ESMF_DSYEVD Subroutine

subroutine ESMF_DSYEVD(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK, INFO)

\brief ESMF_DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices \htmlonly Download ESMF_DSYEVD + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

ESMF_DSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm.

The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

Because of large use of BLAS of level 3, ESMF_DSYEVD needs N*2 more workspace than DSYEVX. \endverbatim \param[in] JOBZ \verbatim JOBZ is CHARACTER1 = ‘N’: Compute eigenvalues only; = ‘V’: Compute eigenvalues and eigenvectors. \endverbatim

\param[in] UPLO \verbatim UPLO is CHARACTER*1 = ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored. \endverbatim

\param[in] N \verbatim N is INTEGER The order of the matrix A. N >= 0. \endverbatim

\param[in,out] A \verbatim A is DOUBLE PRECISION array, dimension (LDA, N) On entry, the symmetric matrix A. If UPLO = ‘U’, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = ‘L’, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = ‘V’, then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = ‘N’, then on exit the lower triangle (if UPLO=’L’) or the upper triangle (if UPLO=’U’) of A, including the diagonal, is destroyed. \endverbatim

\param[in] LDA \verbatim LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). \endverbatim

\param[out] W \verbatim W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. \endverbatim

\param[out] WORK \verbatim WORK is DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. \endverbatim

\param[in] LWORK \verbatim LWORK is INTEGER The dimension of the array WORK. If N <= 1, LWORK must be at least 1. If JOBZ = ‘N’ and N > 1, LWORK must be at least 2N+1. If JOBZ = ‘V’ and N > 1, LWORK must be at least 1 + 6N + 2N*2.

     If LWORK = -1, then a workspace query is assumed; the routine
     only calculates the optimal sizes of the WORK and IWORK
     arrays, returns these values as the first entries of the WORK
     and IWORK arrays, and no error message related to LWORK or
     LIWORK is issued by ESMF_XERBLA.

\endverbatim

\param[out] IWORK \verbatim IWORK is INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. \endverbatim

\param[in] LIWORK \verbatim LIWORK is INTEGER The dimension of the array IWORK. If N <= 1, LIWORK must be at least 1. If JOBZ = ‘N’ and N > 1, LIWORK must be at least 1. If JOBZ = ‘V’ and N > 1, LIWORK must be at least 3 + 5*N.

     If LIWORK = -1, then a workspace query is assumed; the
     routine only calculates the optimal sizes of the WORK and
     IWORK arrays, returns these values as the first entries of
     the WORK and IWORK arrays, and no error message related to
     LWORK or LIWORK is issued by ESMF_XERBLA.

\endverbatim

\param[out] INFO \verbatim INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i and JOBZ = ‘N’, then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = ‘V’, then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1). \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date December 2016 \ingroup doubleSYeigen \par Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA \n Modified by Francoise Tisseur, University of Tennessee \n Modified description of INFO. Sven, 16 Feb 05. \n

Arguments