Ifpack_Chebyshev: class for preconditioning with Chebyshev polynomials in Ifpack. More...

#include <Ifpack_Chebyshev.h>

Inheritance diagram for Ifpack_Chebyshev:

Collaboration diagram for Ifpack_Chebyshev:

Public Member Functions
virtual int	SetUseTranspose (bool UseTranspose_in)


	Ifpack_Chebyshev (const Epetra_Operator *Matrix)
	Ifpack_Chebyshev constructor with given Epetra_Operator/Epetra_RowMatrix. More...

	Ifpack_Chebyshev (const Epetra_RowMatrix *Matrix)
	Ifpack_Chebyshev constructor with given Epetra_Operator/Epetra_RowMatrix. More...

virtual	~Ifpack_Chebyshev ()
	Destructor.


virtual int	Apply (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
	Applies the matrix to an Epetra_MultiVector. More...

virtual int	ApplyInverse (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
	Applies the preconditioner to X, returns the result in Y. More...

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 double	GetLambdaMax ()
	Returns an approximation to the largest eigenvalue.

virtual double	GetLambdaMin ()
	Contains an approximation to the smallest eigenvalue.


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_in=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 std::ostream &	Print (std::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.

Static Public Member Functions

static int	PowerMethod (const Epetra_Operator &Operator, const Epetra_Vector &InvPointDiagonal, const int MaximumIterations, double &LambdaMax, const unsigned int *RngSeed=0)
	Simple power method to compute lambda_max.

static int	CG (const Epetra_Operator &Operator, const Epetra_Vector &InvPointDiagonal, const int MaximumIterations, double &lambda_min, double &lambda_max, const unsigned int *RngSeed=0)
	Uses AztecOO's CG to estimate lambda_min and lambda_max.

Detailed Description

Ifpack_Chebyshev: class for preconditioning with Chebyshev polynomials in Ifpack.

The Ifpack_Chebyshev class enables the construction of preconditioners based on Chebyshev polynomials for an Epetra_RowMatrix. Ifpack_Chebyshev 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.

The class is an adaptation of the routine ML_Cheby in Smoother/ml_smoother.h

(04/04/06) Flops are not counted in the routine ApplyInverse()

(04/04/06) The switch to use the transpose matrix is not used in ApplyInverse()

The list of parameters is

EigRatio_ = List.get("chebyshev: ratio eigenvalue", EigRatio_); this is the ratio to define the lower bound on the spectrum; lambda^* = LambdaMax_ / EigRatio_; a typical value used in ML is 30.0 (30.0 is the default value).
LambdaMin_ = List.get("chebyshev: min eigenvalue", LambdaMin_); this is the smallest eigenvalue; this parameter is optional and is only accessed to check whether the input matrix is equal to identity.
LambdaMax_ = List.get("chebyshev: max eigenvalue", LambdaMax_); this is the largest eigenvalue of the matrix.
PolyDegree_ = List.get("chebyshev: degree",PolyDegree_); this is the polynomial degree.
MinDiagonalValue_ = List.get("chebyshev: min diagonal value", MinDiagonalValue_); this defines the threshold for diagonal values under which they are not inverted
ZeroStartingSolution_ = List.get("chebyshev: zero starting solution", ZeroStartingSolution_); this flag allows to set a non-zero initial guess.

Author: Ulrich Hetmaniuk. SNL 1414.

Date: Last modified on 04-Apr-06.

Definition at line 110 of file Ifpack_Chebyshev.h.

Constructor & Destructor Documentation

Ifpack_Chebyshev::Ifpack_Chebyshev ( const Epetra_Operator * Matrix )

Ifpack_Chebyshev constructor with given Epetra_Operator/Epetra_RowMatrix.

Creates an instance of Ifpack_Chebyshev class.

Parameters

Matrix - (In) Pointer to the operator to precondition.

Definition at line 83 of file Ifpack_Chebyshev.cpp.

Ifpack_Chebyshev::Ifpack_Chebyshev ( const Epetra_RowMatrix * Matrix )

Ifpack_Chebyshev constructor with given Epetra_Operator/Epetra_RowMatrix.

Creates an instance of Ifpack_Chebyshev class.

Parameters

Matrix - (In) Pointer to the matrix to precondition.

Definition at line 125 of file Ifpack_Chebyshev.cpp.

Member Function Documentation

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

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.