Ifpack_PointRelaxation: a class to define point relaxation preconditioners of for Epetra_RowMatrix's. More...

#include <Ifpack_PointRelaxation.h>

Inheritance diagram for Ifpack_PointRelaxation:

Collaboration diagram for Ifpack_PointRelaxation:

Public Member Functions
virtual int	SetUseTranspose (bool UseTranspose_in)

	Ifpack_PointRelaxation (const Epetra_RowMatrix *Matrix)
	Ifpack_PointRelaxation constructor with given Epetra_RowMatrix.
virtual	~Ifpack_PointRelaxation ()
	Destructor.

virtual int	Apply (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
	Applies the matrix to an Epetra_MultiVector.
virtual int	ApplyInverse (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
	Applies the preconditioner to X, returns the result in Y.
virtual double	NormInf () const
	Returns the infinity norm of the global matrix (not implemented)

virtual const char *	Label () const
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 pointer 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 operator.
virtual const Epetra_Map &	OperatorRangeMap () const
	Returns the Epetra_Map object associated with the range of this operator.
virtual int	Initialize ()
	Computes all it is necessary to initialize the preconditioner.
virtual bool	IsInitialized () const
	Returns true if the preconditioner has been successfully initialized, false otherwise.
virtual bool	IsComputed () const
	Returns `true` if the preconditioner has been successfully computed.
virtual int	Compute ()
	Computes the preconditioners.

virtual const Epetra_RowMatrix &	Matrix () const
	Returns a pointer to the matrix to be preconditioned.
virtual double	Condest (const Ifpack_CondestType CT=Ifpack_Cheap, const int MaxIters=1550, const double Tol=1e-9, Epetra_RowMatrix *Matrix=0)
	Computes the condition number estimates and returns the value.
virtual double	Condest () const
	Returns the condition number estimate, or -1.0 if not computed.
virtual int	SetParameters (Teuchos::ParameterList &List)
	Sets all the parameters for the preconditioner.
virtual ostream &	Print (ostream &os) const
	Prints object to an output stream.

virtual int	NumInitialize () const
	Returns the number of calls to Initialize().
virtual int	NumCompute () const
	Returns the number of calls to Compute().
virtual int	NumApplyInverse () const
	Returns the number of calls to ApplyInverse().
virtual double	InitializeTime () const
	Returns the time spent in Initialize().
virtual double	ComputeTime () const
	Returns the time spent in Compute().
virtual double	ApplyInverseTime () const
	Returns the time spent in ApplyInverse().
virtual double	InitializeFlops () const
	Returns the number of flops in the initialization phase.
virtual double	ComputeFlops () const
	Returns the number of flops in the computation phase.
virtual double	ApplyInverseFlops () const
	Returns the number of flops for the application of the preconditioner.

Detailed Description

Ifpack_PointRelaxation: a class to define point relaxation preconditioners of for Epetra_RowMatrix's.

The Ifpack_PointRelaxation class enables the construction of point relaxation preconditioners of an Epetra_RowMatrix. Ifpack_PointRelaxation is derived from the Ifpack_Preconditioner class, which is itself derived from Epetra_Operator. Therefore this object can be used as preconditioner everywhere an ApplyInverse() method is required in the preconditioning step.

This class enables the construction of the following simple preconditioners:

Jacobi;
Gauss-Seidel;
symmetric Gauss-Seidel.

We now briefly describe the main features of the above preconditioners. Consider a linear system of type

$A x = b,$

where $A$ is a square, real matrix, and $x, b$ are two real vectors. We begin with the decomposition

$A = D - E - F$

where $D$ is the diagonal of A, $-E$ is the strict lower part, and $-F$ is the strict upper part. It is assumed that the diagonal entries of $A$ are different from zero.

Given an starting solution $x_0$ , an iteration of the (damped) Jacobi method can be written in matrix form as follows:

$x_{k+1} = \omega D^{-1}(E + F) x_k + D_{-1}b,$

for $k < k_{max}$ , and $\omega$ a damping parameter.

Using Ifpack_Jacobi, the user can apply the specified number of sweeps ( $k_{max}$ ), and the damping parameter. If only one sweep is used, then the class simply applies the inverse of the diagonal of A to the input vector.

Given an starting solution $x_0$ , an iteration of the (damped) GaussSeidel method can be written in matrix form as follows:

$(D - E) x_{k+1} = \omega F x_k + b,$

for $k < k_{max}$ , and $\omega$ a damping parameter. Equivalently, the Gauss-Seidel preconditioner can be defined as

$P_{GS}^{-1} = (D - E)^{-1}.$

Clearly, the role of E and F can be interchanged. However, Ifpack_GaussSeidel does not consider backward Gauss-Seidel methods.

For a list of supported parameters, please refer to page List of Supported Parameters.

The complete list of supported parameters is reported in page List of Supported Parameters. For a presentation of basic relaxation schemes, please refer to page Ifpack_PointRelaxation.

Author:: Marzio Sala, SNL 9214.

Date:: Last modified on 22-Jan-05.

Definition at line 117 of file Ifpack_PointRelaxation.h.

Constructor & Destructor Documentation

Ifpack_PointRelaxation::Ifpack_PointRelaxation ( const Epetra_RowMatrix * Matrix )

Ifpack_PointRelaxation constructor with given Epetra_RowMatrix.

Creates an instance of Ifpack_PointRelaxation class.

Parameters:

Matrix - (In) Pointer to matrix to precondition.

Definition at line 49 of file Ifpack_PointRelaxation.cpp.

Member Function Documentation

virtual int Ifpack_PointRelaxation::Apply	(	const Epetra_MultiVector &	X,
		Epetra_MultiVector &	Y
	)		const `[inline, virtual]`

Applies the matrix to an Epetra_MultiVector.

Parameters:

X	- (In) A Epetra_MultiVector of dimension NumVectors to multiply with matrix.
Y	- (Out) A Epetra_MultiVector of dimension NumVectors containing the result.

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

Definition at line 160 of file Ifpack_PointRelaxation.h.

References IsComputed(), and UseTranspose().

int Ifpack_PointRelaxation::ApplyInverse	(	const Epetra_MultiVector &	X,
		Epetra_MultiVector &	Y
	)		const `[virtual]`

Applies the preconditioner to X, returns the result in Y.

Parameters:

X	- (In) A Epetra_MultiVector of dimension NumVectors to be preconditioned.
Y	- (InOut) A Epetra_MultiVector of dimension NumVectors containing result.

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

Warning:: This routine is NOT AztecOO complaint.

Implements Ifpack_Preconditioner.

Definition at line 375 of file Ifpack_PointRelaxation.cpp.

References IsComputed().

virtual int Ifpack_PointRelaxation::SetUseTranspose ( bool UseTranspose_in ) [inline, virtual]

This flag can be used to apply the preconditioner to the transpose of the input operator.

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

Definition at line 141 of file Ifpack_PointRelaxation.h.

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

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation