A class for constructing and using Hermitian positive definite dense matrices. More...

#include <Teuchos_SerialSpdDenseSolver.hpp>

Inheritance diagram for Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >:

Public Types
typedef Teuchos::ScalarTraits < ScalarType >::magnitudeType	MagnitudeType

Public Types inherited from Teuchos::DefaultBLASImpl< OrdinalType, ScalarType >
typedef details::GivensRotator < ScalarType >::c_type	rotg_c_type
	The type used for c in ROTG. More...

Public Types inherited from Teuchos::LAPACK< OrdinalType, ScalarType >
typedef Teuchos::ScalarTraits < ScalarType >::magnitudeType	MagnitudeType

Protected Member Functions
void	allocateWORK ()

void	allocateIWORK ()

void	resetMatrix ()

void	resetVectors ()

Protected Attributes
bool	equilibrate_

bool	shouldEquilibrate_

bool	equilibratedA_

bool	equilibratedB_

bool	transpose_

bool	factored_

bool	estimateSolutionErrors_

bool	solutionErrorsEstimated_

bool	solved_

bool	inverted_

bool	reciprocalConditionEstimated_

bool	refineSolution_

bool	solutionRefined_

OrdinalType	numRowCols_

OrdinalType	LDA_

OrdinalType	LDAF_

OrdinalType	INFO_

OrdinalType	LWORK_

std::vector< int >	IWORK_

MagnitudeType	ANORM_

MagnitudeType	RCOND_

MagnitudeType	SCOND_

MagnitudeType	AMAX_

RCP< SerialSymDenseMatrix < OrdinalType, ScalarType > >	Matrix_

RCP< SerialDenseMatrix < OrdinalType, ScalarType > >	LHS_

RCP< SerialDenseMatrix < OrdinalType, ScalarType > >	RHS_

RCP< SerialSymDenseMatrix < OrdinalType, ScalarType > >	Factor_

ScalarType *	A_

ScalarType *	AF_

std::vector< MagnitudeType >	FERR_

std::vector< MagnitudeType >	BERR_

std::vector< ScalarType >	WORK_

std::vector< MagnitudeType >	R_

Protected Attributes inherited from Teuchos::CompObject
Flops *	flopCounter_

Private Member Functions
	SerialSpdDenseSolver (const SerialSpdDenseSolver< OrdinalType, ScalarType > &Source)

SerialSpdDenseSolver &	operator= (const SerialSpdDenseSolver< OrdinalType, ScalarType > &Source)

Constructor/Destructor Methods
	SerialSpdDenseSolver ()
	Default constructor; matrix should be set using setMatrix(), LHS and RHS set with setVectors(). More...

virtual	~SerialSpdDenseSolver ()
	SerialSpdDenseSolver destructor. More...

Set Methods
int	setMatrix (const RCP< SerialSymDenseMatrix< OrdinalType, ScalarType > > &A_in)
	Sets the pointers for coefficient matrix. More...

int	setVectors (const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > &X, const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > &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	solveToRefinedSolution (bool flag)
	Causes all solves to compute solution to best ability using iterative refinement. More...

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

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

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

int	invert ()
	Inverts the this matrix. More...

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

int	equilibrateMatrix ()
	Equilibrates the this matrix. More...

int	equilibrateRHS ()
	Equilibrates the current RHS. More...

int	applyRefinement ()
	Apply Iterative Refinement. More...

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

int	reciprocalConditionEstimate (MagnitudeType &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. More...

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

bool	equilibratedA ()
	Returns true if factor is equilibrated (factor available via AF() and LDAF()). More...

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

bool	shouldEquilibrate ()
	Returns true if the LAPACK general rules for equilibration suggest you should equilibrate the system. More...

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

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

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

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

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

Data Accessor methods
RCP< SerialSymDenseMatrix < OrdinalType, ScalarType > >	getMatrix () const
	Returns pointer to current matrix. More...

RCP< SerialSymDenseMatrix < OrdinalType, ScalarType > >	getFactoredMatrix () const
	Returns pointer to factored matrix (assuming factorization has been performed). More...

RCP< SerialDenseMatrix < OrdinalType, ScalarType > >	getLHS () const
	Returns pointer to current LHS. More...

RCP< SerialDenseMatrix < OrdinalType, ScalarType > >	getRHS () const
	Returns pointer to current RHS. More...

OrdinalType	numRows () const
	Returns row dimension of system. More...

OrdinalType	numCols () const
	Returns column dimension of system. More...

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

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

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

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

std::vector< MagnitudeType >	FERR () const
	Returns a pointer to the forward error estimates computed by LAPACK. More...

std::vector< MagnitudeType >	BERR () const
	Returns a pointer to the backward error estimates computed by LAPACK. More...

std::vector< MagnitudeType >	R () const
	Returns a pointer to the row scaling vector used for equilibration. More...

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

Additional Inherited Members
Public Member Functions inherited from Teuchos::CompObject
	CompObject ()
	Default constructor. More...

	CompObject (const CompObject &source)
	Copy Constructor. More...

virtual	~CompObject ()
	Destructor. More...

void	setFlopCounter (const Flops &FlopCounter)
	Set the internal Teuchos::Flops() pointer. More...

void	setFlopCounter (const CompObject &compObject)
	Set the internal Teuchos::Flops() pointer to the flop counter of another Teuchos::CompObject. More...

void	unsetFlopCounter ()
	Set the internal Teuchos::Flops() pointer to 0 (no flops counted). More...

Flops *	getFlopCounter () const
	Get the pointer to the Teuchos::Flops() object associated with this object, returns 0 if none. More...

void	resetFlops () const
	Resets the number of floating point operations to zero for this multi-std::vector. More...

double	getFlops () const
	Returns the number of floating point operations with this multi-std::vector. More...

void	updateFlops (int addflops) const
	Increment Flop count for this object. More...

void	updateFlops (long int addflops) const
	Increment Flop count for this object. More...

void	updateFlops (double addflops) const
	Increment Flop count for this object. More...

void	updateFlops (float addflops) const
	Increment Flop count for this object. More...

Public Member Functions inherited from Teuchos::Object
	Object (int tracebackModeIn=-1)
	Default Constructor. More...

	Object (const char *label, int tracebackModeIn=-1)
	Labeling Constructor. More...

	Object (const std::string &label, int tracebackModeIn=-1)
	Create an Object with the given label, and optionally, with the given traceback mode. More...

virtual	~Object ()
	Destructor (virtual, for safety of derived classes). More...

virtual void	setLabel (const char *theLabel)

virtual const char *	label () const
	Access the object's label (LEGACY; return std::string instead). More...

virtual void	print (std::ostream &os) const
	Print the object to the given output stream. More...

virtual int	reportError (const std::string message, int errorCode) const
	Report an error with this Object. More...

Public Member Functions inherited from Teuchos::BLAS< OrdinalType, ScalarType >
	BLAS (void)
	Default constructor. More...

	BLAS (const BLAS< OrdinalType, ScalarType > &)
	Copy constructor. More...

virtual	~BLAS (void)
	Destructor. More...

Public Member Functions inherited from Teuchos::DefaultBLASImpl< OrdinalType, ScalarType >
	DefaultBLASImpl (void)
	Default constructor. More...

	DefaultBLASImpl (const DefaultBLASImpl< OrdinalType, ScalarType > &)
	Copy constructor. More...

virtual	~DefaultBLASImpl (void)
	Destructor. More...

void	ROTG (ScalarType da, ScalarType db, rotg_c_type c, ScalarType s) const
	Computes a Givens plane rotation. More...

void	ROT (const OrdinalType &n, ScalarType dx, const OrdinalType &incx, ScalarType dy, const OrdinalType &incy, MagnitudeType c, ScalarType s) const
	Applies a Givens plane rotation. More...

void	SCAL (const OrdinalType &n, const ScalarType &alpha, ScalarType *x, const OrdinalType &incx) const
	Scale the vector `x` by the constant `alpha`. More...

void	COPY (const OrdinalType &n, const ScalarType x, const OrdinalType &incx, ScalarType y, const OrdinalType &incy) const
	Copy the vector `x` to the vector `y`. More...

template<typename alpha_type , typename x_type >
void	AXPY (const OrdinalType &n, const alpha_type alpha, const x_type x, const OrdinalType &incx, ScalarType y, const OrdinalType &incy) const
	Perform the operation: `y` `<-` `y+alpha*x`. More...

ScalarTraits< ScalarType > ::magnitudeType	ASUM (const OrdinalType &n, const ScalarType *x, const OrdinalType &incx) const
	Sum the absolute values of the entries of `x`. More...

template<typename x_type , typename y_type >
ScalarType	DOT (const OrdinalType &n, const x_type x, const OrdinalType &incx, const y_type y, const OrdinalType &incy) const
	Form the dot product of the vectors `x` and `y`. More...

ScalarTraits< ScalarType > ::magnitudeType	NRM2 (const OrdinalType &n, const ScalarType *x, const OrdinalType &incx) const
	Compute the 2-norm of the vector `x`. More...

OrdinalType	IAMAX (const OrdinalType &n, const ScalarType *x, const OrdinalType &incx) const
	Return the index of the element of `x` with the maximum magnitude. More...

template<typename alpha_type , typename A_type , typename x_type , typename beta_type >
void	GEMV (ETransp trans, const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const A_type A, const OrdinalType &lda, const x_type x, const OrdinalType &incx, const beta_type beta, ScalarType *y, const OrdinalType &incy) const
	Performs the matrix-vector operation: `y` `<-` `alphaAx+betay` or `y` `<-` `alphaA'x+betay` where `A` is a general `m` by `n` matrix. More...

template<typename A_type >
void	TRMV (EUplo uplo, ETransp trans, EDiag diag, const OrdinalType &n, const A_type A, const OrdinalType &lda, ScalarType x, const OrdinalType &incx) const
	Performs the matrix-vector operation: `x` `<-` `Ax` or `x` `<-` `A'x` where `A` is a unit/non-unit `n` by `n` upper/lower triangular matrix. More...

template<typename alpha_type , typename x_type , typename y_type >
void	GER (const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const x_type x, const OrdinalType &incx, const y_type y, const OrdinalType &incy, ScalarType *A, const OrdinalType &lda) const
	Performs the rank 1 operation: `A` `<-` `alphaxy'+A`. More...

template<typename alpha_type , typename A_type , typename B_type , typename beta_type >
void	GEMM (ETransp transa, ETransp transb, const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, const alpha_type alpha, const A_type A, const OrdinalType &lda, const B_type B, const OrdinalType &ldb, const beta_type beta, ScalarType *C, const OrdinalType &ldc) const
	General matrix-matrix multiply. More...

void	SWAP (const OrdinalType &n, ScalarType const x, const OrdinalType &incx, ScalarType const y, const OrdinalType &incy) const
	Swap the entries of x and y. More...

template<typename alpha_type , typename A_type , typename B_type , typename beta_type >
void	SYMM (ESide side, EUplo uplo, const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const A_type A, const OrdinalType &lda, const B_type B, const OrdinalType &ldb, const beta_type beta, ScalarType *C, const OrdinalType &ldc) const
	Performs the matrix-matrix operation: `C` `<-` `alphaAB+betaC` or `C` `<-` `alphaBA+betaC` where `A` is an `m` by `m` or `n` by `n` symmetric matrix and `B` is a general matrix. More...

template<typename alpha_type , typename A_type , typename beta_type >
void	SYRK (EUplo uplo, ETransp trans, const OrdinalType &n, const OrdinalType &k, const alpha_type alpha, const A_type A, const OrdinalType &lda, const beta_type beta, ScalarType C, const OrdinalType &ldc) const
	Performs the symmetric rank k operation: `C` <- `alphaAA'+betaC` or `C` <- `alphaA'A+betaC`, where `alpha` and `beta` are scalars, `C` is an `n` by `n` symmetric matrix and `A` is an `n` by `k` matrix in the first case or `k` by `n` matrix in the second case. More...

template<typename alpha_type , typename A_type >
void	TRMM (ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const A_type A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb) const
	Performs the matrix-matrix operation: `B` `<-` `alphaop`(A)B or `B` `<-` `alphaBop`(A) where `op(A)` is an unit/non-unit, upper/lower triangular matrix and `B` is a general matrix. More...

template<typename alpha_type , typename A_type >
void	TRSM (ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const A_type A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb) const
	Solves the matrix equations: `op(A)X=alphaB` or `Xop`(A)=alphaB where `X` and `B` are `m` by `n` matrices, `A` is a unit/non-unit, upper/lower triangular matrix and `op(A)` is `A` or `A'`. The matrix `X` is overwritten on `B`. More...

Public Member Functions inherited from Teuchos::LAPACK< OrdinalType, ScalarType >
	LAPACK (void)
	Default Constructor. More...

	LAPACK (const LAPACK< OrdinalType, ScalarType > &lapack)
	Copy Constructor. More...

virtual	~LAPACK (void)
	Destructor. More...

void	PTTRF (const OrdinalType &n, MagnitudeType d, ScalarType e, OrdinalType *info) const
	Computes the `LDL'` factorization of a Hermitian/symmetric positive definite tridiagonal matrix `A`. More...

void	PTTRS (const OrdinalType &n, const OrdinalType &nrhs, const MagnitudeType d, const ScalarType e, ScalarType B, const OrdinalType &ldb, OrdinalType info) const
	Solves a tridiagonal system `AX=B` using the D*L' factorization of `A` computed by PTTRF. More...

void	POTRF (const char &UPLO, const OrdinalType &n, ScalarType A, const OrdinalType &lda, OrdinalType info) const
	Computes Cholesky factorization of a real symmetric positive definite matrix `A`. More...

void	POTRS (const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, OrdinalType *info) const
	Solves a system of linear equations `A*X=B`, where `A` is a symmetric positive definite matrix factored by POTRF and the `nrhs` solutions are returned in `B`. More...

void	POTRI (const char &UPLO, const OrdinalType &n, ScalarType A, const OrdinalType &lda, OrdinalType info) const
	Computes the inverse of a real symmetric positive definite matrix `A` using the Cholesky factorization `A` from POTRF. More...

void	POCON (const char &UPLO, const OrdinalType &n, const ScalarType A, const OrdinalType &lda, const ScalarType &anorm, ScalarType rcond, ScalarType WORK, OrdinalType IWORK, OrdinalType *info) const
	Estimates the reciprocal of the condition number (1-norm) of a real symmetric positive definite matrix `A` using the Cholesky factorization from POTRF. More...

void	POSV (const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, OrdinalType *info) const
	Computes the solution to a real system of linear equations `A*X=B`, where `A` is a symmetric positive definite matrix and the `nrhs` solutions are returned in `B`. More...

void	POEQU (const OrdinalType &n, const ScalarType A, const OrdinalType &lda, MagnitudeType S, MagnitudeType scond, MagnitudeType amax, OrdinalType *info) const
	Computes row and column scalings intended to equilibrate a symmetric positive definite matrix `A` and reduce its condition number (w.r.t. 2-norm). More...

void	PORFS (const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType A, const OrdinalType &lda, const ScalarType AF, const OrdinalType &ldaf, const ScalarType B, const OrdinalType &ldb, ScalarType X, const OrdinalType &ldx, ScalarType FERR, ScalarType BERR, ScalarType WORK, OrdinalType IWORK, OrdinalType *info) const
	Improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, and provides error bounds and backward error estimates for the solution. More...

void	POSVX (const char &FACT, const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, ScalarType A, const OrdinalType &lda, ScalarType AF, const OrdinalType &ldaf, char EQUED, ScalarType S, ScalarType B, const OrdinalType &ldb, ScalarType X, const OrdinalType &ldx, ScalarType rcond, ScalarType FERR, ScalarType BERR, ScalarType WORK, OrdinalType IWORK, OrdinalType info) const
	Uses the Cholesky factorization to compute the solution to a real system of linear equations `A*X=B`, where `A` is symmetric positive definite. System can be equilibrated by POEQU and iteratively refined by PORFS, if requested. More...

void	GELS (const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &nrhs, ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, ScalarType WORK, const OrdinalType &lwork, OrdinalType info) const
	Solves an over/underdetermined real `m` by `n` linear system `A` using QR or LQ factorization of A. More...

void	GELSS (const OrdinalType &m, const OrdinalType &n, const OrdinalType &nrhs, ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, MagnitudeType S, const MagnitudeType rcond, OrdinalType rank, ScalarType WORK, const OrdinalType &lwork, MagnitudeType RWORK, OrdinalType *info) const
	Use the SVD to solve a possibly rank-deficient linear least-squares problem. More...

void	GELSS (const OrdinalType &m, const OrdinalType &n, const OrdinalType &nrhs, ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, ScalarType S, const ScalarType &rcond, OrdinalType rank, ScalarType WORK, const OrdinalType &lwork, OrdinalType info) const
	Legacy GELSS interface for real-valued ScalarType. More...

void	GGLSE (const OrdinalType &m, const OrdinalType &n, const OrdinalType &p, ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, ScalarType C, ScalarType D, ScalarType X, ScalarType WORK, const OrdinalType &lwork, OrdinalType *info) const
	Solves the linear equality-constrained least squares (LSE) problem where `A` is an `m` by `n` matrix,`B` is a `p` by `n` matrix `C` is a given `m-vector`, and D is a given `p-vector`. More...

void	GEQRF (const OrdinalType &m, const OrdinalType &n, ScalarType A, const OrdinalType &lda, ScalarType TAU, ScalarType WORK, const OrdinalType &lwork, OrdinalType info) const
	Computes a QR factorization of a general `m` by `n` matrix `A`. More...

void	GEQR2 (const OrdinalType &m, const OrdinalType &n, ScalarType A, const OrdinalType &lda, ScalarType TAU, ScalarType WORK, OrdinalType const info) const
	BLAS 2 version of GEQRF, with known workspace size. More...

void	GETRF (const OrdinalType &m, const OrdinalType &n, ScalarType A, const OrdinalType &lda, OrdinalType IPIV, OrdinalType *info) const
	Computes an LU factorization of a general `m` by `n` matrix `A` using partial pivoting with row interchanges. More...

void	GETRS (const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType A, const OrdinalType &lda, const OrdinalType IPIV, ScalarType B, const OrdinalType &ldb, OrdinalType info) const
	Solves a system of linear equations `AX=B` or `A'X=B` with a general `n` by `n` matrix `A` using the LU factorization computed by GETRF. More...

void	LASCL (const char &TYPE, const OrdinalType &kl, const OrdinalType &ku, const MagnitudeType cfrom, const MagnitudeType cto, const OrdinalType &m, const OrdinalType &n, ScalarType A, const OrdinalType &lda, OrdinalType info) const
	Multiplies the `m` by `n` matrix `A` by the real scalar `cto/cfrom`. More...

void	GEQP3 (const OrdinalType &m, const OrdinalType &n, ScalarType A, const OrdinalType &lda, OrdinalType jpvt, ScalarType TAU, ScalarType WORK, const OrdinalType &lwork, MagnitudeType RWORK, OrdinalType info) const
	Computes a QR factorization with column pivoting of a matrix `A:` AP = QR using Level 3 BLAS. More...

void	LASWP (const OrdinalType &N, ScalarType A, const OrdinalType &LDA, const OrdinalType &K1, const OrdinalType &K2, const OrdinalType IPIV, const OrdinalType &INCX) const
	Apply a series of row interchanges to the matrix A. More...

void	GBTRF (const OrdinalType &m, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, ScalarType A, const OrdinalType &lda, OrdinalType IPIV, OrdinalType *info) const
	Computes an LU factorization of a general banded `m` by `n` matrix `A` using partial pivoting with row interchanges. More...

void	GBTRS (const char &TRANS, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const OrdinalType &nrhs, const ScalarType A, const OrdinalType &lda, const OrdinalType IPIV, ScalarType B, const OrdinalType &ldb, OrdinalType info) const
	Solves a system of linear equations `AX=B` or `A'X=B` with a general banded `n` by `n` matrix `A` using the LU factorization computed by GBTRF. More...

void	GTTRF (const OrdinalType &n, ScalarType dl, ScalarType d, ScalarType du, ScalarType du2, OrdinalType IPIV, OrdinalType info) const
	Computes an LU factorization of a `n` by `n` tridiagonal matrix `A` using partial pivoting with row interchanges. More...

void	GTTRS (const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType dl, const ScalarType d, const ScalarType du, const ScalarType du2, const OrdinalType IPIV, ScalarType B, const OrdinalType &ldb, OrdinalType *info) const
	Solves a system of linear equations `AX=B` or `A'X=B` or `A^H*X=B` with a tridiagonal matrix `A` using the LU factorization computed by GTTRF. More...

void	GETRI (const OrdinalType &n, ScalarType A, const OrdinalType &lda, const OrdinalType IPIV, ScalarType WORK, const OrdinalType &lwork, OrdinalType info) const
	Computes the inverse of a matrix `A` using the LU factorization computed by GETRF. More...

void	LATRS (const char &UPLO, const char &TRANS, const char &DIAG, const char &NORMIN, const OrdinalType &N, const ScalarType A, const OrdinalType &LDA, ScalarType X, MagnitudeType SCALE, MagnitudeType CNORM, OrdinalType *INFO) const
	Robustly solve a possibly singular triangular linear system. More...

void	GECON (const char &NORM, const OrdinalType &n, const ScalarType A, const OrdinalType &lda, const ScalarType &anorm, ScalarType rcond, ScalarType WORK, OrdinalType IWORK, OrdinalType *info) const
	Estimates the reciprocal of the condition number of a general real matrix `A`, in either the 1-norm or the infinity-norm, using the LU factorization computed by GETRF. More...

void	GBCON (const char &NORM, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const ScalarType A, const OrdinalType &lda, const OrdinalType IPIV, const ScalarType &anorm, ScalarType rcond, ScalarType WORK, OrdinalType IWORK, OrdinalType info) const
	Estimates the reciprocal of the condition number of a general banded real matrix `A`, in either the 1-norm or the infinity-norm, using the LU factorization computed by GETRF. More...

ScalarTraits< ScalarType > ::magnitudeType	LANGB (const char &NORM, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const ScalarType A, const OrdinalType &lda, MagnitudeType WORK) const
	Returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an `n` by `n` band matrix `A`, with `kl` sub-diagonals and `ku` super-diagonals. More...

void	GESV (const OrdinalType &n, const OrdinalType &nrhs, ScalarType A, const OrdinalType &lda, OrdinalType IPIV, ScalarType B, const OrdinalType &ldb, OrdinalType info) const
	Computes the solution to a real system of linear equations `A*X=B`, where `A` is factored through GETRF and the `nrhs` solutions are computed through GETRS. More...

void	GEEQU (const OrdinalType &m, const OrdinalType &n, const ScalarType A, const OrdinalType &lda, ScalarType R, ScalarType C, ScalarType rowcond, ScalarType colcond, ScalarType amax, OrdinalType *info) const
	Computes row and column scalings intended to equilibrate an `m` by `n` matrix `A` and reduce its condition number. More...

void	GERFS (const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType A, const OrdinalType &lda, const ScalarType AF, const OrdinalType &ldaf, const OrdinalType IPIV, const ScalarType B, const OrdinalType &ldb, ScalarType X, const OrdinalType &ldx, ScalarType FERR, ScalarType BERR, ScalarType WORK, OrdinalType IWORK, OrdinalType info) const
	Improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. Use after GETRF/GETRS. More...

void	GBEQU (const OrdinalType &m, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const ScalarType A, const OrdinalType &lda, MagnitudeType R, MagnitudeType C, MagnitudeType rowcond, MagnitudeType colcond, MagnitudeType amax, OrdinalType *info) const
	Computes row and column scalings intended to equilibrate an `m` by `n` banded matrix `A` and reduce its condition number. More...

void	GBRFS (const char &TRANS, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const OrdinalType &nrhs, const ScalarType A, const OrdinalType &lda, const ScalarType AF, const OrdinalType &ldaf, const OrdinalType IPIV, const ScalarType B, const OrdinalType &ldb, ScalarType X, const OrdinalType &ldx, ScalarType FERR, ScalarType BERR, ScalarType WORK, OrdinalType IWORK, OrdinalType info) const
	Improves the computed solution to a banded system of linear equations and provides error bounds and backward error estimates for the solution. Use after GBTRF/GBTRS. More...

void	GESVX (const char &FACT, const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, ScalarType A, const OrdinalType &lda, ScalarType AF, const OrdinalType &ldaf, OrdinalType IPIV, char EQUED, ScalarType R, ScalarType C, ScalarType B, const OrdinalType &ldb, ScalarType X, const OrdinalType &ldx, ScalarType rcond, ScalarType FERR, ScalarType BERR, ScalarType WORK, OrdinalType IWORK, OrdinalType info) const
	Uses the LU factorization to compute the solution to a real system of linear equations `A*X=B`, returning error bounds on the solution and a condition estimate. More...

void	SYTRD (const char &UPLO, const OrdinalType &n, ScalarType A, const OrdinalType &lda, ScalarType D, ScalarType E, ScalarType TAU, ScalarType WORK, const OrdinalType &lwork, OrdinalType info) const
	Reduces a real symmetric matrix `A` to tridiagonal form by orthogonal similarity transformations. More...

void	GEHRD (const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, ScalarType A, const OrdinalType &lda, ScalarType TAU, ScalarType WORK, const OrdinalType &lwork, OrdinalType info) const
	Reduces a real general matrix `A` to upper Hessenberg form by orthogonal similarity transformations. More...

void	TRTRS (const char &UPLO, const char &TRANS, const char &DIAG, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, OrdinalType *info) const
	Solves a triangular linear system of the form `AX=B` or `ATX=B`, where `A` is a triangular matrix. More...

void	TRTRI (const char &UPLO, const char &DIAG, const OrdinalType &n, ScalarType A, const OrdinalType &lda, OrdinalType info) const
	Computes the inverse of an upper or lower triangular matrix `A`. More...

void	SPEV (const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType AP, ScalarType W, ScalarType Z, const OrdinalType &ldz, ScalarType WORK, OrdinalType *info) const
	Computes the eigenvalues and, optionally, eigenvectors of a symmetric `n` by `n` matrix `A` in packed storage. More...

void	SYEV (const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType A, const OrdinalType &lda, ScalarType W, ScalarType WORK, const OrdinalType &lwork, OrdinalType info) const
	Computes all the eigenvalues and, optionally, eigenvectors of a symmetric `n` by `n` matrix A. More...

void	SYGV (const OrdinalType &itype, const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, ScalarType W, ScalarType WORK, const OrdinalType &lwork, OrdinalType *info) const
	Computes all the eigenvalues and, optionally, eigenvectors of a symmetric `n` by `n` matrix pencil `{A`,B}, where `A` is symmetric and `B` is symmetric positive-definite. More...

void	HEEV (const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType A, const OrdinalType &lda, MagnitudeType W, ScalarType WORK, const OrdinalType &lwork, MagnitudeType RWORK, OrdinalType *info) const
	Computes all the eigenvalues and, optionally, eigenvectors of a Hermitian `n` by `n` matrix A. More...

void	HEGV (const OrdinalType &itype, const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, MagnitudeType W, ScalarType WORK, const OrdinalType &lwork, MagnitudeType RWORK, OrdinalType info) const
	Computes all the eigenvalues and, optionally, eigenvectors of a generalized Hermitian-definite `n` by `n` matrix pencil `{A`,B}, where `A` is Hermitian and `B` is Hermitian positive-definite. More...

void	STEQR (const char &COMPZ, const OrdinalType &n, MagnitudeType D, MagnitudeType E, ScalarType Z, const OrdinalType &ldz, MagnitudeType WORK, OrdinalType *info) const
	Computes the eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal `n` by `n` matrix `A` using implicit QL/QR. The eigenvectors can only be computed if `A` was reduced to tridiagonal form by SYTRD. More...

void	PTEQR (const char &COMPZ, const OrdinalType &n, MagnitudeType D, MagnitudeType E, ScalarType Z, const OrdinalType &ldz, MagnitudeType WORK, OrdinalType *info) const
	Computes the eigenvalues and, optionally, eigenvectors of a symmetric positive-definite tridiagonal `n` by `n` matrix `A` using BDSQR, after factoring the matrix with PTTRF. More...

void	HSEQR (const char &JOB, const char &COMPZ, const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, ScalarType H, const OrdinalType &ldh, ScalarType WR, ScalarType WI, ScalarType Z, const OrdinalType &ldz, ScalarType WORK, const OrdinalType &lwork, OrdinalType info) const
	Computes the eigenvalues of a real upper Hessenberg matrix `H` and, optionally, the matrices `T` and `Z` from the Schur decomposition, where T is an upper quasi-triangular matrix and Z contains the Schur vectors. More...

void	GEES (const char &JOBVS, const char &SORT, OrdinalType &(ptr2func)(ScalarType , ScalarType ), const OrdinalType &n, ScalarType A, const OrdinalType &lda, OrdinalType sdim, ScalarType WR, ScalarType WI, ScalarType VS, const OrdinalType &ldvs, ScalarType WORK, const OrdinalType &lwork, OrdinalType BWORK, OrdinalType *info) const

void	GEES (const char &JOBVS, const char &SORT, OrdinalType &(ptr2func)(ScalarType ), const OrdinalType &n, ScalarType A, const OrdinalType &lda, OrdinalType sdim, ScalarType W, ScalarType VS, const OrdinalType &ldvs, ScalarType WORK, const OrdinalType &lwork, MagnitudeType RWORK, OrdinalType BWORK, OrdinalType info) const

void	GEES (const char &JOBVS, const OrdinalType &n, ScalarType A, const OrdinalType &lda, OrdinalType sdim, MagnitudeType WR, MagnitudeType WI, ScalarType VS, const OrdinalType &ldvs, ScalarType WORK, const OrdinalType &lwork, MagnitudeType RWORK, OrdinalType BWORK, OrdinalType *info) const

void	GEEV (const char &JOBVL, const char &JOBVR, const OrdinalType &n, ScalarType A, const OrdinalType &lda, MagnitudeType WR, MagnitudeType WI, ScalarType VL, const OrdinalType &ldvl, ScalarType VR, const OrdinalType &ldvr, ScalarType WORK, const OrdinalType &lwork, MagnitudeType RWORK, OrdinalType info) const
	Computes for an `n` by `n` real nonsymmetric matrix `A`, the eigenvalues and, optionally, the left and/or right eigenvectors. More...

void	GEEVX (const char &BALANC, const char &JOBVL, const char &JOBVR, const char &SENSE, const OrdinalType &n, ScalarType A, const OrdinalType &lda, ScalarType WR, ScalarType WI, ScalarType VL, const OrdinalType &ldvl, ScalarType VR, const OrdinalType &ldvr, OrdinalType ilo, OrdinalType ihi, MagnitudeType SCALE, MagnitudeType abnrm, MagnitudeType RCONDE, MagnitudeType RCONDV, ScalarType WORK, const OrdinalType &lwork, OrdinalType IWORK, OrdinalType info) const

void	GGEVX (const char &BALANC, const char &JOBVL, const char &JOBVR, const char &SENSE, const OrdinalType &n, ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, MagnitudeType ALPHAR, MagnitudeType ALPHAI, ScalarType BETA, ScalarType VL, const OrdinalType &ldvl, ScalarType VR, const OrdinalType &ldvr, OrdinalType ilo, OrdinalType ihi, MagnitudeType lscale, MagnitudeType rscale, MagnitudeType abnrm, MagnitudeType bbnrm, MagnitudeType RCONDE, MagnitudeType RCONDV, ScalarType WORK, const OrdinalType &lwork, OrdinalType IWORK, OrdinalType BWORK, OrdinalType *info) const

void	GGEV (const char &JOBVL, const char &JOBVR, const OrdinalType &n, ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, MagnitudeType ALPHAR, MagnitudeType ALPHAI, ScalarType BETA, ScalarType VL, const OrdinalType &ldvl, ScalarType VR, const OrdinalType &ldvr, ScalarType WORK, const OrdinalType &lwork, OrdinalType *info) const

void	TRSEN (const char &JOB, const char &COMPQ, const OrdinalType SELECT, const OrdinalType &n, ScalarType T, const OrdinalType &ldt, ScalarType Q, const OrdinalType &ldq, MagnitudeType WR, MagnitudeType WI, OrdinalType M, ScalarType S, MagnitudeType SEP, ScalarType WORK, const OrdinalType &lwork, OrdinalType IWORK, const OrdinalType &liwork, OrdinalType *info) const

void	TGSEN (const OrdinalType &ijob, const OrdinalType &wantq, const OrdinalType &wantz, const OrdinalType SELECT, const OrdinalType &n, ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, MagnitudeType ALPHAR, MagnitudeType ALPHAI, MagnitudeType BETA, ScalarType Q, const OrdinalType &ldq, ScalarType Z, const OrdinalType &ldz, OrdinalType M, MagnitudeType PL, MagnitudeType PR, MagnitudeType DIF, ScalarType WORK, const OrdinalType &lwork, OrdinalType IWORK, const OrdinalType &liwork, OrdinalType *info) const

void	GGES (const char &JOBVL, const char &JOBVR, const char &SORT, OrdinalType &(ptr2func)(ScalarType , ScalarType , ScalarType ), const OrdinalType &n, ScalarType A, const OrdinalType &lda, ScalarType B, const OrdinalType &ldb, OrdinalType sdim, MagnitudeType ALPHAR, MagnitudeType ALPHAI, MagnitudeType BETA, ScalarType VL, const OrdinalType &ldvl, ScalarType VR, const OrdinalType &ldvr, ScalarType WORK, const OrdinalType &lwork, OrdinalType BWORK, OrdinalType *info) const

void	GESVD (const char &JOBU, const char &JOBVT, const OrdinalType &m, const OrdinalType &n, ScalarType A, const OrdinalType &lda, MagnitudeType S, ScalarType U, const OrdinalType &ldu, ScalarType V, const OrdinalType &ldv, ScalarType WORK, const OrdinalType &lwork, MagnitudeType RWORK, OrdinalType *info) const
	Computes the singular values (and optionally, vectors) of a real matrix `A`. More...

void	ORMQR (const char &SIDE, const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, const ScalarType A, const OrdinalType &lda, const ScalarType TAU, ScalarType C, const OrdinalType &ldc, ScalarType WORK, const OrdinalType &lwork, OrdinalType *info) const

void	ORM2R (const char &SIDE, const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, const ScalarType A, const OrdinalType &lda, const ScalarType TAU, ScalarType C, const OrdinalType &ldc, ScalarType WORK, OrdinalType *const info) const
	BLAS 2 version of ORMQR; known workspace size. More...

void	UNMQR (const char &SIDE, const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, const ScalarType A, const OrdinalType &lda, const ScalarType TAU, ScalarType C, const OrdinalType &ldc, ScalarType WORK, const OrdinalType &lwork, OrdinalType *info) const
	Apply Householder reflectors (complex case). More...

void	UNM2R (const char &SIDE, const char &TRANS, const OrdinalType &M, const OrdinalType &N, const OrdinalType &K, const ScalarType A, const OrdinalType &LDA, const ScalarType TAU, ScalarType C, const OrdinalType &LDC, ScalarType WORK, OrdinalType *const INFO) const
	BLAS 2 version of UNMQR; known workspace size. More...

void	ORGQR (const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, ScalarType A, const OrdinalType &lda, const ScalarType TAU, ScalarType WORK, const OrdinalType &lwork, OrdinalType info) const
	Compute explicit Q factor from QR factorization (GEQRF) (real case). More...

void	UNGQR (const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, ScalarType A, const OrdinalType &lda, const ScalarType TAU, ScalarType WORK, const OrdinalType &lwork, OrdinalType info) const
	Compute explicit QR factor from QR factorization (GEQRF) (complex case). More...

void	ORGHR (const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, ScalarType A, const OrdinalType &lda, const ScalarType TAU, ScalarType WORK, const OrdinalType &lwork, OrdinalType info) const
	Generates a real orthogonal matrix `Q` which is the product of `ihi-ilo` elementary reflectors of order `n`, as returned by GEHRD. On return `Q` is stored in `A`. More...

void	ORMHR (const char &SIDE, const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, const ScalarType A, const OrdinalType &lda, const ScalarType TAU, ScalarType C, const OrdinalType &ldc, ScalarType WORK, const OrdinalType &lwork, OrdinalType *info) const
	Overwrites the general real `m` by `n` matrix `C` with the product of `C` and `Q`, which is a product of `ihi-ilo` elementary reflectors, as returned by GEHRD. More...

void	TREVC (const char &SIDE, const char &HOWMNY, OrdinalType select, const OrdinalType &n, const ScalarType T, const OrdinalType &ldt, ScalarType VL, const OrdinalType &ldvl, ScalarType VR, const OrdinalType &ldvr, const OrdinalType &mm, OrdinalType m, ScalarType WORK, OrdinalType *info) const

void	TREVC (const char &SIDE, const OrdinalType &n, const ScalarType T, const OrdinalType &ldt, ScalarType VL, const OrdinalType &ldvl, ScalarType VR, const OrdinalType &ldvr, const OrdinalType &mm, OrdinalType m, ScalarType WORK, MagnitudeType RWORK, OrdinalType *info) const

void	TREXC (const char &COMPQ, const OrdinalType &n, ScalarType T, const OrdinalType &ldt, ScalarType Q, const OrdinalType &ldq, OrdinalType ifst, OrdinalType ilst, ScalarType WORK, OrdinalType info) const

void	TGEVC (const char &SIDE, const char &HOWMNY, const OrdinalType SELECT, const OrdinalType &n, const ScalarType S, const OrdinalType &lds, const ScalarType P, const OrdinalType &ldp, ScalarType VL, const OrdinalType &ldvl, ScalarType VR, const OrdinalType &ldvr, const OrdinalType &mm, OrdinalType M, ScalarType WORK, OrdinalType info) const

void	LARTG (const ScalarType &f, const ScalarType &g, MagnitudeType c, ScalarType s, ScalarType *r) const
	Gnerates a plane rotation that zeros out the second component of the input vector. More...

void	LARFG (const OrdinalType &n, ScalarType alpha, ScalarType x, const OrdinalType &incx, ScalarType *tau) const
	Generates an elementary reflector of order `n` that zeros out the last `n-1` components of the input vector. More...

void	GEBAL (const char &JOBZ, const OrdinalType &n, ScalarType A, const OrdinalType &lda, OrdinalType ilo, OrdinalType ihi, MagnitudeType scale, OrdinalType *info) const
	Balances a general matrix A, through similarity transformations to make the rows and columns as close in norm as possible. More...

void	GEBAK (const char &JOBZ, const char &SIDE, const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, const MagnitudeType scale, const OrdinalType &m, ScalarType V, const OrdinalType &ldv, OrdinalType *info) const
	Forms the left or right eigenvectors of a general matrix that has been balanced by GEBAL by backward transformation of the computed eigenvectors `V`. More...

ScalarType	LARND (const OrdinalType &idist, OrdinalType *seed) const
	Returns a random number from a uniform or normal distribution. More...

void	LARNV (const OrdinalType &idist, OrdinalType seed, const OrdinalType &n, ScalarType v) const
	Returns a vector of random numbers from a chosen distribution. More...

ScalarType	LAMCH (const char &CMACH) const
	Determines machine parameters for floating point characteristics. More...

OrdinalType	ILAENV (const OrdinalType &ispec, const std::string &NAME, const std::string &OPTS, const OrdinalType &N1=-1, const OrdinalType &N2=-1, const OrdinalType &N3=-1, const OrdinalType &N4=-1) const
	Chooses problem-dependent parameters for the local environment. More...

ScalarType	LAPY2 (const ScalarType &x, const ScalarType &y) const
	Computes x^2 + y^2 safely, to avoid overflow. More...

Static Public Member Functions inherited from Teuchos::Object
static void	setTracebackMode (int tracebackModeValue)
	Set the value of the Object error traceback report mode. More...

static int	getTracebackMode ()
	Get the value of the Object error traceback report mode. More...

Static Public Attributes inherited from Teuchos::Object
static int	tracebackMode = -1

Related Functions inherited from Teuchos::Object
std::ostream &	operator<< (std::ostream &os, const Teuchos::Object &obj)
	Print the given Object to the given output stream. More...

Detailed Description

template<typename OrdinalType, typename ScalarType>
class Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >

A class for constructing and using Hermitian positive definite dense matrices.

The Teuchos::SerialSpdDenseSolver class enables the construction and use of a templated, Hermitian positive definite, double-precision dense matrices. It is built on the BLAS and LAPACK via the Teuchos::BLAS and Teuchos::LAPACK classes.

The Teuchos::SerialSpdDenseSolver class is intended to provide full-featured support for solving linear system problems for Hermitian 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.

Teuchos::SerialSpdDenseSolver vs. Teuchos::LAPACK

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

When you should use Teuchos::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 Teuchos::LAPACK directly.
When you should use Teuchos::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 Teuchos::SerialSpdDenseSolver.

Extracting Data from Teuchos::SerialSpdDenseSolver Objects

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

Factorizations.
Solves.
Condition estimates.
Equilibration.
Norms.

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.

Teuchos::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.

Teuchos::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 Teuchos::SerialSpdDenseSolver can be found in the Teuchos test directories.

Definition at line 101 of file Teuchos_SerialSpdDenseSolver.hpp.

Member Typedef Documentation

template<typename OrdinalType, typename ScalarType>

typedef Teuchos::ScalarTraits<ScalarType>::magnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::MagnitudeType

Definition at line 106 of file Teuchos_SerialSpdDenseSolver.hpp.

Constructor & Destructor Documentation

template<typename OrdinalType , typename ScalarType >

Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::SerialSpdDenseSolver ( )

Default constructor; matrix should be set using setMatrix(), LHS and RHS set with setVectors().

Definition at line 378 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::~SerialSpdDenseSolver ( )

virtual

SerialSpdDenseSolver destructor.

Definition at line 410 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::SerialSpdDenseSolver ( const SerialSpdDenseSolver< OrdinalType, ScalarType > & Source )

private

Member Function Documentation

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::setMatrix ( const RCP< SerialSymDenseMatrix< OrdinalType, ScalarType > > & A_in )

Sets the pointers for coefficient matrix.

Definition at line 451 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::setVectors	(	const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > &	X,
		const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > &	B
	)

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

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

Definition at line 466 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

void Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::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.

Definition at line 153 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

void Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solveToRefinedSolution ( bool flag )

inline

Causes all solves to compute solution to best ability using iterative refinement.

Definition at line 156 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

void Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::estimateSolutionErrors ( bool flag )

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

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

Definition at line 489 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::factor ( )

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

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

Definition at line 499 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solve ( )

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

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

Definition at line 546 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::invert ( )

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.

Definition at line 805 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::computeEquilibrateScaling ( )

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.

Definition at line 662 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibrateMatrix ( )

Equilibrates the this matrix.

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

Definition at line 681 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibrateRHS ( )

Equilibrates the current RHS.

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

Definition at line 754 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::applyRefinement ( )

Apply Iterative Refinement.

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

Definition at line 627 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::unequilibrateLHS ( )

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.

Definition at line 782 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::reciprocalConditionEstimate ( MagnitudeType & Value )

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

Parameters

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

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

Definition at line 832 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::transpose ( )

inline

Returns true if transpose of this matrix has and will be used.

Definition at line 232 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::factored ( )

inline

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

Definition at line 235 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibratedA ( )

inline

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

Definition at line 238 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibratedB ( )

inline

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

Definition at line 241 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::shouldEquilibrate ( )

inline

Returns true if the LAPACK general rules for equilibration suggest you should equilibrate the system.

Definition at line 244 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solutionErrorsEstimated ( )

inline

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

Definition at line 247 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::inverted ( )

inline

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

Definition at line 250 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::reciprocalConditionEstimated ( )

inline

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

Definition at line 253 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solved ( )

inline

Returns true if the current set of vectors has been solved.

Definition at line 256 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solutionRefined ( )

inline

Returns true if the current set of vectors has been refined.

Definition at line 259 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

RCP<SerialSymDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::getMatrix ( ) const

inline

Returns pointer to current matrix.

Definition at line 266 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

RCP<SerialSymDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::getFactoredMatrix ( ) const

inline

Returns pointer to factored matrix (assuming factorization has been performed).

Definition at line 269 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::getLHS ( ) const

inline

Returns pointer to current LHS.

Definition at line 272 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::getRHS ( ) const

inline

Returns pointer to current RHS.

Definition at line 275 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::numRows ( ) const

inline

Returns row dimension of system.

Definition at line 278 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::numCols ( ) const

inline

Returns column dimension of system.

Definition at line 281 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::ANORM ( ) const

inline

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

Definition at line 284 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::RCOND ( ) const

inline

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

Definition at line 287 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::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.

Definition at line 292 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::AMAX ( ) const

inline

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

Definition at line 295 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

std::vector<MagnitudeType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::FERR ( ) const

inline

Returns a pointer to the forward error estimates computed by LAPACK.

Definition at line 298 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

std::vector<MagnitudeType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::BERR ( ) const

inline

Returns a pointer to the backward error estimates computed by LAPACK.

Definition at line 301 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

std::vector<MagnitudeType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::R ( ) const

inline

Returns a pointer to the row scaling vector used for equilibration.

Definition at line 304 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

void Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::Print ( std::ostream & os ) const

Print service methods; defines behavior of ostream << operator.

Definition at line 865 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

void Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::allocateWORK ( )

inlineprotected

Definition at line 316 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

void Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::allocateIWORK ( )

inlineprotected

Definition at line 317 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

void Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::resetMatrix ( )

protected

Definition at line 429 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

void Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::resetVectors ( )

protected

Definition at line 416 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

SerialSpdDenseSolver& Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::operator= ( const SerialSpdDenseSolver< OrdinalType, ScalarType > & Source )

private

Member Data Documentation

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibrate_

protected

Definition at line 321 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::shouldEquilibrate_

protected

Definition at line 322 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibratedA_

protected

Definition at line 323 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibratedB_

protected

Definition at line 324 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::transpose_

protected

Definition at line 325 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::factored_

protected

Definition at line 326 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::estimateSolutionErrors_

protected

Definition at line 327 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solutionErrorsEstimated_

protected

Definition at line 328 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solved_

protected

Definition at line 329 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::inverted_

protected

Definition at line 330 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::reciprocalConditionEstimated_

protected

Definition at line 331 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::refineSolution_

protected

Definition at line 332 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solutionRefined_

protected

Definition at line 333 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::numRowCols_

protected

Definition at line 335 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::LDA_

protected

Definition at line 336 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::LDAF_

protected

Definition at line 337 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::INFO_

protected

Definition at line 338 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::LWORK_

protected

Definition at line 339 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

std::vector<int> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::IWORK_

protected

Definition at line 341 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::ANORM_

protected

Definition at line 343 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::RCOND_

protected

Definition at line 344 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::SCOND_

protected

Definition at line 345 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::AMAX_

protected

Definition at line 346 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

RCP<SerialSymDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::Matrix_

protected

Definition at line 348 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::LHS_

protected

Definition at line 349 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::RHS_

protected

Definition at line 350 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

RCP<SerialSymDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::Factor_

protected

Definition at line 351 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

ScalarType* Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::A_

protected

Definition at line 353 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

ScalarType* Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::AF_

protected

Definition at line 354 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

std::vector<MagnitudeType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::FERR_

protected

Definition at line 355 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

std::vector<MagnitudeType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::BERR_

protected

Definition at line 356 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

std::vector<ScalarType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::WORK_

protected

Definition at line 357 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

std::vector<MagnitudeType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::R_

protected

Definition at line 358 of file Teuchos_SerialSpdDenseSolver.hpp.

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

Teuchos_SerialSpdDenseSolver.hpp

Public Types

Protected Member Functions

Protected Attributes

Private Member Functions

Constructor/Destructor Methods

Set Methods

Strategy Modifying Methods

Factor/Solve/Invert Methods

Query methods

Data Accessor methods

I/O methods

Additional Inherited Members

Detailed Description

template<typename OrdinalType, typename ScalarType> class Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename OrdinalType, typename ScalarType>
class Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >