esys.downunder.forwardmodels.pressure Package¶
Isostatic Pressure calculation
Classes¶
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class
esys.downunder.forwardmodels.pressure.Data¶ Bases:
Boost.Python.instanceRepresents a collection of datapoints. It is used to store the values of a function. For more details please consult the c++ class documentation.
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__init__((object)arg1) → None¶ __init__( (object)arg1, (object)value [, (object)p2 [, (object)p3 [, (object)p4]]]) -> None
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conjugate((Data)arg1) → Data¶
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copy((Data)arg1, (Data)other) → None :¶ Make this object a copy of
othernote: The two objects will act independently from now on. That is, changing otherafter 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.
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copyWithMask((Data)arg1, (Data)other, (Data)mask) → None :¶ Selectively copy values from
otherData.Datapoints which correspond to positive values inmaskwill be copied fromotherParameters:
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delay((Data)arg1) → Data :¶ Convert this object into lazy representation
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dump((Data)arg1, (str)fileName) → None :¶ Save the data as a netCDF file
Parameters: fileName ( string) –
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expand((Data)arg1) → None :¶ Convert the data to expanded representation if it is not expanded already.
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getDomain((Data)arg1) → Domain :¶ Return type: Domain
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getFunctionSpace((Data)arg1) → FunctionSpace :¶ Return type: FunctionSpace
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getNumberOfDataPoints((Data)arg1) → int :¶ Return type: intReturns: Number of datapoints in the object
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getRank((Data)arg1) → int :¶ Returns: the number of indices required to address a component of a datapoint Return type: positive int
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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
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getTagNumber((Data)arg1, (int)dpno) → int :¶ Return tag number for the specified datapoint
Return type: int Parameters: dpno (int) – datapoint number
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getTupleForDataPoint((Data)arg1, (int)dataPointNo) → object :¶ Returns: Value of the specified datapoint Return type: tupleParameters: dataPointNo ( int) – datapoint to access
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getTupleForGlobalDataPoint((Data)arg1, (int)procNo, (int)dataPointNo) → object :¶ Get a specific datapoint from a specific process
Return type: tupleParameters: - procNo (positive
int) – MPI rank of the process - dataPointNo (int) – datapoint to access
- procNo (positive
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hasInf((Data)arg1) → bool :¶ Returns return true if data contains +-Inf. [Note that for complex values, hasNaN and hasInf are not mutually exclusive.]
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hasNaN((Data)arg1) → bool :¶ Returns return true if data contains NaN. [Note that for complex values, hasNaN and hasInf are not mutually exclusive.]
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imag((Data)arg1) → Data¶
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internal_maxGlobalDataPoint((Data)arg1) → tuple :¶ Please consider using getSupLocator() from pdetools instead.
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internal_minGlobalDataPoint((Data)arg1) → tuple :¶ Please consider using getInfLocator() from pdetools instead.
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interpolate((Data)arg1, (FunctionSpace)functionspace) → Data :¶ Interpolate this object’s values into a new functionspace.
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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)Amust be the outer dimension on the tableparam 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: Dataparam 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 undefrtype: Data
interpolateTable( (Data)arg1, (object)table, (float)Amin, (float)Astep [, (float)undef=1e+50 [, (bool)check_boundaries=False]]) -> Data
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isComplex((Data)arg1) → bool :¶ Return type: boolReturns: True if this Datastores complex values.
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isConstant((Data)arg1) → bool :¶ Return type: boolReturns: True if this Datais an instance ofDataConstantNote: This does not mean the data is immutable.
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isEmpty((Data)arg1) → bool :¶ Is this object an instance of
DataEmptyReturn type: boolNote: This is not the same thing as asking if the object contains datapoints.
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isExpanded((Data)arg1) → bool :¶ Return type: boolReturns: True if this Datais expanded.
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isLazy((Data)arg1) → bool :¶ Return type: boolReturns: True if this Datais lazy.
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isProtected((Data)arg1) → bool :¶ Can this instance be modified. :rtype:
bool
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isReady((Data)arg1) → bool :¶ Return type: boolReturns: True if this Datais not lazy.
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isTagged((Data)arg1) → bool :¶ Return type: boolReturns: True if this Datais expanded.
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nonuniformInterpolate((Data)arg1, (object)in, (object)out, (bool)check_boundaries) → Data :¶ 1D interpolation with non equally spaced points
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nonuniformSlope((Data)arg1, (object)in, (object)out, (bool)check_boundaries) → Data :¶ 1D interpolation of slope with non equally spaced points
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phase((Data)arg1) → Data¶
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promote((Data)arg1) → None¶
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real((Data)arg1) → Data¶
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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].
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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].
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resolve((Data)arg1) → None :¶ Convert the data to non-lazy representation.
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setProtection((Data)arg1) → None :¶ Disallow modifications to this data object
Note: This method does not allow you to undo protection.
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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: stringparam value: value to set tagged data to type value: objectwhich acts like an array,tupleorlist
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setToZero((Data)arg1) → None :¶ After this call the object will store values of the same shape as before but all components will be zero.
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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: floator an object which acts like an array,tupleorlistwarning: Use of this operation is discouraged. It prevents some optimisations from operating.
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tag((Data)arg1) → None :¶ Convert data to tagged representation if it is not already tagged or expanded
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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]
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class
esys.downunder.forwardmodels.pressure.FileWriter(fn, append=False, createLocalFiles=False)¶ Bases:
objectInterface to write data to a file. In essence this class wrappes the standard
fileobject 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 useFileWriterrather thanopenin order to write code that is running with as well as with MPI. It is safe to useopenonder 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
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__init__(fn, append=False, createLocalFiles=False)¶ Opens a file of name
fnfor writing. If running under MPI only the first processor with rank==0 will open the file and write to it. IfcreateLocalFileseach 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.
- fn (
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close()¶ Closes the file
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flush()¶ Flush the internal I/O buffer.
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write(txt)¶ Write string
txtto file.Parameters: txt ( str) – stringtxtto be written to file
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writelines(txts)¶ Write the list
txtof 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.
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class
esys.downunder.forwardmodels.pressure.IsostaticPressure(domain, p0=0.0, level0=0, gravity0=-9.81, background_density=2670.0, gravity_constant=6.6742e-11, coordinates=None, tol=1e-08)¶ Bases:
objectclass to calculate isostatic pressure field correction due to gravity forces
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__init__(domain, p0=0.0, level0=0, gravity0=-9.81, background_density=2670.0, gravity_constant=6.6742e-11, coordinates=None, tol=1e-08)¶ Parameters: - domain (
Domain) – domain of the model - p0 (scalar
Dataorfloat) – pressure at level0 - background_density (
float) – defines background_density in kg/m^3 - coordinates (ReferenceSystem` or
SpatialCoordinateTransformation) – defines coordinate system to be used - tol (positive
float) – tolerance of underlying PDE - level0 (
float) – pressure for z>=`level0` is set to zero. - gravity0 (
float) – vertical background gravity atlevel0
- domain (
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getPressure(g=None, rho=None)¶ return the pressure for gravity force anomaly
gand density anomalyrhoParameters: - g (
Vector) – gravity anomaly data - rho (
Scalar) – gravity anomaly data
Returns: pressure distribution
Return type: Scalar- g (
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Functions¶
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esys.downunder.forwardmodels.pressure.Abs(arg)¶ Returns the absolute value of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray.) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.C_GeneralTensorProduct((Data)arg0, (Data)arg1[, (int)axis_offset=0[, (int)transpose=0]]) → Data :¶ Compute a tensor product of two Data objects.
Return type: Parameters: - arg0 –
- arg1 –
- axis_offset (
int) – - transpose (int) – 0: transpose neither, 1: transpose arg0, 2: transpose arg1
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esys.downunder.forwardmodels.pressure.Function((Domain)domain) → FunctionSpace :¶ Returns: a function FunctionSpaceReturn type: FunctionSpace
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esys.downunder.forwardmodels.pressure.L2(arg)¶ Returns the L2 norm of
argatwhere.Parameters: arg ( escript.DataorSymbol) – function of which the L2 norm is to be calculatedReturns: L2 norm of argReturn type: floatorSymbolNote: L2(arg) is equivalent to sqrt(integrate(inner(arg,arg)))
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esys.downunder.forwardmodels.pressure.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- domain (
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esys.downunder.forwardmodels.pressure.Lsup(arg)¶ Returns the Lsup-norm of argument
arg. This is the maximum absolute value over all data points. This function is equivalent tosup(abs(arg)).Parameters: arg ( float,int,escript.Data,numpy.ndarray) – argumentReturns: maximum value of the absolute value of argover all components and all data pointsReturn type: floatRaises: TypeError – if type of argcannot be processed
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esys.downunder.forwardmodels.pressure.NumpyToData(array, isComplex, functionspace)¶ Uses a numpy ndarray to create a
DataobjectExample usage: NewDataObject = NumpyToData(ndarray, isComplex, FunctionSpace)
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esys.downunder.forwardmodels.pressure.Scalar([(object)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa05352ad50>[, (bool)expanded=False]]]) → Data :¶ Construct a Data object containing scalar data-points.
Parameters: - value (float) – scalar value for all points
- what (
FunctionSpace) – FunctionSpace for Data - expanded (
bool) – If True, a value is stored for each point. If False, more efficient representations may be used
Return type:
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esys.downunder.forwardmodels.pressure.Vector([(float)value=0.0[, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa05352ae10>[, (bool)expanded=False]]]) → Data :¶ Construct a Data object containing rank1 data-points.
param value: scalar value for all points rtype: Datatype value: float param what: FunctionSpace for Data type what: FunctionSpaceparam expanded: If True, a value is stored for each point. If False, more efficient representations may be used type expanded: boolVector( (object)value [, (FunctionSpace)what=<esys.escriptcore.escriptcpp.FunctionSpace object at 0x7fa05352aed0> [, (bool)expanded=False]]) -> Data
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esys.downunder.forwardmodels.pressure.acos(arg)¶ Returns the inverse cosine of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.acosh(arg)¶ Returns the inverse hyperbolic cosine of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.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 argReturn type: numpy.ndarray,escript.Data,Symboldepending on the input
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esys.downunder.forwardmodels.pressure.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 argReturn type: numpy.ndarray,escript.Data,Symboldepending on the input
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esys.downunder.forwardmodels.pressure.asin(arg)¶ Returns the inverse sine of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.asinh(arg)¶ Returns the inverse hyperbolic sine of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.atan(arg)¶ Returns inverse tangent of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.atan2(arg0, arg1)¶ Returns inverse tangent of argument
arg0overarg1
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esys.downunder.forwardmodels.pressure.atanh(arg)¶ Returns the inverse hyperbolic tangent of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.boundingBox(domain)¶ Returns the bounding box of a domain
Parameters: domain ( escript.Domain) – a domainReturns: bounding box of the domain Return type: listof pairs offloat
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esys.downunder.forwardmodels.pressure.boundingBoxEdgeLengths(domain)¶ Returns the edge lengths of the bounding box of a domain
Parameters: domain ( escript.Domain) – a domainReturn type: listoffloat
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esys.downunder.forwardmodels.pressure.clip(arg, minval=None, maxval=None)¶ Cuts the values of
argbetweenminvalandmaxval.Parameters: - arg (
numpy.ndarray,escript.Data,Symbol,intorfloat) – argument - minval (
floatorNone) – lower range. If None no lower range is applied - maxval (
floatorNone) – upper range. If None no upper range is applied
Returns: an object that contains all values from
argbetweenminvalandmaxvalReturn type: numpy.ndarray,escript.Data,Symbol,intorfloatdepending on the inputRaises: ValueError – if
minval>maxval- arg (
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esys.downunder.forwardmodels.pressure.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 dimensionNoneis returned.Return type: intorNoneRaises: ValueError – if the objects with identifiable dimension don’t have the same spatial dimension.
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esys.downunder.forwardmodels.pressure.commonShape(arg0, arg1)¶ Returns a shape to which
arg0can be extended from the right andarg1can be extended from the left.Parameters: Returns: the shape of
arg0orarg1such that the left part equals the shape ofarg0and the right end equals the shape ofarg1Return type: tupleofintRaises: ValueError – if no shape can be found
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esys.downunder.forwardmodels.pressure.condEval(f, tval, fval)¶ Wrapper to allow non-data objects to be used.
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esys.downunder.forwardmodels.pressure.convertToNumpy(data)¶ Writes
Dataobjects to a numpy array.The keyword args are Data objects to save. If a scalar
Dataobject is passed with the namemask, then only samples which correspond to positive values inmaskwill be output.Example usage:
s=Scalar(..) v=Vector(..) t=Tensor(..) f=float() array = getNumpy(a=s, b=v, c=t, d=f)
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esys.downunder.forwardmodels.pressure.cos(arg)¶ Returns cosine of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.cosh(arg)¶ Returns the hyperbolic cosine of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.delay(arg)¶ Returns a lazy version of arg
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esys.downunder.forwardmodels.pressure.deviatoric(arg)¶ Returns the deviatoric version of
arg.
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esys.downunder.forwardmodels.pressure.diameter(domain)¶ Returns the diameter of a domain.
Parameters: domain ( escript.Domain) – a domainReturn type: float
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esys.downunder.forwardmodels.pressure.div(arg, where=None)¶ Returns the divergence of
argatwhere.Parameters: - arg (
escript.DataorSymbol) – function of which the divergence is to be calculated. Its shape has to be (d,) where d is the spatial dimension. - where (
Noneorescript.FunctionSpace) –FunctionSpacein which the divergence will be calculated. If not present orNonean appropriate default is used.
Returns: divergence of
argReturn type: escript.DataorSymbol- arg (
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esys.downunder.forwardmodels.pressure.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,Symboldepending on the inputNote: for escript.DataandSymbolobjects the dimension is restricted to 3.
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esys.downunder.forwardmodels.pressure.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: tupleofescript.DataNote: The dimension is restricted to 3.
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esys.downunder.forwardmodels.pressure.erf(arg)¶ Returns the error function erf of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray.) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.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!!!
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esys.downunder.forwardmodels.pressure.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!!!
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esys.downunder.forwardmodels.pressure.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!!!
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esys.downunder.forwardmodels.pressure.escript_inverse(arg)¶ arg is a Data object!
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esys.downunder.forwardmodels.pressure.exp(arg)¶ Returns e to the power of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray.) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type of argRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.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:]
- s runs through
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
arg0andarg1at each data pointReturn type: numpy.ndarray,escript.Data,Symboldepending on the input
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esys.downunder.forwardmodels.pressure.generalTensorTransposedProduct(arg0, arg1, axis_offset=0)¶ Generalized tensor product of
arg0and transpose ofarg1.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:]
- s runs through
The function call
generalTensorTransposedProduct(arg0,arg1,axis_offset)is equivalent togeneralTensorProduct(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
arg0andtranspose(arg1)at each data pointReturn type: numpy.ndarray,escript.Data,Symboldepending on the input
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esys.downunder.forwardmodels.pressure.generalTransposedTensorProduct(arg0, arg1, axis_offset=0)¶ Generalized tensor product of transposed of
arg0andarg1.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:]
- s runs through
The function call
generalTransposedTensorProduct(arg0,arg1,axis_offset)is equivalent togeneralTensorProduct(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)andarg1at each data pointReturn type: numpy.ndarray,escript.Data,Symboldepending on the input
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esys.downunder.forwardmodels.pressure.getClosestValue(arg, origin=0)¶ Returns the value in
argwhich is closest to origin.Parameters: - arg (
escript.Data) – function - origin (
floatorescript.Data) – reference value
Returns: value in
argclosest to originReturn type: numpy.ndarray- arg (
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esys.downunder.forwardmodels.pressure.getEpsilon()¶
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esys.downunder.forwardmodels.pressure.getMPIRankWorld() → int :¶ Return the rank of this process in the MPI World.
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esys.downunder.forwardmodels.pressure.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
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esys.downunder.forwardmodels.pressure.getMaxFloat()¶
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esys.downunder.forwardmodels.pressure.getNumpy(**data)¶ Writes
Dataobjects to a numpy array.The keyword args are Data objects to save. If a scalar
Dataobject is passed with the namemask, then only samples which correspond to positive values inmaskwill be output.Example usage:
s=Scalar(..) v=Vector(..) t=Tensor(..) f=float() array = getNumpy(a=s, b=v, c=t, d=f)
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esys.downunder.forwardmodels.pressure.getRank(arg)¶ Identifies the rank of the argument.
Parameters: arg ( numpy.ndarray,escript.Data,float,int,Symbol) – an object whose rank is to be returnedReturns: the rank of the argument Return type: intRaises: TypeError – if type of argcannot be processed
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esys.downunder.forwardmodels.pressure.getShape(arg)¶ Identifies the shape of the argument.
Parameters: arg ( numpy.ndarray,escript.Data,float,int,Symbol) – an object whose shape is to be returnedReturns: the shape of the argument Return type: tupleofintRaises: TypeError – if type of argcannot be processed
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esys.downunder.forwardmodels.pressure.getTagNames(domain)¶ Returns a list of tag names used by the domain.
Parameters: domain ( escript.Domain) – a domain objectReturns: a list of tag names used by the domain Return type: listofstr
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esys.downunder.forwardmodels.pressure.getVersion() → int :¶ This method will only report accurate version numbers for clean checkouts.
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esys.downunder.forwardmodels.pressure.gmshGeo2Msh(geoFile, mshFile, numDim, order=1, verbosity=0)¶ Runs gmsh to mesh input
geoFile. Returns 0 on success.
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esys.downunder.forwardmodels.pressure.grad(arg, where=None)¶ Returns the spatial gradient of
argatwhere.If
gis the returned object, then- if
argis rank 0g[s]is the derivative ofargwith respect to thes-th spatial dimension - if
argis rank 1g[i,s]is the derivative ofarg[i]with respect to thes-th spatial dimension - if
argis rank 2g[i,j,s]is the derivative ofarg[i,j]with respect to thes-th spatial dimension - if
argis rank 3g[i,j,k,s]is the derivative ofarg[i,j,k]with respect to thes-th spatial dimension.
Parameters: - arg (
escript.DataorSymbol) – function of which the gradient is to be calculated. Its rank has to be less than 3. - where (
Noneorescript.FunctionSpace) – FunctionSpace in which the gradient is calculated. If not present orNonean appropriate default is used.
Returns: gradient of
argReturn type: escript.DataorSymbol- if
-
esys.downunder.forwardmodels.pressure.grad_n(arg, n, where=None)¶
-
esys.downunder.forwardmodels.pressure.hasFeature((str)name) → bool :¶ Check if escript was compiled with a certain feature
Parameters: name ( string) – feature to lookup
-
esys.downunder.forwardmodels.pressure.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 argReturn type: numpy.ndarray,escript.Data,Symboldepending on the input
-
esys.downunder.forwardmodels.pressure.identity(shape=())¶ Returns the
shapexshapeidentity tensor.Parameters: shape ( tupleofint) – input shape for the identity tensorReturns: 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.ndarrayof rank 1, rank 2 or rank 4Raises: ValueError – if len(shape)>2
-
esys.downunder.forwardmodels.pressure.identityTensor(d=3)¶ Returns the
dxdidentity matrix.Parameters: d ( int,escript.Domainorescript.FunctionSpace) – dimension or an object that has thegetDimmethod defining the dimensionReturns: the object u of rank 2 with u[i,j]=1 for i=j and u[i,j]=0 otherwise Return type: numpy.ndarrayorescript.Dataof rank 2
-
esys.downunder.forwardmodels.pressure.identityTensor4(d=3)¶ Returns the
dxdxdxdidentity tensor.Parameters: d ( intor any object with agetDimmethod) – dimension or an object that has thegetDimmethod defining the dimensionReturns: 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.ndarrayorescript.Dataof rank 4
-
esys.downunder.forwardmodels.pressure.inf(arg)¶ Returns the minimum value over all data points.
Parameters: arg ( float,int,escript.Data,numpy.ndarray) – argumentReturns: minimum value of argover all components and all data pointsReturn type: floatRaises: TypeError – if type of argcannot be processed
-
esys.downunder.forwardmodels.pressure.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.arg0andarg1must 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
arg0andarg1at each data pointReturn type: numpy.ndarray,escript.Data,Symbol,floatdepending on the inputRaises: ValueError – if the shapes of the arguments are not identical
- arg0 (
-
esys.downunder.forwardmodels.pressure.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>
- domain (
-
esys.downunder.forwardmodels.pressure.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> (
floatornumpy.ndarray) – value to be used for <tag_name>
Returns: targetReturn type: escript.Data- target (
-
esys.downunder.forwardmodels.pressure.integrate(arg, where=None)¶ Returns the integral of the function
argover its domain. Ifwhereis presentargis interpolated towherebefore integration.Parameters: - arg (
escript.DataorSymbol) – the function which is integrated - where (
Noneorescript.FunctionSpace) – FunctionSpace in which the integral is calculated. If not present orNonean appropriate default is used.
Returns: integral of
argReturn type: float,numpy.ndarrayorSymbol- arg (
-
esys.downunder.forwardmodels.pressure.interpolate(arg, where)¶ Interpolates the function into the
FunctionSpacewhere. If the argumentarghas the requested function spacewhereno interpolation is performed andargis returned.Parameters: - arg (
escript.DataorSymbol) – interpolant - where (
escript.FunctionSpace) –FunctionSpaceto be interpolated to
Returns: interpolated argument
Return type: escript.DataorSymbol- arg (
-
esys.downunder.forwardmodels.pressure.interpolateTable(tab, dat, start, step, undef=1e+50, check_boundaries=False)¶
-
esys.downunder.forwardmodels.pressure.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 tokronecker(arg.getShape()[0])Return type: numpy.ndarray,escript.Data,Symboldepending on the inputNote: for escript.Dataobjects the dimension is restricted to 3.
-
esys.downunder.forwardmodels.pressure.jump(arg, domain=None)¶ Returns the jump of
argacross the continuity of the domain.Parameters: - arg (
escript.DataorSymbol) – argument - domain (
Noneorescript.Domain) – the domain where the discontinuity is located. If domain is not present or equal toNonethe domain ofargis used.
Returns: jump of
argReturn type: escript.DataorSymbol- arg (
-
esys.downunder.forwardmodels.pressure.kronecker(d=3)¶ Returns the kronecker delta-symbol.
Parameters: d ( int,escript.Domainorescript.FunctionSpace) – dimension or an object that has thegetDimmethod defining the dimensionReturns: the object u of rank 2 with u[i,j]=1 for i=j and u[i,j]=0 otherwise Return type: numpy.ndarrayorescript.Dataof rank 2
-
esys.downunder.forwardmodels.pressure.length(arg)¶ Returns the length (Euclidean norm) of argument
argat each data point.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symboldepending on the type ofarg
-
esys.downunder.forwardmodels.pressure.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.forwardmodels.pressure.log(arg)¶ Returns the natural logarithm of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray.) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
-
esys.downunder.forwardmodels.pressure.log10(arg)¶ Returns base-10 logarithm of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
-
esys.downunder.forwardmodels.pressure.longestEdge(domain)¶ Returns the length of the longest edge of the domain
Parameters: domain ( escript.Domain) – a domainReturns: longest edge of the domain parallel to the Cartesian axis Return type: float
-
esys.downunder.forwardmodels.pressure.makeTagMap(fs)¶ Produce an expanded Data over the function space where the value is the tag associated with the sample
-
esys.downunder.forwardmodels.pressure.makeTransformation(domain, coordinates=None)¶ returns a
SpatialCoordinateTransformationfor the given domainParameters: - domain (
esys.escript.AbstractDomain) – domain in the domain of the coordinate transformation - coordinates (
ReferenceSystemorSpatialCoordinateTransformation) – the reference system or spatial coordinate system.
Returns: the spatial coordinate system for the given domain of the specified reference system
coordinates. Ifcoordinatesis already spatial coordinate system based on the riven domaincoordinatesis returned. Otherwise an appropriate spatial coordinate system is created.Return type: SpatialCoordinateTransformation- domain (
-
esys.downunder.forwardmodels.pressure.matchShape(arg0, arg1)¶ Returns a representation of
arg0andarg1which 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: arg0andarg1where copies are returned when the shape has to be changedReturn type: tuple- arg0 (
-
esys.downunder.forwardmodels.pressure.matchType(arg0=0.0, arg1=0.0)¶ Converts
arg0andarg1both to the same typenumpy.ndarrayorescript.DataParameters: - arg0 (
numpy.ndarray,`escript.Data`,``float``,int,Symbol) – first argument - arg1 (
numpy.ndarray,`escript.Data`,``float``,int,Symbol) – second argument
Returns: a tuple representing
arg0andarg1with the same type or with at least one of them being aSymbolReturn type: tupleof twonumpy.ndarrayor twoescript.DataRaises: TypeError – if type of
arg0orarg1cannot be processed- arg0 (
-
esys.downunder.forwardmodels.pressure.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
arg0and the first dimension ofarg1must 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
arg0andarg1at each data pointReturn type: numpy.ndarray,escript.Data,Symboldepending on the inputRaises: ValueError – if the shapes of the arguments are not appropriate
- arg0 (
-
esys.downunder.forwardmodels.pressure.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 tomatrix_mult(arg0,transpose(arg1)).The last dimensions of
arg0andarg1must 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
arg0and the transposed ofarg1at each data pointReturn type: numpy.ndarray,escript.Data,Symboldepending on the inputRaises: ValueError – if the shapes of the arguments are not appropriate
- arg0 (
-
esys.downunder.forwardmodels.pressure.matrixmult(arg0, arg1)¶ See
matrix_mult.
-
esys.downunder.forwardmodels.pressure.maximum(*args)¶ The maximum over arguments
args.Parameters: args ( numpy.ndarray,escript.Data,Symbol,intorfloat) – argumentsReturns: an object which in each entry gives the maximum of the corresponding values in argsReturn type: numpy.ndarray,escript.Data,Symbol,intorfloatdepending on the input
-
esys.downunder.forwardmodels.pressure.maxval(arg)¶ Returns the maximum value over all components of
argat each data point.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symboldepending on the type ofargRaises: TypeError – if the type of the argument is not expected
-
esys.downunder.forwardmodels.pressure.meanValue(arg)¶ return the mean value of the argument over its domain
Parameters: arg ( escript.Data) – functionReturns: mean value Return type: floatornumpy.ndarray
-
esys.downunder.forwardmodels.pressure.minimum(*args)¶ The minimum over arguments
args.Parameters: args ( numpy.ndarray,escript.Data,Symbol,intorfloat) – argumentsReturns: an object which gives in each entry the minimum of the corresponding values in argsReturn type: numpy.ndarray,escript.Data,Symbol,intorfloatdepending on the input
-
esys.downunder.forwardmodels.pressure.minval(arg)¶ Returns the minimum value over all components of
argat each data point.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symboldepending on the type ofargRaises: TypeError – if the type of the argument is not expected
-
esys.downunder.forwardmodels.pressure.mkDir(*pathname)¶ creates a directory of name
pathnameif the directory does not exist.Parameters: pathname ( strorsequence of strings) – valid path nameNote: The method is MPI safe.
-
esys.downunder.forwardmodels.pressure.mult(arg0, arg1)¶ Product of
arg0andarg1.Parameters: - arg0 (
Symbol,float,int,escript.Dataornumpy.ndarray) – first term - arg1 (
Symbol,float,int,escript.Dataornumpy.ndarray) – second term
Returns: the product of
arg0andarg1Return type: Symbol,float,int,escript.Dataornumpy.ndarrayNote: The shape of both arguments is matched according to the rules used in
matchShape.- arg0 (
-
esys.downunder.forwardmodels.pressure.negative(arg)¶ returns the negative part of arg
-
esys.downunder.forwardmodels.pressure.nonsymmetric(arg)¶ Deprecated alias for antisymmetric
-
esys.downunder.forwardmodels.pressure.normalize(arg, zerolength=0)¶ Returns the normalized version of
arg(=``arg/length(arg)``).Parameters: - arg (
escript.DataorSymbol) – function - zerolength (
float) – relative tolerance for arg == 0
Returns: normalized
argwhereargis non-zero, and zero elsewhereReturn type: escript.DataorSymbol- arg (
-
esys.downunder.forwardmodels.pressure.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
- s runs through
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
arg0andarg1at each data pointReturn type: numpy.ndarray,escript.Data,Symboldepending on the input
-
esys.downunder.forwardmodels.pressure.phase(arg)¶ return the “phase”/”arg”/”angle” of a number
-
esys.downunder.forwardmodels.pressure.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 NoneReturn type: intorNone
-
esys.downunder.forwardmodels.pressure.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.forwardmodels.pressure.positive(arg)¶ returns the positive part of arg
-
esys.downunder.forwardmodels.pressure.printParallelThreadCounts() → None¶
-
esys.downunder.forwardmodels.pressure.reorderComponents(arg, index)¶ Resorts the components of
argaccording to index.
-
esys.downunder.forwardmodels.pressure.resolve(arg)¶ Returns the value of arg resolved.
-
esys.downunder.forwardmodels.pressure.safeDiv(arg0, arg1, rtol=None)¶ returns arg0/arg1 but return 0 where arg1 is (almost) zero
-
esys.downunder.forwardmodels.pressure.saveDataCSV(filename, append=False, refid=False, sep=', ', csep='_', **data)¶ Writes
Dataobjects to a CSV file. These objects must have compatible FunctionSpaces, i.e. it must be possible to interpolate all data to oneFunctionSpace. 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) – IfTrue, then open file at end rather than beginning - refid (
bool) – IfTrue, 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
Dataobject is passed with the namemask, then only samples which correspond to positive values inmaskwill 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.
- filename (
-
esys.downunder.forwardmodels.pressure.saveESD(datasetName, dataDir='.', domain=None, timeStep=0, deltaT=1, dynamicMesh=0, timeStepFormat='%04d', **data)¶ Saves
Dataobjects to files and creates anescript 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 theDataobject(s). If not specified, the domain of the givenDataobjects 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> (
Dataobject) – 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.
- datasetName (
-
esys.downunder.forwardmodels.pressure.showEscriptParams()¶ Displays the parameters escript recognises with an explanation and their current value.
-
esys.downunder.forwardmodels.pressure.sign(arg)¶ Returns the sign of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
-
esys.downunder.forwardmodels.pressure.sin(arg)¶ Returns sine of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray.) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
-
esys.downunder.forwardmodels.pressure.sinh(arg)¶ Returns the hyperbolic sine of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
-
esys.downunder.forwardmodels.pressure.sqrt(arg)¶ Returns the square root of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
-
esys.downunder.forwardmodels.pressure.sup(arg)¶ Returns the maximum value over all data points.
Parameters: arg ( float,int,escript.Data,numpy.ndarray) – argumentReturns: maximum value of argover all components and all data pointsReturn type: floatRaises: TypeError – if type of argcannot be processed
-
esys.downunder.forwardmodels.pressure.swap_axes(arg, axis0=0, axis1=1)¶ Returns the swap of
argby swapping the componentsaxis0andaxis1.Parameters: - arg (
escript.Data,Symbol,numpy.ndarray) – argument - axis0 (
int) – first axis.axis0must be non-negative and less than the rank ofarg. - axis1 (
int) – second axis.axis1must be non-negative and less than the rank ofarg.
Returns: argwith swapped componentsReturn type: escript.Data,Symbolornumpy.ndarraydepending on the type ofarg- arg (
-
esys.downunder.forwardmodels.pressure.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 argReturn type: numpy.ndarray,escript.Data,Symboldepending on the input
-
esys.downunder.forwardmodels.pressure.tan(arg)¶ Returns tangent of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
-
esys.downunder.forwardmodels.pressure.tanh(arg)¶ Returns the hyperbolic tangent of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
-
esys.downunder.forwardmodels.pressure.tensor_mult(arg0, arg1)¶ The tensor product of the two arguments.
For
arg0of rank 2 this isout[s0]=Sigma_{r0} arg0[s0,r0]*arg1[r0]or
out[s0,s1]=Sigma_{r0} arg0[s0,r0]*arg1[r0,s1]and for
arg0of rank 4 this isout[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
arg0and the last dimension ofarg1must match and in the second case the two last dimensions ofarg0must match the two first dimensions ofarg1.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 ofarg0
Returns: the tensor product of
arg0andarg1at each data pointReturn type: numpy.ndarray,escript.Data,Symboldepending on the input- arg0 (
-
esys.downunder.forwardmodels.pressure.tensor_transposed_mult(arg0, arg1)¶ The tensor product of the first and the transpose of the second argument.
For
arg0of rank 2 this isout[s0,s1]=Sigma_{r0} arg0[s0,r0]*arg1[s1,r0]and for
arg0of rank 4 this isout[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
arg0andarg1must match and in the second case the two last dimensions ofarg0must match the two last dimensions ofarg1.The function call
tensor_transpose_mult(arg0,arg1)is equivalent totensor_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 ofarg0
Returns: the tensor product of the transposed of
arg0andarg1at each data pointReturn type: numpy.ndarray,escript.Data,Symboldepending on the input- arg0 (
-
esys.downunder.forwardmodels.pressure.tensormult(arg0, arg1)¶ See
tensor_mult.
-
esys.downunder.forwardmodels.pressure.testForZero(arg)¶ Tests if the argument is identical to zero.
Parameters: arg (typically numpy.ndarray,escript.Data,float,int) – the object to test for zeroReturns: True if the argument is identical to zero, False otherwise Return type: bool
-
esys.downunder.forwardmodels.pressure.trace(arg, axis_offset=0)¶ Returns the trace of
argwhich is the sum ofarg[k,k]over k.Parameters: - arg (
escript.Data,Symbol,numpy.ndarray) – argument - axis_offset (
int) –axis_offsetto components to sum over.axis_offsetmust be non-negative and less than the rank ofarg+1. The dimensions of componentaxis_offsetand axis_offset+1 must be equal.
Returns: trace of arg. The rank of the returned object is rank of
argminus 2.Return type: escript.Data,Symbolornumpy.ndarraydepending on the type ofarg- arg (
-
esys.downunder.forwardmodels.pressure.transpose(arg, axis_offset=None)¶ Returns the transpose of
argby swapping the firstaxis_offsetand the lastrank-axis_offsetcomponents.Parameters: - arg (
escript.Data,Symbol,numpy.ndarray,float,int) – argument - axis_offset (
int) – the firstaxis_offsetcomponents are swapped with the rest.axis_offsetmust be non-negative and less or equal to the rank ofarg. Ifaxis_offsetis not presentint(r/2)where r is the rank ofargis used.
Returns: transpose of
argReturn type: escript.Data,Symbol,numpy.ndarray,float,intdepending on the type ofarg- arg (
-
esys.downunder.forwardmodels.pressure.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 tomatrix_mult(transpose(arg0),arg1).The first dimension of
arg0andarg1must 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
arg0andarg1at each data pointReturn type: numpy.ndarray,escript.Data,Symboldepending on the inputRaises: ValueError – if the shapes of the arguments are not appropriate
- arg0 (
-
esys.downunder.forwardmodels.pressure.transposed_tensor_mult(arg0, arg1)¶ The tensor product of the transpose of the first and the second argument.
For
arg0of rank 2 this isout[s0]=Sigma_{r0} arg0[r0,s0]*arg1[r0]or
out[s0,s1]=Sigma_{r0} arg0[r0,s0]*arg1[r0,s1]and for
arg0of rank 4 this isout[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
arg0and the first dimension ofarg1must match and in the second case the two first dimensions ofarg0must match the two first dimensions ofarg1.The function call
transposed_tensor_mult(arg0,arg1)is equivalent totensor_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 ofarg0
Returns: the tensor product of transpose of arg0 and arg1 at each data point
Return type: numpy.ndarray,escript.Data,Symboldepending on the input- arg0 (
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esys.downunder.forwardmodels.pressure.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.Domainorescript.FunctionSpace) – dimension or an object that has thegetDimmethod 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.ndarrayorescript.Dataof rank 1- i (
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esys.downunder.forwardmodels.pressure.vol(arg)¶ Returns the volume or area of the oject
argParameters: arg ( escript.FunctionSpaceorescript.Domain) – a geometrical objectReturn type: float
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esys.downunder.forwardmodels.pressure.whereNegative(arg)¶ Returns mask of negative values of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.whereNonNegative(arg)¶ Returns mask of non-negative values of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.whereNonPositive(arg)¶ Returns mask of non-positive values of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.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. Iftolis not presentrtol``*```Lsup` (arg)is used.
Return type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: - ValueError – if
rtolis non-negative. - TypeError – if the type of the argument is not expected
- arg (
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esys.downunder.forwardmodels.pressure.wherePositive(arg)¶ Returns mask of positive values of argument
arg.Parameters: arg ( float,escript.Data,Symbol,numpy.ndarray.) – argumentReturn type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: TypeError – if the type of the argument is not expected
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esys.downunder.forwardmodels.pressure.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. Iftolis not presentrtol``*```Lsup` (arg)is used. - rtol (non-negative
float) – relative tolerance used to define the absolute tolerance iftolis not present.
Return type: float,escript.Data,Symbol,numpy.ndarraydepending on the type ofargRaises: - ValueError – if
rtolis non-negative. - TypeError – if the type of the argument is not expected
- arg (
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esys.downunder.forwardmodels.pressure.zeros(shape=())¶ Returns the
shapezero tensor.Parameters: shape ( tupleofint) – input shape for the identity tensorReturns: array of shape filled with zeros Return type: numpy.ndarray
Others¶
- DBLE_MAX
- EPSILON
- PI