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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 >:

## Public Member Functions

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

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

void GETRS (const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, const OrdinalType *IPIV, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
Solves a system of linear equations `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, const ScalarType *A, const OrdinalType &LDA, ScalarType *X, MagnitudeType *SCALE, MagnitudeType *CNORM, OrdinalType *INFO) const
Robustly solve a possibly singular triangular linear system. More...

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

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

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

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

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

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

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

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

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

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

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

void TRTRS (const char &UPLO, const char &TRANS, const char &DIAG, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
Solves a triangular linear system of the form `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, 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, MagnitudeType *D, MagnitudeType *E, ScalarType *Z, const OrdinalType &ldz, MagnitudeType *WORK, OrdinalType *info) const
Computes the eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal `n` by `n` matrix `A` using implicit QL/QR. The eigenvectors can only be computed if `A` was reduced to tridiagonal form by SYTRD. More...

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

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, const ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *C, const OrdinalType &ldc, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const

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

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

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

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

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

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

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

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, const ScalarType *S, const OrdinalType &lds, const ScalarType *P, const OrdinalType &ldp, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, const OrdinalType &mm, OrdinalType *M, ScalarType *WORK, OrdinalType *info) const

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 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 )
inlinevirtual

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, MagnitudeType * d, ScalarType * e, OrdinalType * info ) const

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

Definition at line 118 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
 void Teuchos::LAPACK< OrdinalType, ScalarType >::PTTRS ( const OrdinalType & n, const OrdinalType & nrhs, const MagnitudeType * d, const ScalarType * e, ScalarType * B, const OrdinalType & ldb, OrdinalType * info ) const

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

Definition at line 122 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 126 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 130 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 134 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 138 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 142 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 146 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 149 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 152 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 156 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 652 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 658 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 169 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 173 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
 void Teuchos::LAPACK< OrdinalType, ScalarType >::GEQR2 ( const OrdinalType & m, const OrdinalType & n, ScalarType * A, const OrdinalType & lda, ScalarType * TAU, ScalarType * WORK, OrdinalType *const info ) const

BLAS 2 version of GEQRF, with known workspace size.

Definition at line 176 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 181 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 185 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 189 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 192 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 198 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 203 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 207 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 211 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 215 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 219 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, const 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 227 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, const OrdinalType * IPIV, const ScalarType & anorm, ScalarType * rcond, ScalarType * WORK, OrdinalType * IWORK, OrdinalType * info ) const

Estimates the reciprocal of the condition number of a general banded real matrix `A`, in either the 1-norm or the infinity-norm, using the LU factorization computed by GETRF.

Definition at line 231 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 235 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 239 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 243 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 247 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 251 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 255 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 258 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 262 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 266 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 270 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, ScalarType * A, const OrdinalType & lda, OrdinalType * info ) const

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

Definition at line 274 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 278 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 282 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 286 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 290 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 294 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
 void Teuchos::LAPACK< OrdinalType, ScalarType >::STEQR ( const char & COMPZ, const OrdinalType & n, MagnitudeType * D, MagnitudeType * E, ScalarType * Z, const OrdinalType & ldz, MagnitudeType * WORK, OrdinalType * info ) const

Computes the eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal `n` by `n` matrix `A` using implicit QL/QR. The eigenvectors can only be computed if `A` was reduced to tridiagonal form by SYTRD.

Definition at line 298 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
 void Teuchos::LAPACK< OrdinalType, ScalarType >::PTEQR ( const char & COMPZ, const OrdinalType & n, MagnitudeType * D, MagnitudeType * E, ScalarType * Z, const OrdinalType & ldz, MagnitudeType * WORK, OrdinalType * info ) const

Computes the eigenvalues and, optionally, eigenvectors of a symmetric positive-definite tridiagonal `n` by `n` matrix `A` using BDSQR, after factoring the matrix with PTTRF.

Definition at line 302 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 306 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 1131 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 1137 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 1143 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, 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.

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 322 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 335 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 339 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 347 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 351 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`.

Definition at line 355 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.

Definition at line 359 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 331 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, const ScalarType * A, const OrdinalType & lda, const ScalarType * TAU, ScalarType * C, const OrdinalType & ldc, ScalarType * WORK, const OrdinalType & lwork, OrdinalType * info ) const

Apply Householder reflectors (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 363 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
 void Teuchos::LAPACK< OrdinalType, ScalarType >::ORM2R ( const char & SIDE, const char & TRANS, const OrdinalType & m, const OrdinalType & n, const OrdinalType & k, const ScalarType * A, const OrdinalType & lda, const ScalarType * TAU, ScalarType * C, const OrdinalType & ldc, ScalarType * WORK, OrdinalType *const info ) const

BLAS 2 version of ORMQR; known workspace size.

Note
This method is not defined when ScalarType is complex. Call UNM2R in that case. ("OR" stands for "orthogonal"; "UN" stands for "unitary.")

Definition at line 367 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, const ScalarType * A, const OrdinalType & lda, const ScalarType * TAU, ScalarType * C, const OrdinalType & ldc, ScalarType * WORK, const OrdinalType & lwork, OrdinalType * info ) const

Apply Householder reflectors (complex case).

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 371 of file Teuchos_LAPACK.cpp.

template<typename OrdinalType , typename ScalarType >
 void Teuchos::LAPACK< OrdinalType, ScalarType >::UNM2R ( const char & SIDE, const char & TRANS, const OrdinalType & M, const OrdinalType & N, const OrdinalType & K, const ScalarType * A, const OrdinalType & LDA, const ScalarType * TAU, ScalarType * C, const OrdinalType & LDC, ScalarType * WORK, OrdinalType *const INFO ) const

BLAS 2 version of UNMQR; known workspace size.

Note
This method will call ORM2R when ScalarType is real. (Unitary real matrices are orthogonal.)

Definition at line 377 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 386 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 390 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 394 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 398 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 1248 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 1254 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 413 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, const ScalarType * S, const OrdinalType & lds, const ScalarType * P, const OrdinalType & ldp, ScalarType * VL, const OrdinalType & ldvl, ScalarType * VR, const OrdinalType & ldvr, const OrdinalType & mm, OrdinalType * M, ScalarType * WORK, OrdinalType * info ) const

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 417 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 421 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 425 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 428 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 432 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 1317 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 440 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 444 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 448 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 461 of file Teuchos_LAPACK.cpp.

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