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version 1.7, 2010/12/21 13:53:46 version 1.8, 2011/11/21 20:43:11
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   *> \brief <b> ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b>
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZHEEVD + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zheevd.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zheevd.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zheevd.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
   *                          LRWORK, IWORK, LIWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBZ, UPLO
   *       INTEGER            INFO, LDA, LIWORK, LRWORK, LWORK, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IWORK( * )
   *       DOUBLE PRECISION   RWORK( * ), W( * )
   *       COMPLEX*16         A( LDA, * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
   *> complex Hermitian 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.
   *> \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 COMPLEX*16 array, dimension (LDA, N)
   *>          On entry, the Hermitian 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 COMPLEX*16 array, dimension (MAX(1,LWORK))
   *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is INTEGER
   *>          The length of the array WORK.
   *>          If N <= 1,                LWORK must be at least 1.
   *>          If JOBZ  = 'N' and N > 1, LWORK must be at least N + 1.
   *>          If JOBZ  = 'V' and N > 1, LWORK must be at least 2*N + N**2.
   *>
   *>          If LWORK = -1, then a workspace query is assumed; the routine
   *>          only calculates the optimal sizes of the WORK, RWORK and
   *>          IWORK arrays, returns these values as the first entries of
   *>          the WORK, RWORK and IWORK arrays, and no error message
   *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
   *> \endverbatim
   *>
   *> \param[out] RWORK
   *> \verbatim
   *>          RWORK is DOUBLE PRECISION array,
   *>                                         dimension (LRWORK)
   *>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
   *> \endverbatim
   *>
   *> \param[in] LRWORK
   *> \verbatim
   *>          LRWORK is INTEGER
   *>          The dimension of the array RWORK.
   *>          If N <= 1,                LRWORK must be at least 1.
   *>          If JOBZ  = 'N' and N > 1, LRWORK must be at least N.
   *>          If JOBZ  = 'V' and N > 1, LRWORK must be at least
   *>                         1 + 5*N + 2*N**2.
   *>
   *>          If LRWORK = -1, then a workspace query is assumed; the
   *>          routine only calculates the optimal sizes of the WORK, RWORK
   *>          and IWORK arrays, returns these values as the first entries
   *>          of the WORK, RWORK and IWORK arrays, and no error message
   *>          related to LWORK or LRWORK 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, RWORK
   *>          and IWORK arrays, returns these values as the first entries
   *>          of the WORK, RWORK and IWORK arrays, and no error message
   *>          related to LWORK or LRWORK 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. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16HEeigen
   *
   *> \par Further Details:
   *  =====================
   *>
   *>  Modified description of INFO. Sven, 16 Feb 05.
   *
   *> \par Contributors:
   *  ==================
   *>
   *> Jeff Rutter, Computer Science Division, University of California
   *> at Berkeley, USA
   *>
   *  =====================================================================
       SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,        SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
      $                   LRWORK, IWORK, LIWORK, INFO )       $                   LRWORK, IWORK, LIWORK, INFO )
 *  *
 *  -- LAPACK driver routine (version 3.2) --  *  -- LAPACK driver routine (version 3.4.0) --
 *  -- 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  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOBZ, UPLO        CHARACTER          JOBZ, UPLO
Line 16 Line 220
       COMPLEX*16         A( LDA, * ), WORK( * )        COMPLEX*16         A( LDA, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a  
 *  complex Hermitian 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.  
 *  
 *  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) COMPLEX*16 array, dimension (LDA, N)  
 *          On entry, the Hermitian 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) COMPLEX*16 array, dimension (MAX(1,LWORK))  
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  
 *  
 *  LWORK   (input) INTEGER  
 *          The length of the array WORK.  
 *          If N <= 1,                LWORK must be at least 1.  
 *          If JOBZ  = 'N' and N > 1, LWORK must be at least N + 1.  
 *          If JOBZ  = 'V' and N > 1, LWORK must be at least 2*N + N**2.  
 *  
 *          If LWORK = -1, then a workspace query is assumed; the routine  
 *          only calculates the optimal sizes of the WORK, RWORK and  
 *          IWORK arrays, returns these values as the first entries of  
 *          the WORK, RWORK and IWORK arrays, and no error message  
 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.  
 *  
 *  RWORK   (workspace/output) DOUBLE PRECISION array,  
 *                                         dimension (LRWORK)  
 *          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.  
 *  
 *  LRWORK  (input) INTEGER  
 *          The dimension of the array RWORK.  
 *          If N <= 1,                LRWORK must be at least 1.  
 *          If JOBZ  = 'N' and N > 1, LRWORK must be at least N.  
 *          If JOBZ  = 'V' and N > 1, LRWORK must be at least  
 *                         1 + 5*N + 2*N**2.  
 *  
 *          If LRWORK = -1, then a workspace query is assumed; the  
 *          routine only calculates the optimal sizes of the WORK, RWORK  
 *          and IWORK arrays, returns these values as the first entries  
 *          of the WORK, RWORK and IWORK arrays, and no error message  
 *          related to LWORK or LRWORK 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, RWORK  
 *          and IWORK arrays, returns these values as the first entries  
 *          of the WORK, RWORK and IWORK arrays, and no error message  
 *          related to LWORK or LRWORK 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 description of INFO. Sven, 16 Feb 05.  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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