Bases: esys.escriptcore.escriptcpp.Domain
Class representing continuous domains
Wait until all processes have reached this point
adds a PDE onto the stiffness matrix mat and a rhs
Parameters: |
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adds a PDE onto the stiffness matrix mat and a rhs
Parameters: |
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Parameters: |
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Dumps the domain to a file:param filename: :type filename: string
Returns: | a pair (dps, ns) where dps=the number of data points per sample, and ns=the number of samples |
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Return type: | tuple |
Returns: | a description for this domain |
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Return type: | string |
Returns: | the rank of this process |
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Return type: | int |
Returns: | the number of processes used for this Domain |
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Return type: | int |
Return type: | escript |
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Returns: | Boundary normals |
Returns: | the number of data points summed across all MPI processes |
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Return type: | int |
Returns: | the local size of samples. The function space is chosen appropriately |
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Return type: | Data |
The status of a domain changes whenever the domain is modified
Return type: | int |
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Returns: | the identifier of the matrix type to be used for the global stiffness matrix when a particular solver package and symmetric matrix is used. |
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Return type: | int |
Returns: | tag id for name |
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Return type: | string |
Return type: | Data |
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Returns: | Locations in the`Domain`. FunctionSpace is chosen appropriately |
Returns: | True is name corresponds to a tag |
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Return type: | bool |
creates a SystemMatrixAdapter stiffness matrix and initializes it with zeros
Parameters: |
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creates a TransportProblemAdapter
Parameters: |
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Returns: | True if this code is executing on the master process |
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Return type: | bool |
Parameters: | full (bool) – |
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Give a tag number a name.
Parameters: |
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Note : | Tag names must be unique within a domain |
assigns new location to the domain
Parameters: | arg (Data) – |
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Returns: | A space separated list of tag names |
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Return type: | string |
Does this domain support contact elements.
Bases: Boost.Python.instance
Represents a collection of datapoints. It is used to store the values of a function. For more details please consult the c++ class documentation.
Make this object a copy of other
note: The two objects will act independently from now on. That is, changing other after this call will not change this object and vice versa.
note: | In the no argument form, a new object will be returned which is an independent copy of this object. |
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Selectively copy values from other Data.Datapoints which correspond to positive values in mask will be copied from other
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Convert this object into lazy representation
Save the data as a netCDF file
Parameters: | fileName (string) – |
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Convert the data to expanded representation if it is not expanded already.
Return type: | FunctionSpace |
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Return type: | int |
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Returns: | Number of datapoints in the object |
Returns: | the number of indices required to address a component of a datapoint |
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Return type: | positive int |
Returns the shape of the datapoints in this object as a python tuple. Scalar data has the shape ()
Return type: | tuple |
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Return tag number for the specified datapoint
Return type: | int |
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Parameters: | dpno (int) – datapoint number |
Returns: | Value of the specified datapoint |
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Return type: | tuple |
Parameters: | dataPointNo (int) – datapoint to access |
Get a specific datapoint from a specific process
Return type: | tuple |
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Parameters: |
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Interpolate this object’s values into a new functionspace.
Creates a new Data object by interpolating using the source data (which are looked up in table) A must be the outer dimension on the table
param table: two dimensional collection of values param Amin: The base of locations in table type Amin: float param Astep: size of gap between each item in the table type Astep: float param undef: upper bound on interpolated values type undef: float param B: Scalar representing the second coordinate to be mapped into the table type B: Data param Bmin: The base of locations in table for 2nd dimension type Bmin: float param Bstep: size of gap between each item in the table for 2nd dimension type Bstep: float param check_boundaries: if true, then values outside the boundaries will be rejected. If false, then boundary values will be used. raise RuntimeError(DataException): if the coordinates do not map into the table or if the interpolated value is above undef rtype: Data
interpolateTable( (Data)arg1, (object)table, (float)Amin, (float)Astep [, (float)undef=1e+50 [, (bool)check_boundaries=False]]) -> Data
Return type: | bool |
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Returns: | True if this Data is an instance of DataConstant |
Note : | This does not mean the data is immutable. |
Is this object an instance of DataEmpty
Return type: | bool |
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Note : | This is not the same thing as asking if the object contains datapoints. |
Return type: | bool |
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Returns: | True if this Data is expanded. |
Return type: | bool |
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Returns: | True if this Data is lazy. |
Can this instance be modified. :rtype: bool
Return type: | bool |
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Returns: | True if this Data is not lazy. |
Return type: | bool |
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Returns: | True if this Data is expanded. |
Please consider using getSupLocator() from pdetools instead.
Please consider using getInfLocator() from pdetools instead.
1D interpolation with non equally spaced points
1D interpolation of slope with non equally spaced points
Convert the data to non-lazy representation.
Disallow modifications to this data object
Note : | This method does not allow you to undo protection. |
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Set the value of tagged Data.
param tagKey: tag to update type tagKey: int
param name: | tag to update |
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type name: | string |
param value: | value to set tagged data to |
type value: | object which acts like an array, tuple or list |
After this call the object will store values of the same shape as before but all components will be zero.
setValueOfDataPoint( (Data)arg1, (int)arg2, (object)arg3) -> None
setValueOfDataPoint( (Data)arg1, (int)arg2, (float)arg3) -> None :
Modify the value of a single datapoint.
param dataPointNo: type dataPointNo: int param value: type value: float or an object which acts like an array, tuple or list warning: Use of this operation is discouraged. It prevents some optimisations from operating.
Convert data to tagged representation if it is not already tagged or expanded
Return the datapoints of this object in a list. Each datapoint is stored as a tuple.
Parameters: | scalarastuple – if True, scalar data will be wrapped as a tuple. True => [(0), (1), (2)]; False => [0, 1, 2] |
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Bases: object
Escript data import/export manager.
Example:
dm=DataManager(formats=[DataManager.RESTART,DataManager.VTK])
if dm.hasData():
dom = dm.getDomain()
time = dm.getValue("time")
dt = dm.getValue("dt")
T = dm.getValue("T")
u = dm.getValue("u")
else:
T = ...
u = ...
dm.addData(time=time,dt=dt,T=T,u=u) # add data and variables
dm.setTime(time) # set the simulation timestamp
dm.export() # write out data
Adds ‘escript.Data’ objects and other data to be exported to this manager.
Note : | This method does not make copies of Data objects so any modifications will be carried over until export() is called. |
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Executes the actual data export. Depending on the formats parameter used in the constructor all data added by addData() is written to disk (RESTART,SILO,VTK) or made available through the VisIt simulation interface (VISIT).
Returns the export cycle (=number of times export() has been called)
Returns the domain as recovered from restart files.
Returns an ‘escript.Data’ object or other value that has been loaded from restart files.
Returns True if the manager holds data for restart
Sets the number of calls to export() before new restart files are generated.
Sets the domain without adding data.
Sets labels for the mesh axes. These are currently only used by the Silo exporter.
Sets units for the mesh axes. These are currently only used by the Silo exporter.
Sets metadata namespaces and the corresponding metadata. Only used for the VTK file format at the moment.
Parameters: |
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Sets the simulation timestamp.
Bases: Boost.Python.instance
Base class for all domains.
Wait until all processes have reached this point
Dumps the domain to a file:param filename: :type filename: string
Returns: | the rank of this process |
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Return type: | int |
Returns: | the number of processes used for this Domain |
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Return type: | int |
Return type: | escript |
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Returns: | Boundary normals |
Returns: | the local size of samples. The function space is chosen appropriately |
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Return type: | Data |
The status of a domain changes whenever the domain is modified
Return type: | int |
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Returns: | tag id for name |
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Return type: | string |
Return type: | Data |
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Returns: | Locations in the`Domain`. FunctionSpace is chosen appropriately |
Returns: | True is name corresponds to a tag |
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Return type: | bool |
Returns: | True if this code is executing on the master process |
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Return type: | bool |
Give a tag number a name.
Parameters: |
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Note : | Tag names must be unique within a domain |
Returns: | A space separated list of tag names |
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Return type: | string |
Does this domain support contact elements.
Bases: object
Adds an expression to this evaluator.
Returns: | the modified Evaluator object |
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Evaluates all expressions in this evaluator and returns the result as a tuple.
Returns: | the evaluated expressions in the order they were added to this Evaluator. |
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Symbol substitution.
Returns: | the modified Evaluator object |
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Bases: object
Interface to write data to a file. In essence this class wrappes the standard file object to write data that are global in MPI to a file. In fact, data are writen on the processor with MPI rank 0 only. It is recommended to use FileWriter rather than open in order to write code that is running with as well as with MPI. It is safe to use open onder MPI to read data which are global under MPI. :var name: name of file :var mode: access mode (=’w’ or =’a’) :var closed: True to indicate closed file :var newlines: line seperator
Closes the file
Flush the internal I/O buffer.
Write string txt to file.
Parameters: | txt (str) – string txt to be written to file |
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Write the list txt of strings to the file.
Parameters: | txts (any iterable object producing strings) – sequense of strings to be written to file |
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Note : | Note that newlines are not added. This method is equivalent to call write() for each string. |
Bases: Boost.Python.instance
A FunctionSpace describes which points from the Domain to use to represent functions.
Returns: | the approximation order referring to the maximum degree of a polynomial which can be represented exactly in interpolation and/or integration. |
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Return type: | int |
Returns: | the spatial dimension of the underlying domain. |
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Return type: | int |
Returns: | the underlying Domain for this FunctionSpace. |
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Return type: | Domain |
Returns: | a list of the tags used in this function space |
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Return type: | list |
Returns: | the reference number associated with dataPointNo |
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Return type: | int |
Returns: | the tag associated with the given sample number. |
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Return type: | int |
Returns: | a function whose values are its input coordinates. ie an identity function. |
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Return type: | Data |
Set tags according to a mask
param newtag: tag number to set type newtag: string, non-zero int param mask: Samples which correspond to positive values in the mask will be set to newtag. type mask: scalar Data
setTags( (FunctionSpace)arg1, (str)newtag, (Data)mask) -> None
Bases: esys.downunder.seismic.WaveBase
Solving the HTI wave equation (along the x_0 axis)
Note : | In case of a two dimensional domain a horizontal domain is considered, i.e. the depth component is dropped. |
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returns the solution for the next time marker t which needs to greater than the time marker from the previous call.
Bases: object
This class is used to define a general nonlinear, steady, second order PDE for an unknown function u on a given domain defined through a Domain object.
For a single PDE having a solution with a single component the nonlinear PDE is defined in the following form:
-div(X) + Y = 0
where X,*Y*=f(u,*grad(u)*), div(F) denotes the divergence of F and grad(F) is the spatial derivative of F.
The coefficients X (rank 1) and Y (scalar) have to be specified through Symbol objects.
The following natural boundary conditions are considered:
n[j]*X[j] - y = 0
where n is the outer normal field. Notice that the coefficient X is defined in the PDE. The coefficient y is a scalar Symbol.
Constraints for the solution prescribe the value of the solution at certain locations in the domain. They have the form
u=r where q>0
r and q are each scalar where q is the characteristic function defining where the constraint is applied. The constraints override any other condition set by the PDE or the boundary condition.
For a system of PDEs and a solution with several components, u is rank one, while the PDE coefficient X is rank two and Y and y is rank one.
The PDE is solved by linearising the coefficients and iteratively solving the corresponding linear PDE until the error is smaller than a tolerance or a maximum number of iterations is reached.
Typical usage:
u = Symbol('u', dim=dom.getDim())
p = NonlinearPDE(dom, u)
p.setValue(X=grad(u), Y=5*u)
v = p.getSolution(u=0.)
Creates a new coefficient name as Symbol
Parameters: | name (string) – name of the coefficient requested |
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Returns: | the value of the coefficient |
Return type: | Symbol or Data (for name = “q”) |
Raises IllegalCoefficient: | |
if name is not a coefficient of the PDE |
Returns the value of the coefficient name as Symbol
Parameters: | name (string) – name of the coefficient requested |
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Returns: | the value of the coefficient |
Return type: | Symbol |
Raises IllegalCoefficient: | |
if name is not a coefficient of the PDE |
Returns the linear PDE used to calculate the Newton-Raphson update
Return type: | LinearPDE |
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Returns the options of the linear PDE solver class
Returns the number of the solution components :rtype: int
Calculates the sensitivity of the solution of an input factor f in direction g.
Parameters: |
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Returns: | the sensitivity |
Return type: | Data with shape u.getShape()+(len(g),) if len(g)>1 or u.getShape() if len(g)==1 |
Returns the shape of the coefficient name
Parameters: | name (string) – name of the coefficient enquired |
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Returns: | the shape of the coefficient name |
Return type: | tuple of int |
Raises IllegalCoefficient: | |
if name is not a coefficient of the PDE |
Returns the solution of the PDE.
Parameters: | subs – Substitutions for all symbols used in the coefficients including the initial value for the unknown u. |
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Returns: | the solution |
Return type: | Data |
Returns the symbol of the PDE unknown
Returns: | the symbol of the PDE unknown |
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Return type: | Symbol |
Allows setting options for the nonlinear PDE.
Sets new values to one or more coefficients.
Parameters: |
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Raises: |
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Prints the text message if the debug level is greater than DEBUG0
Parameters: | text (string) – message to be printed |
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Prints the text message if the debug level is greater than DEBUG3
Parameters: | text (string) – message to be printed |
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Bases: Boost.Python.instance
Return type: | bool |
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Returns: | True if matrix is empty |
matrix*vector multiplication
resets the matrix entries
writes the matrix to a file using the Harwell-Boeing file format
writes the matrix to a file using the Matrix Market file format
Bases: esys.downunder.seismic.Wavelet
The Ricker Wavelet w=f(t)
get the acceleration f’‘(t) at time t
return value of wavelet center
returns the time scale which is the inverse of the largest freqence with a significant spectral component.
get value of wavelet at time t
Bases: object
as simple writer for 2D and 3D seimic lines in particular for synthetic data
Typical usage:
from esys.escript import unitsSI as U sw=SimpleSEGYWriter([0.,100*U.m,200*U,m,300.], source=200*U.m, sampling_interval=4*U.msec) while n < 10:
sw.addRecord([i*2., i*0.67, i**2, -i*7])sw.write(‘example.segy’)
Note : | the writer uses obspy |
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adds a record to the traces. a time difference of sample_interval between two records is assumed. The record mast be a list of as many values as given receivers or a float if a single receiver is used.
Parameters: | record – list of tracks to be added to the record. |
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returns the sampling interval in seconds.
writes to segy file
Parameters: | filename – file name |
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Note : | the function uses the obspy module. |
Bases: esys.downunder.seismic.WaveBase
Solving the sonic wave equation
p_tt = (v_p**2 * p_i)_i + f(t) * delta_s where (p-) velocity v_p.
f(t) is wavelet acting at a point source term at positon s
returns the solution for the next time marker t which needs to greater than the time marker from the previous call.
Bases: object
Symbol objects are placeholders for a single mathematical symbol, such as ‘x’, or for arbitrarily complex mathematical expressions such as ‘c*x**4+alpha*exp(x)-2*sin(beta*x)’, where ‘alpha’, ‘beta’, ‘c’, and ‘x’ are also Symbols (the symbolic ‘atoms’ of the expression).
With the help of the ‘Evaluator’ class these symbols and expressions can be resolved by substituting numeric values and/or escript Data objects for the atoms. To facilitate the use of Data objects a Symbol has a shape (and thus a rank) as well as a dimension (see constructor). Symbols are useful to perform mathematical simplifications, compute derivatives and as coefficients for nonlinear PDEs which can be solved by the NonlinearPDE class.
Applies the function f to all elements (if on_type is None) or to all elements of type on_type.
Returns the atoms that form the current Symbol.
By default, only objects that are truly atomic and cannot be divided into smaller pieces are returned: symbols, numbers, and number symbols like I and pi. It is possible to request atoms of any type, however.
Note that if this symbol contains components such as [x]_i_j then only their main symbol ‘x’ is returned.
Parameters: | types – types to restrict result to |
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Returns: | list of atoms of specified type |
Return type: | set |
Returns the coefficient of the term “x” or 0 if there is no “x”.
If “x” is a scalar symbol then “x” is searched in all components of this symbol. Otherwise the shapes must match and the coefficients are checked component by component.
Example:
x=Symbol('x', (2,2))
y=3*x
print y.coeff(x)
print y.coeff(x[1,1])
will print:
[[3 3]
[3 3]]
[[0 0]
[0 3]]
Parameters: | x (Symbol, numpy.ndarray, list) – the term whose coefficients are to be found |
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Returns: | the coefficient(s) of the term |
Return type: | Symbol |
Applies the sympy.expand operation on all elements in this symbol
Returns a dictionary of symbol names and the escript Data objects they represent within this Symbol.
Returns: | the dictionary of substituted Data objects |
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Return type: | dict |
Returns the spatial dimensionality of this symbol.
Returns: | the symbol’s spatial dimensionality, or -1 if undefined |
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Return type: | int |
Returns the rank of this symbol.
Returns: | the symbol’s rank which is equal to the length of the shape. |
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Return type: | int |
Returns the shape of this symbol.
Returns: | the symbol’s shape |
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Return type: | tuple of int |
Returns a symbol which represents the gradient of this symbol. :type where: Symbol, FunctionSpace
Returns an element of this symbol. This method behaves like the item() method of numpy.ndarray. If this is a scalar Symbol, no arguments are allowed and the only element in this Symbol is returned. Otherwise, ‘args’ specifies a flat or nd-index and the element at that index is returned.
Parameters: | args – index of item to be returned |
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Returns: | the requested element |
Return type: | sympy.Symbol, int, or float |
Applies the sympy.simplify operation on all elements in this symbol
Substitutes an expression.
Returns the trace of this Symbol.
Returns the transpose of this Symbol.
Bases: esys.escriptcore.escriptcpp.Domain
Test Class for domains with no structure. May be removed from future releases without notice.
Wait until all processes have reached this point
Dumps the domain to a file:param filename: :type filename: string
Returns: | the rank of this process |
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Return type: | int |
Returns: | the number of processes used for this Domain |
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Return type: | int |
Return type: | escript |
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Returns: | Boundary normals |
Returns: | the local size of samples. The function space is chosen appropriately |
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Return type: | Data |
The status of a domain changes whenever the domain is modified
Return type: | int |
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Returns: | tag id for name |
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Return type: | string |
Return type: | Data |
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Returns: | Locations in the`Domain`. FunctionSpace is chosen appropriately |
Returns: | True is name corresponds to a tag |
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Return type: | bool |
Returns: | True if this code is executing on the master process |
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Return type: | bool |
Give a tag number a name.
Parameters: |
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Note : | Tag names must be unique within a domain |
Returns: | A space separated list of tag names |
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Return type: | string |
Does this domain support contact elements.
Bases: Boost.Python.instance
inserts constraint u_{,t}=r where q>0 into the problem using a weighting factor
Return type: | int |
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resets the transport operator typically as they have been updated.
Bases: esys.downunder.seismic.WaveBase
Solving the VTI wave equation
Note : | In case of a two dimensional domain the second spatial dimenion is depth. |
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returns the solution for the next time marker t which needs to greater than the time marker from the previous call.
Bases: object
Base for wave propagation using the Verlet scheme.
u_tt = A(t,u), u(t=t0)=u0, u_t(t=t0)=v0
with a given acceleration force as function of time.
a_n=A(t_{n-1}) v_n=v_{n-1} + dt * a_n u_n=u_{n-1} + dt * v_n
returns the solution for the next time marker t which needs to greater than the time marker from the previous call.
Bases: object
place holder for source wavelet
Returns the absolute value of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray.) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Compute a tensor product of two Data objects.
Return type: | |
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Parameters: |
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Returns: | a continuous FunctionSpace (overlapped node values) |
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Return type: | FunctionSpace |
Return type: | FunctionSpace |
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Returns: | a function FunctionSpace |
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Return type: | FunctionSpace |
Returns: | a function on boundary FunctionSpace |
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Return type: | FunctionSpace |
Returns: | Return a FunctionSpace on right side of contact |
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Return type: | FunctionSpace |
Returns: | Return a FunctionSpace on left side of contact |
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Return type: | FunctionSpace |
Returns the L2 norm of arg at where.
Parameters: | arg (escript.Data or Symbol) – function of which the L2 norm is to be calculated |
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Returns: | L2 norm of arg |
Return type: | float or Symbol |
Note : | L2(arg) is equivalent to sqrt(integrate(inner(arg,arg))) |
Defines a system of linear PDEs.
Parameters: |
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Return type: | LinearPDE |
Defines a single linear PDE.
Parameters: |
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Return type: | LinearPDE |
Returns the Lsup-norm of argument arg. This is the maximum absolute value over all data points. This function is equivalent to sup(abs(arg)).
Parameters: | arg (float, int, escript.Data, numpy.ndarray) – argument |
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Returns: | maximum value of the absolute value of arg over all components and all data points |
Return type: | float |
Raises TypeError: | |
if type of arg cannot be processed |
Wait until all MPI processes have reached this point.
Creates a new expanded Data object containing pseudo-random values.
Parameters: |
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Returns: | a continuous with reduced order FunctionSpace (overlapped node values on reduced element order) |
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Return type: | FunctionSpace |
Returns: | a function FunctionSpace with reduced integration order |
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Return type: | FunctionSpace |
Returns: | a function on boundary FunctionSpace with reduced integration order |
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Return type: | FunctionSpace |
Returns: | Return a FunctionSpace on right side of contact with reduced integration order |
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Return type: | FunctionSpace |
Returns: | a FunctionSpace on left side of contact with reduced integration order |
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Return type: | FunctionSpace |
Return type: | FunctionSpace |
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Construct a Data object containing scalar data-points.
Parameters: |
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Return type: |
Return type: | FunctionSpace |
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Construct a Data object containing rank2 data-points.
param value: scalar value for all points rtype: Data type value: float param what: FunctionSpace for Data type what: FunctionSpace param expanded: If True, a value is stored for each point. If False, more efficient representations may be used type expanded: bool
Tensor( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x3804850> [, (bool)expanded=False]]) -> Data
Construct a Data object containing rank3 data-points.
param value: scalar value for all points rtype: Data type value: float param what: FunctionSpace for Data type what: FunctionSpace param expanded: If True, a value is stored for each point. If False, more efficient representations may be used type expanded: bool
Tensor3( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x3804950> [, (bool)expanded=False]]) -> Data
Construct a Data object containing rank4 data-points.
param value: scalar value for all points rtype: Data type value: float param what: FunctionSpace for Data type what: FunctionSpace param expanded: If True, a value is stored for each point. If False, more efficient representations may be used type expanded: bool
Tensor4( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x3804a50> [, (bool)expanded=False]]) -> Data
Construct a Data object containing rank1 data-points.
param value: scalar value for all points rtype: Data type value: float param what: FunctionSpace for Data type what: FunctionSpace param expanded: If True, a value is stored for each point. If False, more efficient representations may be used type expanded: bool
Vector( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x3804750> [, (bool)expanded=False]]) -> Data
Returns the inverse cosine of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns the inverse hyperbolic cosine of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns the inverse sine of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns the inverse hyperbolic sine of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns inverse tangent of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns the inverse hyperbolic tangent of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns the bounding box of a domain
Parameters: | domain (escript.Domain) – a domain |
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Returns: | bounding box of the domain |
Return type: | list of pairs of float |
Returns the edge lengths of the bounding box of a domain
Parameters: | domain (escript.Domain) – a domain |
---|---|
Return type: | list of float |
Parameters: |
|
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Returns: | True if src can be interpolated to dest |
Return type: | bool |
Cuts the values of arg between minval and maxval.
Parameters: |
|
---|---|
Returns: | an object that contains all values from arg between minval and maxval |
Return type: | numpy.ndarray, escript.Data, Symbol, int or float depending on the input |
Raises ValueError: | |
if minval>maxval |
Identifies, if possible, the spatial dimension across a set of objects which may or may not have a spatial dimension.
Parameters: | args – given objects |
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Returns: | the spatial dimension of the objects with identifiable dimension (see pokeDim). If none of the objects has a spatial dimension None is returned. |
Return type: | int or None |
Raises ValueError: | |
if the objects with identifiable dimension don’t have the same spatial dimension. |
Returns a shape to which arg0 can be extended from the right and arg1 can be extended from the left.
Parameters: | |
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Returns: | the shape of arg0 or arg1 such that the left part equals the shape of arg0 and the right end equals the shape of arg1 |
Return type: | tuple of int |
Raises ValueError: | |
if no shape can be found |
Wrapper to allow non-data objects to be used.
Returns cosine of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns the hyperbolic cosine of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
creating a distribution which is one in the interior of the domain of x and is falling down to the value ‘absorption_cut’ over a margain of thickness ‘absorption_zone’ toward each boundary except the top of the domain.
Parameters: |
|
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Returns: | function on ‘x’ which is one in the iterior and decays to almost zero over a margin toward the boundary. |
Returns a lazy version of arg
Returns the deviatoric version of arg.
Returns the diameter of a domain.
Parameters: | domain (escript.Domain) – a domain |
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Return type: | float |
Returns the divergence of arg at where.
Parameters: |
|
---|---|
Returns: | divergence of arg |
Return type: | escript.Data or Symbol |
Returns the eigenvalues of the square matrix arg.
Parameters: | arg (numpy.ndarray, escript.Data, Symbol) – square matrix. Must have rank 2 and the first and second dimension must be equal. It must also be symmetric, ie. transpose(arg)==arg (this is not checked). |
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Returns: | the eigenvalues in increasing order |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
Note : | for escript.Data and Symbol objects the dimension is restricted to 3. |
Returns the eigenvalues and eigenvectors of the square matrix arg.
Parameters: | arg (escript.Data) – square matrix. Must have rank 2 and the first and second dimension must be equal. It must also be symmetric, ie. transpose(arg)==arg (this is not checked). |
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Returns: | the eigenvalues and eigenvectors. The eigenvalues are ordered by increasing value. The eigenvectors are orthogonal and normalized. If V are the eigenvectors then V[:,i] is the eigenvector corresponding to the i-th eigenvalue. |
Return type: | tuple of escript.Data |
Note : | The dimension is restricted to 3. |
Returns the error function erf of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray.) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
arg0 and arg1 are both Data objects but not necessarily on the same function space. They could be identical!!!
arg0 and arg1 are both Data objects but not necessarily on the same function space. They could be identical!!!
arg0 and arg1 are both Data objects but not necessarily on the same function space. They could be identical!!!
arg is a Data object!
Returns e to the power of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray.) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Generalized tensor product.
C{out[s,t]=Sigma_r arg0[s,r]*arg1[r,t]}
Parameters: | |
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Returns: | the general tensor product of arg0 and arg1 at each data point |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
Generalized tensor product of arg0 and transpose of arg1.
C{out[s,t]=Sigma_r arg0[s,r]*arg1[t,r]}
The function call generalTensorTransposedProduct(arg0,arg1,axis_offset) is equivalent to generalTensorProduct(arg0,transpose(arg1,arg1.ndim-axis_offset),axis_offset).
Parameters: | |
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Returns: | the general tensor product of arg0 and transpose(arg1) at each data point |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
Generalized tensor product of transposed of arg0 and arg1.
C{out[s,t]=Sigma_r arg0[r,s]*arg1[r,t]}
The function call generalTransposedTensorProduct(arg0,arg1,axis_offset) is equivalent to generalTensorProduct(transpose(arg0,arg0.ndim-axis_offset),arg1,axis_offset).
Parameters: | |
---|---|
Returns: | the general tensor product of transpose(arg0) and arg1 at each data point |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
Returns the value in arg which is closest to origin.
Parameters: |
|
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Returns: | value in arg closest to origin |
Return type: | numpy.ndarray |
Read the value of an escript tuning parameter
Parameters: |
|
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Return the rank of this process in the MPI World.
Return number of MPI processes in the job.
Each MPI process calls this function with a value for arg1. The maximum value is computed and returned.
Return type: | int |
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Each MPI process calls this function with a value for arg1. The values are added up and the total value is returned.
Return type: | int |
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Return the maximum number of threads available to OpenMP.
Identifies the rank of the argument.
Parameters: | arg (numpy.ndarray, escript.Data, float, int, Symbol) – an object whose rank is to be returned |
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Returns: | the rank of the argument |
Return type: | int |
Raises TypeError: | |
if type of arg cannot be processed |
Identifies the shape of the argument.
Parameters: | arg (numpy.ndarray, escript.Data, float, int, Symbol) – an object whose shape is to be returned |
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Returns: | the shape of the argument |
Return type: | tuple of int |
Raises TypeError: | |
if type of arg cannot be processed |
Returns a list of tag names used by the domain.
Parameters: | domain (escript.Domain) – a domain object |
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Returns: | a list of tag names used by the domain |
Return type: | list of str |
For testing only. May be removed without notice.
This method will only report accurate version numbers for clean checkouts.
Returns the spatial gradient of arg at where.
If g is the returned object, then
- if arg is rank 0 g[s] is the derivative of arg with respect to the s-th spatial dimension
- if arg is rank 1 g[i,s] is the derivative of arg[i] with respect to the s-th spatial dimension
- if arg is rank 2 g[i,j,s] is the derivative of arg[i,j] with respect to the s-th spatial dimension
- if arg is rank 3 g[i,j,k,s] is the derivative of arg[i,j,k] with respect to the s-th spatial dimension.
Parameters: |
|
---|---|
Returns: | gradient of arg |
Return type: | escript.Data or Symbol |
Returns the shape x shape identity tensor.
Parameters: | shape (tuple of int) – input shape for the identity tensor |
---|---|
Returns: | array whose shape is shape x shape where u[i,k]=1 for i=k and u[i,k]=0 otherwise for len(shape)=1. If len(shape)=2: u[i,j,k,l]=1 for i=k and j=l and u[i,j,k,l]=0 otherwise. |
Return type: | numpy.ndarray of rank 1, rank 2 or rank 4 |
Raises ValueError: | |
if len(shape)>2 |
Returns the d x d identity matrix.
Parameters: | d (int, escript.Domain or escript.FunctionSpace) – dimension or an object that has the getDim method defining the dimension |
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Returns: | the object u of rank 2 with u[i,j]=1 for i=j and u[i,j]=0 otherwise |
Return type: | numpy.ndarray or escript.Data of rank 2 |
Returns the d x d x d x d identity tensor.
Parameters: | d (int or any object with a getDim method) – dimension or an object that has the getDim method defining the dimension |
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Returns: | the object u of rank 4 with u[i,j,k,l]=1 for i=k and j=l and u[i,j,k,l]=0 otherwise |
Return type: | numpy.ndarray or escript.Data of rank 4 |
Returns the minimum value over all data points.
Parameters: | arg (float, int, escript.Data, numpy.ndarray) – argument |
---|---|
Returns: | minimum value of arg over all components and all data points |
Return type: | float |
Raises TypeError: | |
if type of arg cannot be processed |
Inner product of the two arguments. The inner product is defined as:
C{out=Sigma_s arg0[s]*arg1[s]}
where s runs through arg0.Shape.
arg0 and arg1 must have the same shape.
Parameters: | |
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Returns: | the inner product of arg0 and arg1 at each data point |
Return type: | numpy.ndarray, escript.Data, Symbol, float depending on the input |
Raises ValueError: | |
if the shapes of the arguments are not identical |
Inserts tag names into the domain.
Parameters: |
|
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Inserts tagged values into the target using tag names.
Parameters: |
|
---|---|
Returns: | target |
Return type: | escript.Data |
Returns the integral of the function arg over its domain. If where is present arg is interpolated to where before integration.
Parameters: |
|
---|---|
Returns: | integral of arg |
Return type: | float, numpy.ndarray or Symbol |
Interpolates the function into the FunctionSpace where. If the argument arg has the requested function space where no interpolation is performed and arg is returned.
Parameters: |
|
---|---|
Returns: | interpolated argument |
Return type: | escript.Data or Symbol |
Returns the inverse of the square matrix arg.
Parameters: | arg (numpy.ndarray, escript.Data, Symbol) – square matrix. Must have rank 2 and the first and second dimension must be equal. |
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Returns: | inverse of the argument. matrix_mult(inverse(arg),arg) will be almost equal to kronecker(arg.getShape()[0]) |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
Note : | for escript.Data objects the dimension is restricted to 3. |
Returns the jump of arg across the continuity of the domain.
Parameters: |
|
---|---|
Returns: | jump of arg |
Return type: | escript.Data or Symbol |
Returns the kronecker delta-symbol.
Parameters: | d (int, escript.Domain or escript.FunctionSpace) – dimension or an object that has the getDim method defining the dimension |
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Returns: | the object u of rank 2 with u[i,j]=1 for i=j and u[i,j]=0 otherwise |
Return type: | numpy.ndarray or escript.Data of rank 2 |
Returns the length (Euclidean norm) of argument arg at each data point.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
---|---|
Return type: | float, escript.Data, Symbol depending on the type of arg |
Returns: | A list of pairs (p,d) where p is the name of a parameter for escript and d is a description. |
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reads Data on domain from file in netCDF format
Parameters: |
|
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Returns: | True if the load function is configured. |
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Returns the natural logarithm of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray.) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns base-10 logarithm of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
---|---|
Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns the length of the longest edge of the domain
Parameters: | domain (escript.Domain) – a domain |
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Returns: | longest edge of the domain parallel to the Cartesian axis |
Return type: | float |
Returns a representation of arg0 and arg1 which have the same shape.
Parameters: | |
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Returns: | arg0 and arg1 where copies are returned when the shape has to be changed |
Return type: | tuple |
Converts arg0 and arg1 both to the same type numpy.ndarray or escript.Data
Parameters: |
|
---|---|
Returns: | a tuple representing arg0 and arg1 with the same type or with at least one of them being a Symbol |
Return type: | tuple of two numpy.ndarray or two escript.Data |
Raises TypeError: | |
if type of arg0 or arg1 cannot be processed |
matrix-matrix or matrix-vector product of the two arguments.
C{out[s0]=Sigma_{r0} arg0[s0,r0]*arg1[r0]}
or
C{out[s0,s1]=Sigma_{r0} arg0[s0,r0]*arg1[r0,s1]}
The second dimension of arg0 and the first dimension of arg1 must match.
Parameters: | |
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Returns: | the matrix-matrix or matrix-vector product of arg0 and arg1 at each data point |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
Raises ValueError: | |
if the shapes of the arguments are not appropriate |
matrix-transposed(matrix) product of the two arguments.
C{out[s0,s1]=Sigma_{r0} arg0[s0,r0]*arg1[s1,r0]}
The function call matrix_transposed_mult(arg0,arg1) is equivalent to matrix_mult(arg0,transpose(arg1)).
The last dimensions of arg0 and arg1 must match.
Parameters: | |
---|---|
Returns: | the product of arg0 and the transposed of arg1 at each data point |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
Raises ValueError: | |
if the shapes of the arguments are not appropriate |
See matrix_mult.
The maximum over arguments args.
Parameters: | args (numpy.ndarray, escript.Data, Symbol, int or float) – arguments |
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Returns: | an object which in each entry gives the maximum of the corresponding values in args |
Return type: | numpy.ndarray, escript.Data, Symbol, int or float depending on the input |
Returns the maximum value over all components of arg at each data point.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
return the mean value of the argument over its domain
Parameters: | arg (escript.Data) – function |
---|---|
Returns: | mean value |
Return type: | float or numpy.ndarray |
The minimum over arguments args.
Parameters: | args (numpy.ndarray, escript.Data, Symbol, int or float) – arguments |
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Returns: | an object which gives in each entry the minimum of the corresponding values in args |
Return type: | numpy.ndarray, escript.Data, Symbol, int or float depending on the input |
Returns the minimum value over all components of arg at each data point.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
creates a directory of name pathname if the directory does not exist.
Parameters: | pathname (str or sequence of strings) – valid path name |
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Note : | The method is MPI safe. |
Product of arg0 and arg1.
Parameters: | |
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Returns: | the product of arg0 and arg1 |
Return type: | Symbol, float, int, escript.Data or numpy.ndarray |
Note : | The shape of both arguments is matched according to the rules used in matchShape. |
returns the negative part of arg
Returns the non-symmetric part of the square matrix arg. That is, (arg-transpose(arg))/2.
Parameters: | arg (numpy.ndarray, escript.Data, Symbol) – input matrix. Must have rank 2 or 4 and be square. |
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Returns: | non-symmetric part of arg |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
Returns the normalized version of arg (=``arg/length(arg)``).
Parameters: |
|
---|---|
Returns: | normalized arg where arg is non-zero, and zero elsewhere |
Return type: | escript.Data or Symbol |
The outer product of the two arguments. The outer product is defined as:
out[t,s]=arg0[t]*arg1[s]
Parameters: | |
---|---|
Returns: | the outer product of arg0 and arg1 at each data point |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
Identifies the spatial dimension of the argument.
Parameters: | arg (any) – an object whose spatial dimension is to be returned |
---|---|
Returns: | the spatial dimension of the argument, if available, or None |
Return type: | int or None |
returns the positive part of arg
Resorts the components of arg according to index.
Returns the value of arg resolved.
Spawns an external MPI program using a separate communicator.
returns arg0/arg1 but return 0 where arg1 is (almost) zero
Writes Data objects to a CSV file. These objects must have compatible FunctionSpaces, i.e. it must be possible to interpolate all data to one FunctionSpace. Note, that with more than one MPI rank this function will fail for some function spaces on some domains.
Parameters: |
|
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The keyword args are Data objects to save. If a scalar Data object is passed with the name mask, then only samples which correspond to positive values in mask will be output. Example:
s=Scalar(..)
v=Vector(..)
t=Tensor(..)
f=float()
saveDataCSV("f.csv", a=s, b=v, c=t, d=f)
Will result in a file
a, b0, b1, c0_0, c0_1, .., c1_1, d 1.0, 1.5, 2.7, 3.1, 3.4, .., 0.89, 0.0 0.9, 8.7, 1.9, 3.4, 7.8, .., 1.21, 0.0
The first line is a header, the remaining lines give the values.
Saves Data objects to files and creates an I{escript dataset} (ESD) file for convenient processing/visualisation.
Single timestep example:
tmp = Scalar(..)
v = Vector(..)
saveESD("solution", "data", temperature=tmp, velocity=v)
Time series example:
while t < t_end:
tmp = Scalar(..)
v = Vector(..)
# save every 10 timesteps
if t % 10 == 0:
saveESD("solution", "data", timeStep=t, deltaT=10, temperature=tmp, velocity=v)
t = t + 1
tmp, v and the domain are saved in native format in the “data” directory and the file “solution.esd” is created that refers to tmp by the name “temperature” and to v by the name “velocity”.
Parameters: |
|
---|---|
Note : | The ESD concept is experimental and the file format likely to change so use this function with caution. |
Note : | The data objects have to be defined on the same domain (but not necessarily on the same FunctionSpace). |
Note : | When saving a time series the first timestep must be 0 and it is assumed that data from all timesteps share the domain. The dataset file is updated in each iteration. |
Modify the value of an escript tuning parameter
Parameters: |
|
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Use of this method is strongly discouraged.
Displays the parameters escript recognises with an explanation and their current value.
Returns the sign of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns sine of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray.) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns the hyperbolic sine of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns the square root of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns the maximum value over all data points.
Parameters: | arg (float, int, escript.Data, numpy.ndarray) – argument |
---|---|
Returns: | maximum value of arg over all components and all data points |
Return type: | float |
Raises TypeError: | |
if type of arg cannot be processed |
Returns the swap of arg by swapping the components axis0 and axis1.
Parameters: |
|
---|---|
Returns: | arg with swapped components |
Return type: | escript.Data, Symbol or numpy.ndarray depending on the type of arg |
Returns the symmetric part of the square matrix arg. That is, (arg+transpose(arg))/2.
Parameters: | arg (numpy.ndarray, escript.Data, Symbol) – input matrix. Must have rank 2 or 4 and be square. |
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Returns: | symmetric part of arg |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
Returns tangent of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns the hyperbolic tangent of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
---|---|
Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
The tensor product of the two arguments.
For arg0 of rank 2 this is
C{out[s0]=Sigma_{r0} arg0[s0,r0]*arg1[r0]}
or
C{out[s0,s1]=Sigma_{r0} arg0[s0,r0]*arg1[r0,s1]}
and for arg0 of rank 4 this is
C{out[s0,s1,s2,s3]=Sigma_{r0,r1} arg0[s0,s1,r0,r1]*arg1[r0,r1,s2,s3]}
or
C{out[s0,s1,s2]=Sigma_{r0,r1} arg0[s0,s1,r0,r1]*arg1[r0,r1,s2]}
or
C{out[s0,s1]=Sigma_{r0,r1} arg0[s0,s1,r0,r1]*arg1[r0,r1]}
In the first case the second dimension of arg0 and the last dimension of arg1 must match and in the second case the two last dimensions of arg0 must match the two first dimensions of arg1.
Parameters: | |
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Returns: | the tensor product of arg0 and arg1 at each data point |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
The tensor product of the first and the transpose of the second argument.
For arg0 of rank 2 this is
C{out[s0,s1]=Sigma_{r0} arg0[s0,r0]*arg1[s1,r0]}
and for arg0 of rank 4 this is
C{out[s0,s1,s2,s3]=Sigma_{r0,r1} arg0[s0,s1,r0,r1]*arg1[s2,s3,r0,r1]}
or
C{out[s0,s1,s2]=Sigma_{r0,r1} arg0[s0,s1,r0,r1]*arg1[s2,r0,r1]}
In the first case the second dimension of arg0 and arg1 must match and in the second case the two last dimensions of arg0 must match the two last dimensions of arg1.
The function call tensor_transpose_mult(arg0,arg1) is equivalent to tensor_mult(arg0,transpose(arg1)).
Parameters: | |
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Returns: | the tensor product of the transposed of arg0 and arg1 at each data point |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
See tensor_mult.
Tests if the argument is identical to zero.
Parameters: | arg (typically numpy.ndarray, escript.Data, float, int) – the object to test for zero |
---|---|
Returns: | True if the argument is identical to zero, False otherwise |
Return type: | bool |
Returns the trace of arg which is the sum of arg[k,k] over k.
Parameters: |
|
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Returns: | trace of arg. The rank of the returned object is rank of arg minus 2. |
Return type: | escript.Data, Symbol or numpy.ndarray depending on the type of arg |
Returns the transpose of arg by swapping the first axis_offset and the last rank-axis_offset components.
Parameters: |
|
---|---|
Returns: | transpose of arg |
Return type: | escript.Data, Symbol, numpy.ndarray, float, int depending on the type of arg |
transposed(matrix)-matrix or transposed(matrix)-vector product of the two arguments.
C{out[s0]=Sigma_{r0} arg0[r0,s0]*arg1[r0]}
or
C{out[s0,s1]=Sigma_{r0} arg0[r0,s0]*arg1[r0,s1]}
The function call transposed_matrix_mult(arg0,arg1) is equivalent to matrix_mult(transpose(arg0),arg1).
The first dimension of arg0 and arg1 must match.
Parameters: | |
---|---|
Returns: | the product of the transpose of arg0 and arg1 at each data point |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
Raises ValueError: | |
if the shapes of the arguments are not appropriate |
The tensor product of the transpose of the first and the second argument.
For arg0 of rank 2 this is
C{out[s0]=Sigma_{r0} arg0[r0,s0]*arg1[r0]}
or
C{out[s0,s1]=Sigma_{r0} arg0[r0,s0]*arg1[r0,s1]}
and for arg0 of rank 4 this is
C{out[s0,s1,s2,s3]=Sigma_{r0,r1} arg0[r0,r1,s0,s1]*arg1[r0,r1,s2,s3]}
or
C{out[s0,s1,s2]=Sigma_{r0,r1} arg0[r0,r1,s0,s1]*arg1[r0,r1,s2]}
or
C{out[s0,s1]=Sigma_{r0,r1} arg0[r0,r1,s0,s1]*arg1[r0,r1]}
In the first case the first dimension of arg0 and the first dimension of arg1 must match and in the second case the two first dimensions of arg0 must match the two first dimensions of arg1.
The function call transposed_tensor_mult(arg0,arg1) is equivalent to tensor_mult(transpose(arg0),arg1).
Parameters: | |
---|---|
Returns: | the tensor product of transpose of arg0 and arg1 at each data point |
Return type: | numpy.ndarray, escript.Data, Symbol depending on the input |
Returns a unit vector u of dimension d whose non-zero element is at index i.
Parameters: |
|
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Returns: | the object u of rank 1 with u[j]=1 for j=index and u[j]=0 otherwise |
Return type: | numpy.ndarray or escript.Data of rank 1 |
Returns the volume or area of the oject arg
Parameters: | arg (escript.FunctionSpace or escript.Domain) – a geometrical object |
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Return type: | float |
Returns mask of negative values of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns mask of non-negative values of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns mask of non-positive values of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns mask of values different from zero of argument arg.
Parameters: |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises: |
|
Returns mask of positive values of argument arg.
Parameters: | arg (float, escript.Data, Symbol, numpy.ndarray.) – argument |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises TypeError: | |
if the type of the argument is not expected |
Returns mask of zero entries of argument arg.
Parameters: |
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Return type: | float, escript.Data, Symbol, numpy.ndarray depending on the type of arg |
Raises: |
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Returns the shape zero tensor.
Parameters: | shape (tuple of int) – input shape for the identity tensor |
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Returns: | array of shape filled with zeros |
Return type: | numpy.ndarray |