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

The Templated LAPACK Wrapper Class. More...

#include <Teuchos_LAPACK.hpp>

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 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, ScalarType *S, ScalarType *scond, ScalarType *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, 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 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 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 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 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 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.
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 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.
Hessenberg 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 *SELECT, 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 real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z.
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.
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
 Overwrites the general real matrix m by n matrix C with the product of C and Q, which is the product of k elementary reflectors, as returned by GEQRF.
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
 Computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T.
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
 Reorders the real Schur factorization of a real matrix via orthogonal similarity transformations so that the diagonal block of T with row index ifst is moved to row ilst.
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.
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 --enable-teuchos-complex then these templates are specialized for scalar types complex<float> and 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 112 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 118 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 121 of file Teuchos_LAPACK.hpp.

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

Destructor.

Definition at line 124 of file Teuchos_LAPACK.hpp.


Member Function Documentation

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 281 of file Teuchos_LAPACK.hpp.

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 287 of file Teuchos_LAPACK.hpp.

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 293 of file Teuchos_LAPACK.hpp.

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 299 of file Teuchos_LAPACK.hpp.

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 305 of file Teuchos_LAPACK.hpp.

template<typename OrdinalType, typename ScalarType>
void Teuchos::LAPACK< OrdinalType, ScalarType >::POEQU const OrdinalType  n,
const ScalarType *  A,
const OrdinalType  lda,
ScalarType *  S,
ScalarType *  scond,
ScalarType *  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 311 of file Teuchos_LAPACK.hpp.

template<typename OrdinalType, typename ScalarType>
void Teuchos::LAPACK< OrdinalType, ScalarType >::PORFS const char  UPLO,
const OrdinalType  n,
const OrdinalType  nrhs,
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 317 of file Teuchos_LAPACK.hpp.

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 323 of file Teuchos_LAPACK.hpp.

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 329 of file Teuchos_LAPACK.hpp.

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 335 of file Teuchos_LAPACK.hpp.

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 341 of file Teuchos_LAPACK.hpp.

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 347 of file Teuchos_LAPACK.hpp.

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 353 of file Teuchos_LAPACK.hpp.

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 359 of file Teuchos_LAPACK.hpp.

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 365 of file Teuchos_LAPACK.hpp.

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 371 of file Teuchos_LAPACK.hpp.

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 377 of file Teuchos_LAPACK.hpp.

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 383 of file Teuchos_LAPACK.hpp.

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 complex<float> or complex<double>.

Definition at line 389 of file Teuchos_LAPACK.hpp.

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 395 of file Teuchos_LAPACK.hpp.

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 complex<float> or complex<double>.

Definition at line 401 of file Teuchos_LAPACK.hpp.

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 complex<float> or complex<double>.

Definition at line 407 of file Teuchos_LAPACK.hpp.

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 complex<float> or complex<double>.

Definition at line 413 of file Teuchos_LAPACK.hpp.

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 419 of file Teuchos_LAPACK.hpp.

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 425 of file Teuchos_LAPACK.hpp.

template<typename OrdinalType, typename ScalarType>
void Teuchos::LAPACK< OrdinalType, ScalarType >::GEES const char  JOBVS,
const char  SORT,
OrdinalType *  SELECT,
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 real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z.

Definition at line 431 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 437 of file Teuchos_LAPACK.hpp.

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
 

Overwrites the general real matrix m by n matrix C with the product of C and Q, which is the product of k elementary reflectors, as returned by GEQRF.

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

Definition at line 443 of file Teuchos_LAPACK.hpp.

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 the ScalarType is complex<float> or complex<double>.

Definition at line 449 of file Teuchos_LAPACK.hpp.

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 the ScalarType is complex<float> or complex<double>.

Definition at line 455 of file Teuchos_LAPACK.hpp.

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 a real upper quasi-triangular matrix T.

Definition at line 461 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 real Schur factorization of a real matrix via orthogonal similarity transformations so that the diagonal block of T with row index ifst is moved to row ilst.

Definition at line 467 of file Teuchos_LAPACK.hpp.

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 485 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 491 of file Teuchos_LAPACK.hpp.

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 complex<float> or complex<double>.

Definition at line 473 of file Teuchos_LAPACK.hpp.

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 complex<float> or complex<double>.

Definition at line 479 of file Teuchos_LAPACK.hpp.


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