A class for representing and solving banded dense linear systems. More...

#include <Teuchos_SerialBandDenseSolver.hpp>

Inheritance diagram for Teuchos::SerialBandDenseSolver< 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	resetMatrix ()

void	resetVectors ()

Protected Attributes
bool	equilibrate_

bool	shouldEquilibrate_

bool	equilibratedA_

bool	equilibratedB_

bool	transpose_

bool	factored_

bool	estimateSolutionErrors_

bool	solutionErrorsEstimated_

bool	solved_

bool	reciprocalConditionEstimated_

bool	refineSolution_

bool	solutionRefined_

Teuchos::ETransp	TRANS_

OrdinalType	M_

OrdinalType	N_

OrdinalType	KL_

OrdinalType	KU_

OrdinalType	Min_MN_

OrdinalType	LDA_

OrdinalType	LDAF_

OrdinalType	INFO_

OrdinalType	LWORK_

std::vector< OrdinalType >	IPIV_

std::vector< int >	IWORK_

MagnitudeType	ANORM_

MagnitudeType	RCOND_

MagnitudeType	ROWCND_

MagnitudeType	COLCND_

MagnitudeType	AMAX_

RCP< SerialBandDenseMatrix < OrdinalType, ScalarType > >	Matrix_

RCP< SerialDenseMatrix < OrdinalType, ScalarType > >	LHS_

RCP< SerialDenseMatrix < OrdinalType, ScalarType > >	RHS_

RCP< SerialBandDenseMatrix < OrdinalType, ScalarType > >	Factor_

ScalarType *	A_

ScalarType *	AF_

std::vector< MagnitudeType >	FERR_

std::vector< MagnitudeType >	BERR_

std::vector< ScalarType >	WORK_

std::vector< MagnitudeType >	R_

std::vector< MagnitudeType >	C_

Protected Attributes inherited from Teuchos::CompObject
Flops *	flopCounter_

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

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

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

virtual	~SerialBandDenseSolver ()
	SerialBandDenseSolver destructor. More...

Set Methods
int	setMatrix (const RCP< SerialBandDenseMatrix< OrdinalType, ScalarType > > &AB)
	Sets the pointer 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)

void	solveWithTranspose (bool flag)

void	solveWithTransposeFlag (Teuchos::ETransp trans)

void	solveToRefinedSolution (bool flag)
	Set whether or not to use iterative refinement to improve solutions to linear systems. More...

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

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

int	solve ()
	Computes the solution X to AX = B for the this matrix and the B provided to SetVectors().. 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	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< SerialBandDenseMatrix < OrdinalType, ScalarType > >	getMatrix () const
	Returns pointer to current matrix. More...

RCP< SerialBandDenseMatrix < 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...

OrdinalType	numLower () const
	Returns lower bandwidth of system. More...

OrdinalType	numUpper () const
	Returns upper bandwidth of system. More...

std::vector< OrdinalType >	IPIV () const
	Returns pointer to pivot vector (if factorization has been computed), zero otherwise. 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	ROWCND () const
	Ratio of smallest to largest row scale factors for the this matrix (returns -1 if not yet computed). More...

MagnitudeType	COLCND () const
	Ratio of smallest to largest column 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...

std::vector< MagnitudeType >	C () const
	Returns a pointer to the column scale 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, ScalarType 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 ScalarType 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...

TEUCHOS_DEPRECATED void	POSVX (const char &FACT, const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, ScalarType A, const OrdinalType &lda, ScalarType AF, const OrdinalType &ldaf, const 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	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

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, 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, 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...

TEUCHOS_DEPRECATED 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, const 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	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

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, const 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, 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, 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

TEUCHOS_DEPRECATED void	TREXC (const char &COMPQ, const OrdinalType &n, ScalarType T, const OrdinalType &ldt, ScalarType Q, const OrdinalType &ldq, const OrdinalType &ifst, const OrdinalType &ilst, ScalarType WORK, 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, ScalarType S, const OrdinalType &lds, 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...

TEUCHOS_DEPRECATED void	GEBAL (const char &JOBZ, const OrdinalType &n, ScalarType A, const OrdinalType &lda, const OrdinalType &ilo, const 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	GEBAL (const char &JOBZ, const OrdinalType &n, ScalarType A, const OrdinalType &lda, OrdinalType ilo, OrdinalType ihi, MagnitudeType scale, OrdinalType *info) const

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::SerialBandDenseSolver< OrdinalType, ScalarType >

A class for representing and solving banded dense linear systems.

Template Parameters

OrdinalType	The index type used by the linear algebra implementation. This should always be `int`.
ScalarType	The type of entries in the matrix.

Introduction

This class defines a banded dense matrix, which may have any number of rows or columns (not necessarily equal). It's called "serial" because the matrix lives in a single memory space. Thus, it's the kind of matrix that one might give to the BLAS or LAPACK, not a distributed matrix like one would give to ScaLAPACK.

This class also has methods for computing the (banded) LU factorization of the matrix, and solving linear systems with the matrix. We use instances of SerialDenseVector to represent the right-hand side b or the solution x in the linear system $Ax=b$ . The instance of this class used store the banded matrix must contain KL extra superdiagonals to store the L and U factors (see details below).

Users have the option to do equilibration before factoring the matrix. This may improve accuracy when solving ill-conditioned problems.

SerialBandDenseSolver and LAPACK

Teuchos' LAPACK class wraps LAPACK's LU factorizations, including the banded factorizations. It thus gives access to most of the same functionality as SerialBandDenseSolver. The main difference is that SerialBandDenseSolver offers a higher level of abstraction. It hides the details of which LAPACK routines to call. Furthermore, if you have built Teuchos with support for the third-party library Eigen, SerialBandDenseSolver lets you solve linear systems for ScalarType other than the four supported by the LAPACK library.

Constructing SerialBandDenseSolver objects

There is a single Teuchos::SerialBandDenseSolver 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 a SerialDenseMatrix or a SerialDenseVector object. The set methods are as follows:

setMatrix(): Sets the matrix
setVectors() - Sets the left and right hand side vector(s)

Format of the matrix A

The SerialBandDenseMatrix must contain KL extra superdiagonals to store the L and U factors, where KL is the upper bandwidth. Consider using the non-member conversion routines generalToBanded and bandedToGeneral if the full SerialDenseMatrix is already in storage. However, it is more efficient simply to construct the SerialBandDenseMatrix with the desired parameters and use the provided matrix access operators so that the full rectangular matrix need not be stored. The conversion routine generalToBanded has a flag to store the input Teuchos::SerialDenseMatrix in banded format with KL extra superdiagonals so this class can use it. Again, it is more efficient to simply construct a Teuchos::SerialBandDenseMatrix object with KL extra superdiagonals than are needed for the matrix data and fill the matrix using the matrix access operators.

See the documentation of Teuchos::SerialBandDenseMatrix for further details on the storage format.

Vector and Utility Functions

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

Conversion between storage formats
Factorizations
Solves
Condition estimates
Equilibration
Norms

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.

SerialBandDenseSolver 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.

SerialBandDenseSolver 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 SerialBandDenseSolver can be found in the Teuchos test directories.

Definition at line 166 of file Teuchos_SerialBandDenseSolver.hpp.

Member Typedef Documentation

template<typename OrdinalType, typename ScalarType>

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

Definition at line 172 of file Teuchos_SerialBandDenseSolver.hpp.

Constructor & Destructor Documentation

template<typename OrdinalType , typename ScalarType >

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

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

Definition at line 464 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

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

virtual

SerialBandDenseSolver destructor.

Definition at line 501 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

private

Member Function Documentation

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::setMatrix ( const RCP< SerialBandDenseMatrix< OrdinalType, ScalarType > > & AB )

Sets the pointer for coefficient matrix.

Definition at line 546 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseSolver< 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 576 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

void Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::factorWithEquilibration ( bool flag )

inline

Set whether or not to equilibrate just before the matrix factorization. This function must be called before the factorization is performed.

Definition at line 219 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

void Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::solveWithTranspose ( bool flag )

inline

If flag is true, causes all subsequent function calls to work with the transpose of this matrix, otherwise not.

Note: This interface will not work correctly for complex-valued linear systems, use solveWithTransposeFlag().

Definition at line 224 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

void Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::solveWithTransposeFlag ( Teuchos::ETransp trans )

inline

All subsequent function calls will work with the transpose-type set by this method (Teuchos::NO_TRANS, Teuchos::TRANS, and Teuchos::CONJ_TRANS).

Note: This interface will allow correct behavior for complex-valued linear systems, solveWithTranspose() will not.

Definition at line 228 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

Set whether or not to use iterative refinement to improve solutions to linear systems.

Definition at line 231 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

void Teuchos::SerialBandDenseSolver< 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 599 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

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

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

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

Definition at line 609 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseSolver< 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 667 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseSolver< 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 767 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseSolver< 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 788 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseSolver< 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 844 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseSolver< 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 733 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseSolver< 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 876 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

int Teuchos::SerialBandDenseSolver< 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 902 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 299 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 302 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 305 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 308 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 311 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 314 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 317 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 320 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 323 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

RCP<SerialBandDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::getMatrix ( ) const

inline

Returns pointer to current matrix.

Definition at line 330 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

RCP<SerialBandDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::getFactoredMatrix ( ) const

inline

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

Definition at line 333 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

Returns pointer to current LHS.

Definition at line 336 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

Returns pointer to current RHS.

Definition at line 339 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

Returns row dimension of system.

Definition at line 342 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

Returns column dimension of system.

Definition at line 345 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::numLower ( ) const

inline

Returns lower bandwidth of system.

Definition at line 348 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::numUpper ( ) const

inline

Returns upper bandwidth of system.

Definition at line 351 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

std::vector<OrdinalType> Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::IPIV ( ) const

inline

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

Definition at line 354 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 357 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialBandDenseSolver< 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 360 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::ROWCND ( ) const

inline

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

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

Definition at line 365 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::COLCND ( ) const

inline

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

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

Definition at line 370 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialBandDenseSolver< 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 373 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 376 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 379 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inline

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

Definition at line 382 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

std::vector<MagnitudeType> Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::C ( ) const

inline

Returns a pointer to the column scale vector used for equilibration.

Definition at line 385 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

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

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

Definition at line 935 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

inlineprotected

Definition at line 395 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

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

protected

Definition at line 520 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >

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

protected

Definition at line 507 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

private

Member Data Documentation

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 400 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 401 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 402 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 403 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 404 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 405 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 406 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 407 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 408 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 409 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 410 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 411 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

Teuchos::ETransp Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::TRANS_

protected

Definition at line 413 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::M_

protected

Definition at line 415 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::N_

protected

Definition at line 416 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::KL_

protected

Definition at line 417 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::KU_

protected

Definition at line 418 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

OrdinalType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::Min_MN_

protected

Definition at line 419 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 420 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 421 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 422 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 423 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

std::vector<OrdinalType> Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::IPIV_

protected

Definition at line 425 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 426 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 428 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 429 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::ROWCND_

protected

Definition at line 430 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

MagnitudeType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::COLCND_

protected

Definition at line 431 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 432 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

RCP<SerialBandDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::Matrix_

protected

Definition at line 434 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 435 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 436 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

RCP<SerialBandDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::Factor_

protected

Definition at line 437 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 439 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 440 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 441 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 442 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 443 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

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

protected

Definition at line 444 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>

std::vector<MagnitudeType> Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::C_

protected

Definition at line 445 of file Teuchos_SerialBandDenseSolver.hpp.

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

Teuchos_SerialBandDenseSolver.hpp

Public Types

Protected Member Functions

Protected Attributes

Private Member Functions

Constructor/Destructor Methods

Set Methods

Strategy Modifying Methods

Factor/Solve Methods

Query methods

Data Accessor methods

I/O methods

Additional Inherited Members

Detailed Description

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

Introduction

SerialBandDenseSolver and LAPACK

Constructing SerialBandDenseSolver objects

Setting vectors used for linear solves

Format of the matrix A

Vector and Utility Functions

Strategies for Solving Linear Systems

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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