# esys.downunder.apps Package

Our most general domain representation. Imports submodules into its namespace

## Classes

- `ContinuousDomain`
- `DCResistivityModel`
- `DCResistivityModelNoPrimary`
- `Data`
- `DataManager`
- `Domain`
- `Evaluator`
- `FileWriter`
- `FunctionJob`
- `FunctionSpace`
- `GravityModel`
- `Job`
- `LinearPDE`
- `Locator`
- `MT2DTEModel`
- `MT2DTMModel`
- `MagneticModel2D`
- `MagneticModel3D`
- `NonlinearPDE`
- `Operator`
- `PMLCondition`
- `Reducer`
- `SolverBuddy`
- `SolverOptions`
- `SonicWaveInFrequencyDomain`
- `SplitWorld`
- `SubWorld`
- `Symbol`
- `TestDomain`
- `TransportProblem`

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:

    - rhs (`Data`) –
    - X (`Data`) –
    - Y (`Data`) –
    - y (`Data`) –
    - y_contact (`Data`) –
    - y_dirac (`Data`) –

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

    adds a PDE onto the stiffness matrix mat and a rhs

    Parameters:

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

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

    Parameters:

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

  `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:

    - mat (`OperatorAdapter`) –
    - 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 (`Data`) –

  `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:

    - coefficients – new values assigned to coefficients
    - A (any type that can be cast to a `Data` object on `Function`) – value for coefficient `A`
    - A_reduced (any type that can be cast to a `Data` object on `ReducedFunction`) – value for coefficient `A_reduced`
    - B (any type that can be cast to a `Data` object on `Function`) – value for coefficient `B`
    - B_reduced (any type that can be cast to a `Data` object on `ReducedFunction`) – value for coefficient `B_reduced`
    - C (any type that can be cast to a `Data` object on `Function`) – value for coefficient `C`
    - C_reduced (any type that can be cast to a `Data` object on `ReducedFunction`) – value for coefficient `C_reduced`
    - D (any type that can be cast to a `Data` object on `Function`) – value for coefficient `D`
    - D_reduced (any type that can be cast to a `Data` object on `ReducedFunction`) – value for coefficient `D_reduced`
    - X (any type that can be cast to a `Data` object on `Function`) – value for coefficient `X`
    - X_reduced (any type that can be cast to a `Data` object on `ReducedFunction`) – value for coefficient `X_reduced`
    - Y (any type that can be cast to a `Data` object on `Function`) – value for coefficient `Y`
    - Y_reduced (any type that can be cast to a `Data` object on `ReducedFunction`) – value for coefficient `Y_reduced`
    - d (any type that can be cast to a `Data` object on `FunctionOnBoundary`) – value for coefficient `d`
    - d_reduced (any type that can be cast to a `Data` object on `ReducedFunctionOnBoundary`) – value for coefficient `d_reduced`
    - y (any type that can be cast to a `Data` object on `FunctionOnBoundary`) – value for coefficient `y`
    - d_contact (any type that can be cast to a `Data` object on `FunctionOnContactOne` or `FunctionOnContactZero`) – value for coefficient `d_contact`
    - d_contact_reduced (any type that can be cast to a `Data` object on `ReducedFunctionOnContactOne` or `ReducedFunctionOnContactZero`) – value for coefficient `d_contact_reduced`
    - y_contact (any type that can be cast to a `Data` object on `FunctionOnContactOne` or `FunctionOnContactZero`) – value for coefficient `y_contact`
    - y_contact_reduced (any type that can be cast to a `Data` object on `ReducedFunctionOnContactOne` or `ReducedFunctionOnContactZero`) – value for coefficient `y_contact_reduced`
    - d_dirac (any type that can be cast to a `Data` object on `DiracDeltaFunctions`) – value for coefficient `d_dirac`
    - y_dirac (any type that can be cast to a `Data` object on `DiracDeltaFunctions`) – value for coefficient `y_dirac`
    - r (any type that can be cast to a `Data` object on `Solution` or `ReducedSolution` depending on whether reduced order is used for the solution) – values prescribed to the solution at the locations of constraints
    - q (any type that can be cast to a `Data` object on `Solution` or `ReducedSolution` depending on whether reduced order is used for the representation of the equation) – mask for location of constraints

    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:

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

  `trace1`(text)

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

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

  `trace3`(text)

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

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

class `esys.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`, `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`, `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
  `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
  `as_integer_ratio`()

    Return integer ratio.

    Return a pair of integers, whose ratio is exactly equal to the original int and with a positive denominator.

        >>> (10).as_integer_ratio()
        (10, 1)
        >>> (-10).as_integer_ratio()
        (-10, 1)
        >>> (0).as_integer_ratio()
        (0, 1)

  `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, '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.BICGSTAB, 8: esys.escriptcore.escriptcpp.SolverOptions.CGLS, 9: esys.escriptcore.escriptcpp.SolverOptions.CGS, 10: esys.escriptcore.escriptcpp.SolverOptions.CHOLEVSKY, 11: esys.escriptcore.escriptcpp.SolverOptions.CR, 12: esys.escriptcore.escriptcpp.SolverOptions.DIRECT, 13: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_MUMPS, 14: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_PARDISO, 15: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_SUPERLU, 16: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_TRILINOS, 17: esys.escriptcore.escriptcpp.SolverOptions.GMRES, 18: esys.escriptcore.escriptcpp.SolverOptions.HRZ_LUMPING, 19: esys.escriptcore.escriptcpp.SolverOptions.ITERATIVE, 20: esys.escriptcore.escriptcpp.SolverOptions.LSQR, 21: esys.escriptcore.escriptcpp.SolverOptions.MINRES, 22: esys.escriptcore.escriptcpp.SolverOptions.NONLINEAR_GMRES, 23: esys.escriptcore.escriptcpp.SolverOptions.PCG, 24: esys.escriptcore.escriptcpp.SolverOptions.PRES20, 25: esys.escriptcore.escriptcpp.SolverOptions.ROWSUM_LUMPING, 26: esys.escriptcore.escriptcpp.SolverOptions.TFQMR, 27: esys.escriptcore.escriptcpp.SolverOptions.AMG, 28: esys.escriptcore.escriptcpp.SolverOptions.GAUSS_SEIDEL, 29: esys.escriptcore.escriptcpp.SolverOptions.ILU0, 30: esys.escriptcore.escriptcpp.SolverOptions.ILUT, 31: esys.escriptcore.escriptcpp.SolverOptions.JACOBI, 32: esys.escriptcore.escriptcpp.SolverOptions.NO_PRECONDITIONER, 33: esys.escriptcore.escriptcpp.SolverOptions.REC_ILU, 34: esys.escriptcore.escriptcpp.SolverOptions.RILU, 35: esys.escriptcore.escriptcpp.SolverOptions.BACKWARD_EULER, 36: esys.escriptcore.escriptcpp.SolverOptions.CRANK_NICOLSON, 37: esys.escriptcore.escriptcpp.SolverOptions.LINEAR_CRANK_NICOLSON, 38: esys.escriptcore.escriptcpp.SolverOptions.CLASSIC_INTERPOLATION, 39: esys.escriptcore.escriptcpp.SolverOptions.CLASSIC_INTERPOLATION_WITH_FF_COUPLING, 40: esys.escriptcore.escriptcpp.SolverOptions.DIRECT_INTERPOLATION, 41: esys.escriptcore.escriptcpp.SolverOptions.DEFAULT_REORDERING, 42: esys.escriptcore.escriptcpp.SolverOptions.MINIMUM_FILL_IN, 43: esys.escriptcore.escriptcpp.SolverOptions.NESTED_DISSECTION, 44: 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 0x7f6046e4de70>[, (bool)expanded=False]]) → Data

`esys.downunder.apps.``ComplexScalar`([(object)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f6046e4d810>[, (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 0x7f6046e4da50>[, (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 0x7f6046e4db10> [, (bool)expanded=False]]) -> Data

`esys.downunder.apps.``ComplexTensor3`([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f6046e4dbd0>[, (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 0x7f6046e4dcf0> [, (bool)expanded=False]]) -> Data

`esys.downunder.apps.``ComplexTensor4`([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f6046e4dd50>[, (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 0x7f6046e4de10> [, (bool)expanded=False]]) -> Data

`esys.downunder.apps.``ComplexVector`([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f6046e4d8d0>[, (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 0x7f6046e4d990> [, (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.``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 0x7f6046e4d7b0>[, (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 0x7f6046e4d9f0>[, (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 0x7f6046e4dab0> [, (bool)expanded=False]]) -> Data

`esys.downunder.apps.``Tensor3`([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f6046e4db70>[, (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 0x7f6046e4dc30> [, (bool)expanded=False]]) -> Data

`esys.downunder.apps.``Tensor4`([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f6046e4dc90>[, (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 0x7f6046e4ddb0> [, (bool)expanded=False]]) -> Data

`esys.downunder.apps.``Vector`([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7f6046e4d870>[, (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 0x7f6046e4d930> [, (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