Ifpack_SerialTriDiSolver: A class for solving TriDi linear problems. More...

#include <Ifpack_SerialTriDiSolver.h>

Inheritance diagram for Ifpack_SerialTriDiSolver:

Collaboration diagram for Ifpack_SerialTriDiSolver:

Public Member Functions
Constructor/Destructor Methods
	Ifpack_SerialTriDiSolver ()
	Default constructor; matrix should be set using SetMatrix(), LHS and RHS set with SetVectors().

virtual	~Ifpack_SerialTriDiSolver ()
	Ifpack_SerialTriDiSolver destructor.

Set Methods
int	SetMatrix (Ifpack_SerialTriDiMatrix &A)
	Sets the pointers for coefficient matrix.

int	SetVectors (Epetra_SerialDenseMatrix &X, Epetra_SerialDenseMatrix &B)
	Sets the pointers for left and right hand side vector(s). More...

Strategy modifying Methods
void	SolveWithTranspose (bool Flag)
	Causes equilibration to be called just before the matrix factorization as part of the call to Factor. More...

void	SolveToRefinedSolution (bool Flag)
	Causes all solves to compute solution to best ability using iterative refinement.

void	EstimateSolutionErrors (bool Flag)
	Causes all solves to estimate the forward and backward solution error. More...

Factor/Solve/Invert Methods
virtual int	Factor (void)
	Computes the in-place LU factorization of the matrix using the LAPACK routine DGETRF. More...

virtual int	Solve (void)
	Computes the solution X to AX = B for the this matrix and the B provided to SetVectors().. More...

virtual int	Invert (void)
	Inverts the this matrix. More...

virtual int	ApplyRefinement (void)
	Apply Iterative Refinement. More...

virtual int	ReciprocalConditionEstimate (double &Value)
	Unscales the solution vectors if equilibration was used to solve the system. More...

Query methods
bool	Transpose ()
	Returns true if transpose of this matrix has and will be used.

bool	Factored ()
	Returns true if matrix is factored (factor available via AF() and LDAF()).

bool	SolutionErrorsEstimated ()
	Returns true if forward and backward error estimated have been computed (available via FERR() and BERR()).

bool	Inverted ()
	Returns true if matrix inverse has been computed (inverse available via AF() and LDAF()).

bool	ReciprocalConditionEstimated ()
	Returns true if the condition number of the this matrix has been computed (value available via ReciprocalConditionEstimate()).

bool	Solved ()
	Returns true if the current set of vectors has been solved.

bool	SolutionRefined ()
	Returns true if the current set of vectors has been refined.

Data Accessor methods
Ifpack_SerialTriDiMatrix *	Matrix () const
	Returns pointer to current matrix.

Ifpack_SerialTriDiMatrix *	FactoredMatrix () const
	Returns pointer to factored matrix (assuming factorization has been performed).

Epetra_SerialDenseMatrix *	LHS () const
	Returns pointer to current LHS.

Epetra_SerialDenseMatrix *	RHS () const
	Returns pointer to current RHS.

int	N () const
	Returns column dimension of system.

double *	A () const
	Returns pointer to the this matrix.

int	LDA () const
	Returns the leading dimension of the this matrix.

double *	B () const
	Returns pointer to current RHS.

int	LDB () const
	Returns the leading dimension of the RHS.

int	NRHS () const
	Returns the number of current right hand sides and solution vectors.

double *	X () const
	Returns pointer to current solution.

int	LDX () const
	Returns the leading dimension of the solution.

double *	AF () const
	Returns pointer to the factored matrix (may be the same as A() if factorization done in place).

int	LDAF () const
	Returns the leading dimension of the factored matrix.

int *	IPIV () const
	Returns pointer to pivot vector (if factorization has been computed), zero otherwise.

double	ANORM () const
	Returns the 1-Norm of the this matrix (returns -1 if not yet computed).

double	RCOND () const
	Returns the reciprocal of the condition number of the this matrix (returns -1 if not yet computed).

double	ROWCND () const
	Ratio of smallest to largest row scale factors for the this matrix (returns -1 if not yet computed). More...

double	COLCND () const
	Ratio of smallest to largest column scale factors for the this matrix (returns -1 if not yet computed). More...

double	AMAX () const
	Returns the absolute value of the largest entry of the this matrix (returns -1 if not yet computed).

double *	FERR () const
	Returns a pointer to the forward error estimates computed by LAPACK.

double *	BERR () const
	Returns a pointer to the backward error estimates computed by LAPACK.

I/O methods
virtual void	Print (std::ostream &os) const
	Print service methods; defines behavior of ostream << operator.

Public Member Functions inherited from Epetra_BLAS
	Epetra_BLAS (const Epetra_BLAS &BLAS)

float	ASUM (const int N, const float *X, const int INCX=1) const

double	ASUM (const int N, const double *X, const int INCX=1) const

float	DOT (const int N, const float X, const float Y, const int INCX=1, const int INCY=1) const

double	DOT (const int N, const double X, const double Y, const int INCX=1, const int INCY=1) const

float	NRM2 (const int N, const float *X, const int INCX=1) const

double	NRM2 (const int N, const double *X, const int INCX=1) const

void	SCAL (const int N, const float ALPHA, float *X, const int INCX=1) const

void	SCAL (const int N, const double ALPHA, double *X, const int INCX=1) const

void	COPY (const int N, const float X, float Y, const int INCX=1, const int INCY=1) const

void	COPY (const int N, const double X, double Y, const int INCX=1, const int INCY=1) const

int	IAMAX (const int N, const float *X, const int INCX=1) const

int	IAMAX (const int N, const double *X, const int INCX=1) const

void	AXPY (const int N, const float ALPHA, const float X, float Y, const int INCX=1, const int INCY=1) const

void	AXPY (const int N, const double ALPHA, const double X, double Y, const int INCX=1, const int INCY=1) const

void	GEMV (const char TRANS, const int M, const int N, const float ALPHA, const float A, const int LDA, const float X, const float BETA, float *Y, const int INCX=1, const int INCY=1) const

void	GEMV (const char TRANS, const int M, const int N, const double ALPHA, const double A, const int LDA, const double X, const double BETA, double *Y, const int INCX=1, const int INCY=1) const

void	GEMM (const char TRANSA, const char TRANSB, const int M, const int N, const int K, const float ALPHA, const float A, const int LDA, const float B, const int LDB, const float BETA, float *C, const int LDC) const

void	GEMM (const char TRANSA, const char TRANSB, const int M, const int N, const int K, const double ALPHA, const double A, const int LDA, const double B, const int LDB, const double BETA, double *C, const int LDC) const

void	SYMM (const char SIDE, const char UPLO, const int M, const int N, const float ALPHA, const float A, const int LDA, const float B, const int LDB, const float BETA, float *C, const int LDC) const

void	SYMM (const char SIDE, const char UPLO, const int M, const int N, const double ALPHA, const double A, const int LDA, const double B, const int LDB, const double BETA, double *C, const int LDC) const

void	TRMM (const char SIDE, const char UPLO, const char TRANSA, const char DIAG, const int M, const int N, const float ALPHA, const float A, const int LDA, float B, const int LDB) const

void	TRMM (const char SIDE, const char UPLO, const char TRANSA, const char DIAG, const int M, const int N, const double ALPHA, const double A, const int LDA, double B, const int LDB) const

void	SYRK (const char UPLO, const char TRANS, const int N, const int K, const float ALPHA, const float A, const int LDA, const float BETA, float C, const int LDC) const

void	SYRK (const char UPLO, const char TRANS, const int N, const int K, const double ALPHA, const double A, const int LDA, const double BETA, double C, const int LDC) const

Protected Member Functions
void	AllocateWORK ()

void	AllocateIWORK ()

void	InitPointers ()

void	DeleteArrays ()

void	ResetMatrix ()

void	ResetVectors ()

Protected Attributes
bool	Transpose_

bool	Factored_

bool	EstimateSolutionErrors_

bool	SolutionErrorsEstimated_

bool	Solved_

bool	Inverted_

bool	ReciprocalConditionEstimated_

bool	RefineSolution_

bool	SolutionRefined_

char	TRANS_

int	N_

int	Min_MN_

int	NRHS_

int	LDA_

int	LDAF_

int	LDB_

int	LDX_

int	INFO_

int	LWORK_

int *	IPIV_

int *	IWORK_

double	ANORM_

double	RCOND_

double	ROWCND_

double	COLCND_

double	AMAX_

Ifpack_SerialTriDiMatrix *	Matrix_

Epetra_SerialDenseMatrix *	LHS_

Epetra_SerialDenseMatrix *	RHS_

Ifpack_SerialTriDiMatrix *	Factor_

double *	A_

double *	FERR_

double *	BERR_

double *	AF_

double *	WORK_

double *	B_

double *	X_

Detailed Description

Ifpack_SerialTriDiSolver: A class for solving TriDi linear problems.

The Ifpack_SerialTriDiSolver class enables the definition, in terms of Ifpack_SerialTriDiMatrix
and Ifpack_SerialTriDiVector objects, of a TriDi linear problem, followed by the solution of that problem via the
most sophisticated techniques available in LAPACK.

The Ifpack_SerialTriDiSolver class is intended to provide full-featured support for solving linear problems for general TriDi rectangular (or square) matrices. It is written on top of BLAS and LAPACK and thus has excellent performance and numerical capabilities. Using this class, one can either perform simple factorizations and solves or apply all the tricks available in LAPACK to get the best possible solution for very ill-conditioned problems.

Ifpack_SerialTriDiSolver vs. Epetra_LAPACK

The Epetra_LAPACK class provides access to most of the same functionality as Ifpack_SerialTriDiSolver. The primary difference is that Epetra_LAPACK is a "thin" layer on top of LAPACK and Ifpack_SerialTriDiSolver attempts to provide easy access to the more sophisticated aspects of solving TriDi linear and eigensystems.

When you should use Epetra_LAPACK: If you are simply looking for a convenient wrapper around the Fortran LAPACK routines and you have a well-conditioned problem, you should probably use Epetra_LAPACK directly.
When you should use Ifpack_SerialTriDiSolver: If you want to (or potentially want to) solve ill-conditioned problems or want to work with a more object-oriented interface, you should probably use Ifpack_SerialTriDiSolver.

Constructing Ifpack_SerialTriDiSolver Objects

There is a single Ifpack_SerialTriDiSolver constructor. However, the matrix, right hand side and solution vectors must be set prior to executing most methods in this class.

Setting vectors used for linear solves

The matrix A, the left hand side X and the right hand side B (when solving AX = B, for X), can be set by appropriate set methods. Each of these three objects must be an Ifpack_SerialTriDiMatrix or and Epetra_SerialDenseVector object. The set methods are as follows:

SetMatrix() - Sets the matrix.
SetVectors() - Sets the left and right hand side vector(s).

Vector and Utility Functions

Once a Ifpack_SerialTriDiSolver is constructed, several mathematical functions can be applied to the object. Specifically:

Factorizations.
Solves.
Condition estimates.
Equilibration.
Norms.

Counting floating point operations The Ifpack_SerialTriDiSolver class has Epetra_CompObject as a base class. Thus, floating point operations are counted and accumulated in the Epetra_Flop object (if any) that was set using the SetFlopCounter() method in the Epetra_CompObject base class.

Strategies for Solving Linear Systems In many cases, linear systems can be accurately solved by simply computing the LU factorization of the matrix and then performing a forward back solve with a given set of right hand side vectors. However, in some instances, the factorization may be very poorly conditioned and this simple approach may not work. In these situations, equilibration and iterative refinement may improve the accuracy, or prevent a breakdown in the factorization.

LAPACK does not provide an equilibration functionality for tridiagonal data structures.

Ifpack_SerialTriDiSolver will use iterative refinement after a forward/back solve if you call SolveToRefinedSolution(true). It will also compute forward and backward error estimates if you call EstimateSolutionErrors(true). Access to the forward (back) error estimates is available via FERR() (BERR()).

Examples using Ifpack_SerialTriDiSolver can be found in the Epetra test directories.

Definition at line 130 of file Ifpack_SerialTriDiSolver.h.

Member Function Documentation

int Ifpack_SerialTriDiSolver::ApplyRefinement ( void )

virtual

Apply Iterative Refinement.

Returns: Integer error code, set to 0 if successful. Otherwise returns the LAPACK error code INFO.

Definition at line 295 of file Ifpack_SerialTriDiSolver.cpp.

Referenced by Solve().

double Ifpack_SerialTriDiSolver::COLCND ( ) const

inline

Ratio of smallest to largest column scale factors for the this matrix (returns -1 if not yet computed).

If COLCND() is >= 0.1 then equilibration is not needed.

Definition at line 310 of file Ifpack_SerialTriDiSolver.h.

void Ifpack_SerialTriDiSolver::EstimateSolutionErrors ( bool Flag )

Causes all solves to estimate the forward and backward solution error.

Error estimates will be in the arrays FERR and BERR, resp, after the solve step is complete. These arrays are accessible via the FERR() and BERR() access functions.

Definition at line 192 of file Ifpack_SerialTriDiSolver.cpp.

int Ifpack_SerialTriDiSolver::Factor ( void )

virtual

Computes the in-place LU factorization of the matrix using the LAPACK routine DGETRF.

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

Definition at line 199 of file Ifpack_SerialTriDiSolver.cpp.

References Ifpack_SerialTriDiMatrix::A(), Ifpack_SerialTriDiMatrix::DL(), Factored(), Inverted(), and Ifpack_SerialTriDiMatrix::OneNorm().

Referenced by Ifpack_TriDiContainer::Compute(), Invert(), ReciprocalConditionEstimate(), and Solve().

int Ifpack_SerialTriDiSolver::Invert ( void )

virtual

Inverts the this matrix.

Returns: Integer error code, set to 0 if successful. Otherwise returns the LAPACK error code INFO.

Definition at line 303 of file Ifpack_SerialTriDiSolver.cpp.

References Factor(), and Factored().

int Ifpack_SerialTriDiSolver::ReciprocalConditionEstimate ( double & Value )

virtual

Unscales the solution vectors if equilibration was used to solve the system.

Returns: Integer error code, set to 0 if successful. Otherwise returns the LAPACK error code INFO.Returns the reciprocal of the 1-norm condition number of the this matrix.

Parameters

Value Out On return contains the reciprocal of the 1-norm condition number of the this matrix.

Returns: Integer error code, set to 0 if successful. Otherwise returns the LAPACK error code INFO.

Definition at line 322 of file Ifpack_SerialTriDiSolver.cpp.

References Factor(), Factored(), Ifpack_SerialTriDiMatrix::OneNorm(), and ReciprocalConditionEstimated().

double Ifpack_SerialTriDiSolver::ROWCND ( ) const

inline

Ratio of smallest to largest row scale factors for the this matrix (returns -1 if not yet computed).

If ROWCND() is >= 0.1 and AMAX() is not close to overflow or underflow, then equilibration is not needed.

Definition at line 305 of file Ifpack_SerialTriDiSolver.h.

int Ifpack_SerialTriDiSolver::SetVectors	(	Epetra_SerialDenseMatrix &	X,
		Epetra_SerialDenseMatrix &	B
	)

Sets the pointers for left and right hand side vector(s).

Row dimension of X must match column dimension of matrix A, row dimension of B must match row dimension of A. X and B must have the same dimensions.

Definition at line 176 of file Ifpack_SerialTriDiSolver.cpp.

References Epetra_SerialDenseMatrix::A(), and Epetra_SerialDenseMatrix::N().

Referenced by Ifpack_TriDiContainer::Initialize(), and Ifpack_TriDiContainer::SetNumVectors().

int Ifpack_SerialTriDiSolver::Solve ( void )

virtual

Computes the solution X to AX = B for the this matrix and the B provided to SetVectors()..

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

Definition at line 237 of file Ifpack_SerialTriDiSolver.cpp.

References Epetra_SerialDenseMatrix::A(), ApplyRefinement(), Ifpack_SerialTriDiMatrix::DL(), Factor(), Factored(), and Inverted().

Referenced by Ifpack_TriDiContainer::ApplyInverse().

void Ifpack_SerialTriDiSolver::SolveWithTranspose ( bool Flag )

inline

Causes equilibration to be called just before the matrix factorization as part of the call to Factor.

This function must be called before the factorization is performed.If Flag is true, causes all subsequent function calls to work with the transpose of this matrix, otherwise not.

Definition at line 168 of file Ifpack_SerialTriDiSolver.h.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation