esys.downunder.apps Package

Our most general domain representation. Imports submodules into its namespace

Classes

class esys.downunder.apps.ContinuousDomain

Bases: esys.escriptcore.escriptcpp.Domain

Class representing continuous domains

__init__()

Raises an exception This class cannot be instantiated from Python

MPIBarrier((Domain)arg1) → None :

Wait until all processes have reached this point

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

Dumps the domain to a file

Parameters:filename (string) –
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
getDim((Domain)arg1) → int :
Return type:int
Returns:Spatial dimension of the Domain
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
getNumDataPointsGlobal((ContinuousDomain)arg1) → int :
Returns:the number of data points summed across all MPI processes
Return type:int
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
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
getTag((Domain)arg1, (str)name) → int :
Returns:tag id for name
Return type:string
getTransportTypeId((ContinuousDomain)arg1, (int)solver, (int)preconditioner, (int)package, (bool)symmetry) → int
getX((Domain)arg1) → Data :
Return type:Data
Returns:Locations in the`Domain`. FunctionSpace is chosen appropriately
isValidTagName((Domain)arg1, (str)name) → bool :
Returns:True is name corresponds to a tag
Return type:bool
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) –
onMasterProcessor((Domain)arg1) → bool :
Returns:True if this code is executing on the master process
Return type:bool
print_mesh_info((ContinuousDomain)arg1[, (bool)full=False]) → None :
Parameters:full (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
setX((ContinuousDomain)arg1, (Data)arg) → None :

assigns new location to the domain

Parameters:arg (Data) –
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.downunder.apps.DCResistivityModel(domain, sigma0=0.001, fixAllFaces=True, useFastSolver=False)

Bases: object

This class is a simple wrapper for 3D Dirac function direct current sources PDE model. It solves PDE

  • div (sigma grad u) = sum (I_s d_dirac(x_s))
where
I_s is the applied cirrent at x_s and we sum over all sources s.
Possible boundary conditions included in the class are Dirichlet on
  • top (default) or
  • top and base
It solves just the one load condition, either with
  • sources as list of points with corresponding list of currents (analytic primary solution)
  • or sources as one function = sum (I_s d_dirac(x_s) (FE primary solution)
It has a function to set ground property
  • setConductivity
get ground property
  • getConductivity
It uses primary and secondary potential in solution
  • setPrimaryPotentialForHalfSpace (analytic solution - sources is list of points)
  • setPrimaryPotential (finite element computed solution - sources is a Dirac Delta)
  • getPrimaryPotential
  • getPrimaryField
Output solution
  • getSecondaryPotential
  • getSecondaryField
  • getPotential
  • getField
__init__(domain, sigma0=0.001, fixAllFaces=True, useFastSolver=False)

Initialise the class with domain and boundary conditions. Setup PDE and conductivity. :param domain: the domain :type domain: Domain :param sigma0: background electric conductivity for the primary potential :type sigma0: typically float :param fixAllFaces: if true the potential at all faces except the top are set to zero.

Otherwise only the base is set to zero.
Parameters:useFastSolver (bool) – use multigrid solver. This may fail. (Changing the mesh could stop this fail.)
getConductivity()

returns the conductivity

getField()

returns the total potential. This is -grad(getPotential())

getPotential()

returns total potential

getPrimaryField()

returns the primary electric field. This is -grad(getPrimaryPotential())

getPrimaryPotential()

returns the primary potential

getSecondaryField()

returns secondary electric field. This is -grad(getSecondaryPotential())

getSecondaryPotential()

returns the secondary potential

setConductivity(sigma)

sets the conductivity. This solves a LinearSinglePDE. :param sigma: conductivity distribution. The value at source locations should be sigma0. :type sigma: Data

setPrimaryPotential(source=None)

set the primary potential using the source term source. :param source: source of charges as DiracDeltaFunctions object :type source: Data object

setPrimaryPotentialForHalfSpace(sources=[], charges=[])

sets the primary potential for the infinite half space with constant conductivity sigma0 uses analytic solution. Method of images used for sources at depth) :param sources: list of source locations (x,y,z). Need to be defined on the surface of the domain. :type sources: list of tuples. :param charges: list of charges (in [A]) :type sources: list of floats

class esys.downunder.apps.DCResistivityModelNoPrimary(domain, source, sigma=0.001, fixAllFaces=True, useFastSolver=False)

Bases: object

This class is a simple wrapper for 3D Dirac function direct current sources PDE model. It solves PDE

  • div (sigma grad u) = sum (I_s d_dirac(x_s))
where
I_s is the applied cirrent at x_s and we sum over all sources s.
Possible boundary conditions included in the class are Dirichlet on
  • top (default) or
  • top and base
It solves just the one load condition, either with
  • sources as one function = sum (I_s d_dirac(x_s) (FE primary solution)
It has a function to set ground property
  • setConductivity
get ground property
  • getConductivity

It just solves PDE without splitting into primary and secondary.

Output solution
  • getSecondaryPotential
  • getSecondaryField
  • getPotential
  • getField
__init__(domain, source, sigma=0.001, fixAllFaces=True, useFastSolver=False)

Initialise the class with domain and boundary conditions. Setup PDE and conductivity. :param domain: the domain :type domain: Domain :param sigma0: background electric conductivity for the primary potential :type sigma0: typically float :param fixAllFaces: if true the potential at all faces except the top are set to zero.

Otherwise only the base is set to zero.
Parameters:useFastSolver (bool) – use multigrid solver. This may fail. (Changing the mesh could stop this fail.)
getConductivity()

returns the conductivity

getPotential(source=None)

get the potential using the source term source. :param source: source of charges as DiracDeltaFunctions object :type source: Data object

getPrimaryField()

returns the primary electric field. This is -grad(getPrimaryPotential())

setConductivity(sig)

returns the conductivity

class esys.downunder.apps.Data

Bases: Boost.Python.instance

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

__init__((object)arg1) → None

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

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

Make this object a copy of other

note:The two objects will act independently from now on. That is, changing other after this call will not change this object and vice versa.
copy( (Data)arg1) -> Data :
note:In the no argument form, a new object will be returned which is an independent copy of this object.
copyWithMask((Data)arg1, (Data)other, (Data)mask) → None :

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

Parameters:
  • other (Data) – source of values
  • mask (Scalar Data) –
delay((Data)arg1) → Data :

Convert this object into lazy representation

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

Save the data as a netCDF 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
getNumberOfDataPoints((Data)arg1) → int :
Return type:int
Returns:Number of datapoints in the object
getRank((Data)arg1) → int :
Returns:the number of indices required to address a component of a datapoint
Return type:positive int
getShape((Data)arg1) → tuple :

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

Return type:tuple
getTagNumber((Data)arg1, (int)dpno) → int :

Return tag number for the specified datapoint

Return type:int
Parameters:dpno (int) – datapoint number
getTupleForDataPoint((Data)arg1, (int)dataPointNo) → object :
Returns:Value of the specified datapoint
Return type:tuple
Parameters:dataPointNo (int) – datapoint to access
getTupleForGlobalDataPoint((Data)arg1, (int)procNo, (int)dataPointNo) → object :

Get a specific datapoint from a specific process

Return type:

tuple
Parameters:
  • procNo (positive int) – MPI rank of the process
  • dataPointNo (int) – datapoint to access
getX((Data)arg1) → Data :

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

hasInf((Data)arg1) → bool :

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

hasNaN((Data)arg1) → bool :

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

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

Please consider using getSupLocator() from pdetools instead.

internal_minGlobalDataPoint((Data)arg1) → tuple :

Please consider using getInfLocator() from pdetools instead.

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

Interpolate this object’s values into a new functionspace.

interpolateTable((Data)arg1, (object)table, (float)Amin, (float)Astep, (Data)B, (float)Bmin, (float)Bstep[, (float)undef=1e+50[, (bool)check_boundaries=False]]) → Data :
Creates a new Data object by interpolating using the source data (which are

looked up in table) A must be the outer dimension on the table

param table:two dimensional collection of values
param Amin:The base of locations in table
type Amin:float
param Astep:size of gap between each item in the table
type Astep:float
param undef:upper bound on interpolated values
type undef:float
param B:Scalar representing the second coordinate to be mapped into the table
type B:Data
param Bmin:The base of locations in table for 2nd dimension
type Bmin:float
param Bstep:size of gap between each item in the table for 2nd dimension
type Bstep:float
param check_boundaries:
 if true, then values outside the boundaries will be rejected. If false, then boundary values will be used.
raise RuntimeError(DataException):
 if the coordinates do not map into the table or if the interpolated value is above undef
rtype:Data

interpolateTable( (Data)arg1, (object)table, (float)Amin, (float)Astep [, (float)undef=1e+50 [, (bool)check_boundaries=False]]) -> Data

isComplex((Data)arg1) → bool :
Return type:bool
Returns:True if this Data stores complex values.
isConstant((Data)arg1) → bool :
Return type:bool
Returns:True if this Data is an instance of DataConstant
Note:This does not mean the data is immutable.
isEmpty((Data)arg1) → bool :

Is this object an instance of DataEmpty

Return type:bool
Note:This is not the same thing as asking if the object contains datapoints.
isExpanded((Data)arg1) → bool :
Return type:bool
Returns:True if this Data is expanded.
isLazy((Data)arg1) → bool :
Return type:bool
Returns:True if this Data is lazy.
isProtected((Data)arg1) → bool :

Can this instance be modified. :rtype: bool

isReady((Data)arg1) → bool :
Return type:bool
Returns:True if this Data is not lazy.
isTagged((Data)arg1) → bool :
Return type:bool
Returns:True if this Data is expanded.
nonuniformInterpolate((Data)arg1, (object)in, (object)out, (bool)check_boundaries) → Data :

1D interpolation with non equally spaced points

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

1D interpolation of slope with non equally spaced points

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

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

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

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

resolve((Data)arg1) → None :

Convert the data to non-lazy representation.

setProtection((Data)arg1) → None :

Disallow modifications to this data object

Note:This method does not allow you to undo protection.
setTaggedValue((Data)arg1, (int)tagKey, (object)value) → None :

Set the value of tagged Data.

param tagKey:tag to update
type tagKey:int
setTaggedValue( (Data)arg1, (str)name, (object)value) -> None :
param name:tag to update
type name:string
param value:value to set tagged data to
type value:object which acts like an array, tuple or list
setToZero((Data)arg1) → None :

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

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

setValueOfDataPoint( (Data)arg1, (int)arg2, (object)arg3) -> None

setValueOfDataPoint( (Data)arg1, (int)arg2, (float)arg3) -> None :

Modify the value of a single datapoint.

param dataPointNo:
 
type dataPointNo:
 int
param value:
type value:float or an object which acts like an array, tuple or list
warning:Use of this operation is discouraged. It prevents some optimisations from operating.
tag((Data)arg1) → None :

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

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

Return the datapoints of this object in a list. Each datapoint is stored as a tuple.

Parameters:scalarastuple – if True, scalar data will be wrapped as a tuple. True => [(0), (1), (2)]; False => [0, 1, 2]
class esys.downunder.apps.DataManager(formats=[0], work_dir='.', restart_prefix='restart', do_restart=True)

Bases: object

Escript data import/export manager.

Example:

dm=DataManager(formats=[DataManager.RESTART,DataManager.VTK])
if dm.hasData():
    dom = dm.getDomain()
    time = dm.getValue("time")
    dt = dm.getValue("dt")
    T = dm.getValue("T")
    u = dm.getValue("u")
else:
    T = ...
    u = ...
dm.addData(time=time,dt=dt,T=T,u=u) # add data and variables
dm.setTime(time)                    # set the simulation timestamp
dm.export()                         # write out data
__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)

getDomain()

Returns the domain as recovered from restart files.

getValue(value_name)

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

hasData()

Returns True if the manager holds data for restart

setCheckpointFrequency(freq)

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

setDomain(domain)

Sets the domain without adding data.

setMeshLabels(x, y, z='')

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

setMeshUnits(x, y, z='')

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

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.

class esys.downunder.apps.Domain

Bases: Boost.Python.instance

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
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
isValidTagName((Domain)arg1, (str)name) → bool :
Returns:True is name corresponds to a tag
Return type:bool
onMasterProcessor((Domain)arg1) → bool :
Returns:True if this code is executing on the master process
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.downunder.apps.Evaluator(*expressions)

Bases: object

__init__(*expressions)

Returns a symbolic evaluator.

Parameters:expressions – optional expressions to initialise with
addExpression(expression)

Adds an expression to this evaluator.

Returns:the modified Evaluator object
evaluate(evalf=False, **args)

Evaluates all expressions in this evaluator and returns the result as a tuple.

Returns:the evaluated expressions in the order they were added to this Evaluator.
subs(**args)

Symbol substitution.

Returns:the modified Evaluator object
class esys.downunder.apps.FileWriter(fn, append=False, createLocalFiles=False)

Bases: object

Interface to write data to a file. In essence this class wrappes the standard file object to write data that are global in MPI to a file. In fact, data are writen on the processor with MPI rank 0 only. It is recommended to use FileWriter rather than open in order to write code that is running with as well as with MPI. It is safe to use open onder MPI to read data which are global under MPI.

Variables:
  • name – name of file
  • mode – access mode (=’w’ or =’a’)
  • closed – True to indicate closed file
  • newlines – line seperator
__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) – switches on the creation of local files.
  • 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 txt of strings to the file.

Parameters:txts (any iterable object producing strings) – sequense of strings to be written to file
Note:Note that newlines are not added. This method is equivalent to call write() for each string.
class esys.downunder.apps.FunctionJob(fn, *args, **kwargs)

Bases: esys.escriptcore.splitworld.Job

Takes a python function (with only self and keyword params) to be called as the work method

__init__(fn, *args, **kwargs)

It ignores all of its parameters, except that, it requires the following as keyword arguments

Variables:
  • domain – Domain to be used as the basis for all Data and PDEs in this Job.
  • jobid – sequence number of this job. The first job has id=1
clearExports()

Remove exported values from the map

clearImports()

Remove imported values from their map

declareImport(name)

Adds name to the list of imports

exportValue(name, v)

Make value v available to other Jobs under the label name. name must have already been registered with the SplitWorld instance. For use inside the work() method.

Variables:
  • name – registered label for exported value
  • v – value to be imported
importValue(name)

For use inside the work() method.

Variables:name – label for imported value.
setImportValue(name, v)

Use to make a value available to the job (ie called from outside the job)

Variables:
  • name – label used to identify this import
  • v – value to be imported
work()

Need to be overloaded for the job to actually do anthing. A return value of True indicates this job thinks it is done. A return value of False indicates work still to be done

class esys.downunder.apps.FunctionSpace

Bases: Boost.Python.instance

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
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

param newtag:tag number to set
type newtag:string, non-zero int
param mask:Samples which correspond to positive values in the mask will be set to newtag.
type mask:scalar Data

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

class esys.downunder.apps.GravityModel(domain, fixBase=False)

Bases: object

This class is a simple wrapper for a 2D or 3D gravity PDE model. It solves PDE

  • div (grad u) = -4 pi G rho
where
G is the gravitational constant and rho is density u is computed anomaly potential
Possible boundary conditions included in the class are Dirichlet on
  • top (default) or
  • top and base.
It has a function to set ground property
  • setDensity
get ground property
  • getDensity
and functions to output solutions
  • getgravityPotential : u
  • getzGravity : -grad(u)[2] (3D) or -grad(u)[1] (2D)
  • getGravityVector : grad (u) .
__init__(domain, fixBase=False)

Initialise the class with domain and boundary conditions. Setup PDE and density. : param domain: the domain : type domain: Domain : param fixBase: if true the gravitational potential at the bottom is set to zero. : type fixBase: bool : param fixVert: if true the magnetic field on all vertical sudes is set to zero. : type fixBase: bool : if fixBase is True then gravity field is set to zero at base and top surfaces.

getDensity()

returns density : returns: rho

getGravityPotential()

get the potential of the density anomaly

getGravityVector()

get the Bouger gravity vector

getzGravity()

get Bouger gravity in -z direction (vertical)

setDensity(rho=0)

set density : param rho: density : type rho: Data or float

class esys.downunder.apps.Job(*args, **kwargs)

Bases: object

Describes a sequence of work to be carried out in a subworld. The instances of this class used in the subworlds will be constructed by the system. To do specific work, this class should be subclassed and the work() (and possibly __init__ methods overloaded). The majority of the work done by the job will be in the overloaded work() method. The work() method should retrieve values from the outside using importValue() and pass values to the rest of the system using exportValue(). The rest of the methods should be considered off limits.

__init__(*args, **kwargs)

It ignores all of its parameters, except that, it requires the following as keyword arguments

Variables:
  • domain – Domain to be used as the basis for all Data and PDEs in this Job.
  • jobid – sequence number of this job. The first job has id=1
clearExports()

Remove exported values from the map

clearImports()

Remove imported values from their map

declareImport(name)

Adds name to the list of imports

exportValue(name, v)

Make value v available to other Jobs under the label name. name must have already been registered with the SplitWorld instance. For use inside the work() method.

Variables:
  • name – registered label for exported value
  • v – value to be imported
importValue(name)

For use inside the work() method.

Variables:name – label for imported value.
setImportValue(name, v)

Use to make a value available to the job (ie called from outside the job)

Variables:
  • name – label used to identify this import
  • v – value to be imported
work()

Need to be overloaded for the job to actually do anthing. A return value of True indicates this job thinks it is done. A return value of False indicates work still to be done

class esys.downunder.apps.LinearPDE(domain, numEquations=None, numSolutions=None, isComplex=False, debug=False)

Bases: esys.escriptcore.linearPDEs.LinearProblem

This class is used to define a general linear, 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 linear PDE is defined in the following form:

-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)

where grad(F) denotes the spatial derivative of F. Einstein’s summation convention, ie. summation over indexes appearing twice in a term of a sum performed, is used. The coefficients A, B, C, D, X and Y have to be specified through Data objects in Function and the coefficients A_reduced, B_reduced, C_reduced, D_reduced, X_reduced and Y_reduced have to be specified through Data objects in ReducedFunction. It is also allowed to use objects that can be converted into such Data objects. A and A_reduced are rank two, B, C, X, B_reduced, C_reduced and X_reduced are rank one and D, D_reduced, Y and Y_reduced are scalar.

The following natural boundary conditions are considered:

n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y

where n is the outer normal field. Notice that the coefficients A, A_reduced, B, B_reduced, X and X_reduced are defined in the PDE. The coefficients d and y are each a scalar in FunctionOnBoundary and the coefficients d_reduced and y_reduced are each a scalar in ReducedFunctionOnBoundary.

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.

The PDE is symmetrical if

A[i,j]=A[j,i] and B[j]=C[j] and A_reduced[i,j]=A_reduced[j,i] and B_reduced[j]=C_reduced[j]

For a system of PDEs and a solution with several components the PDE has the form

-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i]

A and A_reduced are of rank four, B, B_reduced, C and C_reduced are each of rank three, D, D_reduced, X_reduced and X are each of rank two and Y and Y_reduced are of rank one. The natural boundary conditions take the form:

n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]

The coefficient d is of rank two and y is of rank one both in FunctionOnBoundary. The coefficients d_reduced is of rank two and y_reduced is of rank one both in ReducedFunctionOnBoundary.

Constraints take the form

u[i]=r[i] where q[i]>0

r and q are each rank one. Notice that at some locations not necessarily all components must have a constraint.

The system of PDEs is symmetrical if

  • A[i,j,k,l]=A[k,l,i,j]
  • A_reduced[i,j,k,l]=A_reduced[k,l,i,j]
  • B[i,j,k]=C[k,i,j]
  • B_reduced[i,j,k]=C_reduced[k,i,j]
  • D[i,k]=D[i,k]
  • D_reduced[i,k]=D_reduced[i,k]
  • d[i,k]=d[k,i]
  • d_reduced[i,k]=d_reduced[k,i]

LinearPDE also supports solution discontinuities over a contact region in the domain. To specify the conditions across the discontinuity we are using the generalised flux J which, in the case of a system of PDEs and several components of the solution, is defined as

J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]

For the case of single solution component and single PDE J is defined as

J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]

In the context of discontinuities n denotes the normal on the discontinuity pointing from side 0 towards side 1 calculated from FunctionSpace.getNormal of FunctionOnContactZero. For a system of PDEs the contact condition takes the form

n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]

where J0 and J1 are the fluxes on side 0 and side 1 of the discontinuity, respectively. jump(u), which is the difference of the solution at side 1 and at side 0, denotes the jump of u across discontinuity along the normal calculated by jump. The coefficient d_contact is of rank two and y_contact is of rank one both in FunctionOnContactZero or FunctionOnContactOne. The coefficient d_contact_reduced is of rank two and y_contact_reduced is of rank one both in ReducedFunctionOnContactZero or ReducedFunctionOnContactOne. In case of a single PDE and a single component solution the contact condition takes the form

n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)

In this case the coefficient d_contact and y_contact are each scalar both in FunctionOnContactZero or FunctionOnContactOne and the coefficient d_contact_reduced and y_contact_reduced are each scalar both in ReducedFunctionOnContactZero or ReducedFunctionOnContactOne.

Typical usage:

p = LinearPDE(dom)
p.setValue(A=kronecker(dom), D=1, Y=0.5)
u = p.getSolution()
__init__(domain, numEquations=None, numSolutions=None, isComplex=False, debug=False)

Initializes a new linear PDE.

Parameters:
  • domain (Domain) – domain of the PDE
  • numEquations – number of equations. If None the number of equations is extracted from the PDE coefficients.
  • numSolutions – number of solution components. If None the number of solution components is extracted from the PDE coefficients.
  • debug – if True debug information is printed
addPDEToLumpedSystem(operator, a, b, c, hrz_lumping)

adds a PDE to the lumped system, results depend on domain

Parameters:
  • mat (OperatorAdapter) –
  • rhs (Data) –
  • a (Data) –
  • b (Data) –
  • c (Data) –
  • hrz_lumping (bool) –
addPDEToRHS(righthandside, X, Y, y, y_contact, y_dirac)

adds a PDE to the right hand side, results depend on domain

Parameters:
  • mat (OperatorAdapter) –
  • righthandside (Data) –
  • X (Data) –
  • Y (Data) –
  • y (Data) –
  • y_contact (Data) –
  • y_dirac (Data) –
addPDEToSystem(operator, righthandside, A, B, C, D, X, Y, d, y, d_contact, y_contact, d_dirac, y_dirac)

adds a PDE to the system, results depend on domain

Parameters:
addToRHS(rhs, data)

adds a PDE to the right hand side, results depend on domain

Parameters:
  • mat (OperatorAdapter) –
  • righthandside (Data) –
  • data (list) –
addToSystem(op, rhs, data)

adds a PDE to the system, results depend on domain

Parameters:
  • mat (OperatorAdapter) –
  • rhs (Data) –
  • data (list) –
alteredCoefficient(name)

Announces that coefficient name has been changed.

Parameters:name (string) – name of the coefficient affected
Raises:IllegalCoefficient – if name is not a coefficient of the PDE
Note:if name is q or r, the method will not trigger a rebuild of the system as constraints are applied to the solved system.
checkReciprocalSymmetry(name0, name1, verbose=True)

Tests two coefficients for reciprocal symmetry.

Parameters:
  • name0 (str) – name of the first coefficient
  • name1 (str) – name of the second coefficient
  • verbose (bool) – if set to True or not present a report on coefficients which break the symmetry is printed
Returns:

True if coefficients name0 and name1 are reciprocally symmetric.
Return type:

bool
checkSymmetricTensor(name, verbose=True)

Tests a coefficient for symmetry.

Parameters:
  • name (str) – name of the coefficient
  • verbose (bool) – if set to True or not present a report on coefficients which break the symmetry is printed.
Returns:

True if coefficient name is symmetric
Return type:

bool
checkSymmetry(verbose=True)

Tests the PDE for symmetry.

Parameters:verbose (bool) – if set to True or not present a report on coefficients which break the symmetry is printed.
Returns:True if the PDE is symmetric
Return type:bool
Note:This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
createCoefficient(name)

Creates a Data object corresponding to coefficient name.

Returns:the coefficient name initialized to 0
Return type:Data
Raises:IllegalCoefficient – if name is not a coefficient of the PDE
createOperator()

Returns an instance of a new operator.

createRightHandSide()

Returns an instance of a new right hand side.

createSolution()

Returns an instance of a new solution.

getCoefficient(name)

Returns the value of the coefficient name.

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

Returns the operator in its current state.

getCurrentRightHandSide()

Returns the right hand side in its current state.

getCurrentSolution()

Returns the solution in its current state.

getDim()

Returns the spatial dimension of the PDE.

Returns:the spatial dimension of the PDE domain
Return type:int
getDomain()

Returns the domain of the PDE.

Returns:the domain of the PDE
Return type:Domain
getDomainStatus()

Return the status indicator of the domain

getFlux(u=None)

Returns the flux J for a given u.

J[i,j]=(A[i,j,k,l]+A_reduced[A[i,j,k,l]]*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])u[k]-X[i,j]-X_reduced[i,j]

or

J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]

Parameters:u (Data or None) – argument in the flux. If u is not present or equals None the current solution is used.
Returns:flux
Return type:Data
getFunctionSpaceForCoefficient(name)

Returns the FunctionSpace to be used for coefficient name.

Parameters:name (string) – name of the coefficient enquired
Returns:the function space to be used for coefficient name
Return type:FunctionSpace
Raises:IllegalCoefficient – if name is not a coefficient of the PDE
getFunctionSpaceForEquation()

Returns the FunctionSpace used to discretize the equation.

Returns:representation space of equation
Return type:FunctionSpace
getFunctionSpaceForSolution()

Returns the FunctionSpace used to represent the solution.

Returns:representation space of solution
Return type:FunctionSpace
getNumEquations()

Returns the number of equations.

Returns:the number of equations
Return type:int
Raises:UndefinedPDEError – if the number of equations is not specified yet
getNumSolutions()

Returns the number of unknowns.

Returns:the number of unknowns
Return type:int
Raises:UndefinedPDEError – if the number of unknowns is not specified yet
getOperator()

Returns the operator of the linear problem.

Returns:the operator of the problem
getOperatorType()

Returns the current system type.

getRequiredOperatorType()

Returns the system type which needs to be used by the current set up.

getResidual(u=None)

Returns the residual of u or the current solution if u is not present.

Parameters:u (Data or None) – argument in the residual calculation. It must be representable in self.getFunctionSpaceForSolution(). If u is not present or equals None the current solution is used.
Returns:residual of u
Return type:Data
getRightHandSide()

Returns the right hand side of the linear problem.

Returns:the right hand side of the problem
Return type:Data
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()

Returns the solution of the PDE.

Returns:the solution
Return type:Data
getSolverOptions()

Returns the solver options

Return type:SolverOptions
getSystem()

Returns the operator and right hand side of the PDE.

Returns:the discrete version of the PDE
Return type:tuple of Operator and Data
getSystemStatus()

Return the domain status used to build the current system

hasCoefficient(name)

Returns True if name is the name of a coefficient.

Parameters:name (string) – name of the coefficient enquired
Returns:True if name is the name of a coefficient of the general PDE, False otherwise
Return type:bool
initializeSystem()

Resets the system clearing the operator, right hand side and solution.

insertConstraint(rhs_only=False)

Applies the constraints defined by q and r to the PDE.

Parameters:rhs_only (bool) – if True only the right hand side is altered by the constraint
introduceCoefficients(**coeff)

Introduces new coefficients into the problem.

Use:

p.introduceCoefficients(A=PDECoef(…), B=PDECoef(…))

to introduce the coefficients A and B.

invalidateOperator()

Indicates the operator has to be rebuilt next time it is used.

invalidateRightHandSide()

Indicates the right hand side has to be rebuilt next time it is used.

invalidateSolution()

Indicates the PDE has to be resolved if the solution is requested.

invalidateSystem()

Announces that everything has to be rebuilt.

isComplex()

Returns true if this is a complex-valued LinearProblem, false if real-valued.

Return type:bool
isHermitian()

Checks if the pde is indicated to be Hermitian.

Returns:True if a Hermitian PDE is indicated, False otherwise
Return type:bool
Note:the method is equivalent to use getSolverOptions().isHermitian()
isOperatorValid()

Returns True if the operator is still valid.

isRightHandSideValid()

Returns True if the operator is still valid.

isSolutionValid()

Returns True if the solution is still valid.

isSymmetric()

Checks if symmetry is indicated.

Returns:True if a symmetric PDE is indicated, False otherwise
Return type:bool
Note:the method is equivalent to use getSolverOptions().isSymmetric()
isSystemValid()

Returns True if the system (including solution) is still vaild.

isUsingLumping()

Checks if matrix lumping is the current solver method.

Returns:True if the current solver method is lumping
Return type:bool
preservePreconditioner(preserve=True)

Notifies the PDE that the preconditioner should not be reset when making changes to the operator.

Building the preconditioner data can be quite expensive (e.g. for multigrid methods) so if it is known that changes to the operator are going to be minor calling this method can speed up successive PDE solves.

Note:Not all operator types support this.
Parameters:preserve (bool) – if True, preconditioner will be preserved, otherwise it will be reset when making changes to the operator, which is the default behaviour.
reduceEquationOrder()

Returns the status of order reduction for the equation.

Returns:True if reduced interpolation order is used for the representation of the equation, False otherwise
Return type:bool
reduceSolutionOrder()

Returns the status of order reduction for the solution.

Returns:True if reduced interpolation order is used for the representation of the solution, False otherwise
Return type:bool
resetAllCoefficients()

Resets all coefficients to their default values.

resetOperator()

Makes sure that the operator is instantiated and returns it initialized with zeros.

resetRightHandSide()

Sets the right hand side to zero.

resetRightHandSideCoefficients()

Resets all coefficients defining the right hand side

resetSolution()

Sets the solution to zero.

setDebug(flag)

Switches debug output on if flag is True otherwise it is switched off.

Parameters:flag (bool) – desired debug status
setDebugOff()

Switches debug output off.

setDebugOn()

Switches debug output on.

setHermitian(flag=False)

Sets the Hermitian flag to flag.

Parameters:flag (bool) – If True, the Hermitian flag is set otherwise reset.
Note:The method overwrites the Hermitian flag set by the solver options
setHermitianOff()

Clears the Hermitian flag. :note: The method overwrites the Hermitian flag set by the solver options

setHermitianOn()

Sets the Hermitian flag. :note: The method overwrites the Hermitian flag set by the solver options

setReducedOrderForEquationOff()

Switches reduced order off for equation representation.

Raises:RuntimeError – if order reduction is altered after a coefficient has been set
setReducedOrderForEquationOn()

Switches reduced order on for equation representation.

Raises:RuntimeError – if order reduction is altered after a coefficient has been set
setReducedOrderForEquationTo(flag=False)

Sets order reduction state for equation representation according to flag.

Parameters:flag (bool) – if flag is True, the order reduction is switched on for equation representation, otherwise or if flag is not present order reduction is switched off
Raises:RuntimeError – if order reduction is altered after a coefficient has been set
setReducedOrderForSolutionOff()

Switches reduced order off for solution representation

Raises:RuntimeError – if order reduction is altered after a coefficient has been set.
setReducedOrderForSolutionOn()

Switches reduced order on for solution representation.

Raises:RuntimeError – if order reduction is altered after a coefficient has been set
setReducedOrderForSolutionTo(flag=False)

Sets order reduction state for solution representation according to flag.

Parameters:flag (bool) – if flag is True, the order reduction is switched on for solution representation, otherwise or if flag is not present order reduction is switched off
Raises:RuntimeError – if order reduction is altered after a coefficient has been set
setReducedOrderOff()

Switches reduced order off for solution and equation representation

Raises:RuntimeError – if order reduction is altered after a coefficient has been set
setReducedOrderOn()

Switches reduced order on for solution and equation representation.

Raises:RuntimeError – if order reduction is altered after a coefficient has been set
setReducedOrderTo(flag=False)

Sets order reduction state for both solution and equation representation according to flag.

Parameters:flag (bool) – if True, the order reduction is switched on for both solution and equation representation, otherwise or if flag is not present order reduction is switched off
Raises:RuntimeError – if order reduction is altered after a coefficient has been set
setSolution(u, validate=True)

Sets the solution assuming that makes the system valid with the tolrance defined by the solver options

setSolverOptions(options=None)

Sets the solver options.

Parameters:options (SolverOptions or None) – the new solver options. If equal None, the solver options are set to the default.
Note:The symmetry flag of options is overwritten by the symmetry flag of the LinearProblem.
setSymmetry(flag=False)

Sets the symmetry flag to flag.

Parameters:flag (bool) – If True, the symmetry flag is set otherwise reset.
Note:The method overwrites the symmetry flag set by the solver options
setSymmetryOff()

Clears the symmetry flag. :note: The method overwrites the symmetry flag set by the solver options

setSymmetryOn()

Sets the symmetry flag. :note: The method overwrites the symmetry flag set by the solver options

setSystemStatus(status=None)

Sets the system status to status if status is not present the current status of the domain is used.

setValue(**coefficients)

Sets new values to coefficients.

Parameters:
Raises:

IllegalCoefficient – if an unknown coefficient keyword is used
shouldPreservePreconditioner()

Returns true if the preconditioner / factorisation should be kept even when resetting the operator.

Return type:bool
trace(text)

Prints the text message if debug mode is switched on.

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

Marks the operator as valid.

validRightHandSide()

Marks the right hand side as valid.

validSolution()

Marks the solution as valid.

class esys.downunder.apps.Locator(where, x=array([0., 0., 0.]))

Bases: object

Locator provides access to the values of data objects at a given spatial coordinate x.

In fact, a Locator object finds the sample in the set of samples of a given function space or domain which is closest to the given point x.

__init__(where, x=array([0., 0., 0.]))

Initializes a Locator to access values in Data objects on the Doamin or FunctionSpace for the sample point which is closest to the given point x.

Parameters:
  • where (escript.FunctionSpace) – function space
  • x (numpy.ndarray or list of numpy.ndarray) – location(s) of the Locator
getFunctionSpace()

Returns the function space of the Locator.

getId(item=None)

Returns the identifier of the location.

getValue(data)

Returns the value of data at the Locator if data is a Data object otherwise the object is returned.

getX()

Returns the exact coordinates of the Locator.

setValue(data, v)

Sets the value of the data at the Locator.

class esys.downunder.apps.MT2DTEModel(domain, fixBottom=False, useFastSolver=False, mu=1.2566370614359173e-06)

Bases: object

This class is a simple wrapper for 2D MT PDE model in the TE mode. MT

curl ((1/sigma) curl H) + i omega H = 0 curl ((1/mu) curl E) + i omega sigma E = 0
2D reduces to
-div (1/mu grad u) + i omega sigma u = 0
where
u = Ex is transverse component of electric field mu is magnetic permeability sigma is electrical conductivity omega is angular frequency i = sqrt(-1)

Domain typically includes air and ground layers. Conductivity sigma = 0 in the air layer.

Boundary conditions included in the class are
  • Ex is set to one at the top of the domain, typically at the top of an air layer.
  • At the bottom of the domain Ex=0 (set `fixBottom`=True) or radiation condition dEx/dn+k*Ex=0 with k^2=2*pi*f*mu*sigma is set
It has a function to set ground property
  • setConductivity
and functions to output solutions
  • getImpedance
  • getApparentResitivity
  • getPhase.
__init__(domain, fixBottom=False, useFastSolver=False, mu=1.2566370614359173e-06)
Parameters:
  • domain (Domain) – the domain
  • fixBottom (bool) – if true the electric field at the bottom is set to zero. Otherwise radiation condition is set.
  • useFastSolver (bool) – use multigrid solver. (not supported yet)
getApparentResitivity(f, Zxy)

return the apparent resistivity from a given frequency f and impedance Zxy

Parameters:
  • f (float) – frequency in [Hz]
  • Zxy (Data or np.array) – impedance
getImpedance(f=1.0)

return the impedance Zxy for frequency f in [Hz]. The electric field and magnetic field cane be accessed as attributes Ex and Hy after completion.

Parameters:f (float) – frequency in [Hz]
Returns:Zxy
getPhase(f, Zxy)

return the phase in [deg] from a given frequency f and impedance Zxy

Parameters:
  • f (float) – frequency in [Hz]
  • Zxy (Data or np.array) – impedance
setConductivity(sigma, sigma_boundary=None)

sets the conductivity sigma.

Parameters:
  • sigma (Data or float) – conductivity distribution.
  • sigma_boundary – conductivity distribution on bottom boundary. Only required if fixBottom is not set and sigma cannot be interpolated to boundary.
class esys.downunder.apps.MT2DTMModel(domain, fixBottom=False, airLayer=None, useFastSolver=False, mu=1.2566370614359173e-06)

Bases: object

This a class for solving the 2D MT model in the TM mode. MT

curl ((1/sigma)curl H) + i omega H = 0 curl ((1/mu)curl E) + i omega sigma E = 0
2D
-div (1/sigma grad u) + i omega mu u = 0
where
u = Hx is transverse component of magnetic field mu is magnetic permeability sigma is electrical conductivity omega is angular frequency i = sqrt(-1)

Hx is set to one in the air layer and the interface of the air layer and the subsurface. At the bottom of the domain Ex=0 (set `fixBottom`=True)

or radiation condition dEx/dn+k*Ex=0 with k^2=2*pi*f*mu*sigma is set.
__init__(domain, fixBottom=False, airLayer=None, useFastSolver=False, mu=1.2566370614359173e-06)
Parameters:
  • domain (Domain) – the domain
  • fixBottom (bool) – if true the potential at all faces except the top is set to zero. Otherwise on the the bottom is set to zero.
  • airLayer (None, float, Data) –

    defines the air layer including the interface between air layer and subsurface. If set to None then just the (plane) top surface is used. If set to a float then the region above airlayer (including the interface)

    is defined as air layer.
    Otherwise airlayer needs to be defined as Data with value 1 marking
    the air layer and its interface.
  • useFastSolver (bool) – use multigrid solver. This may fail.
Note:

the attribute airLayer gives the mask for the air layer including the interface between the air layer and the subsurface.
getApparentResitivity(f, Zyx)

return the apparent resistivity from a given frequency f and impedance Zyx

Parameters:
  • f (float) – frequency in Hz
  • Zyx (Data or np.array) – impedance
getImpedance(f=1.0)

return the impedance Zyx and the electric field Ex for frequency f

Parameters:f (float) – frequency in [Hz]
Returns:Zyx
getPhase(f, Zyx)

return the phase in [deg] from a given frequency f [Hz] and impedance Zyx

Parameters:
  • f (float) – frequency in Hz
  • Zyx (Data or np.array) – impedance
setResistivity(rho, rho_boundary=None)

sets the resistivity. :param rho: resistivity distribution. :type rho: Data :param rho_boundary: rho distribution on bottom boundary. Only required if fixBottom is set and

rho cannot be interpolated to boundary.
class esys.downunder.apps.MagneticModel2D(domain, fixVert=False, fixBase=False)

Bases: object

This class is a simple wrapper for a 2D magnetic PDE model. It solves PDE

  • div (grad u) = -div(k Bh)
where
k is magnetic susceptibility and Bh is background magnetic field. u is computed anomaly potential
Possible boundary conditions are Dirichlet on
  • one corner (bottom left),
  • vertical sides, or
  • base.

Requires domain and possibly boundary condition choice.

Default boundary conditions
  • fix the left bottom corner.
Otherwise add
  • fixVert = True (for all vertical surfaces fixed) or
  • fixBase = True (for base fixed).
It has functions
  • setSusceptibility
  • getSusceptibility
  • setBackgroundMagneticField
  • getAnomalyPotential
  • getMagneticFieldAnomaly.
__init__(domain, fixVert=False, fixBase=False)

Initialise the class with domain and boundary conditions. Setup PDE, susceptibility and background magnetic field. : param domain: the domain : type domain: Domain : param fixBase: if true the magnetic field at the bottom is set to zero. : type fixBase: bool : param fixVert: if true the magnetic field on all vertical sudes is set to zero. : type fixVert: bool : if fixBase and fixVert are False then magnetic field is set to zero at bottom, front, left corner.

getAnomalyPotential()

get the potential of the the magnetic anomaly

getMagneticFieldAnomaly()

get the total Magnetic field

getSusceptibility()

returns susceptibility : returns: k

setBackgroundMagneticField(Bh=[0.0, 45000.0])

sets background magnetic field in nT

setSusceptibility(k=0)

set susceptibility : param k: susceptibility : type k: Data or float

class esys.downunder.apps.MagneticModel3D(domain, fixVert=False, fixBase=False)

Bases: object

This class is a simple wrapper for a 3D magnetic forward model. It solves PDE

  • div (grad u) = -div(k Bh)
where
k is magnetic susceptibility and Bh is background magnetic field.
Possible boundary conditions are Dirichlet on
  • one corner (bottom left),
  • vertical sides, or
  • base.

Input is domain and boundary condition choice. Default boundary conditions fix the left front bottom corner. Otherwise add

  • fixVert = True or
  • fixBase = True.
It has functions
  • setSusceptibility
  • getSusceptibility
  • setBackgroundMagneticField
  • getAnomalyPotential
  • getMagneticFieldAnomaly.
__init__(domain, fixVert=False, fixBase=False)

Initialise the class with domain and boundary conditions. Setup PDE, susceptibility and background magnetic field. :param domain: the domain :type domain: Domain :param fixBase: if true the magnetic field at the bottom is set to zero. . :type fixBottom: bool :param fixVert: if true the magnetic field on all vertical sudes is set to zero. :type fixBottom: bool :if fixBottom and fixBase are False then magnetic field is set to zero at bottom, front, left corner.

getAnomalyPotential()

get the potential of the the magnetic anomaly

getMagneticFieldAnomaly()

get the total Magnetic field

getSusceptibility()

returns the susceptibility : returns: k

setBackgroundMagneticField(Bh=[0.0, 45000.0, 0.0])

sets background magnetic field in nT

setSusceptibility(k=0)

sets susceptibility : param k: susceptibility : type k: Data or float

class esys.downunder.apps.NonlinearPDE(domain, u, debug=0)

Bases: object

This class is used to define a general nonlinear, steady, second order PDE for an unknown function u on a given domain defined through a Domain object.

For a single PDE having a solution with a single component the nonlinear PDE is defined in the following form:

-div(X) + Y = 0

where X,*Y*=f(u,*grad(u)*). div(F) denotes the divergence of F and grad(F) is the spatial derivative of F.

The coefficients X (rank 1) and Y (scalar) have to be specified through Symbol objects.

The following natural boundary conditions are considered:

n[j]*X[j] + y = 0

where n is the outer normal field. Notice that the coefficient X is defined in the PDE. The coefficient y is a scalar Symbol.

Constraints for the solution prescribe the value of the solution at certain locations in the domain. They have the form

u=r where q>0

r and q are each scalar where q is the characteristic function defining where the constraint is applied. The constraints override any other condition set by the PDE or the boundary condition.

For a system of PDEs and a solution with several components, u is rank one, while the PDE coefficient X is rank two and y 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 – 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:
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.downunder.apps.Operator

Bases: Boost.Python.instance

__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.downunder.apps.PMLCondition(sigma0=1.0, Lleft=[None, None, None], Lright=[None, None, None], m=3)

Bases: object

this defines the PML weights over a domain :Lleft: thicknesses of PML to the left, bottom, front (None -> no PML) :Lright: thicknesses of PML to the right, top, back (None -> no PML) :return: return a mask where PML is applied.

__init__(sigma0=1.0, Lleft=[None, None, None], Lright=[None, None, None], m=3)

initializes the PML pml_condition

Parameters:
  • sigma0 (Data) – maximum PML damping
  • Lleft (list of floats, length is domain dimension) – thicknesses of PML to the left, bottom, front (None -> no PML)
  • Lright (list of floats, length is domain dimension) – thicknesses of PML to the right, top, back (None -> no PML)
  • m (int or float) – exponent of increase over PML layer (default 3 )
getPMLMask(domain)

returns the mask for PML layer

getPMLWeights(domain, omega)

this defines the PML weights over a domain :return: weighting alphas, J=product of alphas and J/alpha

class esys.downunder.apps.Reducer

Bases: Boost.Python.instance

__init__()

Raises an exception This class cannot be instantiated from Python

class esys.downunder.apps.SolverBuddy

Bases: Boost.Python.instance

__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.
getPackage((SolverBuddy)arg1) → SolverOptions :

Returns the solver package key

Return type:in the list DEFAULT, PASO, CUSP, MKL, UMFPACK, MUMPS, TRILINOS
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.
setPackage((SolverBuddy)arg1, (int)package) → None :

Sets the solver package to be used as a solver.

Parameters:package (in DEFAULT, PASO, CUSP, MKL, UMFPACK, MUMPS, TRILINOS) – key of the solver package to be used.
Note:Not all packages are support on all implementation. An exception may be thrown on some platforms if a particular package is requested.
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.downunder.apps.SolverOptions

Bases: Boost.Python.enum

__init__()

Initialize self. See help(type(self)) for accurate signature.

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
PASO = esys.escriptcore.escriptcpp.SolverOptions.PASO
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
TRILINOS = esys.escriptcore.escriptcpp.SolverOptions.TRILINOS
UMFPACK = esys.escriptcore.escriptcpp.SolverOptions.UMFPACK
bit_length()

Number of bits necessary to represent self in binary.

>>> bin(37)
'0b100101'
>>> (37).bit_length()
6
conjugate()

Returns self, the complex conjugate of any int.

denominator

the denominator of a rational number in lowest terms

from_bytes()

Return the integer represented by the given array of bytes.

bytes
Holds the array of bytes to convert. The argument must either support the buffer protocol or be an iterable object producing bytes. Bytes and bytearray are examples of built-in objects that support the buffer protocol.
byteorder
The byte order used to represent the integer. If byteorder is ‘big’, the most significant byte is at the beginning of the byte array. If byteorder is ‘little’, the most significant byte is at the end of the byte array. To request the native byte order of the host system, use `sys.byteorder’ as the byte order value.
signed
Indicates whether two’s complement is used to represent the integer.
imag

the imaginary part of a complex number

name
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, 'PASO': esys.escriptcore.escriptcpp.SolverOptions.PASO, '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, 'TRILINOS': esys.escriptcore.escriptcpp.SolverOptions.TRILINOS, 'UMFPACK': esys.escriptcore.escriptcpp.SolverOptions.UMFPACK}
numerator

the numerator of a rational number in lowest terms

real

the real part of a complex number

to_bytes()

Return an array of bytes representing an integer.

length
Length of bytes object to use. An OverflowError is raised if the integer is not representable with the given number of bytes.
byteorder
The byte order used to represent the integer. If byteorder is ‘big’, the most significant byte is at the beginning of the byte array. If byteorder is ‘little’, the most significant byte is at the end of the byte array. To request the native byte order of the host system, use `sys.byteorder’ as the byte order value.
signed
Determines whether two’s complement is used to represent the integer. If signed is False and a negative integer is given, an OverflowError is raised.
values = {0: esys.escriptcore.escriptcpp.SolverOptions.DEFAULT, 3: esys.escriptcore.escriptcpp.SolverOptions.MKL, 4: esys.escriptcore.escriptcpp.SolverOptions.PASO, 5: esys.escriptcore.escriptcpp.SolverOptions.TRILINOS, 6: esys.escriptcore.escriptcpp.SolverOptions.UMFPACK, 7: esys.escriptcore.escriptcpp.SolverOptions.MUMPS, 8: esys.escriptcore.escriptcpp.SolverOptions.BICGSTAB, 9: esys.escriptcore.escriptcpp.SolverOptions.CGLS, 10: esys.escriptcore.escriptcpp.SolverOptions.CGS, 11: esys.escriptcore.escriptcpp.SolverOptions.CHOLEVSKY, 12: esys.escriptcore.escriptcpp.SolverOptions.CR, 13: esys.escriptcore.escriptcpp.SolverOptions.DIRECT, 14: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_MUMPS, 15: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_PARDISO, 16: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_SUPERLU, 17: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_TRILINOS, 18: esys.escriptcore.escriptcpp.SolverOptions.GMRES, 19: esys.escriptcore.escriptcpp.SolverOptions.HRZ_LUMPING, 20: esys.escriptcore.escriptcpp.SolverOptions.ITERATIVE, 21: esys.escriptcore.escriptcpp.SolverOptions.LSQR, 22: esys.escriptcore.escriptcpp.SolverOptions.MINRES, 23: esys.escriptcore.escriptcpp.SolverOptions.NONLINEAR_GMRES, 24: esys.escriptcore.escriptcpp.SolverOptions.PCG, 25: esys.escriptcore.escriptcpp.SolverOptions.PRES20, 26: esys.escriptcore.escriptcpp.SolverOptions.ROWSUM_LUMPING, 27: esys.escriptcore.escriptcpp.SolverOptions.TFQMR, 28: esys.escriptcore.escriptcpp.SolverOptions.AMG, 29: esys.escriptcore.escriptcpp.SolverOptions.GAUSS_SEIDEL, 30: esys.escriptcore.escriptcpp.SolverOptions.ILU0, 31: esys.escriptcore.escriptcpp.SolverOptions.ILUT, 32: esys.escriptcore.escriptcpp.SolverOptions.JACOBI, 33: esys.escriptcore.escriptcpp.SolverOptions.NO_PRECONDITIONER, 34: esys.escriptcore.escriptcpp.SolverOptions.REC_ILU, 35: esys.escriptcore.escriptcpp.SolverOptions.RILU, 36: esys.escriptcore.escriptcpp.SolverOptions.BACKWARD_EULER, 37: esys.escriptcore.escriptcpp.SolverOptions.CRANK_NICOLSON, 38: esys.escriptcore.escriptcpp.SolverOptions.LINEAR_CRANK_NICOLSON, 39: esys.escriptcore.escriptcpp.SolverOptions.CLASSIC_INTERPOLATION, 40: esys.escriptcore.escriptcpp.SolverOptions.CLASSIC_INTERPOLATION_WITH_FF_COUPLING, 41: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_INTERPOLATION, 42: esys.escriptcore.escriptcpp.SolverOptions.DEFAULT_REORDERING, 43: esys.escriptcore.escriptcpp.SolverOptions.MINIMUM_FILL_IN, 44: esys.escriptcore.escriptcpp.SolverOptions.NESTED_DISSECTION, 45: esys.escriptcore.escriptcpp.SolverOptions.NO_REORDERING}
class esys.downunder.apps.SonicWaveInFrequencyDomain(domain, pml_condition=None, frequency=None, vp=None, fix_boundary=True)

Bases: object

This class is a simple wrapper for the solution of the 2D or 3D sonic wave equtaion in the frequency domain. It solves complex PDE

div (grad p) - k^2 p = Q
where
k = omega/c Q = source term : Dirac function
Boundary conditions implemented are NEED TO SET PML CONDITION FIRST
  • perfectly matched layer : see class PMLCondition
  • fixed BC - all but the top surface
It has functions
  • getDomain
  • setFrequency
  • setVp
Output solution
  • getWave
__init__(domain, pml_condition=None, frequency=None, vp=None, fix_boundary=True)

Initialise the class with domain, boundary conditions and frequency. Setup PDE :param domain: the domain : setup with Dirac points :type domain: Domain :param pml_condition: :type pml_condition: :param frequency: :type frequency: :param vp: velocity field :type vp: Data :param fix_boundary: if true fix all the boundaries except the top :type fix_boundary: bool

getDomain()

returns the domain

getWave(source)

solve the PDE

setFrequency(frequency)

sets the frequency

setVp(vp)

sets the velocity for the rock

class esys.downunder.apps.SplitWorld(count)

Bases: object

Wrapper for the C++ class exposed as __SplitWorld. This is a namespace consideration, it allows us to make boost::python::raw_functions into members of a class.

__init__(count)
Variables:count – How many equally sized subworlds should our compute resources be partitioned into?
addJob(jobctr, *vec, **kwargs)

Submit a job to be run later on an available subworld.

Variables:jobctr – class or function to be called to create a job

The remaining parameters are for the arguments of the function.

addJobPerWorld(jobctr, *vec, **kwargs)

Submit one job per subworld to run later.

Variables:jobctr – class or function to be called to create a job

The remaining parameters are for the arguments of the function.

addVariable(vname, vartype, *vec, **kwargs)

Create a variable on all subworlds.

Variables:vartype – the type of variable to be created

The remaining parameters are for optional arguments depending on the variable type.

buildDomains(fn, *vec, **kwargs)

Instruct subworlds how to build the domain.

Variables:fn – The function/class to call to create a domain.

The remaining parameters are for the arguments of the function.

clearVariable(vname)

Clears the value of the named variable. The variable itself still exists.

Variables:vname – variable to clear
copyVariable(src, dest)

copy the contents of one splitworld variable into another

Variables:
  • src – name of variable to copy from
  • dest – name of variable to copy to
getFloatVariable(vname)

Return the value of a floating point variable

getLocalObjectVariable(vname)

Return the value of a local object variable - that is, an object (eg tuple) which does not need to be reduced/shared between worlds

getSubWorldCount()

Return the number of subworlds in this splitworld

getSubWorldID()

Return the id of the subworld which _this_ MPI process belongs to.

getVarInfo()

Returns the names of all declared variables and a description of type. The details of the output are not fixed and may change without notice

getVarList()

Returns the names of all declared variables and a boolean for each indicating whether they have values.

removeVariable(vname)

Removes the named variable from all subworlds.

Variables:vname – What to remove
runJobs()

Executes pending jobs.

class esys.downunder.apps.SubWorld

Bases: Boost.Python.instance

Information about a group of workers.

__init__()

Raises an exception This class cannot be instantiated from Python

class esys.downunder.apps.Symbol(*args, **kwargs)

Bases: object

Symbol objects are placeholders for a single mathematical symbol, such as ‘x’, or for arbitrarily complex mathematical expressions such as ‘c*x**4+alpha*exp(x)-2*sin(beta*x)’, where ‘alpha’, ‘beta’, ‘c’, and ‘x’ are also Symbols (the symbolic ‘atoms’ of the expression).

With the help of the ‘Evaluator’ class these symbols and expressions can be resolved by substituting numeric values and/or escript Data objects for the atoms. To facilitate the use of Data objects a Symbol has a shape (and thus a rank) as well as a dimension (see constructor). Symbols are useful to perform mathematical simplifications, compute derivatives and as coefficients for nonlinear PDEs which can be solved by the NonlinearPDE class.

__init__(*args, **kwargs)

Initialises a new Symbol object in one of three ways:

u=Symbol('u')

returns a scalar symbol by the name ‘u’.

alpha=Symbol(‘alpha’, (4,3))

returns a rank 2 symbol with the shape (4,3), whose elements are named ‘[alpha]_i_j’ (with i=0..3, j=0..2).

a,b,c=symbols(‘a,b,c’) x=Symbol([[a+b,0,0],[0,b-c,0],[0,0,c-a]])

returns a rank 2 symbol with the shape (3,3) whose elements are explicitly specified by numeric values and other symbols/expressions within a list or numpy array.

The dimensionality of the symbol can be specified through the dim keyword. All other keywords are passed to the underlying symbolic library (currently sympy).

Parameters:
  • args – initialisation arguments as described above
  • dim (int) – dimensionality of the new Symbol (default: 2)
applyfunc(f, on_type=None)

Applies the function f to all elements (if on_type is None) or to all elements of type on_type.

atoms(*types)

Returns the atoms that form the current Symbol.

By default, only objects that are truly atomic and cannot be divided into smaller pieces are returned: symbols, numbers, and number symbols like I and pi. It is possible to request atoms of any type, however.

Note that if this symbol contains components such as [x]_i_j then only their main symbol ‘x’ is returned.

Parameters:types – types to restrict result to
Returns:list of atoms of specified type
Return type:set
coeff(x, expand=True)

Returns the coefficient of the term “x” or 0 if there is no “x”.

If “x” is a scalar symbol then “x” is searched in all components of this symbol. Otherwise the shapes must match and the coefficients are checked component by component.

Example:

x=Symbol('x', (2,2))
y=3*x
print y.coeff(x)
print y.coeff(x[1,1])

will print:

[[3 3]
 [3 3]]

[[0 0]
 [0 3]]
Parameters:x (Symbol, numpy.ndarray, list) – the term whose coefficients are to be found
Returns:the coefficient(s) of the term
Return type:Symbol
diff(*symbols, **assumptions)
evalf()

Applies the sympy.evalf operation on all elements in this symbol

expand()

Applies the sympy.expand operation on all elements in this symbol

getDataSubstitutions()

Returns a dictionary of symbol names and the escript Data objects they represent within this Symbol.

Returns:the dictionary of substituted Data objects
Return type:dict
getDim()

Returns the spatial dimensionality of this symbol.

Returns:the symbol’s spatial dimensionality, or -1 if undefined
Return type:int
getRank()

Returns the rank of this symbol.

Returns:the symbol’s rank which is equal to the length of the shape.
Return type:int
getShape()

Returns the shape of this symbol.

Returns:the symbol’s shape
Return type:tuple of int
grad(where=None)

Returns a symbol which represents the gradient of this symbol. :type where: Symbol, FunctionSpace

inverse()
is_Add = False
is_Float = False
item(*args)

Returns an element of this symbol. This method behaves like the item() method of numpy.ndarray. If this is a scalar Symbol, no arguments are allowed and the only element in this Symbol is returned. Otherwise, ‘args’ specifies a flat or nd-index and the element at that index is returned.

Parameters:args – index of item to be returned
Returns:the requested element
Return type:sympy.Symbol, int, or float
lambdarepr()
simplify()

Applies the sympy.simplify operation on all elements in this symbol

subs(old, new)

Substitutes an expression.

swap_axes(axis0, axis1)
tensorProduct(other, axis_offset)
tensorTransposedProduct(other, axis_offset)
trace(axis_offset)

Returns the trace of this Symbol.

transpose(axis_offset)

Returns the transpose of this Symbol.

transposedTensorProduct(other, axis_offset)
class esys.downunder.apps.TestDomain

Bases: esys.escriptcore.escriptcpp.Domain

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

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
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
isValidTagName((Domain)arg1, (str)name) → bool :
Returns:True is name corresponds to a tag
Return type:bool
onMasterProcessor((Domain)arg1) → bool :
Returns:True if this code is executing on the master process
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.downunder.apps.TransportProblem

Bases: Boost.Python.instance

__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) –

Functions

esys.downunder.apps.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.downunder.apps.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.downunder.apps.ComplexData((object)value[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa053554450>[, (bool)expanded=False]]) → Data
esys.downunder.apps.ComplexScalar([(object)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa05352adb0>[, (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.downunder.apps.ComplexTensor([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa053554030>[, (bool)expanded=False]]]) → Data :

Construct a Data object containing rank2 data-points.

param value:scalar value for all points
rtype:Data
type value:float
param what:FunctionSpace for Data
type what:FunctionSpace
param expanded:If True, a value is stored for each point. If False, more efficient representations may be used
type expanded:bool

ComplexTensor( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa0535540f0> [, (bool)expanded=False]]) -> Data

esys.downunder.apps.ComplexTensor3([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa0535541b0>[, (bool)expanded=False]]]) → Data :

Construct a Data object containing rank3 data-points.

param value:scalar value for all points
rtype:Data
type value:float
param what:FunctionSpace for Data
type what:FunctionSpace
param expanded:If True, a value is stored for each point. If False, more efficient representations may be used
type expanded:bool

ComplexTensor3( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa0535542d0> [, (bool)expanded=False]]) -> Data

esys.downunder.apps.ComplexTensor4([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa053554330>[, (bool)expanded=False]]]) → Data :

Construct a Data object containing rank4 data-points.

param value:scalar value for all points
rtype:Data
type value:float
param what:FunctionSpace for Data
type what:FunctionSpace
param expanded:If True, a value is stored for each point. If False, more efficient representations may be used
type expanded:bool

ComplexTensor4( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa0535543f0> [, (bool)expanded=False]]) -> Data

esys.downunder.apps.ComplexVector([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa05352ae70>[, (bool)expanded=False]]]) → Data :

Construct a Data object containing rank1 data-points.

param value:scalar value for all points
rtype:Data
type value:float
param what:FunctionSpace for Data
type what:FunctionSpace
param expanded:If True, a value is stored for each point. If False, more efficient representations may be used
type expanded:bool

ComplexVector( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa05352af30> [, (bool)expanded=False]]) -> Data

esys.downunder.apps.ContinuousFunction((Domain)domain) → FunctionSpace :
Returns:a continuous FunctionSpace (overlapped node values)
Return type:FunctionSpace
esys.downunder.apps.DiracDeltaFunctions((Domain)domain) → FunctionSpace :
Return type:FunctionSpace
esys.downunder.apps.Function((Domain)domain) → FunctionSpace :
Returns:a function FunctionSpace
Return type:FunctionSpace
esys.downunder.apps.FunctionOnBoundary((Domain)domain) → FunctionSpace :
Returns:a function on boundary FunctionSpace
Return type:FunctionSpace
esys.downunder.apps.FunctionOnContactOne((Domain)domain) → FunctionSpace :
Returns:Return a FunctionSpace on right side of contact
Return type:FunctionSpace
esys.downunder.apps.FunctionOnContactZero((Domain)domain) → FunctionSpace :
Returns:Return a FunctionSpace on left side of contact
Return type:FunctionSpace
esys.downunder.apps.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.downunder.apps.LinearSinglePDE(domain, isComplex=False, debug=False)

Defines a single linear PDE.

Parameters:
  • domain (Domain) – domain of the PDE
  • isComplex (boolean) – if true, this coefficient is part of a complex-valued PDE and values will be converted to complex.
  • debug – if True debug information is printed
Return type:

LinearPDE
esys.downunder.apps.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.downunder.apps.MPIBarrierWorld() → None :

Wait until all MPI processes have reached this point.

esys.downunder.apps.NcFType((str)filename) → str :

Return a character indicating what netcdf format a file uses. c or C indicates netCDF3. 4 indicates netCDF4. u indicates unsupported format (eg netCDF4 file in an escript build which does not support it ? indicates unknown.

esys.downunder.apps.NumpyToData(array, isComplex, functionspace)

Uses a numpy ndarray to create a Data object

Example usage: NewDataObject = NumpyToData(ndarray, isComplex, FunctionSpace)

esys.downunder.apps.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.downunder.apps.ReadMesh(filename, integrationOrder=-1, reducedIntegrationOrder=-1, optimize=True, **kwargs)
__ReadMesh_driver( (list)params) -> Domain :

Read a mesh from a file. For MPI parallel runs fan out the mesh to multiple processes.

rtype:Domain
param fileName:
type fileName:string
param integrationOrder:
 order of the quadrature scheme. If integrationOrder<0 the integration order is selected independently.
type integrationOrder:
 int
param reducedIntegrationOrder:
 order of the quadrature scheme. If reducedIntegrationOrder<0 the integration order is selected independently.
param optimize:Enable optimisation of node labels
type optimize:bool
esys.downunder.apps.ReducedContinuousFunction((Domain)domain) → FunctionSpace :
Returns:a continuous with reduced order FunctionSpace (overlapped node values on reduced element order)
Return type:FunctionSpace
esys.downunder.apps.ReducedFunction((Domain)domain) → FunctionSpace :
Returns:a function FunctionSpace with reduced integration order
Return type:FunctionSpace
esys.downunder.apps.ReducedFunctionOnBoundary((Domain)domain) → FunctionSpace :
Returns:a function on boundary FunctionSpace with reduced integration order
Return type:FunctionSpace
esys.downunder.apps.ReducedFunctionOnContactOne((Domain)domain) → FunctionSpace :
Returns:Return a FunctionSpace on right side of contact with reduced integration order
Return type:FunctionSpace
esys.downunder.apps.ReducedFunctionOnContactZero((Domain)domain) → FunctionSpace :
Returns:a FunctionSpace on left side of contact with reduced integration order
Return type:FunctionSpace
esys.downunder.apps.ReducedSolution((Domain)domain) → FunctionSpace :
Return type:FunctionSpace
esys.downunder.apps.Scalar([(object)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa05352ad50>[, (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.downunder.apps.Solution((Domain)domain) → FunctionSpace :
Return type:FunctionSpace
esys.downunder.apps.Tensor([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa05352af90>[, (bool)expanded=False]]]) → Data :

Construct a Data object containing rank2 data-points.

param value:scalar value for all points
rtype:Data
type value:float
param what:FunctionSpace for Data
type what:FunctionSpace
param expanded:If True, a value is stored for each point. If False, more efficient representations may be used
type expanded:bool

Tensor( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa053554090> [, (bool)expanded=False]]) -> Data

esys.downunder.apps.Tensor3([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa053554150>[, (bool)expanded=False]]]) → Data :

Construct a Data object containing rank3 data-points.

param value:scalar value for all points
rtype:Data
type value:float
param what:FunctionSpace for Data
type what:FunctionSpace
param expanded:If True, a value is stored for each point. If False, more efficient representations may be used
type expanded:bool

Tensor3( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa053554210> [, (bool)expanded=False]]) -> Data

esys.downunder.apps.Tensor4([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa053554270>[, (bool)expanded=False]]]) → Data :

Construct a Data object containing rank4 data-points.

param value:scalar value for all points
rtype:Data
type value:float
param what:FunctionSpace for Data
type what:FunctionSpace
param expanded:If True, a value is stored for each point. If False, more efficient representations may be used
type expanded:bool

Tensor4( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa053554390> [, (bool)expanded=False]]) -> Data

esys.downunder.apps.Vector([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa05352ae10>[, (bool)expanded=False]]]) → Data :

Construct a Data object containing rank1 data-points.

param value:scalar value for all points
rtype:Data
type value:float
param what:FunctionSpace for Data
type what:FunctionSpace
param expanded:If True, a value is stored for each point. If False, more efficient representations may be used
type expanded:bool

Vector( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa05352aed0> [, (bool)expanded=False]]) -> Data

esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.atan2(arg0, arg1)

Returns inverse tangent of argument arg0 over arg1

esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.combineData(array, shape)
esys.downunder.apps.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.downunder.apps.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.downunder.apps.condEval(f, tval, fval)

Wrapper to allow non-data objects to be used.

esys.downunder.apps.convertToNumpy(data)

Writes Data objects to a numpy array.

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 usage:

s=Scalar(..) v=Vector(..) t=Tensor(..) f=float() array = getNumpy(a=s, b=v, c=t, d=f)

esys.downunder.apps.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.downunder.apps.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.downunder.apps.delay(arg)

Returns a lazy version of arg

esys.downunder.apps.deviatoric(arg)

Returns the deviatoric version of arg.

esys.downunder.apps.diameter(domain)

Returns the diameter of a domain.

Parameters:domain (escript.Domain) – a domain
Return type:float
esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.escript_generalTensorProduct(arg0, arg1, axis_offset, transpose=0)

arg0 and arg1 are both Data objects but not necessarily on the same function space. They could be identical!!!

esys.downunder.apps.escript_generalTensorTransposedProduct(arg0, arg1, axis_offset)

arg0 and arg1 are both Data objects but not necessarily on the same function space. They could be identical!!!

esys.downunder.apps.escript_generalTransposedTensorProduct(arg0, arg1, axis_offset)

arg0 and arg1 are both Data objects but not necessarily on the same function space. They could be identical!!!

esys.downunder.apps.escript_inverse(arg)

arg is a Data object!

esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.getEpsilon()
esys.downunder.apps.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.downunder.apps.getMPIRankWorld() → int :

Return the rank of this process in the MPI World.

esys.downunder.apps.getMPISizeWorld() → int :

Return number of MPI processes in the job.

esys.downunder.apps.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.downunder.apps.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.downunder.apps.getMachinePrecision() → float
esys.downunder.apps.getMaxFloat()
esys.downunder.apps.getNumberOfThreads() → int :

Return the maximum number of threads available to OpenMP.

esys.downunder.apps.getNumpy(**data)

Writes Data objects to a numpy array.

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 usage:

s=Scalar(..) v=Vector(..) t=Tensor(..) f=float() array = getNumpy(a=s, b=v, c=t, d=f)

esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.getTestDomainFunctionSpace((int)dpps, (int)samples[, (int)size=1]) → FunctionSpace :

For testing only. May be removed without notice.

esys.downunder.apps.getTotalDifferential(f, x, order=0)

This function computes:

| Df/Dx = del_f/del_x + del_f/del_grad(x)*del_grad(x)/del_x + ...
|            \   /         \   /
|              a             b
esys.downunder.apps.getVersion() → int :

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

esys.downunder.apps.gmshGeo2Msh(geoFile, mshFile, numDim, order=1, verbosity=0)

Runs gmsh to mesh input geoFile. Returns 0 on success.

esys.downunder.apps.grad(arg, where=None)

Returns the spatial gradient of arg at where.

If g is the returned object, then

  • if arg is rank 0 g[s] is the derivative of arg with respect to the s-th spatial dimension
  • if arg is rank 1 g[i,s] is the derivative of arg[i] with respect to the s-th spatial dimension
  • if arg is rank 2 g[i,j,s] is the derivative of arg[i,j] with respect to the s-th spatial dimension
  • if arg is rank 3 g[i,j,k,s] is the derivative of arg[i,j,k] with respect to the s-th spatial dimension.
Parameters:
  • arg (escript.Data or Symbol) – function of which the gradient is to be calculated. Its rank has to be less than 3.
  • where (None or escript.FunctionSpace) – FunctionSpace in which the gradient is calculated. If not present or None an appropriate default is used.
Returns:

gradient of arg
Return type:

escript.Data or Symbol
esys.downunder.apps.grad_n(arg, n, where=None)
esys.downunder.apps.hasFeature((str)name) → bool :

Check if escript was compiled with a certain feature

Parameters:name (string) – feature to lookup
esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.interpolateTable(tab, dat, start, step, undef=1e+50, check_boundaries=False)
esys.downunder.apps.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.downunder.apps.isSymbol(arg)

Returns True if the argument arg is an escript Symbol or sympy.Basic object, False otherwise.

esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.listFeatures() → list :
Returns:A list of strings representing the features escript supports.
esys.downunder.apps.load((str)fileName, (Domain)domain) → Data :

reads Data on domain from file in netCDF format

Parameters:
  • fileName (string) –
  • domain (Domain) –
esys.downunder.apps.loadIsConfigured() → bool :
Returns:True if the load function is configured.
esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.makeTagMap(fs)

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

esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.matrixmult(arg0, arg1)

See matrix_mult.

esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.negative(arg)

returns the negative part of arg

esys.downunder.apps.nonsymmetric(arg)

Deprecated alias for antisymmetric

esys.downunder.apps.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.downunder.apps.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.downunder.apps.phase(arg)

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

esys.downunder.apps.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.downunder.apps.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.downunder.apps.positive(arg)

returns the positive part of arg

esys.downunder.apps.pprint(expr, use_unicode=None)

Prints expr in pretty form.

pprint is just a shortcut for this function

esys.downunder.apps.pretty_print(expr, use_unicode=None)

Prints expr in pretty form.

pprint is just a shortcut for this function

esys.downunder.apps.printParallelThreadCounts() → None
esys.downunder.apps.releaseUnusedMemory() → None
esys.downunder.apps.removeFsFromGrad(sym)

Returns sym with all occurrences grad_n(a,b,c) replaced by grad_n(a,b). That is, all functionspace parameters are removed.

esys.downunder.apps.reorderComponents(arg, index)

Resorts the components of arg according to index.

esys.downunder.apps.resolve(arg)

Returns the value of arg resolved.

esys.downunder.apps.resolveGroup((object)arg1) → None
esys.downunder.apps.runMPIProgram((list)arg1) → int :

Spawns an external MPI program using a separate communicator.

esys.downunder.apps.safeDiv(arg0, arg1, rtol=None)

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

esys.downunder.apps.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.downunder.apps.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.downunder.apps.saveSilo(filename, domain=None, write_meshdata=False, time=0.0, cycle=0, **data)

Writes Data objects and their mesh to a file using the SILO file format.

Example:

temp=Scalar(..)
v=Vector(..)
saveSilo("solution.silo", temperature=temp, velocity=v)

temp and v are written to “solution.silo” where temp is named “temperature” and v is named “velocity”.

Parameters:
  • filename (str) – name of the output file (‘.silo’ is added if required)
  • domain (escript.Domain) – domain of the Data objects. If not specified, the domain of the given Data objects is used.
  • write_meshdata (bool) – whether to save mesh-related data such as element identifiers, ownership etc. This is mainly useful for debugging.
  • time (float) – the timestamp to save within the file
  • cycle (int) – the cycle (or timestep) of the data
  • <name> – writes the assigned value to the Silo file using <name> as identifier
Note:

All data objects have to be defined on the same domain but they may be defined on separate FunctionSpace s.
esys.downunder.apps.saveVTK(filename, domain=None, metadata='', metadata_schema=None, write_meshdata=False, time=0.0, cycle=0, **data)

Writes Data objects and their mesh to a file using the VTK XML file format.

Example:

temp=Scalar(..)
v=Vector(..)
saveVTK("solution.vtu", temperature=temp, velocity=v)

temp and v are written to “solution.vtu” where temp is named “temperature” and v is named “velocity”.

Meta tags, e.g. a timeStamp, can be added to the file, for instance:

tmp=Scalar(..)
v=Vector(..)
saveVTK("solution.vtu", temperature=tmp, velocity=v,
        metadata="<timeStamp>1.234</timeStamp>",
        metadata_schema={"gml":"http://www.opengis.net/gml"})

The argument metadata_schema allows the definition of name spaces with a schema used in the definition of meta tags.

Parameters:
  • filename (str) – name of the output file (‘.vtu’ is added if required)
  • domain (escript.Domain) – domain of the Data objects. If not specified, the domain of the given Data objects is used.
  • <name> – writes the assigned value to the VTK file using <name> as identifier
  • metadata (str) – additional XML meta data which are inserted into the VTK file. The meta data are marked by the tag <MetaData>.
  • metadata_schema (dict with metadata_schema[<namespace>]=<URI> to assign the scheme <URI> to the name space <namespace>.) – assigns schemas to namespaces which have been used to define meta data.
  • write_meshdata (bool) – whether to save mesh-related data such as element identifiers, ownership etc. This is mainly useful for debugging.
  • time (float) – the timestamp to save within the file, seperate to metadata
  • cycle (int) – the cycle (or timestep) of the data
Note:

All data objects have to be defined on the same domain. They may not be in the same FunctionSpace but not all combinations of FunctionSpace s can be written to a single VTK file. Typically, data on the boundary and on the interior cannot be mixed.
esys.downunder.apps.setEscriptParamInt((str)name[, (int)value=0]) → None :

Modify the value of an escript tuning parameter

Parameters:
  • name (string) –
  • value (int) –
esys.downunder.apps.setNumberOfThreads((int)arg1) → None :

Use of this method is strongly discouraged.

esys.downunder.apps.showEscriptParams()

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

esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.symbols(*names, **kwargs)

Emulates the behaviour of sympy.symbols.

esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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 the transposed of arg0 and arg1 at each data point
Return type:

numpy.ndarray, escript.Data, Symbol depending on the input
esys.downunder.apps.tensormult(arg0, arg1)

See tensor_mult.

esys.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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.downunder.apps.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 tol are accepted as zero. If tol is not present rtol``*```Lsup` (arg) is used.
Return type:

float, escript.Data, Symbol, numpy.ndarray depending on the type of arg
Raises:
  • ValueError – if rtol is non-negative.
  • TypeError – if the type of the argument is not expected
esys.downunder.apps.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.downunder.apps.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 non-negative.
  • TypeError – if the type of the argument is not expected
esys.downunder.apps.zeros(shape=())

Returns the shape zero tensor.

Parameters:shape (tuple of int) – input shape for the identity tensor
Returns:array of shape filled with zeros
Return type:numpy.ndarray

Others

  • DBLE_MAX
  • EPSILON
  • HAVE_SYMBOLS

Packages