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version 1.5, 2010/08/07 13:22:26 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>
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download DSYEVD + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyevd.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyevd.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyevd.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
   *                          LIWORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBZ, UPLO
   *       INTEGER            INFO, LDA, LIWORK, LWORK, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IWORK( * )
   *       DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> 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, DSYEVD needs N**2 more
   *> workspace than DSYEVX.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] JOBZ
   *> \verbatim
   *>          JOBZ is CHARACTER*1
   *>          = '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 2*N+1.
   *>          If JOBZ = 'V' and N > 1, LWORK must be at least
   *>                                                1 + 6*N + 2*N**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 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 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
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \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
   
   
   *>
   *  =====================================================================
       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  
 *  *
 *     .. 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  
 *  =======  
 *  
 *  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, DSYEVD needs N**2 more  
 *  workspace than DSYEVX.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOBZ    (input) CHARACTER*1  
 *          = 'N':  Compute eigenvalues only;  
 *          = 'V':  Compute eigenvalues and eigenvectors.  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          = 'U':  Upper triangle of A is stored;  
 *          = 'L':  Lower triangle of A is stored.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  A       (input/output) 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.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,N).  
 *  
 *  W       (output) DOUBLE PRECISION array, dimension (N)  
 *          If INFO = 0, the eigenvalues in ascending order.  
 *  
 *  WORK    (workspace/output) DOUBLE PRECISION array,  
 *                                         dimension (LWORK)  
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  
 *  
 *  LWORK   (input) 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 2*N+1.  
 *          If JOBZ = 'V' and N > 1, LWORK must be at least  
 *                                                1 + 6*N + 2*N**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 XERBLA.  
 *  
 *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))  
 *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.  
 *  
 *  LIWORK  (input) 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 XERBLA.  
 *  
 *  INFO    (output) 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).  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *     Jeff Rutter, Computer Science Division, University of California  
 *     at Berkeley, USA  
 *  Modified by Francoise Tisseur, University of Tennessee.  
 *  
 *  Modified description of INFO. Sven, 16 Feb 05.  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. 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 )  
 *  *
 *     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 )  
       END IF        END IF
 *  *
 *     If matrix was scaled, then rescale eigenvalues appropriately.  *     If matrix was scaled, then rescale eigenvalues appropriately.
Removed from v.1.5  
changed lines
  Added in v.1.18

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