.0)*(x4 - x3*x3));
+  gsl_vector_set(f, 3, 1.0 - x3);
+  gsl_vector_set(f, 4, sqrt(10.0)*(x2 + x4 - 2.0));
+  gsl_vector_set(f, 5, (x2 - x4) / sqrt(10.0));
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+wood_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
+         const gsl_vector * u, void * params, gsl_vector * v,
+         gsl_matrix * JTJ)
+{
+  gsl_matrix_view J = gsl_matrix_view_array(wood_J, wood_N, wood_P);
+  double x1 = gsl_vector_get(x, 0);
+  double x3 = gsl_vector_get(x, 2);
+  double s90 = sqrt(90.0);
+  double s10 = sqrt(10.0);
+
+  gsl_matrix_set_zero(&J.matrix);
+
+  gsl_matrix_set(&J.matrix, 0, 0, -20.0*x1);
+  gsl_matrix_set(&J.matrix, 0, 1, 10.0);
+  gsl_matrix_set(&J.matrix, 1, 0, -1.0);
+  gsl_matrix_set(&J.matrix, 2, 2, -2.0*s90*x3);
+  gsl_matrix_set(&J.matrix, 2, 3, s90);
+  gsl_matrix_set(&J.matrix, 3, 2, -1.0);
+  gsl_matrix_set(&J.matrix, 4, 1, s10);
+  gsl_matrix_set(&J.matrix, 4, 3, s10);
+  gsl_matrix_set(&J.matrix, 5, 1, 1.0/s10);
+  gsl_matrix_set(&J.matrix, 5, 3, -1.0/s10);
+
+  if (v)
+    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
+
+  if (JTJ)
+    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
+
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static int
+wood_fvv (const gsl_vector * x, const gsl_vector * v,
+          void *params, gsl_vector * fvv)
+{
+  const double s10 = sqrt(10.0);
+  double v1 = gsl_vector_get(v, 0);
+  double v3 = gsl_vector_get(v, 2);
+
+  gsl_vector_set(fvv, 0, -20.0 * v1 * v1);
+  gsl_vector_set(fvv, 1, 0.0);
+  gsl_vector_set(fvv, 2, -6.0 * s10 * v3 * v3);
+  gsl_vector_set(fvv, 3, 0.0);
+  gsl_vector_set(fvv, 4, 0.0);
+  gsl_vector_set(fvv, 5, 0.0);
+
+  (void)x;      /* avoid unused parameter warning */
+  (void)params; /* avoid unused parameter warning */
+
+  return GSL_SUCCESS;
+}
+
+static gsl_multilarge_nlinear_fdf wood_func =
+{
+  wood_f,
+  wood_df,
+  wood_fvv,
+  wood_N,
+  wood_P,
+  NULL,
+  0,
+  0,
+  0,
+  0
+};
+
+static test_fdf_problem wood_problem =
+{
+  "wood",
+  wood_x0,
+  NULL,
+  &wood_epsrel,
+  &wood_checksol,
+  &wood_func
+};
diff -Nru gsl-doc-1.16/multilarge_nlinear/TODO gsl-doc-2.3/multilarge_nlinear/TODO
--- gsl-doc-1.16/multilarge_nlinear/TODO	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/TODO	2016-11-16 15:38:35.000000000 +0000
@@ -0,0 +1,3 @@
+1. finite difference J and fvv for cholesky solver
+2. Fix biggs test x0 and dogleg / ddogleg convergence issue
+3. add subspaced2D to multilarge example output in docs
diff -Nru gsl-doc-1.16/multilarge_nlinear/trust.c gsl-doc-2.3/multilarge_nlinear/trust.c
--- gsl-doc-1.16/multilarge_nlinear/trust.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/multilarge_nlinear/trust.c	2016-08-19 17:02:40.000000000 +0000
@@ -0,0 +1,569 @@
+/* multilarge_nlinear/trust.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_multilarge_nlinear.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_permutation.h>
+
+#include "common.c"
+#include "nielsen.c"
+
+/*
+ * This module contains a high level driver for a general trust
+ * region nonlinear least squares solver. This container handles
+ * the computation of all of the quantities relevant to all trust
+ * region methods, including:
+ *
+ * residual vector: f_k = f(x_k)
+ * Jacobian matrix: J_k = J(x_k)
+ * gradient vector: g_k = J_k^T f_k
+ * scaling matrix:  D_k
+ */
+
+typedef struct
+{
+  size_t n;                  /* number of observations */
+  size_t p;                  /* number of parameters */
+  double delta;              /* trust region radius */
+  double mu;                 /* LM parameter */
+  long nu;                   /* for updating LM parameter */
+  gsl_vector *diag;          /* D = diag(J^T J) */
+  gsl_vector *x_trial;       /* trial parameter vector */
+  gsl_vector *f_trial;       /* trial function vector */
+  gsl_vector *workn;         /* workspace, length n */
+
+  void *trs_state;           /* workspace for trust region subproblem */
+  void *solver_state;        /* workspace for linear least squares solver */
+
+  double avratio;            /* current |a| / |v| */
+
+  /* tunable parameters */
+  gsl_multilarge_nlinear_parameters params;
+} trust_state_t;
+
+static void * trust_alloc (const gsl_multilarge_nlinear_parameters * params,
+                           const size_t n, const size_t p);
+static void trust_free(void *vstate);
+static int trust_init(void *vstate, const gsl_vector * swts,
+                      gsl_multilarge_nlinear_fdf *fdf, const gsl_vector *x,
+                      gsl_vector *f, gsl_vector *g, gsl_matrix *JTJ);
+static int trust_iterate(void *vstate, const gsl_vector *swts,
+                         gsl_multilarge_nlinear_fdf *fdf,
+                         gsl_vector *x, gsl_vector *f,
+                         gsl_vector *g, gsl_matrix *JTJ, gsl_vector *dx);
+static int trust_rcond(double * rcond, const gsl_matrix * JTJ, void * vstate);
+static int trust_covar(const gsl_matrix * JTJ, gsl_matrix * covar, void * vstate);
+static double trust_avratio(void *vstate);
+static void trust_trial_step(const gsl_vector * x, const gsl_vector * dx,
+                             gsl_vector * x_trial);
+static double trust_calc_rho(const gsl_multilarge_nlinear_trust_state * trust_state,
+                             const gsl_vector * f_trial, const gsl_vector * dx,
+                             trust_state_t * state);
+static int trust_eval_step(const gsl_multilarge_nlinear_trust_state * trust_state,
+                           const gsl_vector * f_trial, const gsl_vector * dx,
+                           double * rho, trust_state_t * state);
+static double trust_scaled_norm(const gsl_vector *D, const gsl_vector *a);
+
+static void *
+trust_alloc (const gsl_multilarge_nlinear_parameters * params,
+             const size_t n, const size_t p)
+{
+  trust_state_t *state;
+  
+  state = calloc(1, sizeof(trust_state_t));
+  if (state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate lm state", GSL_ENOMEM);
+    }
+
+  state->diag = gsl_vector_alloc(p);
+  if (state->diag == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for diag", GSL_ENOMEM);
+    }
+
+  state->workn = gsl_vector_alloc(n);
+  if (state->workn == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workn", GSL_ENOMEM);
+    }
+
+  state->x_trial = gsl_vector_alloc(p);
+  if (state->x_trial == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for x_trial", GSL_ENOMEM);
+    }
+
+  state->f_trial = gsl_vector_alloc(n);
+  if (state->f_trial == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for f_trial", GSL_ENOMEM);
+    }
+
+  state->trs_state = (params->trs->alloc)(params, n, p);
+  if (state->trs_state == NULL)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for trs state", GSL_ENOMEM);
+    }
+
+  if (params->solver != gsl_multilarge_nlinear_solver_none)
+    {
+      state->solver_state = (params->solver->alloc)(n, p);
+      if (state->solver_state == NULL)
+        {
+          GSL_ERROR_NULL ("failed to allocate space for solver state", GSL_ENOMEM);
+        }
+    }
+
+  state->n = n;
+  state->p = p;
+  state->delta = 0.0;
+  state->params = *params;
+
+  return state;
+}
+
+static void
+trust_free(void *vstate)
+{
+  trust_state_t *state = (trust_state_t *) vstate;
+  const gsl_multilarge_nlinear_parameters *params = &(state->params);
+
+  if (state->diag)
+    gsl_vector_free(state->diag);
+
+  if (state->workn)
+    gsl_vector_free(state->workn);
+
+  if (state->x_trial)
+    gsl_vector_free(state->x_trial);
+
+  if (state->f_trial)
+    gsl_vector_free(state->f_trial);
+
+  if (state->trs_state)
+    (params->trs->free)(state->trs_state);
+
+  if (state->solver_state)
+    (params->solver->free)(state->solver_state);
+
+  free(state);
+}
+
+/*
+trust_init()
+  Initialize trust region solver
+
+Inputs: vstate - workspace
+        swts   - sqrt(W) vector
+        fdf    - user callback functions
+        x      - initial parameter values
+        f      - (output) f(x) vector
+        g      - (output) J(x)' f(x) vector
+
+Return: success/error
+*/
+
+static int
+trust_init(void *vstate, const gsl_vector *swts,
+           gsl_multilarge_nlinear_fdf *fdf, const gsl_vector *x,
+           gsl_vector *f, gsl_vector *g, gsl_matrix *JTJ)
+{
+  int status;
+  trust_state_t *state = (trust_state_t *) vstate;
+  const gsl_multilarge_nlinear_parameters *params = &(state->params);
+  double Dx;
+
+  /* evaluate function and Jacobian at x and apply weight transform */
+  status = gsl_multilarge_nlinear_eval_f(fdf, x, swts, f);
+  if (status)
+   return status;
+
+  /* compute g = J^T f and J^T J */
+  status = gsl_multilarge_nlinear_eval_df(CblasTrans, x, f, f,
+                                          swts, params->h_df, params->fdtype,
+                                          fdf, g, JTJ, state->workn);
+  if (status)
+    return status;
+
+  /* initialize diagonal scaling matrix D */
+  if (JTJ != NULL)
+    (params->scale->init)(JTJ, state->diag);
+  else
+    gsl_vector_set_all(state->diag, 1.0);
+
+  /* compute initial trust region radius */
+  Dx = trust_scaled_norm(state->diag, x);
+  state->delta = 0.3 * GSL_MAX(1.0, Dx);
+
+  /* initialize LM parameter */
+  nielsen_init(JTJ, state->diag, &(state->mu), &(state->nu));
+
+  /* initialize trust region method solver */
+  {
+    const gsl_multilarge_nlinear_trust_state trust_state = { x, f, g, JTJ, state->diag,
+                                                             swts, &(state->mu), params,
+                                                             state->solver_state, fdf,
+                                                             &(state->avratio) };
+
+    status = (params->trs->init)(&trust_state, state->trs_state);
+
+    if (status)
+      return status;
+  }
+
+  /* set default parameters */
+
+  state->avratio = 0.0;
+
+  return GSL_SUCCESS;
+}
+
+/*
+trust_iterate()
+  This function performs 1 iteration of the trust region algorithm.
+It calls a user-specified method for computing the next step
+(LM or dogleg), then tests if the computed step is acceptable.
+
+Args: vstate - trust workspace
+      swts   - data weights (NULL if unweighted)
+      fdf    - function and Jacobian pointers
+      x      - on input, current parameter vector
+               on output, new parameter vector x + dx
+      f      - on input, f(x)
+               on output, f(x + dx)
+      g      - on input, g(x) = J(x)' f(x)
+               on output, g(x + dx) = J(x + dx)' f(x + dx)
+      JTJ    - on input, J(x)^T J(x)
+               on output, J(x + dx)^T J(x + dx)
+      dx     - (output only) parameter step vector
+
+Return:
+1) GSL_SUCCESS if we found a step which reduces the cost
+function
+
+2) GSL_ENOPROG if 15 successive attempts were to made to
+find a good step without success
+
+3) If a scaling matrix D is used, inputs and outputs are
+set to the unscaled quantities (ie: J and g)
+*/
+
+static int
+trust_iterate(void *vstate, const gsl_vector *swts,
+              gsl_multilarge_nlinear_fdf *fdf, gsl_vector *x,
+              gsl_vector *f, gsl_vector *g, gsl_matrix *JTJ,
+              gsl_vector *dx)
+{
+  int status;
+  trust_state_t *state = (trust_state_t *) vstate;
+  const gsl_multilarge_nlinear_parameters *params = &(state->params);
+  const gsl_multilarge_nlinear_trs *trs = params->trs;
+
+  /* collect all state parameters needed by low level methods */
+  const gsl_multilarge_nlinear_trust_state trust_state = { x, f, g, JTJ, state->diag,
+                                                         swts, &(state->mu), params,
+                                                         state->solver_state, fdf,
+                                                         &(state->avratio) };
+
+  gsl_vector *x_trial = state->x_trial;       /* trial x + dx */
+  gsl_vector *f_trial = state->f_trial;       /* trial f(x + dx) */
+  double rho;                                 /* ratio actual_reduction/predicted_reduction */
+  int foundstep = 0;                          /* found step dx */
+  int bad_steps = 0;                          /* consecutive rejected steps */
+
+  /* initialize trust region subproblem with this Jacobian */
+  status = (trs->preloop)(&trust_state, state->trs_state);
+  if (status)
+    return status;
+
+  /* loop until we find an acceptable step dx */
+  while (!foundstep)
+    {
+      /* calculate new step */
+      status = (trs->step)(&trust_state, state->delta, dx, state->trs_state);
+
+      /* occasionally the iterative methods (ie: CG Steihaug) can fail to find a step,
+       * so in this case skip rho calculation and count it as a rejected step */
+
+      if (status == GSL_SUCCESS)
+        {
+          /* compute x_trial = x + dx */
+          trust_trial_step(x, dx, x_trial);
+
+          /* compute f_trial = f(x + dx) */
+          status = gsl_multilarge_nlinear_eval_f(fdf, x_trial, swts, f_trial);
+          if (status)
+            return status;
+
+          /* check if step should be accepted or rejected */
+          status = trust_eval_step(&trust_state, f_trial, dx, &rho, state);
+          if (status == GSL_SUCCESS)
+            foundstep = 1;
+
+#if 0 /*XXX*/
+          fprintf(stdout, "delta = %.12e |D dx| = %.12e |dx| = %.12e, dx0 = %.12e dx1 = %.12e |x_trial| = %.12e |f_trial| = %.12e rho = %.12e\n",
+                  state->delta,
+                  scaled_enorm(state->diag, dx),
+                  gsl_blas_dnrm2(dx),
+                  gsl_vector_get(dx, 0),
+                  gsl_vector_get(dx, 1),
+                  gsl_blas_dnrm2(x_trial),
+                  gsl_blas_dnrm2(f_trial),
+                  rho);
+#endif
+        }
+      else
+        {
+          /* an iterative TRS method failed to find a step vector */
+          rho = -1.0;
+        }
+
+      /*
+       * update trust region radius: if rho is large,
+       * then the quadratic model is a good approximation
+       * to the objective function, enlarge trust region.
+       * If rho is small (or negative), the model function
+       * is a poor approximation so decrease trust region. This
+       * can happen even if the step is accepted.
+       */
+      if (rho > 0.75)
+        state->delta *= params->factor_up;
+      else if (rho < 0.25)
+        state->delta /= params->factor_down;
+
+      if (foundstep)
+        {
+          /* step was accepted */
+
+          /* update x <- x + dx */
+          gsl_vector_memcpy(x, x_trial);
+
+          /* update f <- f(x + dx) */
+          gsl_vector_memcpy(f, f_trial);
+
+          /* compute new g = J^T f and J^T J */
+          status = gsl_multilarge_nlinear_eval_df(CblasTrans, x, f, f,
+                                                  swts, params->h_df, params->fdtype,
+                                                  fdf, g, JTJ, state->workn);
+          if (status)
+            return status;
+
+          /* update scaling matrix D */
+          if (JTJ != NULL)
+            (params->scale->update)(JTJ, state->diag);
+
+          /* step accepted, decrease LM parameter */
+          nielsen_accept(rho, &(state->mu), &(state->nu));
+
+          bad_steps = 0;
+        }
+      else
+        {
+          /* step rejected, increase LM parameter */
+          nielsen_reject(&(state->mu), &(state->nu));
+
+          /* if more than 15 consecutive rejected steps, report no progress */
+          if (++bad_steps > 15)
+            {
+              return GSL_ENOPROG;
+            }
+        }
+    }
+
+  return GSL_SUCCESS;
+} /* trust_iterate() */
+
+static int
+trust_rcond(double * rcond, const gsl_matrix * JTJ, void * vstate)
+{
+  int status;
+  trust_state_t *state = (trust_state_t *) vstate;
+  const gsl_multilarge_nlinear_parameters *params = &(state->params);
+
+  status = (params->solver->rcond)(rcond, JTJ, state->solver_state);
+
+  return status;
+}
+
+static int
+trust_covar(const gsl_matrix * JTJ, gsl_matrix * covar, void * vstate)
+{
+  int status;
+  trust_state_t *state = (trust_state_t *) vstate;
+  const gsl_multilarge_nlinear_parameters *params = &(state->params);
+
+  status = (params->solver->covar)(JTJ, covar, state->solver_state);
+
+  return status;
+}
+
+static double
+trust_avratio(void *vstate)
+{
+  trust_state_t *state = (trust_state_t *) vstate;
+  return state->avratio;
+}
+
+/* compute x_trial = x + dx */
+static void
+trust_trial_step(const gsl_vector * x, const gsl_vector * dx,
+                 gsl_vector * x_trial)
+{
+  size_t i, N = x->size;
+
+  for (i = 0; i < N; i++)
+    {
+      double dxi = gsl_vector_get (dx, i);
+      double xi = gsl_vector_get (x, i);
+      gsl_vector_set (x_trial, i, xi + dxi);
+    }
+}
+
+/*
+trust_calc_rho()
+  Calculate ratio of actual reduction to predicted
+reduction.
+
+rho = actual_reduction / predicted_reduction
+
+actual_reduction = 1 - ( ||f+|| / ||f|| )^2
+predicted_reduction = -2 g^T dx / ||f||^2 - ( ||J*dx|| / ||f|| )^2
+                    = -2 fhat . beta - ||beta||^2
+
+where: beta = J*dx / ||f||
+
+Inputs: trust_state - trust state
+        f_trial     - f(x + dx)
+        dx          - proposed step, size p
+        state       - workspace
+
+Return: rho = actual_reduction / predicted_reduction
+If actual_reduction is < 0, return rho = -1
+*/
+
+static double
+trust_calc_rho(const gsl_multilarge_nlinear_trust_state * trust_state,
+               const gsl_vector * f_trial, const gsl_vector * dx,
+               trust_state_t * state)
+{
+  int status;
+  const gsl_multilarge_nlinear_parameters *params = &(state->params);
+  const gsl_multilarge_nlinear_trs *trs = params->trs;
+  const gsl_vector * f = trust_state->f;
+  const double normf = gsl_blas_dnrm2(f);
+  const double normf_trial = gsl_blas_dnrm2(f_trial);
+  double rho;
+  double actual_reduction;
+  double pred_reduction;
+  double u;
+
+  /* if ||f(x+dx)|| > ||f(x)|| reject step immediately */
+  if (normf_trial >= normf)
+    return -1.0;
+
+  /* compute numerator of rho (actual reduction) */
+  u = normf_trial / normf;
+  actual_reduction = 1.0 - u*u;
+
+  /*
+   * compute denominator of rho (predicted reduction); this is calculated
+   * inside each trust region subproblem, since it depends on the local
+   * model used, which can vary according to each TRS
+   */
+  status = (trs->preduction)(trust_state, dx, &pred_reduction, state->trs_state);
+  if (status)
+    return -1.0;
+
+  if (pred_reduction > 0.0)
+    rho = actual_reduction / pred_reduction;
+  else
+    rho = -1.0;
+
+  return rho;
+}
+
+/*
+trust_eval_step()
+  Evaluate proposed step to determine if it should be
+accepted or rejected
+*/
+
+static int
+trust_eval_step(const gsl_multilarge_nlinear_trust_state * trust_state,
+                const gsl_vector * f_trial, const gsl_vector * dx,
+                double * rho, trust_state_t * state)
+{
+  int status = GSL_SUCCESS;
+  const gsl_multilarge_nlinear_parameters *params = &(state->params);
+
+  if (params->trs == gsl_multilarge_nlinear_trs_lmaccel)
+    {
+      /* reject step if acceleration is too large compared to velocity */
+      if (state->avratio > params->avmax)
+        status = GSL_FAILURE;
+    }
+
+  /* compute rho */
+  *rho = trust_calc_rho(trust_state, f_trial, dx, state);
+  if (*rho <= 0.0)
+    status = GSL_FAILURE;
+
+  return status;
+}
+
+/* compute || diag(D) a || */
+static double
+trust_scaled_norm(const gsl_vector *D, const gsl_vector *a)
+{
+  const size_t n = a->size;
+  double e2 = 0.0;
+  size_t i;
+
+  for (i = 0; i < n; ++i)
+    {
+      double Di = gsl_vector_get(D, i);
+      double ai = gsl_vector_get(a, i);
+      double u = Di * ai;
+
+      e2 += u * u;
+    }
+
+  return sqrt (e2);
+}
+
+static const gsl_multilarge_nlinear_type trust_type =
+{
+  "trust-region",
+  trust_alloc,
+  trust_init,
+  trust_iterate,
+  trust_rcond,
+  trust_covar,
+  trust_avratio,
+  trust_free
+};
+
+const gsl_multilarge_nlinear_type *gsl_multilarge_nlinear_trust = &trust_type;
diff -Nru gsl-doc-1.16/multimin/Makefile.am gsl-doc-2.3/multimin/Makefile.am
--- gsl-doc-1.16/multimin/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multimin/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_multimin.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslmultimin_la_SOURCES = fdfminimizer.c steepest_descent.c conjugate_fr.c conjugate_pr.c convergence.c diff.c vector_bfgs.c vector_bfgs2.c fminimizer.c simplex.c simplex2.c
 
diff -Nru gsl-doc-1.16/multimin/Makefile.in gsl-doc-2.3/multimin/Makefile.in
--- gsl-doc-1.16/multimin/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/multimin/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -385,6 +385,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -407,7 +408,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -523,7 +527,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslmultimin.la 
 pkginclude_HEADERS = gsl_multimin.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslmultimin_la_SOURCES = fdfminimizer.c steepest_descent.c conjugate_fr.c conjugate_pr.c convergence.c diff.c vector_bfgs.c vector_bfgs2.c fminimizer.c simplex.c simplex2.c
 noinst_HEADERS = directional_minimize.c linear_minimize.c linear_wrapper.c
 TESTS = $(check_PROGRAMS) 
diff -Nru gsl-doc-1.16/multiroots/Makefile.am gsl-doc-2.3/multiroots/Makefile.am
--- gsl-doc-1.16/multiroots/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multiroots/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -6,7 +6,7 @@
 
 noinst_HEADERS = enorm.c dogleg.c
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslmultiroots_la_SOURCES = fdjac.c fsolver.c fdfsolver.c convergence.c  newton.c gnewton.c dnewton.c broyden.c hybrid.c hybridj.c
 
diff -Nru gsl-doc-1.16/multiroots/Makefile.in gsl-doc-2.3/multiroots/Makefile.in
--- gsl-doc-1.16/multiroots/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/multiroots/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -385,6 +385,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -407,7 +408,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -524,7 +528,7 @@
 noinst_LTLIBRARIES = libgslmultiroots.la 
 pkginclude_HEADERS = gsl_multiroots.h
 noinst_HEADERS = enorm.c dogleg.c
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslmultiroots_la_SOURCES = fdjac.c fsolver.c fdfsolver.c convergence.c  newton.c gnewton.c dnewton.c broyden.c hybrid.c hybridj.c
 TESTS = $(check_PROGRAMS)
 test_SOURCES = test.c test_funcs.c test_funcs.h
diff -Nru gsl-doc-1.16/multiset/Makefile.am gsl-doc-2.3/multiset/Makefile.am
--- gsl-doc-1.16/multiset/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/multiset/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_multiset.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslmultiset_la_SOURCES = init.c file.c multiset.c inline.c
 
diff -Nru gsl-doc-1.16/multiset/Makefile.in gsl-doc-2.3/multiset/Makefile.in
--- gsl-doc-1.16/multiset/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/multiset/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -378,6 +378,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -400,7 +401,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -516,7 +520,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslmultiset.la
 pkginclude_HEADERS = gsl_multiset.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslmultiset_la_SOURCES = init.c file.c multiset.c inline.c
 noinst_HEADERS = 
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/NEWS gsl-doc-2.3/NEWS
--- gsl-doc-1.16/NEWS	2013-07-17 20:33:50.000000000 +0000
+++ gsl-doc-2.3/NEWS	2016-11-29 21:57:24.000000000 +0000
@@ -1,4 +1,195 @@
-* What is new in gsl-1.16:
+* What is new in gsl-2.3:
+
+** bug fix in documentation for gsl_linalg_LU_refine
+   (bug #49728, Joey De Pauw)
+
+** added gsl_multifit_linear_tsvd and gsl_multifit_wlinear_tsvd
+   to give user more control over cutoff for truncated SVD
+
+** added routines for Generalized Cross Validation for
+   regularized linear least squares
+
+** improved rstat example program and added documentation for
+   gsl_rstat_sd_mean (Jonathan Leto)
+
+** added function gsl_multifit_linear_rank
+
+** bug fix in nonlinear least squares when using data weights with
+   finite-difference Jacobian
+
+** add 2D subspace method for large systems (multilarge_nlinear)
+
+** bug fix in gsl_ran_beta for small parameters
+   (bug #47646, Yu Liu)
+
+** bug fix in gsl_complex_tan for negative imaginary arguments
+   (bug #47347, Yu Liu)
+
+** doc bug fix: value of golden ratio
+
+** fixed scaling issue in 2D subspace nonlinear least squares
+   method
+
+** optimize dogleg methods to calculate Gauss-Newton point
+   only when needed
+
+* What was new in gsl-2.2.1:
+
+** reverted gsl_linalg_cholesky_decomp to its previous behavior
+   so it is backward compatible; new cholesky routine is
+   gsl_linalg_cholesky_decomp1
+
+* What was new in gsl-2.2:
+
+** updated gsl_linalg_cholesky_invert to use Level-2 BLAS
+   and added function gsl_linalg_pcholesky_invert
+
+** added functions gsl_linalg_tri_*_invert for inverting
+   triangular matrices
+
+** fix GSL_EIGEN_SORT_VAL_{ASC,DESC} for nonsymmetric
+   eigensystems (Victor Zverovich)
+
+** added complete orthogonal decomposition routines
+   (gsl_linalg_COD)
+
+** bug fix where median calculation wasn't reset in
+   gsl_rstat_reset(); added gsl_rstat_quantile_reset() function
+   (reported by Pedro Donato)
+
+** added multivariate Gaussian random distribution
+   gsl_ran_multivariate_gaussian (Timothée Flutre)
+
+** added functions to estimate the 1-norm reciprocal condition
+   number for various matrix factorizations:
+     * gsl_linalg_cholesky_rcond
+     * gsl_linalg_QRPT_rcond
+
+** added functions gsl_linalg_QRPT_{lssolve,lssolve2} to
+   compute least squares solutions with the QRPT decomposition
+
+** added function gsl_permute_matrix()
+
+** added modified Cholesky factorization (gsl_linalg_mcholesky)
+   to handle symmetric indefinite matrices
+
+** added pivoted Cholesky factorization (gsl_linalg_pcholesky)
+   for ill-conditioned matrices
+
+** rewrote (real) Cholesky decomposition to use
+   a Level-2 blas algorithm instead of Level-1. Flop
+   count is about the same but the code is much simpler
+   and easier to follow
+
+** completely rewritten nonlinear least squares module,
+   including support for large problems; the user may
+   now control the linear solver used, the trust region
+   updating strategy, and the scaling method. In addition,
+   support has been added for the geodesic acceleration
+   step (Transtrum 2011) which can speed up convergence
+   on a wide class of problems.
+
+** added gsl_rstat_rms() for root mean square
+
+** optimized lmniel nonlinear least squares solver
+   (bug #46369)
+
+** improved precision in Bessel K0/K1 near x = 2
+   (Pavel Holoborodko, bug #47401)
+
+** added support for compressed row storage sparse
+   matrices (Alexis Tantet)
+
+** bug fix in convergence check of hypergeometric 2F1
+   function (bug #45926)
+
+** added gsl_multilarge_linear_lcurve() to compute
+   the L-curve for large linear systems
+
+** updated multilarge normal equations method to use
+   new Cholesky scaling for better numerical stability
+
+** added scaling to Cholesky routines to reduce the
+   condition number prior to factorization
+
+* What was new in gsl-2.1:
+
+** added test suite for example programs
+
+** bug fix when compiling with #undef GSL_DISABLE_DEPRECATED
+
+** bug fix in setting libtool age versioning
+
+** bug fix in gsl_multifit_wlinear()
+
+** added gsl_multifit_linear_rcond() to compute reciprocal
+   condition number of least squares matrix
+
+** added gsl_multilarge module for large linear least squares
+   systems
+
+* What was new in gsl-2.0:
+
+** fixed bug #43258 for hypergeometric functions (Raymond Rogers)
+
+** added L-curve analysis routines for linear Tikhonov regression
+
+** add running statistics module
+
+** added bilinear and bicubic interpolation (David Zaslavsky)
+
+** added function gsl_multifit_robust_residuals to compute robust
+   fit residuals
+
+** added Steffen monotonic interpolation method (Jean-François Caron)
+
+** added new nonlinear least squares solver 'lmniel' suitable for
+   systems with large numbers of data
+
+** nonlinear least squares solver now tracks the number of function
+   and Jacobian evaluations, see example program for details
+
+** the 'fdf' field of gsl_multifit_function_fdf is now deprecated
+   and does not need to be specified for nonlinear least squares
+   problems
+
+** added extensive test suite to nonlinear least squares module,
+   resulting in a few minor bug fixes; the routine
+   gsl_multifit_fdfsolver_driver has been rewritten (with API change)
+   to handle the various error codes of the lmsder iterate
+   routine, resulting in a high level caller which is highly robust
+   for a wide class of problems
+
+** added support for sparse matrices, including a GMRES
+   iterative linear solver
+
+** added routines gsl_linalg_givens and gsl_linalg_givens_gv
+   for Givens rotations
+
+** added Tikhonov (ridge) regularization to least squares module
+   (linear and nonlinear)
+
+** removed unused argument 'n' from gsl_sf_ellint_D
+
+** merged bspline_deriv_workspace into bspline_workspace to simplify
+   bspline API; the functions
+     gsl_bspline_deriv_alloc
+     gsl_bspline_deriv_free
+   are now deprecated and will be removed in a future release.
+
+** merged ALF extension into GSL for associated Legendre functions;
+   api has changed; consequently the functions:
+     gsl_sf_legendre_Plm_array
+     gsl_sf_legendre_Plm_deriv_array
+     gsl_sf_legendre_sphPlm_array
+     gsl_sf_legendre_sphPlm_deriv_array
+     gsl_sf_legendre_array_size
+   are now deprecated and will be removed in a future release.
+
+** added function gsl_multifit_robust_weights to allow user to
+   access the various weighting functions
+
+* What was new in gsl-1.16:
 
 ** fixed error in gsl_rng_fwrite where uninitialized padding
    bytes were being written (bug #39104)
diff -Nru gsl-doc-1.16/ntuple/Makefile.am gsl-doc-2.3/ntuple/Makefile.am
--- gsl-doc-1.16/ntuple/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/ntuple/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_ntuple.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslntuple_la_SOURCES = ntuple.c
 
diff -Nru gsl-doc-1.16/ntuple/Makefile.in gsl-doc-2.3/ntuple/Makefile.in
--- gsl-doc-1.16/ntuple/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/ntuple/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -377,6 +377,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -399,7 +400,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -515,7 +519,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslntuple.la
 pkginclude_HEADERS = gsl_ntuple.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslntuple_la_SOURCES = ntuple.c
 TESTS = $(check_PROGRAMS)
 test_SOURCES = test.c
diff -Nru gsl-doc-1.16/ode-initval/Makefile.am gsl-doc-2.3/ode-initval/Makefile.am
--- gsl-doc-1.16/ode-initval/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/ode-initval/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_odeiv.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslodeiv_la_SOURCES = control.c cstd.c cscal.c evolve.c step.c rk2.c rk2imp.c rk2simp.c rk4.c rk4imp.c rkf45.c rk8pd.c rkck.c bsimp.c gear1.c gear2.c
 
diff -Nru gsl-doc-1.16/ode-initval/Makefile.in gsl-doc-2.3/ode-initval/Makefile.in
--- gsl-doc-1.16/ode-initval/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/ode-initval/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -383,6 +383,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -405,7 +406,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -521,7 +525,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslodeiv.la 
 pkginclude_HEADERS = gsl_odeiv.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslodeiv_la_SOURCES = control.c cstd.c cscal.c evolve.c step.c rk2.c rk2imp.c rk2simp.c rk4.c rk4imp.c rkf45.c rk8pd.c rkck.c bsimp.c gear1.c gear2.c
 noinst_HEADERS = odeiv_util.h
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/ode-initval/rk2simp.c gsl-doc-2.3/ode-initval/rk2simp.c
--- gsl-doc-1.16/ode-initval/rk2simp.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/ode-initval/rk2simp.c	2016-08-19 15:37:27.000000000 +0000
@@ -149,6 +149,7 @@
       free (state->ytmp);
       free (state->dfdy);
       free (state->dfdt);
+      free (state->y_onestep);
       free (state);
       GSL_ERROR_NULL ("failed to allocate space for p", GSL_ENOMEM);
     }
diff -Nru gsl-doc-1.16/ode-initval2/driver.c gsl-doc-2.3/ode-initval2/driver.c
--- gsl-doc-1.16/ode-initval2/driver.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/ode-initval2/driver.c	2016-08-19 15:37:27.000000000 +0000
@@ -37,18 +37,19 @@
      another function.
    */
 
-  gsl_odeiv2_driver *state =
-    (gsl_odeiv2_driver *) malloc (sizeof (gsl_odeiv2_driver));
+  gsl_odeiv2_driver *state;
 
-  if (state == NULL)
+  if (sys == NULL)
     {
-      GSL_ERROR_NULL ("failed to allocate space for driver state",
-                      GSL_ENOMEM);
+      GSL_ERROR_NULL ("gsl_odeiv2_system must be defined", GSL_EINVAL);
     }
 
-  if (sys == NULL)
+  state = (gsl_odeiv2_driver *) calloc (1, sizeof (gsl_odeiv2_driver));
+
+  if (state == NULL)
     {
-      GSL_ERROR_NULL ("gsl_odeiv2_system must be defined", GSL_EINVAL);
+      GSL_ERROR_NULL ("failed to allocate space for driver state",
+                      GSL_ENOMEM);
     }
 
   {
@@ -56,6 +57,7 @@
 
     if (dim == 0)
       {
+        gsl_odeiv2_driver_free(state);
         GSL_ERROR_NULL
           ("gsl_odeiv2_system dimension must be a positive integer",
            GSL_EINVAL);
@@ -67,7 +69,7 @@
 
     if (state->s == NULL)
       {
-        free (state);
+        gsl_odeiv2_driver_free(state);
         GSL_ERROR_NULL ("failed to allocate step object", GSL_ENOMEM);
       }
 
@@ -76,8 +78,7 @@
 
   if (state->e == NULL)
     {
-      gsl_odeiv2_step_free (state->s);
-      free (state);
+      gsl_odeiv2_driver_free(state);
       GSL_ERROR_NULL ("failed to allocate evolve object", GSL_ENOMEM);
     }
 
@@ -87,6 +88,7 @@
     }
   else
     {
+      gsl_odeiv2_driver_free(state);
       GSL_ERROR_NULL ("invalid hstart", GSL_EINVAL);
     }
 
@@ -479,12 +481,14 @@
 void
 gsl_odeiv2_driver_free (gsl_odeiv2_driver * state)
 {
-  if (state->c != NULL)
-    {
-      gsl_odeiv2_control_free (state->c);
-    }
+  if (state->c)
+    gsl_odeiv2_control_free (state->c);
+
+  if (state->e)
+    gsl_odeiv2_evolve_free (state->e);
+
+  if (state->s)
+    gsl_odeiv2_step_free (state->s);
 
-  gsl_odeiv2_evolve_free (state->e);
-  gsl_odeiv2_step_free (state->s);
   free (state);
 }
diff -Nru gsl-doc-1.16/ode-initval2/Makefile.am gsl-doc-2.3/ode-initval2/Makefile.am
--- gsl-doc-1.16/ode-initval2/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/ode-initval2/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_odeiv2.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslodeiv2_la_SOURCES = control.c cstd.c cscal.c evolve.c step.c rk2.c rk2imp.c rk4.c rk4imp.c rkf45.c rk8pd.c rkck.c bsimp.c rk1imp.c msadams.c msbdf.c driver.c
 
diff -Nru gsl-doc-1.16/ode-initval2/Makefile.in gsl-doc-2.3/ode-initval2/Makefile.in
--- gsl-doc-1.16/ode-initval2/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/ode-initval2/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -383,6 +383,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -405,7 +406,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -521,7 +525,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslodeiv2.la 
 pkginclude_HEADERS = gsl_odeiv2.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslodeiv2_la_SOURCES = control.c cstd.c cscal.c evolve.c step.c rk2.c rk2imp.c rk4.c rk4imp.c rkf45.c rk8pd.c rkck.c bsimp.c rk1imp.c msadams.c msbdf.c driver.c
 noinst_HEADERS = odeiv_util.h step_utils.c rksubs.c modnewton1.c control_utils.c
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_char.h gsl-doc-2.3/permutation/gsl_permute_matrix_char.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_char.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_char.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_char.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_CHAR_H__
+#define __GSL_PERMUTE_MATRIX_CHAR_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_char.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_char (const gsl_permutation * p, gsl_matrix_char * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_CHAR_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_complex_double.h gsl-doc-2.3/permutation/gsl_permute_matrix_complex_double.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_complex_double.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_complex_double.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_complex_double.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_COMPLEX_DOUBLE_H__
+#define __GSL_PERMUTE_MATRIX_COMPLEX_DOUBLE_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_complex_double.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_complex (const gsl_permutation * p, gsl_matrix_complex * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_COMPLEX_DOUBLE_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_complex_float.h gsl-doc-2.3/permutation/gsl_permute_matrix_complex_float.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_complex_float.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_complex_float.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_complex_float.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_COMPLEX_FLOAT_H__
+#define __GSL_PERMUTE_MATRIX_COMPLEX_FLOAT_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_complex_float.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_complex_float (const gsl_permutation * p, gsl_matrix_complex_float * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_COMPLEX_FLOAT_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_complex_long_double.h gsl-doc-2.3/permutation/gsl_permute_matrix_complex_long_double.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_complex_long_double.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_complex_long_double.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_complex_long_double.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_COMPLEX_LONG_DOUBLE_H__
+#define __GSL_PERMUTE_MATRIX_COMPLEX_LONG_DOUBLE_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_complex_long_double.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_complex_long_double (const gsl_permutation * p, gsl_matrix_complex_long_double * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_COMPLEX_LONG_DOUBLE_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_double.h gsl-doc-2.3/permutation/gsl_permute_matrix_double.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_double.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_double.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_double.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_DOUBLE_H__
+#define __GSL_PERMUTE_MATRIX_DOUBLE_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_double.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix (const gsl_permutation * p, gsl_matrix * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_DOUBLE_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_float.h gsl-doc-2.3/permutation/gsl_permute_matrix_float.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_float.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_float.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_float.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_FLOAT_H__
+#define __GSL_PERMUTE_MATRIX_FLOAT_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_float.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_float (const gsl_permutation * p, gsl_matrix_float * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_FLOAT_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix.h gsl-doc-2.3/permutation/gsl_permute_matrix.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,24 @@
+#ifndef __GSL_PERMUTE_MATRIX_H__
+#define __GSL_PERMUTE_MATRIX_H__
+
+#include <gsl/gsl_permute_matrix_complex_long_double.h>
+#include <gsl/gsl_permute_matrix_complex_double.h>
+#include <gsl/gsl_permute_matrix_complex_float.h>
+
+#include <gsl/gsl_permute_matrix_long_double.h>
+#include <gsl/gsl_permute_matrix_double.h>
+#include <gsl/gsl_permute_matrix_float.h>
+
+#include <gsl/gsl_permute_matrix_ulong.h>
+#include <gsl/gsl_permute_matrix_long.h>
+
+#include <gsl/gsl_permute_matrix_uint.h>
+#include <gsl/gsl_permute_matrix_int.h>
+
+#include <gsl/gsl_permute_matrix_ushort.h>
+#include <gsl/gsl_permute_matrix_short.h>
+
+#include <gsl/gsl_permute_matrix_uchar.h>
+#include <gsl/gsl_permute_matrix_char.h>
+
+#endif /* __GSL_PERMUTE_MATRIX_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_int.h gsl-doc-2.3/permutation/gsl_permute_matrix_int.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_int.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_int.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_int.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_INT_H__
+#define __GSL_PERMUTE_MATRIX_INT_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_int.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_int (const gsl_permutation * p, gsl_matrix_int * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_INT_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_long_double.h gsl-doc-2.3/permutation/gsl_permute_matrix_long_double.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_long_double.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_long_double.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_long_double.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_LONG_DOUBLE_H__
+#define __GSL_PERMUTE_MATRIX_LONG_DOUBLE_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_long_double.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_long_double (const gsl_permutation * p, gsl_matrix_long_double * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_LONG_DOUBLE_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_long.h gsl-doc-2.3/permutation/gsl_permute_matrix_long.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_long.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_long.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_long.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_LONG_H__
+#define __GSL_PERMUTE_MATRIX_LONG_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_long.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_long (const gsl_permutation * p, gsl_matrix_long * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_LONG_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_short.h gsl-doc-2.3/permutation/gsl_permute_matrix_short.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_short.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_short.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_short.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_SHORT_H__
+#define __GSL_PERMUTE_MATRIX_SHORT_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_short.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_short (const gsl_permutation * p, gsl_matrix_short * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_SHORT_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_uchar.h gsl-doc-2.3/permutation/gsl_permute_matrix_uchar.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_uchar.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_uchar.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_uchar.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_UCHAR_H__
+#define __GSL_PERMUTE_MATRIX_UCHAR_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_uchar.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_uchar (const gsl_permutation * p, gsl_matrix_uchar * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_UCHAR_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_uint.h gsl-doc-2.3/permutation/gsl_permute_matrix_uint.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_uint.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_uint.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_uint.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_UINT_H__
+#define __GSL_PERMUTE_MATRIX_UINT_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_uint.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_uint (const gsl_permutation * p, gsl_matrix_uint * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_UINT_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_ulong.h gsl-doc-2.3/permutation/gsl_permute_matrix_ulong.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_ulong.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_ulong.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_ulong.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_ULONG_H__
+#define __GSL_PERMUTE_MATRIX_ULONG_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_ulong.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_ulong (const gsl_permutation * p, gsl_matrix_ulong * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_ULONG_H__ */
diff -Nru gsl-doc-1.16/permutation/gsl_permute_matrix_ushort.h gsl-doc-2.3/permutation/gsl_permute_matrix_ushort.h
--- gsl-doc-1.16/permutation/gsl_permute_matrix_ushort.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/permutation/gsl_permute_matrix_ushort.h	2016-07-07 20:36:11.000000000 +0000
@@ -0,0 +1,44 @@
+/* permutation/gsl_permute_matrix_ushort.h
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_PERMUTE_MATRIX_USHORT_H__
+#define __GSL_PERMUTE_MATRIX_USHORT_H__
+
+#include <stdlib.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_permutation.h>
+#include <gsl/gsl_matrix_ushort.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+int gsl_permute_matrix_ushort (const gsl_permutation * p, gsl_matrix_ushort * A);
+
+__END_DECLS
+
+#endif /* __GSL_PERMUTE_MATRIX_USHORT_H__ */
diff -Nru gsl-doc-1.16/permutation/Makefile.am gsl-doc-2.3/permutation/Makefile.am
--- gsl-doc-1.16/permutation/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/permutation/Makefile.am	2016-07-07 20:36:11.000000000 +0000
@@ -1,8 +1,8 @@
 noinst_LTLIBRARIES = libgslpermutation.la 
 
-pkginclude_HEADERS = gsl_permutation.h gsl_permute.h gsl_permute_char.h gsl_permute_complex_double.h gsl_permute_complex_float.h gsl_permute_complex_long_double.h gsl_permute_double.h gsl_permute_float.h gsl_permute_int.h gsl_permute_long.h gsl_permute_long_double.h gsl_permute_short.h gsl_permute_uchar.h gsl_permute_uint.h gsl_permute_ulong.h gsl_permute_ushort.h gsl_permute_vector.h gsl_permute_vector_char.h gsl_permute_vector_complex_double.h gsl_permute_vector_complex_float.h gsl_permute_vector_complex_long_double.h gsl_permute_vector_double.h gsl_permute_vector_float.h gsl_permute_vector_int.h gsl_permute_vector_long.h gsl_permute_vector_long_double.h gsl_permute_vector_short.h gsl_permute_vector_uchar.h gsl_permute_vector_uint.h gsl_permute_vector_ulong.h gsl_permute_vector_ushort.h
+pkginclude_HEADERS = gsl_permutation.h gsl_permute.h gsl_permute_char.h gsl_permute_complex_double.h gsl_permute_complex_float.h gsl_permute_complex_long_double.h gsl_permute_double.h gsl_permute_float.h gsl_permute_int.h gsl_permute_long.h gsl_permute_long_double.h gsl_permute_short.h gsl_permute_uchar.h gsl_permute_uint.h gsl_permute_ulong.h gsl_permute_ushort.h gsl_permute_vector.h gsl_permute_vector_char.h gsl_permute_vector_complex_double.h gsl_permute_vector_complex_float.h gsl_permute_vector_complex_long_double.h gsl_permute_vector_double.h gsl_permute_vector_float.h gsl_permute_vector_int.h gsl_permute_vector_long.h gsl_permute_vector_long_double.h gsl_permute_vector_short.h gsl_permute_vector_uchar.h gsl_permute_vector_uint.h gsl_permute_vector_ulong.h gsl_permute_vector_ushort.h gsl_permute_matrix_char.h gsl_permute_matrix_complex_long_double.h gsl_permute_matrix.h gsl_permute_matrix_long.h gsl_permute_matrix_uint.h gsl_permute_matrix_complex_double.h gsl_permute_matrix_double.h gsl_permute_matrix_int.h gsl_permute_matrix_short.h gsl_permute_matrix_ulong.h gsl_permute_matrix_complex_float.h gsl_permute_matrix_float.h gsl_permute_matrix_long_double.h gsl_permute_matrix_uchar.h gsl_permute_matrix_ushort.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslpermutation_la_SOURCES = init.c file.c permutation.c permute.c canonical.c inline.c
 
diff -Nru gsl-doc-1.16/permutation/Makefile.in gsl-doc-2.3/permutation/Makefile.in
--- gsl-doc-1.16/permutation/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/permutation/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -379,6 +379,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -401,7 +402,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -516,8 +520,31 @@
 top_builddir = @top_builddir@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslpermutation.la 
-pkginclude_HEADERS = gsl_permutation.h gsl_permute.h gsl_permute_char.h gsl_permute_complex_double.h gsl_permute_complex_float.h gsl_permute_complex_long_double.h gsl_permute_double.h gsl_permute_float.h gsl_permute_int.h gsl_permute_long.h gsl_permute_long_double.h gsl_permute_short.h gsl_permute_uchar.h gsl_permute_uint.h gsl_permute_ulong.h gsl_permute_ushort.h gsl_permute_vector.h gsl_permute_vector_char.h gsl_permute_vector_complex_double.h gsl_permute_vector_complex_float.h gsl_permute_vector_complex_long_double.h gsl_permute_vector_double.h gsl_permute_vector_float.h gsl_permute_vector_int.h gsl_permute_vector_long.h gsl_permute_vector_long_double.h gsl_permute_vector_short.h gsl_permute_vector_uchar.h gsl_permute_vector_uint.h gsl_permute_vector_ulong.h gsl_permute_vector_ushort.h
-INCLUDES = -I$(top_srcdir)
+pkginclude_HEADERS = gsl_permutation.h gsl_permute.h \
+	gsl_permute_char.h gsl_permute_complex_double.h \
+	gsl_permute_complex_float.h gsl_permute_complex_long_double.h \
+	gsl_permute_double.h gsl_permute_float.h gsl_permute_int.h \
+	gsl_permute_long.h gsl_permute_long_double.h \
+	gsl_permute_short.h gsl_permute_uchar.h gsl_permute_uint.h \
+	gsl_permute_ulong.h gsl_permute_ushort.h gsl_permute_vector.h \
+	gsl_permute_vector_char.h gsl_permute_vector_complex_double.h \
+	gsl_permute_vector_complex_float.h \
+	gsl_permute_vector_complex_long_double.h \
+	gsl_permute_vector_double.h gsl_permute_vector_float.h \
+	gsl_permute_vector_int.h gsl_permute_vector_long.h \
+	gsl_permute_vector_long_double.h gsl_permute_vector_short.h \
+	gsl_permute_vector_uchar.h gsl_permute_vector_uint.h \
+	gsl_permute_vector_ulong.h gsl_permute_vector_ushort.h \
+	gsl_permute_matrix_char.h \
+	gsl_permute_matrix_complex_long_double.h gsl_permute_matrix.h \
+	gsl_permute_matrix_long.h gsl_permute_matrix_uint.h \
+	gsl_permute_matrix_complex_double.h \
+	gsl_permute_matrix_double.h gsl_permute_matrix_int.h \
+	gsl_permute_matrix_short.h gsl_permute_matrix_ulong.h \
+	gsl_permute_matrix_complex_float.h gsl_permute_matrix_float.h \
+	gsl_permute_matrix_long_double.h gsl_permute_matrix_uchar.h \
+	gsl_permute_matrix_ushort.h
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslpermutation_la_SOURCES = init.c file.c permutation.c permute.c canonical.c inline.c
 noinst_HEADERS = permute_source.c
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/permutation/permutation.c gsl-doc-2.3/permutation/permutation.c
--- gsl-doc-1.16/permutation/permutation.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/permutation/permutation.c	2015-11-03 16:21:55.000000000 +0000
@@ -250,6 +250,7 @@
 
   return GSL_SUCCESS;
 }
+
 int
 gsl_permutation_memcpy (gsl_permutation * dest,
                         const gsl_permutation * src)
diff -Nru gsl-doc-1.16/permutation/permute.c gsl-doc-2.3/permutation/permute.c
--- gsl-doc-1.16/permutation/permute.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/permutation/permute.c	2016-07-07 20:36:12.000000000 +0000
@@ -1,8 +1,10 @@
 #include <config.h>
 #include <gsl/gsl_errno.h>
 #include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
 #include <gsl/gsl_permute.h>
 #include <gsl/gsl_permute_vector.h>
+#include <gsl/gsl_permute_matrix.h>
 
 #define BASE_GSL_COMPLEX_LONG
 #include "templates_on.h"
diff -Nru gsl-doc-1.16/permutation/permute_source.c gsl-doc-2.3/permutation/permute_source.c
--- gsl-doc-1.16/permutation/permute_source.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/permutation/permute_source.c	2016-07-07 20:36:12.000000000 +0000
@@ -161,3 +161,25 @@
 
   return GSL_SUCCESS;
 }
+
+int
+TYPE (gsl_permute_matrix) (const gsl_permutation * p, TYPE (gsl_matrix) * A)
+{
+  if (A->size2 != p->size)
+    {
+      GSL_ERROR ("matrix columns and permutation must be the same length", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i;
+
+      for (i = 0; i < A->size1; ++i)
+        {
+          QUALIFIED_VIEW (gsl_vector, view) r = FUNCTION (gsl_matrix, row) (A, i);
+
+          TYPE (gsl_permute_vector) (p, &r.vector);
+        }
+
+      return GSL_SUCCESS;
+    }
+}
diff -Nru gsl-doc-1.16/poly/ChangeLog gsl-doc-2.3/poly/ChangeLog
--- gsl-doc-1.16/poly/ChangeLog	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/poly/ChangeLog	2015-11-03 16:21:55.000000000 +0000
@@ -1,3 +1,9 @@
+2013-10-13  Rhys Ulerich <rhys.ulerich@gmail.com>
+
+	* test.c Update stale names from "gsl_poly_eval_dp" to
+	"gsl_poly_eval_derivs" in the test log.  Thanks to Mark
+	Jourdain for pointing out the inconsistency.
+
 2011-04-13  Brian Gough  <bjg@network-theory.co.uk>
 
 	* solve_quadratic.c (gsl_poly_solve_quadratic): simplify the case
diff -Nru gsl-doc-1.16/poly/Makefile.am gsl-doc-2.3/poly/Makefile.am
--- gsl-doc-1.16/poly/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/poly/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_poly.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslpoly_la_SOURCES = dd.c eval.c solve_quadratic.c solve_cubic.c zsolve_quadratic.c zsolve_cubic.c zsolve.c zsolve_init.c deriv.c
 
diff -Nru gsl-doc-1.16/poly/Makefile.in gsl-doc-2.3/poly/Makefile.in
--- gsl-doc-1.16/poly/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/poly/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -379,6 +379,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -401,7 +402,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -517,7 +521,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslpoly.la 
 pkginclude_HEADERS = gsl_poly.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslpoly_la_SOURCES = dd.c eval.c solve_quadratic.c solve_cubic.c zsolve_quadratic.c zsolve_cubic.c zsolve.c zsolve_init.c deriv.c
 noinst_HEADERS = balance.c companion.c qr.c
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/poly/test.c gsl-doc-2.3/poly/test.c
--- gsl-doc-1.16/poly/test.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/poly/test.c	2015-11-03 16:21:55.000000000 +0000
@@ -25,11 +25,21 @@
 #include <gsl/gsl_poly.h>
 #include <gsl/gsl_heapsort.h>
 
+/* sort by Re(z) then by Im(z) */
 static int
 cmp_cplx(const double *a, const double *b)
 {
-	double t = (a[0] * a[0] + a[1] * a[1]) - (b[0] * b[0] + b[1] * b[1]);
-	return t < 0.0 ? -1 : t > 0.0 ? 1 : 0;
+  double r = a[0] - b[0];
+
+  if (r == 0.0)
+    {
+      double t = a[1] - b[1];
+	    return t < 0.0 ? -1 : t > 0.0 ? 1 : 0;
+    }
+  else if (r < 0.0)
+    return -1;
+  else
+    return 1;
 }
 
 int
@@ -534,25 +544,26 @@
        Problem reported by Munagala Ramanath (bug #39055)
     */
 
-    double a[16] = { 32, -48, -8, 28, -8, 16, -16, 12, -16, 6, 10, -17, 10, 2, -4, 1 };
+    double a[16] = { 32, -48, -8, 28, -8, 16, -16, 12,
+                    -16, 6, 10, -17, 10, 2, -4, 1 };
     double z[16*2];
 
-    double expected[16*20] = {
-	   1.0000000000000000,  0.00000000000000000,
-	   1.0000000000000000,  0.00000000000000000,
-	  -1.0000000000000000,  0.00000000000000000,
-	 -0.65893856175240950,  0.83459757287426684,
-	 -0.65893856175240950, -0.83459757287426684,
-	-0.070891117403341281,  -1.1359249087587791,
-	-0.070891117403341281,   1.1359249087587791,
-	   1.1142366961812986, -0.48083981203389980,
-	   1.1142366961812986,  0.48083981203389980,
-	  -1.3066982484920768,  0.00000000000000000,
-	  0.57284747839410854,   1.1987808988289705,
-	  0.57284747839410854,  -1.1987808988289705,
-	  -1.6078107423472359,  0.00000000000000000,
-	   2.0000000000000000,  0.00000000000000000,
-	   2.0000000000000000,  0.00000000000000000 };
+    double expected[16*2] = {
+     -1.6078107423472359,    0.00000000000000000,
+     -1.3066982484920768,    0.00000000000000000,
+     -1.0000000000000000,    0.00000000000000000,
+     -0.65893856175240950,  -0.83459757287426684,
+     -0.65893856175240950,   0.83459757287426684,
+     -0.070891117403341281, -1.1359249087587791,
+     -0.070891117403341281,  1.1359249087587791,
+      0.57284747839410854,  -1.1987808988289705,
+      0.57284747839410854,   1.1987808988289705,
+      1.0000000000000000,    0.00000000000000000,
+      1.0000000000000000,    0.00000000000000000,
+      1.1142366961812986,   -0.48083981203389980,
+      1.1142366961812986,    0.48083981203389980,
+      2.0000000000000000,    0.00000000000000000,
+      2.0000000000000000,    0.00000000000000000 };
 
     int i;
 
@@ -568,8 +579,8 @@
 
     for (i = 0; i<15; i++)
       {
-        gsl_test_abs (z[2*i], expected[2*i], 1e-7, "z%d.real, 15th-order polynomial", i);
-        gsl_test_abs (z[2*i+1], expected[2*i+1], 1e-7, "z%d.imag, 15th-order polynomial", i);
+        gsl_test_rel (z[2*i], expected[2*i], 1e-7, "z%d.real, 15th-order polynomial", i);
+        gsl_test_rel (z[2*i+1], expected[2*i+1], 1e-7, "z%d.imag, 15th-order polynomial", i);
       }
   }
 
@@ -654,12 +665,12 @@
     x = -0.5;
     gsl_poly_eval_derivs(c, 6, x, dc, 6);
 
-    gsl_test_rel (dc[0], c[0] + c[1]*x + c[2]*x*x + c[3]*x*x*x + c[4]*x*x*x*x + c[5]*x*x*x*x*x , eps, "gsl_poly_eval_dp({+1, -2, +3, -4, +5, -6}, 3.75)");
-    gsl_test_rel (dc[1], c[1] + 2.0*c[2]*x + 3.0*c[3]*x*x + 4.0*c[4]*x*x*x + 5.0*c[5]*x*x*x*x , eps, "gsl_poly_eval_dp({+1, -2, +3, -4, +5, -6} deriv 1, -12.375)");
-    gsl_test_rel (dc[2], 2.0*c[2] + 3.0*2.0*c[3]*x + 4.0*3.0*c[4]*x*x + 5.0*4.0*c[5]*x*x*x , eps, "gsl_poly_eval_dp({+1, -2, +3, -4, +5, -6} deriv 2, +48.0)");
-    gsl_test_rel (dc[3], 3.0*2.0*c[3] + 4.0*3.0*2.0*c[4]*x + 5.0*4.0*3.0*c[5]*x*x , eps,"gsl_poly_eval_dp({+1, -2, +3, -4, +5, -6} deriv 3, -174.0)");
-    gsl_test_rel (dc[4], 4.0*3.0*2.0*c[4] + 5.0*4.0*3.0*2.0*c[5]*x, eps, "gsl_poly_eval_dp({+1, -2, +3, -4, +5, -6} deriv 4, +480.0)");
-    gsl_test_rel (dc[5], 5.0*4.0*3.0*2.0*c[5] , eps, "gsl_poly_eval_dp({+1, -2, +3, -4, +5, -6} deriv 5, -720.0)");
+    gsl_test_rel (dc[0], c[0] + c[1]*x + c[2]*x*x + c[3]*x*x*x + c[4]*x*x*x*x + c[5]*x*x*x*x*x , eps, "gsl_poly_eval_derivs({+1, -2, +3, -4, +5, -6}, 3.75)");
+    gsl_test_rel (dc[1], c[1] + 2.0*c[2]*x + 3.0*c[3]*x*x + 4.0*c[4]*x*x*x + 5.0*c[5]*x*x*x*x , eps, "gsl_poly_eval_derivs({+1, -2, +3, -4, +5, -6} deriv 1, -12.375)");
+    gsl_test_rel (dc[2], 2.0*c[2] + 3.0*2.0*c[3]*x + 4.0*3.0*c[4]*x*x + 5.0*4.0*c[5]*x*x*x , eps, "gsl_poly_eval_derivs({+1, -2, +3, -4, +5, -6} deriv 2, +48.0)");
+    gsl_test_rel (dc[3], 3.0*2.0*c[3] + 4.0*3.0*2.0*c[4]*x + 5.0*4.0*3.0*c[5]*x*x , eps,"gsl_poly_eval_derivs({+1, -2, +3, -4, +5, -6} deriv 3, -174.0)");
+    gsl_test_rel (dc[4], 4.0*3.0*2.0*c[4] + 5.0*4.0*3.0*2.0*c[5]*x, eps, "gsl_poly_eval_derivs({+1, -2, +3, -4, +5, -6} deriv 4, +480.0)");
+    gsl_test_rel (dc[5], 5.0*4.0*3.0*2.0*c[5] , eps, "gsl_poly_eval_derivs({+1, -2, +3, -4, +5, -6} deriv 5, -720.0)");
   }
 
 
diff -Nru gsl-doc-1.16/qrng/Makefile.am gsl-doc-2.3/qrng/Makefile.am
--- gsl-doc-1.16/qrng/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/qrng/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_qrng.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslqrng_la_SOURCES =	gsl_qrng.h qrng.c niederreiter-2.c sobol.c halton.c reversehalton.c inline.c
 
diff -Nru gsl-doc-1.16/qrng/Makefile.in gsl-doc-2.3/qrng/Makefile.in
--- gsl-doc-1.16/qrng/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/qrng/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -377,6 +377,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -399,7 +400,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -515,7 +519,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslqrng.la 
 pkginclude_HEADERS = gsl_qrng.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslqrng_la_SOURCES = gsl_qrng.h qrng.c niederreiter-2.c sobol.c halton.c reversehalton.c inline.c
 TESTS = $(check_PROGRAMS)
 test_SOURCES = test.c
diff -Nru gsl-doc-1.16/randist/beta.c gsl-doc-2.3/randist/beta.c
--- gsl-doc-1.16/randist/beta.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/randist/beta.c	2016-09-15 20:18:12.000000000 +0000
@@ -33,10 +33,39 @@
 double
 gsl_ran_beta (const gsl_rng * r, const double a, const double b)
 {
-  double x1 = gsl_ran_gamma (r, a, 1.0);
-  double x2 = gsl_ran_gamma (r, b, 1.0);
-
-  return x1 / (x1 + x2);
+  if ( (a <= 1.0) && (b <= 1.0) )
+    {
+      double U, V, X, Y;
+      while (1)
+        {
+          U = gsl_rng_uniform_pos(r);
+          V = gsl_rng_uniform_pos(r);
+          X = pow(U, 1.0/a);
+          Y = pow(V, 1.0/b);
+          if ((X + Y ) <= 1.0)
+            {
+              if (X + Y > 0)
+                {
+                  return X/ (X + Y);
+                }
+              else
+                {
+                  double logX = log(U)/a;
+                  double logY = log(V)/b;
+                  double logM = logX > logY ? logX: logY;
+                  logX -= logM;
+                  logY -= logM;
+                  return exp(logX - log(exp(logX) + exp(logY)));
+                }
+            }
+        }
+    }
+  else
+    {
+      double x1 = gsl_ran_gamma (r, a, 1.0);
+      double x2 = gsl_ran_gamma (r, b, 1.0);
+      return x1 / (x1 + x2);
+    }
 }
 
 double
diff -Nru gsl-doc-1.16/randist/gsl_randist.h gsl-doc-2.3/randist/gsl_randist.h
--- gsl-doc-1.16/randist/gsl_randist.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/randist/gsl_randist.h	2016-08-10 21:24:45.000000000 +0000
@@ -20,6 +20,8 @@
 #ifndef __GSL_RANDIST_H__
 #define __GSL_RANDIST_H__
 #include <gsl/gsl_rng.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
 
 #undef __BEGIN_DECLS
 #undef __END_DECLS
@@ -93,6 +95,20 @@
 void gsl_ran_bivariate_gaussian (const gsl_rng * r, double sigma_x, double sigma_y, double rho, double *x, double *y);
 double gsl_ran_bivariate_gaussian_pdf (const double x, const double y, const double sigma_x, const double sigma_y, const double rho);
 
+int gsl_ran_multivariate_gaussian (const gsl_rng * r, const gsl_vector * mu, const gsl_matrix * L, gsl_vector * result);
+int gsl_ran_multivariate_gaussian_log_pdf (const gsl_vector * x,
+                                           const gsl_vector * mu,
+                                           const gsl_matrix * L,
+                                           double * result,
+                                           gsl_vector * work);
+int gsl_ran_multivariate_gaussian_pdf (const gsl_vector * x,
+                                       const gsl_vector * mu,
+                                       const gsl_matrix * L,
+                                       double * result,
+                                       gsl_vector * work);
+int gsl_ran_multivariate_gaussian_mean (const gsl_matrix * X, gsl_vector * mu_hat);
+int gsl_ran_multivariate_gaussian_vcov (const gsl_matrix * X, gsl_matrix * sigma_hat);
+
 double gsl_ran_landau (const gsl_rng * r);
 double gsl_ran_landau_pdf (const double x);
 
diff -Nru gsl-doc-1.16/randist/Makefile.am gsl-doc-2.3/randist/Makefile.am
--- gsl-doc-1.16/randist/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/randist/Makefile.am	2016-08-10 21:24:45.000000000 +0000
@@ -2,15 +2,15 @@
 
 pkginclude_HEADERS= gsl_randist.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
-libgslrandist_la_SOURCES = bernoulli.c beta.c bigauss.c binomial.c cauchy.c chisq.c dirichlet.c discrete.c erlang.c exponential.c exppow.c fdist.c flat.c gamma.c gauss.c gausszig.c gausstail.c geometric.c gumbel.c hyperg.c laplace.c levy.c logarithmic.c logistic.c lognormal.c multinomial.c nbinomial.c pareto.c pascal.c poisson.c rayleigh.c shuffle.c sphere.c tdist.c weibull.c landau.c binomial_tpe.c
+libgslrandist_la_SOURCES = bernoulli.c beta.c bigauss.c binomial.c cauchy.c chisq.c dirichlet.c discrete.c erlang.c exponential.c exppow.c fdist.c flat.c gamma.c gauss.c gausszig.c gausstail.c geometric.c gumbel.c hyperg.c laplace.c levy.c logarithmic.c logistic.c lognormal.c multinomial.c mvgauss.c nbinomial.c pareto.c pascal.c poisson.c rayleigh.c shuffle.c sphere.c tdist.c weibull.c landau.c binomial_tpe.c
 
 TESTS = $(check_PROGRAMS)
 
 check_PROGRAMS = test
 
 test_SOURCES = test.c
-test_LDADD = libgslrandist.la ../rng/libgslrng.la ../specfunc/libgslspecfunc.la ../integration/libgslintegration.la ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
+test_LDADD = libgslrandist.la ../rng/libgslrng.la ../cdf/libgslcdf.la ../specfunc/libgslspecfunc.la ../integration/libgslintegration.la ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la ../statistics/libgslstatistics.la ../sort/libgslsort.la ../linalg/libgsllinalg.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la
 
 
diff -Nru gsl-doc-1.16/randist/Makefile.in gsl-doc-2.3/randist/Makefile.in
--- gsl-doc-1.16/randist/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/randist/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -99,8 +99,8 @@
 	erlang.lo exponential.lo exppow.lo fdist.lo flat.lo gamma.lo \
 	gauss.lo gausszig.lo gausstail.lo geometric.lo gumbel.lo \
 	hyperg.lo laplace.lo levy.lo logarithmic.lo logistic.lo \
-	lognormal.lo multinomial.lo nbinomial.lo pareto.lo pascal.lo \
-	poisson.lo rayleigh.lo shuffle.lo sphere.lo tdist.lo \
+	lognormal.lo multinomial.lo mvgauss.lo nbinomial.lo pareto.lo \
+	pascal.lo poisson.lo rayleigh.lo shuffle.lo sphere.lo tdist.lo \
 	weibull.lo landau.lo binomial_tpe.lo
 libgslrandist_la_OBJECTS = $(am_libgslrandist_la_OBJECTS)
 AM_V_lt = $(am__v_lt_@AM_V@)
@@ -110,11 +110,15 @@
 am_test_OBJECTS = test.$(OBJEXT)
 test_OBJECTS = $(am_test_OBJECTS)
 test_DEPENDENCIES = libgslrandist.la ../rng/libgslrng.la \
-	../specfunc/libgslspecfunc.la \
+	../cdf/libgslcdf.la ../specfunc/libgslspecfunc.la \
 	../integration/libgslintegration.la \
 	../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la \
 	../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la \
-	../utils/libutils.la
+	../utils/libutils.la ../statistics/libgslstatistics.la \
+	../sort/libgslsort.la ../linalg/libgsllinalg.la \
+	../blas/libgslblas.la ../cblas/libgslcblas.la \
+	../matrix/libgslmatrix.la ../vector/libgslvector.la \
+	../block/libgslblock.la
 AM_V_P = $(am__v_P_@AM_V@)
 am__v_P_ = $(am__v_P_@AM_DEFAULT_V@)
 am__v_P_0 = false
@@ -386,6 +390,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -408,7 +413,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -524,11 +532,11 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslrandist.la
 pkginclude_HEADERS = gsl_randist.h
-INCLUDES = -I$(top_srcdir)
-libgslrandist_la_SOURCES = bernoulli.c beta.c bigauss.c binomial.c cauchy.c chisq.c dirichlet.c discrete.c erlang.c exponential.c exppow.c fdist.c flat.c gamma.c gauss.c gausszig.c gausstail.c geometric.c gumbel.c hyperg.c laplace.c levy.c logarithmic.c logistic.c lognormal.c multinomial.c nbinomial.c pareto.c pascal.c poisson.c rayleigh.c shuffle.c sphere.c tdist.c weibull.c landau.c binomial_tpe.c
+AM_CPPFLAGS = -I$(top_srcdir)
+libgslrandist_la_SOURCES = bernoulli.c beta.c bigauss.c binomial.c cauchy.c chisq.c dirichlet.c discrete.c erlang.c exponential.c exppow.c fdist.c flat.c gamma.c gauss.c gausszig.c gausstail.c geometric.c gumbel.c hyperg.c laplace.c levy.c logarithmic.c logistic.c lognormal.c multinomial.c mvgauss.c nbinomial.c pareto.c pascal.c poisson.c rayleigh.c shuffle.c sphere.c tdist.c weibull.c landau.c binomial_tpe.c
 TESTS = $(check_PROGRAMS)
 test_SOURCES = test.c
-test_LDADD = libgslrandist.la ../rng/libgslrng.la ../specfunc/libgslspecfunc.la ../integration/libgslintegration.la ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
+test_LDADD = libgslrandist.la ../rng/libgslrng.la ../cdf/libgslcdf.la ../specfunc/libgslspecfunc.la ../integration/libgslintegration.la ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la ../statistics/libgslstatistics.la ../sort/libgslsort.la ../linalg/libgsllinalg.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la
 all: all-am
 
 .SUFFIXES:
@@ -625,6 +633,7 @@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/logistic.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/lognormal.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/multinomial.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/mvgauss.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/nbinomial.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/pareto.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/pascal.Plo@am__quote@
diff -Nru gsl-doc-1.16/randist/mvgauss.c gsl-doc-2.3/randist/mvgauss.c
--- gsl-doc-1.16/randist/mvgauss.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/randist/mvgauss.c	2016-08-10 21:24:45.000000000 +0000
@@ -0,0 +1,242 @@
+/* randist/mvgauss.c
+ * 
+ * Copyright (C) 2016 Timothée Flutre, Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <math.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_randist.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_statistics.h>
+
+static int multivar_vcov (const double data[], size_t d, size_t tda, size_t n,
+                          double vcov[], size_t tda2);
+
+/* Generate a random vector from a multivariate Gaussian distribution using
+ * the Cholesky decomposition of the variance-covariance matrix, following
+ * "Computational Statistics" from Gentle (2009), section 7.4.
+ *
+ * mu      mean vector (dimension d)
+ * L       matrix resulting from the Cholesky decomposition of
+ *         variance-covariance matrix Sigma = L L^T (dimension d x d)
+ * result  output vector (dimension d)
+ */
+int
+gsl_ran_multivariate_gaussian (const gsl_rng * r,
+                               const gsl_vector * mu,
+                               const gsl_matrix * L,
+                               gsl_vector * result)
+{
+  const size_t M = L->size1;
+  const size_t N = L->size2;
+
+  if (M != N)
+    {
+      GSL_ERROR("requires square matrix", GSL_ENOTSQR);
+    }
+  else if (mu->size != M)
+    {
+      GSL_ERROR("incompatible dimension of mean vector with variance-covariance matrix", GSL_EBADLEN);
+    }
+  else if (result->size != M)
+    {
+      GSL_ERROR("incompatible dimension of result vector", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i;
+
+      for (i = 0; i < M; ++i)
+        gsl_vector_set(result, i, gsl_ran_ugaussian(r));
+
+      gsl_blas_dtrmv(CblasLower, CblasNoTrans, CblasNonUnit, L, result);
+      gsl_vector_add(result, mu);
+
+      return GSL_SUCCESS;
+    }
+}
+
+/* Compute the log of the probability density function at a given quantile
+ * vector for a multivariate Gaussian distribution using the Cholesky
+ * decomposition of the variance-covariance matrix.
+ *
+ * x       vector of quantiles (dimension d)
+ * mu      mean vector (dimension d)
+ * L       matrix resulting from the Cholesky decomposition of
+ *         variance-covariance matrix Sigma = L L^T (dimension d x d)
+ * result  output of the density (dimension 1)
+ * work    vector used for intermediate computations (dimension d)
+ */
+int
+gsl_ran_multivariate_gaussian_log_pdf (const gsl_vector * x,
+                                       const gsl_vector * mu,
+                                       const gsl_matrix * L,
+                                       double * result,
+                                       gsl_vector * work)
+{
+  const size_t M = L->size1;
+  const size_t N = L->size2;
+
+  if (M != N)
+    {
+      GSL_ERROR("requires square matrix", GSL_ENOTSQR);
+    }
+  else if (mu->size != M)
+    {
+      GSL_ERROR("incompatible dimension of mean vector with variance-covariance matrix", GSL_EBADLEN);
+    }
+  else if (x->size != M)
+    {
+      GSL_ERROR("incompatible dimension of quantile vector", GSL_EBADLEN);
+    }
+  else if (work->size != M)
+    {
+      GSL_ERROR("incompatible dimension of work vector", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t i;
+      double quadForm;        /* (x - mu)' Sigma^{-1} (x - mu) */
+      double logSqrtDetSigma; /* log [ sqrt(|Sigma|) ] */
+
+      /* compute: work = x - mu */
+      for (i = 0; i < M; ++i)
+        {
+          double xi = gsl_vector_get(x, i);
+          double mui = gsl_vector_get(mu, i);
+          gsl_vector_set(work, i, xi - mui);
+        }
+
+      /* compute: work = L^{-1} * (x - mu) */
+      gsl_blas_dtrsv(CblasLower, CblasNoTrans, CblasNonUnit, L, work);
+
+      /* compute: quadForm = (x - mu)' Sigma^{-1} (x - mu) */
+      gsl_blas_ddot(work, work, &quadForm);
+
+      /* compute: log [ sqrt(|Sigma|) ] = sum_i log L_{ii} */
+      logSqrtDetSigma = 0.0;
+      for (i = 0; i < M; ++i)
+        {
+          double Lii = gsl_matrix_get(L, i, i);
+          logSqrtDetSigma += log(Lii);
+        }
+
+      *result = -0.5*quadForm - logSqrtDetSigma - 0.5*M*log(2.0*M_PI);
+
+      return GSL_SUCCESS;
+    }
+}
+
+int
+gsl_ran_multivariate_gaussian_pdf (const gsl_vector * x,
+                                   const gsl_vector * mu,
+                                   const gsl_matrix * L,
+                                   double * result,
+                                   gsl_vector * work)
+{
+  double logpdf;
+  int status = gsl_ran_multivariate_gaussian_log_pdf(x, mu, L, &logpdf, work);
+
+  if (status == GSL_SUCCESS)
+    *result = exp(logpdf);
+
+  return status;
+}
+
+/* Compute the maximum-likelihood estimate of the mean vector of samples
+ * from a multivariate Gaussian distribution.
+ *
+ * Example from R (GPL): http://www.r-project.org/
+ * (samples <- matrix(c(4.348817, 2.995049, -3.793431, 4.711934, 1.190864, -1.357363), nrow=3, ncol=2))
+ * colMeans(samples) # 1.183478 1.515145
+ */
+int
+gsl_ran_multivariate_gaussian_mean (const gsl_matrix * X, gsl_vector * mu_hat)
+{
+  const size_t M = X->size1;
+  const size_t N = X->size2;
+
+  if (N != mu_hat->size)
+    {
+      GSL_ERROR("mu_hat vector has wrong size", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t j;
+
+      for (j = 0; j < N; ++j)
+        {
+          gsl_vector_const_view c = gsl_matrix_const_column(X, j);
+          double mean = gsl_stats_mean(c.vector.data, c.vector.stride, M);
+          gsl_vector_set(mu_hat, j, mean);
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+/* Compute the maximum-likelihood estimate of the variance-covariance matrix
+ * of samples from a multivariate Gaussian distribution.
+ */
+int
+gsl_ran_multivariate_gaussian_vcov (const gsl_matrix * X, gsl_matrix * sigma_hat)
+{
+  const size_t M = X->size1;
+  const size_t N = X->size2;
+
+  if (sigma_hat->size1 != sigma_hat->size2)
+    {
+      GSL_ERROR("sigma_hat must be a square matrix", GSL_ENOTSQR);
+    }
+  else if (N != sigma_hat->size1)
+    {
+      GSL_ERROR("sigma_hat does not match X matrix dimensions", GSL_EBADLEN);
+    }
+  else
+    {
+      return multivar_vcov (X->data, N, X->tda, M, sigma_hat->data, sigma_hat->tda);
+    }
+}
+
+/* Example from R (GPL): http://www.r-project.org/
+ * (samples <- matrix(c(4.348817, 2.995049, -3.793431, 4.711934, 1.190864, -1.357363), nrow=3, ncol=2))
+ * cov(samples) # 19.03539 11.91384 \n 11.91384  9.28796
+ */
+static int
+multivar_vcov (const double data[], size_t d, size_t tda, size_t n,
+               double vcov[], size_t tda2)
+{
+  size_t j1 = 0, j2 = 0;
+
+  for (j1 = 0; j1 < d; ++j1)
+    {
+      vcov[j1 * tda2 + j1] = gsl_stats_variance(&(data[j1]), tda, n);
+      for (j2 = j1 + 1; j2 < d; ++j2)
+        {
+          vcov[j1 * tda2 + j2] = gsl_stats_covariance(&(data[j1]), tda,
+                                                      &(data[j2]), tda, n);
+          vcov[j2 * tda2 + j1] = vcov[j1 * tda2 + j2];
+        }
+      }
+  
+  return GSL_SUCCESS;
+}
diff -Nru gsl-doc-1.16/randist/test.c gsl-doc-2.3/randist/test.c
--- gsl-doc-1.16/randist/test.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/randist/test.c	2016-09-15 20:16:11.000000000 +0000
@@ -27,6 +27,11 @@
 #include <gsl/gsl_test.h>
 #include <gsl/gsl_ieee_utils.h>
 #include <gsl/gsl_integration.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_cdf.h>
 
 #define N 100000
 
@@ -158,6 +163,9 @@
 double test_bivariate_gaussian3_pdf (double x);
 double test_bivariate_gaussian4 (void);
 double test_bivariate_gaussian4_pdf (double x);
+void test_multivariate_gaussian_log_pdf (void);
+void test_multivariate_gaussian_pdf (void);
+void test_multivariate_gaussian (void);
 double test_gumbel1 (void);
 double test_gumbel1_pdf (double x);
 double test_gumbel2 (void);
@@ -333,6 +341,10 @@
   testPDF (FUNC2 (bivariate_gaussian3));
   testPDF (FUNC2 (bivariate_gaussian4));
 
+  test_multivariate_gaussian_log_pdf ();
+  test_multivariate_gaussian_pdf ();
+  test_multivariate_gaussian ();
+
   testPDF (FUNC2 (gumbel1));
   testPDF (FUNC2 (gumbel2));
   testPDF (FUNC2 (landau));
@@ -1681,6 +1693,165 @@
   return gsl_ran_gaussian_pdf (x, sigma);
 }
 
+/* Examples from R (GPL): http://www.r-project.org/
+ * library(mvtnorm); packageVersion("mvtnorm") # 1.0.5
+ * mu <- c(1, 2)
+ * Sigma <- matrix(c(4,2, 2,3), ncol=2)
+ * x <- c(0, 0)
+ * sprintf("%.15f", dmvnorm(x=x, mean=mu, sigma=Sigma, log=TRUE)) # -3.565097837249263
+ */
+void
+test_multivariate_gaussian_log_pdf (void)
+{
+  size_t d = 2;
+  const double exp_res = -3.565097837249263;
+  double obs_res;
+  gsl_vector * mu = gsl_vector_calloc(d);
+  gsl_matrix * Sigma = gsl_matrix_calloc(d, d);
+  gsl_matrix * L = gsl_matrix_calloc(d, d);
+  gsl_vector * x = gsl_vector_calloc(d);
+  gsl_vector * work = gsl_vector_calloc(d);
+
+  gsl_vector_set(mu, 0, 1);
+  gsl_vector_set(mu, 1, 2);
+
+  gsl_matrix_set(Sigma, 0, 0, 4);
+  gsl_matrix_set(Sigma, 1, 1, 3);
+  gsl_matrix_set(Sigma, 0, 1, 2);
+  gsl_matrix_set(Sigma, 1, 0, 2);
+
+  gsl_matrix_memcpy(L, Sigma);
+  gsl_linalg_cholesky_decomp1(L);
+
+  gsl_ran_multivariate_gaussian_log_pdf(x, mu, L, &obs_res, work);
+  gsl_test_rel(obs_res, exp_res, 1.0e-10, "gsl_ran_multivariate_gaussian_log_pdf");
+
+  gsl_vector_free(mu);
+  gsl_matrix_free(Sigma);
+  gsl_matrix_free(L);
+  gsl_vector_free(x);
+  gsl_vector_free(work);
+}
+
+/* Examples from R (GPL): http://www.r-project.org/
+ * library(mvtnorm); packageVersion("mvtnorm") # 1.0.5
+ * mu <- c(1, 2)
+ * Sigma <- matrix(c(4,2, 2,3), ncol=2)
+ * x <- c(0, 0)
+ * sprintf("%.15f", dmvnorm(x=x, mean=mu, sigma=Sigma, log=FALSE)) # 0.028294217120391
+ */
+void
+test_multivariate_gaussian_pdf (void)
+{
+  size_t d = 2;
+  const double exp_res = 0.028294217120391;
+  double obs_res = 0;
+  gsl_vector * mu = gsl_vector_calloc(d);
+  gsl_matrix * Sigma = gsl_matrix_calloc(d, d);
+  gsl_matrix * L = gsl_matrix_calloc(d, d);
+  gsl_vector * x = gsl_vector_calloc(d);
+  gsl_vector * work = gsl_vector_calloc(d);
+
+  gsl_vector_set(mu, 0, 1);
+  gsl_vector_set(mu, 1, 2);
+
+  gsl_matrix_set(Sigma, 0, 0, 4);
+  gsl_matrix_set(Sigma, 1, 1, 3);
+  gsl_matrix_set(Sigma, 0, 1, 2);
+  gsl_matrix_set(Sigma, 1, 0, 2);
+
+  gsl_matrix_memcpy(L, Sigma);
+  gsl_linalg_cholesky_decomp1(L);
+
+  gsl_ran_multivariate_gaussian_pdf(x, mu, L, &obs_res, work);
+  gsl_test_rel(obs_res, exp_res, 1.0e-10, "gsl_ran_multivariate_gaussian_pdf");
+
+  gsl_vector_free(mu);
+  gsl_matrix_free(Sigma);
+  gsl_matrix_free(L);
+  gsl_vector_free(x);
+  gsl_vector_free(work);
+}
+
+/* Draw N random vectors according to a given MVN(mu,Sigma). Then, check that
+ * one can't reject the null hypothesis that the sample mean is equal to
+ * the true mean, using Hotelling's test statistic at 95% confidence level.
+ * Details in "Applied Multivariate Statistical Analysis" by  Johnson & Wichern
+ * (2001), section 5, page 212.
+ */
+void
+test_multivariate_gaussian (void)
+{
+  size_t d = 2, i = 0;
+  int status = 0;
+  double T2 = 0, threshold = 0, alpha = 0.05, pvalue = 0;
+  gsl_vector * mu = gsl_vector_calloc(d);
+  gsl_matrix * Sigma = gsl_matrix_calloc(d, d);
+  gsl_matrix * L = gsl_matrix_calloc(d, d);
+  gsl_vector * sample = gsl_vector_calloc(d);
+  gsl_matrix * samples = gsl_matrix_calloc(N, d);
+  gsl_vector * mu_hat = gsl_vector_calloc(d);
+  gsl_matrix * Sigma_hat = gsl_matrix_calloc(d, d);
+  gsl_vector * mu_hat_ctr = gsl_vector_calloc(d);
+  gsl_matrix * Sigma_hat_inv = gsl_matrix_calloc(d, d);
+  gsl_vector * tmp = gsl_vector_calloc(d);
+
+  /* set the true values of parameters mu and Sigma */
+  gsl_vector_set(mu, 0, 1);
+  gsl_vector_set(mu, 1, 2);
+  gsl_matrix_set(Sigma, 0, 0, 4);
+  gsl_matrix_set(Sigma, 1, 1, 3);
+  gsl_matrix_set(Sigma, 0, 1, 2);
+  gsl_matrix_set(Sigma, 1, 0, 2);
+
+  /* draw N random vectors */
+  gsl_matrix_memcpy(L, Sigma);
+  gsl_linalg_cholesky_decomp1(L);
+  for (i = 0; i < N; ++i) {
+    gsl_ran_multivariate_gaussian(r_global, mu, L, sample);
+    gsl_matrix_set_row(samples, i, sample);
+  }
+
+  /* compute the maximum-likelihood estimates */
+  gsl_ran_multivariate_gaussian_mean (samples, mu_hat);
+  gsl_ran_multivariate_gaussian_vcov (samples, Sigma_hat);
+
+  /* compute Hotelling's test statistic:
+     T^2 = n (hat{mu} - mu)' hat{Sigma}^-1 (hat{mu} - mu) */
+  gsl_vector_memcpy(mu_hat_ctr, mu_hat);
+  gsl_vector_sub(mu_hat_ctr, mu);
+  gsl_matrix_memcpy(Sigma_hat_inv, Sigma_hat);
+  gsl_linalg_cholesky_decomp1(Sigma_hat_inv);
+  gsl_linalg_cholesky_invert(Sigma_hat_inv);
+  gsl_blas_dgemv(CblasNoTrans, 1, Sigma_hat_inv, mu_hat_ctr, 0, tmp);
+  gsl_blas_ddot(mu_hat_ctr, tmp, &T2);
+  T2 *= N;
+
+  /* test if the null hypothesis (hat{mu} = mu) can be rejected 
+   at the alpha level*/
+  threshold = (N-1) * d / (double)(N-d) * gsl_cdf_fdist_Pinv(1-alpha, d, N-d);
+  status = (T2 > threshold);
+  gsl_test(status,
+           "test gsl_ran_multivariate_gaussian: T2 %f < %f",
+           T2, threshold);
+  pvalue = gsl_cdf_fdist_Q(T2, d, N-d);
+  status = (pvalue < alpha);
+  gsl_test(status,
+           "test gsl_ran_multivariate_gaussian: p value %f > %f",
+           pvalue, alpha);
+
+  gsl_vector_free(mu);
+  gsl_matrix_free(Sigma);
+  gsl_matrix_free(L);
+  gsl_vector_free(sample);
+  gsl_matrix_free(samples);
+  gsl_vector_free(mu_hat);
+  gsl_matrix_free(Sigma_hat);
+  gsl_vector_free(mu_hat_ctr);
+  gsl_matrix_free(Sigma_hat_inv);
+  gsl_vector_free(tmp);
+}
+
 
 double
 test_geometric (void)
diff -Nru gsl-doc-1.16/rng/Makefile.am gsl-doc-2.3/rng/Makefile.am
--- gsl-doc-1.16/rng/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/rng/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_rng.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslrng_la_SOURCES = borosh13.c cmrg.c coveyou.c default.c file.c fishman18.c fishman20.c fishman2x.c gfsr4.c knuthran2.c knuthran.c knuthran2002.c lecuyer21.c minstd.c mrg.c mt.c r250.c ran0.c ran1.c ran2.c ran3.c rand48.c rand.c random.c randu.c ranf.c ranlux.c ranlxd.c ranlxs.c ranmar.c rng.c slatec.c taus.c taus113.c transputer.c tt.c types.c uni32.c uni.c vax.c waterman14.c zuf.c inline.c
 
diff -Nru gsl-doc-1.16/rng/Makefile.in gsl-doc-2.3/rng/Makefile.in
--- gsl-doc-1.16/rng/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/rng/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -384,6 +384,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -406,7 +407,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -522,7 +526,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslrng.la 
 pkginclude_HEADERS = gsl_rng.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslrng_la_SOURCES = borosh13.c cmrg.c coveyou.c default.c file.c fishman18.c fishman20.c fishman2x.c gfsr4.c knuthran2.c knuthran.c knuthran2002.c lecuyer21.c minstd.c mrg.c mt.c r250.c ran0.c ran1.c ran2.c ran3.c rand48.c rand.c random.c randu.c ranf.c ranlux.c ranlxd.c ranlxs.c ranmar.c rng.c slatec.c taus.c taus113.c transputer.c tt.c types.c uni32.c uni.c vax.c waterman14.c zuf.c inline.c
 CLEANFILES = test.dat
 noinst_HEADERS = schrage.c
diff -Nru gsl-doc-1.16/roots/Makefile.am gsl-doc-2.3/roots/Makefile.am
--- gsl-doc-1.16/roots/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/roots/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -6,7 +6,7 @@
 
 noinst_HEADERS = roots.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslroots_la_SOURCES = bisection.c brent.c falsepos.c	newton.c  secant.c steffenson.c	convergence.c fsolver.c fdfsolver.c 
 
diff -Nru gsl-doc-1.16/roots/Makefile.in gsl-doc-2.3/roots/Makefile.in
--- gsl-doc-1.16/roots/Makefile.in	2013-07-19 15:14:54.000000000 +0000
+++ gsl-doc-2.3/roots/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -381,6 +381,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -403,7 +404,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -520,7 +524,7 @@
 noinst_LTLIBRARIES = libgslroots.la 
 pkginclude_HEADERS = gsl_roots.h
 noinst_HEADERS = roots.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslroots_la_SOURCES = bisection.c brent.c falsepos.c	newton.c  secant.c steffenson.c	convergence.c fsolver.c fdfsolver.c 
 TESTS = $(check_PROGRAMS)
 test_SOURCES = test.c test_funcs.c test.h
diff -Nru gsl-doc-1.16/roots/secant.c gsl-doc-2.3/roots/secant.c
--- gsl-doc-1.16/roots/secant.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/roots/secant.c	2015-11-03 16:21:55.000000000 +0000
@@ -79,7 +79,12 @@
 
   double x_new, f_new, df_new;
 
-  if (state->df == 0.0)
+  if(f == 0.0)
+  {
+	  return GSL_SUCCESS;
+  }
+
+  if(df == 0.0)
     {
       GSL_ERROR("derivative is zero", GSL_EZERODIV);
     }
@@ -87,7 +92,7 @@
   x_new = x - (f / df);
 
   f_new = GSL_FN_FDF_EVAL_F(fdf, x_new) ;
-  df_new = (f_new - f) / (x_new - x) ;
+  df_new = df * ((f - f_new) / f);
 
   *root = x_new ;
 
diff -Nru gsl-doc-1.16/roots/test.c gsl-doc-2.3/roots/test.c
--- gsl-doc-1.16/roots/test.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/roots/test.c	2015-11-03 16:21:55.000000000 +0000
@@ -43,10 +43,10 @@
 main (void)
 {
   gsl_function F_sin, F_cos, F_func1, F_func2, F_func3, F_func4,
-    F_func5, F_func6;
+	  F_func5, F_func6;
   
   gsl_function_fdf FDF_sin, FDF_cos, FDF_func1, FDF_func2, FDF_func3, FDF_func4,
-    FDF_func5, FDF_func6;
+	  FDF_func5, FDF_func6, FDF_func7;
 
   const gsl_root_fsolver_type * fsolver[4] ;
   const gsl_root_fdfsolver_type * fdfsolver[4] ;
@@ -83,6 +83,7 @@
   FDF_func4 = create_fdf (func4, func4_df, func4_fdf) ;
   FDF_func5 = create_fdf (func5, func5_df, func5_fdf) ;
   FDF_func6 = create_fdf (func6, func6_df, func6_fdf) ;
+  FDF_func7 = create_fdf(func7, func7_df, func7_fdf) ;
 
   gsl_set_error_handler (&my_error_handler);
 
@@ -118,7 +119,8 @@
       test_fdf (*S,"x exp(-x) {-2}", &FDF_func4, -2.0, 0.0);
       test_fdf_e (*S,"max iterations x -> +Inf, x exp(-x) {2}", &FDF_func4, 2.0, 0.0);
       test_fdf_e (*S,"max iterations x -> -Inf, 1/(1 + exp(-x)) {0}", &FDF_func5, 0.0, 0.0);
-    }
+	  test_fdf(*S, "-pi * x + e {1.5}", &FDF_func7, 1.5, M_E / M_PI);
+  }
 
   test_fdf (gsl_root_fdfsolver_steffenson,
             "(x - 1)^7 {0.9}", &FDF_func6, 0.9, 1.0);    
diff -Nru gsl-doc-1.16/roots/test_funcs.c gsl-doc-2.3/roots/test_funcs.c
--- gsl-doc-1.16/roots/test_funcs.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/roots/test_funcs.c	2015-11-03 16:21:55.000000000 +0000
@@ -227,3 +227,22 @@
   *y = cos (x);
   *yprime = -sin (x);
 }
+
+/* linear function to test that solvers exit correctly 
+   when entered with an exact root */
+
+double func7(double x, void * p)
+{
+	return -M_PI * x + M_E;
+}
+
+double func7_df(double x, void * p)
+{
+	return -M_PI;
+}
+
+void func7_fdf(double x, void * p, double *f, double *df)
+{
+	*f = func7(x, p);
+	*df = func7_df(x, p);
+}
diff -Nru gsl-doc-1.16/roots/test.h gsl-doc-2.3/roots/test.h
--- gsl-doc-1.16/roots/test.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/roots/test.h	2015-11-03 16:21:55.000000000 +0000
@@ -127,3 +127,12 @@
 
 void
   cos_fdf (double x, void * p, double *y, double *yprime);
+
+double
+func7(double x, void * p);
+
+double
+func7_df(double x, void * p);
+
+void
+func7_fdf(double x, void * p, double *y, double *yprime);
diff -Nru gsl-doc-1.16/rstat/gsl_rstat.h gsl-doc-2.3/rstat/gsl_rstat.h
--- gsl-doc-1.16/rstat/gsl_rstat.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/rstat/gsl_rstat.h	2016-08-10 21:24:45.000000000 +0000
@@ -0,0 +1,81 @@
+/* rstat/gsl_rstat.h
+ * 
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_RSTAT_H__
+#define __GSL_RSTAT_H__
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+typedef struct
+{
+  double p;        /* p-quantile */
+  double q[5];     /* heights q_i */
+  int npos[5];     /* positions n_i */
+  double np[5];    /* desired positions n_i' */
+  double dnp[5];   /* increments dn_i' */
+  size_t n;        /* number of data added */
+} gsl_rstat_quantile_workspace;
+
+gsl_rstat_quantile_workspace *gsl_rstat_quantile_alloc(const double p);
+void gsl_rstat_quantile_free(gsl_rstat_quantile_workspace *w);
+int gsl_rstat_quantile_reset(gsl_rstat_quantile_workspace *w);
+int gsl_rstat_quantile_add(const double x, gsl_rstat_quantile_workspace *w);
+double gsl_rstat_quantile_get(gsl_rstat_quantile_workspace *w);
+
+typedef struct
+{
+  double min;      /* minimum value added */
+  double max;      /* maximum value added */
+  double mean;     /* current mean */
+  double M2;       /* M_k = sum_{i=1..n} [ x_i - mean_n ]^k */
+  double M3;
+  double M4;
+  size_t n;        /* number of data points added */
+  gsl_rstat_quantile_workspace *median_workspace_p; /* median workspace */
+} gsl_rstat_workspace;
+
+gsl_rstat_workspace *gsl_rstat_alloc(void);
+void gsl_rstat_free(gsl_rstat_workspace *w);
+size_t gsl_rstat_n(gsl_rstat_workspace *w);
+int gsl_rstat_add(const double x, gsl_rstat_workspace *w);
+double gsl_rstat_min(gsl_rstat_workspace *w);
+double gsl_rstat_max(gsl_rstat_workspace *w);
+double gsl_rstat_mean(gsl_rstat_workspace *w);
+double gsl_rstat_variance(gsl_rstat_workspace *w);
+double gsl_rstat_sd(gsl_rstat_workspace *w);
+double gsl_rstat_rms(gsl_rstat_workspace *w);
+double gsl_rstat_sd_mean(gsl_rstat_workspace *w);
+double gsl_rstat_median(gsl_rstat_workspace *w);
+double gsl_rstat_skew(gsl_rstat_workspace *w);
+double gsl_rstat_kurtosis(gsl_rstat_workspace *w);
+int gsl_rstat_reset(gsl_rstat_workspace *w);
+
+__END_DECLS
+
+#endif /* __GSL_RSTAT_H__ */
diff -Nru gsl-doc-1.16/rstat/Makefile.am gsl-doc-2.3/rstat/Makefile.am
--- gsl-doc-1.16/rstat/Makefile.am	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/rstat/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,15 @@
+noinst_LTLIBRARIES = libgslrstat.la
+
+pkginclude_HEADERS = gsl_rstat.h
+
+AM_CPPFLAGS = -I$(top_srcdir)
+
+libgslrstat_la_SOURCES = rstat.c rquantile.c
+
+check_PROGRAMS = test
+TESTS = $(check_PROGRAMS)
+
+test_SOURCES = test.c
+test_LDADD = libgslrstat.la ../statistics/libgslstatistics.la ../sort/libgslsort.la ../ieee-utils/libgslieeeutils.la ../randist/libgslrandist.la ../rng/libgslrng.la ../specfunc/libgslspecfunc.la ../complex/libgslcomplex.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la ../vector/libgslvector.la
+
+
diff -Nru gsl-doc-1.16/rstat/Makefile.in gsl-doc-2.3/rstat/Makefile.in
--- gsl-doc-1.16/rstat/Makefile.in	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/rstat/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -0,0 +1,1028 @@
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
+# @configure_input@
+
+# Copyright (C) 1994-2013 Free Software Foundation, Inc.
+
+# This Makefile.in is free software; the Free Software Foundation
+# gives unlimited permission to copy and/or distribute it,
+# with or without modifications, as long as this notice is preserved.
+
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY, to the extent permitted by law; without
+# even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+# PARTICULAR PURPOSE.
+
+@SET_MAKE@
+
+
+VPATH = @srcdir@
+am__is_gnu_make = test -n '$(MAKEFILE_LIST)' && test -n '$(MAKELEVEL)'
+am__make_running_with_option = \
+  case $${target_option-} in \
+      ?) ;; \
+      *) echo "am__make_running_with_option: internal error: invalid" \
+              "target option '$${target_option-}' specified" >&2; \
+         exit 1;; \
+  esac; \
+  has_opt=no; \
+  sane_makeflags=$$MAKEFLAGS; \
+  if $(am__is_gnu_make); then \
+    sane_makeflags=$$MFLAGS; \
+  else \
+    case $$MAKEFLAGS in \
+      *\\[\ \	]*) \
+        bs=\\; \
+        sane_makeflags=`printf '%s\n' "$$MAKEFLAGS" \
+          | sed "s/$$bs$$bs[$$bs $$bs	]*//g"`;; \
+    esac; \
+  fi; \
+  skip_next=no; \
+  strip_trailopt () \
+  { \
+    flg=`printf '%s\n' "$$flg" | sed "s/$$1.*$$//"`; \
+  }; \
+  for flg in $$sane_makeflags; do \
+    test $$skip_next = yes && { skip_next=no; continue; }; \
+    case $$flg in \
+      *=*|--*) continue;; \
+        -*I) strip_trailopt 'I'; skip_next=yes;; \
+      -*I?*) strip_trailopt 'I';; \
+        -*O) strip_trailopt 'O'; skip_next=yes;; \
+      -*O?*) strip_trailopt 'O';; \
+        -*l) strip_trailopt 'l'; skip_next=yes;; \
+      -*l?*) strip_trailopt 'l';; \
+      -[dEDm]) skip_next=yes;; \
+      -[JT]) skip_next=yes;; \
+    esac; \
+    case $$flg in \
+      *$$target_option*) has_opt=yes; break;; \
+    esac; \
+  done; \
+  test $$has_opt = yes
+am__make_dryrun = (target_option=n; $(am__make_running_with_option))
+am__make_keepgoing = (target_option=k; $(am__make_running_with_option))
+pkgdatadir = $(datadir)/@PACKAGE@
+pkgincludedir = $(includedir)/@PACKAGE@
+pkglibdir = $(libdir)/@PACKAGE@
+pkglibexecdir = $(libexecdir)/@PACKAGE@
+am__cd = CDPATH="$${ZSH_VERSION+.}$(PATH_SEPARATOR)" && cd
+install_sh_DATA = $(install_sh) -c -m 644
+install_sh_PROGRAM = $(install_sh) -c
+install_sh_SCRIPT = $(install_sh) -c
+INSTALL_HEADER = $(INSTALL_DATA)
+transform = $(program_transform_name)
+NORMAL_INSTALL = :
+PRE_INSTALL = :
+POST_INSTALL = :
+NORMAL_UNINSTALL = :
+PRE_UNINSTALL = :
+POST_UNINSTALL = :
+build_triplet = @build@
+host_triplet = @host@
+check_PROGRAMS = test$(EXEEXT)
+subdir = rstat
+DIST_COMMON = $(srcdir)/Makefile.in $(srcdir)/Makefile.am \
+	$(top_srcdir)/mkinstalldirs $(top_srcdir)/depcomp \
+	$(pkginclude_HEADERS) $(top_srcdir)/test-driver
+ACLOCAL_M4 = $(top_srcdir)/aclocal.m4
+am__aclocal_m4_deps = $(top_srcdir)/configure.ac
+am__configure_deps = $(am__aclocal_m4_deps) $(CONFIGURE_DEPENDENCIES) \
+	$(ACLOCAL_M4)
+mkinstalldirs = $(SHELL) $(top_srcdir)/mkinstalldirs
+CONFIG_HEADER = $(top_builddir)/config.h
+CONFIG_CLEAN_FILES =
+CONFIG_CLEAN_VPATH_FILES =
+LTLIBRARIES = $(noinst_LTLIBRARIES)
+libgslrstat_la_LIBADD =
+am_libgslrstat_la_OBJECTS = rstat.lo rquantile.lo
+libgslrstat_la_OBJECTS = $(am_libgslrstat_la_OBJECTS)
+AM_V_lt = $(am__v_lt_@AM_V@)
+am__v_lt_ = $(am__v_lt_@AM_DEFAULT_V@)
+am__v_lt_0 = --silent
+am__v_lt_1 = 
+am_test_OBJECTS = test.$(OBJEXT)
+test_OBJECTS = $(am_test_OBJECTS)
+test_DEPENDENCIES = libgslrstat.la ../statistics/libgslstatistics.la \
+	../sort/libgslsort.la ../ieee-utils/libgslieeeutils.la \
+	../randist/libgslrandist.la ../rng/libgslrng.la \
+	../specfunc/libgslspecfunc.la ../complex/libgslcomplex.la \
+	../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la \
+	../utils/libutils.la ../vector/libgslvector.la
+AM_V_P = $(am__v_P_@AM_V@)
+am__v_P_ = $(am__v_P_@AM_DEFAULT_V@)
+am__v_P_0 = false
+am__v_P_1 = :
+AM_V_GEN = $(am__v_GEN_@AM_V@)
+am__v_GEN_ = $(am__v_GEN_@AM_DEFAULT_V@)
+am__v_GEN_0 = @echo "  GEN     " $@;
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+# Tell versions [3.59,3.63) of GNU make to not export all variables.
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+.NOEXPORT:
diff -Nru gsl-doc-1.16/rstat/rquantile.c gsl-doc-2.3/rstat/rquantile.c
--- gsl-doc-1.16/rstat/rquantile.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/rstat/rquantile.c	2016-08-10 21:24:45.000000000 +0000
@@ -0,0 +1,207 @@
+/* rstat/rquantile.c
+ * 
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_sort.h>
+#include <gsl/gsl_statistics.h>
+#include <gsl/gsl_rstat.h>
+
+/*
+ * Running quantile calculation based on the paper
+ *
+ * [1] R. Jain and I. Chlamtac, "The P^2 algorithm for dynamic
+ *     calculation of quantiles and histograms without storing
+ *     observations", Communications of the ACM, October 1985
+ */
+
+static double calc_psq(const double qp1, const double q, const double qm1,
+                       const double d, const double np1, const double n, const double nm1);
+
+gsl_rstat_quantile_workspace *
+gsl_rstat_quantile_alloc(const double p)
+{
+  gsl_rstat_quantile_workspace *w;
+
+  w = calloc(1, sizeof(gsl_rstat_quantile_workspace));
+  if (w == 0)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workspace", GSL_ENOMEM);
+    }
+
+  w->p = p;
+
+  gsl_rstat_quantile_reset(w);
+
+  return w;
+} /* gsl_rstat_quantile_alloc() */
+
+void
+gsl_rstat_quantile_free(gsl_rstat_quantile_workspace *w)
+{
+  free(w);
+} /* gsl_rstat_quantile_free() */
+
+int
+gsl_rstat_quantile_reset(gsl_rstat_quantile_workspace *w)
+{
+  const double p = w->p;
+  size_t i;
+
+  /* initialize positions n */
+  for (i = 0; i < 5; ++i)
+    w->npos[i] = i + 1;
+
+  /* initialize n' */
+  w->np[0] = 1.0;
+  w->np[1] = 1.0 + 2.0 * p;
+  w->np[2] = 1.0 + 4.0 * p;
+  w->np[3] = 3.0 + 2.0 * p;
+  w->np[4] = 5.0;
+
+  /* initialize dn' */
+  w->dnp[0] = 0.0;
+  w->dnp[1] = 0.5 * p;
+  w->dnp[2] = p;
+  w->dnp[3] = 0.5 * (1.0 + p);
+  w->dnp[4] = 1.0;
+
+  w->n = 0;
+
+  return GSL_SUCCESS;
+}
+
+int
+gsl_rstat_quantile_add(const double x, gsl_rstat_quantile_workspace *w)
+{
+  if (w->n < 5)
+    {
+      w->q[w->n] = x;
+    }
+  else
+    {
+      int i;
+      int k = -1;
+
+      if (w->n == 5)
+        {
+          /* initialization: sort the first five heights */
+          gsl_sort(w->q, 1, w->n);
+        }
+
+      /* step B1: find k such that q_k <= x < q_{k+1} */
+      if (x < w->q[0])
+        {
+          w->q[0] = x;
+          k = 0;
+        }
+      else if (x >= w->q[4])
+        {
+          w->q[4] = x;
+          k = 3;
+        }
+      else
+        {
+          for (i = 0; i <= 3; ++i)
+            {
+              if (w->q[i] <= x && x < w->q[i + 1])
+                {
+                  k = i;
+                  break;
+                }
+            }
+        }
+
+      if (k < 0)
+        {
+          /* we could get here if x is nan */
+          GSL_ERROR ("invalid input argument x", GSL_EINVAL);
+        }
+
+      /* step B2(a): update n_i */
+      for (i = k + 1; i <= 4; ++i)
+        ++(w->npos[i]);
+
+      /* step B2(b): update n_i' */
+      for (i = 0; i < 5; ++i)
+        w->np[i] += w->dnp[i];
+
+      /* step B3: update heights */
+      for (i = 1; i <= 3; ++i)
+        {
+          double ni = (double) w->npos[i];
+          double d = w->np[i] - ni;
+
+          if ((d >= 1.0 && (w->npos[i + 1] - w->npos[i] > 1)) ||
+              (d <= -1.0 && (w->npos[i - 1] - w->npos[i] < -1)))
+            {
+              int dsign = (d > 0.0) ? 1 : -1;
+              double qp1 = w->q[i + 1];
+              double qi = w->q[i];
+              double qm1 = w->q[i - 1];
+              double np1 = (double) w->npos[i + 1];
+              double nm1 = (double) w->npos[i - 1];
+              double qp = calc_psq(qp1, qi, qm1, (double) dsign,
+                                   np1, ni, nm1);
+
+              if (qm1 < qp && qp < qp1)
+                w->q[i] = qp;
+              else
+                {
+                  /* use linear formula */
+                  w->q[i] += dsign * (w->q[i + dsign] - qi) / ((double) w->npos[i + dsign] - ni);
+                }
+
+              w->npos[i] += dsign;
+            }
+        }
+    }
+
+  ++(w->n);
+
+  return GSL_SUCCESS;
+} /* gsl_rstat_quantile_add() */
+
+double
+gsl_rstat_quantile_get(gsl_rstat_quantile_workspace *w)
+{
+  if (w->n >= 5)
+    {
+      return w->q[2];
+    }
+  else
+    {
+      /* not yet initialized */
+      gsl_sort(w->q, 1, w->n);
+      return gsl_stats_quantile_from_sorted_data(w->q, 1, w->n, w->p);
+    }
+} /* gsl_rstat_quantile_get() */
+
+static double
+calc_psq(const double qp1, const double q, const double qm1,
+         const double d, const double np1, const double n, const double nm1)
+{
+  double outer = d / (np1 - nm1);
+  double inner_left = (n - nm1 + d) * (qp1 - q) / (np1 - n);
+  double inner_right = (np1 - n - d) * (q - qm1) / (n - nm1);
+
+  return q + outer * (inner_left + inner_right);
+} /* calc_psq() */
diff -Nru gsl-doc-1.16/rstat/rstat.c gsl-doc-2.3/rstat/rstat.c
--- gsl-doc-1.16/rstat/rstat.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/rstat/rstat.c	2016-10-03 09:08:46.000000000 +0000
@@ -0,0 +1,221 @@
+/* rstat/rstat.c
+ * 
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_rstat.h>
+
+gsl_rstat_workspace *
+gsl_rstat_alloc(void)
+{
+  gsl_rstat_workspace *w;
+
+  w = calloc(1, sizeof(gsl_rstat_workspace));
+
+  if (w == 0)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for workspace", GSL_ENOMEM);
+    }
+
+  w->median_workspace_p = gsl_rstat_quantile_alloc(0.5);
+
+  if (w->median_workspace_p == 0)
+    {
+      GSL_ERROR_NULL ("failed to allocate space for median workspace",
+                      GSL_ENOMEM);
+    }
+
+  gsl_rstat_reset(w);
+
+  return w;
+} /* gsl_rstat_alloc() */
+
+void
+gsl_rstat_free(gsl_rstat_workspace *w)
+{
+  if (w->median_workspace_p)
+    gsl_rstat_quantile_free(w->median_workspace_p);
+
+  free(w);
+} /* gsl_rstat_free() */
+
+size_t
+gsl_rstat_n(gsl_rstat_workspace *w)
+{
+  return w->n;
+} /* gsl_rstat_n() */
+
+/* add a data point to the running totals */
+int
+gsl_rstat_add(const double x, gsl_rstat_workspace *w)
+{
+  double delta = x - w->mean;
+  double delta_n, delta_nsq, term1, n;
+
+  /* update min and max */
+  if (w->n == 0)
+    {
+      w->min = x;
+      w->max = x;
+    }
+  else
+    {
+      if (x < w->min)
+        w->min = x;
+      if (x > w->max)
+        w->max = x;
+    }
+
+  /* update mean and variance */
+  n = (double) ++(w->n);
+  delta_n = delta / n;
+  delta_nsq = delta_n * delta_n;
+  term1 = delta * delta_n * (n - 1.0);
+  w->mean += delta_n;
+  w->M4 += term1 * delta_nsq * (n * n - 3.0 * n + 3.0) +
+           6.0 * delta_nsq * w->M2 - 4.0 * delta_n * w->M3;
+  w->M3 += term1 * delta_n * (n - 2.0) - 3.0 * delta_n * w->M2;
+  w->M2 += term1;
+
+  /* update median */
+  gsl_rstat_quantile_add(x, w->median_workspace_p);
+
+  return GSL_SUCCESS;
+} /* gsl_rstat_add() */
+
+double
+gsl_rstat_min(gsl_rstat_workspace *w)
+{
+  return w->min;
+} /* gsl_rstat_min() */
+
+double
+gsl_rstat_max(gsl_rstat_workspace *w)
+{
+  return w->max;
+} /* gsl_rstat_max() */
+
+double
+gsl_rstat_mean(gsl_rstat_workspace *w)
+{
+  return w->mean;
+} /* gsl_rstat_mean() */
+
+double
+gsl_rstat_variance(gsl_rstat_workspace *w)
+{
+  if (w->n > 1)
+    {
+      double n = (double) w->n;
+      return (w->M2 / (n - 1.0));
+    }
+  else
+    return 0.0;
+} /* gsl_rstat_variance() */
+
+double
+gsl_rstat_sd(gsl_rstat_workspace *w)
+{
+  double var = gsl_rstat_variance(w);
+
+  return (sqrt(var));
+} /* gsl_rstat_sd() */
+
+double
+gsl_rstat_rms(gsl_rstat_workspace *w)
+{
+  double rms = 0.0;
+
+  if (w->n > 0)
+    {
+      double mean = gsl_rstat_mean(w);
+      double sigma = gsl_rstat_sd(w);
+      double n = (double) w->n;
+      double a = sqrt((n - 1.0) / n);
+      rms = gsl_hypot(mean, a * sigma);
+    }
+
+  return rms;
+}
+
+/* standard deviation of the mean: sigma / sqrt(n) */
+double
+gsl_rstat_sd_mean(gsl_rstat_workspace *w)
+{
+  if (w->n > 0)
+    {
+      double sd = gsl_rstat_sd(w);
+      return (sd / sqrt((double) w->n));
+    }
+  else
+    return 0.0;
+} /* gsl_rstat_sd_mean() */
+
+double
+gsl_rstat_median(gsl_rstat_workspace *w)
+{
+  return gsl_rstat_quantile_get(w->median_workspace_p);
+}
+
+double
+gsl_rstat_skew(gsl_rstat_workspace *w)
+{
+  if (w->n > 0)
+    {
+      double n = (double) w->n;
+      double fac = pow(n - 1.0, 1.5) / n;
+      return ((fac * w->M3) / pow(w->M2, 1.5));
+    }
+  else
+    return 0.0;
+} /* gsl_rstat_skew() */
+
+double
+gsl_rstat_kurtosis(gsl_rstat_workspace *w)
+{
+  if (w->n > 0)
+    {
+      double n = (double) w->n;
+      double fac = ((n - 1.0) / n) * (n - 1.0);
+      return ((fac * w->M4) / (w->M2 * w->M2) - 3.0);
+    }
+  else
+    return 0.0;
+} /* gsl_rstat_kurtosis() */
+
+int
+gsl_rstat_reset(gsl_rstat_workspace *w)
+{
+  int status;
+
+  w->min = 0.0;
+  w->max = 0.0;
+  w->mean = 0.0;
+  w->M2 = 0.0;
+  w->M3 = 0.0;
+  w->M4 = 0.0;
+  w->n = 0;
+
+  status = gsl_rstat_quantile_reset(w->median_workspace_p);
+
+  return status;
+} /* gsl_rstat_reset() */
diff -Nru gsl-doc-1.16/rstat/test.c gsl-doc-2.3/rstat/test.c
--- gsl-doc-1.16/rstat/test.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/rstat/test.c	2016-10-03 09:08:46.000000000 +0000
@@ -0,0 +1,218 @@
+/* rstat/test.c
+ * 
+ * Copyright (C) 2015 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+#include <string.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_rstat.h>
+#include <gsl/gsl_sort.h>
+#include <gsl/gsl_statistics.h>
+#include <gsl/gsl_test.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_randist.h>
+#include <gsl/gsl_ieee_utils.h>
+
+double *
+random_data(const size_t n, gsl_rng *r)
+{
+  size_t i;
+  double *data = malloc(n * sizeof(double));
+
+  for (i = 0; i < n; ++i)
+    data[i] = gsl_rng_uniform(r);
+
+  return data;
+}
+
+void
+test_basic(const size_t n, const double data[], const double tol)
+{
+  gsl_rstat_workspace *rstat_workspace_p = gsl_rstat_alloc();
+  const double expected_mean = gsl_stats_mean(data, 1, n);
+  const double expected_var = gsl_stats_variance(data, 1, n);
+  const double expected_sd = gsl_stats_sd(data, 1, n);
+  const double expected_sd_mean = expected_sd / sqrt((double) n);
+  const double expected_skew = gsl_stats_skew(data, 1, n);
+  const double expected_kurtosis = gsl_stats_kurtosis(data, 1, n);
+  double expected_rms = 0.0;
+  double mean, var, sd, sd_mean, rms, skew, kurtosis;
+  size_t i, num;
+  int status;
+
+  /* compute expected rms */
+  for (i = 0; i < n; ++i)
+    expected_rms += data[i] * data[i];
+
+  expected_rms = sqrt(expected_rms / n);
+
+  /* add data to rstat workspace */
+  for (i = 0; i < n; ++i)
+    gsl_rstat_add(data[i], rstat_workspace_p);
+
+  mean     = gsl_rstat_mean(rstat_workspace_p);
+  var      = gsl_rstat_variance(rstat_workspace_p);
+  sd       = gsl_rstat_sd(rstat_workspace_p);
+  sd_mean  = gsl_rstat_sd_mean(rstat_workspace_p);
+  rms      = gsl_rstat_rms(rstat_workspace_p);
+  skew     = gsl_rstat_skew(rstat_workspace_p);
+  kurtosis = gsl_rstat_kurtosis(rstat_workspace_p);
+  num      = gsl_rstat_n(rstat_workspace_p);
+
+  gsl_test_int(num, n, "n n=%zu" , n);
+  gsl_test_rel(mean, expected_mean, tol, "mean n=%zu", n);
+  gsl_test_rel(var, expected_var, tol, "variance n=%zu", n);
+  gsl_test_rel(sd, expected_sd, tol, "stddev n=%zu", n);
+  gsl_test_rel(sd_mean, expected_sd_mean, tol, "stddev_mean n=%zu", n);
+  gsl_test_rel(rms, expected_rms, tol, "rms n=%zu", n);
+  gsl_test_rel(skew, expected_skew, tol, "skew n=%zu", n);
+  gsl_test_rel(kurtosis, expected_kurtosis, tol, "kurtosis n=%zu", n);
+
+  status = gsl_rstat_reset(rstat_workspace_p);
+  gsl_test_int(status, GSL_SUCCESS, "rstat returned success");
+  num = gsl_rstat_n(rstat_workspace_p);
+
+  gsl_test_int(num, 0, "n n=%zu" , n);
+
+  gsl_rstat_free(rstat_workspace_p);
+}
+
+void
+test_quantile(const double p, const double data[], const size_t n,
+              const double expected, const double tol, const char *desc)
+{
+  gsl_rstat_quantile_workspace *w = gsl_rstat_quantile_alloc(p);
+  double result;
+  size_t i;
+
+  for (i = 0; i < n; ++i)
+    gsl_rstat_quantile_add(data[i], w);
+
+  result = gsl_rstat_quantile_get(w);
+
+  if (fabs(expected) < 1.0e-4)
+    gsl_test_abs(result, expected, tol, "%s p=%g", desc, p);
+  else
+    gsl_test_rel(result, expected, tol, "%s p=%g", desc, p);
+
+  gsl_rstat_quantile_free(w);
+}
+
+int
+main()
+{
+  gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+  const double tol1 = 1.0e-8;
+  const double tol2 = 1.0e-3;
+
+  gsl_ieee_env_setup();
+
+  {
+    const size_t N = 2000000;
+    double *data = random_data(N, r);
+    double data2[] = { 4.0, 7.0, 13.0, 16.0 };
+    size_t i;
+
+    test_basic(2, data, tol1);
+    test_basic(100, data, tol1);
+    test_basic(1000, data, tol1);
+    test_basic(10000, data, tol1);
+    test_basic(50000, data, tol1);
+    test_basic(80000, data, tol1);
+    test_basic(1500000, data, tol1);
+    test_basic(2000000, data, tol1);
+
+    for (i = 0; i < 4; ++i)
+      data2[i] += 1.0e9;
+
+    test_basic(4, data2, tol1);
+
+    free(data);
+  }
+
+  {
+    /* dataset from Jain and Chlamtac paper */
+    const size_t n_jain = 20;
+    const double data_jain[] = {  0.02,  0.15,  0.74,  3.39,  0.83,
+                                  22.37, 10.15, 15.43, 38.62, 15.92,
+                                  34.60, 10.28,  1.47,  0.40,  0.05,
+                                  11.39,  0.27,  0.42,  0.09, 11.37 };
+    double expected_jain = 4.44063435326;
+  
+    test_quantile(0.5, data_jain, n_jain, expected_jain, tol1, "jain");
+  }
+
+  {
+    size_t n = 1000000;
+    double *data = malloc(n * sizeof(double));
+    double *sorted_data = malloc(n * sizeof(double));
+    gsl_rstat_workspace *rstat_workspace_p = gsl_rstat_alloc();
+    double p;
+    size_t i;
+
+    for (i = 0; i < n; ++i)
+      {
+        data[i] = gsl_ran_gaussian_tail(r, 1.3, 1.0);
+        gsl_rstat_add(data[i], rstat_workspace_p);
+      }
+
+    memcpy(sorted_data, data, n * sizeof(double));
+    gsl_sort(sorted_data, 1, n);
+
+    /* test quantile calculation */
+    for (p = 0.1; p <= 0.9; p += 0.1)
+      {
+        double expected = gsl_stats_quantile_from_sorted_data(sorted_data, 1, n, p);
+        test_quantile(p, data, n, expected, tol2, "gauss");
+      }
+
+    /* test mean, variance */
+    {
+      const double expected_mean = gsl_stats_mean(data, 1, n);
+      const double expected_var = gsl_stats_variance(data, 1, n);
+      const double expected_sd = gsl_stats_sd(data, 1, n);
+      const double expected_skew = gsl_stats_skew(data, 1, n);
+      const double expected_kurtosis = gsl_stats_kurtosis(data, 1, n);
+      const double expected_median = gsl_stats_quantile_from_sorted_data(sorted_data, 1, n, 0.5);
+
+      const double mean = gsl_rstat_mean(rstat_workspace_p);
+      const double var = gsl_rstat_variance(rstat_workspace_p);
+      const double sd = gsl_rstat_sd(rstat_workspace_p);
+      const double skew = gsl_rstat_skew(rstat_workspace_p);
+      const double kurtosis = gsl_rstat_kurtosis(rstat_workspace_p);
+      const double median = gsl_rstat_median(rstat_workspace_p);
+
+      gsl_test_rel(mean, expected_mean, tol1, "mean");
+      gsl_test_rel(var, expected_var, tol1, "variance");
+      gsl_test_rel(sd, expected_sd, tol1, "stddev");
+      gsl_test_rel(skew, expected_skew, tol1, "skew");
+      gsl_test_rel(kurtosis, expected_kurtosis, tol1, "kurtosis");
+      gsl_test_abs(median, expected_median, tol2, "median");
+    }
+
+    free(data);
+    free(sorted_data);
+    gsl_rstat_free(rstat_workspace_p);
+  }
+
+  gsl_rng_free(r);
+
+  exit (gsl_test_summary());
+}
diff -Nru gsl-doc-1.16/siman/Makefile.am gsl-doc-2.3/siman/Makefile.am
--- gsl-doc-1.16/siman/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/siman/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -18,4 +18,4 @@
 libgslsiman_la_SOURCES = siman.c
 pkginclude_HEADERS = gsl_siman.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
diff -Nru gsl-doc-1.16/siman/Makefile.in gsl-doc-2.3/siman/Makefile.in
--- gsl-doc-1.16/siman/Makefile.in	2013-07-19 15:14:55.000000000 +0000
+++ gsl-doc-2.3/siman/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -386,6 +386,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -408,7 +409,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -532,7 +536,7 @@
 CLEANFILES = siman_test.out
 libgslsiman_la_SOURCES = siman.c
 pkginclude_HEADERS = gsl_siman.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 all: all-am
 
 .SUFFIXES:
diff -Nru gsl-doc-1.16/sort/Makefile.am gsl-doc-2.3/sort/Makefile.am
--- gsl-doc-1.16/sort/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/sort/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_heapsort.h gsl_sort.h gsl_sort_char.h gsl_sort_double.h gsl_sort_float.h gsl_sort_int.h gsl_sort_long.h gsl_sort_long_double.h gsl_sort_short.h gsl_sort_uchar.h gsl_sort_uint.h gsl_sort_ulong.h gsl_sort_ushort.h gsl_sort_vector.h gsl_sort_vector_char.h gsl_sort_vector_double.h gsl_sort_vector_float.h gsl_sort_vector_int.h gsl_sort_vector_long.h gsl_sort_vector_long_double.h gsl_sort_vector_short.h gsl_sort_vector_uchar.h gsl_sort_vector_uint.h gsl_sort_vector_ulong.h gsl_sort_vector_ushort.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslsort_la_SOURCES = sort.c sortind.c sortvec.c sortvecind.c subset.c subsetind.c
 noinst_HEADERS = sortvec_source.c sortvecind_source.c subset_source.c subsetind_source.c test_source.c test_heapsort.c 
diff -Nru gsl-doc-1.16/sort/Makefile.in gsl-doc-2.3/sort/Makefile.in
--- gsl-doc-1.16/sort/Makefile.in	2013-07-19 15:14:55.000000000 +0000
+++ gsl-doc-2.3/sort/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -379,6 +379,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -401,7 +402,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -517,7 +521,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslsort.la
 pkginclude_HEADERS = gsl_heapsort.h gsl_sort.h gsl_sort_char.h gsl_sort_double.h gsl_sort_float.h gsl_sort_int.h gsl_sort_long.h gsl_sort_long_double.h gsl_sort_short.h gsl_sort_uchar.h gsl_sort_uint.h gsl_sort_ulong.h gsl_sort_ushort.h gsl_sort_vector.h gsl_sort_vector_char.h gsl_sort_vector_double.h gsl_sort_vector_float.h gsl_sort_vector_int.h gsl_sort_vector_long.h gsl_sort_vector_long_double.h gsl_sort_vector_short.h gsl_sort_vector_uchar.h gsl_sort_vector_uint.h gsl_sort_vector_ulong.h gsl_sort_vector_ushort.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslsort_la_SOURCES = sort.c sortind.c sortvec.c sortvecind.c subset.c subsetind.c
 noinst_HEADERS = sortvec_source.c sortvecind_source.c subset_source.c subsetind_source.c test_source.c test_heapsort.c 
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/spblas/gsl_spblas.h gsl-doc-2.3/spblas/gsl_spblas.h
--- gsl-doc-1.16/spblas/gsl_spblas.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spblas/gsl_spblas.h	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,58 @@
+/* gsl_spblas.h
+ * 
+ * Copyright (C) 2012-2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_SPBLAS_H__
+#define __GSL_SPBLAS_H__
+
+#include <stdlib.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_spmatrix.h>
+#include <gsl/gsl_blas.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+/*
+ * Prototypes
+ */
+
+int gsl_spblas_dgemv(const CBLAS_TRANSPOSE_t TransA, const double alpha,
+                     const gsl_spmatrix *A, const gsl_vector *x,
+                     const double beta, gsl_vector *y);
+int gsl_spblas_dgemm(const double alpha, const gsl_spmatrix *A,
+                     const gsl_spmatrix *B, gsl_spmatrix *C);
+size_t gsl_spblas_scatter(const gsl_spmatrix *A, const size_t j,
+                          const double alpha, size_t *w, double *x,
+                          const size_t mark, gsl_spmatrix *C, size_t nz);
+
+__END_DECLS
+
+#endif /* __GSL_SPBLAS_H__ */
diff -Nru gsl-doc-1.16/spblas/Makefile.am gsl-doc-2.3/spblas/Makefile.am
--- gsl-doc-1.16/spblas/Makefile.am	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spblas/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,15 @@
+noinst_LTLIBRARIES = libgslspblas.la 
+
+check_PROGRAMS = test
+
+pkginclude_HEADERS = gsl_spblas.h
+
+libgslspblas_la_SOURCES = spdgemm.c spdgemv.c
+
+AM_CPPFLAGS = -I$(top_srcdir)
+
+TESTS = $(check_PROGRAMS)
+
+test_LDADD = libgslspblas.la ../spmatrix/libgslspmatrix.la ../test/libgsltest.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la  ../sys/libgslsys.la ../err/libgslerr.la ../utils/libutils.la ../rng/libgslrng.la
+
+test_SOURCES = test.c
diff -Nru gsl-doc-1.16/spblas/Makefile.in gsl-doc-2.3/spblas/Makefile.in
--- gsl-doc-1.16/spblas/Makefile.in	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spblas/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -0,0 +1,1028 @@
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
+# @configure_input@
+
+# Copyright (C) 1994-2013 Free Software Foundation, Inc.
+
+# This Makefile.in is free software; the Free Software Foundation
+# gives unlimited permission to copy and/or distribute it,
+# with or without modifications, as long as this notice is preserved.
+
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY, to the extent permitted by law; without
+# even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+# PARTICULAR PURPOSE.
+
+@SET_MAKE@
+
+
+VPATH = @srcdir@
+am__is_gnu_make = test -n '$(MAKEFILE_LIST)' && test -n '$(MAKELEVEL)'
+am__make_running_with_option = \
+  case $${target_option-} in \
+      ?) ;; \
+      *) echo "am__make_running_with_option: internal error: invalid" \
+              "target option '$${target_option-}' specified" >&2; \
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+  esac; \
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+  if $(am__is_gnu_make); then \
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+  strip_trailopt () \
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+  for flg in $$sane_makeflags; do \
+    test $$skip_next = yes && { skip_next=no; continue; }; \
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+am__make_dryrun = (target_option=n; $(am__make_running_with_option))
+am__make_keepgoing = (target_option=k; $(am__make_running_with_option))
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+am__cd = CDPATH="$${ZSH_VERSION+.}$(PATH_SEPARATOR)" && cd
+install_sh_DATA = $(install_sh) -c -m 644
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+INSTALL_HEADER = $(INSTALL_DATA)
+transform = $(program_transform_name)
+NORMAL_INSTALL = :
+PRE_INSTALL = :
+POST_INSTALL = :
+NORMAL_UNINSTALL = :
+PRE_UNINSTALL = :
+POST_UNINSTALL = :
+build_triplet = @build@
+host_triplet = @host@
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+DIST_COMMON = $(srcdir)/Makefile.in $(srcdir)/Makefile.am \
+	$(top_srcdir)/mkinstalldirs $(top_srcdir)/depcomp \
+	$(pkginclude_HEADERS) $(top_srcdir)/test-driver
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+am__configure_deps = $(am__aclocal_m4_deps) $(CONFIGURE_DEPENDENCIES) \
+	$(ACLOCAL_M4)
+mkinstalldirs = $(SHELL) $(top_srcdir)/mkinstalldirs
+CONFIG_HEADER = $(top_builddir)/config.h
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+	../test/libgsltest.la ../blas/libgslblas.la \
+	../cblas/libgslcblas.la ../matrix/libgslmatrix.la \
+	../vector/libgslvector.la ../block/libgslblock.la \
+	../sys/libgslsys.la ../err/libgslerr.la ../utils/libutils.la \
+	../rng/libgslrng.la
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+LTCOMPILE = $(LIBTOOL) $(AM_V_lt) --tag=CC $(AM_LIBTOOLFLAGS) \
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+	@list='$(RECHECK_LOGS)';           test -z "$$list" || rm -f $$list
+	@list='$(RECHECK_LOGS:.log=.trs)'; test -z "$$list" || rm -f $$list
+	@test -z "$(TEST_SUITE_LOG)" || rm -f $(TEST_SUITE_LOG)
+	@set +e; $(am__set_TESTS_bases); \
+	log_list=`for i in $$bases; do echo $$i.log; done`; \
+	trs_list=`for i in $$bases; do echo $$i.trs; done`; \
+	log_list=`echo $$log_list`; trs_list=`echo $$trs_list`; \
+	$(MAKE) $(AM_MAKEFLAGS) $(TEST_SUITE_LOG) TEST_LOGS="$$log_list"; \
+	exit $$?;
+recheck: all $(check_PROGRAMS)
+	@test -z "$(TEST_SUITE_LOG)" || rm -f $(TEST_SUITE_LOG)
+	@set +e; $(am__set_TESTS_bases); \
+	bases=`for i in $$bases; do echo $$i; done \
+	         | $(am__list_recheck_tests)` || exit 1; \
+	log_list=`for i in $$bases; do echo $$i.log; done`; \
+	log_list=`echo $$log_list`; \
+	$(MAKE) $(AM_MAKEFLAGS) $(TEST_SUITE_LOG) \
+	        am__force_recheck=am--force-recheck \
+	        TEST_LOGS="$$log_list"; \
+	exit $$?
+test.log: test$(EXEEXT)
+	@p='test$(EXEEXT)'; \
+	b='test'; \
+	$(am__check_pre) $(LOG_DRIVER) --test-name "$$f" \
+	--log-file $$b.log --trs-file $$b.trs \
+	$(am__common_driver_flags) $(AM_LOG_DRIVER_FLAGS) $(LOG_DRIVER_FLAGS) -- $(LOG_COMPILE) \
+	"$$tst" $(AM_TESTS_FD_REDIRECT)
+.test.log:
+	@p='$<'; \
+	$(am__set_b); \
+	$(am__check_pre) $(TEST_LOG_DRIVER) --test-name "$$f" \
+	--log-file $$b.log --trs-file $$b.trs \
+	$(am__common_driver_flags) $(AM_TEST_LOG_DRIVER_FLAGS) $(TEST_LOG_DRIVER_FLAGS) -- $(TEST_LOG_COMPILE) \
+	"$$tst" $(AM_TESTS_FD_REDIRECT)
+@am__EXEEXT_TRUE@.test$(EXEEXT).log:
+@am__EXEEXT_TRUE@	@p='$<'; \
+@am__EXEEXT_TRUE@	$(am__set_b); \
+@am__EXEEXT_TRUE@	$(am__check_pre) $(TEST_LOG_DRIVER) --test-name "$$f" \
+@am__EXEEXT_TRUE@	--log-file $$b.log --trs-file $$b.trs \
+@am__EXEEXT_TRUE@	$(am__common_driver_flags) $(AM_TEST_LOG_DRIVER_FLAGS) $(TEST_LOG_DRIVER_FLAGS) -- $(TEST_LOG_COMPILE) \
+@am__EXEEXT_TRUE@	"$$tst" $(AM_TESTS_FD_REDIRECT)
+
+distdir: $(DISTFILES)
+	@srcdirstrip=`echo "$(srcdir)" | sed 's/[].[^$$\\*]/\\\\&/g'`; \
+	topsrcdirstrip=`echo "$(top_srcdir)" | sed 's/[].[^$$\\*]/\\\\&/g'`; \
+	list='$(DISTFILES)'; \
+	  dist_files=`for file in $$list; do echo $$file; done | \
+	  sed -e "s|^$$srcdirstrip/||;t" \
+	      -e "s|^$$topsrcdirstrip/|$(top_builddir)/|;t"`; \
+	case $$dist_files in \
+	  */*) $(MKDIR_P) `echo "$$dist_files" | \
+			   sed '/\//!d;s|^|$(distdir)/|;s,/[^/]*$$,,' | \
+			   sort -u` ;; \
+	esac; \
+	for file in $$dist_files; do \
+	  if test -f $$file || test -d $$file; then d=.; else d=$(srcdir); fi; \
+	  if test -d $$d/$$file; then \
+	    dir=`echo "/$$file" | sed -e 's,/[^/]*$$,,'`; \
+	    if test -d "$(distdir)/$$file"; then \
+	      find "$(distdir)/$$file" -type d ! -perm -700 -exec chmod u+rwx {} \;; \
+	    fi; \
+	    if test -d $(srcdir)/$$file && test $$d != $(srcdir); then \
+	      cp -fpR $(srcdir)/$$file "$(distdir)$$dir" || exit 1; \
+	      find "$(distdir)/$$file" -type d ! -perm -700 -exec chmod u+rwx {} \;; \
+	    fi; \
+	    cp -fpR $$d/$$file "$(distdir)$$dir" || exit 1; \
+	  else \
+	    test -f "$(distdir)/$$file" \
+	    || cp -p $$d/$$file "$(distdir)/$$file" \
+	    || exit 1; \
+	  fi; \
+	done
+check-am: all-am
+	$(MAKE) $(AM_MAKEFLAGS) $(check_PROGRAMS)
+	$(MAKE) $(AM_MAKEFLAGS) check-TESTS
+check: check-am
+all-am: Makefile $(LTLIBRARIES) $(HEADERS)
+installdirs:
+	for dir in "$(DESTDIR)$(pkgincludedir)"; do \
+	  test -z "$$dir" || $(MKDIR_P) "$$dir"; \
+	done
+install: install-am
+install-exec: install-exec-am
+install-data: install-data-am
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+install-am: all-am
+	@$(MAKE) $(AM_MAKEFLAGS) install-exec-am install-data-am
+
+installcheck: installcheck-am
+install-strip:
+	if test -z '$(STRIP)'; then \
+	  $(MAKE) $(AM_MAKEFLAGS) INSTALL_PROGRAM="$(INSTALL_STRIP_PROGRAM)" \
+	    install_sh_PROGRAM="$(INSTALL_STRIP_PROGRAM)" INSTALL_STRIP_FLAG=-s \
+	      install; \
+	else \
+	  $(MAKE) $(AM_MAKEFLAGS) INSTALL_PROGRAM="$(INSTALL_STRIP_PROGRAM)" \
+	    install_sh_PROGRAM="$(INSTALL_STRIP_PROGRAM)" INSTALL_STRIP_FLAG=-s \
+	    "INSTALL_PROGRAM_ENV=STRIPPROG='$(STRIP)'" install; \
+	fi
+mostlyclean-generic:
+	-test -z "$(TEST_LOGS)" || rm -f $(TEST_LOGS)
+	-test -z "$(TEST_LOGS:.log=.trs)" || rm -f $(TEST_LOGS:.log=.trs)
+	-test -z "$(TEST_SUITE_LOG)" || rm -f $(TEST_SUITE_LOG)
+
+clean-generic:
+
+distclean-generic:
+	-test -z "$(CONFIG_CLEAN_FILES)" || rm -f $(CONFIG_CLEAN_FILES)
+	-test . = "$(srcdir)" || test -z "$(CONFIG_CLEAN_VPATH_FILES)" || rm -f $(CONFIG_CLEAN_VPATH_FILES)
+
+maintainer-clean-generic:
+	@echo "This command is intended for maintainers to use"
+	@echo "it deletes files that may require special tools to rebuild."
+clean: clean-am
+
+clean-am: clean-checkPROGRAMS clean-generic clean-libtool \
+	clean-noinstLTLIBRARIES mostlyclean-am
+
+distclean: distclean-am
+	-rm -rf ./$(DEPDIR)
+	-rm -f Makefile
+distclean-am: clean-am distclean-compile distclean-generic \
+	distclean-tags
+
+dvi: dvi-am
+
+dvi-am:
+
+html: html-am
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+html-am:
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+info: info-am
+
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+install-data-am: install-pkgincludeHEADERS
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+install-dvi: install-dvi-am
+
+install-dvi-am:
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+install-exec-am:
+
+install-html: install-html-am
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+install-html-am:
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+install-ps-am:
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+
+maintainer-clean: maintainer-clean-am
+	-rm -rf ./$(DEPDIR)
+	-rm -f Makefile
+maintainer-clean-am: distclean-am maintainer-clean-generic
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+mostlyclean: mostlyclean-am
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+mostlyclean-am: mostlyclean-compile mostlyclean-generic \
+	mostlyclean-libtool
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+.MAKE: check-am install-am install-strip
+
+.PHONY: CTAGS GTAGS TAGS all all-am check check-TESTS check-am clean \
+	clean-checkPROGRAMS clean-generic clean-libtool \
+	clean-noinstLTLIBRARIES cscopelist-am ctags ctags-am distclean \
+	distclean-compile distclean-generic distclean-libtool \
+	distclean-tags distdir dvi dvi-am html html-am info info-am \
+	install install-am install-data install-data-am install-dvi \
+	install-dvi-am install-exec install-exec-am install-html \
+	install-html-am install-info install-info-am install-man \
+	install-pdf install-pdf-am install-pkgincludeHEADERS \
+	install-ps install-ps-am install-strip installcheck \
+	installcheck-am installdirs maintainer-clean \
+	maintainer-clean-generic mostlyclean mostlyclean-compile \
+	mostlyclean-generic mostlyclean-libtool pdf pdf-am ps ps-am \
+	recheck tags tags-am uninstall uninstall-am \
+	uninstall-pkgincludeHEADERS
+
+
+# Tell versions [3.59,3.63) of GNU make to not export all variables.
+# Otherwise a system limit (for SysV at least) may be exceeded.
+.NOEXPORT:
diff -Nru gsl-doc-1.16/spblas/spdgemm.c gsl-doc-2.3/spblas/spdgemm.c
--- gsl-doc-1.16/spblas/spdgemm.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spblas/spdgemm.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,182 @@
+/* spdgemm.c
+ * 
+ * Copyright (C) 2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+#include <gsl/gsl_spmatrix.h>
+#include <gsl/gsl_spblas.h>
+#include <gsl/gsl_errno.h>
+
+/*
+gsl_spblas_dgemm()
+  Multiply two sparse matrices
+
+Inputs: alpha - scalar factor
+        A     - sparse matrix
+        B     - sparse matrix
+        C     - (output) C = alpha * A * B
+
+Return: success or error
+
+Notes:
+1) based on CSparse routine cs_multiply
+*/
+
+int
+gsl_spblas_dgemm(const double alpha, const gsl_spmatrix *A,
+                 const gsl_spmatrix *B, gsl_spmatrix *C)
+{
+  if (A->size2 != B->size1 || A->size1 != C->size1 || B->size2 != C->size2)
+    {
+      GSL_ERROR("matrix dimensions do not match", GSL_EBADLEN);
+    }
+  else if (A->sptype != B->sptype || A->sptype != C->sptype)
+    {
+      GSL_ERROR("matrix storage formats do not match", GSL_EINVAL);
+    }
+  else if (!GSL_SPMATRIX_ISCCS(A))
+    {
+      GSL_ERROR("compressed column format required", GSL_EINVAL);
+    }
+  else
+    {
+      int status = GSL_SUCCESS;
+      const size_t M = A->size1;
+      const size_t N = B->size2;
+      size_t *Bi = B->i;
+      size_t *Bp = B->p;
+      double *Bd = B->data;
+      size_t *w = (size_t *) A->work; /* workspace of length M */
+      double *x = (double *) C->work; /* workspace of length M */
+      size_t *Cp, *Ci;
+      double *Cd;
+      size_t j, p;
+      size_t nz = 0;
+
+      if (C->nzmax < A->nz + B->nz)
+        {
+          status = gsl_spmatrix_realloc(A->nz + B->nz, C);
+          if (status)
+            {
+              GSL_ERROR("unable to realloc matrix C", status);
+            }
+        }
+
+      /* initialize workspace to 0 */
+      for (j = 0; j < M; ++j)
+        w[j] = 0;
+
+      Cp = C->p;
+      Ci = C->i;
+      Cd = C->data;
+
+      for (j = 0; j < N; ++j)
+        {
+          if (nz + M > C->nzmax)
+            {
+              status = gsl_spmatrix_realloc(2 * C->nzmax + M, C);
+              if (status)
+                {
+                  GSL_ERROR("unable to realloc matrix C", status);
+                }
+
+              /* these pointers could have changed due to reallocation */
+              Ci = C->i;
+              Cd = C->data;
+            }
+
+          Cp[j] = nz; /* column j of C starts here */
+
+          for (p = Bp[j]; p < Bp[j + 1]; ++p)
+            {
+              nz = gsl_spblas_scatter(A, Bi[p], Bd[p], w, x, j + 1, C, nz);
+            }
+
+          for (p = Cp[j]; p < nz; ++p)
+            Cd[p] = x[Ci[p]];
+        }
+
+      Cp[N] = nz;
+      C->nz = nz;
+
+      /* scale by alpha */
+      gsl_spmatrix_scale(C, alpha);
+
+      return status;
+    }
+} /* gsl_spblas_dgemm() */
+
+/*
+gsl_spblas_scatter()
+
+  Keep a running total x -> x + alpha*A(:,j) for adding matrices together in CCS,
+which will eventually be stored in C(:,j)
+
+  When a new non-zero element with row index i is found, update C->i with
+the row index. C->data is updated only by the calling function after all
+matrices have been added via this function.
+
+Inputs: A     - sparse matrix m-by-n
+        j     - column index
+        alpha - scalar factor
+        w     - keeps track which rows of column j have been added to C;
+                initialize to 0 prior to first call
+        x     - column vector of length m
+        mark  -
+        C     - output matrix whose jth column will be added to A(:,j)
+        nz    - (input/output) number of non-zeros in matrix C
+
+Notes:
+1) This function is designed to be called successively when adding multiple
+matrices together. Column j of C is stored contiguously as per CCS but not
+necessarily in order - ie: the row indices C->i may not be in ascending order.
+
+2) based on CSparse routine cs_scatter
+*/
+
+size_t
+gsl_spblas_scatter(const gsl_spmatrix *A, const size_t j, const double alpha,
+                   size_t *w, double *x, const size_t mark, gsl_spmatrix *C,
+                   size_t nz)
+{
+  size_t p;
+  size_t *Ai = A->i;
+  size_t *Ap = A->p;
+  double *Ad = A->data;
+  size_t *Ci = C->i;
+
+  for (p = Ap[j]; p < Ap[j + 1]; ++p)
+    {
+      size_t i = Ai[p];          /* A(i,j) is nonzero */
+
+      if (w[i] < mark)           /* check if row i has been stored in column j yet */
+        {
+          w[i] = mark;           /* i is new entry in column j */
+          Ci[nz++] = i;          /* add i to pattern of C(:,j) */
+          x[i] = alpha * Ad[p];  /* x(i) = alpha * A(i,j) */
+        }
+      else                       /* this (i,j) exists in C from a previous call */
+        {
+          x[i] += alpha * Ad[p]; /* add alpha*A(i,j) to C(i,j) */
+        }
+    }
+
+  return (nz) ;
+} /* gsl_spblas_scatter() */
diff -Nru gsl-doc-1.16/spblas/spdgemv.c gsl-doc-2.3/spblas/spdgemv.c
--- gsl-doc-1.16/spblas/spdgemv.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spblas/spdgemv.c	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,166 @@
+/* spdgemv.c
+ * 
+ * Copyright (C) 2012-2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_spmatrix.h>
+#include <gsl/gsl_spblas.h>
+#include <gsl/gsl_blas.h>
+
+/*
+gsl_spblas_dgemv()
+  Multiply a sparse matrix and a vector
+
+Inputs: alpha - scalar factor
+        A     - sparse matrix
+        x     - dense vector
+        beta  - scalar factor
+        y     - (input/output) dense vector
+
+Return: y = alpha*op(A)*x + beta*y
+*/
+
+int
+gsl_spblas_dgemv(const CBLAS_TRANSPOSE_t TransA, const double alpha,
+                 const gsl_spmatrix *A, const gsl_vector *x,
+                 const double beta, gsl_vector *y)
+{
+  const size_t M = A->size1;
+  const size_t N = A->size2;
+
+  if ((TransA == CblasNoTrans && N != x->size) ||
+      (TransA == CblasTrans && M != x->size))
+    {
+      GSL_ERROR("invalid length of x vector", GSL_EBADLEN);
+    }
+  else if ((TransA == CblasNoTrans && M != y->size) ||
+           (TransA == CblasTrans && N != y->size))
+    {
+      GSL_ERROR("invalid length of y vector", GSL_EBADLEN);
+    }
+  else
+    {
+      size_t j, p;
+      size_t incX, incY;
+      size_t lenX, lenY;
+      double *X, *Y;
+      double *Ad;
+      size_t *Ap, *Ai, *Aj;
+
+      if (TransA == CblasNoTrans)
+        {
+          lenX = N;
+          lenY = M;
+        }
+      else
+        {
+          lenX = M;
+          lenY = N;
+        }
+
+      /* form y := beta*y */
+
+      Y = y->data;
+      incY = y->stride;
+
+      if (beta == 0.0)
+        {
+          size_t jy = 0;
+          for (j = 0; j < lenY; ++j)
+            {
+              Y[jy] = 0.0;
+              jy += incY;
+            }
+        }
+      else if (beta != 1.0)
+        {
+          size_t jy = 0;
+          for (j = 0; j < lenY; ++j)
+            {
+              Y[jy] *= beta;
+              jy += incY;
+            }
+        }
+
+      if (alpha == 0.0)
+        return GSL_SUCCESS;
+
+      /* form y := alpha*op(A)*x + y */
+      Ap = A->p;
+      Ad = A->data;
+      X = x->data;
+      incX = x->stride;
+
+      if ((GSL_SPMATRIX_ISCCS(A) && (TransA == CblasNoTrans)) ||
+          (GSL_SPMATRIX_ISCRS(A) && (TransA == CblasTrans)))
+        {
+          Ai = A->i;
+
+          for (j = 0; j < lenX; ++j)
+            {
+              for (p = Ap[j]; p < Ap[j + 1]; ++p)
+                {
+                  Y[Ai[p] * incY] += alpha * Ad[p] * X[j * incX];
+                }
+            }
+        }
+      else if ((GSL_SPMATRIX_ISCCS(A) && (TransA == CblasTrans)) ||
+               (GSL_SPMATRIX_ISCRS(A) && (TransA == CblasNoTrans)))
+        {
+          Ai = A->i;
+
+          for (j = 0; j < lenY; ++j)
+            {
+              for (p = Ap[j]; p < Ap[j + 1]; ++p)
+                {
+                  Y[j * incY] += alpha * Ad[p] * X[Ai[p] * incX];
+                }
+            }
+        }
+      else if (GSL_SPMATRIX_ISTRIPLET(A))
+        {
+          if (TransA == CblasNoTrans)
+            {
+              Ai = A->i;
+              Aj = A->p;
+            }
+          else
+            {
+              Ai = A->p;
+              Aj = A->i;
+            }
+
+          for (p = 0; p < A->nz; ++p)
+            {
+              Y[Ai[p] * incY] += alpha * Ad[p] * X[Aj[p] * incX];
+            }
+        }
+      else
+        {
+          GSL_ERROR("unsupported matrix type", GSL_EINVAL);
+        }
+
+      return GSL_SUCCESS;
+    }
+} /* gsl_spblas_dgemv() */
diff -Nru gsl-doc-1.16/spblas/test.c gsl-doc-2.3/spblas/test.c
--- gsl-doc-1.16/spblas/test.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spblas/test.c	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,262 @@
+/* test.c
+ * 
+ * Copyright (C) 2012-2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_randist.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_test.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_spmatrix.h>
+#include <gsl/gsl_spblas.h>
+
+/*
+create_random_sparse()
+  Create a random sparse matrix with approximately
+M*N*density non-zero entries
+
+Inputs: M       - number of rows
+        N       - number of columns
+        density - sparse density \in [0,1]
+                  0 = no non-zero entries
+                  1 = all m*n entries are filled
+        r       - random number generator
+
+Return: pointer to sparse matrix in triplet format (must be freed by caller)
+
+Notes:
+1) non-zero matrix entries are uniformly distributed in [0,1]
+*/
+
+static gsl_spmatrix *
+create_random_sparse(const size_t M, const size_t N, const double density,
+                     const gsl_rng *r)
+{
+  size_t nnzwanted = (size_t) floor(M * N * GSL_MIN(density, 1.0));
+  gsl_spmatrix *m = gsl_spmatrix_alloc_nzmax(M, N,
+                                             nnzwanted,
+                                             GSL_SPMATRIX_TRIPLET);
+
+  while (gsl_spmatrix_nnz(m) < nnzwanted)
+    {
+      /* generate a random row and column */
+      size_t i = gsl_rng_uniform(r) * M;
+      size_t j = gsl_rng_uniform(r) * N;
+
+      /* generate random m_{ij} and add it */
+      double x = gsl_rng_uniform(r);
+      gsl_spmatrix_set(m, i, j, x);
+    }
+
+  return m;
+} /* create_random_sparse() */
+
+static void
+create_random_vector(gsl_vector *v, const gsl_rng *r)
+{
+  size_t i;
+
+  for (i = 0; i < v->size; ++i)
+    {
+      double x = gsl_rng_uniform(r);
+      gsl_vector_set(v, i, x);
+    }
+} /* create_random_vector() */
+
+static int
+test_vectors(gsl_vector *observed, gsl_vector *expected, const double tol,
+             const char *str)
+{
+  int s = 0;
+  size_t N = observed->size;
+  size_t i;
+
+  for (i = 0; i < N; ++i)
+    {
+      double x_obs = gsl_vector_get(observed, i);
+      double x_exp = gsl_vector_get(expected, i);
+
+      gsl_test_rel(x_obs, x_exp, tol, "N=%zu i=%zu %s", N, i, str);
+    }
+
+  return s;
+} /* test_vectors() */
+
+static void
+test_dgemv(const size_t N, const size_t M, const double alpha,
+           const double beta, const CBLAS_TRANSPOSE_t TransA,
+           const gsl_rng *r)
+{
+  gsl_spmatrix *A = create_random_sparse(M, N, 0.2, r);
+  gsl_spmatrix *B, *C;
+  gsl_matrix *A_dense = gsl_matrix_alloc(M, N);
+  gsl_vector *x, *y, *y_gsl, *y_sp;
+  size_t lenX, lenY;
+
+  if (TransA == CblasNoTrans)
+    {
+      lenX = N;
+      lenY = M;
+    }
+  else
+    {
+      lenX = M;
+      lenY = N;
+    }
+
+  x = gsl_vector_alloc(lenX);
+  y = gsl_vector_alloc(lenY);
+  y_gsl = gsl_vector_alloc(lenY);
+  y_sp = gsl_vector_alloc(lenY);
+
+  /* create random dense vectors */
+  create_random_vector(x, r);
+  create_random_vector(y, r);
+
+  /* copy A into A_dense */
+  gsl_spmatrix_sp2d(A_dense, A);
+
+  gsl_vector_memcpy(y_gsl, y);
+  gsl_vector_memcpy(y_sp, y);
+
+  /* compute y = alpha*op(A)*x + beta*y0 with gsl */
+  gsl_blas_dgemv(TransA, alpha, A_dense, x, beta, y_gsl);
+
+  /* compute y = alpha*op(A)*x + beta*y0 with spblas/triplet */
+  gsl_spblas_dgemv(TransA, alpha, A, x, beta, y_sp);
+
+  /* test y_sp = y_gsl */
+  test_vectors(y_sp, y_gsl, 1.0e-10, "test_dgemv: triplet format");
+
+  /* compute y = alpha*op(A)*x + beta*y0 with spblas/CCS */
+  B = gsl_spmatrix_ccs(A);
+  gsl_vector_memcpy(y_sp, y);
+  gsl_spblas_dgemv(TransA, alpha, B, x, beta, y_sp);
+
+  /* test y_sp = y_gsl */
+  test_vectors(y_sp, y_gsl, 1.0e-10, "test_dgemv: CCS format");
+
+  /* compute y = alpha*op(A)*x + beta*y0 with spblas/CRS */
+  C = gsl_spmatrix_crs(A);
+  gsl_vector_memcpy(y_sp, y);
+  gsl_spblas_dgemv(TransA, alpha, C, x, beta, y_sp);
+
+  /* test y_sp = y_gsl */
+  test_vectors(y_sp, y_gsl, 1.0e-10, "test_dgemv: CRS format");
+
+  gsl_spmatrix_free(A);
+  gsl_spmatrix_free(B);
+  gsl_spmatrix_free(C);
+  gsl_matrix_free(A_dense);
+  gsl_vector_free(x);
+  gsl_vector_free(y);
+  gsl_vector_free(y_gsl);
+  gsl_vector_free(y_sp);
+} /* test_dgemv() */
+
+static void
+test_dgemm(const double alpha, const size_t M, const size_t N,
+           const gsl_rng *r)
+{
+  const size_t max = GSL_MAX(M, N);
+  size_t i, j, k;
+  gsl_matrix *A_dense = gsl_matrix_alloc(M, max);
+  gsl_matrix *B_dense = gsl_matrix_alloc(max, N);
+  gsl_matrix *C_dense = gsl_matrix_alloc(M, N);
+  gsl_spmatrix *C = gsl_spmatrix_alloc_nzmax(M, N, 1, GSL_SPMATRIX_CCS);
+
+  for (k = 1; k <= max; ++k)
+    {
+      gsl_matrix_view Ad = gsl_matrix_submatrix(A_dense, 0, 0, M, k);
+      gsl_matrix_view Bd = gsl_matrix_submatrix(B_dense, 0, 0, k, N);
+      gsl_spmatrix *TA = create_random_sparse(M, k, 0.2, r);
+      gsl_spmatrix *TB = create_random_sparse(k, N, 0.2, r);
+      gsl_spmatrix *A = gsl_spmatrix_ccs(TA);
+      gsl_spmatrix *B = gsl_spmatrix_ccs(TB);
+
+      gsl_spmatrix_set_zero(C);
+      gsl_spblas_dgemm(alpha, A, B, C);
+
+      /* make dense matrices and use standard dgemm to multiply them */
+      gsl_spmatrix_sp2d(&Ad.matrix, TA);
+      gsl_spmatrix_sp2d(&Bd.matrix, TB);
+      gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, alpha, &Ad.matrix,
+                     &Bd.matrix, 0.0, C_dense);
+
+      /* compare C and C_dense */
+      for (i = 0; i < M; ++i)
+        {
+          for (j = 0; j < N; ++j)
+            {
+              double Cij = gsl_spmatrix_get(C, i, j);
+              double Dij = gsl_matrix_get(C_dense, i, j);
+
+              gsl_test_rel(Cij, Dij, 1.0e-12, "test_dgemm: _dgemm");
+            }
+        }
+
+      gsl_spmatrix_free(TA);
+      gsl_spmatrix_free(TB);
+      gsl_spmatrix_free(A);
+      gsl_spmatrix_free(B);
+    }
+
+  gsl_spmatrix_free(C);
+  gsl_matrix_free(A_dense);
+  gsl_matrix_free(B_dense);
+  gsl_matrix_free(C_dense);
+} /* test_dgemm() */
+
+int
+main()
+{
+  const size_t N_max = 40;
+  size_t m, n;
+  gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+
+  for (m = 1; m <= N_max; ++m)
+    {
+      for (n = 1; n <= N_max; ++n)
+        {
+          test_dgemv(m, n, 1.0, 0.0, CblasNoTrans, r);
+          test_dgemv(m, n, 1.0, 0.0, CblasTrans, r);
+
+          test_dgemv(m, n, 2.4, -0.5, CblasNoTrans, r);
+          test_dgemv(m, n, 2.4, -0.5, CblasTrans, r);
+
+          test_dgemv(m, n, 0.1, 10.0, CblasNoTrans, r);
+          test_dgemv(m, n, 0.1, 10.0, CblasTrans, r);
+        }
+    }
+
+  test_dgemm(1.0, 10, 10, r);
+  test_dgemm(2.3, 20, 15, r);
+  test_dgemm(1.8, 12, 30, r);
+  test_dgemm(0.4, 45, 35, r);
+
+  gsl_rng_free(r);
+
+  exit (gsl_test_summary());
+} /* main() */
diff -Nru gsl-doc-1.16/specfunc/airy_der.c gsl-doc-2.3/specfunc/airy_der.c
--- gsl-doc-1.16/specfunc/airy_der.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/airy_der.c	2016-08-25 17:13:24.000000000 +0000
@@ -592,7 +592,6 @@
   gsl_sf_result result_p;
   double a, p;
   double sqx;
-  double x32;
 
   if(x <= -4.0) {
     double z = 128.0/(x*x*x) + 1.0;
@@ -621,7 +620,6 @@
   p = -0.625  + result_p.val;
  
   sqx = sqrt(-x);
-  x32   = x*sqx;
 
   ampl->val = sqrt(a * sqx);
   ampl->err = fabs(ampl->val) * (GSL_DBL_EPSILON + fabs(result_a.err/result_a.val));
diff -Nru gsl-doc-1.16/specfunc/airy_zero.c gsl-doc-2.3/specfunc/airy_zero.c
--- gsl-doc-1.16/specfunc/airy_zero.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/airy_zero.c	2015-11-03 16:21:55.000000000 +0000
@@ -28,7 +28,7 @@
 
 static const double zero_Ai[] = {
   0,
-  -2.338107410459767039,
+  -2.3381074104597670385,
   -4.087949444130970617,
   -5.520559828095551059,
   -6.786708090071758999,
diff -Nru gsl-doc-1.16/specfunc/bessel_j.c gsl-doc-2.3/specfunc/bessel_j.c
--- gsl-doc-1.16/specfunc/bessel_j.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/bessel_j.c	2015-11-03 16:21:55.000000000 +0000
@@ -52,12 +52,9 @@
     return GSL_SUCCESS;
   }
   else {
-    gsl_sf_result sin_result;
-    const int stat = gsl_sf_sin_e(x, &sin_result);
-    result->val  = sin_result.val/x;
-    result->err  = fabs(sin_result.err/x);
-    result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
-    return stat;
+    result->val = sin(x) / x;
+    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+    return GSL_SUCCESS;
   }
 }
 
@@ -89,17 +86,12 @@
     return GSL_SUCCESS;
   }
   else {
-    gsl_sf_result cos_result;
-    gsl_sf_result sin_result;
-    const int stat_cos = gsl_sf_cos_e(x, &cos_result);
-    const int stat_sin = gsl_sf_sin_e(x, &sin_result);
-    const double cos_x = cos_result.val;
-    const double sin_x = sin_result.val;
+    const double cos_x = cos(x);
+    const double sin_x = sin(x);
     result->val  = (sin_x/x - cos_x)/x;
-    result->err  = (fabs(sin_result.err/x) + fabs(cos_result.err))/fabs(x);
-    result->err += 2.0 * GSL_DBL_EPSILON * (fabs(sin_x/(x*x)) + fabs(cos_x/x));
+    result->err  = 2.0 * GSL_DBL_EPSILON * (fabs(sin_x/(x*x)) + fabs(cos_x/x));
     result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
-    return GSL_ERROR_SELECT_2(stat_cos, stat_sin);
+    return GSL_SUCCESS;
   }
 }
 
@@ -211,8 +203,9 @@
     double ratio;
     /* The CF1 call will hit 10000 iterations for x > 10000 + l */
     int stat_CF1 = gsl_sf_bessel_J_CF1(l+0.5, x, &ratio, &sgn);
-    double jellp1 = GSL_SQRT_DBL_EPSILON * ratio;
-    double jell   = GSL_SQRT_DBL_EPSILON;
+    const double BESSEL_J_SMALL = GSL_DBL_MIN / GSL_DBL_EPSILON;
+    double jellp1 = BESSEL_J_SMALL * ratio;
+    double jell   = BESSEL_J_SMALL;
     double jellm1;
     int ell;
     for(ell = l; ell > 0; ell--) {
@@ -224,7 +217,7 @@
     if(fabs(jell) > fabs(jellp1)) {
       gsl_sf_result j0_result;
       int stat_j0  = gsl_sf_bessel_j0_e(x, &j0_result);
-      double pre   = GSL_SQRT_DBL_EPSILON / jell;
+      double pre   = BESSEL_J_SMALL / jell;
       result->val  = j0_result.val * pre;
       result->err  = j0_result.err * fabs(pre);
       result->err += 4.0 * GSL_DBL_EPSILON * (0.5*l + 1.0) * fabs(result->val);
@@ -233,7 +226,7 @@
     else {
       gsl_sf_result j1_result;
       int stat_j1  = gsl_sf_bessel_j1_e(x, &j1_result);
-      double pre   = GSL_SQRT_DBL_EPSILON / jellp1;
+      double pre   = BESSEL_J_SMALL / jellp1;
       result->val  = j1_result.val * pre;
       result->err  = j1_result.err * fabs(pre);
       result->err += 4.0 * GSL_DBL_EPSILON * (0.5*l + 1.0) * fabs(result->val);
diff -Nru gsl-doc-1.16/specfunc/bessel_K0.c gsl-doc-2.3/specfunc/bessel_K0.c
--- gsl-doc-1.16/specfunc/bessel_K0.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/bessel_K0.c	2016-07-02 23:02:41.000000000 +0000
@@ -1,6 +1,7 @@
 /* specfunc/bessel_K0.c
  * 
  * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
+ * Copyright (C) 2016 Pavel Holoborodko, Patrick Alken
  * 
  * This program is free software; you can redistribute it and/or modify
  * it under the terms of the GNU General Public License as published by
@@ -22,6 +23,7 @@
 #include <config.h>
 #include <gsl/gsl_math.h>
 #include <gsl/gsl_errno.h>
+#include <gsl/gsl_poly.h>
 #include <gsl/gsl_sf_exp.h>
 #include <gsl/gsl_sf_bessel.h>
 
@@ -32,91 +34,90 @@
 
 /*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
 
-/* based on SLATEC bk0(), bk0e() */
-
-/* chebyshev expansions 
-
- series for bk0        on the interval  0.          to  4.00000d+00
-                                        with weighted error   3.57e-19
-                                         log weighted error  18.45
-                               significant figures required  17.99
-                                    decimal places required  18.97
-
- series for ak0        on the interval  1.25000d-01 to  5.00000d-01
-                                        with weighted error   5.34e-17
-                                         log weighted error  16.27
-                               significant figures required  14.92
-                                    decimal places required  16.89
-
- series for ak02       on the interval  0.          to  1.25000d-01
-                                        with weighted error   2.34e-17
-                                         log weighted error  16.63
-                               significant figures required  14.67
-                                    decimal places required  17.20
+/*
+ Minimax rational approximation for [0,1), peak relative error = 2.04*GSL_DBL_EPSILON.
+ Source: http://www.advanpix.com/?p=3812
 */
-
-static double bk0_data[11] = {
-  -0.03532739323390276872,
-   0.3442898999246284869, 
-   0.03597993651536150163,
-   0.00126461541144692592,
-   0.00002286212103119451,
-   0.00000025347910790261,
-   0.00000000190451637722,
-   0.00000000001034969525,
-   0.00000000000004259816,
-   0.00000000000000013744,
-   0.00000000000000000035
-};
-static cheb_series bk0_cs = {
-  bk0_data,
-  10,
-  -1, 1,
-  10
+static double k0_poly[8] = {
+   1.1593151565841244842077226e-01,
+   2.7898287891460317300886539e-01,
+   2.5248929932161220559969776e-02,
+   8.4603509072136578707676406e-04,
+   1.4914719243067801775856150e-05,
+   1.6271068931224552553548933e-07,
+   1.2082660336282566759313543e-09,
+   6.6117104672254184399933971e-12
+};
+
+static double i0_poly[7] = {
+   1.0000000000000000044974165e+00,
+   2.4999999999999822316775454e-01,
+   2.7777777777892149148858521e-02,
+   1.7361111083544590676709592e-03,
+   6.9444476047072424198677755e-05,
+   1.9288265756466775034067979e-06,
+   3.9908220583262192851839992e-08
+};
+
+/*
+ Chebyshev expansion for [1,8], peak relative error = 1.28*GSL_DBL_EPSILON. 
+ Source: Pavel Holoborodko.
+*/
+static double ak0_data[24] = {
+  -3.28737867094650101e-02,
+  -4.49369057710236880e-02,
+  +2.98149992004308095e-03,
+  -3.03693649396187920e-04,
+  +3.91085569307646836e-05,
+  -5.86872422399215952e-06,
+  +9.82873709937322009e-07,
+  -1.78978645055651171e-07,
+  +3.48332306845240957e-08,
+  -7.15909210462546599e-09,
+  +1.54019930048919494e-09,
+  -3.44555485579194210e-10,
+  +7.97356101783753023e-11,
+  -1.90090968913069735e-11,
+  +4.65295609304114621e-12,
+  -1.16614287433470780e-12,
+  +2.98554375218596891e-13,
+  -7.79276979512292169e-14,
+  +2.07027467168948402e-14,
+  -5.58987860393825313e-15,
+  +1.53202965950646914e-15,
+  -4.25737536712188186e-16,
+  +1.19840238501357389e-16,
+  -3.41407346762502397e-17
 };
 
-static double ak0_data[17] = {
-  -0.07643947903327941,
-  -0.02235652605699819,
-   0.00077341811546938,
-  -0.00004281006688886,
-   0.00000308170017386,
-  -0.00000026393672220,
-   0.00000002563713036,
-  -0.00000000274270554,
-   0.00000000031694296,
-  -0.00000000003902353,
-   0.00000000000506804,
-  -0.00000000000068895,
-   0.00000000000009744,
-  -0.00000000000001427,
-   0.00000000000000215,
-  -0.00000000000000033,
-   0.00000000000000005
-};
 static cheb_series ak0_cs = {
   ak0_data,
-  16,
+  23,
   -1, 1,
   10
 };
 
+/* 
+ Chebyshev expansion for [8,inf), peak relative error = 1.25*GSL_DBL_EPSILON.
+ Source: SLATEC/dbsk0e.f
+*/
 static double ak02_data[14] = {
-  -0.01201869826307592,
-  -0.00917485269102569,
-   0.00014445509317750,
-  -0.00000401361417543,
-   0.00000015678318108,
-  -0.00000000777011043,
-   0.00000000046111825,
-  -0.00000000003158592,
-   0.00000000000243501,
-  -0.00000000000020743,
-   0.00000000000001925,
-  -0.00000000000000192,
-   0.00000000000000020,
-  -0.00000000000000002
+  -.1201869826307592240E-1,
+  -.9174852691025695311E-2,
+  +.1444550931775005821E-3,
+  -.4013614175435709729E-5,
+  +.1567831810852310673E-6,
+  -.7770110438521737710E-8,
+  +.4611182576179717883E-9,
+  -.3158592997860565771E-10,
+  +.2435018039365041128E-11,
+  -.2074331387398347898E-12,
+  +.1925787280589917085E-13,
+  -.1927554805838956104E-14,
+  +.2062198029197818278E-15,
+  -.2341685117579242403E-16
 };
+
 static cheb_series ak02_cs = {
   ak02_data,
   13,
@@ -134,24 +135,20 @@
   if(x <= 0.0) {
     DOMAIN_ERROR(result);
   }
-  else if(x <= 2.0) {
+  else if(x < 1.0) {
     const double lx = log(x);
     const double ex = exp(x);
-    int stat_I0;
-    gsl_sf_result I0;
-    gsl_sf_result c;
-    cheb_eval_e(&bk0_cs, 0.5*x*x-1.0, &c);
-    stat_I0 = gsl_sf_bessel_I0_e(x, &I0);
-    result->val  = ex * ((-lx+M_LN2)*I0.val - 0.25 + c.val);
-    result->err  = ex * ((M_LN2+fabs(lx))*I0.err + c.err);
+    const double x2 = x*x;
+    result->val  = ex * (gsl_poly_eval(k0_poly,8,x2)-lx*(1.0+0.25*x2*gsl_poly_eval(i0_poly,7,0.25*x2)));
+    result->err  = ex * (1.6+fabs(lx)*0.6) * GSL_DBL_EPSILON;
     result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
-    return stat_I0;
+    return GSL_SUCCESS;
   }
   else if(x <= 8.0) {
     const double sx = sqrt(x);
     gsl_sf_result c;
-    cheb_eval_e(&ak0_cs, (16.0/x-5.0)/3.0, &c);
-    result->val  = (1.25 + c.val) / sx;
+    cheb_eval_e(&ak0_cs, (16.0/x-9.0)/7.0, &c);
+    result->val  = (1.203125 + c.val) / sx; /* 1.203125 = 77/64 */
     result->err  = c.err / sx;
     result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
     return GSL_SUCCESS;
@@ -175,17 +172,13 @@
   if(x <= 0.0) {
     DOMAIN_ERROR(result);
   }
-  else if(x <= 2.0) {
+  else if(x < 1.0) {
     const double lx = log(x);
-    int stat_I0;
-    gsl_sf_result I0;
-    gsl_sf_result c;
-    cheb_eval_e(&bk0_cs, 0.5*x*x-1.0, &c);
-    stat_I0 = gsl_sf_bessel_I0_e(x, &I0);
-    result->val  = (-lx+M_LN2)*I0.val - 0.25 + c.val;
-    result->err  = (fabs(lx) + M_LN2) * I0.err + c.err;
+    const double x2 = x*x;
+    result->val  = gsl_poly_eval(k0_poly,8,x2)-lx*(1.0+0.25*x2*gsl_poly_eval(i0_poly,7,0.25*x2));
+    result->err  = (1.6+fabs(lx)*0.6) * GSL_DBL_EPSILON;
     result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
-    return stat_I0;
+    return GSL_SUCCESS;
   }
   else {
     gsl_sf_result K0_scaled;
diff -Nru gsl-doc-1.16/specfunc/bessel_K1.c gsl-doc-2.3/specfunc/bessel_K1.c
--- gsl-doc-1.16/specfunc/bessel_K1.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/bessel_K1.c	2016-07-02 23:02:41.000000000 +0000
@@ -1,6 +1,7 @@
 /* specfunc/bessel_K1.c
  * 
  * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
+ * Copyright (C) 2016 Pavel Holoborodko, Patrick Alken
  * 
  * This program is free software; you can redistribute it and/or modify
  * it under the terms of the GNU General Public License as published by
@@ -22,6 +23,7 @@
 #include <config.h>
 #include <gsl/gsl_math.h>
 #include <gsl/gsl_errno.h>
+#include <gsl/gsl_poly.h>
 #include <gsl/gsl_sf_exp.h>
 #include <gsl/gsl_sf_bessel.h>
 
@@ -32,92 +34,91 @@
 
 /*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
 
-/* based on SLATEC besk1(), besk1e() */
-
-/* chebyshev expansions 
-
- series for bk1        on the interval  0.          to  4.00000d+00
-                                        with weighted error   7.02e-18
-                                         log weighted error  17.15
-                               significant figures required  16.73
-                                    decimal places required  17.67
-
- series for ak1        on the interval  1.25000d-01 to  5.00000d-01
-                                        with weighted error   6.06e-17
-                                         log weighted error  16.22
-                               significant figures required  15.41
-                                    decimal places required  16.83
-
- series for ak12       on the interval  0.          to  1.25000d-01
-                                        with weighted error   2.58e-17
-                                         log weighted error  16.59
-                               significant figures required  15.22
-                                    decimal places required  17.16
+/*
+ Minimax rational approximation for [0,1), peak relative error = 1.83*GSL_DBL_EPSILON.
+ Source: http://www.advanpix.com/?p=3987
 */
-
-static double bk1_data[11] = {
-   0.0253002273389477705,
-  -0.3531559607765448760, 
-  -0.1226111808226571480, 
-  -0.0069757238596398643,
-  -0.0001730288957513052,
-  -0.0000024334061415659,
-  -0.0000000221338763073,
-  -0.0000000001411488392,
-  -0.0000000000006666901,
-  -0.0000000000000024274,
-  -0.0000000000000000070
-};
-
-static cheb_series bk1_cs = {
-  bk1_data,
-  10,
-  -1, 1,
-  8
+static double k1_poly[9] = {
+  -3.0796575782920622440538935e-01,
+  -8.5370719728650778045782736e-02,
+  -4.6421827664715603298154971e-03,
+  -1.1253607036630425931072996e-04,
+  -1.5592887702110907110292728e-06,
+  -1.4030163679125934402498239e-08,
+  -8.8718998640336832196558868e-11,
+  -4.1614323580221539328960335e-13,
+  -1.5261293392975541707230366e-15
+};
+
+static double i1_poly[7] = {
+  8.3333333333333325191635191e-02,
+  6.9444444444467956461838830e-03,
+  3.4722222211230452695165215e-04,
+  1.1574075952009842696580084e-05,
+  2.7555870002088181016676934e-07,
+  4.9724386164128529514040614e-09
+};
+
+/*
+ Chebyshev expansion for [1,8], peak relative error = 1.28*GSL_DBL_EPSILON. 
+ Source: Pavel Holoborodko.
+*/
+static double ak1_data[25] = {
+  +2.07996868001418246e-01,
+  +1.62581565017881476e-01,
+  -5.87070423518863640e-03,
+  +4.95021520115789501e-04,
+  -5.78958347598556986e-05,
+  +8.18614610209334726e-06,
+  -1.31604832009487277e-06,
+  +2.32546031520101213e-07,
+  -4.42206518311557987e-08,
+  +8.92163994883100361e-09,
+  -1.89046270526983427e-09,
+  +4.17568808108504702e-10,
+  -9.55912361791375794e-11,
+  +2.25769353153867758e-11,
+  -5.48128000211158482e-12,
+  +1.36386122546441926e-12,
+  -3.46936690565986409e-13,
+  +9.00354564415705942e-14,
+  -2.37950577776254432e-14,
+  +6.39447503964025336e-15,
+  -1.74498363492322044e-15,
+  +4.82994547989290473e-16,
+  -1.35460927805445606e-16,
+  +3.84604274446777234e-17,
+  -1.10456856122581316e-17
 };
 
-static double ak1_data[17] = {
-   0.27443134069738830, 
-   0.07571989953199368,
-  -0.00144105155647540,
-   0.00006650116955125,
-  -0.00000436998470952,
-   0.00000035402774997,
-  -0.00000003311163779,
-   0.00000000344597758,
-  -0.00000000038989323,
-   0.00000000004720819,
-  -0.00000000000604783,
-   0.00000000000081284,
-  -0.00000000000011386,
-   0.00000000000001654,
-  -0.00000000000000248,
-   0.00000000000000038,
-  -0.00000000000000006
-};
 static cheb_series ak1_cs = {
   ak1_data,
-  16,
+  24,
   -1, 1,
   9
 };
 
+/* 
+ Chebyshev expansion for [8,inf), peak relative error = 1.25*GSL_DBL_EPSILON.
+ Source: SLATEC/dbsk1e.f
+*/
 static double ak12_data[14] = {
-   0.06379308343739001,
-   0.02832887813049721,
-  -0.00024753706739052,
-   0.00000577197245160,
-  -0.00000020689392195,
-   0.00000000973998344,
-  -0.00000000055853361,
-   0.00000000003732996,
-  -0.00000000000282505,
-   0.00000000000023720,
-  -0.00000000000002176,
-   0.00000000000000215,
-  -0.00000000000000022,
-   0.00000000000000002
+  +.637930834373900104E-1,
+  +.283288781304972094E-1,
+  -.247537067390525035E-3,
+  +.577197245160724882E-5,
+  -.206893921953654830E-6,
+  +.973998344138180418E-8,
+  -.558533614038062498E-9,
+  +.373299663404618524E-10,
+  -.282505196102322545E-11,
+  +.237201900248414417E-12,
+  -.217667738799175398E-13,
+  +.215791416161603245E-14,
+  -.229019693071826928E-15,
+  +.258288572982327496E-16
 };
+
 static cheb_series ak12_cs = {
   ak12_data,
   13,
@@ -138,24 +139,22 @@
   else if(x < 2.0*GSL_DBL_MIN) {
     OVERFLOW_ERROR(result);
   }
-  else if(x <= 2.0) {
+  else if(x < 1.0) {
     const double lx = log(x);
     const double ex = exp(x);
-    int stat_I1;
-    gsl_sf_result I1;
-    gsl_sf_result c;
-    cheb_eval_e(&bk1_cs, 0.5*x*x-1.0, &c);
-    stat_I1 = gsl_sf_bessel_I1_e(x, &I1);
-    result->val  = ex * ((lx-M_LN2)*I1.val + (0.75 + c.val)/x);
-    result->err  = ex * (c.err/x + fabs(lx)*I1.err);
+    const double x2 = x*x;
+    const double t  = 0.25*x2;    
+    const double i1 = 0.5 * x * (1.0 + t * (0.5 + t * gsl_poly_eval(i1_poly,6,t)));
+    result->val  = ex * (x2 * gsl_poly_eval(k1_poly,9,x2) + x * lx * i1 + 1) / x;
+    result->err  = ex * (1.6+fabs(lx)*0.6) * GSL_DBL_EPSILON;
     result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
-    return stat_I1;
+    return GSL_SUCCESS;
   }
   else if(x <= 8.0) {
     const double sx = sqrt(x);
     gsl_sf_result c;
-    cheb_eval_e(&ak1_cs, (16.0/x-5.0)/3.0, &c);
-    result->val  = (1.25 + c.val) / sx;
+    cheb_eval_e(&ak1_cs, (16.0/x-9.0)/7.0, &c);
+    result->val  = (1.375 + c.val) / sx; /* 1.375 = 11/8 */
     result->err  = c.err / sx;
     result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
     return GSL_SUCCESS;
@@ -182,17 +181,15 @@
   else if(x < 2.0*GSL_DBL_MIN) {
     OVERFLOW_ERROR(result);
   }
-  else if(x <= 2.0) {
+  else if(x < 1.0) {
     const double lx = log(x);
-    int stat_I1;
-    gsl_sf_result I1;
-    gsl_sf_result c;
-    cheb_eval_e(&bk1_cs, 0.5*x*x-1.0, &c);
-    stat_I1 = gsl_sf_bessel_I1_e(x, &I1);
-    result->val  = (lx-M_LN2)*I1.val + (0.75 + c.val)/x;
-    result->err  = c.err/x + fabs(lx)*I1.err;
+    const double x2 = x*x;
+    const double t  = 0.25*x2;    
+    const double i1 = 0.5 * x * (1.0 + t * (0.5 + t * gsl_poly_eval(i1_poly,6,t)));
+    result->val  = (x2 * gsl_poly_eval(k1_poly,9,x2) + x * lx * i1 + 1) / x;
+    result->err  = (1.6+fabs(lx)*0.6) * GSL_DBL_EPSILON;
     result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
-    return stat_I1;
+    return GSL_SUCCESS;      
   }
   else {
     gsl_sf_result K1_scaled;
diff -Nru gsl-doc-1.16/specfunc/ellint.c gsl-doc-2.3/specfunc/ellint.c
--- gsl-doc-1.16/specfunc/ellint.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/ellint.c	2015-11-03 16:21:55.000000000 +0000
@@ -449,7 +449,7 @@
 
 /* [Carlson, Numer. Math. 33 (1979) 1, (4.4)] */
 int
-gsl_sf_ellint_D_e(double phi, double k, double n, gsl_mode_t mode, gsl_sf_result * result)
+gsl_sf_ellint_D_e(double phi, double k, gsl_mode_t mode, gsl_sf_result * result)
 {
   /* Angular reduction to -pi/2 < phi < pi/2 (we should really use an
      exact reduction but this will have to do for now) BJG */
@@ -625,9 +625,9 @@
   EVAL_RESULT(gsl_sf_ellint_P_e(phi, k, n, mode, &result));
 }
 
-double gsl_sf_ellint_D(double phi, double k, double n, gsl_mode_t mode)
+double gsl_sf_ellint_D(double phi, double k, gsl_mode_t mode)
 {
-  EVAL_RESULT(gsl_sf_ellint_D_e(phi, k, n, mode, &result));
+  EVAL_RESULT(gsl_sf_ellint_D_e(phi, k, mode, &result));
 }
 
 double gsl_sf_ellint_RC(double x, double y, gsl_mode_t mode)
diff -Nru gsl-doc-1.16/specfunc/expint.c gsl-doc-2.3/specfunc/expint.c
--- gsl-doc-1.16/specfunc/expint.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/expint.c	2015-11-03 16:21:55.000000000 +0000
@@ -377,7 +377,7 @@
     OVERFLOW_ERROR(result);
   }
   else if (x == 0.0) {
-    result->val = (scale ? 1.0 : 1.0);
+    result->val = 1.0;
     result->err = 0.0;
     return GSL_SUCCESS;
   } else if(x < 100.0) {
diff -Nru gsl-doc-1.16/specfunc/gegenbauer.c gsl-doc-2.3/specfunc/gegenbauer.c
--- gsl-doc-1.16/specfunc/gegenbauer.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/gegenbauer.c	2015-11-03 16:21:55.000000000 +0000
@@ -107,7 +107,7 @@
     return gsl_sf_gegenpoly_3_e(lambda, x, result);
   }
   else {
-    if(lambda == 0.0 && (x >= -1.0 || x <= 1.0)) {
+    if(lambda == 0.0 && (x >= -1.0 && x <= 1.0)) {
       /* 2 T_n(x)/n */
       const double z = n * acos(x);
       result->val = 2.0 * cos(z) / n;
diff -Nru gsl-doc-1.16/specfunc/gsl_sf_ellint.h gsl-doc-2.3/specfunc/gsl_sf_ellint.h
--- gsl-doc-1.16/specfunc/gsl_sf_ellint.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/gsl_sf_ellint.h	2015-11-03 16:21:55.000000000 +0000
@@ -81,8 +81,8 @@
 int gsl_sf_ellint_P_e(double phi, double k, double n, gsl_mode_t mode, gsl_sf_result * result);
 double gsl_sf_ellint_P(double phi, double k, double n, gsl_mode_t mode);
 
-int gsl_sf_ellint_D_e(double phi, double k, double n, gsl_mode_t mode, gsl_sf_result * result);
-double gsl_sf_ellint_D(double phi, double k, double n, gsl_mode_t mode);
+int gsl_sf_ellint_D_e(double phi, double k, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_D(double phi, double k, gsl_mode_t mode);
 
 
 /* Carlson's symmetric basis of functions
diff -Nru gsl-doc-1.16/specfunc/gsl_sf_legendre.h gsl-doc-2.3/specfunc/gsl_sf_legendre.h
--- gsl-doc-1.16/specfunc/gsl_sf_legendre.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/gsl_sf_legendre.h	2015-11-03 16:21:55.000000000 +0000
@@ -309,6 +309,66 @@
  */
 int gsl_sf_legendre_H3d_array(const int lmax, const double lambda, const double eta, double * result_array);
 
+/* associated legendre P_{lm} routines */
+
+typedef enum
+{
+  GSL_SF_LEGENDRE_SCHMIDT,
+  GSL_SF_LEGENDRE_SPHARM,
+  GSL_SF_LEGENDRE_FULL,
+  GSL_SF_LEGENDRE_NONE
+} gsl_sf_legendre_t;
+
+int gsl_sf_legendre_array(const gsl_sf_legendre_t norm,
+                          const size_t lmax, const double x,
+                          double result_array[]);
+int gsl_sf_legendre_array_e(const gsl_sf_legendre_t norm,
+                            const size_t lmax, const double x,
+                            const double csphase,
+                            double result_array[]);
+int gsl_sf_legendre_deriv_array(const gsl_sf_legendre_t norm,
+                                const size_t lmax, const double x,
+                                double result_array[],
+                                double result_deriv_array[]);
+int gsl_sf_legendre_deriv_array_e(const gsl_sf_legendre_t norm,
+                                  const size_t lmax, const double x,
+                                  const double csphase,
+                                  double result_array[],
+                                  double result_deriv_array[]);
+int gsl_sf_legendre_deriv_alt_array(const gsl_sf_legendre_t norm,
+                                    const size_t lmax, const double x,
+                                    double result_array[],
+                                    double result_deriv_array[]);
+int gsl_sf_legendre_deriv_alt_array_e(const gsl_sf_legendre_t norm,
+                                      const size_t lmax, const double x,
+                                      const double csphase,
+                                      double result_array[],
+                                      double result_deriv_array[]);
+int gsl_sf_legendre_deriv2_array(const gsl_sf_legendre_t norm,
+                                 const size_t lmax, const double x,
+                                 double result_array[],
+                                 double result_deriv_array[],
+                                 double result_deriv2_array[]);
+int gsl_sf_legendre_deriv2_array_e(const gsl_sf_legendre_t norm,
+                                   const size_t lmax, const double x,
+                                   const double csphase,
+                                   double result_array[],
+                                   double result_deriv_array[],
+                                   double result_deriv2_array[]);
+int gsl_sf_legendre_deriv2_alt_array(const gsl_sf_legendre_t norm,
+                                     const size_t lmax, const double x,
+                                     double result_array[],
+                                     double result_deriv_array[],
+                                     double result_deriv2_array[]);
+int gsl_sf_legendre_deriv2_alt_array_e(const gsl_sf_legendre_t norm,
+                                       const size_t lmax, const double x,
+                                       const double csphase,
+                                       double result_array[],
+                                       double result_deriv_array[],
+                                       double result_deriv2_array[]);
+size_t gsl_sf_legendre_array_n(const size_t lmax);
+size_t gsl_sf_legendre_array_index(const size_t l, const size_t m);
+size_t gsl_sf_legendre_nlm(const size_t lmax);
 
 __END_DECLS
 
diff -Nru gsl-doc-1.16/specfunc/gsl_sf_mathieu.h gsl-doc-2.3/specfunc/gsl_sf_mathieu.h
--- gsl-doc-1.16/specfunc/gsl_sf_mathieu.h	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/gsl_sf_mathieu.h	2015-11-03 16:21:55.000000000 +0000
@@ -67,8 +67,10 @@
 
 /* Compute the characteristic value for a Mathieu function of order n and
    type ntype. */
-int gsl_sf_mathieu_a(int order, double qq, gsl_sf_result *result);
-int gsl_sf_mathieu_b(int order, double qq, gsl_sf_result *result);
+int gsl_sf_mathieu_a_e(int order, double qq, gsl_sf_result *result);
+double gsl_sf_mathieu_a(int order, double qq);
+int gsl_sf_mathieu_b_e(int order, double qq, gsl_sf_result *result);
+double gsl_sf_mathieu_b(int order, double qq);
 
 /* Compute the Fourier coefficients for a Mathieu function. */
 int gsl_sf_mathieu_a_coeff(int order, double qq, double aa, double coeff[]);
@@ -80,8 +82,10 @@
 void gsl_sf_mathieu_free(gsl_sf_mathieu_workspace *workspace);
 
 /* Compute an angular Mathieu function. */
-int gsl_sf_mathieu_ce(int order, double qq, double zz, gsl_sf_result *result);
-int gsl_sf_mathieu_se(int order, double qq, double zz, gsl_sf_result *result);
+int gsl_sf_mathieu_ce_e(int order, double qq, double zz, gsl_sf_result *result);
+double gsl_sf_mathieu_ce(int order, double qq, double zz);
+int gsl_sf_mathieu_se_e(int order, double qq, double zz, gsl_sf_result *result);
+double gsl_sf_mathieu_se(int order, double qq, double zz);
 int gsl_sf_mathieu_ce_array(int nmin, int nmax, double qq, double zz,
                             gsl_sf_mathieu_workspace *work,
                             double result_array[]);
@@ -90,10 +94,12 @@
                             double result_array[]);
 
 /* Compute a radial Mathieu function. */
-int gsl_sf_mathieu_Mc(int kind, int order, double qq, double zz,
+int gsl_sf_mathieu_Mc_e(int kind, int order, double qq, double zz,
                       gsl_sf_result *result);
-int gsl_sf_mathieu_Ms(int kind, int order, double qq, double zz,
+double gsl_sf_mathieu_Mc(int kind, int order, double qq, double zz);
+int gsl_sf_mathieu_Ms_e(int kind, int order, double qq, double zz,
                       gsl_sf_result *result);
+double gsl_sf_mathieu_Ms(int kind, int order, double qq, double zz);
 int gsl_sf_mathieu_Mc_array(int kind, int nmin, int nmax, double qq,
                             double zz, gsl_sf_mathieu_workspace *work,
                             double result_array[]);
diff -Nru gsl-doc-1.16/specfunc/hyperg_1F1.c gsl-doc-2.3/specfunc/hyperg_1F1.c
--- gsl-doc-1.16/specfunc/hyperg_1F1.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/hyperg_1F1.c	2015-11-03 16:21:55.000000000 +0000
@@ -1120,7 +1120,7 @@
        * the values near the line b=2a+x. Then recurse
        * forward on a from a0.
        */
-      int a0 = ceil(0.5*(b-x));
+      int a0 = (int) ceil(0.5*(b-x));
       double Ma0b;    /* M(a0,b)   */
       double Ma0bp1;  /* M(a0,b+1) */
       double Ma0p1b;  /* M(a0+1,b) */
diff -Nru gsl-doc-1.16/specfunc/hyperg_2F1.c gsl-doc-2.3/specfunc/hyperg_2F1.c
--- gsl-doc-1.16/specfunc/hyperg_2F1.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/hyperg_2F1.c	2016-07-02 23:02:41.000000000 +0000
@@ -47,6 +47,7 @@
   double del_pos = 1.0;
   double del_neg = 0.0;
   double del = 1.0;
+  double del_prev;
   double k = 0.0;
   int i = 0;
 
@@ -64,6 +65,7 @@
       result->err += 2.0 * GSL_DBL_EPSILON * (2.0*sqrt(k)+1.0) * fabs(result->val);
       GSL_ERROR ("error", GSL_EMAXITER);
     }
+    del_prev = del;
     del *= (a+k)*(b+k) * x / ((c+k) * (k+1.0));  /* Gauss series */
 
     if(del > 0.0) {
@@ -82,6 +84,16 @@
       sum_neg -=  del;
     }
 
+    /*
+     * This stopping criteria is taken from the thesis
+     * "Computation of Hypergeometic Functions" by J. Pearson, pg. 31
+     * (http://people.maths.ox.ac.uk/porterm/research/pearson_final.pdf)
+     * and fixes bug #45926
+     */
+    if (fabs(del_prev / (sum_pos - sum_neg)) < GSL_DBL_EPSILON &&
+        fabs(del / (sum_pos - sum_neg)) < GSL_DBL_EPSILON)
+      break;
+
     k += 1.0;
   } while(fabs((del_pos + del_neg)/(sum_pos-sum_neg)) > GSL_DBL_EPSILON);
 
@@ -599,6 +611,12 @@
     result->err += 2.0 * GSL_DBL_EPSILON * (fabs(pre1.val*F1.val) + fabs(pre2.val*F2.val));
     result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
 
+    if (status_F1)
+      return status_F1;
+
+    if (status_F2)
+      return status_F2;
+
     return GSL_SUCCESS;
   }
 }
diff -Nru gsl-doc-1.16/specfunc/hyperg_U.c gsl-doc-2.3/specfunc/hyperg_U.c
--- gsl-doc-1.16/specfunc/hyperg_U.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/hyperg_U.c	2015-11-03 16:21:55.000000000 +0000
@@ -524,7 +524,7 @@
         t_err = a0_err + b0_err;
         dchu_val += t_val;
         dchu_err += t_err;
-        if(!finite(t_val) || fabs(t_val) < EPS*fabs(dchu_val)) break;
+        if(!gsl_finite(t_val) || fabs(t_val) < EPS*fabs(dchu_val)) break;
       }
 
       result->val  = dchu_val;
@@ -680,6 +680,18 @@
 hyperg_U_series(const double a, const double b, const double x, gsl_sf_result * result)
 {
   const double SQRT_EPS = M_SQRT2 * GSL_SQRT_DBL_EPSILON;
+double bint = ( b < 0.0 ? ceil(b-0.5) : floor(b+0.5) );
+  double beps  = b - bint;
+  double a_beps = a - beps;
+  double r_a_beps = floor(a_beps + 0.5);
+  double a_beps_int = ( fabs(a_beps - r_a_beps) < INT_THRESHOLD );
+/*  double a_b_1 = a-b+1;
+  double r_a_b_1 = floor(a_b_1+0.5);
+  double r_a_b_1_int = (fabs(a_b_1-r_a_b_1)< INT_THRESHOLD);
+  Check for (a-beps) being a member of -N; N being 0,1,... */
+  if (a_beps_int && a_beps <= 0)
+  { 	beps=beps - 1 + floor(a_beps);bint=bint + 1 - floor(a_beps);
+  }
 
   if(fabs(1.0 + a - b) < SQRT_EPS) {
     /* Original Comment: ALGORITHM IS BAD WHEN 1+A-B IS NEAR ZERO FOR SMALL X
@@ -694,9 +706,7 @@
     return stat_e;
   }
   else {
-    double bint = ( b < 0.0 ? ceil(b-0.5) : floor(b+0.5) );
-    double beps  = b - bint;
-    int N = bint;
+     int N = (int) bint;
     
     double lnx  = log(x);
     double xeps = exp(-beps*lnx);
@@ -711,7 +721,7 @@
     if(fabs(xeps-1.0) > 0.5 ) {
       stat_inf = hyperg_U_infinite_sum_stable(N, a, bint, b, beps, x, xeps, sum, result);
     } else if (1+a-b < 0 && 1+a-b==floor(1+a-b) && beps != 0) {
-      stat_inf = hyperg_U_infinite_sum_simple(N, a, bint, b, beps, x, xeps, sum, result);
+       stat_inf = hyperg_U_infinite_sum_simple(N, a, bint, b, beps, x, xeps, sum, result);
     } else {
       stat_inf = hyperg_U_infinite_sum_improved(N, a, bint, b, beps, x, xeps, sum, result);
     }
@@ -1611,7 +1621,25 @@
 static int
 hyperg_U_int_negx (const int a, const int b, const double x, gsl_sf_result_e10 * result)
 {
-  return hyperg_U_negx (a, b, x, result);
+/* Looking at the tests it seems that everything is handled correctly by hyperg_U_negx 
+except a<b<=0.  The b=1 case seems strange since the poch(1+a-b,-a) should blow up. 
+In order to do no (little) harm I fix up only a<b<=0 using DLMF 13.2.11.  These are the failing conditions
+*/
+  if (a<b && b<=0) 
+    {
+      gsl_sf_result_e10 r1;
+      double z21_z = pow(x, 1-b);
+      int status = hyperg_U_negx (1+a-b,2-b, x, &r1);
+      double res_tem=z21_z*r1.val;
+      double res_tem_err = fabs(z21_z)*r1.err;
+      result->val = res_tem;
+      result->err = res_tem_err;
+      return status;
+    }
+  else
+    {
+      return hyperg_U_negx (a, b, x, result);
+    }
 }  
 
 
@@ -1629,7 +1657,7 @@
   }
   else if (x == 0.0) {
     return hyperg_U_int_origin (a, b, result);
-  } else if (x < 0.0) {
+  } else if (x < 0.0)  {
     return hyperg_U_int_negx (a, b, x, result);
   }
   else {
@@ -1677,13 +1705,26 @@
     result->err = 0.0;
     result->e10 = 0;
     return GSL_SUCCESS;
-  } else if (x == 0.0) {
+  } 
+  else if (x == 0.0) {
     return hyperg_U_origin (a, b, result);
-  } else if (x < 0.0) {
-    return hyperg_U_negx (a, b, x, result);
+  } 
+  else if(a_integer && b == a + 1)
+/* This is DLMF 13.6.4 */
+   {
+     gsl_sf_result powx1N_1;
+     gsl_sf_pow_int_e(x, -a, &powx1N_1);
+     result->val = powx1N_1.val;
+     result->err = powx1N_1.err;
+     result->e10 = 0;
+     return GSL_SUCCESS;
+	
+   }  
+   else if(a_integer && b_integer) {
+     return gsl_sf_hyperg_U_int_e10_e(rinta, rintb, x, result);
   }
-  else if(a_integer && b_integer) {
-    return gsl_sf_hyperg_U_int_e10_e(rinta, rintb, x, result);
+  else if (x < 0.0) {
+    return hyperg_U_negx (a, b, x, result);
   }
   else {
     if(b >= 1.0) {
@@ -1714,7 +1755,7 @@
 int
 gsl_sf_hyperg_U_int_e(const int a, const int b, const double x, gsl_sf_result * result)
 {
-  gsl_sf_result_e10 re = {0};
+  gsl_sf_result_e10 re = {0, 0, 0};
   int stat_U = gsl_sf_hyperg_U_int_e10_e(a, b, x, &re);
   int stat_c = gsl_sf_result_smash_e(&re, result);
   return GSL_ERROR_SELECT_2(stat_c, stat_U);
@@ -1724,7 +1765,7 @@
 int
 gsl_sf_hyperg_U_e(const double a, const double b, const double x, gsl_sf_result * result)
 {
-  gsl_sf_result_e10 re = {0};
+  gsl_sf_result_e10 re = {0, 0, 0};
   int stat_U = gsl_sf_hyperg_U_e10_e(a, b, x, &re);
   int stat_c = gsl_sf_result_smash_e(&re, result);
   return GSL_ERROR_SELECT_2(stat_c, stat_U);
diff -Nru gsl-doc-1.16/specfunc/legendre_P.c gsl-doc-2.3/specfunc/legendre_P.c
--- gsl-doc-1.16/specfunc/legendre_P.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/specfunc/legendre_P.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,114 @@
+/* legendre_P.c
+ * 
+ * Copyright (C) 2009-2013 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_sf_legendre.h>
+
+/*
+ * The routines in this module compute associated Legendre functions
+ * (ALFs) up to order and degree 2700, using the method described
+ * in
+ *
+ * [1] S. A. Holmes and W. E. Featherstone, A unified approach
+ *     to the Clenshaw summation and the recursive computation of very
+ *     high degree and order normalised associated Legendre functions,
+ *     Journal of Geodesy, 76, pg. 279-299, 2002.
+ *
+ * Further information on ALFs can be found in
+ *
+ * [2] Abramowitz and Stegun, Handbook of Mathematical Functions,
+ *     Chapter 8, 1972.
+ */
+
+static void legendre_sqrts(const size_t lmax, double *array);
+
+#define LEGENDRE
+#include "legendre_source.c"
+#undef LEGENDRE
+
+#define LEGENDRE_DERIV
+#include "legendre_source.c"
+#undef LEGENDRE_DERIV
+
+#define LEGENDRE_DERIV_ALT
+#include "legendre_source.c"
+#undef LEGENDRE_DERIV_ALT
+
+#define LEGENDRE_DERIV2
+#include "legendre_source.c"
+#undef LEGENDRE_DERIV2
+
+#define LEGENDRE_DERIV2_ALT
+#include "legendre_source.c"
+#undef LEGENDRE_DERIV2_ALT
+
+/* number of P_{lm} functions for a given lmax */
+size_t
+gsl_sf_legendre_nlm(const size_t lmax)
+{
+  return ((lmax + 1) * (lmax + 2) / 2);
+}
+
+/*
+gsl_sf_legendre_array_n()
+  This routine returns the minimum result_array[] size needed
+for a given lmax
+*/
+
+size_t
+gsl_sf_legendre_array_n(const size_t lmax)
+{
+  size_t nlm = gsl_sf_legendre_nlm(lmax);
+  size_t nsqrt = 2 * lmax + 2; /* extra room to precompute sqrt factors */
+
+  return (nlm + nsqrt);
+} /* gsl_sf_legendre_array_n() */
+
+/*
+gsl_sf_legendre_array_index()
+This routine computes the index into a result_array[] corresponding
+to a given (l,m)
+*/
+
+size_t
+gsl_sf_legendre_array_index(const size_t l, const size_t m)
+{
+  return (l * (l + 1) / 2 + m);
+} /* gsl_sf_legendre_array_index() */
+
+/*********************************************************
+ *                 INTERNAL ROUTINES                     *
+ *********************************************************/
+
+/*
+legendre_sqrts()
+  Precompute square root factors needed for Legendre recurrence.
+On output, array[i] = sqrt(i)
+*/
+
+static void
+legendre_sqrts(const size_t lmax, double *array)
+{
+  size_t l;
+  for (l = 0; l <= 2 * lmax + 1; ++l)
+    array[l] = sqrt((double) l);
+}
diff -Nru gsl-doc-1.16/specfunc/legendre_poly.c gsl-doc-2.3/specfunc/legendre_poly.c
--- gsl-doc-1.16/specfunc/legendre_poly.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/legendre_poly.c	2015-11-03 16:21:55.000000000 +0000
@@ -290,7 +290,6 @@
   }
 }
 
-
 int
 gsl_sf_legendre_Plm_e(const int l, const int m, const double x, gsl_sf_result * result)
 {
@@ -357,6 +356,100 @@
   }
 }
 
+int
+gsl_sf_legendre_sphPlm_e(const int l, int m, const double x, gsl_sf_result * result)
+{
+  /* CHECK_POINTER(result) */
+
+  if(m < 0 || l < m || x < -1.0 || x > 1.0) {
+    DOMAIN_ERROR(result);
+  }
+  else if(m == 0) {
+    gsl_sf_result P;
+    int stat_P = gsl_sf_legendre_Pl_e(l, x, &P);
+    double pre = sqrt((2.0*l + 1.0)/(4.0*M_PI));
+    result->val  = pre * P.val;
+    result->err  = pre * P.err;
+    result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+    return stat_P;
+  }
+  else if(x == 1.0 || x == -1.0) {
+    /* m > 0 here */
+    result->val = 0.0;
+    result->err = 0.0;
+    return GSL_SUCCESS;
+  }
+  else {
+    /* m > 0 and |x| < 1 here */
+
+    /* Starting value for recursion.
+     * Y_m^m(x) = sqrt( (2m+1)/(4pi m) gamma(m+1/2)/gamma(m) ) (-1)^m (1-x^2)^(m/2) / pi^(1/4)
+     */
+    gsl_sf_result lncirc;
+    gsl_sf_result lnpoch;
+    double lnpre_val;
+    double lnpre_err;
+    gsl_sf_result ex_pre;
+    double sr;
+    const double sgn = ( GSL_IS_ODD(m) ? -1.0 : 1.0);
+    const double y_mmp1_factor = x * sqrt(2.0*m + 3.0);
+    double y_mm, y_mm_err;
+    double y_mmp1, y_mmp1_err;
+    gsl_sf_log_1plusx_e(-x*x, &lncirc);
+    gsl_sf_lnpoch_e(m, 0.5, &lnpoch);  /* Gamma(m+1/2)/Gamma(m) */
+    lnpre_val = -0.25*M_LNPI + 0.5 * (lnpoch.val + m*lncirc.val);
+    lnpre_err = 0.25*M_LNPI*GSL_DBL_EPSILON + 0.5 * (lnpoch.err + fabs(m)*lncirc.err);
+    /* Compute exp(ln_pre) with error term, avoiding call to gsl_sf_exp_err BJG */
+    ex_pre.val = exp(lnpre_val);
+    ex_pre.err = 2.0*(sinh(lnpre_err) + GSL_DBL_EPSILON)*ex_pre.val;
+    sr     = sqrt((2.0+1.0/m)/(4.0*M_PI));
+    y_mm   = sgn * sr * ex_pre.val;
+    y_mm_err  = 2.0 * GSL_DBL_EPSILON * fabs(y_mm) + sr * ex_pre.err;
+    y_mm_err *= 1.0 + 1.0/(GSL_DBL_EPSILON + fabs(1.0-x));
+    y_mmp1 = y_mmp1_factor * y_mm;
+    y_mmp1_err=fabs(y_mmp1_factor) * y_mm_err;
+
+    if(l == m){
+      result->val  = y_mm;
+      result->err  = y_mm_err;
+      result->err += 2.0 * GSL_DBL_EPSILON * fabs(y_mm);
+      return GSL_SUCCESS;
+    }
+    else if(l == m + 1) {
+      result->val  = y_mmp1;
+      result->err  = y_mmp1_err;
+      result->err += 2.0 * GSL_DBL_EPSILON * fabs(y_mmp1);
+      return GSL_SUCCESS;
+    }
+    else{
+      double y_ell = 0.0;
+      double y_ell_err = 0.0;
+      int ell;
+
+      /* Compute Y_l^m, l > m+1, upward recursion on l. */
+      for(ell=m+2; ell <= l; ell++){
+        const double rat1 = (double)(ell-m)/(double)(ell+m);
+        const double rat2 = (ell-m-1.0)/(ell+m-1.0);
+        const double factor1 = sqrt(rat1*(2.0*ell+1.0)*(2.0*ell-1.0));
+        const double factor2 = sqrt(rat1*rat2*(2.0*ell+1.0)/(2.0*ell-3.0));
+        y_ell = (x*y_mmp1*factor1 - (ell+m-1.0)*y_mm*factor2) / (ell-m);
+        y_mm   = y_mmp1;
+        y_mmp1 = y_ell;
+
+        y_ell_err = 0.5*(fabs(x*factor1)*y_mmp1_err + fabs((ell+m-1.0)*factor2)*y_mm_err) / fabs(ell-m);
+        y_mm_err = y_mmp1_err;
+        y_mmp1_err = y_ell_err;
+      }
+
+      result->val  = y_ell;
+      result->err  = y_ell_err + (0.5*(l-m) + 1.0) * GSL_DBL_EPSILON * fabs(y_ell);
+
+      return GSL_SUCCESS;
+    }
+  }
+}
+
+#ifndef GSL_DISABLE_DEPRECATED
 
 int
 gsl_sf_legendre_Plm_array(const int lmax, const int m, const double x, double * result_array)
@@ -419,7 +512,6 @@
   }
 }
 
-
 int
 gsl_sf_legendre_Plm_deriv_array(
   const int lmax, const int m, const double x,
@@ -498,101 +590,6 @@
   }
 }
 
-
-int
-gsl_sf_legendre_sphPlm_e(const int l, int m, const double x, gsl_sf_result * result)
-{
-  /* CHECK_POINTER(result) */
-
-  if(m < 0 || l < m || x < -1.0 || x > 1.0) {
-    DOMAIN_ERROR(result);
-  }
-  else if(m == 0) {
-    gsl_sf_result P;
-    int stat_P = gsl_sf_legendre_Pl_e(l, x, &P);
-    double pre = sqrt((2.0*l + 1.0)/(4.0*M_PI));
-    result->val  = pre * P.val;
-    result->err  = pre * P.err;
-    result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
-    return stat_P;
-  }
-  else if(x == 1.0 || x == -1.0) {
-    /* m > 0 here */
-    result->val = 0.0;
-    result->err = 0.0;
-    return GSL_SUCCESS;
-  }
-  else {
-    /* m > 0 and |x| < 1 here */
-
-    /* Starting value for recursion.
-     * Y_m^m(x) = sqrt( (2m+1)/(4pi m) gamma(m+1/2)/gamma(m) ) (-1)^m (1-x^2)^(m/2) / pi^(1/4)
-     */
-    gsl_sf_result lncirc;
-    gsl_sf_result lnpoch;
-    double lnpre_val;
-    double lnpre_err;
-    gsl_sf_result ex_pre;
-    double sr;
-    const double sgn = ( GSL_IS_ODD(m) ? -1.0 : 1.0);
-    const double y_mmp1_factor = x * sqrt(2.0*m + 3.0);
-    double y_mm, y_mm_err;
-    double y_mmp1, y_mmp1_err;
-    gsl_sf_log_1plusx_e(-x*x, &lncirc);
-    gsl_sf_lnpoch_e(m, 0.5, &lnpoch);  /* Gamma(m+1/2)/Gamma(m) */
-    lnpre_val = -0.25*M_LNPI + 0.5 * (lnpoch.val + m*lncirc.val);
-    lnpre_err = 0.25*M_LNPI*GSL_DBL_EPSILON + 0.5 * (lnpoch.err + fabs(m)*lncirc.err);
-    /* Compute exp(ln_pre) with error term, avoiding call to gsl_sf_exp_err BJG */
-    ex_pre.val = exp(lnpre_val);
-    ex_pre.err = 2.0*(sinh(lnpre_err) + GSL_DBL_EPSILON)*ex_pre.val;
-    sr     = sqrt((2.0+1.0/m)/(4.0*M_PI));
-    y_mm   = sgn * sr * ex_pre.val;
-    y_mm_err  = 2.0 * GSL_DBL_EPSILON * fabs(y_mm) + sr * ex_pre.err;
-    y_mm_err *= 1.0 + 1.0/(GSL_DBL_EPSILON + fabs(1.0-x));
-    y_mmp1 = y_mmp1_factor * y_mm;
-    y_mmp1_err=fabs(y_mmp1_factor) * y_mm_err;
-
-    if(l == m){
-      result->val  = y_mm;
-      result->err  = y_mm_err;
-      result->err += 2.0 * GSL_DBL_EPSILON * fabs(y_mm);
-      return GSL_SUCCESS;
-    }
-    else if(l == m + 1) {
-      result->val  = y_mmp1;
-      result->err  = y_mmp1_err;
-      result->err += 2.0 * GSL_DBL_EPSILON * fabs(y_mmp1);
-      return GSL_SUCCESS;
-    }
-    else{
-      double y_ell = 0.0;
-      double y_ell_err;
-      int ell;
-
-      /* Compute Y_l^m, l > m+1, upward recursion on l. */
-      for(ell=m+2; ell <= l; ell++){
-        const double rat1 = (double)(ell-m)/(double)(ell+m);
-        const double rat2 = (ell-m-1.0)/(ell+m-1.0);
-        const double factor1 = sqrt(rat1*(2.0*ell+1.0)*(2.0*ell-1.0));
-        const double factor2 = sqrt(rat1*rat2*(2.0*ell+1.0)/(2.0*ell-3.0));
-        y_ell = (x*y_mmp1*factor1 - (ell+m-1.0)*y_mm*factor2) / (ell-m);
-        y_mm   = y_mmp1;
-        y_mmp1 = y_ell;
-
-        y_ell_err = 0.5*(fabs(x*factor1)*y_mmp1_err + fabs((ell+m-1.0)*factor2)*y_mm_err) / fabs(ell-m);
-        y_mm_err = y_mmp1_err;
-        y_mmp1_err = y_ell_err;
-      }
-
-      result->val  = y_ell;
-      result->err  = y_ell_err + (0.5*(l-m) + 1.0) * GSL_DBL_EPSILON * fabs(y_ell);
-
-      return GSL_SUCCESS;
-    }
-  }
-}
-
-
 int
 gsl_sf_legendre_sphPlm_array(const int lmax, int m, const double x, double * result_array)
 {
@@ -743,6 +740,8 @@
   return lmax-m+1;
 }
 
+#endif /* !GSL_DISABLE_DEPRECATED */
+
 /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
 
 #include "eval.h"
@@ -776,4 +775,3 @@
 {
   EVAL_RESULT(gsl_sf_legendre_sphPlm_e(l, m, x, &result));
 }
-
diff -Nru gsl-doc-1.16/specfunc/legendre_source.c gsl-doc-2.3/specfunc/legendre_source.c
--- gsl-doc-1.16/specfunc/legendre_source.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/specfunc/legendre_source.c	2016-08-25 17:15:56.000000000 +0000
@@ -0,0 +1,599 @@
+/* legendre_source.c
+ * 
+ * Copyright (C) 2009-2013 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/* define various macros for functions below */
+
+#define CONCAT2x(a,b)   a ## _ ## b 
+#define CONCAT3x(a,b,c) a ## _ ## b ## _ ## c
+
+#if defined(LEGENDRE)
+#define FUNCTION(dir,name) CONCAT2x(dir,name)
+#define OUTPUT result_array
+#define OUTPUT_ARG double result_array[]
+
+#elif defined(LEGENDRE_DERIV)
+#define FUNCTION(dir,name) CONCAT3x(dir,deriv,name)
+#define OUTPUT result_array, result_deriv_array
+#define OUTPUT_ARG double result_array[], double result_deriv_array[]
+
+#elif defined(LEGENDRE_DERIV_ALT)
+#define FUNCTION(dir,name) CONCAT3x(dir,deriv_alt,name)
+#define OUTPUT result_array, result_deriv_array
+#define OUTPUT_ARG double result_array[], double result_deriv_array[]
+#define LEGENDRE_DERIV
+
+#elif defined(LEGENDRE_DERIV2)
+#define FUNCTION(dir,name) CONCAT3x(dir,deriv2,name)
+#define OUTPUT result_array, result_deriv_array, result_deriv2_array
+#define OUTPUT_ARG double result_array[], double result_deriv_array[], double result_deriv2_array[]
+#define LEGENDRE_DERIV
+
+#elif defined(LEGENDRE_DERIV2_ALT)
+#define FUNCTION(dir,name) CONCAT3x(dir,deriv2_alt,name)
+#define OUTPUT result_array, result_deriv_array, result_deriv2_array
+#define OUTPUT_ARG double result_array[], double result_deriv_array[], double result_deriv2_array[]
+#define LEGENDRE_DERIV
+#define LEGENDRE_DERIV2
+#define LEGENDRE_DERIV_ALT
+
+#endif
+
+static int FUNCTION (legendre, array_schmidt_e)
+(const size_t lmax, const double x, const double csphase, OUTPUT_ARG);
+static int FUNCTION(legendre, array_none_e)
+(const size_t lmax, const double x, const double csphase, OUTPUT_ARG);
+
+/*
+gsl_sf_legendre_array()
+
+Inputs: norm                - normlization type
+        lmax                - maximum degree
+        x                   - input argument
+        result_array        - (output) normalized P_{lm}
+        result_deriv_array  - (output) normalized P'_{lm}
+        result_deriv2_array - (output) normalized P''_{lm}
+*/
+
+int
+FUNCTION (gsl_sf_legendre, array)
+(const gsl_sf_legendre_t norm, const size_t lmax, const double x,
+ OUTPUT_ARG)
+{
+  int s = FUNCTION (gsl_sf_legendre, array_e)(norm, lmax, x, 1.0, OUTPUT);
+  return s;
+}
+
+/*
+gsl_sf_legendre_array_e()
+
+Inputs: norm                - normlization type
+        lmax                - maximum degree
+        x                   - input argument
+        csphase             - Condon-Shortley phase
+        result_array        - (output) normalized P_{lm}
+        result_deriv_array  - (output) normalized P'_{lm}
+        result_deriv2_array - (output) normalized P''_{lm}
+*/
+
+int
+FUNCTION (gsl_sf_legendre, array_e)
+(const gsl_sf_legendre_t norm, const size_t lmax, const double x,
+ const double csphase, OUTPUT_ARG)
+{
+  int s;
+  const size_t nlm = gsl_sf_legendre_nlm(lmax);
+#if !defined(LEGENDRE_DERIV_ALT)
+  size_t i;
+#if defined(LEGENDRE_DERIV) || defined(LEGENDRE_DERIV2)
+  const double u = sqrt((1.0 - x) * (1.0 + x));
+  const double uinv = 1.0 / u;
+#endif
+#if defined(LEGENDRE_DERIV2)
+  const double uinv2 = uinv * uinv;
+#endif
+#endif
+  double fac1 = 0.0, fac2 = 0.0; /* normalization factors */
+
+  if (norm == GSL_SF_LEGENDRE_NONE)
+    {
+      /* compute P_{lm}(x) */
+      s = FUNCTION(legendre,array_none_e)(lmax, x, csphase, OUTPUT);
+    }
+  else
+    {
+      /* compute S_{lm}(x) */
+      s = FUNCTION(legendre,array_schmidt_e)(lmax, x, csphase, OUTPUT);
+    }
+
+#if !defined(LEGENDRE_DERIV_ALT)
+  /* scale derivative arrays to recover P'(x) and P''(x) */
+  for (i = 0; i < nlm; ++i)
+    {
+#if defined(LEGENDRE_DERIV2)
+      double dp = result_deriv_array[i];
+      double d2p = result_deriv2_array[i];
+
+      result_deriv2_array[i] = (d2p - x * uinv * dp) * uinv2;
+#endif
+#if defined(LEGENDRE_DERIV)
+      result_deriv_array[i] *= -uinv;
+#endif
+    }
+#endif
+
+  /* apply scaling for requested normalization */
+  if (norm == GSL_SF_LEGENDRE_SCHMIDT || norm == GSL_SF_LEGENDRE_NONE)
+    {
+      return s;
+    }
+  else if (norm == GSL_SF_LEGENDRE_SPHARM)
+    {
+      fac1 = 1.0 / sqrt(4.0 * M_PI);
+      fac2 = 1.0 / sqrt(8.0 * M_PI);
+    }
+  else if (norm == GSL_SF_LEGENDRE_FULL)
+    {
+      fac1 = 1.0 / sqrt(2.0);
+      fac2 = 1.0 / sqrt(4.0);
+    }
+
+  /*
+   * common code for different normalizations
+   * P_{l0} = fac1 * sqrt(2l + 1) * S_{l0}
+   * P_{lm} = fac2 * sqrt(2l + 1) * S_{lm}, m > 0
+   */
+  {
+    size_t l, m;
+    size_t twoellp1 = 1; /* 2l + 1 */
+    double *sqrts = &(result_array[nlm]);
+
+    for (l = 0; l <= lmax; ++l)
+      {
+        result_array[gsl_sf_legendre_array_index(l, 0)] *=
+          sqrts[twoellp1] * fac1;
+#if defined(LEGENDRE_DERIV)
+        result_deriv_array[gsl_sf_legendre_array_index(l, 0)] *=
+          sqrts[twoellp1] * fac1;
+#endif
+#if defined(LEGENDRE_DERIV2)
+        result_deriv2_array[gsl_sf_legendre_array_index(l, 0)] *=
+          sqrts[twoellp1] * fac1;
+#endif
+
+        for (m = 1; m <= l; ++m)
+          {
+            result_array[gsl_sf_legendre_array_index(l, m)] *=
+              sqrts[twoellp1] * fac2;
+#if defined(LEGENDRE_DERIV)
+            result_deriv_array[gsl_sf_legendre_array_index(l, m)] *=
+              sqrts[twoellp1] * fac2;
+#endif
+#if defined(LEGENDRE_DERIV2)
+            result_deriv2_array[gsl_sf_legendre_array_index(l, m)] *=
+              sqrts[twoellp1] * fac2;
+#endif
+          }
+
+        twoellp1 += 2;
+      }
+  }
+
+  return s;
+}
+
+/*
+legendre,array_schmidt_e()
+  This routine computes Schmidt semi-normalized associated
+Legendre polynomials and their first and second derivatives.
+
+Inputs: lmax                - maximum order
+        x                   - legendre argument in [-1,1]
+        csphase             - -1.0 to include CS phase (-1)^m,
+                               1.0 to not include
+        result_array        - (output) where to store P_{lm}(x) values
+        result_deriv_array  - (output) where to store
+                              d/dtheta P_{lm}(x) values
+        result_deriv2_array - (output) where to store
+                              d^2/dtheta^2 P_{lm}(x) values
+*/
+
+static int
+FUNCTION(legendre, array_schmidt_e)
+(const size_t lmax, const double x, const double csphase, OUTPUT_ARG)
+{
+  if (x > 1.0 || x < -1.0)
+    {
+      GSL_ERROR("x is outside [-1,1]", GSL_EDOM);
+    }
+#if defined(LEGENDRE_DERIV) || defined(LEGENDRE_DERIV2)
+  else if (fabs(x) == 1.0)
+    {
+      GSL_ERROR("x cannot equal 1 or -1 for derivative computation", GSL_EDOM);
+    }
+#endif
+  else if (csphase != 1.0 && csphase != -1.0)
+    {
+      GSL_ERROR("csphase has invalid value", GSL_EDOM);
+    }
+  else
+    {
+      const double eps = 1.0e-280;
+      const double u = sqrt((1.0 - x) * (1.0 + x)); /* sin(theta) */
+#if defined(LEGENDRE_DERIV)
+      const double uinv = 1.0 / u;
+#endif
+#if defined(LEGENDRE_DERIV2)
+      const double uinv2 = 1.0 / u / u;
+#endif
+#if defined(LEGENDRE_DERIV) || defined(LEGENDRE_DERIV2)
+      const double xbyu = x * uinv; /* x / u */
+#endif
+      size_t l, m;
+      size_t k, idxmm;
+      double plm, /* eps * S(l,m) / u^m */
+             pmm; /* eps * S(m,m) / u^m */
+      double rescalem;
+      double pm1, /* S(l-1,m) */
+             pm2; /* S(l-2,m) */
+      size_t nlm = gsl_sf_legendre_nlm(lmax);
+      double *sqrts = &(result_array[nlm]);
+
+      /* precompute square root factors for recurrence */
+      legendre_sqrts(lmax, sqrts);
+
+      /* initial values S(0,0) and S(1,0) */
+      pm2 = 1.0; /* S(0,0) */
+      pm1 = x;   /* S(1,0) */
+
+      result_array[0] = pm2;
+#if defined(LEGENDRE_DERIV)
+      result_deriv_array[0] = 0.0;
+#endif
+#if defined(LEGENDRE_DERIV2)
+      result_deriv2_array[0] = 0.0;
+#endif
+
+      if (lmax == 0)
+        return GSL_SUCCESS;
+
+      result_array[1] = pm1;
+#if defined(LEGENDRE_DERIV)
+      result_deriv_array[1] = -u;
+#endif
+#if defined(LEGENDRE_DERIV2)
+      result_deriv2_array[1] = -x;
+#endif
+
+      /* Compute S(l,0) for l=2..lmax, no scaling required */
+
+      k = 1; /* idx(1,0) */
+      for (l = 2; l <= lmax; ++l)
+        {
+          double linv = 1.0 / (double)l;
+
+          k += l;  /* idx(l,m) = idx(l-1,m) + l */
+
+          plm = (2.0 - linv) * x * pm1 - (1.0 - linv) * pm2;
+          result_array[k] = plm;
+#if defined(LEGENDRE_DERIV)
+          result_deriv_array[k] = uinv * l * (x * plm - pm1);
+#endif
+#if defined(LEGENDRE_DERIV2)
+          result_deriv2_array[k] = -(double) l * (l + 1.0) * plm -
+                                   xbyu * result_deriv_array[k];
+#endif
+          pm2 = pm1;
+          pm1 = plm;
+        }
+
+      /* Compute S(m,m), S(m+1,m) and S(l,m) */
+
+      /*
+       * pi_m = Prod_{i=2}^m sqrt[ (2m - 1) / (2m) ]
+       * but pi_1 = 1.0, so initialize to sqrt(2) so that
+       * the first m = 1 iteration of the loop will reset it
+       * to 1.0. Starting with m = 2 it will begin accumulating
+       * the correct terms.
+       *
+       * pmm = S(m,m) * eps / u^m = pi_m
+       */
+      pmm = sqrt(2.0) * eps;
+
+      rescalem = 1.0 / eps;
+      idxmm = 0; /* tracks idx(m,m), initialize to idx(0,0) */
+
+      for (m = 1; m < lmax; ++m)
+        {
+          /* rescalem = u^m / eps */
+          rescalem *= u;
+
+          /*
+           * compute:
+           * S(m,m) = u * sqrt((2m - 1) / (2m)) S(m-1,m-1) = u^m * pi_m
+           * d_t S(m,m) = m * x / u * S(m,m)
+           */
+
+          idxmm += m + 1; /* idx(m,m) = idx(m-1,m-1) + m + 1 */
+          pmm *= csphase * sqrts[2 * m - 1] / sqrts[2 * m]; /* S(m,m) * eps / u^m */
+          result_array[idxmm] = pmm * rescalem;
+#if defined(LEGENDRE_DERIV)
+          result_deriv_array[idxmm] = m * xbyu * result_array[idxmm];
+#endif
+#if defined(LEGENDRE_DERIV2)
+          result_deriv2_array[idxmm] =
+            m * (uinv2 * m - (m + 1.0)) * result_array[idxmm] -
+            xbyu * result_deriv_array[idxmm];
+#endif
+          pm2 = pmm;
+
+          /*
+           * compute:
+           * S(m+1,m) = sqrt(2 * m + 1) * x * S(m,m)
+           * d_t S(m+1,m) = 1/u * ((m+1)*x*S(m+1,m) - sqrt(2*m+1)*S(m,m))
+           */
+
+          k = idxmm + m + 1; /* idx(m+1,m) = idx(m,m) + m + 1 */
+          pm1 = x * sqrts[2 * m + 1] * pm2;
+          result_array[k] = pm1 * rescalem;
+#if defined(LEGENDRE_DERIV)
+          result_deriv_array[k] =
+            uinv * ((m + 1.0) * x * result_array[k] -
+                    sqrts[2 * m + 1] * result_array[idxmm]);
+#endif
+#if defined(LEGENDRE_DERIV2)
+          result_deriv2_array[k] =
+            (m * m * uinv2 - (m + 1.0) * (m + 2.0)) * result_array[k] -
+            xbyu * result_deriv_array[k];
+#endif
+
+          /* compute S(l,m) for l=m+2...lmax */
+          for (l = m + 2; l <= lmax; ++l)
+            {
+              k += l; /* idx(l,m) = idx(l-1,m) + l */
+              plm =
+                (2*l - 1) / sqrts[l + m] / sqrts[l - m] * x * pm1 -
+                sqrts[l - m - 1] * sqrts[l + m - 1] /
+                sqrts[l + m] / sqrts[l - m] * pm2;
+              result_array[k] = plm * rescalem;
+#if defined(LEGENDRE_DERIV)
+              result_deriv_array[k] =
+                uinv * (l * x * result_array[k] -
+                        sqrts[l + m] * sqrts[l - m] * result_array[k - l]);
+#endif
+#if defined(LEGENDRE_DERIV2)
+              result_deriv2_array[k] =
+                (m * m * uinv2 - l * (l + 1.0)) * result_array[k] -
+                xbyu * result_deriv_array[k];
+#endif
+              pm2 = pm1;
+              pm1 = plm;
+            }
+        } /* for (m = 1; m < lmax; ++m) */
+
+      /* compute S(lmax,lmax) */
+
+      rescalem *= u;
+      idxmm += m + 1; /* idx(lmax,lmax) */
+      pmm *= csphase * sqrts[2 * lmax - 1] / sqrts[2 * lmax];
+      result_array[idxmm] = pmm * rescalem;
+#if defined(LEGENDRE_DERIV)
+      result_deriv_array[idxmm] = lmax * xbyu * result_array[idxmm];
+#endif
+#if defined(LEGENDRE_DERIV2)
+      result_deriv2_array[idxmm] =
+        lmax * (uinv2 * lmax - (lmax + 1.0)) * result_array[idxmm] -
+        xbyu * result_deriv_array[idxmm];
+#endif
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+legendre_array_none_e()
+  This routine computes unnormalized associated Legendre polynomials
+and their derivatives.
+
+Inputs: lmax                - maximum order
+        x                   - legendre argument in [-1,1]
+        csphase             - -1.0 to include CS phase (-1)^m,
+                               1.0 to not include
+        result_array        - (output) where to store P_{lm}(x) values
+        result_deriv_array  - (output) where to store
+                              d/dtheta P_{lm}(x) values
+        result_deriv2_array - (output) where to store
+                              d^2/dtheta^2 P_{lm}(x) values
+*/
+
+static int
+FUNCTION(legendre, array_none_e)
+(const size_t lmax, const double x, const double csphase, OUTPUT_ARG)
+{
+  if (x > 1.0 || x < -1.0)
+    {
+      GSL_ERROR("x is outside [-1,1]", GSL_EDOM);
+    }
+#if defined(LEGENDRE_DERIV) || defined(LEGENDRE_DERIV2)
+  else if (fabs(x) == 1.0)
+    {
+      GSL_ERROR("x cannot equal 1 or -1 for derivative computation", GSL_EDOM);
+    }
+#endif
+  else if (csphase != 1.0 && csphase != -1.0)
+    {
+      GSL_ERROR("csphase has invalid value", GSL_EDOM);
+    }
+  else
+    {
+      const double u = sqrt((1.0 - x) * (1.0 + x)); /* sin(theta) */
+#if defined(LEGENDRE_DERIV)
+      const double uinv = 1.0 / u;
+#endif
+#if defined(LEGENDRE_DERIV2)
+      const double uinv2 = 1.0 / u / u;
+#endif
+#if defined(LEGENDRE_DERIV) || defined(LEGENDRE_DERIV2)
+      const double xbyu = x * uinv; /* x / u */
+#endif
+      size_t l, m;
+      size_t k, idxmm;
+      double plm, pmm;
+      double pm1,    /* P(l-1,m) */
+             pm2;    /* P(l-2,m) */
+      double twomm1; /* 2*m - 1 */
+
+      /* initial values P(0,0) and P(1,0) */
+
+      pm2 = 1.0; /* P(0,0) */
+      pm1 = x;   /* P(1,0) */
+
+      result_array[0] = pm2;
+#if defined(LEGENDRE_DERIV)
+      result_deriv_array[0] = 0.0;
+#endif
+#if defined(LEGENDRE_DERIV2)
+      result_deriv2_array[0] = 0.0;
+#endif
+
+      if (lmax == 0)
+        return 0;
+
+      result_array[1] = pm1;
+#if defined(LEGENDRE_DERIV)
+      result_deriv_array[1] = -u;
+#endif
+#if defined(LEGENDRE_DERIV2)
+      result_deriv2_array[1] = -x;
+#endif
+
+      /* Compute P(l,0) */
+
+      k = 1;
+      for (l = 2; l <= lmax; ++l)
+        {
+          k += l;
+          plm = ((2*l - 1) * x * pm1 - (l - 1) * pm2) / (double) l;
+          result_array[k] = plm;
+#if defined(LEGENDRE_DERIV)
+          result_deriv_array[k] = -(double)l * (pm1 - x * plm) * uinv;
+#endif
+#if defined(LEGENDRE_DERIV2)
+          result_deriv2_array[k] = -(double) l * (l + 1.0) * plm -
+                                   xbyu * result_deriv_array[k];
+#endif
+          pm2 = pm1;
+          pm1 = plm;
+        }
+
+      /* Compute P(m,m), P(m+1,m) and P(l,m) */
+
+      pmm = 1.0;
+      twomm1 = -1.0; /* 2 * m - 1 */
+
+      idxmm = 0; /* tracks idx(m,m), initialize to idx(0,0) */
+
+      for (m = 1; m <= lmax - 1; ++m)
+        {
+          /*
+           * compute
+           *
+           * P(m,m) = u * (2m - 1) P(m-1,m-1)
+           * and
+           * dP(m,m)/dtheta = m * x * P(m,m) / u
+           */
+          idxmm += m + 1;
+          twomm1 += 2.0;
+          pmm *= csphase * u * twomm1;
+          result_array[idxmm] = pmm;
+#if defined(LEGENDRE_DERIV)
+          result_deriv_array[idxmm] = m * xbyu * pmm;
+#endif
+#if defined(LEGENDRE_DERIV2)
+          result_deriv2_array[idxmm] =
+            m * (uinv2 * m - (m + 1.0)) * result_array[idxmm] -
+            xbyu * result_deriv_array[idxmm];
+#endif
+          pm2 = pmm;
+
+          /*
+           * compute
+           *
+           * P(m+1,m) = (2 * m + 1) * x * P(m,m)
+           * and
+           * dP(m+1,m)/dt = -[(2*m + 1) * P(m,m) - (m+1) * x * P(m+1,m)]/u
+           */
+          k = idxmm + m + 1;
+          pm1 = x * pmm * (2*m + 1);
+          result_array[k] = pm1;
+#if defined(LEGENDRE_DERIV)
+          result_deriv_array[k] = -uinv * ((2*m + 1) * pmm - (m + 1) * x * pm1);
+#endif
+#if defined(LEGENDRE_DERIV2)
+          result_deriv2_array[k] =
+            (m * m * uinv2 - (m + 1.0) * (m + 2.0)) * result_array[k] -
+            xbyu * result_deriv_array[k];
+#endif
+
+          /* compute P(l,m) */
+          for (l = m + 2; l <= lmax; ++l)
+            {
+              k += l;
+              plm = ((2*l - 1) * x * pm1 - (l + m - 1) * pm2) /
+                    (double) (l - m);
+              result_array[k] = plm;
+#if defined(LEGENDRE_DERIV)
+              result_deriv_array[k] = -uinv * ((l + m) * pm1 - l * x * plm);
+#endif
+#if defined(LEGENDRE_DERIV2)
+              result_deriv2_array[k] =
+                (m * m * uinv2 - l * (l + 1.0)) * result_array[k] -
+                xbyu * result_deriv_array[k];
+#endif
+              pm2 = pm1;
+              pm1 = plm;
+            }
+        } /* for (m = 1; m <= lmax - 1; ++m) */
+
+      /* compute P(lmax,lmax) */
+
+      idxmm += m + 1;
+      twomm1 += 2.0;
+      pmm *= csphase * u * twomm1;
+      result_array[idxmm] = pmm;
+#if defined(LEGENDRE_DERIV)
+      result_deriv_array[idxmm] = lmax * x * pmm * uinv;
+#endif
+#if defined(LEGENDRE_DERIV2)
+      result_deriv2_array[idxmm] =
+        lmax * (uinv2 * lmax - (lmax + 1.0)) * result_array[idxmm] -
+        xbyu * result_deriv_array[idxmm];
+#endif
+
+      return GSL_SUCCESS;
+    }
+} /* legendre_array_none_e() */
+
+#undef FUNCTION
+#undef CONCAT2x
+#undef CONCAT3x
+#undef OUTPUT
+#undef OUTPUT_ARG
+#undef LEGENDRE_DERIV
+#undef LEGENDRE_DERIV2
+#undef LEGENDRE_DERIV_ALT
diff -Nru gsl-doc-1.16/specfunc/Makefile.am gsl-doc-2.3/specfunc/Makefile.am
--- gsl-doc-1.16/specfunc/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/Makefile.am	2016-08-23 20:38:06.000000000 +0000
@@ -2,17 +2,17 @@
 
 pkginclude_HEADERS = gsl_sf.h gsl_sf_airy.h gsl_sf_bessel.h gsl_sf_clausen.h gsl_sf_coulomb.h gsl_sf_coupling.h gsl_sf_dawson.h gsl_sf_debye.h gsl_sf_dilog.h gsl_sf_elementary.h gsl_sf_ellint.h gsl_sf_elljac.h gsl_sf_erf.h gsl_sf_exp.h gsl_sf_expint.h gsl_sf_fermi_dirac.h gsl_sf_gamma.h gsl_sf_gegenbauer.h gsl_sf_hyperg.h gsl_sf_laguerre.h gsl_sf_lambert.h gsl_sf_legendre.h gsl_sf_log.h gsl_sf_mathieu.h gsl_sf_pow_int.h gsl_sf_psi.h gsl_sf_result.h gsl_sf_synchrotron.h gsl_sf_transport.h gsl_sf_trig.h gsl_sf_zeta.h gsl_specfunc.h
 
-noinst_HEADERS = bessel_amp_phase.h bessel_olver.h bessel_temme.h bessel.h hyperg.h legendre.h eval.h chebyshev.h cheb_eval.c cheb_eval_mode.c check.h error.h
+noinst_HEADERS = bessel_amp_phase.h bessel_olver.h bessel_temme.h bessel.h hyperg.h legendre.h eval.h chebyshev.h cheb_eval.c cheb_eval_mode.c check.h error.h legendre_source.c
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
-libgslspecfunc_la_SOURCES = airy.c airy_der.c airy_zero.c atanint.c bessel.c bessel.h bessel_I0.c bessel_I1.c bessel_In.c bessel_Inu.c bessel_J0.c bessel_J1.c bessel_Jn.c bessel_Jnu.c bessel_K0.c bessel_K1.c bessel_Kn.c bessel_Knu.c bessel_Y0.c bessel_Y1.c bessel_Yn.c bessel_Ynu.c bessel_amp_phase.c bessel_amp_phase.h bessel_i.c bessel_j.c bessel_k.c bessel_olver.c bessel_temme.c bessel_y.c bessel_zero.c bessel_sequence.c beta.c beta_inc.c clausen.c coulomb.c coupling.c coulomb_bound.c dawson.c debye.c dilog.c elementary.c ellint.c elljac.c erfc.c exp.c expint.c expint3.c fermi_dirac.c gegenbauer.c gamma.c gamma_inc.c hyperg_0F1.c hyperg_2F0.c hyperg_1F1.c hyperg_2F1.c hyperg_U.c hyperg.c laguerre.c lambert.c legendre_H3d.c legendre_Qn.c legendre_con.c legendre_poly.c log.c mathieu_angfunc.c mathieu_charv.c mathieu_coeff.c mathieu_radfunc.c mathieu_workspace.c poch.c pow_int.c psi.c recurse.h result.c shint.c sinint.c synchrotron.c transport.c trig.c zeta.c
+libgslspecfunc_la_SOURCES = airy.c airy_der.c airy_zero.c atanint.c bessel.c bessel.h bessel_I0.c bessel_I1.c bessel_In.c bessel_Inu.c bessel_J0.c bessel_J1.c bessel_Jn.c bessel_Jnu.c bessel_K0.c bessel_K1.c bessel_Kn.c bessel_Knu.c bessel_Y0.c bessel_Y1.c bessel_Yn.c bessel_Ynu.c bessel_amp_phase.c bessel_amp_phase.h bessel_i.c bessel_j.c bessel_k.c bessel_olver.c bessel_temme.c bessel_y.c bessel_zero.c bessel_sequence.c beta.c beta_inc.c clausen.c coulomb.c coupling.c coulomb_bound.c dawson.c debye.c dilog.c elementary.c ellint.c elljac.c erfc.c exp.c expint.c expint3.c fermi_dirac.c gegenbauer.c gamma.c gamma_inc.c hyperg_0F1.c hyperg_2F0.c hyperg_1F1.c hyperg_2F1.c hyperg_U.c hyperg.c laguerre.c lambert.c legendre_H3d.c legendre_P.c legendre_Qn.c legendre_con.c legendre_poly.c log.c mathieu_angfunc.c mathieu_charv.c mathieu_coeff.c mathieu_radfunc.c mathieu_workspace.c poch.c pow_int.c psi.c recurse.h result.c shint.c sinint.c synchrotron.c transport.c trig.c zeta.c
 
 TESTS = $(check_PROGRAMS)
 
 check_PROGRAMS = test
 
-test_LDADD = libgslspecfunc.la ../eigen/libgsleigen.la ../linalg/libgsllinalg.la  ../sort/libgslsort.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../block/libgslblock.la ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la  ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
+test_LDADD = libgslspecfunc.la ../eigen/libgsleigen.la ../linalg/libgsllinalg.la  ../sort/libgslsort.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../block/libgslblock.la ../complex/libgslcomplex.la ../poly/libgslpoly.la ../ieee-utils/libgslieeeutils.la  ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
 
 test_SOURCES = test_sf.c test_sf.h test_airy.c test_bessel.c test_coulomb.c test_dilog.c test_gamma.c test_hyperg.c test_legendre.c test_mathieu.c
   
diff -Nru gsl-doc-1.16/specfunc/Makefile.in gsl-doc-2.3/specfunc/Makefile.in
--- gsl-doc-1.16/specfunc/Makefile.in	2013-07-19 15:14:55.000000000 +0000
+++ gsl-doc-2.3/specfunc/Makefile.in	2016-12-09 00:04:22.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -108,11 +108,11 @@
 	exp.lo expint.lo expint3.lo fermi_dirac.lo gegenbauer.lo \
 	gamma.lo gamma_inc.lo hyperg_0F1.lo hyperg_2F0.lo \
 	hyperg_1F1.lo hyperg_2F1.lo hyperg_U.lo hyperg.lo laguerre.lo \
-	lambert.lo legendre_H3d.lo legendre_Qn.lo legendre_con.lo \
-	legendre_poly.lo log.lo mathieu_angfunc.lo mathieu_charv.lo \
-	mathieu_coeff.lo mathieu_radfunc.lo mathieu_workspace.lo \
-	poch.lo pow_int.lo psi.lo result.lo shint.lo sinint.lo \
-	synchrotron.lo transport.lo trig.lo zeta.lo
+	lambert.lo legendre_H3d.lo legendre_P.lo legendre_Qn.lo \
+	legendre_con.lo legendre_poly.lo log.lo mathieu_angfunc.lo \
+	mathieu_charv.lo mathieu_coeff.lo mathieu_radfunc.lo \
+	mathieu_workspace.lo poch.lo pow_int.lo psi.lo result.lo \
+	shint.lo sinint.lo synchrotron.lo transport.lo trig.lo zeta.lo
 libgslspecfunc_la_OBJECTS = $(am_libgslspecfunc_la_OBJECTS)
 AM_V_lt = $(am__v_lt_@AM_V@)
 am__v_lt_ = $(am__v_lt_@AM_DEFAULT_V@)
@@ -129,8 +129,9 @@
 	../matrix/libgslmatrix.la ../vector/libgslvector.la \
 	../blas/libgslblas.la ../cblas/libgslcblas.la \
 	../block/libgslblock.la ../complex/libgslcomplex.la \
-	../ieee-utils/libgslieeeutils.la ../err/libgslerr.la \
-	../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
+	../poly/libgslpoly.la ../ieee-utils/libgslieeeutils.la \
+	../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la \
+	../utils/libutils.la
 AM_V_P = $(am__v_P_@AM_V@)
 am__v_P_ = $(am__v_P_@AM_DEFAULT_V@)
 am__v_P_0 = false
@@ -402,6 +403,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -424,7 +426,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -540,11 +545,11 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslspecfunc.la 
 pkginclude_HEADERS = gsl_sf.h gsl_sf_airy.h gsl_sf_bessel.h gsl_sf_clausen.h gsl_sf_coulomb.h gsl_sf_coupling.h gsl_sf_dawson.h gsl_sf_debye.h gsl_sf_dilog.h gsl_sf_elementary.h gsl_sf_ellint.h gsl_sf_elljac.h gsl_sf_erf.h gsl_sf_exp.h gsl_sf_expint.h gsl_sf_fermi_dirac.h gsl_sf_gamma.h gsl_sf_gegenbauer.h gsl_sf_hyperg.h gsl_sf_laguerre.h gsl_sf_lambert.h gsl_sf_legendre.h gsl_sf_log.h gsl_sf_mathieu.h gsl_sf_pow_int.h gsl_sf_psi.h gsl_sf_result.h gsl_sf_synchrotron.h gsl_sf_transport.h gsl_sf_trig.h gsl_sf_zeta.h gsl_specfunc.h
-noinst_HEADERS = bessel_amp_phase.h bessel_olver.h bessel_temme.h bessel.h hyperg.h legendre.h eval.h chebyshev.h cheb_eval.c cheb_eval_mode.c check.h error.h
-INCLUDES = -I$(top_srcdir)
-libgslspecfunc_la_SOURCES = airy.c airy_der.c airy_zero.c atanint.c bessel.c bessel.h bessel_I0.c bessel_I1.c bessel_In.c bessel_Inu.c bessel_J0.c bessel_J1.c bessel_Jn.c bessel_Jnu.c bessel_K0.c bessel_K1.c bessel_Kn.c bessel_Knu.c bessel_Y0.c bessel_Y1.c bessel_Yn.c bessel_Ynu.c bessel_amp_phase.c bessel_amp_phase.h bessel_i.c bessel_j.c bessel_k.c bessel_olver.c bessel_temme.c bessel_y.c bessel_zero.c bessel_sequence.c beta.c beta_inc.c clausen.c coulomb.c coupling.c coulomb_bound.c dawson.c debye.c dilog.c elementary.c ellint.c elljac.c erfc.c exp.c expint.c expint3.c fermi_dirac.c gegenbauer.c gamma.c gamma_inc.c hyperg_0F1.c hyperg_2F0.c hyperg_1F1.c hyperg_2F1.c hyperg_U.c hyperg.c laguerre.c lambert.c legendre_H3d.c legendre_Qn.c legendre_con.c legendre_poly.c log.c mathieu_angfunc.c mathieu_charv.c mathieu_coeff.c mathieu_radfunc.c mathieu_workspace.c poch.c pow_int.c psi.c recurse.h result.c shint.c sinint.c synchrotron.c transport.c trig.c zeta.c
+noinst_HEADERS = bessel_amp_phase.h bessel_olver.h bessel_temme.h bessel.h hyperg.h legendre.h eval.h chebyshev.h cheb_eval.c cheb_eval_mode.c check.h error.h legendre_source.c
+AM_CPPFLAGS = -I$(top_srcdir)
+libgslspecfunc_la_SOURCES = airy.c airy_der.c airy_zero.c atanint.c bessel.c bessel.h bessel_I0.c bessel_I1.c bessel_In.c bessel_Inu.c bessel_J0.c bessel_J1.c bessel_Jn.c bessel_Jnu.c bessel_K0.c bessel_K1.c bessel_Kn.c bessel_Knu.c bessel_Y0.c bessel_Y1.c bessel_Yn.c bessel_Ynu.c bessel_amp_phase.c bessel_amp_phase.h bessel_i.c bessel_j.c bessel_k.c bessel_olver.c bessel_temme.c bessel_y.c bessel_zero.c bessel_sequence.c beta.c beta_inc.c clausen.c coulomb.c coupling.c coulomb_bound.c dawson.c debye.c dilog.c elementary.c ellint.c elljac.c erfc.c exp.c expint.c expint3.c fermi_dirac.c gegenbauer.c gamma.c gamma_inc.c hyperg_0F1.c hyperg_2F0.c hyperg_1F1.c hyperg_2F1.c hyperg_U.c hyperg.c laguerre.c lambert.c legendre_H3d.c legendre_P.c legendre_Qn.c legendre_con.c legendre_poly.c log.c mathieu_angfunc.c mathieu_charv.c mathieu_coeff.c mathieu_radfunc.c mathieu_workspace.c poch.c pow_int.c psi.c recurse.h result.c shint.c sinint.c synchrotron.c transport.c trig.c zeta.c
 TESTS = $(check_PROGRAMS)
-test_LDADD = libgslspecfunc.la ../eigen/libgsleigen.la ../linalg/libgsllinalg.la  ../sort/libgslsort.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../block/libgslblock.la ../complex/libgslcomplex.la ../ieee-utils/libgslieeeutils.la  ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
+test_LDADD = libgslspecfunc.la ../eigen/libgsleigen.la ../linalg/libgsllinalg.la  ../sort/libgslsort.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../block/libgslblock.la ../complex/libgslcomplex.la ../poly/libgslpoly.la ../ieee-utils/libgslieeeutils.la  ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
 test_SOURCES = test_sf.c test_sf.h test_airy.c test_bessel.c test_coulomb.c test_dilog.c test_gamma.c test_hyperg.c test_legendre.c test_mathieu.c
 all: all-am
 
@@ -673,6 +678,7 @@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/laguerre.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/lambert.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/legendre_H3d.Plo@am__quote@
+@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/legendre_P.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/legendre_Qn.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/legendre_con.Plo@am__quote@
 @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/legendre_poly.Plo@am__quote@
diff -Nru gsl-doc-1.16/specfunc/mathieu_angfunc.c gsl-doc-2.3/specfunc/mathieu_angfunc.c
--- gsl-doc-1.16/specfunc/mathieu_angfunc.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/mathieu_angfunc.c	2015-11-03 16:21:55.000000000 +0000
@@ -27,7 +27,7 @@
 #include <gsl/gsl_sf_mathieu.h>
 
 
-int gsl_sf_mathieu_ce(int order, double qq, double zz, gsl_sf_result *result)
+int gsl_sf_mathieu_ce_e(int order, double qq, double zz, gsl_sf_result *result)
 {
   int even_odd, ii, status;
   double coeff[GSL_SF_MATHIEU_COEFF], norm, fn, factor;
@@ -63,7 +63,7 @@
       order *= -1;
 
   /* Compute the characteristic value. */
-  status = gsl_sf_mathieu_a(order, qq, &aa);
+  status = gsl_sf_mathieu_a_e(order, qq, &aa);
   if (status != GSL_SUCCESS)
   {
       return status;
@@ -109,7 +109,7 @@
 }
 
 
-int gsl_sf_mathieu_se(int order, double qq, double zz, gsl_sf_result *result)
+int gsl_sf_mathieu_se_e(int order, double qq, double zz, gsl_sf_result *result)
 {
   int even_odd, ii, status;
   double coeff[GSL_SF_MATHIEU_COEFF], norm, fn, factor;
@@ -149,7 +149,7 @@
       order *= -1;
 
   /* Compute the characteristic value. */
-  status = gsl_sf_mathieu_b(order, qq, &aa);
+  status = gsl_sf_mathieu_b_e(order, qq, &aa);
   if (status != GSL_SUCCESS)
   {
       return status;
@@ -348,3 +348,18 @@
 
   return GSL_SUCCESS;
 }
+
+
+/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
+
+#include "eval.h"                                                           
+
+double gsl_sf_mathieu_ce(int order, double qq, double zz)
+{
+	EVAL_RESULT(gsl_sf_mathieu_ce_e(order, qq, zz, &result));
+}
+
+double gsl_sf_mathieu_se(int order, double qq, double zz)
+{
+	EVAL_RESULT(gsl_sf_mathieu_se_e(order, qq, zz, &result));
+}
diff -Nru gsl-doc-1.16/specfunc/mathieu_charv.c gsl-doc-2.3/specfunc/mathieu_charv.c
--- gsl-doc-1.16/specfunc/mathieu_charv.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/mathieu_charv.c	2015-11-03 16:21:55.000000000 +0000
@@ -367,7 +367,7 @@
 }
 
 
-int gsl_sf_mathieu_a(int order, double qq, gsl_sf_result *result)
+int gsl_sf_mathieu_a_e(int order, double qq, gsl_sf_result *result)
 {
   int even_odd, nterms = 50, ii, counter = 0, maxcount = 1000;
   int dir = 0;  /* step direction for new search */
@@ -395,9 +395,9 @@
   if (qq < 0.0)
   {
       if (even_odd == 0)
-          return gsl_sf_mathieu_a(order, -qq, result);
+          return gsl_sf_mathieu_a_e(order, -qq, result);
       else
-          return gsl_sf_mathieu_b(order, -qq, result);
+          return gsl_sf_mathieu_b_e(order, -qq, result);
   }
   
   /* Compute an initial approximation for the characteristic value. */
@@ -493,7 +493,7 @@
 }
 
 
-int gsl_sf_mathieu_b(int order, double qq, gsl_sf_result *result)
+int gsl_sf_mathieu_b_e(int order, double qq, gsl_sf_result *result)
 {
   int even_odd, nterms = 50, ii, counter = 0, maxcount = 1000;
   int dir = 0;  /* step direction for new search */
@@ -527,9 +527,9 @@
   if (qq < 0.0)
   {
       if (even_odd == 0)
-          return gsl_sf_mathieu_b(order, -qq, result);
+          return gsl_sf_mathieu_b_e(order, -qq, result);
       else
-          return gsl_sf_mathieu_a(order, -qq, result);
+          return gsl_sf_mathieu_a_e(order, -qq, result);
   }
   
   /* Compute an initial approximation for the characteristic value. */
@@ -873,3 +873,18 @@
 
   return GSL_SUCCESS;
 }
+
+
+/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
+
+#include "eval.h"                                                          
+
+double gsl_sf_mathieu_a(int order, double qq)
+{
+	EVAL_RESULT(gsl_sf_mathieu_a_e(order, qq, &result));
+}
+
+double gsl_sf_mathieu_b(int order, double qq)
+{
+	EVAL_RESULT(gsl_sf_mathieu_b_e(order, qq, &result));
+}
diff -Nru gsl-doc-1.16/specfunc/mathieu_radfunc.c gsl-doc-2.3/specfunc/mathieu_radfunc.c
--- gsl-doc-1.16/specfunc/mathieu_radfunc.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/mathieu_radfunc.c	2015-11-03 16:21:55.000000000 +0000
@@ -27,7 +27,7 @@
 #include <gsl/gsl_sf_mathieu.h>
 
 
-int gsl_sf_mathieu_Mc(int kind, int order, double qq, double zz,
+int gsl_sf_mathieu_Mc_e(int kind, int order, double qq, double zz,
                       gsl_sf_result *result)
 {
   int even_odd, kk, mm, status;
@@ -59,7 +59,7 @@
       even_odd = 1;
 
   /* Compute the characteristic value. */
-  status = gsl_sf_mathieu_a(order, qq, &aa);
+  status = gsl_sf_mathieu_a_e(order, qq, &aa);
   if (status != GSL_SUCCESS)
   {
       return status;
@@ -133,7 +133,7 @@
 }
 
 
-int gsl_sf_mathieu_Ms(int kind, int order, double qq, double zz,
+int gsl_sf_mathieu_Ms_e(int kind, int order, double qq, double zz,
                       gsl_sf_result *result)
 {
   int even_odd, kk, mm, status;
@@ -173,7 +173,7 @@
       even_odd = 1;
   
   /* Compute the characteristic value. */
-  status = gsl_sf_mathieu_b(order, qq, &aa);
+  status = gsl_sf_mathieu_b_e(order, qq, &aa);
   if (status != GSL_SUCCESS)
   {
       return status;
@@ -472,3 +472,18 @@
   
   return GSL_SUCCESS;
 }
+
+
+/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
+
+#include "eval.h"                                                           
+
+double gsl_sf_mathieu_Mc(int kind, int order, double qq, double zz)
+{
+	EVAL_RESULT(gsl_sf_mathieu_Mc_e(kind, order, qq, zz, &result));
+}
+
+double gsl_sf_mathieu_Ms(int kind, int order, double qq, double zz)
+{
+	EVAL_RESULT(gsl_sf_mathieu_Ms_e(kind, order, qq, zz, &result));
+}
diff -Nru gsl-doc-1.16/specfunc/test_bessel.c gsl-doc-2.3/specfunc/test_bessel.c
--- gsl-doc-1.16/specfunc/test_bessel.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/test_bessel.c	2016-07-02 23:02:41.000000000 +0000
@@ -125,11 +125,15 @@
 
 
   TEST_SF(s, gsl_sf_bessel_K0_scaled_e, (0.1, &r), 2.6823261022628943831, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s, gsl_sf_bessel_K0_scaled_e, (1.95, &r), 0.8513330938802157074894, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_bessel_K0_scaled_e, (2.0, &r), 0.8415682150707714179, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s, gsl_sf_bessel_K0_scaled_e, (6.0, &r), 0.50186313086214003217346, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_bessel_K0_scaled_e, (100.0, &r), 0.1251756216591265789, TEST_TOL0, GSL_SUCCESS);
 
   TEST_SF(s, gsl_sf_bessel_K1_scaled_e, (0.1, &r), 10.890182683049696574, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s, gsl_sf_bessel_K1_scaled_e, (1.95, &r), 1.050086915104152747182, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_bessel_K1_scaled_e, (2.0, &r), 1.0334768470686885732, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s, gsl_sf_bessel_K1_scaled_e, (6.0, &r), 0.5421759102771335382849, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_bessel_K1_scaled_e, (100.0, &r), 0.1257999504795785293, TEST_TOL0, GSL_SUCCESS);
 
   TEST_SF(s, gsl_sf_bessel_Kn_scaled_e, (   4,    0.1, &r), 530040.2483725626207, TEST_TOL1, GSL_SUCCESS);
@@ -137,10 +141,12 @@
   TEST_SF(s, gsl_sf_bessel_Kn_scaled_e, ( 100,  100.0, &r), 2.0475736731166756813e+19, TEST_TOL1, GSL_SUCCESS);
 
   TEST_SF(s, gsl_sf_bessel_K0_e, (0.1, &r), 2.4270690247020166125, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s, gsl_sf_bessel_K0_e, (1.95, &r), 0.1211226255426818887894, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_bessel_K0_e, (2.0, &r), 0.11389387274953343565, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_bessel_K0_e, (100.0, &r), 4.656628229175902019e-45, TEST_TOL2, GSL_SUCCESS);
 
   TEST_SF(s, gsl_sf_bessel_K1_e, (0.1, &r), 9.853844780870606135,       TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s, gsl_sf_bessel_K1_e, (1.95, &r), 0.1494001409315894276793,     TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_bessel_K1_e, (2.0, &r), 0.13986588181652242728,     TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_bessel_K1_e, (100.0, &r), 4.679853735636909287e-45, TEST_TOL2, GSL_SUCCESS);
 
@@ -153,7 +159,15 @@
   TEST_SF(s,  gsl_sf_bessel_j0_e, (  1.0, &r), 0.84147098480789650670, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s,  gsl_sf_bessel_j0_e, ( 10.0, &r), -0.05440211108893698134, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s,  gsl_sf_bessel_j0_e, (100.0, &r), -0.005063656411097587937, TEST_TOL1, GSL_SUCCESS);
+#ifdef FIXME
   TEST_SF(s,  gsl_sf_bessel_j0_e, (1048576.0, &r), 3.1518281938718287624e-07, TEST_TOL2, GSL_SUCCESS);
+#endif
+
+  /* these values are from Mathematica */
+#ifdef FIXME
+  TEST_SF(s,  gsl_sf_bessel_j0_e, (1.0e18, &r), -9.9296932074040507620955e-19, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_bessel_j0_e, (1.0e20, &r), -6.4525128526578084420581e-21, TEST_TOL0, GSL_SUCCESS);
+#endif
 
   TEST_SF(s,  gsl_sf_bessel_j1_e, (-10.0, &r), -0.07846694179875154709, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s,  gsl_sf_bessel_j1_e, (0.01, &r), 0.003333300000119047399, TEST_TOL0, GSL_SUCCESS);
@@ -162,6 +176,8 @@
   TEST_SF(s,  gsl_sf_bessel_j1_e, (100.0, &r), -0.008673825286987815220, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s,  gsl_sf_bessel_j1_e, (1048576.0, &r), -9.000855242905546158e-07, TEST_TOL0, GSL_SUCCESS);
 
+  /*TEST_SF(s,  gsl_sf_bessel_j1_e, (1.0e18, &r), -1.183719902187107336049e-19, TEST_TOL0, GSL_SUCCESS);*/
+
   TEST_SF(s,  gsl_sf_bessel_j2_e, (-10.0, &r), 0.07794219362856244547, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s,  gsl_sf_bessel_j2_e, (0.01, &r), 6.666619047751322551e-06, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s,  gsl_sf_bessel_j2_e, (  1.0, &r), 0.06203505201137386110, TEST_TOL0, GSL_SUCCESS);
@@ -192,6 +208,10 @@
   TEST_SF(s,  gsl_sf_bessel_jl_e, (49, 9950.35, &r), 5.0077368819565969286578715503E-5 , TEST_TOL4, GSL_SUCCESS);
   TEST_SF(s,  gsl_sf_bessel_jl_e, (52, 9930.51, &r), -7.4838588266727718650124475651E-6 , TEST_TOL4, GSL_SUCCESS);
 
+  /* bug report #37209 */
+  TEST_SF(s,  gsl_sf_bessel_jl_e, (364, 36.62, &r), 1.118907148986954E-318, TEST_TOL0, GSL_SUCCESS);
+  /*TEST_SF(s,  gsl_sf_bessel_jl_e, (149, 1.0, &r), 2.6599182755508469E-307, TEST_TOL0, GSL_SUCCESS);*/
+
   TEST_SF(s,  gsl_sf_bessel_y0_e, (0.001, &r), -999.99950000004166670, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s,  gsl_sf_bessel_y0_e, (  1.0, &r), -0.5403023058681397174, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s,  gsl_sf_bessel_y0_e, ( 10.0, &r), 0.08390715290764524523, TEST_TOL0, GSL_SUCCESS);
diff -Nru gsl-doc-1.16/specfunc/test_hyperg.c gsl-doc-2.3/specfunc/test_hyperg.c
--- gsl-doc-1.16/specfunc/test_hyperg.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/test_hyperg.c	2016-07-02 23:02:41.000000000 +0000
@@ -460,14 +460,12 @@
   /* Tests for b >= 0 */
 
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 0, 0, -0.1, &r), 1, TEST_TOL0, GSL_SUCCESS);
-#ifdef FIXME  /* unimplemented case */
   TEST_SF(s, gsl_sf_hyperg_U_e, (-1, 0, -0.1, &r), -0.1, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-2, 0, -0.1, &r), 0.21, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-3, 0, -0.1, &r), -0.661, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-4, 0, -0.1, &r), 2.7721, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-5, 0, -0.1, &r), -14.52201, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-6, 0, -0.1, &r), 91.230301, TEST_TOL0, GSL_SUCCESS);
-#endif
 
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 0, 1, -0.1, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-1, 1, -0.1, &r), -1.1, TEST_TOL0, GSL_SUCCESS);
@@ -477,9 +475,7 @@
   TEST_SF(s, gsl_sf_hyperg_U_e, (-5, 1, -0.1, &r), -186.20251, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-6, 1, -0.1, &r), 1208.445361, TEST_TOL2, GSL_SUCCESS);
 
-#ifdef FIXME  /* unimplemented case */
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 1, 2, -0.1, &r), -10.0, TEST_TOL0, GSL_SUCCESS);
-#endif
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 0, 2, -0.1, &r), 1.0, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-1, 2, -0.1, &r), -2.1, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-2, 2, -0.1, &r), 6.61, TEST_TOL2, GSL_SUCCESS);
@@ -488,9 +484,7 @@
   TEST_SF(s, gsl_sf_hyperg_U_e, (-5, 2, -0.1, &r), -912.30301, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-6, 2, -0.1, &r), 6682.263421, TEST_TOL2, GSL_SUCCESS);
 
-#ifdef FIXME  /* unimplemented case */
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 2, 3, -0.1, &r), 100.0, TEST_TOL0, GSL_SUCCESS);
-#endif
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 1, 3, -0.1, &r), 90.0, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 0, 3, -0.1, &r), 1.0, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-1, 3, -0.1, &r), -3.10, TEST_TOL2, GSL_SUCCESS);
@@ -500,9 +494,7 @@
   TEST_SF(s, gsl_sf_hyperg_U_e, (-5, 3, -0.1, &r), -2961.42351, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-6, 3, -0.1, &r), 24450.804481, TEST_TOL2, GSL_SUCCESS);
 
-#ifdef FIXME  /* unimplemented case */
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 3, 4, -0.1, &r), -1000.0, TEST_TOL0, GSL_SUCCESS);
-#endif
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 2, 4, -0.1, &r), -1900.0, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 1, 4, -0.1, &r), -1810.0, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 0, 4, -0.1, &r), 1.0, TEST_TOL2, GSL_SUCCESS);
@@ -516,45 +508,37 @@
   /* Tests for b < 0 */
 
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 0, -1, -0.1, &r), 1.0, TEST_TOL2, GSL_SUCCESS);
-#ifdef FIXME  /* unimplemented case */
   TEST_SF(s, gsl_sf_hyperg_U_e, (-1, -1, -0.1, &r), 0.9, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-2, -1, -0.1, &r), 0.01, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-3, -1, -0.1, &r), -0.031, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-4, -1, -0.1, &r), 0.1281, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-5, -1, -0.1, &r), -0.66151, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-6, -1, -0.1, &r), 4.098241, TEST_TOL0, GSL_SUCCESS);
-#endif
 
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 0, -2, -0.1, &r), 1.0, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-1, -2, -0.1, &r), 1.9, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-2, -2, -0.1, &r), 1.81, TEST_TOL2, GSL_SUCCESS);
-#ifdef FIXME  /* unimplemented case */
   TEST_SF(s, gsl_sf_hyperg_U_e, (-3, -2, -0.1, &r), -0.001, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-4, -2, -0.1, &r), 0.0041, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-5, -2, -0.1, &r), -0.02101, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-6, -2, -0.1, &r), 0.129181, TEST_TOL0, GSL_SUCCESS);
-#endif
 
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 0, -3, -0.1, &r), 1.0, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-1, -3, -0.1, &r), 2.9, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-2, -3, -0.1, &r), 5.61, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-3, -3, -0.1, &r), 5.429, TEST_TOL2, GSL_SUCCESS);
-#ifdef FIXME  /* unimplemented case */
   TEST_SF(s, gsl_sf_hyperg_U_e, (-4, -3, -0.1, &r), 0.0001, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-5, -3, -0.1, &r), -0.00051, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-6, -3, -0.1, &r), 0.003121, TEST_TOL0, GSL_SUCCESS);
-#endif
 
   TEST_SF(s, gsl_sf_hyperg_U_e, ( 0, -4, -0.1, &r), 1.0, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-1, -4, -0.1, &r), 3.9, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-2, -4, -0.1, &r), 11.41, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-3, -4, -0.1, &r), 22.259, TEST_TOL2, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-4, -4, -0.1, &r), 21.7161, TEST_TOL2, GSL_SUCCESS);
-#ifdef FIXME  /* unimplemented case */
   TEST_SF(s, gsl_sf_hyperg_U_e, (-5, -4, -0.1, &r), -1e-5, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-6, -4, -0.1, &r), 0.000061, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-7, -4, -0.1, &r), -0.0004341, TEST_TOL0, GSL_SUCCESS);
-#endif
 
   /* Tests for integer a */
 
@@ -573,11 +557,9 @@
   TEST_SF(s, gsl_sf_hyperg_U_e, (0, 1, -0.001, &r), 1, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-1, 0.99, -0.1, &r), -1.09, TEST_TOL2, GSL_SUCCESS);
 
-#ifdef FIXME  /* unimplemented case */
   TEST_SF(s, gsl_sf_hyperg_U_e, (-1, 0, -0.5, &r), -0.5, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-2, 0, -0.5, &r), 1.25, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_e, (-7, 0, -0.1, &r), -668.2263421, TEST_TOL0, GSL_SUCCESS);
-#endif
 
   TEST_SF(s, gsl_sf_hyperg_U_int_e, (3, 6, -0.5, &r), -296.0, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_hyperg_U_int_e, (3, 7, -0.5, &r), 2824, TEST_TOL0, GSL_SUCCESS);
@@ -586,6 +568,12 @@
   /* Bug report from Raymond Rogers */
 
   TEST_SF(s, gsl_sf_hyperg_U_e, (4.11, 0.11, 6.4, &r), 6.422378238765078623739153038e-5, TEST_TOL2, GSL_SUCCESS);
+  /* Addition tests from Raymond Rogers */
+TEST_SF(s, gsl_sf_hyperg_U_e, (5, 4, 6.4, &r), 3.2586223825343211136628535e-05, TEST_TOL2, GSL_SUCCESS);
+TEST_SF(s, gsl_sf_hyperg_U_e, (2.2,1.2 , 8.7, &r), 5.7250017539318661177749625e-03, TEST_TOL2, GSL_SUCCESS);
+TEST_SF(s, gsl_sf_hyperg_U_e, (2, -6.4, 1, &r),1.2141502795806162484648638e-02
+, TEST_TOL2, GSL_SUCCESS);
+
 
   /* 2F1 */
 
@@ -644,6 +632,10 @@
   /* Didier Pinchon also bug #24812 */
   TEST_SF(s, gsl_sf_hyperg_2F1_e, (11, -1, 11.0/2.0, 0.125 , &r), 0.75, TEST_TOL2, GSL_SUCCESS);
 
+  /* Bill Maier - bug #45926 */
+  TEST_SF(s, gsl_sf_hyperg_2F1_e, (-0.2, 8.8, 10.0, 0.8, &r), 0.77998971427681563, TEST_TOL1, GSL_SUCCESS);
+  TEST_SF(s, gsl_sf_hyperg_2F1_e, (-0.2, 9.8, 11.0, 0.8, &r), 0.77574573497387267, TEST_TOL0, GSL_SUCCESS);
+
 #if 0 /* XXX - bug #39056 */
   /* Test case from Hatef Monajemi <monajemi@stanford.edu> */
 
@@ -652,6 +644,10 @@
   /* Test case from Robert L Wolpert <Wolpert@stat.duke.edu> */
 
   TEST_SF(s, gsl_sf_hyperg_2F1_e, (-1.0, -10.0, 1.0, 0.5, &r), 6.0, TEST_TOL0, GSL_SUCCESS);
+
+  /* Test case from ldnlwm@163.com */
+
+  TEST_SF(s, gsl_sf_hyperg_2F1_e, (3.23191, -4.0229, 8.02291, 0.5, &r), 0.4300243900348170646, TEST_TOL2, GSL_SUCCESS);
 #endif
 
   /* 2F1 conj */
diff -Nru gsl-doc-1.16/specfunc/test_legendre.c gsl-doc-2.3/specfunc/test_legendre.c
--- gsl-doc-1.16/specfunc/test_legendre.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/test_legendre.c	2016-08-25 17:10:30.000000000 +0000
@@ -1,6 +1,7 @@
 /* specfunc/test_legendre.c
  * 
  * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2004 Gerard Jungman
+ * Copyright (C) 2013 Patrick Alken
  * 
  * This program is free software; you can redistribute it and/or modify
  * it under the terms of the GNU General Public License as published by
@@ -24,6 +25,510 @@
 #include <gsl/gsl_sf.h>
 #include "test_sf.h"
 
+static double
+test_legendre_dx(const size_t l)
+{
+  const double dx_max = 0.4;
+  double dx;
+
+  if (l < 1000)
+    dx = exp((double)l / 1000.0) / exp(2.0);
+  else
+    dx = dx_max;
+
+  return dx;
+} /* test_legendre_dx() */
+
+/*
+test_legendre_sum()
+  This routine computes the sum:
+
+  Sum_{m=0}^l [P(l,m)(x)]^2
+
+This sum should equate to 1.0 for Schmidt semi-normalized
+ALFs for all l.
+*/
+
+static double
+test_legendre_sum(const size_t l, double *p)
+{
+  double sum = 0.0;
+  size_t idx;
+  size_t m;
+
+  for (m = 0; m <= l; ++m)
+    {
+      idx = gsl_sf_legendre_array_index(l, m);
+      sum += p[idx] * p[idx];
+    }
+
+  return sum;
+} /* test_legendre_sum() */
+
+/*
+test_legendre_sum_deriv()
+  This routine computes the sum:
+
+  Sum_{m=0}^l P(l,m)(x) * dP(l,m)/dx
+
+which should equal 0 in the case of Schmidt normalized ALFs.
+*/
+
+static double
+test_legendre_sum_deriv(const int l, double *p, double *dp)
+{
+  double sum = 0.0;
+  size_t idx;
+  int m;
+
+  for (m = 0; m <= l; ++m)
+    {
+      idx = gsl_sf_legendre_array_index(l, m);
+      sum += p[idx] * dp[idx];
+    }
+
+  return sum;
+} /* test_legendre_sum_deriv() */
+
+/*
+test_legendre_sum_deriv2()
+  This routine computes the sum:
+
+  Sum_{m=0}^l P(l,m)(x) * dP(l,m)/dx
+
+which should equal 0 in the case of Schmidt normalized ALFs.
+*/
+
+static double
+test_legendre_sum_deriv2(const int l, double *p, double *dp, double *d2p)
+{
+  double sum = 0.0;
+  int m;
+
+  for (m = 0; m <= l; ++m)
+    {
+      size_t idx = gsl_sf_legendre_array_index(l, m);
+      sum += dp[idx] * dp[idx] + p[idx] * d2p[idx];
+    }
+
+  return sum;
+} /* test_legendre_sum_deriv2() */
+
+static void
+test_value(const size_t lmax, const size_t l, const size_t m,
+           const double *p, const double expected, const double tol,
+           const char *desc, const char *desc2)
+{
+  size_t idx = gsl_sf_legendre_array_index(l, m);
+  double value;
+
+  if (l > lmax)
+    return;
+
+  value = p[idx];
+
+  gsl_test_rel(value, expected, tol, "%s %s lmax=%zu l=%zu m=%zu", desc, desc2, lmax, l, m);
+} /* test_value() */
+
+/* Y_{lm} = factor * S_{lm} */
+static double
+test_factor_spharm(const size_t l, const size_t m)
+{
+  double factor = sqrt( (2.0 * l + 1.0) / 4.0 / M_PI);
+
+  if (m == 0)
+    return factor;
+  else
+    return (factor / sqrt(2.0));
+} /* test_factor_spharm() */
+
+/* N_{lm} = factor * S_{lm} */
+static double
+test_factor_full(const size_t l, const size_t m)
+{
+  double factor = sqrt(l + 0.5);
+
+  if (m == 0)
+    return factor;
+  else
+    return (factor / sqrt(2.0));
+} /* test_factor_full() */
+
+/* test that p = factor * p_expected */
+static int
+test_legendre_compare(const size_t lmax, const double *p_expected,
+                      const double *p,
+                      double (*factor)(const size_t l, const size_t m),
+                      const char *desc, const char *desc2)
+{
+  size_t l, m;
+
+  for (l = 0; l <= lmax; ++l)
+    {
+      for (m = 0; m <= l; ++m)
+        {
+          size_t idx = gsl_sf_legendre_array_index(l, m);
+          double fac = (*factor)(l, m);
+
+          if (fabs(p_expected[idx]) < GSL_DBL_MIN)
+            continue;
+
+          gsl_test_rel(p[idx] / fac, p_expected[idx], 1.0e-10,
+                       "%s %s l=%zu m=%zu", desc, desc2, l, m);
+        }
+    }
+
+  return 0;
+} /* test_legendre_compare() */
+
+static int
+test_legendre_schmidt(const size_t lmax, const double csphase, const char *desc)
+{
+  int s = 0;
+  const size_t nlm = gsl_sf_legendre_nlm(lmax);
+  size_t l;
+  double x, dx;
+  double *p, *p2, *dp, *d2p, *p_alt, *dp_alt;
+  size_t dim;
+  size_t i;
+  const gsl_sf_legendre_t norm = GSL_SF_LEGENDRE_SCHMIDT;
+
+  dim = gsl_sf_legendre_array_n(lmax);
+  p = malloc(sizeof(double) * dim);
+  p2 = malloc(sizeof(double) * dim);
+  dp = malloc(sizeof(double) * dim);
+  d2p = malloc(sizeof(double) * dim);
+  p_alt = malloc(sizeof(double) * dim);
+  dp_alt = malloc(sizeof(double) * dim);
+
+  /* test specific values */
+  x = 0.5;
+  gsl_sf_legendre_array(norm, lmax, x, p);
+  test_value(lmax, 0, 0, p, 1.000000000000000, 1.0e-10, desc, "x=0.5");
+  test_value(lmax, 1, 0, p, 0.500000000000000, 1.0e-10, desc, "x=0.5");
+  test_value(lmax, 1, 1, p, 0.866025403784439, 1.0e-10, desc, "x=0.5");
+  test_value(lmax, 2, 0, p, -0.125000000000000, 1.0e-10, desc, "x=0.5");
+  test_value(lmax, 2, 1, p, 0.750000000000000, 1.0e-10, desc, "x=0.5");
+  test_value(lmax, 2, 2, p, 0.649519052838329, 1.0e-10, desc, "x=0.5");
+  test_value(lmax, 3, 0, p, -0.437500000000000, 1.0e-10, desc, "x=0.5");
+  test_value(lmax, 3, 2, p, 0.726184377413891, 1.0e-10, desc, "x=0.5");
+  test_value(lmax, 3, 3, p, 0.513489897661093, 1.0e-10, desc, "x=0.5");
+
+  x = 0.1;
+  gsl_sf_legendre_array(norm, lmax, x, p);
+  test_value(lmax, 2700, 500, p, -7.421910573369699e-3, 1.0e-10, desc, "x=0.1");
+  test_value(lmax, 2700, 2500, p, 2.717612388452281e-2, 1.0e-10, desc, "x=0.1");
+  test_value(lmax, 2700, 2700, p, 1.887509917445211e-7, 1.0e-10, desc, "x=0.1");
+
+  x = 0.15;
+  gsl_sf_legendre_deriv_array(norm, lmax, x, p, dp);
+  test_value(lmax, 0, 0, dp, 0.000000000000000, 1.0e-10, desc, "deriv x=0.15");
+  test_value(lmax, 1, 0, dp, 1.000000000000000, 1.0e-10, desc, "deriv x=0.15");
+  test_value(lmax, 1, 1, dp, -0.151716521227252, 1.0e-10, desc, "deriv x=0.15");
+  test_value(lmax, 2, 1, dp, 1.67303727048739, 1.0e-10, desc, "deriv x=0.15");
+
+  x = 0.23;
+  gsl_sf_legendre_deriv2_array(norm, lmax, x, p, dp, d2p);
+  test_value(lmax, 0, 0, d2p, 0.000000000000000, 1.0e-10, desc, "deriv2 x=0.23");
+  test_value(lmax, 1, 0, d2p, 0.000000000000000, 1.0e-10, desc, "deriv2 x=0.23");
+  test_value(lmax, 1, 1, d2p, -1.08494130865644, 1.0e-10, desc, "deriv2 x=0.23");
+  test_value(lmax, 2, 0, d2p, 3.000000000000000, 1.0e-10, desc, "deriv2 x=0.23");
+  test_value(lmax, 2, 1, d2p, -1.25090188696335, 1.0e-10, desc, "deriv2 x=0.23");
+
+  /* test array routines */
+  dx = test_legendre_dx(lmax);
+  for (x = -1.0; x <= 1.0; x += dx)
+    {
+      s += gsl_sf_legendre_array_e(norm, lmax, x, csphase, p);
+
+      for (l = 0; l <= lmax; ++l)
+        {
+          double sum = test_legendre_sum(l, p);
+          double rhs = 1.0;
+
+          gsl_test_rel(sum, rhs, 1.0e-10,
+                       "%s l=%zu, x=%f, sum=%.12e", desc, l, x, sum);
+        }
+    }
+
+  /* test deriv array routines */
+  for (x = -1.0 + dx; x < 1.0 - dx; x += dx)
+    {
+      double u = sqrt((1.0 - x) * (1.0 + x));
+      double uinv = 1.0 / u;
+
+      s += gsl_sf_legendre_array(norm, lmax, x, p2);
+      s += gsl_sf_legendre_deriv_array(norm, lmax, x, p, dp);
+      s += gsl_sf_legendre_deriv_alt_array(norm, lmax, x, p_alt, dp_alt);
+
+      for (i = 0; i < nlm; ++i)
+        {
+          if (fabs(p2[i]) < GSL_DBL_MIN)
+            continue;
+
+          /* check p = p_alt = p2 */
+          gsl_test_rel(p[i], p2[i], 1.0e-10, "%s deriv i=%zu", desc, i);
+          gsl_test_rel(p_alt[i], p2[i], 1.0e-10, "%s deriv_alt i=%zu", desc, i);
+
+          /* check dp = -1/u*dp_alt */
+          gsl_test_rel(-uinv * dp_alt[i], dp[i], 1.0e-10,
+                       "%s deriv_alt x=%f i=%zu", desc, x, i);
+        }
+
+      for (l = 0; l <= lmax; ++l)
+        {
+          double sum = test_legendre_sum_deriv(l, p, dp);
+
+          gsl_test_abs(sum, 0.0, 1.0e-10,
+                       "%s deriv l=%zu, x=%f, sum=%.12e", desc, l, x, sum);
+        }
+    }
+
+  /* test deriv2 array routines */
+  for (x = -1.0 + dx; x < 1.0 - dx; x += dx)
+    {
+      s += gsl_sf_legendre_array(norm, lmax, x, p2);
+      s += gsl_sf_legendre_deriv2_array(norm, lmax, x, p, dp, d2p);
+
+      /* check p = p2 */
+      for (i = 0; i < nlm; ++i)
+        {
+          if (fabs(p2[i]) < GSL_DBL_MIN)
+            continue;
+
+          gsl_test_rel(p[i], p2[i], 1.0e-10, "%s deriv2 i=%zu", desc, i);
+        }
+
+      for (l = 0; l <= lmax; ++l)
+        {
+          double sum = test_legendre_sum_deriv(l, p, dp);
+          double sum2 = test_legendre_sum_deriv2(l, p, dp, d2p);
+
+          gsl_test_abs(sum, 0.0, 1.0e-10,
+                       "%s deriv2 l=%zu, x=%f, sum=%.12e", desc, l, x, sum);
+          gsl_test_abs(sum2, 0.0, 1.0e-6,
+                       "%s deriv2 l=%zu, x=%f, sum=%.12e", desc, l, x, sum2);
+        }
+    }
+
+  free(p);
+  free(p2);
+  free(dp);
+  free(d2p);
+  free(p_alt);
+  free(dp_alt);
+
+  return s;
+} /* test_legendre_schmidt() */
+
+/* test other normalizations (other than schmidt) */
+static int
+test_legendre_norm(const gsl_sf_legendre_t norm_type, const size_t lmax,
+                   const double csphase, const char *desc)
+{
+  int s = 0;
+  double x, dx;
+  double *p_schmidt, *dp_schmidt, *d2p_schmidt;
+  double *p, *dp, *d2p;
+  size_t dim;
+  double (*factor)(const size_t l, const size_t m) = NULL;
+
+  dim = gsl_sf_legendre_array_n(lmax);
+  p = malloc(sizeof(double) * dim);
+  dp = malloc(sizeof(double) * dim);
+  d2p = malloc(sizeof(double) * dim);
+  p_schmidt = malloc(sizeof(double) * dim);
+  dp_schmidt = malloc(sizeof(double) * dim);
+  d2p_schmidt = malloc(sizeof(double) * dim);
+
+  if (norm_type == GSL_SF_LEGENDRE_SPHARM)
+    {
+      factor = &test_factor_spharm;
+    }
+  else if (norm_type == GSL_SF_LEGENDRE_FULL)
+    {
+      factor = &test_factor_full;
+
+      /* test specific values (computed from GNU octave) */
+      x = 0.45;
+      s += gsl_sf_legendre_array(norm_type, lmax, x, p);
+      test_value(lmax, 0, 0, p, 0.707106781186548, 1.0e-10, desc, "x=0.45");
+      test_value(lmax, 1, 0, p, 0.551135192126215, 1.0e-10, desc, "x=0.45");
+      test_value(lmax, 1, 1, p, 0.773385414912901, 1.0e-10, desc, "x=0.45");
+      test_value(lmax, 2, 0, p, -0.310298495404022, 1.0e-10, desc, "x=0.45");
+      test_value(lmax, 2, 1, p, 0.778204062248457, 1.0e-10, desc, "x=0.45");
+      test_value(lmax, 2, 2, p, 0.772176054650104, 1.0e-10, desc, "x=0.45");
+      test_value(lmax, 3, 0, p, -0.83661120632398589, 1.0e-10, desc, "x=0.45");
+      test_value(lmax, 3, 1, p, 0.00904294765791280, 1.0e-10, desc, "x=0.45");
+      test_value(lmax, 3, 2, p, 0.91934361403343767, 1.0e-10, desc, "x=0.45");
+      test_value(lmax, 3, 3, p, 0.74482641545541073, 1.0e-10, desc, "x=0.45");
+    }
+
+  /*
+   * test the scale factors between the Schmidts and these
+   * normalized functions
+   */
+
+  dx = test_legendre_dx(lmax);
+  for (x = -1.0; x <= 1.0; x += dx)
+    {
+      s += gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_SCHMIDT, lmax, x,
+             csphase, p_schmidt);
+      s += gsl_sf_legendre_array_e(norm_type, lmax, x, csphase, p);
+      test_legendre_compare(lmax, p_schmidt, p, factor, desc, "p");
+    }
+
+  /* test derivatives */
+  for (x = -1.0 + dx; x < 1.0 - dx; x += dx)
+    {
+      s += gsl_sf_legendre_deriv_array_e(GSL_SF_LEGENDRE_SCHMIDT,
+             lmax, x, csphase, p_schmidt, dp_schmidt);
+      s += gsl_sf_legendre_deriv_array_e(norm_type, lmax, x, csphase, p, dp);
+      test_legendre_compare(lmax, p_schmidt, p, factor, desc, "deriv p");
+      test_legendre_compare(lmax, dp_schmidt, dp, factor, desc, "deriv dp");
+
+      s += gsl_sf_legendre_deriv2_array_e(GSL_SF_LEGENDRE_SCHMIDT,
+             lmax, x, csphase, p_schmidt, dp_schmidt, d2p_schmidt);
+      s += gsl_sf_legendre_deriv2_array_e(norm_type, lmax, x, csphase,
+             p, dp, d2p);
+      test_legendre_compare(lmax, p_schmidt, p, factor, desc, "deriv2 p");
+      test_legendre_compare(lmax, dp_schmidt, dp, factor, desc, "deriv2 dp");
+      test_legendre_compare(lmax, d2p_schmidt, d2p, factor, desc, "deriv2 d2p");
+    }
+
+  free(p);
+  free(dp);
+  free(d2p);
+  free(p_schmidt);
+  free(dp_schmidt);
+  free(d2p_schmidt);
+
+  return s;
+} /* test_legendre_norm() */
+
+/*
+test_legendre_unnorm()
+  This routine tests the unnormalized ALFs using the relation
+
+S(l,m)(x) = a(l,m) * P(l,m)(x)
+
+where
+
+a(l,0) = 1
+a(l,1) = -sqrt(2)/sqrt(l * (l+1))
+a(l,m+1) = a(l,m) / sqrt((l+m+1) * (l-m)), m > 1
+
+and
+
+S(l,m) are the Schmidt semi-normalized ALFs
+*/
+
+static int
+test_legendre_unnorm(const size_t lmax_orig, const char *desc)
+{
+  int s = 0;
+  const int lmax = GSL_MIN(lmax_orig, 140);
+  size_t l, m;
+  double x, dx;
+  double *p, *dp, *d2p, *p2;
+  double *p_schmidt, *dp_schmidt, *d2p_schmidt;
+  size_t dim;
+
+  dim = gsl_sf_legendre_array_n(lmax);
+  p = malloc(sizeof(double) * dim);
+  dp = malloc(sizeof(double) * dim);
+  d2p = malloc(sizeof(double) * dim);
+  p2 = malloc(sizeof(double) * dim);
+  p_schmidt = malloc(sizeof(double) * dim);
+  dp_schmidt = malloc(sizeof(double) * dim);
+  d2p_schmidt = malloc(sizeof(double) * dim);
+
+  dx = test_legendre_dx(lmax);
+
+  for (x = -1.0 + dx; x < 1.0 - dx; x += dx)
+    {
+      gsl_sf_legendre_deriv2_array(GSL_SF_LEGENDRE_SCHMIDT, lmax, x,
+                                   p_schmidt, dp_schmidt, d2p_schmidt);
+      gsl_sf_legendre_deriv2_array(GSL_SF_LEGENDRE_NONE, lmax, x, p, dp, d2p);
+
+      for (l = 0; l <= lmax; ++l)
+        {
+          double a_lm = sqrt(2.0 / (double)l / (l + 1.0));
+          size_t idx;
+
+          /* test S(l,0) = P(l,0) */
+          idx = gsl_sf_legendre_array_index(l, 0);
+          gsl_test_rel(p[idx], p_schmidt[idx], 1.0e-10,
+                       "unnorm l=%zu, m=0, x=%f", l, x);
+          gsl_test_rel(dp[idx], dp_schmidt[idx], 1.0e-10,
+                       "unnorm deriv l=%zu, m=0, x=%f", l, x);
+          gsl_test_rel(d2p[idx], d2p_schmidt[idx], 1.0e-10,
+                       "unnorm deriv2 l=%zu, m=0, x=%f", l, x);
+
+          /* test S(l,m) = a_{lm} * P(l,m) for m > 0 */
+          for (m = 1; m <= l; ++m)
+            {
+              idx = gsl_sf_legendre_array_index(l, m);
+
+              gsl_test_rel(a_lm * p[idx], p_schmidt[idx], 1.0e-9,
+                           "unnorm l=%zu, m=%zu, x=%f", l, m, x);
+              gsl_test_abs(a_lm * dp[idx], dp_schmidt[idx], 1.0e-10,
+                           "unnorm deriv l=%zu, m=%zu, x=%f", l, m, x);
+              gsl_test_abs(a_lm * d2p[idx], d2p_schmidt[idx], 1.0e-10,
+                           "unnorm deriv2 l=%zu, m=%zu, x=%f", l, m, x);
+
+              a_lm /= sqrt((double) (l + m + 1)) *
+                      sqrt((double) (l - m));
+            }
+        }
+
+      gsl_sf_legendre_array(GSL_SF_LEGENDRE_NONE, lmax, x, p2);
+      /* test if p = p2 */
+      for (l = 0; l <= lmax; ++l)
+        {
+          for (m = 0; m <= l; ++m)
+            {
+              size_t idx = gsl_sf_legendre_array_index(l, m);
+              gsl_test_rel(p2[idx], p[idx], 1.0e-10,
+                           "%s compare l=%zu, m=%zu, x=%f",
+                           desc, l, m, x);
+            }
+        }
+    }
+
+  free(p);
+  free(p2);
+  free(dp);
+  free(d2p);
+  free(p_schmidt);
+  free(dp_schmidt);
+  free(d2p_schmidt);
+
+  return s;
+} /* test_legendre_unnorm() */
+
+static int
+test_legendre_all(const size_t lmax)
+{
+  int s = 0;
+
+  s += test_legendre_schmidt(lmax, 1.0, "schmidt csphase=1");
+  s += test_legendre_schmidt(lmax, -1.0, "schmidt csphase=-1");
+
+  s += test_legendre_norm(GSL_SF_LEGENDRE_SPHARM, lmax, 1.0,
+                          "spharm csphase=1");
+  s += test_legendre_norm(GSL_SF_LEGENDRE_SPHARM, lmax, -1.0,
+                          "spharm csphase=-1");
+
+  s += test_legendre_norm(GSL_SF_LEGENDRE_FULL, lmax, 1.0,
+                          "full csphase=1");
+  s += test_legendre_norm(GSL_SF_LEGENDRE_FULL, lmax, -1.0,
+                          "full csphase=-1");
+
+  s += test_legendre_unnorm(lmax, "unnorm csphase=1");
+
+  return s;
+} /* test_legendre_all() */
 
 int test_legendre(void)
 {
@@ -117,7 +622,6 @@
   gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, -1.0 + 1.0e-11)");
   s += sa;
 
-
   TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 0, -0.5, &r), -0.18822860717773437500, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 0, 1.0e-08, &r), -0.24609374999999864648, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 0, 0.5, &r), -0.18822860717773437500, TEST_TOL0, GSL_SUCCESS);
@@ -136,6 +640,7 @@
   TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, 0.5, &r), 6.617107444248382171e+08, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, 0.999, &r), -1.9831610803806212189e+09, TEST_TOL2, GSL_SUCCESS);
 
+#ifndef GSL_DISABLE_DEPRECATED
 
   sa = 0;
   gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 1.0/1125899906842624.0, L, DL);
@@ -218,6 +723,8 @@
   gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 5, 0.999)");
   s += sa;
 
+#endif /* !GSL_DISABLE_DEPRECATED */
+
   TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, -0.5, &r), -0.24332702369300133776, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, 0.5, &r), -0.24332702369300133776, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, 0.999, &r), 1.2225754122797385990, TEST_TOL1, GSL_SUCCESS);
@@ -250,6 +757,8 @@
   TEST_SF(s, gsl_sf_legendre_sphPlm_e, (140,135,0.99998689456491752,&r), -6.54265253269093276310395668335e-305, TEST_TOL6, GSL_SUCCESS);
 #endif
 
+#ifndef GSL_DISABLE_DEPRECATED
+
   sa = 0;
   gsl_sf_legendre_sphPlm_array(100, 5, 0.5, L);
   TEST_SF_VAL(sa, L[0],  +0.0, -0.22609703187800460722, TEST_TOL1);
@@ -337,6 +846,8 @@
   gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 5, -1.0 + 2^(-50))");
   s += sa;
 
+#endif /* !GSL_DISABLE_DEPRECATED */
+
   TEST_SF(s, gsl_sf_conicalP_half_e, (0.0, -0.5, &r),   0.8573827581049917129, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_conicalP_half_e, (0.0,  0.5, &r),   0.8573827581049917129, TEST_TOL0, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_conicalP_half_e, (0.0,  2.0, &r),   0.6062611623284649811, TEST_TOL0, GSL_SUCCESS);
@@ -548,5 +1059,17 @@
   TEST_SF(s, gsl_sf_legendre_Ql_e, (1000,  0.5, &r), 0.030105074974005303500,  TEST_TOL1, GSL_SUCCESS);
   TEST_SF(s, gsl_sf_legendre_Ql_e, (1000,  1.1, &r), 1.0757258447825356443e-194, TEST_TOL3, GSL_SUCCESS);
 
+  /* test associated legendre functions */
+  {
+    size_t l;
+
+    for (l = 0; l <= 10; ++l)
+      test_legendre_all(l);
+
+    test_legendre_all(140);
+    test_legendre_all(1000);
+    /*test_legendre_all(2700);*/
+  }
+
   return s;
 }
diff -Nru gsl-doc-1.16/specfunc/test_mathieu.c gsl-doc-2.3/specfunc/test_mathieu.c
--- gsl-doc-1.16/specfunc/test_mathieu.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/test_mathieu.c	2015-11-03 16:21:55.000000000 +0000
@@ -34,149 +34,149 @@
   int s = 0;
   int sa;
 
-  TEST_SF(s, gsl_sf_mathieu_ce, (0, 0.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (0, 0.0, 0.0, &r),
           0.7071067811865475, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (0, 0.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (0, 0.0, M_PI_2, &r),
           0.7071067811865475, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (0, 5.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (0, 5.0, 0.0, &r),
           0.04480018165188902, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (0, 5.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (0, 5.0, M_PI_2, &r),
           1.334848674698019, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (0, 10.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (0, 10.0, 0.0, &r),
           0.007626517570935782, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (0, 10.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (0, 10.0, M_PI_2, &r),
           1.468660470712856, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (0, 15.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (0, 15.0, 0.0, &r),
           0.001932508315204592, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (0, 15.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (0, 15.0, M_PI_2, &r),
           1.550108146686649, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (0, 20.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (0, 20.0, 0.0, &r),
           0.0006037438292242197, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (0, 20.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (0, 20.0, M_PI_2, &r),
           1.609890857395926, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (0, 25.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (0, 25.0, 0.0, &r),
           0.0002158630184146612, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (0, 25.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (0, 25.0, M_PI_2, &r),
           1.657510298323475, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (1, 0.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (1, 0.0, 0.0, &r),
           1.00000000, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (1, 5.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (1, 5.0, 0.0, &r),
           0.2565428793223637, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (1, 10.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (1, 10.0, 0.0, &r),
           0.05359874774717657, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (1, 15.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (1, 15.0, 0.0, &r),
           0.01504006645382623, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (1, 20.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (1, 20.0, 0.0, &r),
           0.005051813764712904, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (1, 25.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (1, 25.0, 0.0, &r),
           0.001911051506657645, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (1, 0.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (1, 0.0, M_PI_2, &r),
           1.0000000, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (1, 5.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (1, 5.0, M_PI_2, &r),
           1.337433887022345, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (1, 10.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (1, 10.0, M_PI_2, &r),
           1.468755664102938, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (1, 15.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (1, 15.0, M_PI_2, &r),
           1.550115074357552, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (1, 20.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (1, 20.0, M_PI_2, &r),
           1.609891592603772, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (1, 25.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (1, 25.0, M_PI_2, &r),
           1.657510398374516, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (2, 0.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (2, 0.0, 0.0, &r),
           1.00000000, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (2, 0.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (2, 0.0, M_PI_2, &r),
           -1.00000000, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (2, 5.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (2, 5.0, 0.0, &r),
           0.7352943084006845, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (2, 5.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (2, 5.0, M_PI_2, &r),
           -0.7244881519676682, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (2, 10.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (2, 10.0, 0.0, &r),
           0.2458883492913189, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (2, 10.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (2, 10.0, M_PI_2, &r),
           -0.9267592641263211, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (2, 15.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (2, 15.0, 0.0, &r),
           0.07879282784639313, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (2, 15.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (2, 15.0, M_PI_2, &r),
           -1.019966226030262, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (2, 20.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (2, 20.0, 0.0, &r),
           0.02864894314707431, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (2, 20.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (2, 20.0, M_PI_2, &r),
           -1.075293228779687, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (2, 25.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (2, 25.0, 0.0, &r),
           0.0115128663308875, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (2, 25.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (2, 25.0, M_PI_2, &r),
           -1.116278953295253, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (5, 0.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (5, 0.0, 0.0, &r),
           1.00000000, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (5, 5.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (5, 5.0, 0.0, &r),
           1.12480725063848, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (5, 10.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (5, 10.0, 0.0, &r),
           1.258019941308287, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (5, 15.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (5, 15.0, 0.0, &r),
           1.193432230413072, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (5, 20.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (5, 20.0, 0.0, &r),
           0.9365755314226215, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (5, 25.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (5, 25.0, 0.0, &r),
           0.6106943100506986, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (5, 0.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (5, 0.0, M_PI_2, &r),
           1.0000000, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (5, 5.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (5, 5.0, M_PI_2, &r),
           0.9060779302023551, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (5, 10.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (5, 10.0, M_PI_2, &r),
           0.8460384335355106, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (5, 15.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (5, 15.0, M_PI_2, &r),
           0.837949340012484, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (5, 20.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (5, 20.0, M_PI_2, &r),
           0.8635431218533667, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (5, 25.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (5, 25.0, M_PI_2, &r),
           0.8992683245108413, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (10, 0.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (10, 0.0, 0.0, &r),
           1.00000000, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (10, 0.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (10, 0.0, M_PI_2, &r),
           -1.00000000, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (10, 5.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (10, 5.0, 0.0, &r),
           1.025995027089438, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (10, 5.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (10, 5.0, M_PI_2, &r),
           -0.975347487235964, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (10, 10.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (10, 10.0, 0.0, &r),
           1.053815992100935, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (10, 10.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (10, 10.0, M_PI_2, &r),
           -0.9516453181789554, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (10, 15.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (10, 15.0, 0.0, &r),
           1.084106311839221, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (10, 15.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (10, 15.0, M_PI_2, &r),
           -0.9285480638845388, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (10, 20.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (10, 20.0, 0.0, &r),
           1.117788631259397, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (10, 20.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (10, 20.0, M_PI_2, &r),
           -0.9057107845940974, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (10, 25.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (10, 25.0, 0.0, &r),
           1.156239918632239, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (10, 25.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (10, 25.0, M_PI_2, &r),
           -0.8826919105636903, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (15, 0.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (15, 0.0, 0.0, &r),
           1.00000000, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (15, 5.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (15, 5.0, 0.0, &r),
           1.011293732529566, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (15, 10.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (15, 10.0, 0.0, &r),
           1.022878282438181, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (15, 15.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (15, 15.0, 0.0, &r),
           1.034793652236873, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (15, 20.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (15, 20.0, 0.0, &r),
           1.047084344162887, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_ce, (15, 25.0, 0.0, &r),
+  TEST_SF(s, gsl_sf_mathieu_ce_e, (15, 25.0, 0.0, &r),
           1.059800441813937, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (15, 0.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (15, 0.0, M_PI_2, &r),
           -1.0000000, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (15, 5.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (15, 5.0, M_PI_2, &r),
           -0.9889607027406357, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (15, 10.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (15, 10.0, M_PI_2, &r),
           -0.9781423471832157, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (15, 15.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (15, 15.0, M_PI_2, &r),
           -0.9675137031854538, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (15, 20.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (15, 20.0, M_PI_2, &r),
           -0.9570452540612817, TEST_SNGL, GSL_SUCCESS);
-  TEST_SF(s, gsl_sf_mathieu_se, (15, 25.0, M_PI_2, &r),
+  TEST_SF(s, gsl_sf_mathieu_se_e, (15, 25.0, M_PI_2, &r),
           -0.9467086958780897, TEST_SNGL, GSL_SUCCESS);
 
   work = gsl_sf_mathieu_alloc(NVAL, 20.0);
diff -Nru gsl-doc-1.16/specfunc/test_sf.c gsl-doc-2.3/specfunc/test_sf.c
--- gsl-doc-1.16/specfunc/test_sf.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/specfunc/test_sf.c	2015-11-03 16:21:55.000000000 +0000
@@ -814,71 +814,71 @@
 
   /* D, argument phi > pi/2  */
 
-  TEST_SF(s,  gsl_sf_ellint_D_e, (M_PI/2.0, 0.99, 0, mode, &r), 2.375395076351788975665323192, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (M_PI/2.0, 0.50, 0, mode, &r), 0.8731525818926755496456335628, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (M_PI/2.0, 0.01, 0, mode, &r), 0.7854276176694868932799393751, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (2*M_PI/3.0, 0.99, 0, mode, &r), 4.305885125424644860264320635, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (2*M_PI/3.0, 0.50, 0, mode, &r), 1.418324704155697579394036402, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (2*M_PI/3.0, 0.01, 0, mode, &r), 1.263755353901126149206022061, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (M_PI, 0.99, 0, mode, &r), 4.750790152703577951330646444, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (M_PI, 0.50, 0, mode, &r), 1.746305163785351099291267125, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (M_PI, 0.01, 0, mode, &r), 1.570855235338973786559878750, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (4*M_PI/3, 0.99, 0, mode, &r), 5.195695179982511042396972113, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (4*M_PI/3, 0.50, 0, mode, &r), 2.074285623415004619188497818, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (4*M_PI/3, 0.01, 0, mode, &r), 1.877955116776821423913735408, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (3*M_PI/2.0, 0.99, 0, mode, &r), 7.126185229055366926995969476, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (3*M_PI/2.0, 0.50, 0, mode, &r), 2.619457745678026648936900687, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (3*M_PI/2.0, 0.01, 0, mode, &r), 2.356282853008460679839818125, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (5*M_PI/3, 0.99, 0, mode, &r), 9.056675278128222811594967044, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (5*M_PI/3, 0.50, 0, mode, &r), 3.164629867941048678685303509, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (5*M_PI/3, 0.01, 0, mode, &r), 2.834610589240099935765900794, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (2*M_PI, 0.99, 0, mode, &r), 9.501580305407155902661292832, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (2*M_PI, 0.50, 0, mode, &r), 3.492610327570702198582534249, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (2*M_PI, 0.01, 0, mode, &r), 3.141710470677947573119757500, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (7*M_PI/3.0, 0.99, 0, mode, &r), 9.946485332686088993727618315, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (7*M_PI/3.0, 0.50, 0, mode, &r), 3.820590787200355718479764901, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (7*M_PI/3.0, 0.01, 0, mode, &r), 3.448810352115795210473614120, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (M_PI/2.0, 0.99, mode, &r), 2.375395076351788975665323192, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (M_PI/2.0, 0.50, mode, &r), 0.8731525818926755496456335628, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (M_PI/2.0, 0.01, mode, &r), 0.7854276176694868932799393751, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (2*M_PI/3.0, 0.99, mode, &r), 4.305885125424644860264320635, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (2*M_PI/3.0, 0.50, mode, &r), 1.418324704155697579394036402, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (2*M_PI/3.0, 0.01, mode, &r), 1.263755353901126149206022061, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (M_PI, 0.99, mode, &r), 4.750790152703577951330646444, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (M_PI, 0.50, mode, &r), 1.746305163785351099291267125, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (M_PI, 0.01, mode, &r), 1.570855235338973786559878750, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (4*M_PI/3, 0.99, mode, &r), 5.195695179982511042396972113, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (4*M_PI/3, 0.50, mode, &r), 2.074285623415004619188497818, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (4*M_PI/3, 0.01, mode, &r), 1.877955116776821423913735408, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (3*M_PI/2.0, 0.99, mode, &r), 7.126185229055366926995969476, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (3*M_PI/2.0, 0.50, mode, &r), 2.619457745678026648936900687, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (3*M_PI/2.0, 0.01, mode, &r), 2.356282853008460679839818125, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (5*M_PI/3, 0.99, mode, &r), 9.056675278128222811594967044, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (5*M_PI/3, 0.50, mode, &r), 3.164629867941048678685303509, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (5*M_PI/3, 0.01, mode, &r), 2.834610589240099935765900794, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (2*M_PI, 0.99, mode, &r), 9.501580305407155902661292832, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (2*M_PI, 0.50, mode, &r), 3.492610327570702198582534249, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (2*M_PI, 0.01, mode, &r), 3.141710470677947573119757500, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (7*M_PI/3.0, 0.99, mode, &r), 9.946485332686088993727618315, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (7*M_PI/3.0, 0.50, mode, &r), 3.820590787200355718479764901, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (7*M_PI/3.0, 0.01, mode, &r), 3.448810352115795210473614120, TEST_TOL0, GSL_SUCCESS);
 
   /* P, negative argument phi < 0  */
 
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-M_PI/2.0, 0.99, 0, mode, &r), -2.375395076351788975665323192, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-M_PI/2.0, 0.50, 0, mode, &r), -0.8731525818926755496456335628, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-M_PI/2.0, 0.01, 0, mode, &r), -0.7854276176694868932799393751, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-2*M_PI/3.0, 0.99, 0, mode, &r), -4.305885125424644860264320635, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-2*M_PI/3.0, 0.50, 0, mode, &r), -1.418324704155697579394036402, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-2*M_PI/3.0, 0.01, 0, mode, &r), -1.263755353901126149206022061, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-M_PI, 0.99, 0, mode, &r), -4.750790152703577951330646444, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-M_PI, 0.50, 0, mode, &r), -1.746305163785351099291267125, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-M_PI, 0.01, 0, mode, &r), -1.570855235338973786559878750, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-4*M_PI/3, 0.99, 0, mode, &r), -5.195695179982511042396972113, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-4*M_PI/3, 0.50, 0, mode, &r), -2.074285623415004619188497818, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-4*M_PI/3, 0.01, 0, mode, &r), -1.877955116776821423913735408, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-3*M_PI/2.0, 0.99, 0, mode, &r), -7.126185229055366926995969476, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-3*M_PI/2.0, 0.50, 0, mode, &r), -2.619457745678026648936900687, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-3*M_PI/2.0, 0.01, 0, mode, &r), -2.356282853008460679839818125, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-5*M_PI/3, 0.99, 0, mode, &r), -9.056675278128222811594967044, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-5*M_PI/3, 0.50, 0, mode, &r), -3.164629867941048678685303509, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-5*M_PI/3, 0.01, 0, mode, &r), -2.834610589240099935765900794, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-2*M_PI, 0.99, 0, mode, &r), -9.501580305407155902661292832, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-2*M_PI, 0.50, 0, mode, &r), -3.492610327570702198582534249, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-2*M_PI, 0.01, 0, mode, &r), -3.141710470677947573119757500, TEST_TOL0, GSL_SUCCESS);
-
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-7*M_PI/3.0, 0.99, 0, mode, &r), -9.946485332686088993727618315, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-7*M_PI/3.0, 0.50, 0, mode, &r), -3.820590787200355718479764901, TEST_TOL0, GSL_SUCCESS);
-  TEST_SF(s,  gsl_sf_ellint_D_e, (-7*M_PI/3.0, 0.01, 0, mode, &r), -3.448810352115795210473614120, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-M_PI/2.0, 0.99, mode, &r), -2.375395076351788975665323192, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-M_PI/2.0, 0.50, mode, &r), -0.8731525818926755496456335628, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-M_PI/2.0, 0.01, mode, &r), -0.7854276176694868932799393751, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-2*M_PI/3.0, 0.99, mode, &r), -4.305885125424644860264320635, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-2*M_PI/3.0, 0.50, mode, &r), -1.418324704155697579394036402, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-2*M_PI/3.0, 0.01, mode, &r), -1.263755353901126149206022061, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-M_PI, 0.99, mode, &r), -4.750790152703577951330646444, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-M_PI, 0.50, mode, &r), -1.746305163785351099291267125, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-M_PI, 0.01, mode, &r), -1.570855235338973786559878750, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-4*M_PI/3, 0.99, mode, &r), -5.195695179982511042396972113, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-4*M_PI/3, 0.50, mode, &r), -2.074285623415004619188497818, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-4*M_PI/3, 0.01, mode, &r), -1.877955116776821423913735408, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-3*M_PI/2.0, 0.99, mode, &r), -7.126185229055366926995969476, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-3*M_PI/2.0, 0.50, mode, &r), -2.619457745678026648936900687, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-3*M_PI/2.0, 0.01, mode, &r), -2.356282853008460679839818125, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-5*M_PI/3, 0.99, mode, &r), -9.056675278128222811594967044, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-5*M_PI/3, 0.50, mode, &r), -3.164629867941048678685303509, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-5*M_PI/3, 0.01, mode, &r), -2.834610589240099935765900794, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-2*M_PI, 0.99, mode, &r), -9.501580305407155902661292832, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-2*M_PI, 0.50, mode, &r), -3.492610327570702198582534249, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-2*M_PI, 0.01, mode, &r), -3.141710470677947573119757500, TEST_TOL0, GSL_SUCCESS);
+
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-7*M_PI/3.0, 0.99, mode, &r), -9.946485332686088993727618315, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-7*M_PI/3.0, 0.50, mode, &r), -3.820590787200355718479764901, TEST_TOL0, GSL_SUCCESS);
+  TEST_SF(s,  gsl_sf_ellint_D_e, (-7*M_PI/3.0, 0.01, mode, &r), -3.448810352115795210473614120, TEST_TOL0, GSL_SUCCESS);
 
   return s;
 }
diff -Nru gsl-doc-1.16/splinalg/gmres.c gsl-doc-2.3/splinalg/gmres.c
--- gsl-doc-1.16/splinalg/gmres.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/splinalg/gmres.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,435 @@
+/* gmres.c
+ * 
+ * Copyright (C) 2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_spmatrix.h>
+#include <gsl/gsl_spblas.h>
+#include <gsl/gsl_splinalg.h>
+
+/*
+ * The code in this module is based on the Householder GMRES
+ * algorithm described in
+ *
+ * [1] H. F. Walker, Implementation of the GMRES method using
+ *     Householder transformations, SIAM J. Sci. Stat. Comput.
+ *     9(1), 1988.
+ *
+ * [2] Y. Saad, Iterative methods for sparse linear systems,
+ *     2nd edition, SIAM, 2003.
+ */
+
+typedef struct
+{
+  size_t n;        /* size of linear system */
+  size_t m;        /* dimension of Krylov subspace K_m */
+  gsl_vector *r;   /* residual vector r = b - A*x */
+  gsl_matrix *H;   /* Hessenberg matrix n-by-(m+1) */
+  gsl_vector *tau; /* householder scalars */
+  gsl_vector *y;   /* least squares rhs and solution vector */
+
+  double *c;       /* Givens rotations */
+  double *s;
+
+  double normr;    /* residual norm ||r|| */
+} gmres_state_t;
+
+static void gmres_free(void *vstate);
+static int gmres_iterate(const gsl_spmatrix *A, const gsl_vector *b,
+                         const double tol, gsl_vector *x, void *vstate);
+
+/*
+gmres_alloc()
+  Allocate a GMRES workspace for solving an n-by-n system A x = b
+
+Inputs: n        - size of system
+        krylov_m - size of Krylov subspace (ie: number of inner iterations)
+                   if this parameter is 0, the value GSL_MIN(n,10) is
+                   used
+
+Return: pointer to workspace
+*/
+
+static void *
+gmres_alloc(const size_t n, const size_t m)
+{
+  gmres_state_t *state;
+
+  if (n == 0)
+    {
+      GSL_ERROR_NULL("matrix dimension n must be a positive integer",
+                     GSL_EINVAL);
+    }
+
+  state = calloc(1, sizeof(gmres_state_t));
+  if (!state)
+    {
+      GSL_ERROR_NULL("failed to allocate gmres state", GSL_ENOMEM);
+    }
+
+  state->n = n;
+
+  /* compute size of Krylov subspace */
+  if (m == 0)
+    state->m = GSL_MIN(n, 10);
+  else
+    state->m = GSL_MIN(n, m);
+
+  state->r = gsl_vector_alloc(n);
+  if (!state->r)
+    {
+      gmres_free(state);
+      GSL_ERROR_NULL("failed to allocate r vector", GSL_ENOMEM);
+    }
+
+  state->H = gsl_matrix_alloc(n, state->m + 1);
+  if (!state->H)
+    {
+      gmres_free(state);
+      GSL_ERROR_NULL("failed to allocate H matrix", GSL_ENOMEM);
+    }
+
+  state->tau = gsl_vector_alloc(state->m + 1);
+  if (!state->tau)
+    {
+      gmres_free(state);
+      GSL_ERROR_NULL("failed to allocate tau vector", GSL_ENOMEM);
+    }
+
+  state->y = gsl_vector_alloc(state->m + 1);
+  if (!state->y)
+    {
+      gmres_free(state);
+      GSL_ERROR_NULL("failed to allocate y vector", GSL_ENOMEM);
+    }
+
+  state->c = malloc(state->m * sizeof(double));
+  state->s = malloc(state->m * sizeof(double));
+  if (!state->c || !state->s)
+    {
+      gmres_free(state);
+      GSL_ERROR_NULL("failed to allocate Givens vectors", GSL_ENOMEM);
+    }
+
+  state->normr = 0.0;
+
+  return state;
+} /* gmres_alloc() */
+
+static void
+gmres_free(void *vstate)
+{
+  gmres_state_t *state = (gmres_state_t *) vstate;
+
+  if (state->r)
+    gsl_vector_free(state->r);
+
+  if (state->H)
+    gsl_matrix_free(state->H);
+
+  if (state->tau)
+    gsl_vector_free(state->tau);
+
+  if (state->y)
+    gsl_vector_free(state->y);
+
+  if (state->c)
+    free(state->c);
+
+  if (state->s)
+    free(state->s);
+
+  free(state);
+} /* gmres_free() */
+
+/*
+gmres_iterate()
+  Solve A*x = b using GMRES algorithm
+
+Inputs: A    - sparse square matrix
+        b    - right hand side vector
+        tol  - stopping tolerance (see below)
+        x    - (input/output) on input, initial estimate x_0;
+               on output, solution vector
+        work - workspace
+
+Return:
+GSL_SUCCESS if converged to solution (solution stored in x). In
+this case the following will be true:
+
+||b - A*x|| <= tol * ||b||
+
+GSL_CONTINUE if not yet converged; in this case x contains the
+most recent solution vector and calling this function more times
+with the input x could result in convergence (ie: restarted GMRES)
+
+Notes:
+1) Based on algorithm 2.2 of (Walker, 1998 [1]) and algorithm 6.10 of
+(Saad, 2003 [2])
+
+2) On output, work->normr contains ||b - A*x||
+*/
+
+static int
+gmres_iterate(const gsl_spmatrix *A, const gsl_vector *b,
+              const double tol, gsl_vector *x,
+              void *vstate)
+{
+  const size_t N = A->size1;
+  gmres_state_t *state = (gmres_state_t *) vstate;
+
+  if (N != A->size2)
+    {
+      GSL_ERROR("matrix must be square", GSL_ENOTSQR);
+    }
+  else if (N != b->size)
+    {
+      GSL_ERROR("matrix does not match right hand side", GSL_EBADLEN);
+    }
+  else if (N != x->size)
+    {
+      GSL_ERROR("matrix does not match solution vector", GSL_EBADLEN);
+    }
+  else if (N != state->n)
+    {
+      GSL_ERROR("matrix does not match workspace", GSL_EBADLEN);
+    }
+  else
+    {
+      int status = GSL_SUCCESS;
+      const size_t maxit = state->m;
+      const double normb = gsl_blas_dnrm2(b); /* ||b|| */
+      const double reltol = tol * normb;      /* tol*||b|| */
+      double normr;                           /* ||r|| */
+      size_t m, k;
+      double tau;                             /* householder scalar */
+      gsl_matrix *H = state->H;               /* Hessenberg matrix */
+      gsl_vector *r = state->r;               /* residual vector */
+      gsl_vector *w = state->y;               /* least squares RHS */
+      gsl_matrix_view Rm;                     /* R_m = H(1:m,2:m+1) */
+      gsl_vector_view ym;                     /* y(1:m) */
+      gsl_vector_view h0 = gsl_matrix_column(H, 0);
+
+      /*
+       * The Hessenberg matrix will have the following structure:
+       *
+       * H = [ ||r_0|| | v_1 v_2 ... v_m     ]
+       *     [   u_1   | u_2 u_3 ... u_{m+1} ]
+       *
+       * where v_j are the orthonormal vectors spanning the Krylov
+       * subpsace of length j + 1 and u_{j+1} are the householder
+       * vectors of length n - j - 1.
+       * In fact, u_{j+1} has length n - j since u_{j+1}[0] = 1,
+       * but this 1 is not stored.
+       */
+      gsl_matrix_set_zero(H);
+
+      /* Step 1a: compute r = b - A*x_0 */
+      gsl_vector_memcpy(r, b);
+      gsl_spblas_dgemv(CblasNoTrans, -1.0, A, x, 1.0, r);
+
+      /* Step 1b */
+      gsl_vector_memcpy(&h0.vector, r);
+      tau = gsl_linalg_householder_transform(&h0.vector);
+
+      /* store tau_1 */
+      gsl_vector_set(state->tau, 0, tau);
+
+      /* initialize w (stored in state->y) */
+      gsl_vector_set_zero(w);
+      gsl_vector_set(w, 0, gsl_vector_get(&h0.vector, 0));
+
+      for (m = 1; m <= maxit; ++m)
+        {
+          size_t j = m - 1; /* C indexing */
+          double c, s;      /* Givens rotation */
+
+          /* v_m */
+          gsl_vector_view vm = gsl_matrix_column(H, m);
+
+          /* v_m(m:end) */
+          gsl_vector_view vv = gsl_vector_subvector(&vm.vector, j, N - j);
+
+          /* householder vector u_m for projection P_m */
+          gsl_vector_view um = gsl_matrix_subcolumn(H, j, j, N - j);
+
+          /* Step 2a: form v_m = P_m e_m = e_m - tau_m w_m */
+          gsl_vector_set_zero(&vm.vector);
+          gsl_vector_memcpy(&vv.vector, &um.vector);
+          tau = gsl_vector_get(state->tau, j); /* tau_m */
+          gsl_vector_scale(&vv.vector, -tau);
+          gsl_vector_set(&vv.vector, 0, 1.0 - tau);
+
+          /* Step 2a: v_m <- P_1 P_2 ... P_{m-1} v_m */
+          for (k = j; k > 0 && k--; )
+            {
+              gsl_vector_view uk =
+                gsl_matrix_subcolumn(H, k, k, N - k);
+              gsl_vector_view vk =
+                gsl_vector_subvector(&vm.vector, k, N - k);
+              tau = gsl_vector_get(state->tau, k);
+              gsl_linalg_householder_hv(tau, &uk.vector, &vk.vector);
+            }
+
+          /* Step 2a: v_m <- A*v_m */
+          gsl_spblas_dgemv(CblasNoTrans, 1.0, A, &vm.vector, 0.0, r);
+          gsl_vector_memcpy(&vm.vector, r);
+
+          /* Step 2a: v_m <- P_m ... P_1 v_m */
+          for (k = 0; k <= j; ++k)
+            {
+              gsl_vector_view uk = gsl_matrix_subcolumn(H, k, k, N - k);
+              gsl_vector_view vk = gsl_vector_subvector(&vm.vector, k, N - k);
+              tau = gsl_vector_get(state->tau, k);
+              gsl_linalg_householder_hv(tau, &uk.vector, &vk.vector);
+            }
+
+          /* Steps 2c,2d: find P_{m+1} and set v_m <- P_{m+1} v_m */
+          if (m < N)
+            {
+              /* householder vector u_{m+1} for projection P_{m+1} */
+              gsl_vector_view ump1 = gsl_matrix_subcolumn(H, m, m, N - m);
+
+              tau = gsl_linalg_householder_transform(&ump1.vector);
+              gsl_vector_set(state->tau, j + 1, tau);
+            }
+
+          /* Step 2e: v_m <- J_{m-1} ... J_1 v_m */
+          for (k = 0; k < j; ++k)
+            {
+              gsl_linalg_givens_gv(&vm.vector, k, k + 1,
+                                   state->c[k], state->s[k]);
+            }
+
+          if (m < N)
+            {
+              /* Step 2g: find givens rotation J_m for v_m(m:m+1) */
+              gsl_linalg_givens(gsl_vector_get(&vm.vector, j),
+                                gsl_vector_get(&vm.vector, j + 1),
+                                &c, &s);
+
+              /* store givens rotation for later use */
+              state->c[j] = c;
+              state->s[j] = s;
+
+              /* Step 2h: v_m <- J_m v_m */
+              gsl_linalg_givens_gv(&vm.vector, j, j + 1, c, s);
+
+              /* Step 2h: w <- J_m w */
+              gsl_linalg_givens_gv(w, j, j + 1, c, s);
+            }
+
+          /*
+           * Step 2i: R_m = [ R_{m-1}, v_m ] - already taken care
+           * of due to our memory storage scheme
+           */
+
+          /* Step 2j: check residual w_{m+1} for convergence */
+          normr = fabs(gsl_vector_get(w, j + 1));
+          if (normr <= reltol)
+            {
+              /*
+               * method has converged, break out of loop to compute
+               * update to solution vector x
+               */
+              break;
+            }
+        }
+
+      /*
+       * At this point, we have either converged to a solution or
+       * completed all maxit iterations. In either case, compute
+       * an update to the solution vector x and test again for
+       * convergence.
+       */
+
+      /* rewind m if we exceeded maxit iterations */
+      if (m > maxit)
+        m--;
+
+      /* Step 3a: solve triangular system R_m y_m = w, in place */
+      Rm = gsl_matrix_submatrix(H, 0, 1, m, m);
+      ym = gsl_vector_subvector(w, 0, m);
+      gsl_blas_dtrsv(CblasUpper, CblasNoTrans, CblasNonUnit,
+                     &Rm.matrix, &ym.vector);
+
+      /*
+       * Step 3b: update solution vector x; the loop below
+       * uses a different but equivalent formulation from
+       * Saad, algorithm 6.10, step 14; store Krylov projection
+       * V_m y_m in 'r'
+       */
+      gsl_vector_set_zero(r);
+      for (k = m; k > 0 && k--; )
+        {
+          double ymk = gsl_vector_get(&ym.vector, k);
+          gsl_vector_view uk = gsl_matrix_subcolumn(H, k, k, N - k);
+          gsl_vector_view rk = gsl_vector_subvector(r, k, N - k);
+
+          /* r <- n_k e_k + r */
+          gsl_vector_set(r, k, gsl_vector_get(r, k) + ymk);
+
+          /* r <- P_k r */
+          tau = gsl_vector_get(state->tau, k);
+          gsl_linalg_householder_hv(tau, &uk.vector, &rk.vector);
+        }
+
+      /* x <- x + V_m y_m */
+      gsl_vector_add(x, r);
+
+      /* compute new residual r = b - A*x */
+      gsl_vector_memcpy(r, b);
+      gsl_spblas_dgemv(CblasNoTrans, -1.0, A, x, 1.0, r);
+      normr = gsl_blas_dnrm2(r);
+
+      if (normr <= reltol)
+        status = GSL_SUCCESS;  /* converged */
+      else
+        status = GSL_CONTINUE; /* not yet converged */
+
+      /* store residual norm */
+      state->normr = normr;
+
+      return status;
+    }
+} /* gmres_iterate() */
+
+static double
+gmres_normr(const void *vstate)
+{
+  const gmres_state_t *state = (const gmres_state_t *) vstate;
+  return state->normr;
+} /* gmres_normr() */
+
+static const gsl_splinalg_itersolve_type gmres_type =
+{
+  "gmres",
+  &gmres_alloc,
+  &gmres_iterate,
+  &gmres_normr,
+  &gmres_free
+};
+
+const gsl_splinalg_itersolve_type * gsl_splinalg_itersolve_gmres =
+  &gmres_type;
diff -Nru gsl-doc-1.16/splinalg/gsl_splinalg.h gsl-doc-2.3/splinalg/gsl_splinalg.h
--- gsl-doc-1.16/splinalg/gsl_splinalg.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/splinalg/gsl_splinalg.h	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,79 @@
+/* gsl_splinalg.h
+ * 
+ * Copyright (C) 2012-2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_SPLINALG_H__
+#define __GSL_SPLINALG_H__
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_spmatrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_types.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+/* iteration solver type */
+typedef struct
+{
+  const char *name;
+  void * (*alloc) (const size_t n, const size_t m);
+  int (*iterate) (const gsl_spmatrix *A, const gsl_vector *b,
+                  const double tol, gsl_vector *x, void *);
+  double (*normr)(const void *);
+  void (*free) (void *);
+} gsl_splinalg_itersolve_type;
+
+typedef struct
+{
+  const gsl_splinalg_itersolve_type * type;
+  double normr; /* current residual norm || b - A x || */
+  void * state;
+} gsl_splinalg_itersolve;
+
+/* available types */
+GSL_VAR const gsl_splinalg_itersolve_type * gsl_splinalg_itersolve_gmres;
+
+/*
+ * Prototypes
+ */
+gsl_splinalg_itersolve *
+gsl_splinalg_itersolve_alloc(const gsl_splinalg_itersolve_type *T,
+                             const size_t n, const size_t m);
+void gsl_splinalg_itersolve_free(gsl_splinalg_itersolve *w);
+const char *gsl_splinalg_itersolve_name(const gsl_splinalg_itersolve *w);
+int gsl_splinalg_itersolve_iterate(const gsl_spmatrix *A,
+                                   const gsl_vector *b,
+                                   const double tol, gsl_vector *x,
+                                   gsl_splinalg_itersolve *w);
+double gsl_splinalg_itersolve_normr(const gsl_splinalg_itersolve *w);
+
+__END_DECLS
+
+#endif /* __GSL_SPLINALG_H__ */
diff -Nru gsl-doc-1.16/splinalg/itersolve.c gsl-doc-2.3/splinalg/itersolve.c
--- gsl-doc-1.16/splinalg/itersolve.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/splinalg/itersolve.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,90 @@
+/* itersolve.c
+ * 
+ * Copyright (C) 2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_spmatrix.h>
+#include <gsl/gsl_spblas.h>
+#include <gsl/gsl_splinalg.h>
+
+gsl_splinalg_itersolve *
+gsl_splinalg_itersolve_alloc(const gsl_splinalg_itersolve_type *T,
+                             const size_t n, const size_t m)
+{
+  gsl_splinalg_itersolve *w;
+
+  w = calloc(1, sizeof(gsl_splinalg_itersolve));
+  if (w == NULL)
+    {
+      GSL_ERROR_NULL("failed to allocate space for itersolve struct",
+                     GSL_ENOMEM);
+    }
+
+  w->type = T;
+  w->normr = 0.0;
+
+  w->state = w->type->alloc(n, m);
+  if (w->state == NULL)
+    {
+      gsl_splinalg_itersolve_free(w);
+      GSL_ERROR_NULL("failed to allocate space for itersolve state",
+                     GSL_ENOMEM);
+    }
+
+  return w;
+} /* gsl_splinalg_itersolve_alloc() */
+
+void
+gsl_splinalg_itersolve_free(gsl_splinalg_itersolve *w)
+{
+  RETURN_IF_NULL(w);
+
+  if (w->state)
+    w->type->free(w->state);
+
+  free(w);
+}
+
+const char *
+gsl_splinalg_itersolve_name(const gsl_splinalg_itersolve *w)
+{
+  return w->type->name;
+}
+
+int
+gsl_splinalg_itersolve_iterate(const gsl_spmatrix *A, const gsl_vector *b,
+                               const double tol, gsl_vector *x,
+                               gsl_splinalg_itersolve *w)
+{
+  int status = w->type->iterate(A, b, tol, x, w->state);
+
+  /* store current residual */
+  w->normr = w->type->normr(w->state);
+
+  return status;
+}
+
+double
+gsl_splinalg_itersolve_normr(const gsl_splinalg_itersolve *w)
+{
+  return w->normr;
+}
diff -Nru gsl-doc-1.16/splinalg/Makefile.am gsl-doc-2.3/splinalg/Makefile.am
--- gsl-doc-1.16/splinalg/Makefile.am	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/splinalg/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,15 @@
+noinst_LTLIBRARIES = libgslsplinalg.la 
+
+check_PROGRAMS = test
+
+pkginclude_HEADERS = gsl_splinalg.h
+
+libgslsplinalg_la_SOURCES = itersolve.c gmres.c
+
+AM_CPPFLAGS = -I$(top_srcdir)
+
+TESTS = $(check_PROGRAMS)
+
+test_LDADD = libgslsplinalg.la ../spmatrix/libgslspmatrix.la ../spblas/libgslspblas.la ../test/libgsltest.la ../linalg/libgsllinalg.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la  ../sys/libgslsys.la ../utils/libutils.la ../rng/libgslrng.la ../err/libgslerr.la
+
+test_SOURCES = test.c
diff -Nru gsl-doc-1.16/splinalg/Makefile.in gsl-doc-2.3/splinalg/Makefile.in
--- gsl-doc-1.16/splinalg/Makefile.in	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/splinalg/Makefile.in	2016-12-09 00:04:23.000000000 +0000
@@ -0,0 +1,1029 @@
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+# Tell versions [3.59,3.63) of GNU make to not export all variables.
+# Otherwise a system limit (for SysV at least) may be exceeded.
+.NOEXPORT:
diff -Nru gsl-doc-1.16/splinalg/test.c gsl-doc-2.3/splinalg/test.c
--- gsl-doc-1.16/splinalg/test.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/splinalg/test.c	2015-11-03 16:21:55.000000000 +0000
@@ -0,0 +1,372 @@
+/* test.c
+ * 
+ * Copyright (C) 2012-2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_randist.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_test.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_spmatrix.h>
+#include <gsl/gsl_spblas.h>
+#include <gsl/gsl_splinalg.h>
+
+/*
+create_random_sparse()
+  Create a random sparse matrix with approximately
+M*N*density non-zero entries
+
+Inputs: M       - number of rows
+        N       - number of columns
+        density - sparse density \in [0,1]
+                  0 = no non-zero entries
+                  1 = all m*n entries are filled
+        r       - random number generator
+
+Return: pointer to sparse matrix in triplet format (must be freed by caller)
+
+Notes:
+1) non-zero matrix entries are uniformly distributed in [0,1]
+*/
+
+static gsl_spmatrix *
+create_random_sparse(const size_t M, const size_t N, const double density,
+                     const gsl_rng *r)
+{
+  size_t nnzwanted = (size_t) floor(M * N * GSL_MIN(density, 1.0));
+  gsl_spmatrix *m = gsl_spmatrix_alloc_nzmax(M, N,
+                                             nnzwanted,
+                                             GSL_SPMATRIX_TRIPLET);
+  size_t i;
+
+  /* set diagonal entries to try to ensure non-singularity */
+  for (i = 0; i < GSL_MIN(M, N); ++i)
+    {
+      double x = gsl_rng_uniform(r);
+      gsl_spmatrix_set(m, i, i, x);
+    }
+
+  while (gsl_spmatrix_nnz(m) < nnzwanted)
+    {
+      /* generate a random row and column */
+      size_t i = gsl_rng_uniform(r) * M;
+      size_t j = gsl_rng_uniform(r) * N;
+
+      /* generate random m_{ij} and add it */
+      double x = gsl_rng_uniform(r);
+      gsl_spmatrix_set(m, i, j, x);
+    }
+
+  return m;
+} /* create_random_sparse() */
+
+static void
+create_random_vector(gsl_vector *v, const gsl_rng *r)
+{
+  size_t i;
+
+  for (i = 0; i < v->size; ++i)
+    {
+      double x = gsl_rng_uniform(r);
+      gsl_vector_set(v, i, x);
+    }
+} /* create_random_vector() */
+
+/*
+test_poisson()
+  Solve u''(x) = -pi^2 sin(pi*x), u(x) = sin(pi*x)
+  epsrel is the relative error threshold with the exact solution
+*/
+static void
+test_poisson(const size_t N, const double epsrel, const int compress)
+{
+  const gsl_splinalg_itersolve_type *T = gsl_splinalg_itersolve_gmres;
+  const size_t n = N - 2;                     /* subtract 2 to exclude boundaries */
+  const double h = 1.0 / (N - 1.0);           /* grid spacing */
+  const double tol = 1.0e-9;
+  const size_t max_iter = 10;
+  size_t iter = 0;
+  gsl_spmatrix *A = gsl_spmatrix_alloc(n ,n); /* triplet format */
+  gsl_spmatrix *B;
+  gsl_vector *b = gsl_vector_alloc(n);        /* right hand side vector */
+  gsl_vector *u = gsl_vector_calloc(n);       /* solution vector, u0 = 0 */
+  gsl_splinalg_itersolve *w = gsl_splinalg_itersolve_alloc(T, n, 0);
+  const char *desc = gsl_splinalg_itersolve_name(w);
+  size_t i;
+  int status;
+
+  /* construct the sparse matrix for the finite difference equation */
+
+  /* first row of matrix */
+  gsl_spmatrix_set(A, 0, 0, -2.0);
+  gsl_spmatrix_set(A, 0, 1, 1.0);
+
+  /* loop over interior grid points */
+  for (i = 1; i < n - 1; ++i)
+    {
+      gsl_spmatrix_set(A, i, i + 1, 1.0);
+      gsl_spmatrix_set(A, i, i, -2.0);
+      gsl_spmatrix_set(A, i, i - 1, 1.0);
+    }
+
+  /* last row of matrix */
+  gsl_spmatrix_set(A, n - 1, n - 1, -2.0);
+  gsl_spmatrix_set(A, n - 1, n - 2, 1.0);
+
+  /* scale by h^2 */
+  gsl_spmatrix_scale(A, 1.0 / (h * h));
+
+  /* construct right hand side vector */
+  for (i = 0; i < n; ++i)
+    {
+      double xi = (i + 1) * h;
+      double bi = -M_PI * M_PI * sin(M_PI * xi);
+      gsl_vector_set(b, i, bi);
+    }
+
+  if (compress)
+    B = gsl_spmatrix_compcol(A);
+  else
+    B = A;
+
+  /* solve the system */
+  do
+    {
+      status = gsl_splinalg_itersolve_iterate(B, b, tol, u, w);
+    }
+  while (status == GSL_CONTINUE && ++iter < max_iter);
+
+  gsl_test(status, "%s poisson status s=%d N=%zu", desc, status, N);
+
+  /* check solution against analytic */
+  for (i = 0; i < n; ++i)
+    {
+      double xi = (i + 1) * h;
+      double u_gsl = gsl_vector_get(u, i);
+      double u_exact = sin(M_PI * xi);
+
+      gsl_test_rel(u_gsl, u_exact, epsrel, "%s poisson N=%zu i=%zu",
+                   desc, N, i);
+    }
+
+  /* check that the residual satisfies ||r|| <= tol*||b|| */
+  {
+    gsl_vector *r = gsl_vector_alloc(n);
+    double normr, normb;
+
+    gsl_vector_memcpy(r, b);
+    gsl_spblas_dgemv(CblasNoTrans, -1.0, A, u, 1.0, r);
+
+    normr = gsl_blas_dnrm2(r);
+    normb = gsl_blas_dnrm2(b);
+
+    status = (normr <= tol*normb) != 1;
+    gsl_test(status, "%s poisson residual N=%zu normr=%.12e normb=%.12e",
+             desc, N, normr, normb);
+
+    gsl_vector_free(r);
+  }
+
+  gsl_splinalg_itersolve_free(w);
+  gsl_spmatrix_free(A);
+  gsl_vector_free(b);
+  gsl_vector_free(u);
+
+  if (compress)
+    gsl_spmatrix_free(B);
+} /* test_poisson() */
+
+/*
+test_toeplitz()
+  Test Toeplitz matrix T = A + B + C where:
+A = diag(a,-1)
+B = diag(b)
+C = diag(c,1)
+
+rhs = ones(n,1)
+*/
+
+static void
+test_toeplitz(const size_t N, const double a, const double b,
+              const double c)
+{
+  int status;
+  const double tol = 1.0e-10;
+  const size_t max_iter = 10;
+  const gsl_splinalg_itersolve_type *T = gsl_splinalg_itersolve_gmres;
+  const char *desc;
+  gsl_spmatrix *A;
+  gsl_vector *rhs, *x;
+  gsl_splinalg_itersolve *w;
+  size_t i, iter = 0;
+
+  if (N <= 1)
+    return;
+
+  A = gsl_spmatrix_alloc(N ,N);
+  rhs = gsl_vector_alloc(N);
+  x = gsl_vector_calloc(N);
+  w = gsl_splinalg_itersolve_alloc(T, N, 0);
+  desc = gsl_splinalg_itersolve_name(w);
+
+  /* first row */
+  gsl_spmatrix_set(A, 0, 0, b);
+  gsl_spmatrix_set(A, 0, 1, c);
+
+  /* interior rows */
+  for (i = 1; i < N - 1; ++i)
+    {
+      gsl_spmatrix_set(A, i, i - 1, a);
+      gsl_spmatrix_set(A, i, i, b);
+      gsl_spmatrix_set(A, i, i + 1, c);
+    }
+
+  /* last row */
+  gsl_spmatrix_set(A, N - 1, N - 2, a);
+  gsl_spmatrix_set(A, N - 1, N - 1, b);
+
+  /* set rhs vector */
+  gsl_vector_set_all(rhs, 1.0);
+
+  /* solve the system */
+  do
+    {
+      status = gsl_splinalg_itersolve_iterate(A, rhs, tol, x, w);
+    }
+  while (status == GSL_CONTINUE && ++iter < max_iter);
+
+  gsl_test(status, "%s toeplitz status s=%d N=%zu a=%f b=%f c=%f",
+           desc, status, N, a, b, c);
+
+  /* check that the residual satisfies ||r|| <= tol*||b|| */
+  {
+    gsl_vector *r = gsl_vector_alloc(N);
+    double normr, normb;
+
+    gsl_vector_memcpy(r, rhs);
+    gsl_spblas_dgemv(CblasNoTrans, -1.0, A, x, 1.0, r);
+
+    normr = gsl_blas_dnrm2(r);
+    normb = gsl_blas_dnrm2(rhs);
+
+    status = (normr <= tol*normb) != 1;
+    gsl_test(status, "%s toeplitz residual N=%zu a=%f b=%f c=%f normr=%.12e normb=%.12e",
+             desc, N, a, b, c, normr, normb);
+
+    gsl_vector_free(r);
+  }
+
+  gsl_vector_free(x);
+  gsl_vector_free(rhs);
+  gsl_spmatrix_free(A);
+  gsl_splinalg_itersolve_free(w);
+} /* test_toeplitz() */
+
+static void
+test_random(const size_t N, const gsl_rng *r, const int compress)
+{
+  const gsl_splinalg_itersolve_type *T = gsl_splinalg_itersolve_gmres;
+  const double tol = 1.0e-8;
+  int status;
+  gsl_spmatrix *A = create_random_sparse(N, N, 0.3, r);
+  gsl_spmatrix *B;
+  gsl_vector *b = gsl_vector_alloc(N);
+  gsl_vector *x = gsl_vector_calloc(N);
+
+  /* these random matrices require all N iterations to converge */
+  gsl_splinalg_itersolve *w = gsl_splinalg_itersolve_alloc(T, N, N);
+
+  const char *desc = gsl_splinalg_itersolve_name(w);
+
+  create_random_vector(b, r);
+
+  if (compress)
+    B = gsl_spmatrix_compcol(A);
+  else
+    B = A;
+
+  status = gsl_splinalg_itersolve_iterate(B, b, tol, x, w);
+  gsl_test(status, "%s random status s=%d N=%zu", desc, status, N);
+
+  /* check that the residual satisfies ||r|| <= tol*||b|| */
+  {
+    gsl_vector *res = gsl_vector_alloc(N);
+    double normr, normb;
+
+    gsl_vector_memcpy(res, b);
+    gsl_spblas_dgemv(CblasNoTrans, -1.0, A, x, 1.0, res);
+
+    normr = gsl_blas_dnrm2(res);
+    normb = gsl_blas_dnrm2(b);
+
+    status = (normr <= tol*normb) != 1;
+    gsl_test(status, "%s random residual N=%zu normr=%.12e normb=%.12e",
+             desc, N, normr, normb);
+
+    gsl_vector_free(res);
+  }
+
+  gsl_spmatrix_free(A);
+  gsl_vector_free(b);
+  gsl_vector_free(x);
+  gsl_splinalg_itersolve_free(w);
+
+  if (compress)
+    gsl_spmatrix_free(B);
+} /* test_random() */
+
+int
+main()
+{
+  gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+  size_t n;
+
+  test_poisson(7, 1.0e-1, 0);
+  test_poisson(7, 1.0e-1, 1);
+
+  test_poisson(543, 1.0e-5, 0);
+  test_poisson(543, 1.0e-5, 1);
+
+  test_poisson(1000, 1.0e-6, 0);
+  test_poisson(1000, 1.0e-6, 1);
+
+  test_poisson(5000, 1.0e-7, 0);
+  test_poisson(5000, 1.0e-7, 1);
+
+  test_toeplitz(15, 0.01, 1.0, 0.01);
+  test_toeplitz(15, 1.0, 1.0, 0.01);
+  test_toeplitz(50, 1.0, 2.0, 0.01);
+  test_toeplitz(1000, 0.5, 1.0, 0.01);
+
+  for (n = 1; n <= 100; ++n)
+    {
+      test_random(n, r, 0);
+      test_random(n, r, 1);
+    }
+
+  gsl_rng_free(r);
+
+  exit (gsl_test_summary());
+} /* main() */
diff -Nru gsl-doc-1.16/spmatrix/avl.c gsl-doc-2.3/spmatrix/avl.c
--- gsl-doc-1.16/spmatrix/avl.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/avl.c	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,611 @@
+/* avl.c
+ * 
+ * Copyright (C) 1998, 1999, 2000, 2001, 2002, 2004 Free Software
+ * Foundation, Inc.
+ * Copyright (C) 2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/*
+ * This code is originally from GNU libavl. The memory management
+ * was slightly modified for use with preallocating GSL sparse matrices
+ *
+ * The allocator->libavl_malloc function is called only for creating
+ * a new avl_node (tree node). This allows GSL to preallocate some number
+ * of avl_node structs and then return pointers to them while the tree
+ * is being assembled, avoiding multiple malloc calls
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <stddef.h>
+#include <string.h>
+
+/* Function types. */
+typedef int avl_comparison_func (const void *avl_a, const void *avl_b,
+                                 void *avl_param);
+typedef void avl_item_func (void *avl_item, void *avl_param);
+typedef void *avl_copy_func (void *avl_item, void *avl_param);
+
+/* Memory allocator. */
+struct libavl_allocator
+  {
+    void *(*libavl_malloc) (size_t libavl_size, void *param);
+    void (*libavl_free) (void *libavl_block, void *param);
+  };
+
+/* Default memory allocator. */
+static struct libavl_allocator avl_allocator_default;
+static void *avl_malloc (size_t, void *param);
+static void avl_free (void *, void *param);
+
+/* Maximum AVL tree height. */
+#ifndef AVL_MAX_HEIGHT
+#define AVL_MAX_HEIGHT 92
+#endif
+
+/* An AVL tree node. */
+struct avl_node
+  {
+    struct avl_node *avl_link[2];  /* Subtrees. */
+    void *avl_data;                /* Pointer to data. */
+    signed char avl_balance;       /* Balance factor. */
+  };
+
+/* Tree data structure. */
+struct avl_table
+  {
+    struct avl_node *avl_root;          /* Tree's root. */
+    avl_comparison_func *avl_compare;   /* Comparison function. */
+    void *avl_param;                    /* Extra argument to |avl_compare|. */
+    struct libavl_allocator *avl_alloc; /* Memory allocator. */
+    size_t avl_count;                   /* Number of items in tree. */
+    unsigned long avl_generation;       /* Generation number. */
+  };
+
+/* Table functions. */
+static struct avl_table *avl_create (avl_comparison_func *, void *,
+                                     struct libavl_allocator *);
+static struct avl_table *avl_copy (const struct avl_table *, avl_copy_func *,
+                                   avl_item_func *, struct libavl_allocator *);
+static void avl_empty (struct avl_table *, avl_item_func *);
+static void avl_destroy (struct avl_table *, avl_item_func *);
+static void **avl_probe (struct avl_table *, void *);
+static void *avl_insert (struct avl_table *, void *);
+static void *avl_replace (struct avl_table *, void *);
+static void *avl_delete (struct avl_table *, const void *);
+static void *avl_find (const struct avl_table *, const void *);
+
+/* Creates and returns a new table
+   with comparison function |compare| using parameter |param|
+   and memory allocator |allocator|.
+   Returns |NULL| if memory allocation failed. */
+static struct avl_table *
+avl_create (avl_comparison_func *compare, void *param,
+            struct libavl_allocator *allocator)
+{
+  struct avl_table *tree;
+
+  if (allocator == NULL)
+    allocator = &avl_allocator_default;
+
+  /*tree = allocator->libavl_malloc (allocator, sizeof *tree);*/
+  tree = malloc(sizeof *tree);
+  if (tree == NULL)
+    return NULL;
+
+  tree->avl_root = NULL;
+  tree->avl_compare = compare;
+  tree->avl_param = param;
+  tree->avl_alloc = allocator;
+  tree->avl_count = 0;
+  tree->avl_generation = 0;
+
+  return tree;
+}
+
+/* Search |tree| for an item matching |item|, and return it if found.
+   Otherwise return |NULL|. */
+static void *
+avl_find (const struct avl_table *tree, const void *item)
+{
+  const struct avl_node *p;
+
+  for (p = tree->avl_root; p != NULL; )
+    {
+      int cmp = tree->avl_compare (item, p->avl_data, tree->avl_param);
+
+      if (cmp < 0)
+        p = p->avl_link[0];
+      else if (cmp > 0)
+        p = p->avl_link[1];
+      else /* |cmp == 0| */
+        return p->avl_data;
+    }
+
+  return NULL;
+}
+
+/* Inserts |item| into |tree| and returns a pointer to |item|'s address.
+   If a duplicate item is found in the tree,
+   returns a pointer to the duplicate without inserting |item|.
+   Returns |NULL| in case of memory allocation failure. */
+static void **
+avl_probe (struct avl_table *tree, void *item)
+{
+  struct avl_node *y, *z; /* Top node to update balance factor, and parent. */
+  struct avl_node *p, *q; /* Iterator, and parent. */
+  struct avl_node *n;     /* Newly inserted node. */
+  struct avl_node *w;     /* New root of rebalanced subtree. */
+  int dir;                /* Direction to descend. */
+
+  unsigned char da[AVL_MAX_HEIGHT]; /* Cached comparison results. */
+  int k = 0;              /* Number of cached results. */
+
+  z = (struct avl_node *) &tree->avl_root;
+  y = tree->avl_root;
+  dir = 0;
+  for (q = z, p = y; p != NULL; q = p, p = p->avl_link[dir])
+    {
+      int cmp = tree->avl_compare (item, p->avl_data, tree->avl_param);
+      if (cmp == 0)
+        return &p->avl_data;
+
+      if (p->avl_balance != 0)
+        z = q, y = p, k = 0;
+      da[k++] = dir = cmp > 0;
+    }
+
+  n = q->avl_link[dir] =
+    tree->avl_alloc->libavl_malloc (sizeof *n, tree->avl_param);
+  if (n == NULL)
+    return NULL;
+
+  tree->avl_count++;
+  n->avl_data = item;
+  n->avl_link[0] = n->avl_link[1] = NULL;
+  n->avl_balance = 0;
+  if (y == NULL)
+    return &n->avl_data;
+
+  for (p = y, k = 0; p != n; p = p->avl_link[da[k]], k++)
+    if (da[k] == 0)
+      p->avl_balance--;
+    else
+      p->avl_balance++;
+
+  if (y->avl_balance == -2)
+    {
+      struct avl_node *x = y->avl_link[0];
+      if (x->avl_balance == -1)
+        {
+          w = x;
+          y->avl_link[0] = x->avl_link[1];
+          x->avl_link[1] = y;
+          x->avl_balance = y->avl_balance = 0;
+        }
+      else
+        {
+          w = x->avl_link[1];
+          x->avl_link[1] = w->avl_link[0];
+          w->avl_link[0] = x;
+          y->avl_link[0] = w->avl_link[1];
+          w->avl_link[1] = y;
+          if (w->avl_balance == -1)
+            x->avl_balance = 0, y->avl_balance = +1;
+          else if (w->avl_balance == 0)
+            x->avl_balance = y->avl_balance = 0;
+          else /* |w->avl_balance == +1| */
+            x->avl_balance = -1, y->avl_balance = 0;
+          w->avl_balance = 0;
+        }
+    }
+  else if (y->avl_balance == +2)
+    {
+      struct avl_node *x = y->avl_link[1];
+      if (x->avl_balance == +1)
+        {
+          w = x;
+          y->avl_link[1] = x->avl_link[0];
+          x->avl_link[0] = y;
+          x->avl_balance = y->avl_balance = 0;
+        }
+      else
+        {
+          w = x->avl_link[0];
+          x->avl_link[0] = w->avl_link[1];
+          w->avl_link[1] = x;
+          y->avl_link[1] = w->avl_link[0];
+          w->avl_link[0] = y;
+          if (w->avl_balance == +1)
+            x->avl_balance = 0, y->avl_balance = -1;
+          else if (w->avl_balance == 0)
+            x->avl_balance = y->avl_balance = 0;
+          else /* |w->avl_balance == -1| */
+            x->avl_balance = +1, y->avl_balance = 0;
+          w->avl_balance = 0;
+        }
+    }
+  else
+    return &n->avl_data;
+  z->avl_link[y != z->avl_link[0]] = w;
+
+  tree->avl_generation++;
+  return &n->avl_data;
+}
+
+/* Inserts |item| into |table|.
+   Returns |NULL| if |item| was successfully inserted
+   or if a memory allocation error occurred.
+   Otherwise, returns the duplicate item. */
+static void *
+avl_insert (struct avl_table *table, void *item)
+{
+  void **p = avl_probe (table, item);
+  return p == NULL || *p == item ? NULL : *p;
+}
+
+/* Inserts |item| into |table|, replacing any duplicate item.
+   Returns |NULL| if |item| was inserted without replacing a duplicate,
+   or if a memory allocation error occurred.
+   Otherwise, returns the item that was replaced. */
+static void *
+avl_replace (struct avl_table *table, void *item)
+{
+  void **p = avl_probe (table, item);
+  if (p == NULL || *p == item)
+    return NULL;
+  else
+    {
+      void *r = *p;
+      *p = item;
+      return r;
+    }
+}
+
+/* Deletes from |tree| and returns an item matching |item|.
+   Returns a null pointer if no matching item found. */
+static void *
+avl_delete (struct avl_table *tree, const void *item)
+{
+  /* Stack of nodes. */
+  struct avl_node *pa[AVL_MAX_HEIGHT]; /* Nodes. */
+  unsigned char da[AVL_MAX_HEIGHT];    /* |avl_link[]| indexes. */
+  int k;                               /* Stack pointer. */
+
+  struct avl_node *p;   /* Traverses tree to find node to delete. */
+  int cmp;              /* Result of comparison between |item| and |p|. */
+
+  k = 0;
+  p = (struct avl_node *) &tree->avl_root;
+  for (cmp = -1; cmp != 0;
+       cmp = tree->avl_compare (item, p->avl_data, tree->avl_param))
+    {
+      int dir = cmp > 0;
+
+      pa[k] = p;
+      da[k++] = dir;
+
+      p = p->avl_link[dir];
+      if (p == NULL)
+        return NULL;
+    }
+  item = p->avl_data;
+
+  if (p->avl_link[1] == NULL)
+    pa[k - 1]->avl_link[da[k - 1]] = p->avl_link[0];
+  else
+    {
+      struct avl_node *r = p->avl_link[1];
+      if (r->avl_link[0] == NULL)
+        {
+          r->avl_link[0] = p->avl_link[0];
+          r->avl_balance = p->avl_balance;
+          pa[k - 1]->avl_link[da[k - 1]] = r;
+          da[k] = 1;
+          pa[k++] = r;
+        }
+      else
+        {
+          struct avl_node *s;
+          int j = k++;
+
+          for (;;)
+            {
+              da[k] = 0;
+              pa[k++] = r;
+              s = r->avl_link[0];
+              if (s->avl_link[0] == NULL)
+                break;
+
+              r = s;
+            }
+
+          s->avl_link[0] = p->avl_link[0];
+          r->avl_link[0] = s->avl_link[1];
+          s->avl_link[1] = p->avl_link[1];
+          s->avl_balance = p->avl_balance;
+
+          pa[j - 1]->avl_link[da[j - 1]] = s;
+          da[j] = 1;
+          pa[j] = s;
+        }
+    }
+
+  tree->avl_alloc->libavl_free (p, tree->avl_param);
+
+  while (--k > 0)
+    {
+      struct avl_node *y = pa[k];
+
+      if (da[k] == 0)
+        {
+          y->avl_balance++;
+          if (y->avl_balance == +1)
+            break;
+          else if (y->avl_balance == +2)
+            {
+              struct avl_node *x = y->avl_link[1];
+              if (x->avl_balance == -1)
+                {
+                  struct avl_node *w;
+                  w = x->avl_link[0];
+                  x->avl_link[0] = w->avl_link[1];
+                  w->avl_link[1] = x;
+                  y->avl_link[1] = w->avl_link[0];
+                  w->avl_link[0] = y;
+                  if (w->avl_balance == +1)
+                    x->avl_balance = 0, y->avl_balance = -1;
+                  else if (w->avl_balance == 0)
+                    x->avl_balance = y->avl_balance = 0;
+                  else /* |w->avl_balance == -1| */
+                    x->avl_balance = +1, y->avl_balance = 0;
+                  w->avl_balance = 0;
+                  pa[k - 1]->avl_link[da[k - 1]] = w;
+                }
+              else
+                {
+                  y->avl_link[1] = x->avl_link[0];
+                  x->avl_link[0] = y;
+                  pa[k - 1]->avl_link[da[k - 1]] = x;
+                  if (x->avl_balance == 0)
+                    {
+                      x->avl_balance = -1;
+                      y->avl_balance = +1;
+                      break;
+                    }
+                  else
+                    x->avl_balance = y->avl_balance = 0;
+                }
+            }
+        }
+      else
+        {
+          y->avl_balance--;
+          if (y->avl_balance == -1)
+            break;
+          else if (y->avl_balance == -2)
+            {
+              struct avl_node *x = y->avl_link[0];
+              if (x->avl_balance == +1)
+                {
+                  struct avl_node *w;
+                  w = x->avl_link[1];
+                  x->avl_link[1] = w->avl_link[0];
+                  w->avl_link[0] = x;
+                  y->avl_link[0] = w->avl_link[1];
+                  w->avl_link[1] = y;
+                  if (w->avl_balance == -1)
+                    x->avl_balance = 0, y->avl_balance = +1;
+                  else if (w->avl_balance == 0)
+                    x->avl_balance = y->avl_balance = 0;
+                  else /* |w->avl_balance == +1| */
+                    x->avl_balance = -1, y->avl_balance = 0;
+                  w->avl_balance = 0;
+                  pa[k - 1]->avl_link[da[k - 1]] = w;
+                }
+              else
+                {
+                  y->avl_link[0] = x->avl_link[1];
+                  x->avl_link[1] = y;
+                  pa[k - 1]->avl_link[da[k - 1]] = x;
+                  if (x->avl_balance == 0)
+                    {
+                      x->avl_balance = +1;
+                      y->avl_balance = -1;
+                      break;
+                    }
+                  else
+                    x->avl_balance = y->avl_balance = 0;
+                }
+            }
+        }
+    }
+
+  tree->avl_count--;
+  tree->avl_generation++;
+  return (void *) item;
+}
+
+/* Destroys |new| with |avl_destroy (new, destroy)|,
+   first setting right links of nodes in |stack| within |new|
+   to null pointers to avoid touching uninitialized data. */
+static void
+copy_error_recovery (struct avl_node **stack, int height,
+                     struct avl_table *new, avl_item_func *destroy)
+{
+  for (; height > 2; height -= 2)
+    stack[height - 1]->avl_link[1] = NULL;
+  avl_destroy (new, destroy);
+}
+
+/* Copies |org| to a newly created tree, which is returned.
+   If |copy != NULL|, each data item in |org| is first passed to |copy|,
+   and the return values are inserted into the tree,
+   with |NULL| return values taken as indications of failure.
+   On failure, destroys the partially created new tree,
+   applying |destroy|, if non-null, to each item in the new tree so far,
+   and returns |NULL|.
+   If |allocator != NULL|, it is used for allocation in the new tree.
+   Otherwise, the same allocator used for |org| is used. */
+static struct avl_table *
+avl_copy (const struct avl_table *org, avl_copy_func *copy,
+          avl_item_func *destroy, struct libavl_allocator *allocator)
+{
+  struct avl_node *stack[2 * (AVL_MAX_HEIGHT + 1)];
+  int height = 0;
+
+  struct avl_table *new;
+  const struct avl_node *x;
+  struct avl_node *y;
+
+  new = avl_create (org->avl_compare, org->avl_param,
+                    allocator != NULL ? allocator : org->avl_alloc);
+  if (new == NULL)
+    return NULL;
+  new->avl_count = org->avl_count;
+  if (new->avl_count == 0)
+    return new;
+
+  x = (const struct avl_node *) &org->avl_root;
+  y = (struct avl_node *) &new->avl_root;
+  for (;;)
+    {
+      while (x->avl_link[0] != NULL)
+        {
+          y->avl_link[0] =
+            new->avl_alloc->libavl_malloc (sizeof *y->avl_link[0],
+                                           new->avl_param);
+          if (y->avl_link[0] == NULL)
+            {
+              if (y != (struct avl_node *) &new->avl_root)
+                {
+                  y->avl_data = NULL;
+                  y->avl_link[1] = NULL;
+                }
+
+              copy_error_recovery (stack, height, new, destroy);
+              return NULL;
+            }
+
+          stack[height++] = (struct avl_node *) x;
+          stack[height++] = y;
+          x = x->avl_link[0];
+          y = y->avl_link[0];
+        }
+      y->avl_link[0] = NULL;
+
+      for (;;)
+        {
+          y->avl_balance = x->avl_balance;
+          if (copy == NULL)
+            y->avl_data = x->avl_data;
+          else
+            {
+              y->avl_data = copy (x->avl_data, org->avl_param);
+              if (y->avl_data == NULL)
+                {
+                  y->avl_link[1] = NULL;
+                  copy_error_recovery (stack, height, new, destroy);
+                  return NULL;
+                }
+            }
+
+          if (x->avl_link[1] != NULL)
+            {
+              y->avl_link[1] =
+                new->avl_alloc->libavl_malloc (sizeof *y->avl_link[1],
+                                               new->avl_param);
+              if (y->avl_link[1] == NULL)
+                {
+                  copy_error_recovery (stack, height, new, destroy);
+                  return NULL;
+                }
+
+              x = x->avl_link[1];
+              y = y->avl_link[1];
+              break;
+            }
+          else
+            y->avl_link[1] = NULL;
+
+          if (height <= 2)
+            return new;
+
+          y = stack[--height];
+          x = stack[--height];
+        }
+    }
+}
+
+/* empty tree (delete all nodes) but do not free the tree itself */
+static void
+avl_empty (struct avl_table *tree, avl_item_func *destroy)
+{
+  struct avl_node *p, *q;
+
+  for (p = tree->avl_root; p != NULL; p = q)
+    if (p->avl_link[0] == NULL)
+      {
+        q = p->avl_link[1];
+        if (destroy != NULL && p->avl_data != NULL)
+          destroy (p->avl_data, tree->avl_param);
+        tree->avl_alloc->libavl_free (p, tree->avl_param);
+      }
+    else
+      {
+        q = p->avl_link[0];
+        p->avl_link[0] = q->avl_link[1];
+        q->avl_link[1] = p;
+      }
+
+  tree->avl_root = NULL;
+  tree->avl_count = 0;
+  tree->avl_generation = 0;
+}
+
+/* Frees storage allocated for |tree|.
+   If |destroy != NULL|, applies it to each data item in inorder. */
+static void
+avl_destroy (struct avl_table *tree, avl_item_func *destroy)
+{
+  avl_empty(tree, destroy);
+  free(tree);
+}
+
+/* Allocates |size| bytes of space using |malloc()|.
+   Returns a null pointer if allocation fails. */
+static void *
+avl_malloc (size_t size, void *param)
+{
+  (void)param; /* avoid unused parameter warning */
+  return malloc (size);
+}
+
+/* Frees |block|. */
+static void
+avl_free (void *block, void *param)
+{
+  (void)param; /* avoid unused parameter warning */
+  free (block);
+}
+
+/* Default memory allocator that uses |malloc()| and |free()|. */
+static struct libavl_allocator avl_allocator_default =
+  {
+    avl_malloc,
+    avl_free
+  };
diff -Nru gsl-doc-1.16/spmatrix/gsl_spmatrix.h gsl-doc-2.3/spmatrix/gsl_spmatrix.h
--- gsl-doc-1.16/spmatrix/gsl_spmatrix.h	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/gsl_spmatrix.h	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,179 @@
+/* gsl_spmatrix.h
+ * 
+ * Copyright (C) 2012-2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#ifndef __GSL_SPMATRIX_H__
+#define __GSL_SPMATRIX_H__
+
+#include <stdlib.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+/*
+ * Binary tree data structure for storing sparse matrix elements
+ * in triplet format. This is used for efficiently detecting
+ * duplicates and element retrieval via gsl_spmatrix_get
+ */
+typedef struct
+{
+  void *tree;       /* tree structure */
+  void *node_array; /* preallocated array of tree nodes */
+  size_t n;         /* number of tree nodes in use (<= nzmax) */
+} gsl_spmatrix_tree;
+
+/*
+ * Triplet format:
+ *
+ * If data[n] = A_{ij}, then:
+ *   i = A->i[n]
+ *   j = A->p[n]
+ *
+ * Compressed column format (CCS):
+ *
+ * If data[n] = A_{ij}, then:
+ *   i = A->i[n]
+ *   A->p[j] <= n < A->p[j+1]
+ * so that column j is stored in
+ * [ data[p[j]], data[p[j] + 1], ..., data[p[j+1] - 1] ]
+ *
+ * Compressed row format (CRS):
+ *
+ * If data[n] = A_{ij}, then:
+ *   j = A->i[n]
+ *   A->p[i] <= n < A->p[i+1]
+ * so that row i is stored in
+ * [ data[p[i]], data[p[i] + 1], ..., data[p[i+1] - 1] ]
+ */
+
+typedef struct
+{
+  size_t size1;  /* number of rows */
+  size_t size2;  /* number of columns */
+
+  /* i (size nzmax) contains:
+   *
+   * Triplet/CCS: row indices
+   * CRS: column indices
+   */
+  size_t *i;
+
+  double *data;  /* matrix elements of size nzmax */
+
+  /*
+   * p contains the column indices (triplet) or column pointers (compcol)
+   *
+   * triplet: p[n] = column number of element data[n]
+   * CCS:     p[j] = index in data of first non-zero element in column j
+   * CRS:     p[i] = index in data of first non-zero element in row i
+   */
+  size_t *p;
+
+  size_t nzmax;  /* maximum number of matrix elements */
+  size_t nz;     /* number of non-zero values in matrix */
+
+  gsl_spmatrix_tree *tree_data; /* binary tree for sorting triplet data */
+
+  /*
+   * workspace of size MAX(size1,size2)*MAX(sizeof(double),sizeof(size_t))
+   * used in various routines
+   */
+  void *work;
+
+  size_t sptype; /* sparse storage type */
+} gsl_spmatrix;
+
+#define GSL_SPMATRIX_TRIPLET      (0)
+#define GSL_SPMATRIX_CCS          (1)
+#define GSL_SPMATRIX_CRS          (2)
+
+#define GSL_SPMATRIX_ISTRIPLET(m) ((m)->sptype == GSL_SPMATRIX_TRIPLET)
+#define GSL_SPMATRIX_ISCCS(m)     ((m)->sptype == GSL_SPMATRIX_CCS)
+#define GSL_SPMATRIX_ISCRS(m)     ((m)->sptype == GSL_SPMATRIX_CRS)
+
+/*
+ * Prototypes
+ */
+
+gsl_spmatrix *gsl_spmatrix_alloc(const size_t n1, const size_t n2);
+gsl_spmatrix *gsl_spmatrix_alloc_nzmax(const size_t n1, const size_t n2,
+                                       const size_t nzmax, const size_t flags);
+void gsl_spmatrix_free(gsl_spmatrix *m);
+int gsl_spmatrix_realloc(const size_t nzmax, gsl_spmatrix *m);
+int gsl_spmatrix_set_zero(gsl_spmatrix *m);
+size_t gsl_spmatrix_nnz(const gsl_spmatrix *m);
+int gsl_spmatrix_compare_idx(const size_t ia, const size_t ja,
+                             const size_t ib, const size_t jb);
+int gsl_spmatrix_tree_rebuild(gsl_spmatrix * m);
+
+/* spcopy.c */
+int gsl_spmatrix_memcpy(gsl_spmatrix *dest, const gsl_spmatrix *src);
+
+/* spgetset.c */
+double gsl_spmatrix_get(const gsl_spmatrix *m, const size_t i,
+                        const size_t j);
+int gsl_spmatrix_set(gsl_spmatrix *m, const size_t i, const size_t j,
+                     const double x);
+double *gsl_spmatrix_ptr(gsl_spmatrix *m, const size_t i, const size_t j);
+
+/* spcompress.c */
+gsl_spmatrix *gsl_spmatrix_compcol(const gsl_spmatrix *T);
+gsl_spmatrix *gsl_spmatrix_ccs(const gsl_spmatrix *T);
+gsl_spmatrix *gsl_spmatrix_crs(const gsl_spmatrix *T);
+void gsl_spmatrix_cumsum(const size_t n, size_t *c);
+
+/* spio.c */
+int gsl_spmatrix_fprintf(FILE *stream, const gsl_spmatrix *m,
+                         const char *format);
+gsl_spmatrix * gsl_spmatrix_fscanf(FILE *stream);
+int gsl_spmatrix_fwrite(FILE *stream, const gsl_spmatrix *m);
+int gsl_spmatrix_fread(FILE *stream, gsl_spmatrix *m);
+
+/* spoper.c */
+int gsl_spmatrix_scale(gsl_spmatrix *m, const double x);
+int gsl_spmatrix_minmax(const gsl_spmatrix *m, double *min_out,
+                        double *max_out);
+int gsl_spmatrix_add(gsl_spmatrix *c, const gsl_spmatrix *a,
+                     const gsl_spmatrix *b);
+int gsl_spmatrix_d2sp(gsl_spmatrix *S, const gsl_matrix *A);
+int gsl_spmatrix_sp2d(gsl_matrix *A, const gsl_spmatrix *S);
+
+/* spprop.c */
+int gsl_spmatrix_equal(const gsl_spmatrix *a, const gsl_spmatrix *b);
+
+/* spswap.c */
+int gsl_spmatrix_transpose(gsl_spmatrix * m);
+int gsl_spmatrix_transpose2(gsl_spmatrix * m);
+int gsl_spmatrix_transpose_memcpy(gsl_spmatrix *dest, const gsl_spmatrix *src);
+
+__END_DECLS
+
+#endif /* __GSL_SPMATRIX_H__ */
diff -Nru gsl-doc-1.16/spmatrix/Makefile.am gsl-doc-2.3/spmatrix/Makefile.am
--- gsl-doc-1.16/spmatrix/Makefile.am	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/Makefile.am	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,17 @@
+noinst_LTLIBRARIES = libgslspmatrix.la 
+
+check_PROGRAMS = test
+
+pkginclude_HEADERS = gsl_spmatrix.h
+
+libgslspmatrix_la_SOURCES = spcompress.c spcopy.c spgetset.c spio.c spmatrix.c spoper.c spprop.c spswap.c
+
+AM_CPPFLAGS = -I$(top_srcdir)
+
+noinst_HEADERS = avl.c
+
+TESTS = $(check_PROGRAMS)
+
+test_LDADD = libgslspmatrix.la ../spblas/libgslspblas.la ../test/libgsltest.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la  ../sys/libgslsys.la ../err/libgslerr.la ../utils/libutils.la ../rng/libgslrng.la
+
+test_SOURCES = test.c
diff -Nru gsl-doc-1.16/spmatrix/Makefile.in gsl-doc-2.3/spmatrix/Makefile.in
--- gsl-doc-1.16/spmatrix/Makefile.in	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/Makefile.in	2016-12-09 00:04:23.000000000 +0000
@@ -0,0 +1,1037 @@
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
+# @configure_input@
+
+# Copyright (C) 1994-2013 Free Software Foundation, Inc.
+
+# This Makefile.in is free software; the Free Software Foundation
+# gives unlimited permission to copy and/or distribute it,
+# with or without modifications, as long as this notice is preserved.
+
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY, to the extent permitted by law; without
+# even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+# PARTICULAR PURPOSE.
+
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+
+
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+	  if test -f $$file || test -d $$file; then d=.; else d=$(srcdir); fi; \
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+	-test . = "$(srcdir)" || test -z "$(CONFIG_CLEAN_VPATH_FILES)" || rm -f $(CONFIG_CLEAN_VPATH_FILES)
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+	@echo "This command is intended for maintainers to use"
+	@echo "it deletes files that may require special tools to rebuild."
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+# Tell versions [3.59,3.63) of GNU make to not export all variables.
+# Otherwise a system limit (for SysV at least) may be exceeded.
+.NOEXPORT:
diff -Nru gsl-doc-1.16/spmatrix/spcompress.c gsl-doc-2.3/spmatrix/spcompress.c
--- gsl-doc-1.16/spmatrix/spcompress.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/spcompress.c	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,198 @@
+/* spcompress.c
+ * 
+ * Copyright (C) 2012-2014, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_spmatrix.h>
+
+/*
+gsl_spmatrix_ccs()
+  Create a sparse matrix in compressed column format
+
+Inputs: T - sparse matrix in triplet format
+
+Return: pointer to new matrix (should be freed when finished with it)
+*/
+
+gsl_spmatrix *
+gsl_spmatrix_ccs(const gsl_spmatrix *T)
+{
+  if (!GSL_SPMATRIX_ISTRIPLET(T))
+    {
+      GSL_ERROR_NULL("matrix must be in triplet format", GSL_EINVAL);
+    }
+  else
+    {
+      const size_t *Tj; /* column indices of triplet matrix */
+      size_t *Cp;       /* column pointers of compressed column matrix */
+      size_t *w;        /* copy of column pointers */
+      gsl_spmatrix *m;
+      size_t n;
+
+      m = gsl_spmatrix_alloc_nzmax(T->size1, T->size2, T->nz,
+                                   GSL_SPMATRIX_CCS);
+      if (!m)
+        return NULL;
+
+      Tj = T->p;
+      Cp = m->p;
+
+      /* initialize column pointers to 0 */
+      for (n = 0; n < m->size2 + 1; ++n)
+        Cp[n] = 0;
+
+      /*
+       * compute the number of elements in each column:
+       * Cp[j] = # non-zero elements in column j
+       */
+      for (n = 0; n < T->nz; ++n)
+        Cp[Tj[n]]++;
+
+      /* compute column pointers: p[j] = p[j-1] + nnz[j-1] */
+      gsl_spmatrix_cumsum(m->size2, Cp);
+
+      /* make a copy of the column pointers */
+      w = (size_t *) m->work;
+      for (n = 0; n < m->size2; ++n)
+        w[n] = Cp[n];
+
+      /* transfer data from triplet format to CCS */
+      for (n = 0; n < T->nz; ++n)
+        {
+          size_t k = w[Tj[n]]++;
+          m->i[k] = T->i[n];
+          m->data[k] = T->data[n];
+        }
+
+      m->nz = T->nz;
+
+      return m;
+    }
+}
+
+gsl_spmatrix *
+gsl_spmatrix_compcol(const gsl_spmatrix *T)
+{
+  return gsl_spmatrix_ccs(T);
+}
+
+/*
+gsl_spmatrix_crs()
+  Create a sparse matrix in compressed row format
+
+Inputs: T - sparse matrix in triplet format
+
+Return: pointer to new matrix (should be freed when finished with it)
+*/
+
+gsl_spmatrix *
+gsl_spmatrix_crs(const gsl_spmatrix *T)
+{
+  if (!GSL_SPMATRIX_ISTRIPLET(T))
+    {
+      GSL_ERROR_NULL("matrix must be in triplet format", GSL_EINVAL);
+    }
+  else
+    {
+      const size_t *Ti; /* row indices of triplet matrix */
+      size_t *Cp;       /* row pointers of compressed row matrix */
+      size_t *w;        /* copy of column pointers */
+      gsl_spmatrix *m;
+      size_t n;
+
+      m = gsl_spmatrix_alloc_nzmax(T->size1, T->size2, T->nz,
+                                   GSL_SPMATRIX_CRS);
+      if (!m)
+        return NULL;
+
+      Ti = T->i;
+      Cp = m->p;
+
+      /* initialize row pointers to 0 */
+      for (n = 0; n < m->size1 + 1; ++n)
+        Cp[n] = 0;
+
+      /*
+       * compute the number of elements in each row:
+       * Cp[i] = # non-zero elements in row i
+       */
+      for (n = 0; n < T->nz; ++n)
+        Cp[Ti[n]]++;
+
+      /* compute row pointers: p[i] = p[i-1] + nnz[i-1] */
+      gsl_spmatrix_cumsum(m->size1, Cp);
+
+      /* make a copy of the row pointers */
+      w = (size_t *) m->work;
+      for (n = 0; n < m->size1; ++n)
+        w[n] = Cp[n];
+
+      /* transfer data from triplet format to CRS */
+      for (n = 0; n < T->nz; ++n)
+        {
+          size_t k = w[Ti[n]]++;
+          m->i[k] = T->p[n];
+          m->data[k] = T->data[n];
+        }
+
+      m->nz = T->nz;
+
+      return m;
+    }
+}
+
+/*
+gsl_spmatrix_cumsum()
+
+Compute the cumulative sum:
+
+p[j] = Sum_{k=0...j-1} c[k]
+
+0 <= j < n + 1
+
+Alternatively,
+p[0] = 0
+p[j] = p[j - 1] + c[j - 1]
+
+Inputs: n - length of input array
+        c - (input/output) array of size n + 1
+            on input, contains the n values c[k]
+            on output, contains the n + 1 values p[j]
+
+Return: success or error
+*/
+
+void
+gsl_spmatrix_cumsum(const size_t n, size_t *c)
+{
+  size_t sum = 0;
+  size_t k;
+
+  for (k = 0; k < n; ++k)
+    {
+      size_t ck = c[k];
+      c[k] = sum;
+      sum += ck;
+    }
+
+  c[n] = sum;
+} /* gsl_spmatrix_cumsum() */
diff -Nru gsl-doc-1.16/spmatrix/spcopy.c gsl-doc-2.3/spmatrix/spcopy.c
--- gsl-doc-1.16/spmatrix/spcopy.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/spcopy.c	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,109 @@
+/* spcopy.c
+ * 
+ * Copyright (C) 2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+#include <gsl/gsl_spmatrix.h>
+#include <gsl/gsl_errno.h>
+
+#include "avl.c"
+
+int
+gsl_spmatrix_memcpy(gsl_spmatrix *dest, const gsl_spmatrix *src)
+{
+  const size_t M = src->size1;
+  const size_t N = src->size2;
+
+  if (M != dest->size1 || N != dest->size2)
+    {
+      GSL_ERROR("matrix sizes are different", GSL_EBADLEN);
+    }
+  else if (dest->sptype != src->sptype)
+    {
+      GSL_ERROR("cannot copy matrices of different storage formats",
+                GSL_EINVAL);
+    }
+  else
+    {
+      int s = GSL_SUCCESS;
+      size_t n;
+
+      if (dest->nzmax < src->nz)
+        {
+          s = gsl_spmatrix_realloc(src->nz, dest);
+          if (s)
+            return s;
+        }
+
+      /* copy indices and data to dest */
+      if (GSL_SPMATRIX_ISTRIPLET(src))
+        {
+          void *ptr;
+
+          for (n = 0; n < src->nz; ++n)
+            {
+              dest->i[n] = src->i[n];
+              dest->p[n] = src->p[n];
+              dest->data[n] = src->data[n];
+
+              /* copy binary tree data */
+              ptr = avl_insert(dest->tree_data->tree, &dest->data[n]);
+              if (ptr != NULL)
+                {
+                  GSL_ERROR("detected duplicate entry", GSL_EINVAL);
+                }
+            }
+        }
+      else if (GSL_SPMATRIX_ISCCS(src))
+        {
+          for (n = 0; n < src->nz; ++n)
+            {
+              dest->i[n] = src->i[n];
+              dest->data[n] = src->data[n];
+            }
+
+          for (n = 0; n < src->size2 + 1; ++n)
+            {
+              dest->p[n] = src->p[n];
+            }
+        }
+      else if (GSL_SPMATRIX_ISCRS(src))
+        {
+          for (n = 0; n < src->nz; ++n)
+            {
+              dest->i[n] = src->i[n];
+              dest->data[n] = src->data[n];
+            }
+
+          for (n = 0; n < src->size1 + 1; ++n)
+            {
+              dest->p[n] = src->p[n];
+            }
+        }
+      else
+        {
+          GSL_ERROR("invalid matrix type for src", GSL_EINVAL);
+        }
+
+      dest->nz = src->nz;
+
+      return s;
+    }
+} /* gsl_spmatrix_memcpy() */
diff -Nru gsl-doc-1.16/spmatrix/spgetset.c gsl-doc-2.3/spmatrix/spgetset.c
--- gsl-doc-1.16/spmatrix/spgetset.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/spgetset.c	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,251 @@
+/* spgetset.c
+ * 
+ * Copyright (C) 2012 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_spmatrix.h>
+
+#include "avl.c"
+
+static void *tree_find(const gsl_spmatrix *m, const size_t i, const size_t j);
+
+double
+gsl_spmatrix_get(const gsl_spmatrix *m, const size_t i, const size_t j)
+{
+  if (i >= m->size1)
+    {
+      GSL_ERROR_VAL("first index out of range", GSL_EINVAL, 0.0);
+    }
+  else if (j >= m->size2)
+    {
+      GSL_ERROR_VAL("second index out of range", GSL_EINVAL, 0.0);
+    }
+  else
+    {
+      if (GSL_SPMATRIX_ISTRIPLET(m))
+        {
+          /* traverse binary tree to search for (i,j) element */
+          void *ptr = tree_find(m, i, j);
+          double x = ptr ? *(double *) ptr : 0.0;
+
+          return x;
+        }
+      else if (GSL_SPMATRIX_ISCCS(m))
+        {
+          const size_t *mi = m->i;
+          const size_t *mp = m->p;
+          size_t p;
+
+          /* loop over column j and search for row index i */
+          for (p = mp[j]; p < mp[j + 1]; ++p)
+            {
+              if (mi[p] == i)
+                return m->data[p];
+            }
+        }
+      else if (GSL_SPMATRIX_ISCRS(m))
+        {
+          const size_t *mj = m->i;
+          const size_t *mp = m->p;
+          size_t p;
+
+          /* loop over row i and search for column index j */
+          for (p = mp[i]; p < mp[i + 1]; ++p)
+            {
+              if (mj[p] == j)
+                return m->data[p];
+            }
+        }
+      else
+        {
+          GSL_ERROR_VAL("unknown sparse matrix type", GSL_EINVAL, 0.0);
+        }
+
+      /* element not found; return 0 */
+      return 0.0;
+    }
+} /* gsl_spmatrix_get() */
+
+/*
+gsl_spmatrix_set()
+  Add an element to a matrix in triplet form
+
+Inputs: m - spmatrix
+        i - row index
+        j - column index
+        x - matrix value
+*/
+
+int
+gsl_spmatrix_set(gsl_spmatrix *m, const size_t i, const size_t j,
+                 const double x)
+{
+  if (!GSL_SPMATRIX_ISTRIPLET(m))
+    {
+      GSL_ERROR("matrix not in triplet representation", GSL_EINVAL);
+    }
+  else if (x == 0.0)
+    {
+      /* traverse binary tree to search for (i,j) element */
+      void *ptr = tree_find(m, i, j);
+
+      /*
+       * just set the data element to 0; it would be easy to
+       * delete the node from the tree with avl_delete(), but
+       * we'd also have to delete it from the data arrays which
+       * is less simple
+       */
+      if (ptr != NULL)
+        *(double *) ptr = 0.0;
+
+      return GSL_SUCCESS;
+    }
+  else
+    {
+      int s = GSL_SUCCESS;
+      void *ptr;
+
+      /* check if matrix needs to be realloced */
+      if (m->nz >= m->nzmax)
+        {
+          s = gsl_spmatrix_realloc(2 * m->nzmax, m);
+          if (s)
+            return s;
+        }
+
+      /* store the triplet (i, j, x) */
+      m->i[m->nz] = i;
+      m->p[m->nz] = j;
+      m->data[m->nz] = x;
+
+      ptr = avl_insert(m->tree_data->tree, &m->data[m->nz]);
+      if (ptr != NULL)
+        {
+          /* found duplicate entry (i,j), replace with new x */
+          *((double *) ptr) = x;
+        }
+      else
+        {
+          /* no duplicate (i,j) found, update indices as needed */
+
+          /* increase matrix dimensions if needed */
+          m->size1 = GSL_MAX(m->size1, i + 1);
+          m->size2 = GSL_MAX(m->size2, j + 1);
+
+          ++(m->nz);
+        }
+
+      return s;
+    }
+} /* gsl_spmatrix_set() */
+
+double *
+gsl_spmatrix_ptr(gsl_spmatrix *m, const size_t i, const size_t j)
+{
+  if (i >= m->size1)
+    {
+      GSL_ERROR_NULL("first index out of range", GSL_EINVAL);
+    }
+  else if (j >= m->size2)
+    {
+      GSL_ERROR_NULL("second index out of range", GSL_EINVAL);
+    }
+  else
+    {
+      if (GSL_SPMATRIX_ISTRIPLET(m))
+        {
+          /* traverse binary tree to search for (i,j) element */
+          void *ptr = tree_find(m, i, j);
+          return (double *) ptr;
+        }
+      else if (GSL_SPMATRIX_ISCCS(m))
+        {
+          const size_t *mi = m->i;
+          const size_t *mp = m->p;
+          size_t p;
+
+          /* loop over column j and search for row index i */
+          for (p = mp[j]; p < mp[j + 1]; ++p)
+            {
+              if (mi[p] == i)
+                return &(m->data[p]);
+            }
+        }
+      else if (GSL_SPMATRIX_ISCRS(m))
+        {
+          const size_t *mj = m->i;
+          const size_t *mp = m->p;
+          size_t p;
+
+          /* loop over row i and search for column index j */
+          for (p = mp[i]; p < mp[i + 1]; ++p)
+            {
+              if (mj[p] == j)
+                return &(m->data[p]);
+            }
+        }
+      else
+        {
+          GSL_ERROR_NULL("unknown sparse matrix type", GSL_EINVAL);
+        }
+
+      /* element not found; return 0 */
+      return NULL;
+    }
+} /* gsl_spmatrix_ptr() */
+
+/*
+tree_find()
+  Find node in tree corresponding to matrix entry (i,j). Adapted
+from avl_find()
+
+Inputs: m - spmatrix
+        i - row index
+        j - column index
+
+Return: pointer to tree node data if found, NULL if not found
+*/
+
+static void *
+tree_find(const gsl_spmatrix *m, const size_t i, const size_t j)
+{
+  const struct avl_table *tree = (struct avl_table *) m->tree_data->tree;
+  const struct avl_node *p;
+
+  for (p = tree->avl_root; p != NULL; )
+    {
+      size_t n = (double *) p->avl_data - m->data;
+      size_t pi = m->i[n];
+      size_t pj = m->p[n];
+      int cmp = gsl_spmatrix_compare_idx(i, j, pi, pj);
+
+      if (cmp < 0)
+        p = p->avl_link[0];
+      else if (cmp > 0)
+        p = p->avl_link[1];
+      else /* |cmp == 0| */
+        return p->avl_data;
+    }
+
+  return NULL;
+} /* tree_find() */
diff -Nru gsl-doc-1.16/spmatrix/spio.c gsl-doc-2.3/spmatrix/spio.c
--- gsl-doc-1.16/spmatrix/spio.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/spio.c	2016-12-07 17:53:17.000000000 +0000
@@ -0,0 +1,368 @@
+/* spio.c
+ * 
+ * Copyright (C) 2016 Patrick Alken
+ * Copyright (C) 2016 Alexis Tantet
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_spmatrix.h>
+
+/*
+gsl_spmatrix_fprintf()
+  Print sparse matrix to file in MatrixMarket format:
+
+M  N  NNZ
+I1 J1 A(I1,J1)
+...
+
+Note that indices start at 1 and not 0
+*/
+
+int
+gsl_spmatrix_fprintf(FILE *stream, const gsl_spmatrix *m,
+                     const char *format)
+{
+  int status;
+
+  /* print header */
+  status = fprintf(stream, "%%%%MatrixMarket matrix coordinate real general\n");
+  if (status < 0)
+    {
+      GSL_ERROR("fprintf failed for header", GSL_EFAILED);
+    }
+
+  /* print rows,columns,nnz */
+  status = fprintf(stream, "%u\t%u\t%u\n",
+                   (unsigned int) m->size1,
+                   (unsigned int) m->size2,
+                   (unsigned int) m->nz);
+  if (status < 0)
+    {
+      GSL_ERROR("fprintf failed for dimension header", GSL_EFAILED);
+    }
+
+  if (GSL_SPMATRIX_ISTRIPLET(m))
+    {
+      size_t n;
+
+      for (n = 0; n < m->nz; ++n)
+        {
+          status = fprintf(stream, "%u\t%u\t", (unsigned int) m->i[n] + 1, (unsigned int) m->p[n] + 1);
+          if (status < 0)
+            {
+              GSL_ERROR("fprintf failed", GSL_EFAILED);
+            }
+
+          status = fprintf(stream, format, m->data[n]);
+          if (status < 0)
+            {
+              GSL_ERROR("fprintf failed", GSL_EFAILED);
+            }
+
+          status = putc('\n', stream);
+          if (status == EOF)
+            {
+              GSL_ERROR("putc failed", GSL_EFAILED);
+            }
+        }
+    }
+  else if (GSL_SPMATRIX_ISCCS(m))
+    {
+      size_t j, p;
+
+      for (j = 0; j < m->size2; ++j)
+        {
+          for (p = m->p[j]; p < m->p[j + 1]; ++p)
+            {
+              status = fprintf(stream, "%u\t%u\t", (unsigned int) m->i[p] + 1, (unsigned int) j + 1);
+              if (status < 0)
+                {
+                  GSL_ERROR("fprintf failed", GSL_EFAILED);
+                }
+
+              status = fprintf(stream, format, m->data[p]);
+              if (status < 0)
+                {
+                  GSL_ERROR("fprintf failed", GSL_EFAILED);
+                }
+
+              status = putc('\n', stream);
+              if (status == EOF)
+                {
+                  GSL_ERROR("putc failed", GSL_EFAILED);
+                }
+            }
+        }
+    }
+  else if (GSL_SPMATRIX_ISCRS(m))
+    {
+      size_t i, p;
+
+      for (i = 0; i < m->size1; ++i)
+        {
+          for (p = m->p[i]; p < m->p[i + 1]; ++p)
+            {
+              status = fprintf(stream, "%u\t%u\t", (unsigned int) i + 1, (unsigned int) m->i[p] + 1);
+              if (status < 0)
+                {
+                  GSL_ERROR("fprintf failed", GSL_EFAILED);
+                }
+
+              status = fprintf(stream, format, m->data[p]);
+              if (status < 0)
+                {
+                  GSL_ERROR("fprintf failed", GSL_EFAILED);
+                }
+
+              status = putc('\n', stream);
+              if (status == EOF)
+                {
+                  GSL_ERROR("putc failed", GSL_EFAILED);
+                }
+            }
+        }
+    }
+  else
+    {
+      GSL_ERROR("unknown sparse matrix type", GSL_EINVAL);
+    }
+
+  return GSL_SUCCESS;
+}
+
+gsl_spmatrix *
+gsl_spmatrix_fscanf(FILE *stream)
+{
+  gsl_spmatrix *m;
+  unsigned int size1, size2, nz;
+  char buf[1024];
+  int found_header = 0;
+
+  /* read file until we find rows,cols,nz header */
+  while (fgets(buf, 1024, stream) != NULL)
+    {
+      int c;
+
+      /* skip comments */
+      if (*buf == '%')
+        continue;
+
+      c = sscanf(buf, "%u %u %u",
+                 &size1, &size2, &nz);
+      if (c == 3)
+        {
+          found_header = 1;
+          break;
+        }
+    }
+
+  if (!found_header)
+    {
+      GSL_ERROR_NULL ("fscanf failed reading header", GSL_EFAILED);
+    }
+
+  m = gsl_spmatrix_alloc_nzmax((size_t) size1, (size_t) size2, (size_t) nz, GSL_SPMATRIX_TRIPLET);
+  if (!m)
+    {
+      GSL_ERROR_NULL ("error allocating m", GSL_ENOMEM);
+    }
+
+  {
+    unsigned int i, j;
+    double val;
+
+    while (fgets(buf, 1024, stream) != NULL)
+      {
+        int c = sscanf(buf, "%u %u %lg", &i, &j, &val);
+        if (c < 3 || (i == 0) || (j == 0))
+          {
+            GSL_ERROR_NULL ("error in input file format", GSL_EFAILED);
+          }
+        else if ((i > size1) || (j > size2))
+          {
+            GSL_ERROR_NULL ("element exceeds matrix dimensions", GSL_EBADLEN);
+          }
+        else
+          {
+            /* subtract 1 from (i,j) since indexing starts at 1 */
+            gsl_spmatrix_set(m, i - 1, j - 1, val);
+          }
+      }
+  }
+
+  return m;
+}
+
+int
+gsl_spmatrix_fwrite(FILE *stream, const gsl_spmatrix *m)
+{
+  size_t items;
+
+  /* write header: size1, size2, nz */
+
+  items = fwrite(&(m->size1), sizeof(size_t), 1, stream);
+  if (items != 1)
+    {
+      GSL_ERROR("fwrite failed on size1", GSL_EFAILED);
+    }
+
+  items = fwrite(&(m->size2), sizeof(size_t), 1, stream);
+  if (items != 1)
+    {
+      GSL_ERROR("fwrite failed on size2", GSL_EFAILED);
+    }
+
+  items = fwrite(&(m->nz), sizeof(size_t), 1, stream);
+  if (items != 1)
+    {
+      GSL_ERROR("fwrite failed on nz", GSL_EFAILED);
+    }
+
+  /* write m->i and m->data which are size nz in all storage formats */
+
+  items = fwrite(m->i, sizeof(size_t), m->nz, stream);
+  if (items != m->nz)
+    {
+      GSL_ERROR("fwrite failed on row indices", GSL_EFAILED);
+    }
+
+  items = fwrite(m->data, sizeof(double), m->nz, stream);
+  if (items != m->nz)
+    {
+      GSL_ERROR("fwrite failed on data", GSL_EFAILED);
+    }
+
+  if (GSL_SPMATRIX_ISTRIPLET(m))
+    {
+      items = fwrite(m->p, sizeof(size_t), m->nz, stream);
+      if (items != m->nz)
+        {
+          GSL_ERROR("fwrite failed on column indices", GSL_EFAILED);
+        }
+    }
+  else if (GSL_SPMATRIX_ISCCS(m))
+    {
+      items = fwrite(m->p, sizeof(size_t), m->size2 + 1, stream);
+      if (items != m->size2 + 1)
+        {
+          GSL_ERROR("fwrite failed on column indices", GSL_EFAILED);
+        }
+    }
+  else if (GSL_SPMATRIX_ISCRS(m))
+    {
+      items = fwrite(m->p, sizeof(size_t), m->size1 + 1, stream);
+      if (items != m->size1 + 1)
+        {
+          GSL_ERROR("fwrite failed on column indices", GSL_EFAILED);
+        }
+    }
+
+  return GSL_SUCCESS;
+}
+
+int
+gsl_spmatrix_fread(FILE *stream, gsl_spmatrix *m)
+{
+  size_t size1, size2, nz;
+  size_t items;
+
+  /* read header: size1, size2, nz */
+
+  items = fread(&size1, sizeof(size_t), 1, stream);
+  if (items != 1)
+    {
+      GSL_ERROR("fread failed on size1", GSL_EFAILED);
+    }
+
+  items = fread(&size2, sizeof(size_t), 1, stream);
+  if (items != 1)
+    {
+      GSL_ERROR("fread failed on size2", GSL_EFAILED);
+    }
+
+  items = fread(&nz, sizeof(size_t), 1, stream);
+  if (items != 1)
+    {
+      GSL_ERROR("fread failed on nz", GSL_EFAILED);
+    }
+
+  if (m->size1 != size1)
+    {
+      GSL_ERROR("matrix has wrong size1", GSL_EBADLEN);
+    }
+  else if (m->size2 != size2)
+    {
+      GSL_ERROR("matrix has wrong size2", GSL_EBADLEN);
+    }
+  else if (nz > m->nzmax)
+    {
+      GSL_ERROR("matrix nzmax is too small", GSL_EBADLEN);
+    }
+  else
+    {
+      /* read m->i and m->data arrays, which are size nz for all formats */
+
+      items = fread(m->i, sizeof(size_t), nz, stream);
+      if (items != nz)
+        {
+          GSL_ERROR("fread failed on row indices", GSL_EFAILED);
+        }
+
+      items = fread(m->data, sizeof(double), nz, stream);
+      if (items != nz)
+        {
+          GSL_ERROR("fread failed on data", GSL_EFAILED);
+        }
+
+      m->nz = nz;
+
+      if (GSL_SPMATRIX_ISTRIPLET(m))
+        {
+          items = fread(m->p, sizeof(size_t), nz, stream);
+          if (items != nz)
+            {
+              GSL_ERROR("fread failed on column indices", GSL_EFAILED);
+            }
+
+          /* build binary search tree for m */
+          gsl_spmatrix_tree_rebuild(m);
+        }
+      else if (GSL_SPMATRIX_ISCCS(m))
+        {
+          items = fread(m->p, sizeof(size_t), size2 + 1, stream);
+          if (items != size2 + 1)
+            {
+              GSL_ERROR("fread failed on row pointers", GSL_EFAILED);
+            }
+        }
+      else if (GSL_SPMATRIX_ISCRS(m))
+        {
+          items = fread(m->p, sizeof(size_t), size1 + 1, stream);
+          if (items != size1 + 1)
+            {
+              GSL_ERROR("fread failed on column pointers", GSL_EFAILED);
+            }
+        }
+    }
+
+  return GSL_SUCCESS;
+}
diff -Nru gsl-doc-1.16/spmatrix/spmatrix.c gsl-doc-2.3/spmatrix/spmatrix.c
--- gsl-doc-1.16/spmatrix/spmatrix.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/spmatrix.c	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,489 @@
+/* spmatrix.c
+ * 
+ * Copyright (C) 2012 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_spmatrix.h>
+
+#include "avl.c"
+
+static int compare_triplet(const void *pa, const void *pb, void *param);
+static void *avl_spmalloc (size_t size, void *param);
+static void avl_spfree (void *block, void *param);
+
+static struct libavl_allocator avl_allocator_spmatrix =
+{
+  avl_spmalloc,
+  avl_spfree
+};
+
+/*
+gsl_spmatrix_alloc()
+  Allocate a sparse matrix in triplet representation
+
+Inputs: n1 - number of rows
+        n2 - number of columns
+
+Notes: if (n1,n2) are not known at allocation time, they can each be
+set to 1, and they will be expanded as elements are added to the matrix
+*/
+
+gsl_spmatrix *
+gsl_spmatrix_alloc(const size_t n1, const size_t n2)
+{
+  const double density = 0.1; /* estimate */
+  size_t nzmax = (size_t) floor(n1 * n2 * density);
+
+  if (nzmax == 0)
+    nzmax = 10;
+
+  return gsl_spmatrix_alloc_nzmax(n1, n2, nzmax, GSL_SPMATRIX_TRIPLET);
+} /* gsl_spmatrix_alloc() */
+
+/*
+gsl_spmatrix_alloc_nzmax()
+  Allocate a sparse matrix with given nzmax
+
+Inputs: n1     - number of rows
+        n2     - number of columns
+        nzmax  - maximum number of matrix elements
+        sptype - type of matrix (triplet, CCS, CRS)
+
+Notes: if (n1,n2) are not known at allocation time, they can each be
+set to 1, and they will be expanded as elements are added to the matrix
+*/
+
+gsl_spmatrix *
+gsl_spmatrix_alloc_nzmax(const size_t n1, const size_t n2,
+                         const size_t nzmax, const size_t sptype)
+{
+  gsl_spmatrix *m;
+
+  if (n1 == 0)
+    {
+      GSL_ERROR_NULL ("matrix dimension n1 must be positive integer",
+                      GSL_EINVAL);
+    }
+  else if (n2 == 0)
+    {
+      GSL_ERROR_NULL ("matrix dimension n2 must be positive integer",
+                      GSL_EINVAL);
+    }
+
+  m = calloc(1, sizeof(gsl_spmatrix));
+  if (!m)
+    {
+      GSL_ERROR_NULL("failed to allocate space for spmatrix struct",
+                     GSL_ENOMEM);
+    }
+
+  m->size1 = n1;
+  m->size2 = n2;
+  m->nz = 0;
+  m->nzmax = GSL_MAX(nzmax, 1);
+  m->sptype = sptype;
+
+  m->i = malloc(m->nzmax * sizeof(size_t));
+  if (!m->i)
+    {
+      gsl_spmatrix_free(m);
+      GSL_ERROR_NULL("failed to allocate space for row indices",
+                     GSL_ENOMEM);
+    }
+
+  if (sptype == GSL_SPMATRIX_TRIPLET)
+    {
+      m->tree_data = malloc(sizeof(gsl_spmatrix_tree));
+      if (!m->tree_data)
+        {
+          gsl_spmatrix_free(m);
+          GSL_ERROR_NULL("failed to allocate space for AVL tree struct",
+                         GSL_ENOMEM);
+        }
+
+      m->tree_data->n = 0;
+
+      /* allocate tree data structure */
+      m->tree_data->tree = avl_create(compare_triplet, (void *) m,
+                                      &avl_allocator_spmatrix);
+      if (!m->tree_data->tree)
+        {
+          gsl_spmatrix_free(m);
+          GSL_ERROR_NULL("failed to allocate space for AVL tree",
+                         GSL_ENOMEM);
+        }
+
+      /* preallocate nzmax tree nodes */
+      m->tree_data->node_array = malloc(m->nzmax * sizeof(struct avl_node));
+      if (!m->tree_data->node_array)
+        {
+          gsl_spmatrix_free(m);
+          GSL_ERROR_NULL("failed to allocate space for AVL tree nodes",
+                         GSL_ENOMEM);
+        }
+
+      m->p = malloc(m->nzmax * sizeof(size_t));
+      if (!m->p)
+        {
+          gsl_spmatrix_free(m);
+          GSL_ERROR_NULL("failed to allocate space for column indices",
+                         GSL_ENOMEM);
+        }
+    }
+  else if (sptype == GSL_SPMATRIX_CCS)
+    {
+      m->p = malloc((n2 + 1) * sizeof(size_t));
+      m->work = malloc(GSL_MAX(n1, n2) *
+                       GSL_MAX(sizeof(size_t), sizeof(double)));
+      if (!m->p || !m->work)
+        {
+          gsl_spmatrix_free(m);
+          GSL_ERROR_NULL("failed to allocate space for column pointers",
+                         GSL_ENOMEM);
+        }
+    }
+  else if (sptype == GSL_SPMATRIX_CRS)
+    {
+      m->p = malloc((n1 + 1) * sizeof(size_t));
+      m->work = malloc(GSL_MAX(n1, n2) *
+                       GSL_MAX(sizeof(size_t), sizeof(double)));
+      if (!m->p || !m->work)
+        {
+          gsl_spmatrix_free(m);
+          GSL_ERROR_NULL("failed to allocate space for row pointers",
+                         GSL_ENOMEM);
+        }
+    }
+
+  m->data = malloc(m->nzmax * sizeof(double));
+  if (!m->data)
+    {
+      gsl_spmatrix_free(m);
+      GSL_ERROR_NULL("failed to allocate space for data",
+                     GSL_ENOMEM);
+    }
+
+  return m;
+} /* gsl_spmatrix_alloc_nzmax() */
+
+/*
+gsl_spmatrix_free()
+  Free sparse matrix object
+*/
+
+void
+gsl_spmatrix_free(gsl_spmatrix *m)
+{
+  if (m->i)
+    free(m->i);
+
+  if (m->p)
+    free(m->p);
+
+  if (m->data)
+    free(m->data);
+
+  if (m->work)
+    free(m->work);
+
+  if (m->tree_data)
+    {
+      if (m->tree_data->tree)
+        avl_destroy(m->tree_data->tree, NULL);
+
+      if (m->tree_data->node_array)
+        free(m->tree_data->node_array);
+
+      free(m->tree_data);
+    }
+
+  free(m);
+} /* gsl_spmatrix_free() */
+
+/*
+gsl_spmatrix_realloc()
+  As elements are added to the sparse matrix, its possible that they
+will exceed the previously specified nzmax - reallocate the matrix
+with a new nzmax
+*/
+
+int
+gsl_spmatrix_realloc(const size_t nzmax, gsl_spmatrix *m)
+{
+  int s = GSL_SUCCESS;
+  void *ptr;
+
+  if (nzmax < m->nz)
+    {
+      GSL_ERROR("new nzmax is less than current nz", GSL_EINVAL);
+    }
+
+  ptr = realloc(m->i, nzmax * sizeof(size_t));
+  if (!ptr)
+    {
+      GSL_ERROR("failed to allocate space for row indices", GSL_ENOMEM);
+    }
+
+  m->i = (size_t *) ptr;
+
+  if (GSL_SPMATRIX_ISTRIPLET(m))
+    {
+      ptr = realloc(m->p, nzmax * sizeof(size_t));
+      if (!ptr)
+        {
+          GSL_ERROR("failed to allocate space for column indices", GSL_ENOMEM);
+        }
+
+      m->p = (size_t *) ptr;
+    }
+
+  ptr = realloc(m->data, nzmax * sizeof(double));
+  if (!ptr)
+    {
+      GSL_ERROR("failed to allocate space for data", GSL_ENOMEM);
+    }
+
+  m->data = (double *) ptr;
+
+  /* rebuild binary tree */
+  if (GSL_SPMATRIX_ISTRIPLET(m))
+    {
+      size_t n;
+
+      /* reset tree to empty state, but don't free root tree ptr */
+      avl_empty(m->tree_data->tree, NULL);
+      m->tree_data->n = 0;
+
+      ptr = realloc(m->tree_data->node_array, nzmax * sizeof(struct avl_node));
+      if (!ptr)
+        {
+          GSL_ERROR("failed to allocate space for AVL tree nodes", GSL_ENOMEM);
+        }
+
+      m->tree_data->node_array = ptr;
+
+      /*
+       * need to reinsert all tree elements since the m->data addresses
+       * have changed
+       */
+      for (n = 0; n < m->nz; ++n)
+        {
+          ptr = avl_insert(m->tree_data->tree, &m->data[n]);
+          if (ptr != NULL)
+            {
+              GSL_ERROR("detected duplicate entry", GSL_EINVAL);
+            }
+        }
+    }
+
+  /* update to new nzmax */
+  m->nzmax = nzmax;
+
+  return s;
+} /* gsl_spmatrix_realloc() */
+
+int
+gsl_spmatrix_set_zero(gsl_spmatrix *m)
+{
+  m->nz = 0;
+
+  if (GSL_SPMATRIX_ISTRIPLET(m))
+    {
+      /* reset tree to empty state and node index pointer to 0 */
+      avl_empty(m->tree_data->tree, NULL);
+      m->tree_data->n = 0;
+    }
+
+  return GSL_SUCCESS;
+} /* gsl_spmatrix_set_zero() */
+
+size_t
+gsl_spmatrix_nnz(const gsl_spmatrix *m)
+{
+  return m->nz;
+} /* gsl_spmatrix_nnz() */
+
+/*
+gsl_spmatrix_compare_idx()
+  Comparison function for searching binary tree in triplet
+representation.
+
+To detect duplicate elements in the tree, we want to determine
+if there already exists an entry for (i,j) in the tree. Since
+the actual tree node stores only the data elements data[n],
+we will do pointer arithmetic to get from the given data[n]
+to the row/column indices i[n] and j[n].
+
+This compare function will sort the tree first by row i,
+and for equal rows, it will then sort by column j
+
+Inputs: ia - row index of element a
+        ja - column index of element a
+        ib - row index of element b
+        jb - column index of element b
+
+Return:
+  -1 if pa < pb: (ia,ja) < (ib,jb)
+  +1 if pa > pb: (ia,ja) > (ib,jb)
+   0 if pa = pb: (ia,ja) == (ib,jb)
+*/
+
+int
+gsl_spmatrix_compare_idx(const size_t ia, const size_t ja,
+                         const size_t ib, const size_t jb)
+{
+  if (ia < ib)
+    return -1;
+  else if (ia > ib)
+    return 1;
+  else
+    {
+      /* row indices are equal, sort by column index */
+      if (ja < jb)
+        return -1;
+      else if (ja > jb)
+        return 1;
+      else
+        return 0; /* row and column indices are equal */
+    }
+}
+
+/*
+gsl_spmatrix_tree_rebuild()
+  When reading a triplet matrix from disk, or when
+copying a triplet matrix, it is necessary to rebuild the
+binary tree for element searches.
+
+Inputs: m - triplet matrix
+*/
+
+int
+gsl_spmatrix_tree_rebuild(gsl_spmatrix * m)
+{
+  if (!GSL_SPMATRIX_ISTRIPLET(m))
+    {
+      GSL_ERROR("m must be in triplet format", GSL_EINVAL);
+    }
+  else
+    {
+      size_t n;
+
+      /* reset tree to empty state, but don't free root tree ptr */
+      avl_empty(m->tree_data->tree, NULL);
+      m->tree_data->n = 0;
+
+      /* insert all tree elements */
+      for (n = 0; n < m->nz; ++n)
+        {
+          void *ptr = avl_insert(m->tree_data->tree, &m->data[n]);
+          if (ptr != NULL)
+            {
+              GSL_ERROR("detected duplicate entry", GSL_EINVAL);
+            }
+        }
+
+      return GSL_SUCCESS;
+    }
+}
+
+/*
+compare_triplet()
+  Comparison function for searching binary tree in triplet
+representation.
+
+To detect duplicate elements in the tree, we want to determine
+if there already exists an entry for (i,j) in the tree. Since
+the actual tree node stores only the data elements data[n],
+we will do pointer arithmetic to get from the given data[n]
+to the row/column indices i[n] and j[n].
+
+This compare function will sort the tree first by row i,
+and for equal rows, it will then sort by column j
+
+Inputs: pa    - element 1 for comparison (double *) 
+        pb    - element 2 for comparison (double *)
+        param - parameter (gsl_spmatrix)
+
+Return:
+  -1 if pa < pb: (ia,ja) < (ib,jb)
+  +1 if pa > pb: (ia,ja) > (ib,jb)
+   0 if pa = pb: (ia,ja) == (ib,jb)
+*/
+
+static int
+compare_triplet(const void *pa, const void *pb, void *param)
+{
+  gsl_spmatrix *m = (gsl_spmatrix *) param;
+
+  /* pointer arithmetic to find indices in data array */
+  const size_t idxa = (const double *) pa - m->data;
+  const size_t idxb = (const double *) pb - m->data;
+
+  return gsl_spmatrix_compare_idx(m->i[idxa], m->p[idxa],
+                                  m->i[idxb], m->p[idxb]);
+} /* compare_triplet() */
+
+static void *
+avl_spmalloc (size_t size, void *param)
+{
+  gsl_spmatrix *m = (gsl_spmatrix *) param;
+
+  if (size != sizeof(struct avl_node))
+    {
+      GSL_ERROR_NULL("attemping to allocate incorrect node size", GSL_EBADLEN);
+    }
+
+  /*
+   * return the next available avl_node slot; index
+   * m->tree_data->n keeps track of next open slot
+   */
+  if (m->tree_data->n < m->nzmax)
+    {
+      /* cast to char* for pointer arithmetic */
+      unsigned char *node_ptr = (unsigned char *) m->tree_data->node_array;
+
+      /* offset in bytes for next node slot */
+      size_t offset = (m->tree_data->n)++ * sizeof(struct avl_node);
+
+      return node_ptr + offset;
+    }
+  else
+    {
+      /*
+       * we should never get here - gsl_spmatrix_realloc() should
+       * be called before exceeding nzmax nodes
+       */
+      GSL_ERROR_NULL("attemping to allocate tree node past nzmax", GSL_EINVAL);
+    }
+}
+
+static void
+avl_spfree (void *block, void *param)
+{
+  (void)block;
+  (void)param;
+  /*
+   * do nothing - instead of allocating/freeing individual nodes,
+   * we malloc and free nzmax nodes at a time
+   */
+}
diff -Nru gsl-doc-1.16/spmatrix/spoper.c gsl-doc-2.3/spmatrix/spoper.c
--- gsl-doc-1.16/spmatrix/spoper.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/spoper.c	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,234 @@
+/* spoper.c
+ * 
+ * Copyright (C) 2012 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_spmatrix.h>
+#include <gsl/gsl_spblas.h>
+
+int
+gsl_spmatrix_scale(gsl_spmatrix *m, const double x)
+{
+  size_t i;
+
+  for (i = 0; i < m->nz; ++i)
+    m->data[i] *= x;
+
+  return GSL_SUCCESS;
+} /* gsl_spmatrix_scale() */
+
+int
+gsl_spmatrix_minmax(const gsl_spmatrix *m, double *min_out, double *max_out)
+{
+  double min, max;
+  size_t n;
+
+  if (m->nz == 0)
+    {
+      GSL_ERROR("matrix is empty", GSL_EINVAL);
+    }
+
+  min = m->data[0];
+  max = m->data[0];
+
+  for (n = 1; n < m->nz; ++n)
+    {
+      double x = m->data[n];
+
+      if (x < min)
+        min = x;
+
+      if (x > max)
+        max = x;
+    }
+
+  *min_out = min;
+  *max_out = max;
+
+  return GSL_SUCCESS;
+} /* gsl_spmatrix_minmax() */
+
+/*
+gsl_spmatrix_add()
+  Add two sparse matrices
+
+Inputs: c - (output) a + b
+        a - (input) sparse matrix
+        b - (input) sparse matrix
+
+Return: success or error
+*/
+
+int
+gsl_spmatrix_add(gsl_spmatrix *c, const gsl_spmatrix *a,
+                 const gsl_spmatrix *b)
+{
+  const size_t M = a->size1;
+  const size_t N = a->size2;
+
+  if (b->size1 != M || b->size2 != N || c->size1 != M || c->size2 != N)
+    {
+      GSL_ERROR("matrices must have same dimensions", GSL_EBADLEN);
+    }
+  else if (a->sptype != b->sptype || a->sptype != c->sptype)
+    {
+      GSL_ERROR("matrices must have same sparse storage format",
+                GSL_EINVAL);
+    }
+  else if (GSL_SPMATRIX_ISTRIPLET(a))
+    {
+      GSL_ERROR("triplet format not yet supported", GSL_EINVAL);
+    }
+  else
+    {
+      int status = GSL_SUCCESS;
+      size_t *w = (size_t *) a->work;
+      double *x = (double *) b->work;
+      size_t *Cp, *Ci;
+      double *Cd;
+      size_t j, p;
+      size_t nz = 0; /* number of non-zeros in c */
+      size_t inner_size, outer_size;
+
+      if (GSL_SPMATRIX_ISCCS(a))
+        {
+          inner_size = M;
+          outer_size = N;
+        }
+      else if (GSL_SPMATRIX_ISCRS(a))
+        {
+          inner_size = N;
+          outer_size = M;
+        }
+      else
+        {
+          GSL_ERROR("unknown sparse matrix type", GSL_EINVAL);
+        }
+
+      if (c->nzmax < a->nz + b->nz)
+        {
+          status = gsl_spmatrix_realloc(a->nz + b->nz, c);
+          if (status)
+            return status;
+        }
+
+      /* initialize w = 0 */
+      for (j = 0; j < inner_size; ++j)
+        w[j] = 0;
+
+      Ci = c->i;
+      Cp = c->p;
+      Cd = c->data;
+
+      for (j = 0; j < outer_size; ++j)
+        {
+          Cp[j] = nz;
+
+          /* CCS: x += A(:,j); CRS: x += A(j,:) */
+          nz = gsl_spblas_scatter(a, j, 1.0, w, x, j + 1, c, nz);
+
+          /* CCS: x += B(:,j); CRS: x += B(j,:) */
+          nz = gsl_spblas_scatter(b, j, 1.0, w, x, j + 1, c, nz);
+
+          for (p = Cp[j]; p < nz; ++p)
+            Cd[p] = x[Ci[p]];
+        }
+
+      /* finalize last column of c */
+      Cp[j] = nz;
+      c->nz = nz;
+
+      return status;
+    }
+} /* gsl_spmatrix_add() */
+
+/*
+gsl_spmatrix_d2sp()
+  Convert a dense gsl_matrix to sparse (triplet) format
+
+Inputs: S - (output) sparse matrix in triplet format
+        A - (input) dense matrix to convert
+*/
+
+int
+gsl_spmatrix_d2sp(gsl_spmatrix *S, const gsl_matrix *A)
+{
+  int s = GSL_SUCCESS;
+  size_t i, j;
+
+  gsl_spmatrix_set_zero(S);
+  S->size1 = A->size1;
+  S->size2 = A->size2;
+
+  for (i = 0; i < A->size1; ++i)
+    {
+      for (j = 0; j < A->size2; ++j)
+        {
+          double x = gsl_matrix_get(A, i, j);
+
+          if (x != 0.0)
+            gsl_spmatrix_set(S, i, j, x);
+        }
+    }
+
+  return s;
+} /* gsl_spmatrix_d2sp() */
+
+/*
+gsl_spmatrix_sp2d()
+  Convert a sparse matrix to dense format
+*/
+
+int
+gsl_spmatrix_sp2d(gsl_matrix *A, const gsl_spmatrix *S)
+{
+  if (A->size1 != S->size1 || A->size2 != S->size2)
+    {
+      GSL_ERROR("matrix sizes do not match", GSL_EBADLEN);
+    }
+  else
+    {
+      gsl_matrix_set_zero(A);
+
+      if (GSL_SPMATRIX_ISTRIPLET(S))
+        {
+          size_t n;
+
+          for (n = 0; n < S->nz; ++n)
+            {
+              size_t i = S->i[n];
+              size_t j = S->p[n];
+              double x = S->data[n];
+
+              gsl_matrix_set(A, i, j, x);
+            }
+        }
+      else
+        {
+          GSL_ERROR("non-triplet formats not yet supported", GSL_EINVAL);
+        }
+
+      return GSL_SUCCESS;
+    }
+} /* gsl_spmatrix_sp2d() */
diff -Nru gsl-doc-1.16/spmatrix/spprop.c gsl-doc-2.3/spmatrix/spprop.c
--- gsl-doc-1.16/spmatrix/spprop.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/spprop.c	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,116 @@
+/* spprop.c
+ * 
+ * Copyright (C) 2014 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+
+#include <gsl/gsl_spmatrix.h>
+#include <gsl/gsl_errno.h>
+
+/*
+gsl_spmatrix_equal()
+  Return 1 if a = b, 0 otherwise
+*/
+
+int
+gsl_spmatrix_equal(const gsl_spmatrix *a, const gsl_spmatrix *b)
+{
+  const size_t M = a->size1;
+  const size_t N = a->size2;
+
+  if (b->size1 != M || b->size2 != N)
+    {
+      GSL_ERROR_VAL("matrices must have same dimensions", GSL_EBADLEN, 0);
+    }
+  else if (a->sptype != b->sptype)
+    {
+      GSL_ERROR_VAL("trying to compare different sparse matrix types", GSL_EINVAL, 0);
+    }
+  else
+    {
+      const size_t nz = a->nz;
+      size_t n;
+
+      if (nz != b->nz)
+        return 0; /* different number of non-zero elements */
+
+      if (GSL_SPMATRIX_ISTRIPLET(a))
+        {
+          /*
+           * triplet formats could be out of order but identical, so use
+           * gsl_spmatrix_get() on b for each aij
+           */
+          for (n = 0; n < nz; ++n)
+            {
+              double bij = gsl_spmatrix_get(b, a->i[n], a->p[n]);
+
+              if (a->data[n] != bij)
+                return 0;
+            }
+        }
+      else if (GSL_SPMATRIX_ISCCS(a))
+        {
+          /*
+           * for CCS, both matrices should have everything
+           * in the same order
+           */
+
+          /* check row indices and data */
+          for (n = 0; n < nz; ++n)
+            {
+              if ((a->i[n] != b->i[n]) || (a->data[n] != b->data[n]))
+                return 0;
+            }
+
+          /* check column pointers */
+          for (n = 0; n < a->size2 + 1; ++n)
+            {
+              if (a->p[n] != b->p[n])
+                return 0;
+            }
+        }
+      else if (GSL_SPMATRIX_ISCRS(a))
+        {
+          /*
+           * for CRS, both matrices should have everything
+           * in the same order
+           */
+
+          /* check column indices and data */
+          for (n = 0; n < nz; ++n)
+            {
+              if ((a->i[n] != b->i[n]) || (a->data[n] != b->data[n]))
+                return 0;
+            }
+
+          /* check row pointers */
+          for (n = 0; n < a->size1 + 1; ++n)
+            {
+              if (a->p[n] != b->p[n])
+                return 0;
+            }
+        }
+      else
+        {
+          GSL_ERROR_VAL("unknown sparse matrix type", GSL_EINVAL, 0);
+        }
+
+      return 1;
+    }
+} /* gsl_spmatrix_equal() */
diff -Nru gsl-doc-1.16/spmatrix/spswap.c gsl-doc-2.3/spmatrix/spswap.c
--- gsl-doc-1.16/spmatrix/spswap.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/spswap.c	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,243 @@
+/* spswap.c
+ * 
+ * Copyright (C) 2014 Patrick Alken
+ * Copyright (C) 2016 Alexis Tantet
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_spmatrix.h>
+
+#include "avl.c"
+
+/*
+gsl_spmatrix_transpose()
+  Replace the sparse matrix src by its transpose,
+keeping the matrix in the same storage format
+
+Inputs: A - (input/output) sparse matrix to transpose.
+*/
+
+int
+gsl_spmatrix_transpose(gsl_spmatrix * m)
+{
+  if (GSL_SPMATRIX_ISTRIPLET(m))
+    {
+      size_t n;
+
+      /* swap row/column indices */
+      for (n = 0; n < m->nz; ++n)
+        {
+          size_t tmp = m->p[n];
+          m->p[n] = m->i[n];
+          m->i[n] = tmp;
+        }
+
+      /* need to rebuild AVL tree, or element searches won't
+       * work correctly with transposed indices */
+      gsl_spmatrix_tree_rebuild(m);
+    }
+  else
+    {
+      GSL_ERROR("unknown sparse matrix type", GSL_EINVAL);
+    }
+  
+  /* swap dimensions */
+  if (m->size1 != m->size2)
+    {
+      size_t tmp = m->size1;
+      m->size1 = m->size2;
+      m->size2 = tmp;
+    }
+  
+  return GSL_SUCCESS;
+}
+
+/*
+gsl_spmatrix_transpose2()
+  Replace the sparse matrix src by its transpose either by
+  swapping its row and column indices if it is in triplet storage,
+  or by switching its major if it is in compressed storage.
+
+Inputs: A - (input/output) sparse matrix to transpose.
+*/
+
+int
+gsl_spmatrix_transpose2(gsl_spmatrix * m)
+{
+  if (GSL_SPMATRIX_ISTRIPLET(m))
+    {
+      return gsl_spmatrix_transpose(m);
+    }
+  else if (GSL_SPMATRIX_ISCCS(m))
+    {
+      m->sptype = GSL_SPMATRIX_CRS;
+    }
+  else if (GSL_SPMATRIX_ISCRS(m))
+    {
+      m->sptype = GSL_SPMATRIX_CCS;
+    }
+  else
+    {
+      GSL_ERROR("unknown sparse matrix type", GSL_EINVAL);
+    }
+  
+  /* swap dimensions */
+  if (m->size1 != m->size2)
+    {
+      size_t tmp = m->size1;
+      m->size1 = m->size2;
+      m->size2 = tmp;
+    }
+  
+  return GSL_SUCCESS;
+}
+
+int
+gsl_spmatrix_transpose_memcpy(gsl_spmatrix *dest, const gsl_spmatrix *src)
+{
+  const size_t M = src->size1;
+  const size_t N = src->size2;
+
+  if (M != dest->size2 || N != dest->size1)
+    {
+      GSL_ERROR("dimensions of dest must be transpose of src matrix",
+                GSL_EBADLEN);
+    }
+  else if (dest->sptype != src->sptype)
+    {
+      GSL_ERROR("cannot copy matrices of different storage formats",
+                GSL_EINVAL);
+    }
+  else
+    {
+      int s = GSL_SUCCESS;
+      const size_t nz = src->nz;
+
+      if (dest->nzmax < src->nz)
+        {
+          s = gsl_spmatrix_realloc(src->nz, dest);
+          if (s)
+            return s;
+        }
+
+      if (GSL_SPMATRIX_ISTRIPLET(src))
+        {
+          size_t n;
+          void *ptr;
+
+          for (n = 0; n < nz; ++n)
+            {
+              dest->i[n] = src->p[n];
+              dest->p[n] = src->i[n];
+              dest->data[n] = src->data[n];
+
+              /* copy binary tree data */
+              ptr = avl_insert(dest->tree_data->tree, &dest->data[n]);
+              if (ptr != NULL)
+                {
+                  GSL_ERROR("detected duplicate entry", GSL_EINVAL);
+                }
+            }
+        }
+      else if (GSL_SPMATRIX_ISCCS(src))
+        {
+          size_t *Ai = src->i;
+          size_t *Ap = src->p;
+          double *Ad = src->data;
+          size_t *ATi = dest->i;
+          size_t *ATp = dest->p;
+          double *ATd = dest->data;
+          size_t *w = (size_t *) dest->work;
+          size_t p, j;
+
+          /* initialize to 0 */
+          for (p = 0; p < M + 1; ++p)
+            ATp[p] = 0;
+
+          /* compute row counts of A (= column counts for A^T) */
+          for (p = 0; p < nz; ++p)
+            ATp[Ai[p]]++;
+
+          /* compute row pointers for A (= column pointers for A^T) */
+          gsl_spmatrix_cumsum(M, ATp);
+
+          /* make copy of row pointers */
+          for (j = 0; j < M; ++j)
+            w[j] = ATp[j];
+
+          for (j = 0; j < N; ++j)
+            {
+              for (p = Ap[j]; p < Ap[j + 1]; ++p)
+                {
+                  size_t k = w[Ai[p]]++;
+                  ATi[k] = j;
+                  ATd[k] = Ad[p];
+                }
+            }
+        }
+      else if (GSL_SPMATRIX_ISCRS(src))
+        {
+          size_t *Aj = src->i;
+          size_t *Ap = src->p;
+          double *Ad = src->data;
+          size_t *ATj = dest->i;
+          size_t *ATp = dest->p;
+          double *ATd = dest->data;
+          size_t *w = (size_t *) dest->work;
+          size_t p, i;
+
+          /* initialize to 0 */
+          for (p = 0; p < N + 1; ++p)
+            ATp[p] = 0;
+
+          /* compute column counts of A (= row counts for A^T) */
+          for (p = 0; p < nz; ++p)
+            ATp[Aj[p]]++;
+
+          /* compute column pointers for A (= row pointers for A^T) */
+          gsl_spmatrix_cumsum(N, ATp);
+
+          /* make copy of column pointers */
+          for (i = 0; i < N; ++i)
+            w[i] = ATp[i];
+
+          for (i = 0; i < M; ++i)
+            {
+              for (p = Ap[i]; p < Ap[i + 1]; ++p)
+                {
+                  size_t k = w[Aj[p]]++;
+                  ATj[k] = i;
+                  ATd[k] = Ad[p];
+                }
+            }
+        }
+      else
+        {
+          GSL_ERROR("unknown sparse matrix type", GSL_EINVAL);
+        }
+
+      dest->nz = nz;
+
+      return s;
+    }
+} /* gsl_spmatrix_transpose_memcpy() */
diff -Nru gsl-doc-1.16/spmatrix/test.c gsl-doc-2.3/spmatrix/test.c
--- gsl-doc-1.16/spmatrix/test.c	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/test.c	2016-12-07 17:47:52.000000000 +0000
@@ -0,0 +1,756 @@
+/* test.c
+ * 
+ * Copyright (C) 2012-2014, 2016 Patrick Alken
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <stdlib.h>
+#include <math.h>
+#include <unistd.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_randist.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_test.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_spmatrix.h>
+
+/*
+create_random_sparse()
+  Create a random sparse matrix with approximately
+M*N*density non-zero entries
+
+Inputs: M       - number of rows
+        N       - number of columns
+        density - sparse density \in [0,1]
+                  0 = no non-zero entries
+                  1 = all m*n entries are filled
+        r       - random number generator
+
+Return: pointer to sparse matrix in triplet format (must be freed by caller)
+
+Notes:
+1) non-zero matrix entries are uniformly distributed in [0,1]
+*/
+
+static gsl_spmatrix *
+create_random_sparse(const size_t M, const size_t N, const double density,
+                     const gsl_rng *r)
+{
+  size_t nnzwanted = (size_t) floor(M * N * GSL_MIN(density, 1.0));
+  gsl_spmatrix *m = gsl_spmatrix_alloc_nzmax(M, N,
+                                             nnzwanted,
+                                             GSL_SPMATRIX_TRIPLET);
+
+  while (gsl_spmatrix_nnz(m) < nnzwanted)
+    {
+      /* generate a random row and column */
+      size_t i = gsl_rng_uniform(r) * M;
+      size_t j = gsl_rng_uniform(r) * N;
+
+      /* generate random m_{ij} and add it */
+      double x = gsl_rng_uniform(r);
+      gsl_spmatrix_set(m, i, j, x);
+    }
+
+  return m;
+} /* create_random_sparse() */
+
+static gsl_spmatrix *
+create_random_sparse_int(const size_t M, const size_t N, const double density,
+                         const gsl_rng *r)
+{
+  const double lower = 1.0;
+  const double upper = 10.0;
+  size_t nnzwanted = (size_t) floor(M * N * GSL_MIN(density, 1.0));
+  gsl_spmatrix *m = gsl_spmatrix_alloc_nzmax(M, N,
+                                             nnzwanted,
+                                             GSL_SPMATRIX_TRIPLET);
+
+  while (gsl_spmatrix_nnz(m) < nnzwanted)
+    {
+      /* generate a random row and column */
+      size_t i = gsl_rng_uniform(r) * M;
+      size_t j = gsl_rng_uniform(r) * N;
+
+      /* generate random m_{ij} and add it */
+      int x = (int) (gsl_rng_uniform(r) * (upper - lower) + lower);
+      gsl_spmatrix_set(m, i, j, (double) x);
+    }
+
+  return m;
+}
+
+static void
+test_getset(const size_t M, const size_t N,
+            const double density, const gsl_rng *r)
+{
+  int status;
+  size_t i, j;
+
+  /* test triplet versions of _get and _set */
+  {
+    const double val = 0.75;
+    size_t k = 0;
+    gsl_spmatrix *m = gsl_spmatrix_alloc(M, N);
+
+    status = 0;
+    for (i = 0; i < M; ++i)
+      {
+        for (j = 0; j < N; ++j)
+          {
+            double x = (double) ++k;
+            double y;
+
+            gsl_spmatrix_set(m, i, j, x);
+            y = gsl_spmatrix_get(m, i, j);
+            if (x != y)
+              status = 1;
+          }
+      }
+
+    gsl_test(status, "test_getset: M=%zu N=%zu _get != _set", M, N);
+
+    /* test setting an element to 0 */
+    gsl_spmatrix_set(m, 0, 0, 1.0);
+    gsl_spmatrix_set(m, 0, 0, 0.0);
+
+    status = gsl_spmatrix_get(m, 0, 0) != 0.0;
+    gsl_test(status, "test_getset: M=%zu N=%zu m(0,0) = %f",
+             M, N, gsl_spmatrix_get(m, 0, 0));
+
+    /* test gsl_spmatrix_set_zero() */
+    gsl_spmatrix_set(m, 0, 0, 1.0);
+    gsl_spmatrix_set_zero(m);
+    status = gsl_spmatrix_get(m, 0, 0) != 0.0;
+    gsl_test(status, "test_getset: M=%zu N=%zu set_zero m(0,0) = %f",
+             M, N, gsl_spmatrix_get(m, 0, 0));
+
+    /* resassemble matrix to ensure nz is calculated correctly */
+    k = 0;
+    for (i = 0; i < M; ++i)
+      {
+        for (j = 0; j < N; ++j)
+          {
+            double x = (double) ++k;
+            gsl_spmatrix_set(m, i, j, x);
+          }
+      }
+
+    status = gsl_spmatrix_nnz(m) != M * N;
+    gsl_test(status, "test_getset: M=%zu N=%zu set_zero nz = %zu",
+             M, N, gsl_spmatrix_nnz(m));
+
+    /* test gsl_spmatrix_ptr() */
+    status = 0;
+    for (i = 0; i < M; ++i)
+      {
+        for (j = 0; j < N; ++j)
+          {
+            double mij = gsl_spmatrix_get(m, i, j);
+            double *ptr = gsl_spmatrix_ptr(m, i, j);
+
+            *ptr += val;
+            if (gsl_spmatrix_get(m, i, j) != mij + val)
+              status = 2;
+          }
+      }
+
+    gsl_test(status == 2, "test_getset: M=%zu N=%zu triplet ptr", M, N);
+
+    gsl_spmatrix_free(m);
+  }
+
+  /* test duplicate values are handled correctly */
+  {
+    size_t min = GSL_MIN(M, N);
+    size_t expected_nnz = min;
+    size_t nnz;
+    size_t k = 0;
+    gsl_spmatrix *m = gsl_spmatrix_alloc(M, N);
+
+    status = 0;
+    for (i = 0; i < min; ++i)
+      {
+        for (j = 0; j < 5; ++j)
+          {
+            double x = (double) ++k;
+            double y;
+
+            gsl_spmatrix_set(m, i, i, x);
+            y = gsl_spmatrix_get(m, i, i);
+            if (x != y)
+              status = 1;
+          }
+      }
+
+    gsl_test(status, "test_getset: duplicate test M=%zu N=%zu _get != _set", M, N);
+
+    nnz = gsl_spmatrix_nnz(m);
+    status = nnz != expected_nnz;
+    gsl_test(status, "test_getset: duplicate test M=%zu N=%zu nnz=%zu, expected=%zu",
+             M, N, nnz, expected_nnz);
+
+    gsl_spmatrix_free(m);
+  }
+
+  /* test CCS version of gsl_spmatrix_get() */
+  {
+    const double val = 0.75;
+    gsl_spmatrix *T = create_random_sparse(M, N, density, r);
+    gsl_spmatrix *C = gsl_spmatrix_ccs(T);
+
+    status = 0;
+    for (i = 0; i < M; ++i)
+      {
+        for (j = 0; j < N; ++j)
+          {
+            double Tij = gsl_spmatrix_get(T, i, j);
+            double Cij = gsl_spmatrix_get(C, i, j);
+            double *ptr = gsl_spmatrix_ptr(C, i, j);
+
+            if (Tij != Cij)
+              status = 1;
+
+            if (ptr)
+              {
+                *ptr += val;
+                Cij = gsl_spmatrix_get(C, i, j);
+                if (Tij + val != Cij)
+                  status = 2;
+              }
+          }
+      }
+
+    gsl_test(status == 1, "test_getset: M=%zu N=%zu CCS get", M, N);
+    gsl_test(status == 2, "test_getset: M=%zu N=%zu CCS ptr", M, N);
+
+    gsl_spmatrix_free(T);
+    gsl_spmatrix_free(C);
+  }
+
+  /* test CRS version of gsl_spmatrix_get() */
+  {
+    const double val = 0.75;
+    gsl_spmatrix *T = create_random_sparse(M, N, density, r);
+    gsl_spmatrix *C = gsl_spmatrix_crs(T);
+
+    status = 0;
+    for (i = 0; i < M; ++i)
+      {
+        for (j = 0; j < N; ++j)
+          {
+            double Tij = gsl_spmatrix_get(T, i, j);
+            double Cij = gsl_spmatrix_get(C, i, j);
+            double *ptr = gsl_spmatrix_ptr(C, i, j);
+
+            if (Tij != Cij)
+              status = 1;
+
+            if (ptr)
+              {
+                *ptr += val;
+                Cij = gsl_spmatrix_get(C, i, j);
+                if (Tij + val != Cij)
+                  status = 2;
+              }
+          }
+      }
+
+    gsl_test(status == 1, "test_getset: M=%zu N=%zu CRS get", M, N);
+    gsl_test(status == 2, "test_getset: M=%zu N=%zu CRS ptr", M, N);
+
+    gsl_spmatrix_free(T);
+    gsl_spmatrix_free(C);
+  }
+} /* test_getset() */
+
+static void
+test_memcpy(const size_t M, const size_t N,
+            const double density, const gsl_rng *r)
+{
+  int status;
+
+  {
+    gsl_spmatrix *A = create_random_sparse(M, N, density, r);
+    gsl_spmatrix *A_ccs = gsl_spmatrix_ccs(A);
+    gsl_spmatrix *A_crs = gsl_spmatrix_crs(A);
+    gsl_spmatrix *B_t, *B_ccs, *B_crs;
+  
+    B_t = gsl_spmatrix_alloc(M, N);
+    gsl_spmatrix_memcpy(B_t, A);
+
+    status = gsl_spmatrix_equal(A, B_t) != 1;
+    gsl_test(status, "test_memcpy: _memcpy M=%zu N=%zu triplet format", M, N);
+
+    B_ccs = gsl_spmatrix_alloc_nzmax(M, N, A_ccs->nzmax, GSL_SPMATRIX_CCS);
+    B_crs = gsl_spmatrix_alloc_nzmax(M, N, A_ccs->nzmax, GSL_SPMATRIX_CRS);
+
+    gsl_spmatrix_memcpy(B_ccs, A_ccs);
+    gsl_spmatrix_memcpy(B_crs, A_crs);
+
+    status = gsl_spmatrix_equal(A_ccs, B_ccs) != 1;
+    gsl_test(status, "test_memcpy: _memcpy M=%zu N=%zu CCS", M, N);
+
+    status = gsl_spmatrix_equal(A_crs, B_crs) != 1;
+    gsl_test(status, "test_memcpy: _memcpy M=%zu N=%zu CRS", M, N);
+
+    gsl_spmatrix_free(A);
+    gsl_spmatrix_free(A_ccs);
+    gsl_spmatrix_free(A_crs);
+    gsl_spmatrix_free(B_t);
+    gsl_spmatrix_free(B_ccs);
+    gsl_spmatrix_free(B_crs);
+  }
+
+  /* test transpose_memcpy */
+  {
+    gsl_spmatrix *A = create_random_sparse(M, N, density, r);
+    gsl_spmatrix *AT = gsl_spmatrix_alloc(N, M);
+    gsl_spmatrix *B = gsl_spmatrix_ccs(A);
+    gsl_spmatrix *BT = gsl_spmatrix_alloc_nzmax(N, M, 1, GSL_SPMATRIX_CCS);
+    gsl_spmatrix *C = gsl_spmatrix_crs(A);
+    gsl_spmatrix *CT = gsl_spmatrix_alloc_nzmax(N, M, 1, GSL_SPMATRIX_CRS);
+    size_t i, j;
+
+    gsl_spmatrix_transpose_memcpy(AT, A);
+    gsl_spmatrix_transpose_memcpy(BT, B);
+    gsl_spmatrix_transpose_memcpy(CT, C);
+
+    status = 0;
+    for (i = 0; i < M; ++i)
+      {
+        for (j = 0; j < N; ++j)
+          {
+            double Aij = gsl_spmatrix_get(A, i, j);
+            double ATji = gsl_spmatrix_get(AT, j, i);
+
+            if (Aij != ATji)
+              status = 1;
+          }
+      }
+
+    gsl_test(status, "test_memcpy: _transpose_memcpy M=%zu N=%zu triplet format", M, N);
+
+    status = 0;
+    for (i = 0; i < M; ++i)
+      {
+        for (j = 0; j < N; ++j)
+          {
+            double Aij = gsl_spmatrix_get(A, i, j);
+            double Bij = gsl_spmatrix_get(B, i, j);
+            double BTji = gsl_spmatrix_get(BT, j, i);
+
+            if ((Bij != BTji) || (Aij != Bij))
+              status = 1;
+          }
+      }
+
+    gsl_test(status, "test_memcpy: _transpose_memcpy M=%zu N=%zu CCS format", M, N);
+
+    status = 0;
+    for (i = 0; i < M; ++i)
+      {
+        for (j = 0; j < N; ++j)
+          {
+            double Aij = gsl_spmatrix_get(A, i, j);
+            double Cij = gsl_spmatrix_get(C, i, j);
+            double CTji = gsl_spmatrix_get(CT, j, i);
+
+            if ((Cij != CTji) || (Aij != Cij))
+              status = 1;
+          }
+      }
+
+    gsl_test(status, "test_memcpy: _transpose_memcpy M=%zu N=%zu CRS format", M, N);
+
+    gsl_spmatrix_free(A);
+    gsl_spmatrix_free(AT);
+    gsl_spmatrix_free(B);
+    gsl_spmatrix_free(BT);
+    gsl_spmatrix_free(C);
+    gsl_spmatrix_free(CT);
+  }
+} /* test_memcpy() */
+
+static void
+test_transpose(const size_t M, const size_t N,
+               const double density, const gsl_rng *r)
+{
+  int status;
+  gsl_spmatrix *A = create_random_sparse(M, N, density, r);
+  gsl_spmatrix *AT = gsl_spmatrix_alloc_nzmax(M, N, A->nz, A->sptype);
+  gsl_spmatrix *AT2 = gsl_spmatrix_alloc_nzmax(M, N, A->nz, A->sptype);
+  gsl_spmatrix *AT2_ccs, *AT2_crs;
+  size_t i, j;
+
+  /* test triplet transpose */
+
+  gsl_spmatrix_memcpy(AT, A);
+  gsl_spmatrix_memcpy(AT2, A);
+
+  gsl_spmatrix_transpose(AT);
+  gsl_spmatrix_transpose2(AT2);
+
+  status = 0;
+  for (i = 0; i < M; ++i)
+    {
+      for (j = 0; j < N; ++j)
+        {
+          double Aij = gsl_spmatrix_get(A, i, j);
+          double ATji = gsl_spmatrix_get(AT, j, i);
+          double AT2ji = gsl_spmatrix_get(AT2, j, i);
+
+          if (Aij != ATji)
+            status = 1;
+
+          if (Aij != AT2ji)
+            status = 2;
+        }
+    }
+
+  gsl_test(status == 1, "test_transpose: transpose M=%zu N=%zu triplet format",
+           M, N);
+  gsl_test(status == 2, "test_transpose: transpose2 M=%zu N=%zu triplet format",
+           M, N);
+
+  /* test CCS transpose */
+
+  AT2_ccs = gsl_spmatrix_ccs(A);
+  gsl_spmatrix_transpose2(AT2_ccs);
+
+  status = 0;
+  for (i = 0; i < M; ++i)
+    {
+      for (j = 0; j < N; ++j)
+        {
+          double Aij = gsl_spmatrix_get(A, i, j);
+          double AT2ji = gsl_spmatrix_get(AT2_ccs, j, i);
+
+          if (Aij != AT2ji)
+            status = 2;
+        }
+    }
+
+  gsl_test(status == 2, "test_transpose: transpose2 M=%zu N=%zu CCS format",
+           M, N);
+
+  /* test CRS transpose */
+
+  AT2_crs = gsl_spmatrix_crs(A);
+  gsl_spmatrix_transpose2(AT2_crs);
+
+  status = 0;
+  for (i = 0; i < M; ++i)
+    {
+      for (j = 0; j < N; ++j)
+        {
+          double Aij = gsl_spmatrix_get(A, i, j);
+          double AT2ji = gsl_spmatrix_get(AT2_crs, j, i);
+
+          if (Aij != AT2ji)
+            status = 2;
+        }
+    }
+
+  gsl_test(status == 2, "test_transpose: transpose2 M=%zu N=%zu CRS format",
+           M, N);
+
+  gsl_spmatrix_free(A);
+  gsl_spmatrix_free(AT);
+  gsl_spmatrix_free(AT2);
+  gsl_spmatrix_free(AT2_ccs);
+  gsl_spmatrix_free(AT2_crs);
+}
+
+static void
+test_ops(const size_t M, const size_t N,
+         const double density, const gsl_rng *r)
+{
+  size_t i, j;
+  int status;
+
+  /* test gsl_spmatrix_add */
+  {
+    gsl_spmatrix *A = create_random_sparse(M, N, density, r);
+    gsl_spmatrix *B = create_random_sparse(M, N, density, r);
+
+    gsl_spmatrix *A_ccs = gsl_spmatrix_ccs(A);
+    gsl_spmatrix *B_ccs = gsl_spmatrix_ccs(B);
+    gsl_spmatrix *C_ccs = gsl_spmatrix_alloc_nzmax(M, N, 1, GSL_SPMATRIX_CCS);
+
+    gsl_spmatrix *A_crs = gsl_spmatrix_crs(A);
+    gsl_spmatrix *B_crs = gsl_spmatrix_crs(B);
+    gsl_spmatrix *C_crs = gsl_spmatrix_alloc_nzmax(M, N, 1, GSL_SPMATRIX_CRS);
+    
+    gsl_spmatrix_add(C_ccs, A_ccs, B_ccs);
+    gsl_spmatrix_add(C_crs, A_crs, B_crs);
+
+    status = 0;
+    for (i = 0; i < M; ++i)
+      {
+        for (j = 0; j < N; ++j)
+          {
+            double aij, bij, cij;
+
+            aij = gsl_spmatrix_get(A_ccs, i, j);
+            bij = gsl_spmatrix_get(B_ccs, i, j);
+            cij = gsl_spmatrix_get(C_ccs, i, j);
+            if (aij + bij != cij)
+              status = 1;
+
+            aij = gsl_spmatrix_get(A_crs, i, j);
+            bij = gsl_spmatrix_get(B_crs, i, j);
+            cij = gsl_spmatrix_get(C_crs, i, j);
+            if (aij + bij != cij)
+              status = 2;
+          }
+      }
+
+    gsl_test(status == 1, "test_ops: add M=%zu N=%zu CCS", M, N);
+    gsl_test(status == 2, "test_ops: add M=%zu N=%zu CRS", M, N);
+
+    gsl_spmatrix_free(A);
+    gsl_spmatrix_free(B);
+    gsl_spmatrix_free(A_ccs);
+    gsl_spmatrix_free(B_ccs);
+    gsl_spmatrix_free(C_ccs);
+    gsl_spmatrix_free(A_crs);
+    gsl_spmatrix_free(B_crs);
+    gsl_spmatrix_free(C_crs);
+  }
+} /* test_ops() */
+
+static void
+test_io_ascii(const size_t M, const size_t N,
+              const double density, const gsl_rng *r)
+{
+  int status;
+  gsl_spmatrix *A = create_random_sparse_int(M, N, density, r);
+
+  char filename[] = "test.XXXXXX";
+#if !defined( _WIN32 )
+  int fd = mkstemp(filename);
+#else
+  char * fd = _mktemp(filename);
+# define fdopen fopen
+#endif
+
+  /* test triplet I/O */
+  {
+    FILE *f = fdopen(fd, "w");
+
+    gsl_spmatrix_fprintf(f, A, "%g");
+
+    fclose(f);
+  }
+
+  {
+    FILE *f = fopen(filename, "r");
+    gsl_spmatrix *B = gsl_spmatrix_fscanf(f);
+
+    status = gsl_spmatrix_equal(A, B) != 1;
+    gsl_test(status, "test_io_ascii: fprintf/fscanf M=%zu N=%zu triplet format", M, N);
+
+    fclose(f);
+    gsl_spmatrix_free(B);
+  }
+
+  /* test CCS I/O */
+  {
+    FILE *f = fopen(filename, "w");
+    gsl_spmatrix *A_ccs = gsl_spmatrix_ccs(A);
+
+    gsl_spmatrix_fprintf(f, A_ccs, "%g");
+
+    fclose(f);
+    gsl_spmatrix_free(A_ccs);
+  }
+
+  {
+    FILE *f = fopen(filename, "r");
+    gsl_spmatrix *B = gsl_spmatrix_fscanf(f);
+
+    status = gsl_spmatrix_equal(A, B) != 1;
+    gsl_test(status, "test_io_ascii: fprintf/fscanf M=%zu N=%zu CCS format", M, N);
+
+    fclose(f);
+    gsl_spmatrix_free(B);
+  }
+
+  /* test CRS I/O */
+  {
+    FILE *f = fopen(filename, "w");
+    gsl_spmatrix *A_crs = gsl_spmatrix_crs(A);
+
+    gsl_spmatrix_fprintf(f, A_crs, "%g");
+
+    fclose(f);
+    gsl_spmatrix_free(A_crs);
+  }
+
+  {
+    FILE *f = fopen(filename, "r");
+    gsl_spmatrix *B = gsl_spmatrix_fscanf(f);
+
+    status = gsl_spmatrix_equal(A, B) != 1;
+    gsl_test(status, "test_io_ascii: fprintf/fscanf M=%zu N=%zu CRS format", M, N);
+
+    fclose(f);
+    gsl_spmatrix_free(B);
+  }
+
+  unlink(filename);
+
+  gsl_spmatrix_free(A);
+}
+
+static void
+test_io_binary(const size_t M, const size_t N,
+               const double density, const gsl_rng *r)
+{
+  int status;
+  gsl_spmatrix *A = create_random_sparse(M, N, density, r);
+  gsl_spmatrix *A_ccs, *A_crs;
+
+  char filename[] = "test.XXXXXX";
+#if !defined( _WIN32 )
+  int fd = mkstemp(filename);
+#else
+  char * fd = _mktemp(filename);
+# define fdopen fopen
+#endif
+
+  /* test triplet I/O */
+  {
+    FILE *f = fdopen(fd, "wb");
+
+    gsl_spmatrix_fwrite(f, A);
+
+    fclose(f);
+  }
+
+  {
+    FILE *f = fopen(filename, "rb");
+    gsl_spmatrix *B = gsl_spmatrix_alloc_nzmax(M, N, A->nz, A->sptype);
+
+    gsl_spmatrix_fread(f, B);
+
+    status = gsl_spmatrix_equal(A, B) != 1;
+    gsl_test(status, "test_io_binary: fwrite/fread M=%zu N=%zu triplet format", M, N);
+
+    fclose(f);
+    gsl_spmatrix_free(B);
+  }
+
+  /* test CCS I/O */
+  A_ccs = gsl_spmatrix_ccs(A);
+
+  {
+    FILE *f = fopen(filename, "wb");
+
+    gsl_spmatrix_fwrite(f, A_ccs);
+
+    fclose(f);
+  }
+
+  {
+    FILE *f = fopen(filename, "rb");
+    gsl_spmatrix *B = gsl_spmatrix_alloc_nzmax(M, N, A->nz, GSL_SPMATRIX_CCS);
+
+    gsl_spmatrix_fread(f, B);
+
+    status = gsl_spmatrix_equal(A_ccs, B) != 1;
+    gsl_test(status, "test_io_binary: fwrite/fread M=%zu N=%zu CCS format", M, N);
+
+    fclose(f);
+    gsl_spmatrix_free(B);
+  }
+
+  /* test CRS I/O */
+  A_crs = gsl_spmatrix_crs(A);
+
+  {
+    FILE *f = fopen(filename, "wb");
+
+    gsl_spmatrix_fwrite(f, A_crs);
+
+    fclose(f);
+  }
+
+  {
+    FILE *f = fopen(filename, "rb");
+    gsl_spmatrix *B = gsl_spmatrix_alloc_nzmax(M, N, A->nz, GSL_SPMATRIX_CRS);
+
+    gsl_spmatrix_fread(f, B);
+
+    status = gsl_spmatrix_equal(A_crs, B) != 1;
+    gsl_test(status, "test_io_binary: fwrite/fread M=%zu N=%zu CRS format", M, N);
+
+    fclose(f);
+    gsl_spmatrix_free(B);
+  }
+
+  unlink(filename);
+
+  gsl_spmatrix_free(A);
+  gsl_spmatrix_free(A_ccs);
+  gsl_spmatrix_free(A_crs);
+}
+
+int
+main()
+{
+  gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
+
+  test_memcpy(10, 10, 0.2, r);
+  test_memcpy(10, 15, 0.3, r);
+  test_memcpy(53, 213, 0.4, r);
+  test_memcpy(920, 2, 0.2, r);
+  test_memcpy(2, 920, 0.3, r);
+
+  test_getset(20, 20, 0.3, r);
+  test_getset(30, 20, 0.3, r);
+  test_getset(15, 210, 0.3, r);
+
+  test_transpose(50, 50, 0.5, r);
+  test_transpose(10, 40, 0.3, r);
+  test_transpose(40, 10, 0.3, r);
+  test_transpose(57, 13, 0.2, r);
+
+  test_ops(20, 20, 0.2, r);
+  test_ops(50, 20, 0.3, r);
+  test_ops(20, 50, 0.3, r);
+  test_ops(76, 43, 0.4, r);
+
+  test_io_ascii(30, 30, 0.3, r);
+  test_io_ascii(20, 10, 0.2, r);
+  test_io_ascii(10, 20, 0.2, r);
+  test_io_ascii(34, 78, 0.3, r);
+
+  test_io_binary(50, 50, 0.3, r);
+  test_io_binary(25, 10, 0.2, r);
+  test_io_binary(10, 25, 0.2, r);
+  test_io_binary(101, 253, 0.3, r);
+
+  gsl_rng_free(r);
+
+  exit (gsl_test_summary());
+} /* main() */
diff -Nru gsl-doc-1.16/spmatrix/TODO gsl-doc-2.3/spmatrix/TODO
--- gsl-doc-1.16/spmatrix/TODO	1970-01-01 00:00:00.000000000 +0000
+++ gsl-doc-2.3/spmatrix/TODO	2016-07-02 23:02:41.000000000 +0000
@@ -0,0 +1,2 @@
+1. extend transpose to CCS/CRS (in-place)
+2. extend spblas_dgemm to CRS
diff -Nru gsl-doc-1.16/statistics/Makefile.am gsl-doc-2.3/statistics/Makefile.am
--- gsl-doc-1.16/statistics/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/statistics/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -4,7 +4,7 @@
 
 pkginclude_HEADERS = gsl_statistics.h gsl_statistics_char.h gsl_statistics_double.h gsl_statistics_float.h gsl_statistics_int.h gsl_statistics_long.h gsl_statistics_long_double.h gsl_statistics_short.h gsl_statistics_uchar.h gsl_statistics_uint.h gsl_statistics_ulong.h gsl_statistics_ushort.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslstatistics_la_SOURCES =  mean.c variance.c absdev.c skew.c kurtosis.c lag1.c p_variance.c minmax.c ttest.c median.c covariance.c quantiles.c wmean.c wvariance.c wabsdev.c wskew.c wkurtosis.c
 
diff -Nru gsl-doc-1.16/statistics/Makefile.in gsl-doc-2.3/statistics/Makefile.in
--- gsl-doc-1.16/statistics/Makefile.in	2013-07-19 15:14:55.000000000 +0000
+++ gsl-doc-2.3/statistics/Makefile.in	2016-12-09 00:04:23.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -381,6 +381,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -403,7 +404,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -519,7 +523,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslstatistics.la
 pkginclude_HEADERS = gsl_statistics.h gsl_statistics_char.h gsl_statistics_double.h gsl_statistics_float.h gsl_statistics_int.h gsl_statistics_long.h gsl_statistics_long_double.h gsl_statistics_short.h gsl_statistics_uchar.h gsl_statistics_uint.h gsl_statistics_ulong.h gsl_statistics_ushort.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslstatistics_la_SOURCES = mean.c variance.c absdev.c skew.c kurtosis.c lag1.c p_variance.c minmax.c ttest.c median.c covariance.c quantiles.c wmean.c wvariance.c wabsdev.c wskew.c wkurtosis.c
 noinst_HEADERS = mean_source.c variance_source.c covariance_source.c absdev_source.c skew_source.c kurtosis_source.c lag1_source.c p_variance_source.c minmax_source.c ttest_source.c median_source.c quantiles_source.c wmean_source.c wvariance_source.c wabsdev_source.c wskew_source.c wkurtosis_source.c test_float_source.c test_int_source.c
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/sum/Makefile.am gsl-doc-2.3/sum/Makefile.am
--- gsl-doc-1.16/sum/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/sum/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_sum.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslsum_la_SOURCES = levin_u.c levin_utrunc.c work_u.c work_utrunc.c
 
diff -Nru gsl-doc-1.16/sum/Makefile.in gsl-doc-2.3/sum/Makefile.in
--- gsl-doc-1.16/sum/Makefile.in	2013-07-19 15:14:55.000000000 +0000
+++ gsl-doc-2.3/sum/Makefile.in	2016-12-09 00:04:23.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -377,6 +377,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -399,7 +400,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -515,7 +519,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslsum.la 
 pkginclude_HEADERS = gsl_sum.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslsum_la_SOURCES = levin_u.c levin_utrunc.c work_u.c work_utrunc.c
 TESTS = $(check_PROGRAMS)
 test_LDADD = libgslsum.la ../ieee-utils/libgslieeeutils.la  ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
diff -Nru gsl-doc-1.16/sys/ldfrexp.c gsl-doc-2.3/sys/ldfrexp.c
--- gsl-doc-1.16/sys/ldfrexp.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/sys/ldfrexp.c	2015-11-03 16:21:55.000000000 +0000
@@ -60,7 +60,7 @@
       *e = 0;
       return 0.0;
     }
-  else if (!finite (x))
+  else if (!gsl_finite (x))
     {
       *e = 0;
       return x;
@@ -85,7 +85,7 @@
 
       f = x * pow (2.0, -ei);
 
-      if (!finite (f))
+      if (!gsl_finite (f))
         {
           /* This should not happen */
           *e = 0;
diff -Nru gsl-doc-1.16/sys/Makefile.am gsl-doc-2.3/sys/Makefile.am
--- gsl-doc-1.16/sys/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/sys/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -4,7 +4,7 @@
 
 libgslsys_la_SOURCES = minmax.c prec.c hypot.c log1p.c expm1.c coerce.c invhyp.c pow_int.c infnan.c fdiv.c fcmp.c ldfrexp.c
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 check_PROGRAMS = test
 TESTS = $(check_PROGRAMS)
diff -Nru gsl-doc-1.16/sys/Makefile.in gsl-doc-2.3/sys/Makefile.in
--- gsl-doc-1.16/sys/Makefile.in	2013-07-19 15:14:55.000000000 +0000
+++ gsl-doc-2.3/sys/Makefile.in	2016-12-09 00:04:23.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -378,6 +378,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -400,7 +401,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -517,7 +521,7 @@
 noinst_LTLIBRARIES = libgslsys.la 
 pkginclude_HEADERS = gsl_sys.h
 libgslsys_la_SOURCES = minmax.c prec.c hypot.c log1p.c expm1.c coerce.c invhyp.c pow_int.c infnan.c fdiv.c fcmp.c ldfrexp.c
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 TESTS = $(check_PROGRAMS)
 test_SOURCES = test.c
 test_LDADD = libgslsys.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la libgslsys.la ../utils/libutils.la
diff -Nru gsl-doc-1.16/sys/test.c gsl-doc-2.3/sys/test.c
--- gsl-doc-1.16/sys/test.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/sys/test.c	2015-11-03 16:21:55.000000000 +0000
@@ -563,7 +563,7 @@
     s = gsl_isnan (-inf);
     gsl_test_int (s, 0, "gsl_isnan(-inf)");
 
-    s = gsl_isnan (nan);
+    s = gsl_isnan (nan) != 0;
     gsl_test_int (s, 1, "gsl_isnan(nan)");
 
 
diff -Nru gsl-doc-1.16/test/Makefile.in gsl-doc-2.3/test/Makefile.in
--- gsl-doc-1.16/test/Makefile.in	2013-07-19 15:14:55.000000000 +0000
+++ gsl-doc-2.3/test/Makefile.in	2016-12-09 00:04:23.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -193,6 +193,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -215,7 +216,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
diff -Nru gsl-doc-1.16/THANKS gsl-doc-2.3/THANKS
--- gsl-doc-1.16/THANKS	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/THANKS	2016-07-07 20:36:10.000000000 +0000
@@ -13,7 +13,7 @@
 * Thomas Walter <walter@pctc.chemie.uni-erlangen.de> for heapsort
 routines, cholesky decomposition, bug reports and useful suggestions
 
-* Jorma Olavi Tähtinen <jotahtin@cc.hut.fi> for complex arithmetic
+* Jorma Olavi Tähtinen <jotahtin@cc.hut.fi> for complex arithmetic
 functions
 
 * Barak Pearlmutter <bap@cs.unm.edu>
@@ -140,7 +140,7 @@
 
 * Vladimir Savichev <vlad@ariel.phys.wesleyan.edu> bug reports
 
-* Jochen Küpper <jochen@jochen-kuepper.de> doc bug fixes, additional
+* Jochen Küpper <jochen@jochen-kuepper.de> doc bug fixes, additional
 constants
 
 * John Ketchum <johnk@qualcomm.com> for bug reports for the blas library
@@ -297,7 +297,7 @@
 
 * James Scott <j.scott@runbox.com> fix for linalg tests on MSVC
 
-* Rémi Butel <r.butel@epoc.u-bordeaux1.fr> fixes for multimin overflow
+* Rémi Butel <r.butel@epoc.u-bordeaux1.fr> fixes for multimin overflow
 conditions
 
 * Andris Pavenis <pavenis@latnet.lv> Makefile fix for EXEEXT
@@ -336,7 +336,7 @@
 * Dirk Eddelbuettel <edd@debian.org> for bug reports and testing, and
 maintaining the Debian package for GSL.
 
-* Jari Häkkinen <jari@chiralcomp.com> for svd bug reports, rng bug reports
+* Jari Häkkinen <jari@chiralcomp.com> for svd bug reports, rng bug reports
 
 * Marco Canini <marco.canini@fastwebnet.it> patch for IXP2400 Xscale
 
@@ -424,7 +424,7 @@
 * Justin Lenzo <j-lenzo@northwestern.edu> bug reports for
 vector/matrix tests.
 
-* Sebastian Queißer <sebastian@queisser-net.de> bug report for
+* Sebastian Queißer <sebastian@queisser-net.de> bug report for
 gsl_cdf_beta_Pinv
 
 * Andries Brouwer <Andries.Brouwer@cwi.nl> bug report for
@@ -464,7 +464,7 @@
 
 * Marco Maggi <mrc.mgg@gmail.com> bug fix for gsl_blas_drotm
 
-* Mateus Araújo Santos - bug fix for LM set
+* Mateus Araújo Santos - bug fix for LM set
 
 * James Howse - quad_golden minimisation algorithm
 
@@ -484,7 +484,7 @@
 
 * Sam Mason <sam@samason.me.uk> - bug fix for gsl_pow_int
 
-* José Luis García Pallero <jgpallero@gmail.com> - error checking for GSL cblas
+* José Luis García Pallero <jgpallero@gmail.com> - error checking for GSL cblas
 
 * Teemu Ikonen <tpikonen@gmail.com> patch for gsl_ran_chisq_pdf
 
@@ -508,3 +508,6 @@
 
 * Matthias Sitte <matthias.sitte@gmail.com> - bug report and patch for
   failing complex matrix IO routines
+
+* Raymond Rogers <raymond.rogers72@gmail.com> - bug fixes for confluent
+  hypergeometric functions
diff -Nru gsl-doc-1.16/TODO gsl-doc-2.3/TODO
--- gsl-doc-1.16/TODO	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/TODO	2015-11-03 16:21:55.000000000 +0000
@@ -19,8 +19,6 @@
 
 ** Incomplete Fermi-Dirac functions
 
-** General Legendre functions
-
 ** Spheroidal wave functions
 
 ** Weierstrass elliptic functions
@@ -56,11 +54,28 @@
 vs _inverse). Also adopt a convection for functions which can operate
 in place vs use of workspace (e.g linalg_solve functions).
 
-** gsl_sf_ellint_D  - remove useless argument n?
-
 ** gsl_roots doesn't store function value, so testing the residual requires function to be recomputed
 Generally all the iterative routines should follow a consistent approach
 to outputting everything that is necessary for the next iteration 
+
+** gsl_roots - consider having two returns from solvers - GSL_SUCCESS
+if a root has been found or GSL_CONTINUE if further iterations may
+be needed.
+
+** mathieu functions - bring functional interfaces into line with GSL
+conventions for special functions.
+
+** rewriting the spherical Bessel routines (there are
+around 3 separate bug reports for these)
+
+** the nonlinear least squares Levenberg-Marquardt solver should be 
+rewritten from scratch - the current version is filled with goto 
+statements, and while its supposed to be based on MINPACK, I've found 
+numerous examples where GSL fails to converge when MINPACK succeeds, so 
+something was not implemented correctly.
+
+** import 2D interpolation code; 3d or nd linear interpolation?
+
 * Other tasks
 
 ** Remove use of long double internally, e.g. as an accumulator in
diff -Nru gsl-doc-1.16/utils/Makefile.in gsl-doc-2.3/utils/Makefile.in
--- gsl-doc-1.16/utils/Makefile.in	2013-07-19 15:14:55.000000000 +0000
+++ gsl-doc-2.3/utils/Makefile.in	2016-12-09 00:04:23.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -163,6 +163,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -185,7 +186,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
diff -Nru gsl-doc-1.16/vector/init.c gsl-doc-2.3/vector/init.c
--- gsl-doc-1.16/vector/init.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/vector/init.c	2015-11-03 16:21:55.000000000 +0000
@@ -1,5 +1,6 @@
 #include <config.h>
 #include <stdlib.h>
+#include <string.h>
 #include <gsl/gsl_vector.h>
 
 #define BASE_GSL_COMPLEX_LONG
diff -Nru gsl-doc-1.16/vector/init_source.c gsl-doc-2.3/vector/init_source.c
--- gsl-doc-1.16/vector/init_source.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/vector/init_source.c	2015-11-03 16:21:55.000000000 +0000
@@ -66,7 +66,8 @@
   if (v == 0)
     return 0;
 
-  /* initialize vector to zero */
+  /* initialize vector to zero; memset takes care of the padding bytes */
+  memset(v->data, 0, MULTIPLICITY * n * sizeof(ATOMIC));
 
   for (i = 0; i < MULTIPLICITY * n; i++)
     {
diff -Nru gsl-doc-1.16/vector/Makefile.am gsl-doc-2.3/vector/Makefile.am
--- gsl-doc-1.16/vector/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/vector/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -4,7 +4,7 @@
 
 pkginclude_HEADERS = gsl_vector.h gsl_vector_char.h gsl_vector_complex.h gsl_vector_complex_double.h gsl_vector_complex_float.h gsl_vector_complex_long_double.h gsl_vector_double.h gsl_vector_float.h gsl_vector_int.h gsl_vector_long.h gsl_vector_long_double.h gsl_vector_short.h gsl_vector_uchar.h gsl_vector_uint.h gsl_vector_ulong.h gsl_vector_ushort.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 TESTS = $(check_PROGRAMS)
 
diff -Nru gsl-doc-1.16/vector/Makefile.in gsl-doc-2.3/vector/Makefile.in
--- gsl-doc-1.16/vector/Makefile.in	2013-07-19 15:14:55.000000000 +0000
+++ gsl-doc-2.3/vector/Makefile.in	2016-12-09 00:04:23.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -385,6 +385,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -407,7 +408,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -523,7 +527,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslvector.la 
 pkginclude_HEADERS = gsl_vector.h gsl_vector_char.h gsl_vector_complex.h gsl_vector_complex_double.h gsl_vector_complex_float.h gsl_vector_complex_long_double.h gsl_vector_double.h gsl_vector_float.h gsl_vector_int.h gsl_vector_long.h gsl_vector_long_double.h gsl_vector_short.h gsl_vector_uchar.h gsl_vector_uint.h gsl_vector_ulong.h gsl_vector_ushort.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 TESTS = $(check_PROGRAMS)
 test_LDADD = libgslvector.la ../block/libgslblock.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
 test_static_LDADD = libgslvector.la ../block/libgslblock.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la
diff -Nru gsl-doc-1.16/vector/test.c gsl-doc-2.3/vector/test.c
--- gsl-doc-1.16/vector/test.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/vector/test.c	2015-11-03 16:21:55.000000000 +0000
@@ -19,12 +19,18 @@
 
 #include <config.h>
 
+#if defined( _MSC_VER ) && defined( GSL_DLL )
+#undef inline
+#define inline __forceinline 
+#endif
+
 #if (!GSL_RANGE_CHECK) && defined(HAVE_INLINE)
 #undef GSL_RANGE_CHECK
 #define GSL_RANGE_CHECK 1
 #endif
 
 #include <stdlib.h>
+#include <unistd.h>
 #include <fcntl.h>
 #include <stdio.h>
 #include <gsl/gsl_math.h>
diff -Nru gsl-doc-1.16/vector/test_complex_source.c gsl-doc-2.3/vector/test_complex_source.c
--- gsl-doc-1.16/vector/test_complex_source.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/vector/test_complex_source.c	2015-11-03 16:21:55.000000000 +0000
@@ -638,8 +638,16 @@
 
   size_t i;
 
+  char filename[] = "test.XXXXXX";
+#if !defined( _WIN32 )
+  int fd = mkstemp(filename);
+#else
+  char * fd = _mktemp(filename);
+# define fdopen fopen
+#endif
+
   {
-    FILE *f = fopen ("test.dat", "wb");
+    FILE *f = fdopen(fd, "wb");
 
     for (i = 0; i < N; i++)
       {
@@ -655,7 +663,7 @@
   }
 
   {
-    FILE *f = fopen ("test.dat", "rb");
+    FILE *f = fopen(filename, "rb");
 
     FUNCTION (gsl_vector, fread) (f, w);
 
@@ -668,11 +676,12 @@
     fclose (f);
   }
 
+  unlink(filename);
+
   FUNCTION (gsl_vector, free) (v);
   FUNCTION (gsl_vector, free) (w);
 
   gsl_test (status, NAME (gsl_vector) "_write and read work");
-
 }
 
 #if USES_LONGDOUBLE && ! HAVE_PRINTF_LONGDOUBLE
@@ -686,8 +695,16 @@
 
   size_t i;
 
+  char filename[] = "test.XXXXXX";
+#if !defined( _WIN32 )
+  int fd = mkstemp(filename);
+#else
+  char * fd = _mktemp(filename);
+# define fdopen fopen
+#endif
+
   {
-    FILE *f = fopen ("test.txt", "w");
+    FILE *f = fdopen(fd, "w");
 
     for (i = 0; i < N; i++)
       {
@@ -703,7 +720,7 @@
   }
 
   {
-    FILE *f = fopen ("test.txt", "r");
+    FILE *f = fopen(filename, "r");
 
     FUNCTION (gsl_vector, fscanf) (f, w);
 
@@ -716,6 +733,8 @@
     fclose (f);
   }
 
+  unlink(filename);
+
   FUNCTION (gsl_vector, free) (v);
   FUNCTION (gsl_vector, free) (w);
 
diff -Nru gsl-doc-1.16/vector/test_source.c gsl-doc-2.3/vector/test_source.c
--- gsl-doc-1.16/vector/test_source.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/vector/test_source.c	2015-11-03 16:21:55.000000000 +0000
@@ -357,7 +357,7 @@
 
     for (i = 0; i < N; i++)
       {
-        if (FUNCTION (gsl_vector, get) (v, i) != (ATOMIC) (i*2.0))
+        if (FUNCTION (gsl_vector, get) (v, i) != (ATOMIC) ((ATOMIC)i*(ATOMIC)2.0))
           status = 1;
       };
 
@@ -371,7 +371,7 @@
 
     for (i = 0; i < N; i++)
       {
-        if (FUNCTION (gsl_vector, get) (v, i) != (ATOMIC) (i*2.0 + 7))
+        if (FUNCTION (gsl_vector, get) (v, i) != (ATOMIC) ((ATOMIC)i*(ATOMIC)2.0 + (ATOMIC)7))
           status = 1;
       };
 
@@ -718,8 +718,15 @@
 
   size_t i;
 
+  char filename[] = "test.XXXXXX";
+#if !defined( _WIN32 )
+  int fd = mkstemp(filename);
+#else
+  char * fd = _mktemp(filename);
+#  define fdopen fopen
+#endif
   {
-    FILE *f = fopen ("test.dat", "wb");
+    FILE *f = fdopen (fd, "wb");
 
     for (i = 0; i < N; i++)
       {
@@ -732,7 +739,7 @@
   }
 
   {
-    FILE *f = fopen ("test.dat", "rb");
+    FILE *f = fopen (filename, "rb");
 
     FUNCTION (gsl_vector, fread) (f, w);
 
@@ -748,6 +755,8 @@
     fclose (f);
   }
 
+  unlink(filename);
+
   FUNCTION (gsl_vector, free) (v);      /* free whatever is in v */
   FUNCTION (gsl_vector, free) (w);      /* free whatever is in w */
 }
@@ -763,8 +772,15 @@
 
   size_t i;
 
+  char filename[] = "test.XXXXXX";
+#if !defined( _WIN32 )
+   int fd = mkstemp(filename);
+#else
+   char * fd = _mktemp(filename);
+#  define fdopen fopen
+#endif
   {
-    FILE *f = fopen ("test.txt", "w");
+    FILE *f = fdopen (fd, "w");
 
     for (i = 0; i < N; i++)
       {
@@ -777,7 +793,7 @@
   }
 
   {
-    FILE *f = fopen ("test.txt", "r");
+    FILE *f = fopen (filename, "r");
 
     FUNCTION (gsl_vector, fscanf) (f, w);
 
@@ -793,6 +809,8 @@
     fclose (f);
   }
 
+  unlink(filename);
+
   FUNCTION (gsl_vector, free) (v);
   FUNCTION (gsl_vector, free) (w);
 }
diff -Nru gsl-doc-1.16/wavelet/dwt.c gsl-doc-2.3/wavelet/dwt.c
--- gsl-doc-1.16/wavelet/dwt.c	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/wavelet/dwt.c	2015-11-03 16:21:55.000000000 +0000
@@ -44,7 +44,7 @@
       logn++;
     }
 
-  ntest = (1 << logn);
+  ntest = ((size_t)1 << logn);
 
   if (n != ntest)
     {
diff -Nru gsl-doc-1.16/wavelet/Makefile.am gsl-doc-2.3/wavelet/Makefile.am
--- gsl-doc-1.16/wavelet/Makefile.am	2013-07-17 20:04:26.000000000 +0000
+++ gsl-doc-2.3/wavelet/Makefile.am	2015-11-03 16:21:55.000000000 +0000
@@ -2,7 +2,7 @@
 
 pkginclude_HEADERS = gsl_wavelet.h gsl_wavelet2d.h
 
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 
 libgslwavelet_la_SOURCES = dwt.c wavelet.c bspline.c daubechies.c haar.c
 
diff -Nru gsl-doc-1.16/wavelet/Makefile.in gsl-doc-2.3/wavelet/Makefile.in
--- gsl-doc-1.16/wavelet/Makefile.in	2013-07-19 15:14:55.000000000 +0000
+++ gsl-doc-2.3/wavelet/Makefile.in	2016-12-09 00:04:23.000000000 +0000
@@ -1,4 +1,4 @@
-# Makefile.in generated by automake 1.13.2 from Makefile.am.
+# Makefile.in generated by automake 1.13.4 from Makefile.am.
 # @configure_input@
 
 # Copyright (C) 1994-2013 Free Software Foundation, Inc.
@@ -379,6 +379,7 @@
 AMTAR = @AMTAR@
 AM_DEFAULT_VERBOSITY = @AM_DEFAULT_VERBOSITY@
 AR = @AR@
+AS = @AS@
 AUTOCONF = @AUTOCONF@
 AUTOHEADER = @AUTOHEADER@
 AUTOMAKE = @AUTOMAKE@
@@ -401,7 +402,10 @@
 EXEEXT = @EXEEXT@
 FGREP = @FGREP@
 GREP = @GREP@
+GSLCBLAS_LDFLAGS = @GSLCBLAS_LDFLAGS@
 GSL_CFLAGS = @GSL_CFLAGS@
+GSL_LDFLAGS = @GSL_LDFLAGS@
+GSL_LIBADD = @GSL_LIBADD@
 GSL_LIBM = @GSL_LIBM@
 GSL_LIBS = @GSL_LIBS@
 GSL_LT_CBLAS_VERSION = @GSL_LT_CBLAS_VERSION@
@@ -517,7 +521,7 @@
 top_srcdir = @top_srcdir@
 noinst_LTLIBRARIES = libgslwavelet.la 
 pkginclude_HEADERS = gsl_wavelet.h gsl_wavelet2d.h
-INCLUDES = -I$(top_srcdir)
+AM_CPPFLAGS = -I$(top_srcdir)
 libgslwavelet_la_SOURCES = dwt.c wavelet.c bspline.c daubechies.c haar.c
 TESTS = $(check_PROGRAMS)
 test_LDADD = libgslwavelet.la ../blas/libgslblas.la ../cblas/libgslcblas.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la ../ieee-utils/libgslieeeutils.la  ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la