version 1.6, 2010/08/13 21:03:58
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version 1.18, 2023/08/07 08:39:08
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*> \brief <b> DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices</b> |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download DSYEVD + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyevd.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyevd.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyevd.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, |
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* LIWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER JOBZ, UPLO |
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* INTEGER INFO, LDA, LIWORK, LWORK, N |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IWORK( * ) |
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* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DSYEVD computes all eigenvalues and, optionally, eigenvectors of a |
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*> real symmetric matrix A. If eigenvectors are desired, it uses a |
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*> divide and conquer algorithm. |
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*> |
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*> The divide and conquer algorithm makes very mild assumptions about |
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*> floating point arithmetic. It will work on machines with a guard |
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*> digit in add/subtract, or on those binary machines without guard |
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*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or |
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*> Cray-2. It could conceivably fail on hexadecimal or decimal machines |
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*> without guard digits, but we know of none. |
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*> |
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*> Because of large use of BLAS of level 3, DSYEVD needs N**2 more |
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*> workspace than DSYEVX. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] JOBZ |
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*> \verbatim |
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*> JOBZ is CHARACTER*1 |
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*> = 'N': Compute eigenvalues only; |
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*> = 'V': Compute eigenvalues and eigenvectors. |
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*> \endverbatim |
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*> |
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*> \param[in] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> = 'U': Upper triangle of A is stored; |
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*> = 'L': Lower triangle of A is stored. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] A |
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*> \verbatim |
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*> A is DOUBLE PRECISION array, dimension (LDA, N) |
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*> On entry, the symmetric matrix A. If UPLO = 'U', the |
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*> leading N-by-N upper triangular part of A contains the |
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*> upper triangular part of the matrix A. If UPLO = 'L', |
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*> the leading N-by-N lower triangular part of A contains |
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*> the lower triangular part of the matrix A. |
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*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the |
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*> orthonormal eigenvectors of the matrix A. |
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*> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') |
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*> or the upper triangle (if UPLO='U') of A, including the |
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*> diagonal, is destroyed. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] W |
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*> \verbatim |
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*> W is DOUBLE PRECISION array, dimension (N) |
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*> If INFO = 0, the eigenvalues in ascending order. |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is DOUBLE PRECISION array, |
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*> dimension (LWORK) |
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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*> \endverbatim |
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*> |
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*> \param[in] LWORK |
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*> \verbatim |
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*> LWORK is INTEGER |
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*> The dimension of the array WORK. |
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*> If N <= 1, LWORK must be at least 1. |
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*> If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1. |
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*> If JOBZ = 'V' and N > 1, LWORK must be at least |
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*> 1 + 6*N + 2*N**2. |
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*> |
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*> If LWORK = -1, then a workspace query is assumed; the routine |
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*> only calculates the optimal sizes of the WORK and IWORK |
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*> arrays, returns these values as the first entries of the WORK |
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*> and IWORK arrays, and no error message related to LWORK or |
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*> LIWORK is issued by XERBLA. |
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*> \endverbatim |
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*> |
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*> \param[out] IWORK |
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*> \verbatim |
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*> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) |
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*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. |
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*> \endverbatim |
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*> |
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*> \param[in] LIWORK |
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*> \verbatim |
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*> LIWORK is INTEGER |
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*> The dimension of the array IWORK. |
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*> If N <= 1, LIWORK must be at least 1. |
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*> If JOBZ = 'N' and N > 1, LIWORK must be at least 1. |
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*> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. |
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*> |
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*> If LIWORK = -1, then a workspace query is assumed; the |
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*> routine only calculates the optimal sizes of the WORK and |
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*> IWORK arrays, returns these values as the first entries of |
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*> the WORK and IWORK arrays, and no error message related to |
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*> LWORK or LIWORK is issued by XERBLA. |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> > 0: if INFO = i and JOBZ = 'N', then the algorithm failed |
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*> to converge; i off-diagonal elements of an intermediate |
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*> tridiagonal form did not converge to zero; |
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*> if INFO = i and JOBZ = 'V', then the algorithm failed |
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*> to compute an eigenvalue while working on the submatrix |
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*> lying in rows and columns INFO/(N+1) through |
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*> mod(INFO,N+1). |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \ingroup doubleSYeigen |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> Jeff Rutter, Computer Science Division, University of California |
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*> at Berkeley, USA \n |
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*> Modified by Francoise Tisseur, University of Tennessee \n |
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*> Modified description of INFO. Sven, 16 Feb 05. \n |
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*> |
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* ===================================================================== |
SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, |
SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, |
$ LIWORK, INFO ) |
$ LIWORK, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER JOBZ, UPLO |
CHARACTER JOBZ, UPLO |
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DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) |
DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DSYEVD computes all eigenvalues and, optionally, eigenvectors of a |
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* 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 |
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* Cray-2. It could conceivably fail on hexadecimal or decimal machines |
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* without guard digits, but we know of none. |
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* |
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* Because of large use of BLAS of level 3, DSYEVD needs N**2 more |
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* workspace than DSYEVX. |
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* |
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* Arguments |
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* ========= |
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* |
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* JOBZ (input) CHARACTER*1 |
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* = 'N': Compute eigenvalues only; |
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* = 'V': Compute eigenvalues and eigenvectors. |
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* |
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* UPLO (input) CHARACTER*1 |
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* = 'U': Upper triangle of A is stored; |
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* = 'L': Lower triangle of A is stored. |
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* |
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* N (input) INTEGER |
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* The order of the matrix A. N >= 0. |
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* |
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* A (input/output) DOUBLE PRECISION array, dimension (LDA, N) |
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* On entry, the symmetric matrix A. If UPLO = 'U', the |
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* leading N-by-N upper triangular part of A contains the |
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* upper triangular part of the matrix A. If UPLO = 'L', |
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* the leading N-by-N lower triangular part of A contains |
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* the lower triangular part of the matrix A. |
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* On exit, if JOBZ = 'V', then if INFO = 0, A contains the |
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* orthonormal eigenvectors of the matrix A. |
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* If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') |
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* or the upper triangle (if UPLO='U') of A, including the |
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* diagonal, is destroyed. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,N). |
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* |
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* W (output) DOUBLE PRECISION array, dimension (N) |
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* If INFO = 0, the eigenvalues in ascending order. |
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* |
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* WORK (workspace/output) DOUBLE PRECISION array, |
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* dimension (LWORK) |
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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* |
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* LWORK (input) INTEGER |
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* The dimension of the array WORK. |
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* If N <= 1, LWORK must be at least 1. |
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* If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1. |
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* If JOBZ = 'V' and N > 1, LWORK must be at least |
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* 1 + 6*N + 2*N**2. |
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* |
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* If LWORK = -1, then a workspace query is assumed; the routine |
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* only calculates the optimal sizes of the WORK and IWORK |
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* arrays, returns these values as the first entries of the WORK |
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* and IWORK arrays, and no error message related to LWORK or |
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* LIWORK is issued by XERBLA. |
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* |
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* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) |
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* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. |
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* |
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* LIWORK (input) INTEGER |
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* The dimension of the array IWORK. |
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* If N <= 1, LIWORK must be at least 1. |
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* If JOBZ = 'N' and N > 1, LIWORK must be at least 1. |
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* If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. |
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* |
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* If LIWORK = -1, then a workspace query is assumed; the |
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* routine only calculates the optimal sizes of the WORK and |
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* IWORK arrays, returns these values as the first entries of |
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* the WORK and IWORK arrays, and no error message related to |
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* LWORK or LIWORK is issued by XERBLA. |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* > 0: if INFO = i and JOBZ = 'N', then the algorithm failed |
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* to converge; i off-diagonal elements of an intermediate |
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* tridiagonal form did not converge to zero; |
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* if INFO = i and JOBZ = 'V', then the algorithm failed |
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* to compute an eigenvalue while working on the submatrix |
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* lying in rows and columns INFO/(N+1) through |
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* mod(INFO,N+1). |
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* |
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* Further Details |
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* =============== |
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* |
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* Based on contributions by |
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* Jeff Rutter, Computer Science Division, University of California |
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* at Berkeley, USA |
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* Modified by Francoise Tisseur, University of Tennessee. |
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* |
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* Modified description of INFO. Sven, 16 Feb 05. |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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LWMIN = 2*N + 1 |
LWMIN = 2*N + 1 |
END IF |
END IF |
LOPT = MAX( LWMIN, 2*N + |
LOPT = MAX( LWMIN, 2*N + |
$ ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) ) |
$ N*ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) ) |
LIOPT = LIWMIN |
LIOPT = LIWMIN |
END IF |
END IF |
WORK( 1 ) = LOPT |
WORK( 1 ) = LOPT |
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* |
* |
CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ), |
CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ), |
$ WORK( INDWRK ), LLWORK, IINFO ) |
$ WORK( INDWRK ), LLWORK, IINFO ) |
LOPT = 2*N + WORK( INDWRK ) |
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* |
* |
* For eigenvalues only, call DSTERF. For eigenvectors, first call |
* For eigenvalues only, call DSTERF. For eigenvectors, first call |
* DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the |
* DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the |
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CALL DORMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ), |
CALL DORMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ), |
$ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO ) |
$ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO ) |
CALL DLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA ) |
CALL DLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA ) |
LOPT = MAX( LOPT, 1+6*N+2*N**2 ) |
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END IF |
END IF |
* |
* |
* If matrix was scaled, then rescale eigenvalues appropriately. |
* If matrix was scaled, then rescale eigenvalues appropriately. |