18 #if !defined escript_LocalOps_H
19 #define escript_LocalOps_H
20 #if defined(_WIN32) && defined(__INTEL_COMPILER)
26 # define M_PI 3.14159265358979323846
99 void eigenvalues2(
const double A00,
const double A01,
const double A11,
100 double* ev0,
double* ev1) {
101 const register double trA=(A00+A11)/2.;
102 const register double A_00=A00-trA;
103 const register double A_11=A11-trA;
104 const register double s=sqrt(A01*A01-A_00*A_11);
123 void eigenvalues3(
const double A00,
const double A01,
const double A02,
124 const double A11,
const double A12,
126 double* ev0,
double* ev1,
double* ev2) {
128 const register double trA=(A00+A11+A22)/3.;
129 const register double A_00=A00-trA;
130 const register double A_11=A11-trA;
131 const register double A_22=A22-trA;
132 const register double A01_2=A01*A01;
133 const register double A02_2=A02*A02;
134 const register double A12_2=A12*A12;
135 const register double p=A02_2+A12_2+A01_2+(A_00*A_00+A_11*A_11+A_22*A_22)/2.;
142 const register double q=(A02_2*A_11+A12_2*A_00+A01_2*A_22)-(A_00*A_11*A_22+2*A01*A12*A02);
143 const register double sq_p=sqrt(p/3.);
144 register double z=-q/(2*pow(sq_p,3));
150 const register double alpha_3=acos(z)/3.;
151 *ev2=trA+2.*sq_p*cos(alpha_3);
152 *ev1=trA-2.*sq_p*cos(alpha_3+
M_PI/3.);
153 *ev0=trA-2.*sq_p*cos(alpha_3-
M_PI/3.);
184 void vectorInKernel2(
const double A00,
const double A10,
const double A01,
const double A11,
185 double* V0,
double*V1)
187 register double absA00=fabs(A00);
188 register double absA10=fabs(A10);
189 register double absA01=fabs(A01);
190 register double absA11=fabs(A11);
191 register double m=absA11>absA10 ? absA11 : absA10;
192 if (absA00>m || absA01>m) {
225 const double A01,
const double A11,
const double A21,
226 const double A02,
const double A12,
const double A22,
227 double* V0,
double* V1,
double* V2)
230 register const double I00=1./A00;
231 register const double IA10=I00*A10;
232 register const double IA20=I00*A20;
234 A21-IA20*A01,A22-IA20*A02,&TEMP0,&TEMP1);
235 *V0=-(A10*TEMP0+A20*TEMP1);
259 double* ev0,
double* ev1,
260 double* V00,
double* V10,
double* V01,
double* V11,
265 const register double absev0=fabs(*ev0);
266 const register double absev1=fabs(*ev1);
267 register double max_ev=absev0>absev1 ? absev0 : absev1;
268 if (fabs((*ev0)-(*ev1))<tol*max_ev) {
275 const register double scale=1./sqrt(TEMP0*TEMP0+TEMP1*TEMP1);
286 }
else if (TEMP0>0.) {
317 s=1./sqrt((*V0)*(*V0)+(*V1)*(*V1)+(*V2)*(*V2));
322 s=-1./sqrt((*V0)*(*V0)+(*V1)*(*V1)+(*V2)*(*V2));
328 s=1./sqrt((*V1)*(*V1)+(*V2)*(*V2));
332 s=-1./sqrt((*V1)*(*V1)+(*V2)*(*V2));
368 const double A11,
const double A12,
const double A22,
369 double* ev0,
double* ev1,
double* ev2,
370 double* V00,
double* V10,
double* V20,
371 double* V01,
double* V11,
double* V21,
372 double* V02,
double* V12,
double* V22,
375 register const double absA01=fabs(A01);
376 register const double absA02=fabs(A02);
377 register const double m=absA01>absA02 ? absA01 : absA02;
379 double TEMP_V00,TEMP_V10,TEMP_V01,TEMP_V11,TEMP_EV0,TEMP_EV1;
382 &TEMP_V00,&TEMP_V10,&TEMP_V01,&TEMP_V11,tol);
396 }
else if (A00>TEMP_EV1) {
425 const register double absev0=fabs(*ev0);
426 const register double absev1=fabs(*ev1);
427 const register double absev2=fabs(*ev2);
428 register double max_ev=absev0>absev1 ? absev0 : absev1;
429 max_ev=max_ev>absev2 ? max_ev : absev2;
430 const register double d_01=fabs((*ev0)-(*ev1));
431 const register double d_12=fabs((*ev1)-(*ev2));
432 const register double max_d=d_01>d_12 ? d_01 : d_12;
433 if (max_d<=tol*max_ev) {
444 const register double S00=A00-(*ev0);
445 const register double absS00=fabs(S00);
447 vectorInKernel3__nonZeroA00(S00,A01,A02,A01,A11-(*ev0),A12,A02,A12,A22-(*ev0),V00,V10,V20);
448 }
else if (absA02<m) {
449 vectorInKernel3__nonZeroA00(A01,A11-(*ev0),A12,S00,A01,A02,A02,A12,A22-(*ev0),V00,V10,V20);
451 vectorInKernel3__nonZeroA00(A02,A12,A22-(*ev0),S00,A01,A02,A01,A11-(*ev0),A12,V00,V10,V20);
454 const register double T00=A00-(*ev2);
455 const register double absT00=fabs(T00);
457 vectorInKernel3__nonZeroA00(T00,A01,A02,A01,A11-(*ev2),A12,A02,A12,A22-(*ev2),V02,V12,V22);
458 }
else if (absA02<m) {
459 vectorInKernel3__nonZeroA00(A01,A11-(*ev2),A12,T00,A01,A02,A02,A12,A22-(*ev2),V02,V12,V22);
461 vectorInKernel3__nonZeroA00(A02,A12,A22-(*ev2),T00,A01,A02,A01,A11-(*ev2),A12,V02,V12,V22);
463 const register double dot=(*V02)*(*V00)+(*V12)*(*V10)+(*V22)*(*V20);
468 *V01=(*V10)*(*V22)-(*V12)*(*V20);
469 *V11=(*V20)*(*V02)-(*V00)*(*V22);
470 *V21=(*V00)*(*V12)-(*V02)*(*V10);
481 if (transpose == 0) {
482 for (
int i=0; i<SL; i++) {
483 for (
int j=0; j<SR; j++) {
485 for (
int l=0; l<SM; l++) {
486 sum += A[i+SL*l] * B[l+SM*j];
492 else if (transpose == 1) {
493 for (
int i=0; i<SL; i++) {
494 for (
int j=0; j<SR; j++) {
496 for (
int l=0; l<SM; l++) {
497 sum += A[i*SM+l] * B[l+SM*j];
503 else if (transpose == 2) {
504 for (
int i=0; i<SL; i++) {
505 for (
int j=0; j<SR; j++) {
507 for (
int l=0; l<SM; l++) {
508 sum += A[i+SL*l] * B[l*SR+j];
516 template <
typename UnaryFunction>
520 UnaryFunction operation)
522 for (
int i = 0; i < size; ++i) {
523 argRes[i] = operation(arg1[i]);
528 template <
typename BinaryFunction>
533 BinaryFunction operation)
535 for (
int i = 0; i < size; ++i) {
536 argRes[i] = operation(arg1[i], arg2[i]);
541 template <
typename BinaryFunction>
546 BinaryFunction operation)
548 for (
int i = 0; i < size; ++i) {
549 argRes[i] = operation(arg1, arg2[i]);
554 template <
typename BinaryFunction>
559 BinaryFunction operation)
561 for (
int i = 0; i < size; ++i) {
562 argRes[i] = operation(arg1[i], arg2);
void tensor_unary_operation(const int size, const double *arg1, double *argRes, UnaryFunction operation)
Definition: LocalOps.h:517
void transpose(const DataTypes::ValueType &in, const DataTypes::ShapeType &inShape, DataTypes::ValueType::size_type inOffset, DataTypes::ValueType &ev, const DataTypes::ShapeType &evShape, DataTypes::ValueType::size_type evOffset, int axis_offset)
Transpose each data point of this Data object around the given axis.
Definition: DataMaths.h:394
void vectorInKernel2(const double A00, const double A10, const double A01, const double A11, double *V0, double *V1)
returns a non-zero vector in the kernel of [[A00,A01],[A01,A11]] assuming that the kernel dimension i...
Definition: LocalOps.h:184
double makeNaN()
returns a NaN.
Definition: LocalOps.h:64
#define M_PI
Definition: LocalOps.h:26
void eigenvalues2(const double A00, const double A01, const double A11, double *ev0, double *ev1)
solves a 2x2 eigenvalue A*V=ev*V problem for symmetric A
Definition: LocalOps.h:99
bool nancheck(double d)
acts as a wrapper to isnan.
Definition: LocalOps.h:45
void scale(dim_t N, double *x, double a)
x = a*x
Definition: PasoUtil.h:93
void matrix_matrix_product(const int SL, const int SM, const int SR, const double *A, const double *B, double *C, int transpose)
Definition: LocalOps.h:479
void eigenvalues_and_eigenvectors1(const double A00, double *ev0, double *V00, const double tol)
solves a 1x1 eigenvalue A*V=ev*V problem for symmetric A
Definition: LocalOps.h:166
void eigenvalues1(const double A00, double *ev0)
solves a 1x1 eigenvalue A*V=ev*V problem
Definition: LocalOps.h:83
void normalizeVector3(double *V0, double *V1, double *V2)
nomalizes a 3-d vector such that length is one and first non-zero component is positive.
Definition: LocalOps.h:313
void eigenvalues_and_eigenvectors2(const double A00, const double A01, const double A11, double *ev0, double *ev1, double *V00, double *V10, double *V01, double *V11, const double tol)
solves a 2x2 eigenvalue A*V=ev*V problem for symmetric A. Eigenvectors are ordered by increasing valu...
Definition: LocalOps.h:258
void eigenvalues3(const double A00, const double A01, const double A02, const double A11, const double A12, const double A22, double *ev0, double *ev1, double *ev2)
solves a 3x3 eigenvalue A*V=ev*V problem for symmetric A
Definition: LocalOps.h:123
void eigenvalues_and_eigenvectors3(const double A00, const double A01, const double A02, const double A11, const double A12, const double A22, double *ev0, double *ev1, double *ev2, double *V00, double *V10, double *V20, double *V01, double *V11, double *V21, double *V02, double *V12, double *V22, const double tol)
solves a 2x2 eigenvalue A*V=ev*V problem for symmetric A. Eigenvectors are ordered by increasing valu...
Definition: LocalOps.h:367
void vectorInKernel3__nonZeroA00(const double A00, const double A10, const double A20, const double A01, const double A11, const double A21, const double A02, const double A12, const double A22, double *V0, double *V1, double *V2)
returns a non-zero vector in the kernel of [[A00,A01,A02],[A10,A11,A12],[A20,A21,A22]] assuming that ...
Definition: LocalOps.h:224
void tensor_binary_operation(const int size, const double *arg1, const double *arg2, double *argRes, BinaryFunction operation)
Definition: LocalOps.h:529