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Ifpack_Chebyshev Class Reference

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

#include <Ifpack_Chebyshev.h>

Inheritance diagram for Ifpack_Chebyshev:
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Collaboration diagram for Ifpack_Chebyshev:
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## 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_CommComm () const
Returns a pointer to the Epetra_Comm communicator associated with this operator.

virtual const Epetra_MapOperatorDomainMap () const
Returns the Epetra_Map object associated with the domain of this operator.

virtual const Epetra_MapOperatorRangeMap () 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_RowMatrixMatrix () 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.
Date

Definition at line 104 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.
Returns
Integer error code, set to 0 if successful.

Implements Epetra_Operator.

Definition at line 228 of file Ifpack_Chebyshev.cpp.

References IsComputed(), and UseTranspose().

 int Ifpack_Chebyshev::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 467 of file Ifpack_Chebyshev.cpp.

References IsComputed().

 virtual int Ifpack_Chebyshev::SetUseTranspose ( bool UseTranspose_in )
inlinevirtual

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.

Implements Epetra_Operator.

Definition at line 136 of file Ifpack_Chebyshev.h.

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