esys.escript Package¶

Classes and tools that form the basis of the escript system. Specific solvers and domains are found in their respective packages.

Classes¶

BBxInterval
ContinuousDomain
Data
DataManager
Domain
FileWriter
FunctionSpace
InterpolationTable
NonlinearPDE
Operator
SolverBuddy
SolverFramework
SolverOptions
TestDomain
TransportProblem
sym

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

Represents an interval for bounding box coordinates.

__init__(minval=0, maxval=0)¶

class esys.escript.ContinuousDomain¶

Class representing continuous domains

__init__()¶: Raises an exception This class cannot be instantiated from Python

addPDEToRHS((ContinuousDomain)arg1, (Data)rhs, (Data)X, (Data)Y, (Data)y, (Data)y_contact, (Data)y_dirac) → None :¶

adds a PDE onto the stiffness matrix mat and a rhs

Parameters:

rhs (Data)
X (Data)
Y (Data)
y (Data)
y_contact (Data)
y_dirac (Data)

addPDEToSystem((ContinuousDomain)arg1, (Operator)mat, (Data)rhs, (Data)A, (Data)B, (Data)C, (Data)D, (Data)X, (Data)Y, (Data)d, (Data)y, (Data)d_contact, (Data)y_contact, (Data)d_dirac, (Data)y_dirac) → None :¶

adds a PDE onto the stiffness matrix mat and a rhs

Parameters:

mat (OperatorAdapter)
rhs (Data)
A (Data)
B (Data)
C (Data)
D (Data)
X (Data)
Y (Data)
d (Data)
d_contact (Data)
y_contact (Data)
d_dirac (Data)
y_dirac (Data)

addPDEToTransportProblem((ContinuousDomain)arg1, (TransportProblem)tp, (Data)source, (Data)M, (Data)A, (Data)B, (Data)C, (Data)D, (Data)X, (Data)Y, (Data)d, (Data)y, (Data)d_contact, (Data)y_contact, (Data)d_dirac, (Data)y_dirac) → None :¶

Parameters:

tp (TransportProblemAdapter)
source (Data)
M (Data)
A (Data)
B (Data)
C (Data)
D (Data)
X (Data)
Y (Data)
d (Data)
y (Data)
d_contact (Data)
y_contact (Data)
d_dirac (Data)
y_dirac (Data)

getDataShape((ContinuousDomain)arg1, (int)functionSpaceCode) → object :¶

Returns:: a pair (dps, ns) where dps=the number of data points per sample, and ns=the number of samples
Return type:: tuple

getDescription((ContinuousDomain)arg1) → str :¶

Returns:: a description for this domain
Return type:: string

getFramework((ContinuousDomain)arg1) → SolverFramework :¶

Returns the SolverFramework attached to this domain.

Return type:: SolverFramework

getNumDataPointsGlobal((ContinuousDomain)arg1) → int :¶

Returns:: the number of data points summed across all MPI processes
Return type:: int

getSystemMatrixTypeId((ContinuousDomain)arg1, (object)options) → int :¶

Returns:: the identifier of the matrix type to be used for the global stiffness matrix when particular solver options are used.
Return type:: int

getTransportTypeId((ContinuousDomain)arg1, (int)solver, (int)preconditioner, (int)package, (bool)symmetry) → int¶

newOperator((ContinuousDomain)arg1, (int)row_blocksize, (FunctionSpace)row_functionspace, (int)column_blocksize, (FunctionSpace)column_functionspace, (int)type) → Operator :¶

creates a SystemMatrixAdapter stiffness matrix and initializes it with zeros

Parameters:

row_blocksize (int)
row_functionspace (FunctionSpace)
column_blocksize (int)
column_functionspace (FunctionSpace)
type (int)

newTransportProblem((ContinuousDomain)theta, (int)blocksize, (FunctionSpace)functionspace, (int)type) → TransportProblem :¶

creates a TransportProblemAdapter

Parameters:

theta (float)
blocksize (int)
functionspace (FunctionSpace)
type (int)

print_mesh_info((ContinuousDomain)arg1[, (bool)full=False]) → None :¶

Parameters:: full (bool)

setFramework((ContinuousDomain)arg1, (SolverFramework)framework) → None :¶

Attach a SolverFramework to this domain. Must be called before the domain is first used for solving. Raises an exception if called a second time.

Parameters:: framework (SolverFramework) – the solver backend to use

setX((ContinuousDomain)arg1, (Data)arg) → None :¶

assigns new location to the domain

Parameters:: arg (Data)

class esys.escript.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

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.

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 :

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.DataManager(formats=[0], work_dir='.', restart_prefix='restart', do_restart=True)¶

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

__init__(formats=[0], work_dir='.', restart_prefix='restart', do_restart=True)¶

Initialises the data manager. If do_restart is True and a restart directory is found the contained data is loaded (hasData() returns True) otherwise restart directories are removed (hasData() returns False). Values are only written to disk when export() is called.

Parameters:

formats – A list of export file formats to use. Allowed values are RESTART, SILO, VISIT, VTK.
work_dir – top-level directory where files are exported to
restart_prefix – prefix for restart directories. Will be used to load restart files (if do_restart is True) and store new restart files (if RESTART is used)
do_restart – whether to attempt to load restart files

RESTART = 0¶

SILO = 1¶

VISIT = 2¶

VTK = 3¶

addData(**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.

export()¶: 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).

getCycle()¶

Returns the export cycle (=number of times export() has been called).

Returns:: the current export cycle number
Return type:: int

getDomain()¶

Returns the domain as recovered from restart files.

Returns:: the domain loaded from restart files
Return type:: Domain
Raises:: ValueError – if no restart data is available

getValue(value_name)¶

Returns an ‘escript.Data’ object or other value that has been loaded from restart files.

Parameters:: value_name (str) – name of the value to retrieve
Returns:: the requested data object or value
Return type:: Data or other type depending on what was stored
Raises:: ValueError – if no restart data is available

hasData()¶

Returns True if the manager holds data for restart.

Returns:: True if restart data is available, False otherwise
Return type:: bool

setCheckpointFrequency(freq)¶

Sets the number of calls to export() before new restart files are generated.

Parameters:: freq (int) – checkpoint frequency (1 = every export, 2 = every other, etc.)

setDomain(domain)¶

Sets the domain without adding data.

Parameters:: domain (Domain) – the escript domain to set
Raises:: ValueError – if a different domain has already been set

setMeshLabels(x, y, z='')¶

Sets labels for the mesh axes. These are currently only used by the Silo exporter.

Parameters:

x (str) – label for the x-axis
y (str) – label for the y-axis
z (str) – label for the z-axis (optional for 2D)

setMeshUnits(x, y, z='')¶

Sets units for the mesh axes. These are currently only used by the Silo exporter.

Parameters:

x (str) – unit for the x-axis
y (str) – unit for the y-axis
z (str) – unit for the z-axis (optional for 2D)

setMetadataSchemaString(schema, metadata='')¶

Sets metadata namespaces and the corresponding metadata. Only used for the VTK file format at the moment.

Parameters:

schema – A dictionary that maps namespace prefixes to namespace names, e.g. {‘gml’:’http://www.opengis.net/gml’}
metadata – The actual metadata string which will be enclosed in ‘<MetaData>’ tags.

setTime(time)¶

Sets the simulation timestamp.

Parameters:: time (float) – the current simulation time

class esys.escript.Domain¶

Base class for all domains.

__init__()¶: Raises an exception This class cannot be instantiated from Python

MPIBarrier((Domain)arg1) → None :¶: Wait until all processes have reached this point

dump((Domain)arg1, (str)filename) → None :¶

Dumps the domain to a file

Parameters:: filename (string)

getDim((Domain)arg1) → int :¶

Return type:: int
Returns:: Spatial dimension of the Domain

getMPIComm((Domain)arg1) → object :¶

Returns:: the MPI communicator for this domain as an mpi4py.MPI.Comm object (or None if MPI/mpi4py not enabled)
Return type:: mpi4py.MPI.Comm or None

getMPIRank((Domain)arg1) → int :¶

Returns:: the rank of this process
Return type:: int

getMPISize((Domain)arg1) → int :¶

Returns:: the number of processes used for this Domain
Return type:: int

getNormal((Domain)arg1) → Data :¶

Return type:: escript
Returns:: Boundary normals

getSize((Domain)arg1) → Data :¶

Returns:: the local size of samples. The function space is chosen appropriately
Return type:: Data

getStatus((Domain)arg1) → int :¶

The status of a domain changes whenever the domain is modified

Return type:: int

getTag((Domain)arg1, (str)name) → int :¶

Returns:: tag id for name
Return type:: string

getX((Domain)arg1) → Data :¶

Return type:: Data
Returns:: Locations in the`Domain`. FunctionSpace is chosen appropriately

isRootRank((Domain)arg1) → bool :¶

Returns:: True if this code is executing on the root rank (rank 0)
Return type:: bool

isValidTagName((Domain)arg1, (str)name) → bool :¶

Returns:: True is name corresponds to a tag
Return type:: bool

setTagMap((Domain)arg1, (str)name, (int)tag) → None :¶

Give a tag number a name.

Parameters:

name (string) – Name for the tag
tag (int) – numeric id

Note:

Tag names must be unique within a domain

showTagNames((Domain)arg1) → str :¶

Returns:: A space separated list of tag names
Return type:: string

supportsContactElements((Domain)arg1) → bool :¶: Does this domain support contact elements.

class esys.escript.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.FunctionSpace¶

A FunctionSpace describes which points from the Domain to use to represent functions.

__init__((object)arg1) → None¶

getApproximationOrder((FunctionSpace)arg1) → int :¶

Returns:: the approximation order referring to the maximum degree of a polynomial which can be represented exactly in interpolation and/or integration.
Return type:: int

getDim((FunctionSpace)arg1) → int :¶

Returns:: the spatial dimension of the underlying domain.
Return type:: int

getDomain((FunctionSpace)arg1) → Domain :¶

Returns:: the underlying Domain for this FunctionSpace.
Return type:: Domain

getListOfTags((FunctionSpace)arg1) → list :¶

Returns:: a list of the tags used in this function space
Return type:: list

getMPIComm((FunctionSpace)arg1) → object :¶

Returns:: the MPI communicator for this function space’s domain as an mpi4py.MPI.Comm object (or None if MPI/mpi4py not enabled)
Return type:: mpi4py.MPI.Comm or None

getNormal((FunctionSpace)arg1) → Data :¶

Returns:: the surface normal field.
Return type:: Data

getReferenceIDFromDataPointNo((FunctionSpace)arg1, (int)dataPointNo) → int :¶

Returns:: the reference number associated with dataPointNo
Return type:: int

getSize((FunctionSpace)arg1) → Data :¶

Returns:: sample size
Return type:: Data

getTagFromDataPointNo((FunctionSpace)arg1, (int)arg2) → int :¶

Returns:: the tag associated with the given sample number.
Return type:: int

getTypeCode((FunctionSpace)arg1) → int :¶

Return type:: int

getX((FunctionSpace)arg1) → Data :¶

Returns:: a function whose values are its input coordinates. ie an identity function.
Return type:: Data

setTags((FunctionSpace)arg1, (int)newtag, (Data)mask) → None :¶

Set tags according to a mask

setTags( (FunctionSpace)arg1, (str)newtag, (Data)mask) -> None

class esys.escript.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.NonlinearPDE(domain, u, debug=0)¶

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 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=1+5*u)
v = p.getSolution(u=0.)

__init__(domain, u, debug=0)¶

Initializes a new nonlinear PDE.

Parameters:

domain (Domain) – domain of the PDE
u (Symbol) – The symbol for the unknown PDE function u.
debug (int (one of DEBUG0, DEBUG1, DEBUG2, DEBUG3, DEBUG4)) – level of debug information to be printed

DEBUG0 = 0¶

DEBUG1 = 1¶

DEBUG2 = 2¶

DEBUG3 = 3¶

DEBUG4 = 4¶

ORDER = 0¶

createCoefficient(name)¶

Creates a new coefficient name as Symbol

Parameters:: name (string) – name of the coefficient requested
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

getCoefficient(name)¶

Returns the value of the coefficient name as Symbol

Parameters:: name (string) – name of the coefficient requested
Returns:: the value of the coefficient
Return type:: Symbol
Raises:: IllegalCoefficient – if name is not a coefficient of the PDE

getLinearPDE()¶

Returns the linear PDE used to calculate the Newton-Raphson update

Return type:: LinearPDE

getLinearSolverOptions()¶: Returns the options of the linear PDE solver class

getNumSolutions()¶: Returns the number of the solution components :rtype: int

getSensitivity(f, g=None, **subs)¶

Calculates the sensitivity of the solution of an input factor f in direction g.

Parameters:

f (Symbol) – the input factor to be investigated. f may be of rank 0 or 1.
g (list or single of float, numpy.array or Data.) – the direction(s) of change. If not present, it is g=eye(n) where n is the number of components of f.
subs – Substitutions for all symbols used in the coefficients including unknown u and the input factor f to be investigated

Returns:

the sensitivity

Return type:

Data with shape u.getShape()+(len(g),) if len(g)>1 or u.getShape() if len(g)==1

getShapeOfCoefficient(name)¶

Returns the shape of the coefficient name

Parameters:: name (string) – name of the coefficient enquired
Returns:: the shape of the coefficient name
Return type:: tuple of int
Raises:: IllegalCoefficient – if name is not a coefficient of the PDE

getSolution(**subs)¶

Returns the solution of the PDE.

Parameters:: subs – Substitutions for all symbols used in the coefficients including the initial value for the unknown u.
Returns:: the solution
Return type:: Data

getUnknownSymbol()¶

Returns the symbol of the PDE unknown

Returns:: the symbol of the PDE unknown
Return type:: Symbol

setOptions(**opts)¶

Allows setting options for the nonlinear PDE.

The supported options are:

tolerance: error tolerance for the Newton method
iteration_steps_max: maximum number of Newton iterations
omega_min: minimum relaxation factor
atol: solution norms less than atol are assumed to be atol. This can be useful if one of your solutions is expected to be zero.
quadratic_convergence_limit: if the norm of the Newton-Raphson correction is reduced by less than quadratic_convergence_limit between two iteration steps quadratic convergence is assumed.
simplified_newton_limit: if the norm of the defect is reduced by less than simplified_newton_limit between two iteration steps and quadratic convergence is detected the iteration switches to the simplified Newton-Raphson scheme.

setValue(**coefficients)¶

Sets new values to one or more coefficients.

Parameters:

coefficients – new values assigned to coefficients
coefficients – new values assigned to coefficients
X (Symbol or any type that can be cast to a Data object) – value for coefficient X
Y (Symbol or any type that can be cast to a Data object) – value for coefficient Y
y (Symbol or any type that can be cast to a Data object) – value for coefficient y
y_contact (Symbol or any type that can be cast to a Data object) – value for coefficient y_contact
y_dirac (Symbol or any type that can be cast to a Data object) – value for coefficient y_dirac
q (any type that can be cast to a Data object) – mask for location of constraint
r (Symbol or any type that can be cast to a Data object) – value of solution prescribed by constraint

Raises:

IllegalCoefficient – if an unknown coefficient keyword is used
IllegalCoefficientValue – if a supplied coefficient value has an invalid shape

trace1(text)¶

Prints the text message if the debug level is greater than DEBUG0

Parameters:: text (string) – message to be printed

trace3(text)¶

Prints the text message if the debug level is greater than DEBUG3

Parameters:: text (string) – message to be printed

class esys.escript.Operator¶

__init__((object)arg1) → None¶

isEmpty((Operator)arg1) → bool :¶

Return type:: bool
Returns:: True if matrix is empty

nullifyRowsAndCols((Operator)arg1, (Data)arg2, (Data)arg3, (float)arg4) → None¶

of((Operator)arg1, (Data)right) → Data :¶: matrix*vector multiplication

resetValues((Operator)arg1, (bool)arg2) → None :¶: resets the matrix entries

saveHB((Operator)arg1, (str)filename) → None :¶: writes the matrix to a file using the Harwell-Boeing file format

saveMM((Operator)arg1, (str)fileName) → None :¶: writes the matrix to a file using the Matrix Market file format

solve((Operator)arg1, (Data)in, (object)options) → Data :¶

Returns:: the solution u of the linear system this*u=in
Parameters:: in (Data)

class esys.escript.SolverBuddy¶

__init__((object)arg1) → None¶

acceptConvergenceFailure((SolverBuddy)arg1) → bool :¶

Returns True if a failure to meet the stopping criteria within the given number of iteration steps is not raising in exception. This is useful if a solver is used in a non-linear context where the non-linear solver can continue even if the returned the solution does not necessarily meet the stopping criteria. One can use the hasConverged method to check if the last call to the solver was successful.

Returns:: True if a failure to achieve convergence is accepted.
Return type:: bool

adaptInnerTolerance((SolverBuddy)arg1) → bool :¶

Returns True if the tolerance of the inner solver is selected automatically. Otherwise the inner tolerance set by setInnerTolerance is used.

Returns:: True if inner tolerance adaption is chosen.
Return type:: bool

getAbsoluteTolerance((SolverBuddy)arg1) → float :¶

Returns the absolute tolerance for the solver

Return type:: float

getDiagnostics((SolverBuddy)arg1, (str)name) → float :¶

Returns the diagnostic information name. Possible values are:

‘num_iter’: the number of iteration steps
‘cum_num_iter’: the cumulative number of iteration steps
‘num_level’: the number of level in multi level solver
‘num_inner_iter’: the number of inner iteration steps
‘cum_num_inner_iter’: the cumulative number of inner iteration steps
‘time’: execution time
‘cum_time’: cumulative execution time
‘set_up_time’: time to set up of the solver, typically this includes factorization and reordering
‘cum_set_up_time’: cumulative time to set up of the solver
‘net_time’: net execution time, excluding setup time for the solver and execution time for preconditioner
‘cum_net_time’: cumulative net execution time
‘preconditioner_size’: size of preconditioner [Bytes]
‘converged’: return True if solution has converged.
‘time_step_backtracking_used’: returns True if time step back tracking has been used.
‘coarse_level_sparsity’: returns the sparsity of the matrix on the coarsest level
‘num_coarse_unknowns’: returns the number of unknowns on the coarsest level

Parameters:: name (str in the list above.) – name of diagnostic information to return
Returns:: requested value. 0 is returned if the value is yet to be defined.
Note:: If the solver has thrown an exception diagnostic values have an undefined status.

getDim((SolverBuddy)arg1) → int :¶

Returns the dimension of the problem.

Return type:: int

getDropStorage((SolverBuddy)arg1) → float :¶

Returns the maximum allowed increase in storage for ILUT

Return type:: float

getDropTolerance((SolverBuddy)arg1) → float :¶

Returns the relative drop tolerance in ILUT

Return type:: float

getInnerIterMax((SolverBuddy)arg1) → int :¶

Returns maximum number of inner iteration steps

Return type:: int

getInnerTolerance((SolverBuddy)arg1) → float :¶

Returns the relative tolerance for an inner iteration scheme

Return type:: float

getIterMax((SolverBuddy)arg1) → int :¶

Returns maximum number of iteration steps

Return type:: int

getName((SolverBuddy)arg1, (int)key) → str :¶

Returns the name of a given key

Parameters:: key – a valid key

getNumRefinements((SolverBuddy)arg1) → int :¶

Returns the number of refinement steps to refine the solution when a direct solver is applied.

Return type:: non-negative int

getNumSweeps((SolverBuddy)arg1) → int :¶

Returns the number of sweeps in a Jacobi or Gauss-Seidel/SOR preconditioner.

Return type:: int

getODESolver((SolverBuddy)arg1) → SolverOptions :¶

Returns key of the solver method for ODEs.

Parameters:: method (in CRANK_NICOLSON, BACKWARD_EULER, LINEAR_CRANK_NICOLSON) – key of the ODE solver method to be used.

getOxleyDomain((SolverBuddy)arg1) → bool :¶

True if we are using an Oxley domain, False otherwise.

Return type:: non-negative int

getPackage((SolverBuddy)arg1) → SolverOptions :¶

Returns the solver package key

Return type:: in the list DEFAULT, MKL, UMFPACK, MUMPS

getPreconditioner((SolverBuddy)arg1) → SolverOptions :¶

Returns the key of the preconditioner to be used.

Return type:: in the list ILU0, ILUT, JACOBI, AMG, REC_ILU, GAUSS_SEIDEL, RILU, NO_PRECONDITIONER

getRelaxationFactor((SolverBuddy)arg1) → float :¶

Returns the relaxation factor used to add dropped elements in RILU to the main diagonal.

Return type:: float

getReordering((SolverBuddy)arg1) → SolverOptions :¶

Returns the key of the reordering method to be applied if supported by the solver.

Return type:: in NO_REORDERING, MINIMUM_FILL_IN, NESTED_DISSECTION, DEFAULT_REORDERING

getRestart((SolverBuddy)arg1) → int :¶

Returns the number of iterations steps after which GMRES performs a restart. If 0 is returned no restart is performed.

Return type:: int

getSolverMethod((SolverBuddy)arg1) → SolverOptions :¶

Returns key of the solver method to be used.

Return type:: in the list DEFAULT, DIRECT, CHOLEVSKY, PCG, CR, CGS, BICGSTAB, GMRES, PRES20, ROWSUM_LUMPING, HRZ_LUMPING, MINRES, ITERATIVE, NONLINEAR_GMRES, TFQMR

getSummary((SolverBuddy)arg1) → str :¶: Returns a string reporting the current settings

getTolerance((SolverBuddy)arg1) → float :¶

Returns the relative tolerance for the solver

Return type:: float

getTrilinosParameters((SolverBuddy)arg1) → dict :¶

Returns a dictionary of set Trilinos parameters.

:note This method returns an empty dictionary in a non-Trilinos build.

getTruncation((SolverBuddy)arg1) → int :¶

Returns the number of residuals in GMRES to be stored for orthogonalization

Return type:: int

hasConverged((SolverBuddy)arg1) → bool :¶

Returns True if the last solver call has been finalized successfully.

Note:: if an exception has been thrown by the solver the status of thisflag is undefined.

isComplex((SolverBuddy)arg1) → bool :¶

Checks if the coefficient matrix is set to be complex-valued.

Returns:: True if a complex-valued PDE is indicated, False otherwise
Return type:: bool

isHermitian((SolverBuddy)arg1) → bool :¶

Checks if the coefficient matrix is indicated to be Hermitian.

Returns:: True if a hermitian PDE is indicated, False otherwise
Return type:: bool

isSymmetric((SolverBuddy)arg1) → bool :¶

Checks if symmetry of the coefficient matrix is indicated.

Returns:: True if a symmetric PDE is indicated, False otherwise
Return type:: bool

isVerbose((SolverBuddy)arg1) → bool :¶

Returns True if the solver is expected to be verbose.

Returns:: True if verbosity of switched on.
Return type:: bool

resetDiagnostics((SolverBuddy)arg1[, (bool)all=False]) → None :¶

Resets the diagnostics

Parameters:: all (bool) – if all is True all diagnostics including accumulative counters are reset.

setAbsoluteTolerance((SolverBuddy)arg1, (float)atol) → None :¶

Sets the absolute tolerance for the solver

Parameters:: atol (non-negative float) – absolute tolerance

setAcceptanceConvergenceFailure((SolverBuddy)arg1, (bool)accept) → None :¶

Sets the flag to indicate the acceptance of a failure of convergence.

Parameters:: accept (bool) – If True, any failure to achieve convergence is accepted.

setAcceptanceConvergenceFailureOff((SolverBuddy)arg1) → None :¶: Switches the acceptance of a failure of convergence off.

setAcceptanceConvergenceFailureOn((SolverBuddy)arg1) → None :¶: Switches the acceptance of a failure of convergence on

setComplex((SolverBuddy)arg1, (bool)complex) → None :¶

Sets the complex flag for the coefficient matrix to flag.

Parameters:: flag (bool) – If True, the complex flag is set otherwise reset.

setDim((SolverBuddy)arg1, (int)dim) → None :¶

Sets the dimension of the problem.

Parameters:: dim – Either 2 or 3.
Return type:: int

setDropStorage((SolverBuddy)arg1, (float)drop) → None :¶

Sets the maximum allowed increase in storage for ILUT. storage =2 would mean that a doubling of the storage needed for the coefficient matrix is allowed in the ILUT factorization.

Parameters:: storage (float) – allowed storage increase

setDropTolerance((SolverBuddy)arg1, (float)drop_tol) → None :¶

Sets the relative drop tolerance in ILUT

Parameters:: drop_tol (positive float) – drop tolerance

setHermitian((SolverBuddy)arg1, (bool)hermitian) → None :¶

Sets the hermitian flag for the coefficient matrix to flag.

Parameters:: flag (bool) – If True, the hermitian flag is set otherwise reset.

setHermitianOff((SolverBuddy)arg1) → None :¶: Clears the hermitian flag for the coefficient matrix.

setHermitianOn((SolverBuddy)arg1) → None :¶: Sets the hermitian flag to indicate that the coefficient matrix is hermitian.

setInnerIterMax((SolverBuddy)arg1, (int)iter_max) → None :¶

Sets the maximum number of iteration steps for the inner iteration.

Parameters:: iter_max (int) – maximum number of inner iterations

setInnerTolerance((SolverBuddy)arg1, (float)rtol) → None :¶

Sets the relative tolerance for an inner iteration scheme, for instance on the coarsest level in a multi-level scheme.

Parameters:: rtol (positive float) – inner relative tolerance

setInnerToleranceAdaption((SolverBuddy)arg1, (bool)adapt) → None :¶

Sets the flag to indicate automatic selection of the inner tolerance.

Parameters:: adapt (bool) – If True, the inner tolerance is selected automatically.

setInnerToleranceAdaptionOff((SolverBuddy)arg1) → None :¶: Switches the automatic selection of inner tolerance off.

setInnerToleranceAdaptionOn((SolverBuddy)arg1) → None :¶: Switches the automatic selection of inner tolerance on

setIterMax((SolverBuddy)arg1, (int)iter_max) → None :¶

Sets the maximum number of iteration steps

Parameters:: iter_max (int) – maximum number of iteration steps

setLocalPreconditioner((SolverBuddy)arg1, (bool)local) → None :¶

Sets the flag to use local preconditioning

Parameters:: use (bool) – If True, local preconditioning on each MPI rank is applied

setLocalPreconditionerOff((SolverBuddy)arg1) → None :¶: Sets the flag to use local preconditioning to off

setLocalPreconditionerOn((SolverBuddy)arg1) → None :¶: Sets the flag to use local preconditioning to on

setNumRefinements((SolverBuddy)arg1, (int)refinements) → None :¶

Sets the number of refinement steps to refine the solution when a direct solver is applied.

Parameters:: refinements (non-negative int) – number of refinements

setNumSweeps((SolverBuddy)arg1, (int)sweeps) → None :¶

Sets the number of sweeps in a Jacobi or Gauss-Seidel/SOR preconditioner.

Parameters:: sweeps (positive int) – number of sweeps

setODESolver((SolverBuddy)arg1, (int)solver) → None :¶

Set the solver method for ODEs.

Parameters:: method (in CRANK_NICOLSON, BACKWARD_EULER, LINEAR_CRANK_NICOLSON) – key of the ODE solver method to be used.

setOxleyDomain((SolverBuddy)arg1, (bool)using_oxley) → None :¶

Sets the parameter Oxley_Domain.

Return type:: non-negative int

setPackage((SolverBuddy)arg1, (int)package) → None :¶

Sets the direct-solver sub-library to use within the Paso framework.

Parameters:: package (in DEFAULT, MKL, UMFPACK, MUMPS) – key of the solver package to be used.
Note:: Not all packages are supported on all platforms. An exception may be thrown if a particular package is not available.

setPreconditioner((SolverBuddy)arg1, (int)preconditioner) → None :¶

Sets the preconditioner to be used.

Parameters:: preconditioner (in ILU0, ILUT, JACOBI, AMG, , REC_ILU, GAUSS_SEIDEL, RILU, NO_PRECONDITIONER) – key of the preconditioner to be used.
Note:: Not all packages support all preconditioner. It can be assumed that a package makes a reasonable choice if it encounters an unknownpreconditioner.

setRelaxationFactor((SolverBuddy)arg1, (float)relaxation) → None :¶

Sets the relaxation factor used to add dropped elements in RILU to the main diagonal.

Parameters:: factor (float) – relaxation factor
Note:: RILU with a relaxation factor 0 is identical to ILU0

setReordering((SolverBuddy)arg1, (int)ordering) → None :¶

Sets the key of the reordering method to be applied if supported by the solver. Some direct solvers support reordering to optimize compute time and storage use during elimination.

Parameters:: ordering (in 'NO_REORDERING', 'MINIMUM_FILL_IN', 'NESTED_DISSECTION', 'DEFAULT_REORDERING') – selects the reordering strategy.

setRestart((SolverBuddy)arg1, (int)restart) → None :¶

Sets the number of iterations steps after which GMRES performs a restart.

Parameters:: restart (int) – number of iteration steps after which to perform a restart. If 0 no restart is performed.

setSolverMethod((SolverBuddy)arg1, (int)method) → None :¶

Sets the solver method to be used. Use method``=``DIRECT to indicate that a direct rather than an iterative solver should be used and use method``=``ITERATIVE to indicate that an iterative rather than a direct solver should be used.

Parameters:: method (in DEFAULT, DIRECT, CHOLEVSKY, PCG, CR, CGS, BICGSTAB, GMRES, PRES20, ROWSUM_LUMPING, HRZ_LUMPING, ITERATIVE, NONLINEAR_GMRES, TFQMR, MINRES) – key of the solver method to be used.
Note:: Not all packages support all solvers. It can be assumed that a package makes a reasonable choice if it encounters an unknown solver method.

setSymmetry((SolverBuddy)arg1, (bool)symmetry) → None :¶

Sets the symmetry flag for the coefficient matrix to flag.

Parameters:: flag (bool) – If True, the symmetry flag is set otherwise reset.

setSymmetryOff((SolverBuddy)arg1) → None :¶: Clears the symmetry flag for the coefficient matrix.

setSymmetryOn((SolverBuddy)arg1) → None :¶: Sets the symmetry flag to indicate that the coefficient matrix is symmetric.

setTolerance((SolverBuddy)arg1, (float)rtol) → None :¶

Sets the relative tolerance for the solver

Parameters:: rtol (non-negative float) – relative tolerance

setTrilinosParameter((SolverBuddy)arg1, (str)arg2, (object)arg3) → None :¶

Sets a Trilinos preconditioner/solver parameter.

:note Escript does not check for validity of the parameter name (e.g. spelling mistakes). Parameters are passed 1:1 to escript’s Trilinos wrapper and from there to the relevant Trilinos package. See the relevant Trilinos documentation for valid parameter strings and values.:note This method does nothing in a non-Trilinos build.

setTruncation((SolverBuddy)arg1, (int)truncation) → None :¶

Sets the number of residuals in GMRES to be stored for orthogonalization. The more residuals are stored the faster GMRES converged

Parameters:: truncation (int) – truncation

setVerbosity((SolverBuddy)arg1, (bool)verbosity) → None :¶

Sets the verbosity flag for the solver to flag.

Parameters:: verbose (bool) – If True, the verbosity of the solver is switched on.

setVerbosityOff((SolverBuddy)arg1) → None :¶: Switches the verbosity of the solver off.

setVerbosityOn((SolverBuddy)arg1) → None :¶: Switches the verbosity of the solver on.

useLocalPreconditioner((SolverBuddy)arg1) → bool :¶

Returns True if the preconditoner is applied locally on each MPI. This reduces communication costs and speeds up the application of the preconditioner but at the costs of more iteration steps. This can be an advantage on clusters with slower interconnects.

Returns:: True if local preconditioning is applied
Return type:: bool

class esys.escript.SolverFramework¶

Represents a solver backend (PASO or TRILINOS) attached to a domain.

Use the static factory methods to create an instance and pass it to a domain constructor to fix the solver backend for all solves on that domain:

from esys.escript import SolverFramework
pkg = SolverFramework.trilinos()
domain = Rectangle(20, 20, 1, framework=pkg)

When no framework is provided to the domain constructor, the process-wide default framework is used (Trilinos if available, Paso otherwise).

__init__()¶: Raises an exception This class cannot be instantiated from Python

PASO = 0¶

TRILINOS = 1¶

static getDefault() → SolverFramework :¶

Returns the process-wide default SolverFramework (Trilinos when available, Paso otherwise).

Return type:: SolverFramework

getName((SolverFramework)arg1) → str :¶

Returns the framework name as a string ('TRILINOS' or 'PASO').

Return type:: str

getType((SolverFramework)arg1) → int :¶

Returns the framework type identifier (SolverFramework.PASO or SolverFramework.TRILINOS).

Return type:: int

static isAvailable((int)type) → bool :¶

Returns True if the given package type is available in this build.

Parameters:: type – package type integer constant
Return type:: bool

isPaso((SolverFramework)arg1) → bool :¶

Returns True if this is the Paso backend.

Return type:: bool

isTrilinos((SolverFramework)arg1) → bool :¶

Returns True if this is the Trilinos backend.

Return type:: bool

static paso() → SolverFramework :¶

Returns a SolverFramework for the Paso backend.

Return type:: SolverFramework
Raises:: EsysException – if Paso is not available in this build.

static trilinos() → SolverFramework :¶

Returns a SolverFramework for the Trilinos backend.

Return type:: SolverFramework
Raises:: EsysException – if Trilinos is not available in this build.

class esys.escript.SolverOptions¶

__init__()¶

AMG = esys.escriptcore.escriptcpp.SolverOptions.AMG¶

BACKWARD_EULER = esys.escriptcore.escriptcpp.SolverOptions.BACKWARD_EULER¶

BICGSTAB = esys.escriptcore.escriptcpp.SolverOptions.BICGSTAB¶

CGLS = esys.escriptcore.escriptcpp.SolverOptions.CGLS¶

CGS = esys.escriptcore.escriptcpp.SolverOptions.CGS¶

CHOLEVSKY = esys.escriptcore.escriptcpp.SolverOptions.CHOLEVSKY¶

CLASSIC_INTERPOLATION = esys.escriptcore.escriptcpp.SolverOptions.CLASSIC_INTERPOLATION¶

CLASSIC_INTERPOLATION_WITH_FF_COUPLING = esys.escriptcore.escriptcpp.SolverOptions.CLASSIC_INTERPOLATION_WITH_FF_COUPLING¶

CR = esys.escriptcore.escriptcpp.SolverOptions.CR¶

CRANK_NICOLSON = esys.escriptcore.escriptcpp.SolverOptions.CRANK_NICOLSON¶

DEFAULT = esys.escriptcore.escriptcpp.SolverOptions.DEFAULT¶

DEFAULT_REORDERING = esys.escriptcore.escriptcpp.SolverOptions.DEFAULT_REORDERING¶

DIRECT = esys.escriptcore.escriptcpp.SolverOptions.DIRECT¶

DIRECT_INTERPOLATION = esys.escriptcore.escriptcpp.SolverOptions.DIRECT_INTERPOLATION¶

DIRECT_MUMPS = esys.escriptcore.escriptcpp.SolverOptions.DIRECT_MUMPS¶

DIRECT_PARDISO = esys.escriptcore.escriptcpp.SolverOptions.DIRECT_PARDISO¶

DIRECT_SUPERLU = esys.escriptcore.escriptcpp.SolverOptions.DIRECT_SUPERLU¶

DIRECT_TRILINOS = esys.escriptcore.escriptcpp.SolverOptions.DIRECT_TRILINOS¶

GAUSS_SEIDEL = esys.escriptcore.escriptcpp.SolverOptions.GAUSS_SEIDEL¶

GMRES = esys.escriptcore.escriptcpp.SolverOptions.GMRES¶

HRZ_LUMPING = esys.escriptcore.escriptcpp.SolverOptions.HRZ_LUMPING¶

ILU0 = esys.escriptcore.escriptcpp.SolverOptions.ILU0¶

ILUT = esys.escriptcore.escriptcpp.SolverOptions.ILUT¶

ITERATIVE = esys.escriptcore.escriptcpp.SolverOptions.ITERATIVE¶

JACOBI = esys.escriptcore.escriptcpp.SolverOptions.JACOBI¶

LINEAR_CRANK_NICOLSON = esys.escriptcore.escriptcpp.SolverOptions.LINEAR_CRANK_NICOLSON¶

LSQR = esys.escriptcore.escriptcpp.SolverOptions.LSQR¶

LUMPING = esys.escriptcore.escriptcpp.SolverOptions.LUMPING¶

MINIMUM_FILL_IN = esys.escriptcore.escriptcpp.SolverOptions.MINIMUM_FILL_IN¶

MINRES = esys.escriptcore.escriptcpp.SolverOptions.MINRES¶

MKL = esys.escriptcore.escriptcpp.SolverOptions.MKL¶

MUMPS = esys.escriptcore.escriptcpp.SolverOptions.MUMPS¶

NESTED_DISSECTION = esys.escriptcore.escriptcpp.SolverOptions.NESTED_DISSECTION¶

NONLINEAR_GMRES = esys.escriptcore.escriptcpp.SolverOptions.NONLINEAR_GMRES¶

NO_PRECONDITIONER = esys.escriptcore.escriptcpp.SolverOptions.NO_PRECONDITIONER¶

NO_REORDERING = esys.escriptcore.escriptcpp.SolverOptions.NO_REORDERING¶

PCG = esys.escriptcore.escriptcpp.SolverOptions.PCG¶

PRES20 = esys.escriptcore.escriptcpp.SolverOptions.PRES20¶

REC_ILU = esys.escriptcore.escriptcpp.SolverOptions.REC_ILU¶

RILU = esys.escriptcore.escriptcpp.SolverOptions.RILU¶

ROWSUM_LUMPING = esys.escriptcore.escriptcpp.SolverOptions.ROWSUM_LUMPING¶

TFQMR = esys.escriptcore.escriptcpp.SolverOptions.TFQMR¶

UMFPACK = esys.escriptcore.escriptcpp.SolverOptions.UMFPACK¶

names = {'AMG': esys.escriptcore.escriptcpp.SolverOptions.AMG, 'BACKWARD_EULER': esys.escriptcore.escriptcpp.SolverOptions.BACKWARD_EULER, 'BICGSTAB': esys.escriptcore.escriptcpp.SolverOptions.BICGSTAB, 'CGLS': esys.escriptcore.escriptcpp.SolverOptions.CGLS, 'CGS': esys.escriptcore.escriptcpp.SolverOptions.CGS, 'CHOLEVSKY': esys.escriptcore.escriptcpp.SolverOptions.CHOLEVSKY, 'CLASSIC_INTERPOLATION': esys.escriptcore.escriptcpp.SolverOptions.CLASSIC_INTERPOLATION, 'CLASSIC_INTERPOLATION_WITH_FF_COUPLING': esys.escriptcore.escriptcpp.SolverOptions.CLASSIC_INTERPOLATION_WITH_FF_COUPLING, 'CR': esys.escriptcore.escriptcpp.SolverOptions.CR, 'CRANK_NICOLSON': esys.escriptcore.escriptcpp.SolverOptions.CRANK_NICOLSON, 'DEFAULT': esys.escriptcore.escriptcpp.SolverOptions.DEFAULT, 'DEFAULT_REORDERING': esys.escriptcore.escriptcpp.SolverOptions.DEFAULT_REORDERING, 'DIRECT': esys.escriptcore.escriptcpp.SolverOptions.DIRECT, 'DIRECT_INTERPOLATION': esys.escriptcore.escriptcpp.SolverOptions.DIRECT_INTERPOLATION, 'DIRECT_MUMPS': esys.escriptcore.escriptcpp.SolverOptions.DIRECT_MUMPS, 'DIRECT_PARDISO': esys.escriptcore.escriptcpp.SolverOptions.DIRECT_PARDISO, 'DIRECT_SUPERLU': esys.escriptcore.escriptcpp.SolverOptions.DIRECT_SUPERLU, 'DIRECT_TRILINOS': esys.escriptcore.escriptcpp.SolverOptions.DIRECT_TRILINOS, 'GAUSS_SEIDEL': esys.escriptcore.escriptcpp.SolverOptions.GAUSS_SEIDEL, 'GMRES': esys.escriptcore.escriptcpp.SolverOptions.GMRES, 'HRZ_LUMPING': esys.escriptcore.escriptcpp.SolverOptions.HRZ_LUMPING, 'ILU0': esys.escriptcore.escriptcpp.SolverOptions.ILU0, 'ILUT': esys.escriptcore.escriptcpp.SolverOptions.ILUT, 'ITERATIVE': esys.escriptcore.escriptcpp.SolverOptions.ITERATIVE, 'JACOBI': esys.escriptcore.escriptcpp.SolverOptions.JACOBI, 'LINEAR_CRANK_NICOLSON': esys.escriptcore.escriptcpp.SolverOptions.LINEAR_CRANK_NICOLSON, 'LSQR': esys.escriptcore.escriptcpp.SolverOptions.LSQR, 'LUMPING': esys.escriptcore.escriptcpp.SolverOptions.LUMPING, 'MINIMUM_FILL_IN': esys.escriptcore.escriptcpp.SolverOptions.MINIMUM_FILL_IN, 'MINRES': esys.escriptcore.escriptcpp.SolverOptions.MINRES, 'MKL': esys.escriptcore.escriptcpp.SolverOptions.MKL, 'MUMPS': esys.escriptcore.escriptcpp.SolverOptions.MUMPS, 'NESTED_DISSECTION': esys.escriptcore.escriptcpp.SolverOptions.NESTED_DISSECTION, 'NONLINEAR_GMRES': esys.escriptcore.escriptcpp.SolverOptions.NONLINEAR_GMRES, 'NO_PRECONDITIONER': esys.escriptcore.escriptcpp.SolverOptions.NO_PRECONDITIONER, 'NO_REORDERING': esys.escriptcore.escriptcpp.SolverOptions.NO_REORDERING, 'PCG': esys.escriptcore.escriptcpp.SolverOptions.PCG, 'PRES20': esys.escriptcore.escriptcpp.SolverOptions.PRES20, 'REC_ILU': esys.escriptcore.escriptcpp.SolverOptions.REC_ILU, 'RILU': esys.escriptcore.escriptcpp.SolverOptions.RILU, 'ROWSUM_LUMPING': esys.escriptcore.escriptcpp.SolverOptions.ROWSUM_LUMPING, 'TFQMR': esys.escriptcore.escriptcpp.SolverOptions.TFQMR, 'UMFPACK': esys.escriptcore.escriptcpp.SolverOptions.UMFPACK}¶

values = {0: esys.escriptcore.escriptcpp.SolverOptions.DEFAULT, 3: esys.escriptcore.escriptcpp.SolverOptions.MKL, 4: esys.escriptcore.escriptcpp.SolverOptions.UMFPACK, 5: esys.escriptcore.escriptcpp.SolverOptions.MUMPS, 6: esys.escriptcore.escriptcpp.SolverOptions.BICGSTAB, 7: esys.escriptcore.escriptcpp.SolverOptions.CGLS, 8: esys.escriptcore.escriptcpp.SolverOptions.CGS, 9: esys.escriptcore.escriptcpp.SolverOptions.CHOLEVSKY, 10: esys.escriptcore.escriptcpp.SolverOptions.CR, 11: esys.escriptcore.escriptcpp.SolverOptions.DIRECT, 12: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_MUMPS, 13: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_PARDISO, 14: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_SUPERLU, 15: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_TRILINOS, 16: esys.escriptcore.escriptcpp.SolverOptions.GMRES, 17: esys.escriptcore.escriptcpp.SolverOptions.HRZ_LUMPING, 18: esys.escriptcore.escriptcpp.SolverOptions.ITERATIVE, 19: esys.escriptcore.escriptcpp.SolverOptions.LSQR, 20: esys.escriptcore.escriptcpp.SolverOptions.MINRES, 21: esys.escriptcore.escriptcpp.SolverOptions.NONLINEAR_GMRES, 22: esys.escriptcore.escriptcpp.SolverOptions.PCG, 23: esys.escriptcore.escriptcpp.SolverOptions.PRES20, 24: esys.escriptcore.escriptcpp.SolverOptions.ROWSUM_LUMPING, 25: esys.escriptcore.escriptcpp.SolverOptions.TFQMR, 26: esys.escriptcore.escriptcpp.SolverOptions.AMG, 27: esys.escriptcore.escriptcpp.SolverOptions.GAUSS_SEIDEL, 28: esys.escriptcore.escriptcpp.SolverOptions.ILU0, 29: esys.escriptcore.escriptcpp.SolverOptions.ILUT, 30: esys.escriptcore.escriptcpp.SolverOptions.JACOBI, 31: esys.escriptcore.escriptcpp.SolverOptions.NO_PRECONDITIONER, 32: esys.escriptcore.escriptcpp.SolverOptions.REC_ILU, 33: esys.escriptcore.escriptcpp.SolverOptions.RILU, 34: esys.escriptcore.escriptcpp.SolverOptions.BACKWARD_EULER, 35: esys.escriptcore.escriptcpp.SolverOptions.CRANK_NICOLSON, 36: esys.escriptcore.escriptcpp.SolverOptions.LINEAR_CRANK_NICOLSON, 37: esys.escriptcore.escriptcpp.SolverOptions.CLASSIC_INTERPOLATION, 38: esys.escriptcore.escriptcpp.SolverOptions.CLASSIC_INTERPOLATION_WITH_FF_COUPLING, 39: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_INTERPOLATION, 40: esys.escriptcore.escriptcpp.SolverOptions.DEFAULT_REORDERING, 41: esys.escriptcore.escriptcpp.SolverOptions.MINIMUM_FILL_IN, 42: esys.escriptcore.escriptcpp.SolverOptions.NESTED_DISSECTION, 43: esys.escriptcore.escriptcpp.SolverOptions.NO_REORDERING}¶

class esys.escript.TestDomain¶

Test Class for domains with no structure. May be removed from future releases without notice.

__init__()¶: Raises an exception This class cannot be instantiated from Python

class esys.escript.TransportProblem¶

__init__((object)arg1) → None¶

getSafeTimeStepSize((TransportProblem)arg1) → float¶

getUnlimitedTimeStepSize((TransportProblem)arg1) → float¶

insertConstraint((TransportProblem)source, (Data)q, (Data)r, (Data)factor) → None :¶: inserts constraint u_{,t}=r where q>0 into the problem using a weighting factor

isEmpty((TransportProblem)arg1) → int :¶

Return type:: int

reset((TransportProblem)arg1, (bool)arg2) → None :¶: resets the transport operator typically as they have been updated.

resetValues((TransportProblem)arg1, (bool)arg2) → None¶

solve((TransportProblem)arg1, (Data)u0, (Data)source, (float)dt, (object)options) → Data :¶

returns the solution u for a time step dt>0 with initial value u0

Return type:: Data
Parameters:: source (Data)

class esys.escript.sym¶

__init__()¶

Symbol¶: alias of memoryview

Functions¶

esys.escript.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.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.ComplexData((object)value[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd8c0>[, (bool)expanded=False]]) → Data¶

esys.escript.ComplexScalar([(object)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd040>[, (bool)expanded=False]]]) → Data :¶

Construct a Data object containing scalar data-points.

Parameters:

value (float) – scalar value for all points
what (FunctionSpace) – FunctionSpace for Data
expanded (bool) – If True, a value is stored for each point. If False, more efficient representations may be used

Return type:

Data

esys.escript.ComplexTensor([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd340>[, (bool)expanded=False]]]) → Data :¶

Construct a Data object containing rank2 data-points.

ComplexTensor( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd440> [, (bool)expanded=False]]) -> Data

esys.escript.ComplexTensor3([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd540>[, (bool)expanded=False]]]) → Data :¶

Construct a Data object containing rank3 data-points.

ComplexTensor3( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd6c0> [, (bool)expanded=False]]) -> Data

esys.escript.ComplexTensor4([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd740>[, (bool)expanded=False]]]) → Data :¶

Construct a Data object containing rank4 data-points.

ComplexTensor4( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd840> [, (bool)expanded=False]]) -> Data

esys.escript.ComplexVector([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd140>[, (bool)expanded=False]]]) → Data :¶

Construct a Data object containing rank1 data-points.

ComplexVector( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd240> [, (bool)expanded=False]]) -> Data

esys.escript.ContinuousFunction((Domain)domain) → FunctionSpace :¶

Returns:: a continuous FunctionSpace (overlapped node values)
Return type:: FunctionSpace

esys.escript.DiracDeltaFunctions((Domain)domain) → FunctionSpace :¶

Return type:: FunctionSpace

esys.escript.Function((Domain)domain) → FunctionSpace :¶

Returns:: a function FunctionSpace
Return type:: FunctionSpace

esys.escript.FunctionOnBoundary((Domain)domain) → FunctionSpace :¶

Returns:: a function on boundary FunctionSpace
Return type:: FunctionSpace

esys.escript.FunctionOnContactOne((Domain)domain) → FunctionSpace :¶

Returns:: Return a FunctionSpace on right side of contact
Return type:: FunctionSpace

esys.escript.FunctionOnContactZero((Domain)domain) → FunctionSpace :¶

Returns:: Return a FunctionSpace on left side of contact
Return type:: FunctionSpace

esys.escript.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.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.MPIBarrierWorld() → None :¶: Wait until all MPI processes have reached this point.

esys.escript.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.RandomData((tuple)shape, (FunctionSpace)fs[, (int)seed=0[, (tuple)filter=()]]) → Data :¶

Creates a new expanded Data object containing pseudo-random values. With no filter, values are drawn uniformly at random from [0,1].

Parameters:

shape (tuple) – datapoint shape
fs (FunctionSpace) – function space for data object.
seed (long) – seed for random number generator.

esys.escript.ReducedContinuousFunction((Domain)domain) → FunctionSpace :¶

Returns:: a continuous with reduced order FunctionSpace (overlapped node values on reduced element order)
Return type:: FunctionSpace

esys.escript.ReducedFunction((Domain)domain) → FunctionSpace :¶

Returns:: a function FunctionSpace with reduced integration order
Return type:: FunctionSpace

esys.escript.ReducedFunctionOnBoundary((Domain)domain) → FunctionSpace :¶

Returns:: a function on boundary FunctionSpace with reduced integration order
Return type:: FunctionSpace

esys.escript.ReducedFunctionOnContactOne((Domain)domain) → FunctionSpace :¶

Returns:: Return a FunctionSpace on right side of contact with reduced integration order
Return type:: FunctionSpace

esys.escript.ReducedFunctionOnContactZero((Domain)domain) → FunctionSpace :¶

Returns:: a FunctionSpace on left side of contact with reduced integration order
Return type:: FunctionSpace

esys.escript.ReducedSolution((Domain)domain) → FunctionSpace :¶

Return type:: FunctionSpace

esys.escript.Scalar([(object)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6ccfc0>[, (bool)expanded=False]]]) → Data :¶

Construct a Data object containing scalar data-points.

Parameters:

value (float) – scalar value for all points
what (FunctionSpace) – FunctionSpace for Data
expanded (bool) – If True, a value is stored for each point. If False, more efficient representations may be used

Return type:

Data

esys.escript.Solution((Domain)domain) → FunctionSpace :¶

Return type:: FunctionSpace

esys.escript.Tensor([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd2c0>[, (bool)expanded=False]]]) → Data :¶

Construct a Data object containing rank2 data-points.

Tensor( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd3c0> [, (bool)expanded=False]]) -> Data

esys.escript.Tensor3([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd4c0>[, (bool)expanded=False]]]) → Data :¶

Construct a Data object containing rank3 data-points.

Tensor3( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd5c0> [, (bool)expanded=False]]) -> Data

esys.escript.Tensor4([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd640>[, (bool)expanded=False]]]) → Data :¶

Construct a Data object containing rank4 data-points.

Tensor4( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd7c0> [, (bool)expanded=False]]) -> Data

esys.escript.Vector([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd0c0>[, (bool)expanded=False]]]) → Data :¶

Construct a Data object containing rank1 data-points.

Vector( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f350c6cd1c0> [, (bool)expanded=False]]) -> Data

esys.escript.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.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.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.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.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.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.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.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.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.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.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.canInterpolate((FunctionSpace)src, (FunctionSpace)dest) → bool :¶

Parameters:

src – Source FunctionSpace
dest – Destination FunctionSpace

Returns:

True if src can be interpolated to dest

Return type:

bool

esys.escript.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.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.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.condEval(f, tval, fval)¶: Wrapper to allow non-data objects to be used.

esys.escript.conjugate(arg)¶: returns the complex conjugate of arg

esys.escript.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.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.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.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.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.delay(arg)¶: Returns a lazy version of arg

esys.escript.deviatoric(arg)¶: Returns the deviatoric version of arg.

esys.escript.diameter(domain)¶

Returns the diameter of a domain.

Parameters:: domain (escript.Domain) – a domain
Return type:: float

esys.escript.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.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.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.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.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.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.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.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.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.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.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.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.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.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.getEpsilon()¶

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

Returns:: machine precision epsilon
Return type:: float

esys.escript.getEscriptParamInt((str)name[, (int)sentinel=0]) → int :¶

Read the value of an escript tuning parameter

Parameters:

name (string) – parameter to lookup
sentinel (int) – Value to be returned if name is not a known parameter

esys.escript.getMPIRankWorld() → int :¶: Return the rank of this process in the MPI World.

esys.escript.getMPISizeWorld() → int :¶: Return number of MPI processes in the job.

esys.escript.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.getMPIWorldSum((int)arg1) → int :¶

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

esys.escript.getMachinePrecision() → float¶

esys.escript.getMaxFloat()¶

Returns the largest representable positive floating point number.

Returns:: maximum float value
Return type:: float

esys.escript.getNumberOfThreads() → int :¶: Return the maximum number of threads available to OpenMP.

esys.escript.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.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.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.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.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.getTestDomainFunctionSpace((int)dpps, (int)samples[, (int)size=1]) → FunctionSpace :¶: For testing only. May be removed without notice.

esys.escript.getVersion() → str :¶: This method will only report accurate version numbers for clean checkouts.

esys.escript.grad(arg, where=None)¶

Returns the spatial gradient of arg at where.

If g is the returned object, then

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.grad_n(arg, n, where=None)¶

esys.escript.hasFeature((str)name) → bool :¶

Check if escript was compiled with a certain feature

Parameters:: name (string) – feature to lookup

esys.escript.haveMPI4Py() → bool :¶: Returns True if escript was built with mpi4py support.

esys.escript.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.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.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.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.imag(arg)¶: returns the imaginary part of arg

esys.escript.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.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.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.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.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.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.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.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.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.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.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.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.listFeatures() → list :¶

Returns:: A list of strings representing the features escript supports.

esys.escript.load((str)fileName, (Domain)domain) → Data :¶

reads real Data on domain from file in HDF5 format

Parameters:

fileName (string)
domain (Domain)

esys.escript.loadIsConfigured() → bool :¶

Returns:: True if the load function is configured.

esys.escript.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.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.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.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.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.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.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.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.matrixmult(arg0, arg1)¶: See matrix_mult.

esys.escript.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.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.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.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.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.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.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.negative(arg)¶: returns the negative part of arg

esys.escript.nonsymmetric(arg)¶: Deprecated alias for antisymmetric.

esys.escript.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.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.phase(arg)¶: return the “phase”/”arg”/”angle” of a number

esys.escript.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.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.positive(arg)¶: returns the positive part of arg

esys.escript.printParallelThreadCounts() → None¶

esys.escript.real(arg)¶: returns the real part of arg

esys.escript.releaseUnusedMemory() → None¶

esys.escript.reorderComponents(arg, index)¶: Resorts the components of arg according to index.

esys.escript.resolve(arg)¶: Returns the value of arg resolved.

esys.escript.resolveGroup((object)arg1) → None¶

esys.escript.runMPIProgram((list)arg1) → int :¶: Spawns an external MPI program using a separate communicator.

esys.escript.safeDiv(arg0, arg1, rtol=None)¶: returns arg0/arg1 but return 0 where arg1 is (almost) zero

esys.escript.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.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.setEscriptParamInt((str)name[, (int)value=0]) → None :¶

Modify the value of an escript tuning parameter

Parameters:

name (string)
value (int)

esys.escript.setNumberOfThreads((int)arg1) → None :¶: Use of this method is strongly discouraged.

esys.escript.showEscriptParams()¶: Displays the parameters escript recognises with an explanation and their current value.

esys.escript.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.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.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.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.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.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.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.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.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.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.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.tensormult(arg0, arg1)¶: See tensor_mult.

esys.escript.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.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.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.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.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.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.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.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.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.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.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.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.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.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
DataCoupler
EPSILON
HAVE_MPI4PY
HAVE_SYMBOLS
MPIDomainArray
esys_lib_path
esys_packages
esys_paths
package_prefix

esys.escript Package¶

Classes¶

Functions¶

Others¶

Packages¶

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