Epetra  Development
 All Classes Namespaces Files Functions Variables Enumerations Enumerator Pages
Protected Member Functions | Protected Attributes | List of all members
Epetra_SerialDenseSolver Class Reference

Epetra_SerialDenseSolver: A class for solving dense linear problems. More...

#include <Epetra_SerialDenseSolver.h>

Inheritance diagram for Epetra_SerialDenseSolver:
Inheritance graph
[legend]
Collaboration diagram for Epetra_SerialDenseSolver:
Collaboration graph
[legend]

Public Member Functions

Constructor/Destructor Methods
 Epetra_SerialDenseSolver ()
 Default constructor; matrix should be set using SetMatrix(), LHS and RHS set with SetVectors().
 
virtual ~Epetra_SerialDenseSolver ()
 Epetra_SerialDenseSolver destructor.
 
Set Methods
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...
 
Strategy modifying Methods
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...
 
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 ComputeEquilibrateScaling (void)
 Computes the scaling vector S(i) = 1/sqrt(A(i,i)) of the this matrix. More...
 
virtual int EquilibrateMatrix (void)
 Equilibrates the this matrix. More...
 
int EquilibrateRHS (void)
 Equilibrates the current RHS. More...
 
virtual int ApplyRefinement (void)
 Apply Iterative Refinement. More...
 
int UnequilibrateLHS (void)
 Unscales the solution vectors if equilibration was used to solve the system. More...
 
virtual int ReciprocalConditionEstimate (double &Value)
 Returns the reciprocal of the 1-norm condition number of the this matrix. 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 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()).
 
virtual bool ShouldEquilibrate ()
 Returns true if the LAPACK general rules for equilibration suggest you should equilibrate the system.
 
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
Epetra_SerialDenseMatrixMatrix () const
 Returns pointer to current matrix.
 
Epetra_SerialDenseMatrixFactoredMatrix () const
 Returns pointer to factored matrix (assuming factorization has been performed).
 
Epetra_SerialDenseMatrixLHS () const
 Returns pointer to current LHS.
 
Epetra_SerialDenseMatrixRHS () 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.
 
I/O methods
virtual void Print (std::ostream &os) const
 Print service methods; defines behavior of ostream << operator.
 
- Public Member Functions inherited from Epetra_CompObject
Epetra_CompObjectoperator= (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_FlopsGetFlopCounter () 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 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(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 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(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 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(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 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(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 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(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 A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(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...
 

Protected Member Functions

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

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_SerialDenseMatrixMatrix_
 
Epetra_SerialDenseMatrixLHS_
 
Epetra_SerialDenseMatrixRHS_
 
Epetra_SerialDenseMatrixFactor_
 
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_FlopsFlopCounter_
 

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
 

Detailed Description

Epetra_SerialDenseSolver: A class for solving dense linear problems.

The Epetra_SerialDenseSolver class enables the definition, in terms of Epetra_SerialDenseMatrix and Epetra_SerialDenseVector objects, of a dense linear problem, followed by the solution of that problem via the most sophisticated techniques available in LAPACK.

The Epetra_SerialDenseSolver class is intended to provide full-featured support for solving linear problems for general dense 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.

Epetra_SerialDenseSolver vs. Epetra_LAPACK

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

Constructing Epetra_SerialDenseSolver Objects

There is a single Epetra_SerialDenseSolver 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 Epetra_SerialDenseMatrix or and Epetra_SerialDenseVector object. The set methods are as follows:

Vector and Utility Functions

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

Counting floating point operations The Epetra_SerialDenseSolver 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.

Epetra_SerialDenseSolver 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_SerialDenseSolver 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_SerialDenseSolver can be found in the Epetra test directories.

Member Function Documentation

virtual int Epetra_SerialDenseSolver::ApplyRefinement ( void  )
virtual

Apply Iterative Refinement.

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

Reimplemented in Epetra_SerialSpdDenseSolver.

double Epetra_SerialDenseSolver::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.

virtual int Epetra_SerialDenseSolver::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 in Epetra_SerialSpdDenseSolver.

Referenced by Epetra_SerialSpdDenseSolver::ShouldEquilibrate().

virtual int Epetra_SerialDenseSolver::EquilibrateMatrix ( void  )
virtual

Equilibrates the this matrix.

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

Reimplemented in Epetra_SerialSpdDenseSolver.

int Epetra_SerialDenseSolver::EquilibrateRHS ( void  )

Equilibrates the current RHS.

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

virtual int Epetra_SerialDenseSolver::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.

Reimplemented in Epetra_SerialSpdDenseSolver.

void Epetra_SerialDenseSolver::FactorWithEquilibration ( 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.

virtual int Epetra_SerialDenseSolver::Invert ( void  )
virtual

Inverts the this matrix.

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

Reimplemented in Epetra_SerialSpdDenseSolver.

virtual int Epetra_SerialDenseSolver::ReciprocalConditionEstimate ( double &  Value)
virtual

Returns the reciprocal of the 1-norm condition number of the this matrix.

Parameters
ValueOut 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 in Epetra_SerialSpdDenseSolver.

double Epetra_SerialDenseSolver::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.

int Epetra_SerialDenseSolver::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.

virtual int Epetra_SerialDenseSolver::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 in Epetra_SerialSpdDenseSolver.

int Epetra_SerialDenseSolver::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: