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Teuchos::LAPACK< OrdinalType, ScalarType > Class Template Reference

The Templated LAPACK Wrapper Class. More...

#include <Teuchos_LAPACK.hpp>

Inheritance diagram for Teuchos::LAPACK< OrdinalType, ScalarType >:
Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType > Teuchos::SerialDenseSolver< OrdinalType, ScalarType > Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >

List of all members.

Public Member Functions

Constructors/Destructors.
 LAPACK (void)
 Default Constructor.
 LAPACK (const LAPACK< OrdinalType, ScalarType > &lapack)
 Copy Constructor.
virtual ~LAPACK (void)
 Destructor.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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, ScalarType *WR, ScalarType *WI, ScalarType *VL, const OrdinalType ldvl, ScalarType *VR, const OrdinalType ldvr, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const
 Computes for an n by n real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.
void GEEVX (const char BALANC, const char JOBVL, const char JOBVR, const char SENSE, const 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.
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).
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).
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).
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.
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.
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.
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.
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.
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.
Random number generators
ScalarType LARND (const OrdinalType idist, OrdinalType *seed) const
 Returns a random number from a uniform or normal distribution.
void LARNV (const OrdinalType idist, OrdinalType *seed, const OrdinalType n, ScalarType *v) const
 Returns a vector of random numbers from a chosen distribution.
Machine Characteristics Routines.
ScalarType LAMCH (const char CMACH) const
 Determines machine parameters for floating point characteristics.
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.
Miscellaneous Utilities.
ScalarType LAPY2 (const ScalarType x, const ScalarType y) const
 Computes x^2 + y^2 safely, to avoid overflow.

Detailed Description

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

The Templated LAPACK Wrapper Class.

The Teuchos::LAPACK class is a wrapper that encapsulates LAPACK (Linear Algebra Package). LAPACK provides portable, high- performance implementations of linear, eigen, SVD, etc solvers.

The standard LAPACK interface is Fortran-specific. Unfortunately, the interface between C++ and Fortran is not standard across all computer platforms. The Teuchos::LAPACK class provides C++ wrappers for the LAPACK kernels in order to insulate the rest of Teuchos from the details of C++ to Fortran translation. A Teuchos::LAPACK object is essentially nothing, but allows access to the LAPACK wrapper functions.

Teuchos::LAPACK is a serial interface only. This is appropriate since the standard LAPACK are only specified for serial execution (or shared memory parallel).

Note:
  1. These templates are specialized to use the Fortran LAPACK routines for scalar types float and double.

  2. If Teuchos is configured with -DTeuchos_ENABLE_COMPLEX:BOOL=ON then these templates are specialized for scalar types std::complex<float> and std::complex<double> also.

  3. A short description is given for each method. For more detailed documentation, see the LAPACK website (http://www.netlib.org/lapack/ ).
Examples:

LAPACK/cxx_main.cpp.

Definition at line 96 of file Teuchos_LAPACK.hpp.


Constructor & Destructor Documentation

template<typename OrdinalType, typename ScalarType>
Teuchos::LAPACK< OrdinalType, ScalarType >::LAPACK ( void  ) [inline]

Default Constructor.

Definition at line 106 of file Teuchos_LAPACK.hpp.

template<typename OrdinalType, typename ScalarType>
Teuchos::LAPACK< OrdinalType, ScalarType >::LAPACK ( const LAPACK< OrdinalType, ScalarType > &  lapack) [inline]

Copy Constructor.

Definition at line 109 of file Teuchos_LAPACK.hpp.

template<typename OrdinalType, typename ScalarType>
virtual Teuchos::LAPACK< OrdinalType, ScalarType >::~LAPACK ( void  ) [inline, virtual]

Destructor.

Definition at line 112 of file Teuchos_LAPACK.hpp.


Member Function Documentation

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 101 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 105 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 109 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 113 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 117 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 121 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 125 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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).

Definition at line 129 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 133 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 137 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 141 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

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 657 of file Teuchos_LAPACK.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 663 of file Teuchos_LAPACK.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 154 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 158 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 162 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 166 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 170 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 175 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 191 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 202 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 206 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 210 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 214 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 218 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

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

Definition at line 222 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 248 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 252 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
ScalarTraits< ScalarType >::magnitudeType Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 256 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 260 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 264 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 268 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 272 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 276 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 280 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

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

Definition at line 284 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 288 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 292 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 296 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

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

Definition at line 300 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

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

Definition at line 304 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

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

Definition at line 308 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

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

Definition at line 312 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

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

Definition at line 316 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 320 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 324 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 1155 of file Teuchos_LAPACK.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 1161 of file Teuchos_LAPACK.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 1167 of file Teuchos_LAPACK.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::GEEV ( const char  JOBVL,
const char  JOBVR,
const OrdinalType  n,
ScalarType *  A,
const OrdinalType  lda,
ScalarType *  WR,
ScalarType *  WI,
ScalarType *  VL,
const OrdinalType  ldvl,
ScalarType *  VR,
const OrdinalType  ldvr,
ScalarType *  WORK,
const OrdinalType  lwork,
OrdinalType *  info 
) const

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

Definition at line 340 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 348 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 352 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 356 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 360 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 364 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 368 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 344 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 372 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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).

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 375 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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).

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 383 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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).

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 387 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Note:
This method is not defined when ScalarType is complex.

Definition at line 391 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Note:
This method is not defined when ScalarType is complex.

Definition at line 395 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 1260 of file Teuchos_LAPACK.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 1266 of file Teuchos_LAPACK.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 411 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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

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 415 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 419 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 423 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 427 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::LAPACK< OrdinalType, ScalarType >::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.

Definition at line 431 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
ScalarType Teuchos::LAPACK< OrdinalType, ScalarType >::LARND ( const OrdinalType  idist,
OrdinalType *  seed 
) const

Returns a random number from a uniform or normal distribution.

Definition at line 1329 of file Teuchos_LAPACK.hpp.

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

Returns a vector of random numbers from a chosen distribution.

Definition at line 439 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
ScalarType Teuchos::LAPACK< OrdinalType, ScalarType >::LAMCH ( const char  CMACH) const

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 443 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
OrdinalType Teuchos::LAPACK< OrdinalType, ScalarType >::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.

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

Definition at line 447 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
ScalarType Teuchos::LAPACK< OrdinalType, ScalarType >::LAPY2 ( const ScalarType  x,
const ScalarType  y 
) const

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 460 of file Teuchos_LAPACK.cpp.


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