Epetra operator representing a $n+m$ bordered matrix. More...

#include <LOCA_Epetra_AugmentedOp.H>

Inheritance diagram for LOCA::Epetra::AugmentedOp:

Collaboration diagram for LOCA::Epetra::AugmentedOp:

Public Member Functions
	AugmentedOp (const Teuchos::RCP< LOCA::GlobalData > &global_data, const Teuchos::RCP< Epetra_Operator > &jac, const Teuchos::RCP< const Epetra_MultiVector > &a, const Teuchos::RCP< const Epetra_MultiVector > &b, const Teuchos::RCP< const NOX::Abstract::MultiVector::DenseMatrix > c)
	Constructor. More...

virtual	~AugmentedOp ()
	Destructor.

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

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

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

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_Map object associated with the domain of this matrix operator.

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

virtual void	init (const Epetra_MultiVector &x)
	Initialiazes operator for a solve.

virtual Teuchos::RCP < Epetra_MultiVector >	buildEpetraAugmentedMultiVec (const Epetra_MultiVector &x, const NOX::Abstract::MultiVector::DenseMatrix *y, bool doCopy) const
	Builds an extended vector from components. More...

virtual void	setEpetraAugmentedMultiVec (Epetra_MultiVector &x, NOX::Abstract::MultiVector::DenseMatrix &y, const Epetra_MultiVector &augMultiVec) const
	Sets components from extended vector. More...

Protected Member Functions
void	buildExtendedMap (const Epetra_BlockMap &map, Epetra_Map *&extMapPtr, bool buildImporter, bool haveParam)
	Builds extended domain, range maps.

int	blockMap2PointMap (const Epetra_BlockMap &BlockMap, Epetra_Map *&PointMap) const
	Converts a block map to an equivalent point map.

Protected Attributes
Teuchos::RCP< LOCA::GlobalData >	globalData
	LOCA global data object.

std::string	label
	Label for operator.

Teuchos::RCP< Epetra_Operator >	jacOperator
	Stores operator representing .

const Epetra_BlockMap &	underlyingMap
	Stores underlying domain map.

const Epetra_Comm &	underlyingComm
	Stores comm.

Epetra_LocalMap	localMap
	Local map for generating Epetra matrices.

Teuchos::RCP< const Epetra_MultiVector >	a
	Stores pointer to a multivector.

Teuchos::RCP< const Epetra_MultiVector >	b
	Stores pointer to b multivector.

Epetra_MultiVector	c
	Stores c matrix.

int	underlyingLength
	Stores underlying vector local length.

int	numConstraints
	Number of constraints.

Epetra_Map *	extendedMapPtr
	Stores extended domain map.

Epetra_Map *	extendedImportMapPtr
	Stores extended turning point map for importing param component.

Epetra_Import *	extendedImporter
	Stores importer object for importing param component.

Epetra_MultiVector *	importedInput
	Stores imported input multivector.

Epetra_MultiVector *	result_y
	Stores parameter component of result multivector.

Epetra_MultiVector *	tmp
	Stores temporary multivector used in ApplyInverse()

bool	haveParamComponent
	Flag indicating whether we have the parameter component.

bool	useTranspose
	Flag indicating whether to use transpose of operator.

Teuchos::LAPACK< int, double >	dlapack
	LAPACK Wrappers.

Detailed Description

Epetra operator representing a $n+m$ bordered matrix.

The LOCA::Epetra::AugmentedOp is an Epetra_Operator representing the $n+m$ bordered matrix

$\begin{bmatrix} J & A \\ B^T & C \end{bmatrix}$

where $J$ is an Epetra_Operator representing an $n\times n$ matrix, and $A$ and $B$ are length $n$ Epetra_MultiVector's with $m$ columns, and $C$ is an $m\times m$ dense matrix. It is assumed the Epetra_Map's for $A$ , $B$ , and $J$ are the same and the corresponding map for the bordered matrix is constructed from this map by storing the additional components on processor 0. The buildEpetraAugmentedMultiVec() method can be used to construct an Epetra_MultiVector using this map, a supplied length $n$ Epetra_MultiVector and an $m\times m$ matrix, while setEpetraAugmentedMultiVec() splits an extended multivector into its length $n$ and $m$ components. The Apply() method performs the $n+m\times n+m$ matrix multiplication while ApplyInverse() uses a block-elimination algorithm to compute the inverse using the ApplyInverse() method of the underlying operator $J$ . In this way, linear systems of the form

$\begin{bmatrix} J & A \\ B^T & C \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} F \\ G \end{bmatrix}$

can be solved in a matrix-free mode using the Apply() method. This operator can also represent a preconditioner of the form

$\begin{bmatrix} M & A \\ B^T & C \end{bmatrix}$

using the ApplyInvese() method, where $M$ is a preconditioner for $J$ . Note that if $J$ is nearly singular, the preconditioner should not be too good because otherwise the preconditining operation represented by ApplyInverse() becomes unstable.

Constructor & Destructor Documentation

LOCA::Epetra::AugmentedOp::AugmentedOp	(	const Teuchos::RCP< LOCA::GlobalData > &	global_data,
		const Teuchos::RCP< Epetra_Operator > &	jac,
		const Teuchos::RCP< const Epetra_MultiVector > &	a,
		const Teuchos::RCP< const Epetra_MultiVector > &	b,
		const Teuchos::RCP< const NOX::Abstract::MultiVector::DenseMatrix >	c
	)

Constructor.

Builds the bordered operator using the supplied operator jac and Epetra_Vector's a and b. It is assumed a, b, and jac all have the same map.

References buildExtendedMap(), extendedImporter, extendedImportMapPtr, extendedMapPtr, haveParamComponent, Epetra_Comm::MyPID(), underlyingComm, underlyingMap, and View.

Member Function Documentation

int LOCA::Epetra::AugmentedOp::Apply	(	const Epetra_MultiVector &	Input,
		Epetra_MultiVector &	Result
	)		const

virtual

Returns the result of a Epetra_Operator applied to a Epetra_MultiVector Input in Result.

Computes the extended matrix-vector product

$\begin{bmatrix} J & A \\ B^T & C \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} JX + AY \\ B^T X + CY \end{bmatrix}$

or its transpose if UseTranpose() is true.

Implements Epetra_Operator.

References Insert, and View.

int LOCA::Epetra::AugmentedOp::ApplyInverse	(	const Epetra_MultiVector &	X,
		Epetra_MultiVector &	Y
	)		const

virtual

Returns the result of a Epetra_Operator inverse applied to an Epetra_MultiVector Input in Result.

Solves the extended system

$\begin{bmatrix} J & A \\ B^T & C \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} F \\ G \end{bmatrix}$

using the following block-elimination algorithm:

$\begin{split} X_1 &= J^{-1} F, \\ X_2 &= J^{-1} A, \\ Y &= (C-B^T X_2)^{-1}(G-B^T X_1), \\ X &= X_1 - X_2 Y \end{split}$

If UseTranpose() is true, the tranpose of the system is solved.

Implements Epetra_Operator.

References Insert, and View.

Teuchos::RCP< Epetra_MultiVector > LOCA::Epetra::AugmentedOp::buildEpetraAugmentedMultiVec	(	const Epetra_MultiVector &	x,
		const NOX::Abstract::MultiVector::DenseMatrix *	y,
		bool	doCopy
	)		const

virtual

Builds an extended vector from components.

Builds an extended vector using the map representing the bordered matrix. If doCopy is true, the contents of x are copied into the extended vector, otherwise only space for the extended vector is created.

References Teuchos::rcp().

Referenced by LOCA::BorderedSolver::EpetraAugmented::applyInverse().

double LOCA::Epetra::AugmentedOp::NormInf ( ) const

virtual

Returns the infinity norm of the bordered matrix.

This is defined only if NormInf() of the underlying operator $J$ is defined and is given by $\|J\|_\infty+\|A\|_\infty+\|B\|_\infty$ .

Implements Epetra_Operator.

void LOCA::Epetra::AugmentedOp::setEpetraAugmentedMultiVec	(	Epetra_MultiVector &	x,
		NOX::Abstract::MultiVector::DenseMatrix &	y,
		const Epetra_MultiVector &	augMultiVec
	)		const

virtual

Sets components from extended vector.

Splits the extended vector augMultiVec into components x and y by copying values out of extVec.

References Insert.

Referenced by LOCA::BorderedSolver::EpetraAugmented::applyInverse().

int LOCA::Epetra::AugmentedOp::SetUseTranspose ( bool UseTranspose )

virtual

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

Note that is only valid if the underlying operator $J$ supports a transpose.

Implements Epetra_Operator.

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

LOCA_Epetra_AugmentedOp.H
LOCA_Epetra_AugmentedOp.C

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation