esys.escript.util Package

Classes

class esys.escript.util.BBxInterval(minval=0, maxval=0)

Represents an interval for bounding box coordinates.

__init__(minval=0, maxval=0)
class esys.escript.util.Data

Represents a collection of datapoints. It is used to store the values of a function. For more details please consult the c++ class documentation.

__init__((object)arg1) → None

__init__( (object)arg1, (object)value [, (object)p2 [, (object)p3 [, (object)p4]]]) -> None

conjugate((Data)arg1) → Data
copy((Data)arg1, (Data)other) → None :

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.

copy( (Data)arg1) -> Data :
note:

In the no argument form, a new object will be returned which is an independent copy of this object.

copyWithMask((Data)arg1, (Data)other, (Data)mask) → None :

Selectively copy values from other Data.Datapoints which correspond to positive values in mask will be copied from other

Parameters:

  • other (Data) – source of values

  • mask (Scalar Data)

delay((Data)arg1) → Data :

Convert this object into lazy representation

dump((Data)arg1, (str)fileName) → None :

Save the data as a HDF5 file

Parameters:

fileName (string)

expand((Data)arg1) → None :

Convert the data to expanded representation if it is not expanded already.

getDomain((Data)arg1) → Domain :
Return type:

Domain

getFunctionSpace((Data)arg1) → FunctionSpace :
Return type:

FunctionSpace

getMPIComm((Data)arg1) → object :
Returns:

the MPI communicator for this data’s domain as an mpi4py.MPI.Comm object (or None if MPI/mpi4py not enabled)

Return type:

mpi4py.MPI.Comm or None

getNumberOfDataPoints((Data)arg1) → int :
Return type:

int

Returns:

Number of datapoints in the object

getRank((Data)arg1) → int :
Returns:

the number of indices required to address a component of a datapoint

Return type:

positive int

getShape((Data)arg1) → tuple :

Returns the shape of the datapoints in this object as a python tuple. Scalar data has the shape ()

Return type:

tuple

getTagNumber((Data)arg1, (int)dpno) → int :

Return tag number for the specified datapoint

Return type:

int

Parameters:

dpno (int) – datapoint number

getTupleForDataPoint((Data)arg1, (int)dataPointNo) → object :
Returns:

Value of the specified datapoint

Return type:

tuple

Parameters:

dataPointNo (int) – datapoint to access

getTupleForGlobalDataPoint((Data)arg1, (int)procNo, (int)dataPointNo) → object :

Get a specific datapoint from a specific process

Return type:

tuple

Parameters:

  • procNo (positive int) – MPI rank of the process

  • dataPointNo (int) – datapoint to access

getX((Data)arg1) → Data :

Returns the spatial coordinates of the spatial nodes. :rtype: Data

hasInf((Data)arg1) → bool :

Returns return true if data contains +-Inf. [Note that for complex values, hasNaN and hasInf are not mutually exclusive.]

hasNaN((Data)arg1) → bool :

Returns return true if data contains NaN. [Note that for complex values, hasNaN and hasInf are not mutually exclusive.]

imag((Data)arg1) → Data
internal_maxGlobalDataPoint((Data)arg1) → tuple :

Please consider using getSupLocator() from pdetools instead.

internal_minGlobalDataPoint((Data)arg1) → tuple :

Please consider using getInfLocator() from pdetools instead.

interpolate((Data)arg1, (FunctionSpace)functionspace) → Data :

Interpolate this object’s values into a new functionspace.

interpolateTable((Data)arg1, (object)table, (float)Amin, (float)Astep, (Data)B, (float)Bmin, (float)Bstep[, (float)undef=1e+50[, (bool)check_boundaries=False]]) → Data :
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

isComplex((Data)arg1) → bool :
Return type:

bool

Returns:

True if this Data stores complex values.

isConstant((Data)arg1) → bool :
Return type:

bool

Returns:

True if this Data is an instance of DataConstant

Note:

This does not mean the data is immutable.

isEmpty((Data)arg1) → bool :

Is this object an instance of DataEmpty

Return type:

bool

Note:

This is not the same thing as asking if the object contains datapoints.

isExpanded((Data)arg1) → bool :
Return type:

bool

Returns:

True if this Data is expanded.

isLazy((Data)arg1) → bool :
Return type:

bool

Returns:

True if this Data is lazy.

isProtected((Data)arg1) → bool :

Can this instance be modified. :rtype: bool

isReady((Data)arg1) → bool :
Return type:

bool

Returns:

True if this Data is not lazy.

isTagged((Data)arg1) → bool :
Return type:

bool

Returns:

True if this Data is expanded.

nonuniformInterpolate((Data)arg1, (object)in, (object)out, (bool)check_boundaries) → Data :

1D interpolation with non equally spaced points

nonuniformSlope((Data)arg1, (object)in, (object)out, (bool)check_boundaries) → Data :

1D interpolation of slope with non equally spaced points

phase((Data)arg1) → Data
promote((Data)arg1) → None
real((Data)arg1) → Data
replaceInf((Data)arg1, (object)value) → None :

Replaces +-Inf values with value. [Note, for complex Data, both real and imaginary components are replaced even if only one part is Inf].

replaceNaN((Data)arg1, (object)value) → None :

Replaces NaN values with value. [Note, for complex Data, both real and imaginary components are replaced even if only one part is NaN].

resolve((Data)arg1) → None :

Convert the data to non-lazy representation.

setProtection((Data)arg1) → None :

Disallow modifications to this data object

Note:

This method does not allow you to undo protection.

setTaggedValue((Data)arg1, (int)tagKey, (object)value) → None :

Set the value of tagged Data.

param tagKey:

tag to update

type tagKey:

int

setTaggedValue( (Data)arg1, (str)name, (object)value) -> None :
param name:

tag to update

type name:

string

param value:

value to set tagged data to

type value:

object which acts like an array, tuple or list

setToZero((Data)arg1) → None :

After this call the object will store values of the same shape as before but all components will be zero.

setValueOfDataPoint((Data)arg1, (int)dataPointNo, (object)value) → None

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.

tag((Data)arg1) → None :

Convert data to tagged representation if it is not already tagged or expanded

toListOfTuples((Data)arg1[, (bool)scalarastuple=False]) → object :

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]

class esys.escript.util.FileWriter(fn, append=False, createLocalFiles=False)

Interface to write data to a file. In essence this class wraps the standard file object to write data that are global in MPI to a file. In fact, data are written 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 without MPI. It is safe to use open under MPI to read data which are global under MPI.

Variables:

  • name – name of file

  • mode – access mode (=’w’ or =’a’)

  • closed – True to indicate closed file

  • newlines – line separator

__init__(fn, append=False, createLocalFiles=False)

Opens a file of name fn for writing. If running under MPI only the first processor with rank==0 will open the file and write to it. If createLocalFiles each individual processor will create a file where for any processor with rank>0 the file name is extended by its rank. This option is normally only used for debug purposes.

Parameters:

  • fn (str) – filename.

  • append (bool) – if True, open file for appending rather than overwriting

  • createLocalFiles (bool) – switches on the creation of local files.

close()

Closes the file

flush()

Flush the internal I/O buffer.

write(txt)

Write string txt to file.

Parameters:

txt (str) – string txt to be written to file

writelines(txts)

Write the list txts of strings to the file.

Parameters:

txts (any iterable object producing strings) – sequence of strings to be written to file

Note:

Note that newlines are not added. This method is equivalent to calling write() for each string.

class esys.escript.util.InterpolationTable(table, origin, step=None, extend=None, order=1, undef=1e+50, check_boundaries=False, table_indexing='ijk')

Interpolates values from a regular-grid lookup table onto a mesh.

The coordinate data x passed to __call__() determines the interpolation dimension:

x.getShape()

Lookup dim

Required table rank

()

1-D

1 — shape (nx,)

(1,)

1-D

1 — shape (nx,)

(2,)

2-D

2

(3,)

3-D

3

The returned Data object is always scalar (shape ()). If the table contains complex values the result is complex Data; the coordinate Data x must always be real.

Table indexing convention (controlled by table_indexing):

  • "ijk" (default) — natural numpy order: the first index varies along the x-axis, the second along y, the third along z. Shapes: (nx,) / (nx, ny) / (nx, ny, nz).

  • "kji" — legacy / C++ order: the first index varies along the z-axis, the second along y, the third along x. Shapes: (nx,) / (ny, nx) / (nz, ny, nx).

Example usage:

import numpy as np
from esys.finley import Rectangle
from esys.escript import Function
from esys.escriptcore.interpolation import InterpolationTable

dom = Rectangle(20, 20)
x = Function(dom).getX()   # shape (2,)

# 2-D scalar table, "ijk" convention: shape (nx, ny)
t = np.random.rand(5, 5)
interp = InterpolationTable(t, origin=(0., 0.), step=(0.25, 0.25))
result = interp(x)

# Equivalent using total extent (covers [0,1] x [0,1])
interp = InterpolationTable(t, origin=(0., 0.), extend=(1., 1.))
result = interp(x)

# Order-0 (piecewise constant) interpolation
interp0 = InterpolationTable(t, origin=(0., 0.), extend=(1., 1.), order=0)
result0 = interp0(x)
Parameters:

  • table (numpy.ndarray) – lookup table as a numpy array of rank 1, 2, or 3

  • origin (float or tuple of float) – coordinate(s) of the first table entry; a single float for 1-D or a tuple for 2-D / 3-D

  • step (float or tuple of float) – cell size(s), i.e. the spacing between adjacent table entries; all values must be strictly positive. Exactly one of step and extend must be supplied.

  • extend (float or tuple of float) – total extent of the table domain along each coordinate axis. For order-1: distance from the first to the last sample point along axis i (step[i] = extend[i] / (n_i - 1)). For order-0: total domain width along axis i (step[i] = extend[i] / n_i), where n_i is the number of cells along that axis. Exactly one of step and extend must be supplied.

  • order (int) – interpolation order — 0 for piecewise constant, 1 for linear (default)

  • undef (float) – upper threshold; result values above this trigger a RuntimeError

  • check_boundaries (bool) – if True, a RuntimeError is raised when a coordinate lies outside the table extent; otherwise the nearest boundary value is used

  • table_indexing (str) – indexing convention for the table array. "ijk" (default) — first index = x-axis, natural numpy order. "kji" — first index = z-axis, legacy C++ order.

__init__(table, origin, step=None, extend=None, order=1, undef=1e+50, check_boundaries=False, table_indexing='ijk')
getExtend()

Return the tuple of domain extents along each coordinate axis.

For order-1: extend[i] = step[i] * (n_i - 1) (distance from first to last sample point along axis i).

For order-0: extend[i] = step[i] * n_i (total domain width; domain along axis i is [origin[i], origin[i] + extend[i]]).

Here n_i is the number of table entries along coordinate axis i (independent of the table_indexing convention).

getNdim()

Return the number of coordinate dimensions (1, 2, or 3).

getOrder()

Return the interpolation order (0 or 1).

getOrigin()

Return the tuple of starting coordinates.

getStep()

Return the tuple of cell sizes.

getTableIndexing()

Return the table indexing convention ('ijk' or 'kji').

interpolate(x)

Alias for __call__().

class esys.escript.util.sym
__init__()
Symbol

alias of memoryview

Functions

esys.escript.util.Abs(arg)

Returns the absolute value 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

esys.escript.util.C_GeneralTensorProduct((Data)arg0, (Data)arg1[, (int)axis_offset=0[, (int)transpose=0]]) → Data :

Compute a tensor product of two Data objects.

Return type:

Data

Parameters:

  • arg0

  • arg1

  • axis_offset (int)

  • transpose (int) – 0: transpose neither, 1: transpose arg0, 2: transpose arg1

esys.escript.util.L2(arg)

Returns the L2 norm of arg at where.

Parameters:

arg (escript.Data or Symbol) – function of which the L2 norm is to be calculated

Returns:

L2 norm of arg

Return type:

float or Symbol

Note:

L2(arg) is equivalent to sqrt(integrate(inner(arg,arg)))

esys.escript.util.Lsup(arg)

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

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

esys.escript.util.NumpyToData(array, isComplex, functionspace)

Creates a Data object from a numpy ndarray.

Parameters:

  • array (numpy.ndarray) – the numpy array to convert

  • isComplex (bool) – whether the data contains complex values

  • functionspace (FunctionSpace) – the function space for the new Data object

Returns:

Data object created from the numpy array

Return type:

Data

Raises:

ValueError – if arguments are invalid or boost numpy is not available

Example usage:

NewDataObject = NumpyToData(ndarray, isComplex, FunctionSpace)
esys.escript.util.acos(arg)

Returns the inverse cosine 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

esys.escript.util.acosh(arg)

Returns the inverse hyperbolic cosine 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

esys.escript.util.antihermitian(arg)

Returns the anti-hermitian part of the square matrix arg. That is, (arg-adjoint(arg))/2.

Parameters:

arg (numpy.ndarray, escript.Data, Symbol) – input matrix. Must have rank 2 or 4 and be square.

Returns:

anti-hermitian part of arg

Return type:

numpy.ndarray, escript.Data, Symbol depending on the input

esys.escript.util.antisymmetric(arg)

Returns the anti-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.

Returns:

anti-symmetric part of arg

Return type:

numpy.ndarray, escript.Data, Symbol depending on the input

esys.escript.util.asin(arg)

Returns the inverse sine 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

esys.escript.util.asinh(arg)

Returns the inverse hyperbolic sine 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

esys.escript.util.atan(arg)

Returns inverse 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

esys.escript.util.atan2(arg0, arg1)

Returns inverse tangent of arg0/arg1, handling quadrant correctly.

Parameters:

  • arg0 (float, escript.Data, numpy.ndarray) – numerator argument (y coordinate)

  • arg1 (float, escript.Data, numpy.ndarray) – denominator argument (x coordinate)

Returns:

angle in radians between -pi and pi

Return type:

float, escript.Data, numpy.ndarray depending on input types

esys.escript.util.atanh(arg)

Returns the inverse 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

esys.escript.util.boundingBox(domain)

Returns the bounding box of a domain

Parameters:

domain (escript.Domain) – a domain

Returns:

bounding box of the domain

Return type:

list of pairs of float

esys.escript.util.boundingBoxEdgeLengths(domain)

Returns the edge lengths of the bounding box of a domain

Parameters:

domain (escript.Domain) – a domain

Return type:

list of float

esys.escript.util.clip(arg, minval=None, maxval=None)

Cuts the values of arg between minval and maxval.

Parameters:

  • arg (numpy.ndarray, escript.Data, Symbol, int or float) – argument

  • minval (float or None) – lower range. If None no lower range is applied

  • maxval (float or None) – upper range. If None no upper range is applied

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

esys.escript.util.commonDim(*args)

Identifies, if possible, the spatial dimension across a set of objects which may or may not have a spatial dimension.

Parameters:

args – given objects

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.

esys.escript.util.commonShape(arg0, arg1)

Returns a shape to which arg0 can be extended from the right and arg1 can be extended from the left.

Parameters:

  • arg0 – an object with a shape (see getShape)

  • arg1 – an object with a shape (see getShape)

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

esys.escript.util.condEval(f, tval, fval)

Wrapper to allow non-data objects to be used.

esys.escript.util.conjugate(arg)

returns the complex conjugate of arg

esys.escript.util.convertToNumpy(data)

Converts a Data object to a numpy array.

Parameters:

data (Data) – the Data object to convert

Returns:

numpy array containing the data values

Return type:

numpy.ndarray

esys.escript.util.cos(arg)

Returns cosine 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

esys.escript.util.cosh(arg)

Returns the hyperbolic cosine 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

esys.escript.util.cross(arg0, arg1)

Cross product of the two arguments arg0 and arg1 which need to be shape (3,).

Parameters:

  • arg0 (numpy.ndarray, escript.Data, Symbol) – first argument

  • arg1 (numpy.ndarray, escript.Data, Symbol) – second argument

Returns:

the cross product of arg0 and arg1 at each data point

Return type:

numpy.ndarray, escript.Data, Symbol depending on arg0

Raises:

ValueError – if the shapes of the arguments are not (3,)

esys.escript.util.curl(arg, where=None)

Returns the (spatial) curl of arg at where..

Parameters:

  • arg (escript.Data or Symbol) – function of which the curl is to be calculated. Its shape has to be (), (2,) or (3,)

  • where (None or escript.FunctionSpace) – FunctionSpace in which the gradient is calculated. If not present or None an appropriate default is used.

Returns:

curl of arg

Return type:

escript.Data or Symbol

esys.escript.util.delay(arg)

Returns a lazy version of arg

esys.escript.util.deviatoric(arg)

Returns the deviatoric version of arg.

esys.escript.util.diameter(domain)

Returns the diameter of a domain.

Parameters:

domain (escript.Domain) – a domain

Return type:

float

esys.escript.util.div(arg, where=None)

Returns the divergence of arg at where.

Parameters:

  • arg (escript.Data or Symbol) – function of which the divergence is to be calculated. Its shape has to be (d,) where d is the spatial dimension.

  • where (None or escript.FunctionSpace) – FunctionSpace in which the divergence will be calculated. If not present or None an appropriate default is used.

Returns:

divergence of arg

Return type:

escript.Data or Symbol

esys.escript.util.eigenvalues(arg)

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).

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.

esys.escript.util.eigenvalues_and_eigenvectors(arg)

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).

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.

esys.escript.util.erf(arg)

Returns the error function erf 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

esys.escript.util.escript_generalTensorProduct(arg0, arg1, axis_offset, transpose=0)

Generalized tensor product for escript Data objects.

Parameters:

  • arg0 (escript.Data) – first Data object

  • arg1 (escript.Data) – second Data object (not necessarily on the same function space)

  • axis_offset (int) – axis offset for the tensor product

  • transpose (int) – transpose mode (0=none, 1=transpose arg0, 2=transpose arg1)

Returns:

tensor product result

Return type:

escript.Data

esys.escript.util.escript_generalTensorTransposedProduct(arg0, arg1, axis_offset)

Generalized tensor product of arg0 and transposed arg1 for escript Data objects.

Parameters:

  • arg0 (escript.Data) – first Data object

  • arg1 (escript.Data) – second Data object (will be transposed, not necessarily on the same function space)

  • axis_offset (int) – axis offset for the tensor product

Returns:

tensor product of arg0 and transpose(arg1)

Return type:

escript.Data

esys.escript.util.escript_generalTransposedTensorProduct(arg0, arg1, axis_offset)

Generalized tensor product of transposed arg0 and arg1 for escript Data objects.

Parameters:

  • arg0 (escript.Data) – first Data object (will be transposed)

  • arg1 (escript.Data) – second Data object (not necessarily on the same function space)

  • axis_offset (int) – axis offset for the tensor product

Returns:

tensor product of transpose(arg0) and arg1

Return type:

escript.Data

esys.escript.util.escript_inverse(arg)

Returns the inverse of an escript Data matrix.

Parameters:

arg (escript.Data) – square matrix Data object (dimension restricted to 3)

Returns:

inverse of the matrix

Return type:

escript.Data

esys.escript.util.exp(arg)

Returns e to the power 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

esys.escript.util.generalTensorProduct(arg0, arg1, axis_offset=0)

Generalized tensor product.

out[s,t]=Sigma_r arg0[s,r]*arg1[r,t]

where

  • s runs through arg0.Shape[:arg0.ndim-axis_offset]

  • r runs through arg1.Shape[:axis_offset]

  • t runs through arg1.Shape[axis_offset:]

Parameters:

  • arg0 (numpy.ndarray, escript.Data, Symbol, float, int) – first argument

  • arg1 (numpy.ndarray, escript.Data, Symbol, float, int) – second argument

Returns:

the general tensor product of arg0 and arg1 at each data point

Return type:

numpy.ndarray, escript.Data, Symbol depending on the input

esys.escript.util.generalTensorTransposedProduct(arg0, arg1, axis_offset=0)

Generalized tensor product of arg0 and transpose of arg1.

out[s,t]=Sigma_r arg0[s,r]*arg1[t,r]

where

  • s runs through arg0.Shape[:arg0.ndim-axis_offset]

  • r runs through arg0.Shape[arg1.ndim-axis_offset:]

  • t runs through arg1.Shape[arg1.ndim-axis_offset:]

The function call generalTensorTransposedProduct(arg0,arg1,axis_offset) is equivalent to generalTensorProduct(arg0,transpose(arg1,arg1.ndim-axis_offset),axis_offset).

Parameters:

  • arg0 (numpy.ndarray, escript.Data, Symbol, float, int) – first argument

  • arg1 (numpy.ndarray, escript.Data, Symbol, float, int) – second argument

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

esys.escript.util.generalTransposedTensorProduct(arg0, arg1, axis_offset=0)

Generalized tensor product of transposed of arg0 and arg1.

out[s,t]=Sigma_r arg0[r,s]*arg1[r,t]

where

  • s runs through arg0.Shape[axis_offset:]

  • r runs through arg0.Shape[:axis_offset]

  • t runs through arg1.Shape[axis_offset:]

The function call generalTransposedTensorProduct(arg0,arg1,axis_offset) is equivalent to generalTensorProduct(transpose(arg0,arg0.ndim-axis_offset),arg1,axis_offset).

Parameters:

  • arg0 (numpy.ndarray, escript.Data, Symbol, float, int) – first argument

  • arg1 (numpy.ndarray, escript.Data, Symbol, float, int) – second argument

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

esys.escript.util.getBoundingBox(domain)

Returns the bounding box of a domain as a list of intervals

Parameters:

domain (escript.Domain) – a domain

Returns:

bounding box of the domain

Return type:

list of BBxInterval

esys.escript.util.getClosestValue(arg, origin=0)

Returns the value in arg which is closest to origin.

Parameters:

  • arg (escript.Data) – function

  • origin (float or escript.Data) – reference value

Returns:

value in arg closest to origin

Return type:

numpy.ndarray

esys.escript.util.getEpsilon()

Returns the machine epsilon (smallest positive value where 1.0 + epsilon != 1.0).

Returns:

machine precision epsilon

Return type:

float

esys.escript.util.getMPIRankWorld() → int :

Return the rank of this process in the MPI World.

esys.escript.util.getMPIWorldMax((int)arg1) → int :

Each MPI process calls this function with a value for arg1. The maximum value is computed and returned.

Return type:

int

esys.escript.util.getMaxFloat()

Returns the largest representable positive floating point number.

Returns:

maximum float value

Return type:

float

esys.escript.util.getNumpy(**data)

Converts Data objects to numpy arrays.

The keyword args are Data objects to convert. If a scalar Data object is passed with the name mask, then only samples which correspond to positive values in mask will be output.

Parameters:

<name> (Data or float) – Data object or scalar to convert

Returns:

dictionary mapping names to numpy record arrays

Return type:

dict of numpy.ndarray

Raises:

ValueError – if no Data object is provided

Example usage:

s=Scalar(..)
v=Vector(..)
t=Tensor(..)
f=float()
array = getNumpy(a=s, b=v, c=t, d=f)
esys.escript.util.getRank(arg)

Identifies the rank of the argument.

Parameters:

arg (numpy.ndarray, escript.Data, float, int, Symbol) – an object whose rank is to be returned

Returns:

the rank of the argument

Return type:

int

Raises:

TypeError – if type of arg cannot be processed

esys.escript.util.getRegionTags(function_space)

Returns the tag distribution of a function_space as a Data object.

Parameters:

function_space (escript.FunctionSpace) – function_space to be used

Returns:

a data object which contains the tag distribution

Return type:

escript.Data of rank 0 with ReducedFunction attributes.

esys.escript.util.getShape(arg)

Identifies the shape of the argument.

Parameters:

arg (numpy.ndarray, escript.Data, float, int, Symbol) – an object whose shape is to be returned

Returns:

the shape of the argument

Return type:

tuple of int

Raises:

TypeError – if type of arg cannot be processed

esys.escript.util.getTagNames(domain)

Returns a list of tag names used by the domain.

Parameters:

domain (escript.Domain) – a domain object

Returns:

a list of tag names used by the domain

Return type:

list of str

esys.escript.util.getVersion() → str :

This method will only report accurate version numbers for clean checkouts.

esys.escript.util.grad(arg, where=None)

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:

  • arg (escript.Data or Symbol) – function of which the gradient is to be calculated. Its rank has to be less than 3.

  • where (None or escript.FunctionSpace) – FunctionSpace in which the gradient is calculated. If not present or None an appropriate default is used.

Returns:

gradient of arg

Return type:

escript.Data or Symbol

esys.escript.util.grad_n(arg, n, where=None)
esys.escript.util.hasFeature((str)name) → bool :

Check if escript was compiled with a certain feature

Parameters:

name (string) – feature to lookup

esys.escript.util.hermitian(arg)

Returns the hermitian part of the square matrix arg. That is, (arg+adjoint(arg))/2.

Parameters:

arg (numpy.ndarray, escript.Data, Symbol) – input matrix. Must have rank 2 or 4 and be square.

Returns:

hermitian part of arg

Return type:

numpy.ndarray, escript.Data, Symbol depending on the input

esys.escript.util.identity(shape=())

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

esys.escript.util.identityTensor(d=3)

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

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

esys.escript.util.identityTensor4(d=3)

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

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

esys.escript.util.imag(arg)

returns the imaginary part of arg

esys.escript.util.inf(arg)

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

esys.escript.util.inner(arg0, arg1)

Inner product of the two arguments. The inner product is defined as:

out=Sigma_s arg0[s]*arg1[s]

where s runs through arg0.Shape.

arg0 and arg1 must have the same shape.

Parameters:

  • arg0 (numpy.ndarray, escript.Data, Symbol, float, int) – first argument

  • arg1 (numpy.ndarray, escript.Data, Symbol, float, int) – second argument

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

esys.escript.util.insertTagNames(domain, **kwargs)

Inserts tag names into the domain.

Parameters:

  • domain (escript.Domain) – a domain object

  • <tag_name> (int) – tag key assigned to <tag_name>

esys.escript.util.insertTaggedValues(target, **kwargs)

Inserts tagged values into the target using tag names.

Parameters:

  • target (escript.Data) – data to be filled by tagged values

  • <tag_name> (float or numpy.ndarray) – value to be used for <tag_name>

Returns:

target

Return type:

escript.Data

esys.escript.util.integrate(arg, where=None)

Returns the integral of the function arg over its domain. If where is present arg is interpolated to where before integration.

Parameters:

  • arg (escript.Data or Symbol) – the function which is integrated

  • where (None or escript.FunctionSpace) – FunctionSpace in which the integral is calculated. If not present or None an appropriate default is used.

Returns:

integral of arg

Return type:

float, numpy.ndarray or Symbol

esys.escript.util.interpolate(arg, where)

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:

  • arg (escript.Data or Symbol) – interpolant

  • where (escript.FunctionSpace) – FunctionSpace to be interpolated to

Returns:

interpolated argument

Return type:

escript.Data or Symbol

esys.escript.util.interpolateTable(tab, dat, start, step, undef=1e+50, check_boundaries=False)

Interpolates values from a lookup table.

Deprecated since version Use: InterpolationTable instead. This function delegates to InterpolationTable with order=1.

Parameters:

  • tab (numpy.ndarray) – the lookup table array

  • dat (Data) – coordinate data — scalar Data for 1-D or vector Data for 2-D/3-D

  • start (float or tuple of float) – starting coordinate(s) for the table

  • step (float or tuple of float) – step size(s) for the table

  • undef (float) – upper bound on interpolated values

  • check_boundaries (bool) – if True, raise an error for out-of-bounds coordinates

Returns:

interpolated values

Return type:

Data

esys.escript.util.inverse(arg)

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.

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.

esys.escript.util.jump(arg, domain=None)

Returns the jump of arg across the continuity of the domain.

Parameters:

  • arg (escript.Data or Symbol) – argument

  • domain (None or escript.Domain) – the domain where the discontinuity is located. If domain is not present or equal to None the domain of arg is used.

Returns:

jump of arg

Return type:

escript.Data or Symbol

esys.escript.util.kronecker(d=3)

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

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

esys.escript.util.length(arg)

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

esys.escript.util.listEscriptParams() → list :
Returns:

A list of tuples (p,v,d) where p is the name of a parameter for escript, v is its current value, and d is a description.

esys.escript.util.log(arg)

Returns the natural 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

esys.escript.util.log10(arg)

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

esys.escript.util.longestEdge(domain)

Returns the length of the longest edge of the domain

Parameters:

domain (escript.Domain) – a domain

Returns:

longest edge of the domain parallel to the Cartesian axis

Return type:

float

esys.escript.util.makeTagMap(fs)

Produces an expanded Data over the function space where the value is the tag associated with the sample.

Parameters:

fs (escript.FunctionSpace) – the function space

Returns:

Data object with tag values at each sample point

Return type:

escript.Data

esys.escript.util.matchShape(arg0, arg1)

Returns a representation of arg0 and arg1 which have the same shape.

Parameters:

  • arg0 (numpy.ndarray,`escript.Data`,``float``, int, Symbol) – first argument

  • arg1 (numpy.ndarray,`escript.Data`,``float``, int, Symbol) – second argument

Returns:

arg0 and arg1 where copies are returned when the shape has to be changed

Return type:

tuple

esys.escript.util.matchType(arg0=0.0, arg1=0.0)

Converts arg0 and arg1 both to the same type numpy.ndarray or escript.Data

Parameters:

  • arg0 (numpy.ndarray,`escript.Data`,``float``, int, Symbol) – first argument

  • arg1 (numpy.ndarray,`escript.Data`,``float``, int, Symbol) – second argument

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

esys.escript.util.matrix_mult(arg0, arg1)

matrix-matrix or matrix-vector product of the two arguments.

out[s0]=Sigma_{r0} arg0[s0,r0]*arg1[r0]

or

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:

  • arg0 (numpy.ndarray, escript.Data, Symbol) – first argument of rank 2

  • arg1 (numpy.ndarray, escript.Data, Symbol) – second argument of at least rank 1

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

esys.escript.util.matrix_transposed_mult(arg0, arg1)

matrix-transposed(matrix) product of the two arguments.

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:

  • arg0 (numpy.ndarray, escript.Data, Symbol) – first argument of rank 2

  • arg1 (numpy.ndarray, escript.Data, Symbol) – second argument of rank 1 or 2

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

esys.escript.util.matrixmult(arg0, arg1)

See matrix_mult.

esys.escript.util.maximum(*args)

The maximum over arguments args.

Parameters:

args (numpy.ndarray, escript.Data, Symbol, int or float) – arguments

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

esys.escript.util.maxval(arg)

Returns the maximum value over all components of 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

Raises:

TypeError – if the type of the argument is not expected

esys.escript.util.meanValue(arg)

return the mean value of the argument over its domain

Parameters:

arg (escript.Data) – function

Returns:

mean value

Return type:

float or numpy.ndarray

esys.escript.util.minimum(*args)

The minimum over arguments args.

Parameters:

args (numpy.ndarray, escript.Data, Symbol, int or float) – arguments

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

esys.escript.util.minval(arg)

Returns the minimum value over all components of 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

Raises:

TypeError – if the type of the argument is not expected

esys.escript.util.mkDir(*pathname)

creates a directory of name pathname if the directory does not exist.

Parameters:

pathname (str or sequence of strings) – valid path name

Note:

The method is MPI safe.

esys.escript.util.mult(arg0, arg1)

Product of arg0 and arg1.

Parameters:

  • arg0 (Symbol, float, int, escript.Data or numpy.ndarray) – first term

  • arg1 (Symbol, float, int, escript.Data or numpy.ndarray) – second term

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.

esys.escript.util.negative(arg)

returns the negative part of arg

esys.escript.util.nonsymmetric(arg)

Deprecated alias for antisymmetric.

esys.escript.util.normalize(arg, zerolength=0)

Returns the normalized version of arg (=``arg/length(arg)``).

Parameters:

  • arg (escript.Data or Symbol) – function

  • zerolength (float) – relative tolerance for arg == 0

Returns:

normalized arg where arg is non-zero, and zero elsewhere

Return type:

escript.Data or Symbol

esys.escript.util.outer(arg0, arg1)

The outer product of the two arguments. The outer product is defined as:

out[t,s]=arg0[t]*arg1[s]

where

  • s runs through arg0.Shape

  • t runs through arg1.Shape

Parameters:

  • arg0 (numpy.ndarray, escript.Data, Symbol, float, int) – first argument

  • arg1 (numpy.ndarray, escript.Data, Symbol, float, int) – second argument

Returns:

the outer product of arg0 and arg1 at each data point

Return type:

numpy.ndarray, escript.Data, Symbol depending on the input

esys.escript.util.phase(arg)

return the “phase”/”arg”/”angle” of a number

esys.escript.util.pokeDim(arg)

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

esys.escript.util.polarToCart(r, phase)

conversion from cartesian to polar coordinates

Parameters:

  • r (any float type object) – length

  • phase (any float type object) – the phase angle in rad

Returns:

cartesian representation as complex number

Return type:

appropriate complex

esys.escript.util.positive(arg)

returns the positive part of arg

esys.escript.util.real(arg)

returns the real part of arg

esys.escript.util.reorderComponents(arg, index)

Resorts the components of arg according to index.

esys.escript.util.resolve(arg)

Returns the value of arg resolved.

esys.escript.util.safeDiv(arg0, arg1, rtol=None)

returns arg0/arg1 but return 0 where arg1 is (almost) zero

esys.escript.util.saveDataCSV(filename, append=False, refid=False, sep=', ', csep='_', **data)

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:

  • filename (string) – file to save data to.

  • append (bool) – If True, then open file at end rather than beginning

  • refid (bool) – If True, then a list of reference ids will be printed in the first column

  • sep (string) – separator between fields

  • csep – separator for components of rank 2 and above (e.g. ‘_’ -> c0_1)

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.

esys.escript.util.saveESD(datasetName, dataDir='.', domain=None, timeStep=0, deltaT=1, dynamicMesh=0, timeStepFormat='%04d', **data)

Saves Data objects to files and creates an 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:

  • datasetName (str) – name of the dataset, used to name the ESD file

  • dataDir (str) – optional directory where the data files should be saved

  • domain (escript.Domain) – domain of the Data object(s). If not specified, the domain of the given Data objects is used.

  • timeStep (int) – current timestep or sequence number - first one must be 0

  • deltaT (int) – timestep or sequence increment, see example above

  • dynamicMesh (int) – by default the mesh is assumed to be static and thus only saved once at timestep 0 to save disk space. Setting this to 1 changes the behaviour and the mesh is saved at each timestep.

  • timeStepFormat (str) – timestep format string (defaults to “%04d”)

  • <name> (Data object) – writes the assigned value to the file using <name> as identifier

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.

esys.escript.util.showEscriptParams()

Displays the parameters escript recognises with an explanation and their current value.

esys.escript.util.sign(arg)

Returns the sign 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

esys.escript.util.sin(arg)

Returns sine 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

esys.escript.util.sinh(arg)

Returns the hyperbolic sine 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

esys.escript.util.sqrt(arg)

Returns the square root 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

esys.escript.util.sup(arg)

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

esys.escript.util.swap_axes(arg, axis0=0, axis1=1)

Returns the swap of arg by swapping the components axis0 and axis1.

Parameters:

  • arg (escript.Data, Symbol, numpy.ndarray) – argument

  • axis0 (int) – first axis. axis0 must be non-negative and less than the rank of arg.

  • axis1 (int) – second axis. axis1 must be non-negative and less than the rank of arg.

Returns:

arg with swapped components

Return type:

escript.Data, Symbol or numpy.ndarray depending on the type of arg

esys.escript.util.symmetric(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.

Returns:

symmetric part of arg

Return type:

numpy.ndarray, escript.Data, Symbol depending on the input

esys.escript.util.tan(arg)

Returns 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

esys.escript.util.tanh(arg)

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

esys.escript.util.tensor_mult(arg0, arg1)

The tensor product of the two arguments.

For arg0 of rank 2 this is

out[s0]=Sigma_{r0} arg0[s0,r0]*arg1[r0]

or

out[s0,s1]=Sigma_{r0} arg0[s0,r0]*arg1[r0,s1]

and for arg0 of rank 4 this is

out[s0,s1,s2,s3]=Sigma_{r0,r1} arg0[s0,s1,r0,r1]*arg1[r0,r1,s2,s3]

or

out[s0,s1,s2]=Sigma_{r0,r1} arg0[s0,s1,r0,r1]*arg1[r0,r1,s2]

or

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:

  • arg0 (numpy.ndarray, escript.Data, Symbol) – first argument of rank 2 or 4

  • arg1 (numpy.ndarray, escript.Data, Symbol) – second argument of shape greater than 1 or 2 depending on the rank of arg0

Returns:

the tensor product of arg0 and arg1 at each data point

Return type:

numpy.ndarray, escript.Data, Symbol depending on the input

esys.escript.util.tensor_transposed_mult(arg0, arg1)

The tensor product of the first and the transpose of the second argument.

For arg0 of rank 2 this is

out[s0,s1]=Sigma_{r0} arg0[s0,r0]*arg1[s1,r0]

and for arg0 of rank 4 this is

out[s0,s1,s2,s3]=Sigma_{r0,r1} arg0[s0,s1,r0,r1]*arg1[s2,s3,r0,r1]

or

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:

  • arg0 (numpy.ndarray, escript.Data, Symbol) – first argument of rank 2 or 4

  • arg1 (numpy.ndarray, escript.Data, Symbol) – second argument of shape greater of 1 or 2 depending on rank of arg0

Returns:

the tensor product of arg0 and the transposed of arg1 at each data point

Return type:

numpy.ndarray, escript.Data, Symbol depending on the input

esys.escript.util.tensormult(arg0, arg1)

See tensor_mult.

esys.escript.util.testForZero(arg)

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

esys.escript.util.trace(arg, axis_offset=0)

Returns the trace of arg which is the sum of arg[k,k] over k.

Parameters:

  • arg (escript.Data, Symbol, numpy.ndarray) – argument

  • axis_offset (int) – axis_offset to components to sum over. axis_offset must be non-negative and less than the rank of arg +1. The dimensions of component axis_offset and axis_offset+1 must be equal.

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

esys.escript.util.transpose(arg, axis_offset=None)

Returns the transpose of arg by swapping the first axis_offset and the last rank-axis_offset components.

Parameters:

  • arg (escript.Data, Symbol, numpy.ndarray, float, int) – argument

  • axis_offset (int) – the first axis_offset components are swapped with the rest. axis_offset must be non-negative and less or equal to the rank of arg. If axis_offset is not present int(r/2) where r is the rank of arg is used.

Returns:

transpose of arg

Return type:

escript.Data, Symbol, numpy.ndarray, float, int depending on the type of arg

esys.escript.util.transposed_matrix_mult(arg0, arg1)

transposed(matrix)-matrix or transposed(matrix)-vector product of the two arguments.

out[s0]=Sigma_{r0} arg0[r0,s0]*arg1[r0]

or

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:

  • arg0 (numpy.ndarray, escript.Data, Symbol) – first argument of rank 2

  • arg1 (numpy.ndarray, escript.Data, Symbol) – second argument of at least rank 1

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

esys.escript.util.transposed_tensor_mult(arg0, arg1)

The tensor product of the transpose of the first and the second argument.

For arg0 of rank 2 this is

out[s0]=Sigma_{r0} arg0[r0,s0]*arg1[r0]

or

out[s0,s1]=Sigma_{r0} arg0[r0,s0]*arg1[r0,s1]

and for arg0 of rank 4 this is

out[s0,s1,s2,s3]=Sigma_{r0,r1} arg0[r0,r1,s0,s1]*arg1[r0,r1,s2,s3]

or

out[s0,s1,s2]=Sigma_{r0,r1} arg0[r0,r1,s0,s1]*arg1[r0,r1,s2]

or

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:

  • arg0 (numpy.ndarray, escript.Data, Symbol) – first argument of rank 2 or 4

  • arg1 (numpy.ndarray, escript.Data, Symbol) – second argument of shape greater of 1 or 2 depending on the rank of arg0

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

esys.escript.util.unitVector(i=0, d=3)

Returns a unit vector u of dimension d whose non-zero element is at index i.

Parameters:

  • i (int) – index for non-zero element

  • d (int, escript.Domain or escript.FunctionSpace) – dimension or an object that has the getDim method defining the dimension

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

esys.escript.util.vol(arg)

Returns the volume or area of the oject arg

Parameters:

arg (escript.FunctionSpace or escript.Domain) – a geometrical object

Return type:

float

esys.escript.util.whereNegative(arg)

Returns mask of negative values 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

esys.escript.util.whereNonNegative(arg)

Returns mask of non-negative values 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

esys.escript.util.whereNonPositive(arg)

Returns mask of non-positive values 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

esys.escript.util.whereNonZero(arg, tol=0.0)

Returns mask of values different from zero of argument arg.

Parameters:

  • arg (float, escript.Data, Symbol, numpy.ndarray) – argument

  • tol (float) – absolute tolerance. Values with absolute value less than or equal to tol are considered zero.

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

esys.escript.util.wherePositive(arg)

Returns mask of positive values 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

esys.escript.util.whereZero(arg, tol=None, rtol=1.4901161193847656e-08)

Returns mask of zero entries of argument arg.

Parameters:

  • arg (float, escript.Data, Symbol, numpy.ndarray) – argument

  • tol (float) – absolute tolerance. Values with absolute value less than tol are accepted as zero. If tol is not present rtol * Lsup(arg) is used.

  • rtol (non-negative float) – relative tolerance used to define the absolute tolerance if tol is not present.

Return type:

float, escript.Data, Symbol, numpy.ndarray depending on the type of arg

Raises:

  • ValueError – if rtol is negative.

  • TypeError – if the type of the argument is not expected

esys.escript.util.zeros(shape=())

Returns the shape zero tensor.

Parameters:

shape (tuple of int) – input shape for the zero tensor

Returns:

array of shape filled with zeros

Return type:

numpy.ndarray

Others

  • DBLE_MAX

  • EPSILON

  • HAVE_SYMBOLS

Packages