Epetra_SerialSpdDenseSolver: A class for constructing and using symmetric positive definite dense matrices. More...

#include <Epetra_SerialSpdDenseSolver.h>

Inheritance diagram for Epetra_SerialSpdDenseSolver:

Collaboration diagram for Epetra_SerialSpdDenseSolver:

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

virtual	~Epetra_SerialSpdDenseSolver ()
	Epetra_SerialDenseSolver destructor.

Set Methods
int	SetMatrix (Epetra_SerialSymDenseMatrix &A_in)
	Sets the pointers for coefficient matrix; special version for symmetric matrices.

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

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

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

int	ComputeEquilibrateScaling (void)
	Computes the scaling vector S(i) = 1/sqrt(A(i,i) of the this matrix. More...

int	EquilibrateMatrix (void)
	Equilibrates the this matrix. More...

int	EquilibrateRHS (void)
	Equilibrates the current RHS. More...

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

int	UnequilibrateLHS (void)
	Unscales the solution vectors if equilibration was used to solve the system. More...

int	ReciprocalConditionEstimate (double &Value)
	Returns the reciprocal of the 1-norm condition number of the this matrix. More...

Query methods
bool	ShouldEquilibrate ()
	Returns true if the LAPACK general rules for equilibration suggest you should equilibrate the system.

Data Accessor methods
Epetra_SerialSymDenseMatrix *	SymMatrix () const
	Returns pointer to current matrix.

Epetra_SerialSymDenseMatrix *	SymFactoredMatrix () const
	Returns pointer to factored matrix (assuming factorization has been performed).

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

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

Public Member Functions inherited from Epetra_SerialDenseSolver
	Epetra_SerialDenseSolver ()
	Default constructor; matrix should be set using SetMatrix(), LHS and RHS set with SetVectors().

virtual	~Epetra_SerialDenseSolver ()
	Epetra_SerialDenseSolver destructor.

int	SetMatrix (Epetra_SerialDenseMatrix &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...

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

void	SolveWithTranspose (bool Flag)
	If Flag is true, causes all subsequent function calls to work with the transpose of this matrix, otherwise not.

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...

int	EquilibrateRHS (void)
	Equilibrates the current RHS. More...

int	UnequilibrateLHS (void)
	Unscales the solution vectors if equilibration was used to solve the system. More...

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	A_Equilibrated ()
	Returns true if factor is equilibrated (factor available via AF() and LDAF()).

bool	B_Equilibrated ()
	Returns true if RHS is equilibrated (RHS available via B() and LDB()).

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.

Epetra_SerialDenseMatrix *	Matrix () const
	Returns pointer to current matrix.

Epetra_SerialDenseMatrix *	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	M () const
	Returns row dimension of system.

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.

double *	R () const
	Returns a pointer to the row scaling vector used for equilibration.

double *	C () const
	Returns a pointer to the column scale vector used for equilibration.

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

Public Member Functions inherited from Epetra_CompObject
Epetra_CompObject &	operator= (const Epetra_CompObject &src)

	Epetra_CompObject ()
	Basic Epetra_CompObject constuctor.

	Epetra_CompObject (const Epetra_CompObject &Source)
	Epetra_CompObject copy constructor.

virtual	~Epetra_CompObject ()
	Epetra_CompObject destructor.

void	SetFlopCounter (const Epetra_Flops &FlopCounter_in)
	Set the internal Epetra_Flops() pointer.

void	SetFlopCounter (const Epetra_CompObject &CompObject)
	Set the internal Epetra_Flops() pointer to the flop counter of another Epetra_CompObject.

void	UnsetFlopCounter ()
	Set the internal Epetra_Flops() pointer to 0 (no flops counted).

Epetra_Flops *	GetFlopCounter () const
	Get the pointer to the Epetra_Flops() object associated with this object, returns 0 if none.

void	ResetFlops () const
	Resets the number of floating point operations to zero for this multi-vector.

double	Flops () const
	Returns the number of floating point operations with this multi-vector.

void	UpdateFlops (int Flops_in) const
	Increment Flop count for this object.

void	UpdateFlops (long int Flops_in) const
	Increment Flop count for this object.

void	UpdateFlops (long long Flops_in) const
	Increment Flop count for this object.

void	UpdateFlops (double Flops_in) const
	Increment Flop count for this object.

void	UpdateFlops (float Flops_in) const
	Increment Flop count for this object.

Public Member Functions inherited from Epetra_BLAS
	Epetra_BLAS (void)
	Epetra_BLAS Constructor. More...

	Epetra_BLAS (const Epetra_BLAS &BLAS)
	Epetra_BLAS Copy Constructor. More...

virtual	~Epetra_BLAS (void)
	Epetra_BLAS Destructor.

float	ASUM (const int N, const float *X, const int INCX=1) const
	Epetra_BLAS one norm function (SASUM).

double	ASUM (const int N, const double *X, const int INCX=1) const
	Epetra_BLAS one norm function (DASUM).

float	DOT (const int N, const float X, const float Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS dot product function (SDOT).

double	DOT (const int N, const double X, const double Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS dot product function (DDOT).

float	NRM2 (const int N, const float *X, const int INCX=1) const
	Epetra_BLAS norm function (SNRM2).

double	NRM2 (const int N, const double *X, const int INCX=1) const
	Epetra_BLAS norm function (DNRM2).

void	SCAL (const int N, const float ALPHA, float *X, const int INCX=1) const
	Epetra_BLAS vector scale function (SSCAL)

void	SCAL (const int N, const double ALPHA, double *X, const int INCX=1) const
	Epetra_BLAS vector scale function (DSCAL)

void	COPY (const int N, const float X, float Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS vector copy function (SCOPY)

void	COPY (const int N, const double X, double Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS vector scale function (DCOPY)

int	IAMAX (const int N, const float *X, const int INCX=1) const
	Epetra_BLAS arg maximum of absolute value function (ISAMAX)

int	IAMAX (const int N, const double *X, const int INCX=1) const
	Epetra_BLAS arg maximum of absolute value function (IDAMAX)

void	AXPY (const int N, const float ALPHA, const float X, float Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS vector update function (SAXPY)

void	AXPY (const int N, const double ALPHA, const double X, double Y, const int INCX=1, const int INCY=1) const
	Epetra_BLAS vector update function (DAXPY)

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
	Epetra_BLAS matrix-vector multiply function (SGEMV)

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
	Epetra_BLAS matrix-vector multiply function (DGEMV)

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
	Epetra_BLAS matrix-matrix multiply function (SGEMM)

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
	Epetra_BLAS matrix-matrix multiply function (DGEMM)

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
	Epetra_BLAS symmetric matrix-matrix multiply function (SSYMM)

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
	Epetra_BLAS matrix-matrix multiply function (DSYMM)

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
	Epetra_BLAS triangular matrix-matrix multiply function (STRMM)

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
	Epetra_BLAS triangular matrix-matrix multiply function (DTRMM)

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
	Eperta_BLAS symetric rank k funtion (ssyrk)

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
	Eperta_BLAS symetric rank k funtion (dsyrk)

Public Member Functions inherited from Epetra_LAPACK
	Epetra_LAPACK (void)
	Epetra_LAPACK Constructor. More...

	Epetra_LAPACK (const Epetra_LAPACK &LAPACK)
	Epetra_LAPACK Copy Constructor. More...

virtual	~Epetra_LAPACK (void)
	Epetra_LAPACK Destructor.

void	POTRF (const char UPLO, const int N, float A, const int LDA, int INFO) const
	Epetra_LAPACK factorization for positive definite matrix (SPOTRF)

void	POTRF (const char UPLO, const int N, double A, const int LDA, int INFO) const
	Epetra_LAPACK factorization for positive definite matrix (DPOTRF)

void	POTRS (const char UPLO, const int N, const int NRHS, const float A, const int LDA, float X, const int LDX, int *INFO) const
	Epetra_LAPACK solve (after factorization) for positive definite matrix (SPOTRS)

void	POTRS (const char UPLO, const int N, const int NRHS, const double A, const int LDA, double X, const int LDX, int *INFO) const
	Epetra_LAPACK solve (after factorization) for positive definite matrix (DPOTRS)

void	POTRI (const char UPLO, const int N, float A, const int LDA, int INFO) const
	Epetra_LAPACK inversion for positive definite matrix (SPOTRI)

void	POTRI (const char UPLO, const int N, double A, const int LDA, int INFO) const
	Epetra_LAPACK inversion for positive definite matrix (DPOTRI)

void	POCON (const char UPLO, const int N, const float A, const int LDA, const float ANORM, float RCOND, float WORK, int IWORK, int *INFO) const
	Epetra_LAPACK condition number estimator for positive definite matrix (SPOCON)

void	POCON (const char UPLO, const int N, const double A, const int LDA, const double ANORM, double RCOND, double WORK, int IWORK, int *INFO) const
	Epetra_LAPACK condition number estimator for positive definite matrix (DPOCON)

void	POSV (const char UPLO, const int N, const int NRHS, float A, const int LDA, float X, const int LDX, int *INFO) const
	Epetra_LAPACK factor and solve for positive definite matrix (SPOSV)

void	POSV (const char UPLO, const int N, const int NRHS, double A, const int LDA, double X, const int LDX, int *INFO) const
	Epetra_LAPACK factor and solve for positive definite matrix (DPOSV)

void	POEQU (const int N, const float A, const int LDA, float S, float SCOND, float AMAX, int *INFO) const
	Epetra_LAPACK equilibration for positive definite matrix (SPOEQU)

void	POEQU (const int N, const double A, const int LDA, double S, double SCOND, double AMAX, int *INFO) const
	Epetra_LAPACK equilibration for positive definite matrix (DPOEQU)

void	PORFS (const char UPLO, const int N, const int NRHS, const float A, const int LDA, const float AF, const int LDAF, const float B, const int LDB, float X, const int LDX, float FERR, float BERR, float WORK, int IWORK, int *INFO) const
	Epetra_LAPACK solve driver for positive definite matrix (SPOSVX)

void	PORFS (const char UPLO, const int N, const int NRHS, const double A, const int LDA, const double AF, const int LDAF, const double B, const int LDB, double X, const int LDX, double FERR, double BERR, double WORK, int IWORK, int *INFO) const
	Epetra_LAPACK solve driver for positive definite matrix (DPOSVX)

void	POSVX (const char FACT, const char UPLO, const int N, const int NRHS, float A, const int LDA, float AF, const int LDAF, const char EQUED, float S, float B, const int LDB, float X, const int LDX, float RCOND, float FERR, float BERR, float WORK, int IWORK, int *INFO) const
	Epetra_LAPACK solve driver for positive definite matrix (SPOSVX)

void	POSVX (const char FACT, const char UPLO, const int N, const int NRHS, double A, const int LDA, double AF, const int LDAF, const char EQUED, double S, double B, const int LDB, double X, const int LDX, double RCOND, double FERR, double BERR, double WORK, int IWORK, int *INFO) const
	Epetra_LAPACK solve driver for positive definite matrix (DPOSVX)

void	GELS (const char TRANS, const int M, const int N, const int NRHS, double A, const int LDA, double B, const int LDB, double WORK, const int LWORK, int INFO) const
	Epetra_LAPACK simple driver to solve least-squares systems.

void	GETRF (const int M, const int N, float A, const int LDA, int IPIV, int *INFO) const
	Epetra_LAPACK factorization for general matrix (SGETRF)

void	GETRF (const int M, const int N, double A, const int LDA, int IPIV, int *INFO) const
	Epetra_LAPACK factorization for general matrix (DGETRF)

void	GEQRF (const int M, const int N, float A, const int LDA, float TAU, float WORK, const int lwork, int INFO) const
	Epetra_LAPACK QR factorization for general matrix (SGEQRF)

void	GEQRF (const int M, const int N, double A, const int LDA, double TAU, double WORK, const int lwork, int INFO) const
	Epetra_LAPACK factorization for general matrix (DGEQRF)

void	GETRS (const char TRANS, const int N, const int NRHS, const float A, const int LDA, const int IPIV, float X, const int LDX, int INFO) const
	Epetra_LAPACK solve (after factorization) for general matrix (SGETRS)

void	GETRS (const char TRANS, const int N, const int NRHS, const double A, const int LDA, const int IPIV, double X, const int LDX, int INFO) const
	Epetra_LAPACK solve (after factorization) for general matrix (DGETRS)

void	GETRI (const int N, float A, const int LDA, int IPIV, float WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK inversion for general matrix (SGETRI)

void	GETRI (const int N, double A, const int LDA, int IPIV, double WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK inversion for general matrix (DGETRI)

void	GECON (const char NORM, const int N, const float A, const int LDA, const float ANORM, float RCOND, float WORK, int IWORK, int *INFO) const
	Epetra_LAPACK condition number estimator for general matrix (SGECON)

void	GECON (const char NORM, const int N, const double A, const int LDA, const double ANORM, double RCOND, double WORK, int IWORK, int *INFO) const
	Epetra_LAPACK condition number estimator for general matrix (DGECON)

void	GESV (const int N, const int NRHS, float A, const int LDA, int IPIV, float X, const int LDX, int INFO) const
	Epetra_LAPACK factor and solve for general matrix (SGESV)

void	GESV (const int N, const int NRHS, double A, const int LDA, int IPIV, double X, const int LDX, int INFO) const
	Epetra_LAPACK factor and solve for general matrix (DGESV)

void	GEEQU (const int M, const int N, const float A, const int LDA, float R, float C, float ROWCND, float COLCND, float AMAX, int *INFO) const
	Epetra_LAPACK equilibration for general matrix (SGEEQU)

void	GEEQU (const int M, const int N, const double A, const int LDA, double R, double C, double ROWCND, double COLCND, double AMAX, int *INFO) const
	Epetra_LAPACK equilibration for general matrix (DGEEQU)

void	GERFS (const char TRANS, const int N, const int NRHS, const float A, const int LDA, const float AF, const int LDAF, const int IPIV, const float B, const int LDB, float X, const int LDX, float FERR, float BERR, float WORK, int IWORK, int INFO) const
	Epetra_LAPACK Refine solution (GERFS)

void	GERFS (const char TRANS, const int N, const int NRHS, const double A, const int LDA, const double AF, const int LDAF, const int IPIV, const double B, const int LDB, double X, const int LDX, double FERR, double BERR, double WORK, int IWORK, int INFO) const
	Epetra_LAPACK Refine solution (GERFS)

void	GESVX (const char FACT, const char TRANS, const int N, const int NRHS, float A, const int LDA, float AF, const int LDAF, int IPIV, const char EQUED, float R, float C, float B, const int LDB, float X, const int LDX, float RCOND, float FERR, float BERR, float WORK, int IWORK, int *INFO) const
	Epetra_LAPACK solve driver for general matrix (SGESVX)

void	GESVX (const char FACT, const char TRANS, const int N, const int NRHS, double A, const int LDA, double AF, const int LDAF, int IPIV, const char EQUED, double R, double C, double B, const int LDB, double X, const int LDX, double RCOND, double FERR, double BERR, double WORK, int IWORK, int *INFO) const
	Epetra_LAPACK solve driver for general matrix (DGESVX)

void	GEHRD (const int N, const int ILO, const int IHI, float A, const int LDA, float TAU, float WORK, const int LWORK, int INFO) const
	Epetra_LAPACK wrapper for reduction to Hessenberg form (SGEHRD)

void	GEHRD (const int N, const int ILO, const int IHI, double A, const int LDA, double TAU, double WORK, const int LWORK, int INFO) const
	Epetra_LAPACK wrapper for reduction to Hessenberg form (DGEHRD)

void	HSEQR (const char JOB, const char COMPZ, const int N, const int ILO, const int IHI, float H, const int LDH, float WR, float WI, float Z, const int LDZ, float WORK, const int LWORK, int INFO) const
	Epetra_LAPACK wrapper for computing the eigenvalues of a real upper Hessenberg matrix (SHSEQR)

void	HSEQR (const char JOB, const char COMPZ, const int N, const int ILO, const int IHI, double H, const int LDH, double WR, double WI, double Z, const int LDZ, double WORK, const int LWORK, int INFO) const
	Epetra_LAPACK wrapper for computing the eigenvalues of a real upper Hessenberg matrix (DHSEQR)

void	ORGQR (const int M, const int N, const int K, float A, const int LDA, float TAU, float WORK, const int LWORK, int INFO) const
	Epetra_LAPACK wrapper for generating a m x n real matrix Q with orthonormal columns, defined as the product of k elementary reflectors. (SORGQR)

void	ORGQR (const int M, const int N, const int K, double A, const int LDA, double TAU, double WORK, const int LWORK, int INFO) const
	Epetra_LAPACK wrapper for generating a m x n real matrix Q with orthonormal columns, defined as the product of k elementary reflectors. (DORGQR)

void	ORGHR (const int N, const int ILO, const int IHI, float A, const int LDA, float TAU, float WORK, const int LWORK, int INFO) const
	Epetra_LAPACK wrapper for generating a real orthogonal matrix Q defined by elementary reflectors. (SORGHR)

void	ORGHR (const int N, const int ILO, const int IHI, double A, const int LDA, double TAU, double WORK, const int LWORK, int INFO) const
	Epetra_LAPACK wrapper for generating a real orthogonal matrix Q defined by elementary reflectors. (DORGHR)

void	ORMHR (const char SIDE, const char TRANS, const int M, const int N, const int ILO, const int IHI, const float A, const int LDA, const float TAU, float C, const int LDC, float WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK wrapper for applying an orthogonal matrix in-place (SORMHR)

void	ORMHR (const char SIDE, const char TRANS, const int M, const int N, const int ILO, const int IHI, const double A, const int LDA, const double TAU, double C, const int LDC, double WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK wrapper for applying an orthogonal matrix in-place (DORMHR)

void	LARFT (const char DIRECT, const char STOREV, const int N, const int K, double V, const int LDV, double TAU, double *T, const int LDT) const
	Epetra_LAPACK for forming the triangular factor of a product of elementary Householder reflectors (SLARFT).

void	LARFT (const char DIRECT, const char STOREV, const int N, const int K, float V, const int LDV, float TAU, float *T, const int LDT) const
	Epetra_LAPACK for forming the triangular factor of a product of elementary Householder reflectors (DLARFT).

void	TREVC (const char SIDE, const char HOWMNY, int SELECT, const int N, const float T, const int LDT, float VL, const int LDVL, float VR, const int LDVR, const int MM, int M, float WORK, int *INFO) const
	Epetra_LAPACK wrapper for computing eigenvectors of a quasi-triangular/triagnular matrix (STREVC) More...

void	TREVC (const char SIDE, const char HOWMNY, int SELECT, const int N, const double T, const int LDT, double VL, const int LDVL, double VR, const int LDVR, const int MM, int M, double WORK, int *INFO) const
	Epetra_LAPACK wrapper for computing eigenvectors of a quasi-triangular/triagnular matrix (DTREVC) More...

void	TREXC (const char COMPQ, const int N, float T, const int LDT, float Q, const int LDQ, int IFST, int ILST, float WORK, int INFO) const
	Epetra_LAPACK wrapper for reordering the real-Schur/Schur factorization of a matrix (STREXC)

void	TREXC (const char COMPQ, const int N, double T, const int LDT, double Q, const int LDQ, int IFST, int ILST, double WORK, int INFO) const
	Epetra_LAPACK wrapper for reordering the real-Schur/Schur factorization of a matrix (DTREXC)

void	GESVD (const char JOBU, const char JOBVT, const int M, const int N, float A, const int LDA, float S, float U, const int LDU, float VT, const int LDVT, float WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK wrapper for computing the singular value decomposition (SGESVD)

void	GESVD (const char JOBU, const char JOBVT, const int M, const int N, double A, const int LDA, double S, double U, const int LDU, double VT, const int LDVT, double WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK wrapper for computing the singular value decomposition (DGESVD)

void	GGSVD (const char JOBU, const char JOBV, const char JOBQ, const int M, const int N, const int P, int K, int L, double A, const int LDA, double B, const int LDB, double ALPHA, double BETA, double U, const int LDU, double V, const int LDV, double Q, const int LDQ, double WORK, int IWORK, int INFO) const
	Epetra_LAPACK wrapper to compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B.

void	GGSVD (const char JOBU, const char JOBV, const char JOBQ, const int M, const int N, const int P, int K, int L, float A, const int LDA, float B, const int LDB, float ALPHA, float BETA, float U, const int LDU, float V, const int LDV, float Q, const int LDQ, float WORK, int IWORK, int INFO) const
	Epetra_LAPACK wrapper to compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B.

void	GEEV (const char JOBVL, const char JOBVR, const int N, double A, const int LDA, double WR, double WI, double VL, const int LDVL, double VR, const int LDVR, double WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK wrapper to compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.

void	GEEV (const char JOBVL, const char JOBVR, const int N, float A, const int LDA, float WR, float WI, float VL, const int LDVL, float VR, const int LDVR, float WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK wrapper to compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.

void	SPEV (const char JOBZ, const char UPLO, const int N, double AP, double W, double Z, int LDZ, double WORK, int *INFO) const
	Epetra_LAPACK wrapper to compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage.

void	SPEV (const char JOBZ, const char UPLO, const int N, float AP, float W, float Z, int LDZ, float WORK, int *INFO) const
	Epetra_LAPACK wrapper to compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage.

void	SPGV (const int ITYPE, const char JOBZ, const char UPLO, const int N, double AP, double BP, double W, double Z, const int LDZ, double WORK, int INFO) const
	Epetra_LAPACK wrapper to compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form Ax=(lambda)Bx, ABx=(lambda)x, or BAx=(lambda)x.

void	SPGV (const int ITYPE, const char JOBZ, const char UPLO, const int N, float AP, float BP, float W, float Z, const int LDZ, float WORK, int INFO) const
	Epetra_LAPACK wrapper to compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form Ax=(lambda)Bx, ABx=(lambda)x, or BAx=(lambda)x.

void	SYEV (const char JOBZ, const char UPLO, const int N, double A, const int LDA, double W, double WORK, const int LWORK, int INFO) const
	Epetra_LAPACK wrapper to compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.

void	SYEV (const char JOBZ, const char UPLO, const int N, float A, const int LDA, float W, float WORK, const int LWORK, int INFO) const
	Epetra_LAPACK wrapper to compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.

void	SYEVD (const char JOBZ, const char UPLO, const int N, double A, const int LDA, double W, double WORK, const int LWORK, int IWORK, const int LIWORK, int *INFO) const
	Epetra_LAPACK wrapper to compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.

void	SYEVD (const char JOBZ, const char UPLO, const int N, float A, const int LDA, float W, float WORK, const int LWORK, int IWORK, const int LIWORK, int *INFO) const
	Epetra_LAPACK wrapper to compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.

void	SYEVX (const char JOBZ, const char RANGE, const char UPLO, const int N, double A, const int LDA, const double VL, const double VU, const int IL, const int IU, const double ABSTOL, int M, double W, double Z, const int LDZ, double WORK, const int LWORK, int IWORK, int IFAIL, int INFO) const
	Epetra_LAPACK wrapper to compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.

void	SYEVX (const char JOBZ, const char RANGE, const char UPLO, const int N, float A, const int LDA, const float VL, const float VU, const int IL, const int IU, const float ABSTOL, int M, float W, float Z, const int LDZ, float WORK, const int LWORK, int IWORK, int IFAIL, int INFO) const
	Epetra_LAPACK wrapper to compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.

void	SYGV (const int ITYPE, const char JOBZ, const char UPLO, const int N, double A, const int LDA, double B, const int LDB, double W, double WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK wrapper to compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form Ax=(lambda)Bx, ABx=(lambda)x, or BAx=(lambda)x.

void	SYGV (const int ITYPE, const char JOBZ, const char UPLO, const int N, float A, const int LDA, float B, const int LDB, float W, float WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK wrapper to compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form Ax=(lambda)Bx, ABx=(lambda)x, or BAx=(lambda)x.

void	SYGVX (const int ITYPE, const char JOBZ, const char RANGE, const char UPLO, const int N, double A, const int LDA, double B, const int LDB, const double VL, const double VU, const int IL, const int IU, const double ABSTOL, int M, double W, double Z, const int LDZ, double WORK, const int LWORK, int IWORK, int IFAIL, int *INFO) const
	Epetra_LAPACK wrapper to compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form Ax=(lambda)Bx, ABx=(lambda)x, or BAx=(lambda)x.

void	SYGVX (const int ITYPE, const char JOBZ, const char RANGE, const char UPLO, const int N, float A, const int LDA, float B, const int LDB, const float VL, const float VU, const int IL, const int IU, const float ABSTOL, int M, float W, float Z, const int LDZ, float WORK, const int LWORK, int IWORK, int IFAIL, int *INFO) const
	Epetra_LAPACK wrapper to compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form Ax=(lambda)Bx, ABx=(lambda)x, or BAx=(lambda)x.

void	SYEVR (const char JOBZ, const char RANGE, const char UPLO, const int N, double A, const int LDA, const double VL, const double VU, const int IL, const int IU, const double ABSTOL, int M, double W, double Z, const int LDZ, int ISUPPZ, double WORK, const int LWORK, int IWORK, const int LIWORK, int INFO) const
	Epetra_LAPACK wrapper to compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix T.

void	SYEVR (const char JOBZ, const char RANGE, const char UPLO, const int N, float A, const int LDA, const float VL, const float VU, const int IL, const int IU, const float ABSTOL, int M, float W, float Z, const int LDZ, int ISUPPZ, float WORK, const int LWORK, int IWORK, const int LIWORK, int INFO) const
	Epetra_LAPACK wrapper to compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix T.

void	GEEVX (const char BALANC, const char JOBVL, const char JOBVR, const char SENSE, const int N, double A, const int LDA, double WR, double WI, double VL, const int LDVL, double VR, const int LDVR, int ILO, int IHI, double SCALE, double ABNRM, double RCONDE, double RCONDV, double WORK, const int LWORK, int IWORK, int INFO) const
	Epetra_LAPACK wrapper to compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.

void	GEEVX (const char BALANC, const char JOBVL, const char JOBVR, const char SENSE, const int N, float A, const int LDA, float WR, float WI, float VL, const int LDVL, float VR, const int LDVR, int ILO, int IHI, float SCALE, float ABNRM, float RCONDE, float RCONDV, float WORK, const int LWORK, int IWORK, int INFO) const
	Epetra_LAPACK wrapper to compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.

void	GESDD (const char JOBZ, const int M, const int N, double A, const int LDA, double S, double U, const int LDU, double VT, const int LDVT, double WORK, const int LWORK, int IWORK, int *INFO) const
	Epetra_LAPACK wrapper to compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors.

void	GESDD (const char JOBZ, const int M, const int N, float A, const int LDA, float S, float U, const int LDU, float VT, const int LDVT, float WORK, const int LWORK, int IWORK, int *INFO) const
	Epetra_LAPACK wrapper to.

void	GGEV (const char JOBVL, const char JOBVR, const int N, double A, const int LDA, double B, const int LDB, double ALPHAR, double ALPHAI, double BETA, double VL, const int LDVL, double VR, const int LDVR, double WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK wrapper to compute for a pair of N-by-N real nonsymmetric matrices (A,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.

void	GGEV (const char JOBVL, const char JOBVR, const int N, float A, const int LDA, float B, const int LDB, float ALPHAR, float ALPHAI, float BETA, float VL, const int LDVL, float VR, const int LDVR, float WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK wrapper to compute for a pair of N-by-N real nonsymmetric matrices (A,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.

void	GGLSE (const int M, const int N, const int P, double A, const int LDA, double B, const int LDB, double C, double D, double X, double WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK wrapper to solve the linear equality-constrained least squares (LSE) problem.

void	GGLSE (const int M, const int N, const int P, float A, const int LDA, float B, const int LDB, float C, float D, float X, float WORK, const int LWORK, int *INFO) const
	Epetra_LAPACK wrapper to solve the linear equality-constrained least squares (LSE) problem.

void	LAMCH (const char CMACH, float &T) const
	Epetra_LAPACK wrapper for DLAMCH routine. On out, T holds machine double precision floating point characteristics. This information is returned by the Lapack routine.

void	LAMCH (const char CMACH, double &T) const
	Epetra_LAPACK wrapper for SLAMCH routine. On out, T holds machine single precision floating point characteristics. This information is returned by the Lapack routine.

void	TRTRS (const char UPLO, const char TRANS, const char DIAG, const int N, const int NRHS, const float A, const int LDA, float B, const int LDB, int *INFO) const
	Epetra_LAPACK wrapper for TRTRS routine.

void	TRTRS (const char UPLO, const char TRANS, const char DIAG, const int N, const int NRHS, const double A, const int LDA, double B, const int LDB, int *INFO) const
	Epetra_LAPACK wrapper for TRTRS routine.

Public Member Functions inherited from Epetra_Object
	Epetra_Object (int TracebackModeIn=-1, bool set_label=true)
	Epetra_Object Constructor. More...

	Epetra_Object (const char *const Label, int TracebackModeIn=-1)
	Epetra_Object Constructor. More...

	Epetra_Object (const Epetra_Object &Object)
	Epetra_Object Copy Constructor. More...

virtual	~Epetra_Object ()
	Epetra_Object Destructor. More...

virtual int	ReportError (const std::string Message, int ErrorCode) const
	Error reporting method.

virtual void	SetLabel (const char *const Label)
	Epetra_Object Label definition using char *. More...

virtual const char *	Label () const
	Epetra_Object Label access funtion. More...

Additional Inherited Members
Static Public Member Functions inherited from Epetra_Object
static void	SetTracebackMode (int TracebackModeValue)
	Set the value of the Epetra_Object error traceback report mode. More...

static int	GetTracebackMode ()
	Get the value of the Epetra_Object error report mode.

static std::ostream &	GetTracebackStream ()
	Get the output stream for error reporting.

Static Public Attributes inherited from Epetra_Object
static int	TracebackMode

Protected Member Functions inherited from Epetra_SerialDenseSolver
void	AllocateWORK ()

void	AllocateIWORK ()

void	InitPointers ()

void	DeleteArrays ()

void	ResetMatrix ()

void	ResetVectors ()

Protected Member Functions inherited from Epetra_Object
std::string	toString (const int &x) const

std::string	toString (const long long &x) const

std::string	toString (const double &x) const

Protected Attributes inherited from Epetra_SerialDenseSolver
bool	Equilibrate_

bool	ShouldEquilibrate_

bool	A_Equilibrated_

bool	B_Equilibrated_

bool	Transpose_

bool	Factored_

bool	EstimateSolutionErrors_

bool	SolutionErrorsEstimated_

bool	Solved_

bool	Inverted_

bool	ReciprocalConditionEstimated_

bool	RefineSolution_

bool	SolutionRefined_

char	TRANS_

int	M_

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_

Epetra_SerialDenseMatrix *	Matrix_

Epetra_SerialDenseMatrix *	LHS_

Epetra_SerialDenseMatrix *	RHS_

Epetra_SerialDenseMatrix *	Factor_

double *	A_

double *	FERR_

double *	BERR_

double *	AF_

double *	WORK_

double *	R_

double *	C_

double *	B_

double *	X_

Protected Attributes inherited from Epetra_CompObject
Epetra_Flops *	FlopCounter_

Detailed Description

Epetra_SerialSpdDenseSolver: A class for constructing and using symmetric positive definite dense matrices.

The Epetra_SerialSpdDenseSolver class enables the construction and use of real-valued, symmetric positive definite,
double-precision dense matrices.  It is built on the Epetra_DenseMatrix class which in turn is built on the
BLAS and LAPACK via the Epetra_BLAS and
Epetra_LAPACK classes.

The Epetra_SerialSpdDenseSolver class is intended to provide full-featured support for solving linear and eigen system problems for symmetric positive definite 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.

Epetra_SerialSpdDenseSolver vs. Epetra_LAPACK

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

Constructing Epetra_SerialSpdDenseSolver Objects

There are three Epetra_DenseMatrix constructors. The first constructs a zero-sized object which should be made to appropriate length using the Shape() or Reshape() functions and then filled with the [] or () operators. The second is a constructor that accepts user data as a 2D array, the third is a copy constructor. The second constructor has two data access modes (specified by the Epetra_DataAccess argument):

Copy mode - Allocates memory and makes a copy of the user-provided data. In this case, the user data is not needed after construction.
View mode - Creates a "view" of the user data. In this case, the user data is required to remain intact for the life of the object.

Warning: View mode is extremely dangerous from a data hiding perspective. Therefore, we strongly encourage users to develop code using Copy mode first and only use the View mode in a secondary optimization phase.

Setting vectors used for linear solves

Setting the X and B vectors (which are Epetra_DenseMatrix objects) used for solving linear systems is done separately from the constructor. This allows a single matrix factor to be used for multiple solves. Similar to the constructor, the vectors X and B can be copied or viewed using the Epetra_DataAccess argument.

Extracting Data from Epetra_SerialSpdDenseSolver Objects

Once a Epetra_SerialSpdDenseSolver is constructed, it is possible to view the data via access functions.

Warning: Use of these access functions cam be extremely dangerous from a data hiding perspective.

Vector and Utility Functions

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

Factorizations.
Solves.
Condition estimates.
Equilibration.
Norms.

The final useful function is Flops(). Each Epetra_SerialSpdDenseSolver object keep track of the number of serial floating point operations performed using the specified object as the this argument to the function. The Flops() function returns this number as a double precision number. Using this information, in conjunction with the Epetra_Time class, one can get accurate parallel performance numbers.

Strategies for Solving Linear Systems In many cases, linear systems can be accurately solved by simply computing the Cholesky 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 the simple approach may not work. In these situations, equilibration and iterative refinement may improve the accuracy, or prevent a breakdown in the factorization.

Epetra_SerialSpdDenseSolver will use equilibration with the factorization if, once the object is constructed and before it is factored, you call the function FactorWithEquilibration(true) to force equilibration to be used. If you are uncertain if equilibration should be used, you may call the function ShouldEquilibrate() which will return true if equilibration could possibly help. ShouldEquilibrate() uses guidelines specified in the LAPACK User Guide, namely if SCOND < 0.1 and AMAX < Underflow or AMAX > Overflow, to determine if equilibration might be useful.

Epetra_SerialSpdDenseSolver 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 Epetra_SerialSpdDenseSolver can be found in the Epetra test directories.

Member Function Documentation

int Epetra_SerialSpdDenseSolver::ApplyRefinement ( void )

virtual

Apply Iterative Refinement.

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

Reimplemented from Epetra_SerialDenseSolver.

int Epetra_SerialSpdDenseSolver::ComputeEquilibrateScaling ( void )

virtual

Computes the scaling vector S(i) = 1/sqrt(A(i,i) of the this matrix.

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

Reimplemented from Epetra_SerialDenseSolver.

int Epetra_SerialSpdDenseSolver::EquilibrateMatrix ( void )

virtual

Equilibrates the this matrix.

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

Reimplemented from Epetra_SerialDenseSolver.

int Epetra_SerialSpdDenseSolver::EquilibrateRHS ( void )

Equilibrates the current RHS.

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

int Epetra_SerialSpdDenseSolver::Factor ( void )

virtual

Computes the in-place Cholesky factorization of the matrix using the LAPACK routine DPOTRF.

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

Reimplemented from Epetra_SerialDenseSolver.

int Epetra_SerialSpdDenseSolver::Invert ( void )

virtual

Inverts the this matrix.

Note: This function works a little differently that DPOTRI in that it fills the entire matrix with the inverse, independent of the UPLO specification.

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

Reimplemented from Epetra_SerialDenseSolver.

int Epetra_SerialSpdDenseSolver::ReciprocalConditionEstimate ( double & Value )

virtual

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.

Reimplemented from Epetra_SerialDenseSolver.

double Epetra_SerialSpdDenseSolver::SCOND ( )

inline

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

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

int Epetra_SerialSpdDenseSolver::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.

Reimplemented from Epetra_SerialDenseSolver.

int Epetra_SerialSpdDenseSolver::UnequilibrateLHS ( void )

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.

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

Epetra_SerialSpdDenseSolver.h

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation