Concrete implementation for creating an Epetra_Operator Jacobian based on the Matrix-Free Newton-Krylov method. More...

#include <NOX_Epetra_MatrixFree.H>

Inheritance diagram for NOX::Epetra::MatrixFree:

Collaboration diagram for NOX::Epetra::MatrixFree:

Public Types
enum	DifferenceType { Forward, Backward, Centered }
	Define types for use of the perturbation parameter $\delta$ .

Public Member Functions
	MatrixFree (Teuchos::ParameterList &printParams, const Teuchos::RCP< NOX::Epetra::Interface::Required > &i, const NOX::Epetra::Vector &cloneVector, bool useNewPerturbation=false)
	Constructor. More...

virtual	~MatrixFree ()
	Pure virtual destructor.

virtual int	SetUseTranspose (bool UseTranspose)
	If set true, transpose of this operator will be applied. More...

virtual int	Apply (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
	Returns the result of a Epetra_Operator applied to a Epetra_MultiVector X in Y. More...

virtual int	ApplyInverse (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
	Returns the result of a Epetra_Operator inverse applied to an Epetra_MultiVector X in Y. More...

virtual double	NormInf () const
	Returns the infinity norm of the global matrix.

virtual const char *	Label () const
	Returns a character std::string describing the operator.

virtual bool	UseTranspose () const
	Returns the current UseTranspose setting.

virtual bool	HasNormInf () const
	Returns true if the this object can provide an approximate Inf-norm, false otherwise.

virtual const Epetra_Comm &	Comm () const
	Returns a reference to the Epetra_Comm communicator associated with this operator.

virtual const Epetra_Map &	OperatorDomainMap () const
	Returns the Epetra_BlockMap object associated with the domain of this matrix operator.

virtual const Epetra_Map &	OperatorRangeMap () const
	Returns the Epetra_BlockMap object associated with the range of this matrix operator.

virtual bool	computeJacobian (const Epetra_Vector &x, Epetra_Operator &Jac)
	Compute Jacobian given the specified input vector, x. Returns true if computation was successful.

virtual void	setDifferenceMethod (DifferenceType type)
	Set the type of perturbation method used (default is Forward)

void	setLambda (double lambda_)
	Allows the user to change the value of $\lambda$ in the perturbation calculation.

void	setComputePerturbation (bool bVal)

void	setPerturbation (double eta_)
	Set the perturbation parameter $\eta$ .

double	getPerturbation () const
	Returns the most recently used value of the perturbation parameter $\eta$ .

void	setGroupForComputeF (const NOX::Abstract::Group &group)
	Clone 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.

void	setSolverForComputeJacobian (const Teuchos::RCP< NOX::Solver::Generic > &slvr)
	Save a RCP to a solver, and use the Solver's current Group's computeF() in the computeJacobian call, which can save a function call by respecting the isValid flag.

Public Member Functions inherited from NOX::Epetra::Interface::Jacobian
	Jacobian ()
	Constructor.

virtual	~Jacobian ()
	Destructor.

Protected Attributes
std::string	label
	Label for matrix.

Teuchos::RCP < NOX::Epetra::Interface::Required >	interface
	User provided interface function.

NOX::Epetra::Vector	currentX
	The current solution vector.

NOX::Epetra::Vector	perturbX
	Perturbed solution vector.

NOX::Epetra::Vector	fo
	Function evaluation at currentX.

NOX::Epetra::Vector	fp
	Function evaluation at perturbX.

Teuchos::RCP< NOX::Epetra::Vector >	fmPtr
	Optional pointer to function evaluation at -perturbX - needed only for centered finite differencing.

Teuchos::RCP< const Epetra_Map >	epetraMap

DifferenceType	diffType
	Define types for use of the perturbation parameter $\delta$ .

double	lambda
	Scale factor for eta calculation.

double	eta
	Perturbation value to use in the directional derivative.

double	userEta
	User specified perturbation value to use in the directional derivative. Set by setPerturbation().

bool	computeEta
	Flag that determines if we should calculate eta or use a value set by the user.

bool	useGroupForComputeF
	Flag to enables the use of a group instead of the interface for the computeF() calls in the directional difference calculation.

bool	useSolverForComputeJacobian
	Flag to enables the use of Solver's Group instead of the interface for the computeF() calls in the directional difference calculation, to make use of isValid flags.

bool	useNewPerturbation
	A new perturbation formulation developed by C. T. Kelley and A. G. Salinger can be used by the constructor flag useNewPerturbation = true.

Teuchos::RCP < NOX::Abstract::Group >	groupPtr
	Pointer to the group for possible use in computeF() calls.

Teuchos::RCP < NOX::Solver::Generic >	slvrPtr
	Pointer to the Solver for possible use in computeF() calls.

NOX::Utils	utils
	Printing utilities.

Detailed Description

Concrete implementation for creating an Epetra_Operator Jacobian based on the Matrix-Free Newton-Krylov method.

Matrix-Free Newton-Krylov is a method that takes advantage of the fact the Newton Krylov solvers do not require an explicit Jacobian matrix. Newton-Krylov solvers only require the matrix-vector product $ Jy$ in the iteration sequence. This product can approximated by the following:

$Jy = \frac{F(x + \delta y) - F(x)}{\delta}$

where $ J$ is the Jacobian, $ F$ is the function evaluation, $ x$ is the solution vector, $ y$ is the vector to be operated on, and $\delta$ is a scalar perturbation calculated by:

$\delta = \lambda * (\lambda + \frac{\| x\|}{\| y\|} )$

where $\lambda = 1.0e-6$ .

Constructor & Destructor Documentation

MatrixFree::MatrixFree	(	Teuchos::ParameterList &	printParams,
		const Teuchos::RCP< NOX::Epetra::Interface::Required > &	i,
		const NOX::Epetra::Vector &	cloneVector,
		bool	useNewPerturbation = `false`
	)

Constructor.

The vector x is used to clone the solution vector.

References currentX, epetraMap, fo, fp, NOX::Epetra::Vector::getEpetraVector(), NOX::Epetra::Vector::init(), perturbX, and Teuchos::rcp().

Member Function Documentation

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

virtual

Returns the result of a Epetra_Operator applied to a Epetra_MultiVector X in Y.

Parameters

X	- A Epetra_MultiVector of dimension NumVectors to multiply with matrix.
Y	-A Epetra_MultiVector of dimension NumVectors containing result.

Returns: Integer error code, set to 0 if successful.

Implements Epetra_Operator.

References computeEta, NOX::Epetra::Interface::Required::computeF(), NOX::Abstract::Group::computeF(), NOX::Epetra::Vector::CreateView, currentX, diffType, eta, fmPtr, fo, fp, NOX::Epetra::Vector::getEpetraVector(), NOX::Abstract::Group::getF(), NOX::Epetra::Vector::getVectorSpace(), groupPtr, interface, Teuchos::is_null(), lambda, NOX::Epetra::Interface::Required::MF_Res, NOX::Epetra::Vector::norm(), perturbX, Teuchos::rcp(), NOX::Epetra::Vector::scale(), NOX::Abstract::Group::setX(), useGroupForComputeF, useNewPerturbation, userEta, and View.

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

virtual

Returns the result of a Epetra_Operator inverse applied to an Epetra_MultiVector X in Y.

Parameters

X	- A Epetra_MultiVector of dimension NumVectors to solve for.
Y	-A Epetra_MultiVector of dimension NumVectors containing result.

Returns: Integer error code, set to 0 if successful.

Warning: In order to work with AztecOO, any implementation of this method must support the case where X and Y are the same object.

Implements Epetra_Operator.

References NOX::Utils::out(), TEUCHOS_UNREACHABLE_RETURN, and utils.

void MatrixFree::setComputePerturbation ( bool bVal )

Flag that toggles whether MatrixFree should compute the perturbation parameter $\eta$ or use a value supplied by the user through setPerturbation().

References computeEta.

int MatrixFree::SetUseTranspose ( bool UseTranspose )

virtual

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

This flag allows the transpose of the given operator to be used implicitly. Setting this flag affects only the Apply() and ApplyInverse() methods. If the implementation of this interface does not support transpose use, this method should return a value of -1.

Parameters

UseTranspose -If true, multiply by the transpose of operator, otherwise just use operator.

Returns: Integer error code, set to 0 if successful. Set to -1 if this implementation does not support transpose.

Implements Epetra_Operator.

References NOX::Utils::out(), and utils.

Member Data Documentation

Teuchos::RCP<const Epetra_Map> NOX::Epetra::MatrixFree::epetraMap

protected

Epetra_Map object used in the returns of the Epetra_Operator derived methods.

If the user is using Epetra_BlockMaps, then NOX::Epetra::MatrixFree must create an equivalent Epetra_Map from the Epetra_BlockMap that can be used as the return object of the OperatorDomainMap() and OperatorRangeMap() methods.

Referenced by MatrixFree(), OperatorDomainMap(), and OperatorRangeMap().

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

NOX_Epetra_MatrixFree.H
NOX_Epetra_MatrixFree.C

Public Types

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation