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Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > > Class Template Reference

#include <Teuchos_LAPACK_MP_Vector.hpp>

Public Types

typedef Sacado::MP::Vector
< Storage > 		ScalarType
 
typedef Teuchos::ScalarTraits
< ScalarType >::magnitudeType 		MagnitudeType
 

Public Member Functions

void PTEQR (const char COMPZ, const OrdinalType n, ScalarType *D, ScalarType *E, ScalarType *Z, const OrdinalType ldz, ScalarType *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...
 

Private Member Functions

void throw_error (const char *func) const
 

Constructors/Destructors.

 LAPACK (void)
 Default Constructor. More...
 
 LAPACK (const LAPACK< OrdinalType, ScalarType > &lapack)
 Copy Constructor. More...
 
virtual ~LAPACK (void)
 Destructor. More...
 

Symmetric Positive Definite Linear System Routines.

void PTTRF (const OrdinalType n, ScalarType *d, ScalarType *e, OrdinalType *info) const
 Computes the L*D*L' 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 A*X=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...
 

General Linear System Routines.

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 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 A*X=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: A*P = Q*R 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 A*X=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 A*X=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...
 
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 A*X=B or A**T*X=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...
 

Symmetric Eigenproblem Routines

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, ScalarType *D, ScalarType *E, ScalarType *Z, const OrdinalType ldz, ScalarType *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...
 

Non-Hermitian Eigenproblem Routines

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
 

Singular Value Decompositon Routines

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...
 

Orthogonal matrix routines

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 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 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...
 

Triangular Matrix Routines

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, 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
 

Rotation/Reflection generators

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...
 

Matrix Balancing Routines

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...
 

Random number generators

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...
 

Machine Characteristics Routines.

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...
 

Miscellaneous Utilities.

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

Detailed Description

template<typename OrdinalType, typename Storage>
class Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >

Definition at line 59 of file Teuchos_LAPACK_MP_Vector.hpp.

Member Typedef Documentation

template<typename OrdinalType , typename Storage >
typedef Sacado::MP::Vector<Storage> Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::ScalarType

Definition at line 63 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
typedef Teuchos::ScalarTraits<ScalarType>::magnitudeType Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::MagnitudeType

Definition at line 64 of file Teuchos_LAPACK_MP_Vector.hpp.

Constructor & Destructor Documentation

template<typename OrdinalType , typename Storage >
Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::LAPACK ( void  )
inline

Default Constructor.

Definition at line 70 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::LAPACK ( const LAPACK< OrdinalType, ScalarType > &  lapack)
inline

Copy Constructor.

Definition at line 73 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
virtual Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::~LAPACK ( void  )
inlinevirtual

Destructor.

Definition at line 76 of file Teuchos_LAPACK_MP_Vector.hpp.

Member Function Documentation

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::PTTRF ( const OrdinalType  n,
ScalarType *  d,
ScalarType *  e,
OrdinalType *  info 
) const
inline

Computes the L*D*L' factorization of a Hermitian/symmetric positive definite tridiagonal matrix A.

Definition at line 83 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::PTTRS ( const OrdinalType  n,
const OrdinalType  nrhs,
const ScalarType *  d,
const ScalarType *  e,
ScalarType *  B,
const OrdinalType  ldb,
OrdinalType *  info 
) const
inline

Solves a tridiagonal system A*X=B using the *D*L' factorization of A computed by PTTRF.

Definition at line 87 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::POTRF ( const char  UPLO,
const OrdinalType  n,
ScalarType *  A,
const OrdinalType  lda,
OrdinalType *  info 
) const
inline

Computes Cholesky factorization of a real symmetric positive definite matrix A.

Definition at line 91 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::POTRS ( const char  UPLO,
const OrdinalType  n,
const OrdinalType  nrhs,
const ScalarType *  A,
const OrdinalType  lda,
ScalarType *  B,
const OrdinalType  ldb,
OrdinalType *  info 
) const
inline

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.

Definition at line 95 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::POTRI ( const char  UPLO,
const OrdinalType  n,
ScalarType *  A,
const OrdinalType  lda,
OrdinalType *  info 
) const
inline

Computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A from POTRF.

Definition at line 99 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Estimates the reciprocal of the condition number (1-norm) of a real symmetric positive definite matrix A using the Cholesky factorization from POTRF.

Definition at line 104 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::POSV ( const char  UPLO,
const OrdinalType  n,
const OrdinalType  nrhs,
ScalarType *  A,
const OrdinalType  lda,
ScalarType *  B,
const OrdinalType  ldb,
OrdinalType *  info 
) const
inline

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.

Definition at line 108 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::POEQU ( const OrdinalType  n,
const ScalarType *  A,
const OrdinalType  lda,
MagnitudeType *  S,
MagnitudeType *  scond,
MagnitudeType *  amax,
OrdinalType *  info 
) const
inline

Computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (w.r.t. 2-norm).

Definition at line 112 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Definition at line 116 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Definition at line 120 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Solves an over/underdetermined real m by n linear system A using QR or LQ factorization of A.

Definition at line 128 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Use the SVD to solve a possibly rank-deficient linear least-squares problem.

GELSS uses the singular value decomposition (SVD) to compute the minimum-norm solution to a possibly rank-deficient linear least-squares problem. The problem may be under- or overdetermined.

LAPACK's _GELSS routines take different arguments, depending on whether they are for real or complex arithmetic. This is because _GELSS imitates the interface of LAPACK's SVD routine. LAPACK's SVD routine takes an additional RWORK workspace array argument for COMPLEX*8 (CGELSS) and COMPLEX*16 (ZGELSS). LAPACK's real SVD routines (SGELSS and DGELSS) do not take the RWORK argument.

This class had already exposed GELSS for ScalarType = float and double that does not include an RWORK argument. Backwards compatibility requirements prevent us from simply changing that interface. We could provide a different interface for LAPACK specializations with ScalarType = std::complex<T>, but that would make the GELSS interface not generic at compile time. This would make using GELSS in generic code harder (for example, you would need to specialize code that uses GELSS on a Boolean, which specifies whether ScalarType is complex).

We fix this problem by providing an overloaded generic GELSS interface that does take an RWORK argument. This does not change the existing interface, but provides the additional capability to solve complex-valued least-squares problems. The RWORK argument is ignored when ScalarType is real, and may therefore be set to NULL in that case.

Definition at line 164 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Legacy GELSS interface for real-valued ScalarType.

Definition at line 168 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Definition at line 172 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::GEQRF ( const OrdinalType  m,
const OrdinalType  n,
ScalarType *  A,
const OrdinalType  lda,
ScalarType *  TAU,
ScalarType *  WORK,
const OrdinalType  lwork,
OrdinalType *  info 
) const
inline

Computes a QR factorization of a general m by n matrix A.

Definition at line 176 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::GETRF ( const OrdinalType  m,
const OrdinalType  n,
ScalarType *  A,
const OrdinalType  lda,
OrdinalType *  IPIV,
OrdinalType *  info 
) const
inline

Computes an LU factorization of a general m by n matrix A using partial pivoting with row interchanges.

Definition at line 180 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Solves a system of linear equations A*X=B or A'*X=B with a general n by n matrix A using the LU factorization computed by GETRF.

Definition at line 184 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Multiplies the m by n matrix A by the real scalar cto/cfrom.

Definition at line 188 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.

Definition at line 193 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::LASWP ( const OrdinalType  N,
ScalarType  A[],
const OrdinalType  LDA,
const OrdinalType  K1,
const OrdinalType  K2,
const OrdinalType  IPIV[],
const OrdinalType  INCX 
) const
inline

Apply a series of row interchanges to the matrix A.

Definition at line 206 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::GBTRF ( const OrdinalType  m,
const OrdinalType  n,
const OrdinalType  kl,
const OrdinalType  ku,
ScalarType *  A,
const OrdinalType  lda,
OrdinalType *  IPIV,
OrdinalType *  info 
) const
inline

Computes an LU factorization of a general banded m by n matrix A using partial pivoting with row interchanges.

Definition at line 216 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Solves a system of linear equations A*X=B or A'*X=B with a general banded n by n matrix A using the LU factorization computed by GBTRF.

Definition at line 220 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::GTTRF ( const OrdinalType  n,
ScalarType *  dl,
ScalarType *  d,
ScalarType *  du,
ScalarType *  du2,
OrdinalType *  IPIV,
OrdinalType *  info 
) const
inline

Computes an LU factorization of a n by n tridiagonal matrix A using partial pivoting with row interchanges.

Definition at line 224 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Solves a system of linear equations A*X=B or A'*X=B or A^H*X=B with a tridiagonal matrix A using the LU factorization computed by GTTRF.

Definition at line 228 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::GETRI ( const OrdinalType  n,
ScalarType *  A,
const OrdinalType  lda,
const OrdinalType *  IPIV,
ScalarType *  WORK,
const OrdinalType  lwork,
OrdinalType *  info 
) const
inline

Computes the inverse of a matrix A using the LU factorization computed by GETRF.

Definition at line 232 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Robustly solve a possibly singular triangular linear system.

Note
This routine is slower than the BLAS' TRSM, but can detect possible singularity of A.

Definition at line 240 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Definition at line 254 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Definition at line 258 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
ScalarTraits<ScalarType>::magnitudeType Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::LANGB ( const char  NORM,
const OrdinalType  n,
const OrdinalType  kl,
const OrdinalType  ku,
const ScalarType *  A,
const OrdinalType  lda,
MagnitudeType *  WORK 
) const
inline

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.

Definition at line 262 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::GESV ( const OrdinalType  n,
const OrdinalType  nrhs,
ScalarType *  A,
const OrdinalType  lda,
OrdinalType *  IPIV,
ScalarType *  B,
const OrdinalType  ldb,
OrdinalType *  info 
) const
inline

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.

Definition at line 266 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes row and column scalings intended to equilibrate an m by n matrix A and reduce its condition number.

Definition at line 270 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Definition at line 274 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes row and column scalings intended to equilibrate an m by n banded matrix A and reduce its condition number.

Definition at line 278 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Definition at line 282 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Definition at line 286 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Reduces a real symmetric matrix A to tridiagonal form by orthogonal similarity transformations.

Note
This method is not defined when the ScalarType is std::complex<float> or std::complex<double>.

Definition at line 292 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Reduces a real general matrix A to upper Hessenberg form by orthogonal similarity transformations.

Definition at line 296 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Solves a triangular linear system of the form A*X=B or A**T*X=B, where A is a triangular matrix.

Definition at line 300 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::TRTRI ( const char  UPLO,
const char  DIAG,
const OrdinalType  n,
const ScalarType *  A,
const OrdinalType  lda,
OrdinalType *  info 
) const
inline

Computes the inverse of an upper or lower triangular matrix A.

Definition at line 304 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::SPEV ( const char  JOBZ,
const char  UPLO,
const OrdinalType  n,
ScalarType *  AP,
ScalarType *  W,
ScalarType *  Z,
const OrdinalType  ldz,
ScalarType *  WORK,
OrdinalType *  info 
) const
inline

Computes the eigenvalues and, optionally, eigenvectors of a symmetric n by n matrix A in packed storage.

Note
This method is not defined when the ScalarType is std::complex<float> or std::complex<double>.

Definition at line 313 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes all the eigenvalues and, optionally, eigenvectors of a symmetric n by n matrix A.

Note
This method is not defined when the ScalarType is std::complex<float> or std::complex<double>.

Definition at line 319 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Note
This method is not defined when the ScalarType is std::complex<float> or std::complex<double>.

Definition at line 325 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes all the eigenvalues and, optionally, eigenvectors of a Hermitian n by n matrix A.

Note
This method will call SYEV when ScalarType is float or double.

Definition at line 331 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Note
This method will call SYGV when ScalarType is float or double.

Definition at line 337 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::STEQR ( const char  COMPZ,
const OrdinalType  n,
ScalarType *  D,
ScalarType *  E,
ScalarType *  Z,
const OrdinalType  ldz,
ScalarType *  WORK,
OrdinalType *  info 
) const
inline

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.

Definition at line 341 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::PTEQR ( const char  COMPZ,
const OrdinalType  n,
ScalarType *  D,
ScalarType *  E,
ScalarType *  Z,
const OrdinalType  ldz,
ScalarType *  WORK,
OrdinalType *  info 
) const
inline

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.

Definition at line 346 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Definition at line 353 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::GEES ( const char  JOBVS,
const char  SORT,
OrdinalType(*)(ScalarType *, ScalarType *)  ptr2func,
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
inline

Computes for an n by n nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z. When ScalarType is float or double, the real Schur form is computed.

Note
(This is the version used for float and double, where select requires two arguments to represent a complex eigenvalue.)

Definition at line 359 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::GEES ( const char  JOBVS,
const char  SORT,
OrdinalType(*)(ScalarType *)  ptr2func,
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
inline

Computes for an n by n nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z. When ScalarType is float or double, the real Schur form is computed.

Note
(This is the version used for std::complex<float> and std::complex<double>, where select requires one arguments to represent a complex eigenvalue.)

Definition at line 365 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes for an n by n nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z. When ScalarType is float or double, the real Schur form is computed.

Note
(This is the version used for any ScalarType, when the user doesn't want to enable the sorting functionality.)

Definition at line 371 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes for an n by n real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.

Real and imaginary parts of the eigenvalues are returned in separate arrays, WR for real and WI for complex. The RWORK array is only referenced if ScalarType is complex.

Definition at line 379 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes for an n by n real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. Optionally, it can compute a balancing transformation to improve the conditioning of the eigenvalues and eigenvectors.

Note
(This is the function is only defined for ScalarType = float or double.)

Definition at line 386 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes for a pair of n by n nonsymmetric matrices (A,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors. Optionally, it can compute a balancing transformation to improve the conditioning of the eigenvalues and eigenvectors.

Note
(This is the function is only defined for ScalarType = float or double.)

Definition at line 393 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes for a pair of n by n nonsymmetric matrices (A,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.

Note
(This is the function is only defined for ScalarType = float or double.)

Definition at line 399 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Reorders the real Schur factorization of a real matrix so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace.

Note
(This function is only defined for ScalarType = float or double.)

Definition at line 406 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Reorders the generalized real Schur decomposition of a real matrix pair (A, B), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix A and the upper triangular B.

Note
(This function is only defined for ScalarType = float or double.)

Definition at line 413 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::GGES ( const char  JOBVL,
const char  JOBVR,
const char  SORT,
OrdinalType(*)(ScalarType *, ScalarType *, ScalarType *)  ptr2func,
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
inline

Computes for a pair of n by n nonsymmetric matrices (A,B) the generalized eigenvalues, the generalized real Schur form (S,T), optionally, the left and/or right matrices of Schur vectors.

Note
(This is the function is only defined for ScalarType = float or double.)

Definition at line 420 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes the singular values (and optionally, vectors) of a real matrix A.

Definition at line 429 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Apply Householder reflectors (real case).

Overwrite the general real m by n matrix C with the product of Q and C, whiere Q is the product of k elementary (Householder) reflectors as returned by GEQRF.

Note
This method is not defined when ScalarType is complex. Call UNMQR in that case. ("OR" stands for "orthogonal"; "UN" stands for "unitary.")

Definition at line 446 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Apply Householder reflectors (complex case).

Overwrite the general complex m by n matrix C with the product of Q and C, where Q is the product of k elementary (Householder) reflectors as returned by GEQRF.

Note
This method will call ORMQR when ScalarType is real. (Unitary real matrices are orthogonal.)

Definition at line 457 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Compute explicit Q factor from QR factorization (GEQRF) (real case).

Generate the m by n matrix Q with orthonormal columns corresponding to the first n columns of a product of k elementary reflectors of order m, as returned by GEQRF.

Note
This method is not defined when ScalarType is complex. Call UNGQR in that case. ("OR" stands for "orthogonal"; "UN" stands for "unitary.")

Definition at line 469 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Compute explicit QR factor from QR factorization (GEQRF) (complex case).

Generate the m by n matrix Q with orthonormal columns corresponding tothe first n columns of a product of k elementary reflectors of order m, as returned by GEQRF.

Note
This method will call ORGQR when ScalarType is real. (Unitary real matrices are orthogonal.)

Definition at line 480 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Note
This method is not defined when ScalarType is complex.

Definition at line 486 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

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.

Note
This method is not defined when ScalarType is complex.

Definition at line 492 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes some or all of the right and/or left eigenvectors of an upper triangular matrix T. If ScalarType is float or double, then the matrix is quasi-triangular and arugments RWORK is ignored.

Definition at line 501 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes some or all of the right and/or left eigenvectors of an upper triangular matrix T. If ScalarType is float or double, then the matrix is quasi-triangular and arugments RWORK is ignored.

Note
(This is the version used for any ScalarType, when the user doesn't want to enable the selecting functionality, with HOWMNY='A'.)

Definition at line 507 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Reorders the Schur factorization of a matrix T via unitary similarity transformations so that the diagonal element of T with row index ifst is moved to row ilst. If ScalarType is float or double, then T should be in real Schur form and the operation affects the diagonal block referenced by ifst.

Note
This method will ignore the WORK vector when ScalarType is std::complex<float> or std::complex<double>.

Definition at line 513 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Computes some or all of the right and/or left eigenvectors of a pair of real matrices ( S, P ), where S is a quasi-triangular matrix and P is upper triangular.

Note
This method is only defined for ScalarType = float or double.

Definition at line 519 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::LARTG ( const ScalarType  f,
const ScalarType  g,
MagnitudeType *  c,
ScalarType *  s,
ScalarType *  r 
) const
inline

Gnerates a plane rotation that zeros out the second component of the input vector.

Definition at line 529 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::LARFG ( const OrdinalType  n,
ScalarType *  alpha,
ScalarType *  x,
const OrdinalType  incx,
ScalarType *  tau 
) const
inline

Generates an elementary reflector of order n that zeros out the last n-1 components of the input vector.

Definition at line 533 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::GEBAL ( const char  JOBZ,
const OrdinalType  n,
ScalarType *  A,
const OrdinalType  lda,
OrdinalType  ilo,
OrdinalType  ihi,
MagnitudeType *  scale,
OrdinalType *  info 
) const
inline

Balances a general matrix A, through similarity transformations to make the rows and columns as close in norm as possible.

Definition at line 542 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Forms the left or right eigenvectors of a general matrix that has been balanced by GEBAL by backward transformation of the computed eigenvectors V.

Definition at line 546 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
ScalarType Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::LARND ( const OrdinalType  idist,
OrdinalType *  seed 
) const
inline

Returns a random number from a uniform or normal distribution.

Definition at line 554 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::LARNV ( const OrdinalType  idist,
OrdinalType *  seed,
const OrdinalType  n,
ScalarType *  v 
) const
inline

Returns a vector of random numbers from a chosen distribution.

Definition at line 558 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
ScalarType Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::LAMCH ( const char  CMACH) const
inline

Determines machine parameters for floating point characteristics.

Note
This method is not defined when the ScalarType is std::complex<float> or std::complex<double>.

Definition at line 567 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
OrdinalType Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::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
inline

Chooses problem-dependent parameters for the local environment.

Note
This method should give parameters for good, but not optimal, performance on many currently available computers.

Definition at line 574 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
ScalarType Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::LAPY2 ( const ScalarType  x,
const ScalarType  y 
) const
inline

Computes x^2 + y^2 safely, to avoid overflow.

Note
This method is not defined when the ScalarType is std::complex<float> or std::complex<double>.

Definition at line 583 of file Teuchos_LAPACK_MP_Vector.hpp.

template<typename OrdinalType , typename Storage >
void Teuchos::LAPACK< OrdinalType, Sacado::MP::Vector< Storage > >::throw_error ( const char *  func) const
inlineprivate

Definition at line 589 of file Teuchos_LAPACK_MP_Vector.hpp.

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