Inheritance diagram for PyTrilinos.NOX.Epetra.FiniteDifference:

Collaboration diagram for PyTrilinos.NOX.Epetra.FiniteDifference:

Public Member Functions
def	__init__
def	Label
def	SetUseTranspose
def	Apply
def	ApplyInverse
def	UseTranspose
def	HasNormInf
def	OperatorDomainMap
def	OperatorRangeMap
def	Filled
def	NumMyRowEntries
def	MaxNumEntries
def	ExtractMyRowCopy
def	ExtractDiagonalCopy
def	Multiply
def	Solve
def	InvRowSums
def	LeftScale
def	InvColSums
def	RightScale
def	NormInf
def	NormOne
def	NumGlobalNonzeros
def	NumGlobalNonzeros64
def	NumGlobalRows
def	NumGlobalRows64
def	NumGlobalCols
def	NumGlobalCols64
def	NumGlobalDiagonals
def	NumGlobalDiagonals64
def	NumMyNonzeros
def	NumMyRows
def	NumMyCols
def	NumMyDiagonals
def	LowerTriangular
def	UpperTriangular
def	Comm
def	RowMatrixRowMap
def	RowMatrixColMap
def	RowMatrixImporter
def	Map
def	computeJacobian
def	computePreconditioner
def	setDifferenceMethod
def	getUnderlyingMatrix
def	setGroupForComputeF
Public Attributes
	this
Static Public Attributes
	Forward = ___init__.FiniteDifference_Forward
	Backward = ___init__.FiniteDifference_Backward
	Centered = ___init__.FiniteDifference_Centered

Detailed Description

Concrete implementation for creating an Epetra_RowMatrix Jacobian via
finite differencing of the residual.

The Jacobian entries are calculated via 1st order finite differencing.
This requires $ N + 1 $ calls to computeF() where $ N $ is the number
of unknowns in the problem.

\\[ J_{ij} = \\frac{\\partial F_i}{\\partial x_j} =
\\frac{F_i(x+\\delta\\mathbf{e}_j) - F_i(x)}{\\delta} \\]

where $J$ is the Jacobian, $F$ is the function evaluation, $x$ is the
solution vector, and $\\delta$ is a small perturbation to the $x_j$
entry.

The perturbation, $ \\delta $, is calculated based on one of the
following equations:

\\[ \\delta = \\alpha * | x_j | + \\beta \\] \\[ \\delta
= \\alpha * | x_j | + \\beta_j \\]

where $ \\alpha $ is a scalar value (defaults to 1.0e-4) and $
\\beta $ can be either a scalar or a vector (defaults to a scalar
value of 1.0e-6). The choice is defined by the type of constructor
used. All parameters are supplied in the constructor. In addition to
the forward difference derivative approximation, backward or centered
differences can be used via the setDifferenceMethod function. Note
that centered difference provides second order spatial accuracy but at
the cost of twice as many function evaluations.

Since this inherits from the Epetra_RowMatrix class, it can be used as
the preconditioning matrix for AztecOO preconditioners. This method is
very inefficient when computing the Jacobian and is not recommended
for large-scale systems but only for debugging purposes.

C++ includes: NOX_Epetra_FiniteDifference.H

Constructor & Destructor Documentation

def PyTrilinos.NOX.Epetra.FiniteDifference.__init__	(	self,
		args
	)

__init__(NOX::Epetra::FiniteDifference self, ParameterList printingParams, Teuchos::RCP< NOX::Epetra::Interface::Required > const & i, 
    Vector initialGuess, double beta=1.0e-6, double alpha=1.0e-4) -> FiniteDifference
__init__(NOX::Epetra::FiniteDifference self, ParameterList printingParams, Teuchos::RCP< NOX::Epetra::Interface::Required > const & i, 
    Vector initialGuess, Teuchos::RCP< Epetra_Vector const > const & beta, 
    double alpha=1.0e-4) -> FiniteDifference
__init__(NOX::Epetra::FiniteDifference self, ParameterList printingParams, Teuchos::RCP< NOX::Epetra::Interface::Required > const & i, 
    Vector initialGuess, Teuchos::RCP< Epetra_CrsGraph > const & g, double beta=1.0e-6, 
    double alpha=1.0e-4) -> FiniteDifference
__init__(NOX::Epetra::FiniteDifference self, ParameterList printingParams, Teuchos::RCP< NOX::Epetra::Interface::Required > const & i, 
    Vector initialGuess, Teuchos::RCP< Epetra_CrsGraph > const & g, Teuchos::RCP< Epetra_Vector const > const & beta, 
    double alpha=1.0e-4) -> FiniteDifference

FiniteDifference::FiniteDifference(Teuchos::ParameterList
&printingParams, const Teuchos::RCP< NOX::Epetra::Interface::Required
> &i, const NOX::Epetra::Vector &initialGuess, const Teuchos::RCP<
Epetra_CrsGraph > &g, const Teuchos::RCP< const Epetra_Vector > &beta,
double alpha=1.0e-4)

Constructor with output control that takes a pre-constructed
Epetra_CrsGraph so it does not have to determine the non-zero entries
in the matrix.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

Reimplemented in PyTrilinos.NOX.Epetra.FiniteDifferenceColoring.

Member Function Documentation

def PyTrilinos.NOX.Epetra.FiniteDifference.Apply	(	self,
		args
	)

Apply(FiniteDifference self, Epetra_MultiVector X, Epetra_MultiVector Y) -> int

int
FiniteDifference::Apply(const Epetra_MultiVector &X,
Epetra_MultiVector &Y) const

Return the result on an Epetra_Operator applied to an
Epetra_MultiVector X in Y.

Reimplemented from PyTrilinos.NOX.Epetra.Operator.

def PyTrilinos.NOX.Epetra.FiniteDifference.ApplyInverse	(	self,
		args
	)

ApplyInverse(FiniteDifference self, Epetra_MultiVector X, Epetra_MultiVector Y) -> int

int FiniteDifference::ApplyInverse(const Epetra_MultiVector &X,
Epetra_MultiVector &Y) const

Return the result on an Epetra_Operator inverse applied to an
Epetra_MultiVector X in Y.

Reimplemented from PyTrilinos.NOX.Epetra.Operator.

def PyTrilinos.NOX.Epetra.FiniteDifference.Comm	(	self,
		args
	)

Comm(FiniteDifference self) -> Comm

const
Epetra_Comm & FiniteDifference::Comm() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.Operator.

def PyTrilinos.NOX.Epetra.FiniteDifference.computeJacobian	(	self,
		args
	)

computeJacobian(FiniteDifference self, Epetra_Vector x, Operator Jac) -> bool
computeJacobian(FiniteDifference self, Epetra_Vector x) -> bool

bool FiniteDifference::computeJacobian(const Epetra_Vector &x)

Compute Jacobian given the specified input vector, x. Returns true if
computation was successful.

Reimplemented from PyTrilinos.NOX.Epetra.Interface.Jacobian.

Reimplemented in PyTrilinos.NOX.Epetra.FiniteDifferenceColoring.

def PyTrilinos.NOX.Epetra.FiniteDifference.computePreconditioner	(	self,
		args
	)

computePreconditioner(FiniteDifference self, Epetra_Vector x, Operator Prec, ParameterList precParams=None) -> bool

bool
FiniteDifference::computePreconditioner(const Epetra_Vector &x,
Epetra_Operator &Prec, Teuchos::ParameterList *precParams=0)

Compute an Epetra_RowMatrix to be used by Aztec preconditioners given
the specified input vector, x. Returns true if computation was
successful.

Reimplemented from PyTrilinos.NOX.Epetra.Interface.Preconditioner.

def PyTrilinos.NOX.Epetra.FiniteDifference.ExtractDiagonalCopy	(	self,
		args
	)

ExtractDiagonalCopy(FiniteDifference self, Epetra_Vector Diagonal) -> int

int
FiniteDifference::ExtractDiagonalCopy(Epetra_Vector &Diagonal) const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.ExtractMyRowCopy	(	self,
		args
	)

ExtractMyRowCopy(FiniteDifference self, int MyRow, int Length, int & NumEntries, double * Values, int * Indices) -> int

int FiniteDifference::ExtractMyRowCopy(int MyRow, int Length, int
&NumEntries, double *Values, int *Indices) const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.Filled	(	self,
		args
	)

Filled(FiniteDifference self) -> bool

bool
FiniteDifference::Filled() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.getUnderlyingMatrix	(	self,
		args
	)

getUnderlyingMatrix(FiniteDifference self) -> CrsMatrix

Epetra_CrsMatrix
& FiniteDifference::getUnderlyingMatrix() const

An accessor method for the underlying Epetra_CrsMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.HasNormInf	(	self,
		args
	)

HasNormInf(FiniteDifference self) -> bool

bool FiniteDifference::HasNormInf() const

Returns true if the this object can provide an approximate Inf-norm,
false otherwise.

Reimplemented from PyTrilinos.NOX.Epetra.Operator.

def PyTrilinos.NOX.Epetra.FiniteDifference.InvColSums	(	self,
		args
	)

InvColSums(FiniteDifference self, Epetra_Vector x) -> int

int
FiniteDifference::InvColSums(Epetra_Vector &x) const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.InvRowSums	(	self,
		args
	)

InvRowSums(FiniteDifference self, Epetra_Vector x) -> int

int
FiniteDifference::InvRowSums(Epetra_Vector &x) const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.Label	(	self,
		args
	)

Label(FiniteDifference self) -> char const *

const
char * FiniteDifference::Label() const

Returns a character string describing the name of the operator.

Reimplemented from PyTrilinos.NOX.Epetra.Operator.

def PyTrilinos.NOX.Epetra.FiniteDifference.LeftScale	(	self,
		args
	)

LeftScale(FiniteDifference self, Epetra_Vector x) -> int

int
FiniteDifference::LeftScale(const Epetra_Vector &x)

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.LowerTriangular	(	self,
		args
	)

LowerTriangular(FiniteDifference self) -> bool

bool FiniteDifference::LowerTriangular() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.Map	(	self,
		args
	)

Map(FiniteDifference self) -> BlockMap

const
Epetra_BlockMap & FiniteDifference::Map() const

See Epetra_SrcDistObj documentation.

Reimplemented from PyTrilinos.NOX.Epetra.SrcDistObject.

def PyTrilinos.NOX.Epetra.FiniteDifference.MaxNumEntries	(	self,
		args
	)

MaxNumEntries(FiniteDifference self) -> int

int FiniteDifference::MaxNumEntries() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.Multiply	(	self,
		args
	)

Multiply(FiniteDifference self, bool TransA, Epetra_MultiVector X, Epetra_MultiVector Y) -> int

int
FiniteDifference::Multiply(bool TransA, const Epetra_MultiVector &X,
Epetra_MultiVector &Y) const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NormInf	(	self,
		args
	)

NormInf(FiniteDifference self) -> double

double
FiniteDifference::NormInf() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NormOne	(	self,
		args
	)

NormOne(FiniteDifference self) -> double

double
FiniteDifference::NormOne() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumGlobalCols	(	self,
		args
	)

NumGlobalCols(FiniteDifference self) -> int

int FiniteDifference::NumGlobalCols() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumGlobalCols64	(	self,
		args
	)

NumGlobalCols64(FiniteDifference self) -> long long

long long FiniteDifference::NumGlobalCols64() const

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumGlobalDiagonals	(	self,
		args
	)

NumGlobalDiagonals(FiniteDifference self) -> int

int
FiniteDifference::NumGlobalDiagonals() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumGlobalDiagonals64	(	self,
		args
	)

NumGlobalDiagonals64(FiniteDifference self) -> long long

long long
FiniteDifference::NumGlobalDiagonals64() const

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumGlobalNonzeros	(	self,
		args
	)

NumGlobalNonzeros(FiniteDifference self) -> int

int
FiniteDifference::NumGlobalNonzeros() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumGlobalNonzeros64	(	self,
		args
	)

NumGlobalNonzeros64(FiniteDifference self) -> long long

long long
FiniteDifference::NumGlobalNonzeros64() const

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumGlobalRows	(	self,
		args
	)

NumGlobalRows(FiniteDifference self) -> int

int FiniteDifference::NumGlobalRows() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumGlobalRows64	(	self,
		args
	)

NumGlobalRows64(FiniteDifference self) -> long long

long long FiniteDifference::NumGlobalRows64() const

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumMyCols	(	self,
		args
	)

NumMyCols(FiniteDifference self) -> int

int
FiniteDifference::NumMyCols() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumMyDiagonals	(	self,
		args
	)

NumMyDiagonals(FiniteDifference self) -> int

int FiniteDifference::NumMyDiagonals() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumMyNonzeros	(	self,
		args
	)

NumMyNonzeros(FiniteDifference self) -> int

int FiniteDifference::NumMyNonzeros() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumMyRowEntries	(	self,
		args
	)

NumMyRowEntries(FiniteDifference self, int MyRow, int & NumEntries) -> int

int FiniteDifference::NumMyRowEntries(int MyRow, int &NumEntries)
const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.NumMyRows	(	self,
		args
	)

NumMyRows(FiniteDifference self) -> int

int
FiniteDifference::NumMyRows() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.OperatorDomainMap	(	self,
		args
	)

OperatorDomainMap(FiniteDifference self) -> Map

const Epetra_Map &
FiniteDifference::OperatorDomainMap() const

Returns the Epetra_BlockMap object associated with the domain of this
matrix operator.

Reimplemented from PyTrilinos.NOX.Epetra.Operator.

def PyTrilinos.NOX.Epetra.FiniteDifference.OperatorRangeMap	(	self,
		args
	)

OperatorRangeMap(FiniteDifference self) -> Map

const Epetra_Map & FiniteDifference::OperatorRangeMap() const

Returns the Epetra_BlockMap object associated with the range of this
matrix operator.

Reimplemented from PyTrilinos.NOX.Epetra.Operator.

def PyTrilinos.NOX.Epetra.FiniteDifference.RightScale	(	self,
		args
	)

RightScale(FiniteDifference self, Epetra_Vector x) -> int

int
FiniteDifference::RightScale(const Epetra_Vector &x)

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.RowMatrixColMap	(	self,
		args
	)

RowMatrixColMap(FiniteDifference self) -> Map

const Epetra_Map & FiniteDifference::RowMatrixColMap() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.RowMatrixImporter	(	self,
		args
	)

RowMatrixImporter(FiniteDifference self) -> Import

const Epetra_Import
* FiniteDifference::RowMatrixImporter() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.RowMatrixRowMap	(	self,
		args
	)

RowMatrixRowMap(FiniteDifference self) -> Map

const Epetra_Map & FiniteDifference::RowMatrixRowMap() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.setDifferenceMethod	(	self,
		args
	)

setDifferenceMethod(FiniteDifference self, NOX::Epetra::FiniteDifference::DifferenceType type)

void
FiniteDifference::setDifferenceMethod(DifferenceType type)

Set the type of perturbation method used (default is Forward)

def PyTrilinos.NOX.Epetra.FiniteDifference.setGroupForComputeF	(	self,
		args
	)

setGroupForComputeF(FiniteDifference self, Group group)

void
FiniteDifference::setGroupForComputeF(NOX::Abstract::Group &group)

Register a NOX::Abstract::Group derived object and use the computeF()
method of that group for the perturbation instead of the
NOX::Epetra::Interface::Required::computeF() method. This is required
for LOCA to get the operators correct during homotopy.

def PyTrilinos.NOX.Epetra.FiniteDifference.SetUseTranspose	(	self,
		args
	)

SetUseTranspose(FiniteDifference self, bool UseTranspose) -> int

int FiniteDifference::SetUseTranspose(bool UseTranspose)

If set true, the transpose of this operator will be applied.

Reimplemented from PyTrilinos.NOX.Epetra.Operator.

def PyTrilinos.NOX.Epetra.FiniteDifference.Solve	(	self,
		args
	)

Solve(FiniteDifference self, bool Upper, bool Trans, bool UnitDiagonal, Epetra_MultiVector X, Epetra_MultiVector Y) -> int

int
FiniteDifference::Solve(bool Upper, bool Trans, bool UnitDiagonal,
const Epetra_MultiVector &X, Epetra_MultiVector &Y) const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.UpperTriangular	(	self,
		args
	)

UpperTriangular(FiniteDifference self) -> bool

bool FiniteDifference::UpperTriangular() const

See Epetra_RowMatrix documentation.

Reimplemented from PyTrilinos.NOX.Epetra.RowMatrix.

def PyTrilinos.NOX.Epetra.FiniteDifference.UseTranspose	(	self,
		args
	)

UseTranspose(FiniteDifference self) -> bool

bool FiniteDifference::UseTranspose() const

Returns the current use transpose setting.

Reimplemented from PyTrilinos.NOX.Epetra.Operator.

The documentation for this class was generated from the following file:

NOX/Epetra/__init__.py

Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation