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version 1.3, 2010/08/06 15:28:51 version 1.14, 2016/08/27 15:34:45
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   *> \brief <b> ZGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices</b>
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZGEES + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgees.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgees.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgees.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS,
   *                         LDVS, WORK, LWORK, RWORK, BWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBVS, SORT
   *       INTEGER            INFO, LDA, LDVS, LWORK, N, SDIM
   *       ..
   *       .. Array Arguments ..
   *       LOGICAL            BWORK( * )
   *       DOUBLE PRECISION   RWORK( * )
   *       COMPLEX*16         A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * )
   *       ..
   *       .. Function Arguments ..
   *       LOGICAL            SELECT
   *       EXTERNAL           SELECT
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZGEES computes for an N-by-N complex nonsymmetric matrix A, the
   *> eigenvalues, the Schur form T, and, optionally, the matrix of Schur
   *> vectors Z.  This gives the Schur factorization A = Z*T*(Z**H).
   *>
   *> Optionally, it also orders the eigenvalues on the diagonal of the
   *> Schur form so that selected eigenvalues are at the top left.
   *> The leading columns of Z then form an orthonormal basis for the
   *> invariant subspace corresponding to the selected eigenvalues.
   *>
   *> A complex matrix is in Schur form if it is upper triangular.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] JOBVS
   *> \verbatim
   *>          JOBVS is CHARACTER*1
   *>          = 'N': Schur vectors are not computed;
   *>          = 'V': Schur vectors are computed.
   *> \endverbatim
   *>
   *> \param[in] SORT
   *> \verbatim
   *>          SORT is CHARACTER*1
   *>          Specifies whether or not to order the eigenvalues on the
   *>          diagonal of the Schur form.
   *>          = 'N': Eigenvalues are not ordered:
   *>          = 'S': Eigenvalues are ordered (see SELECT).
   *> \endverbatim
   *>
   *> \param[in] SELECT
   *> \verbatim
   *>          SELECT is a LOGICAL FUNCTION of one COMPLEX*16 argument
   *>          SELECT must be declared EXTERNAL in the calling subroutine.
   *>          If SORT = 'S', SELECT is used to select eigenvalues to order
   *>          to the top left of the Schur form.
   *>          IF SORT = 'N', SELECT is not referenced.
   *>          The eigenvalue W(j) is selected if SELECT(W(j)) is true.
   *> \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 N-by-N matrix A.
   *>          On exit, A has been overwritten by its Schur form T.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] SDIM
   *> \verbatim
   *>          SDIM is INTEGER
   *>          If SORT = 'N', SDIM = 0.
   *>          If SORT = 'S', SDIM = number of eigenvalues for which
   *>                         SELECT is true.
   *> \endverbatim
   *>
   *> \param[out] W
   *> \verbatim
   *>          W is COMPLEX*16 array, dimension (N)
   *>          W contains the computed eigenvalues, in the same order that
   *>          they appear on the diagonal of the output Schur form T.
   *> \endverbatim
   *>
   *> \param[out] VS
   *> \verbatim
   *>          VS is COMPLEX*16 array, dimension (LDVS,N)
   *>          If JOBVS = 'V', VS contains the unitary matrix Z of Schur
   *>          vectors.
   *>          If JOBVS = 'N', VS is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDVS
   *> \verbatim
   *>          LDVS is INTEGER
   *>          The leading dimension of the array VS.  LDVS >= 1; if
   *>          JOBVS = 'V', LDVS >= N.
   *> \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 dimension of the array WORK.  LWORK >= max(1,2*N).
   *>          For good performance, LWORK must generally be larger.
   *>
   *>          If LWORK = -1, then a workspace query is assumed; the routine
   *>          only calculates the optimal size of the WORK array, returns
   *>          this value as the first entry of the WORK array, and no error
   *>          message related to LWORK is issued by XERBLA.
   *> \endverbatim
   *>
   *> \param[out] RWORK
   *> \verbatim
   *>          RWORK is DOUBLE PRECISION array, dimension (N)
   *> \endverbatim
   *>
   *> \param[out] BWORK
   *> \verbatim
   *>          BWORK is LOGICAL array, dimension (N)
   *>          Not referenced if SORT = 'N'.
   *> \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 i is
   *>               <= N:  the QR algorithm failed to compute all the
   *>                      eigenvalues; elements 1:ILO-1 and i+1:N of W
   *>                      contain those eigenvalues which have converged;
   *>                      if JOBVS = 'V', VS contains the matrix which
   *>                      reduces A to its partially converged Schur form.
   *>               = N+1: the eigenvalues could not be reordered because
   *>                      some eigenvalues were too close to separate (the
   *>                      problem is very ill-conditioned);
   *>               = N+2: after reordering, roundoff changed values of
   *>                      some complex eigenvalues so that leading
   *>                      eigenvalues in the Schur form no longer satisfy
   *>                      SELECT = .TRUE..  This could also be caused by
   *>                      underflow due to scaling.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16GEeigen
   *
   *  =====================================================================
       SUBROUTINE ZGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS,        SUBROUTINE ZGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS,
      $                  LDVS, WORK, LWORK, RWORK, BWORK, INFO )       $                  LDVS, WORK, LWORK, RWORK, BWORK, 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          JOBVS, SORT        CHARACTER          JOBVS, SORT
Line 20 Line 216
       EXTERNAL           SELECT        EXTERNAL           SELECT
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZGEES computes for an N-by-N complex nonsymmetric matrix A, the  
 *  eigenvalues, the Schur form T, and, optionally, the matrix of Schur  
 *  vectors Z.  This gives the Schur factorization A = Z*T*(Z**H).  
 *  
 *  Optionally, it also orders the eigenvalues on the diagonal of the  
 *  Schur form so that selected eigenvalues are at the top left.  
 *  The leading columns of Z then form an orthonormal basis for the  
 *  invariant subspace corresponding to the selected eigenvalues.  
 *  
 *  A complex matrix is in Schur form if it is upper triangular.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOBVS   (input) CHARACTER*1  
 *          = 'N': Schur vectors are not computed;  
 *          = 'V': Schur vectors are computed.  
 *  
 *  SORT    (input) CHARACTER*1  
 *          Specifies whether or not to order the eigenvalues on the  
 *          diagonal of the Schur form.  
 *          = 'N': Eigenvalues are not ordered:  
 *          = 'S': Eigenvalues are ordered (see SELECT).  
 *  
 *  SELECT  (external procedure) LOGICAL FUNCTION of one COMPLEX*16 argument  
 *          SELECT must be declared EXTERNAL in the calling subroutine.  
 *          If SORT = 'S', SELECT is used to select eigenvalues to order  
 *          to the top left of the Schur form.  
 *          IF SORT = 'N', SELECT is not referenced.  
 *          The eigenvalue W(j) is selected if SELECT(W(j)) is true.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A. N >= 0.  
 *  
 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)  
 *          On entry, the N-by-N matrix A.  
 *          On exit, A has been overwritten by its Schur form T.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,N).  
 *  
 *  SDIM    (output) INTEGER  
 *          If SORT = 'N', SDIM = 0.  
 *          If SORT = 'S', SDIM = number of eigenvalues for which  
 *                         SELECT is true.  
 *  
 *  W       (output) COMPLEX*16 array, dimension (N)  
 *          W contains the computed eigenvalues, in the same order that  
 *          they appear on the diagonal of the output Schur form T.  
 *  
 *  VS      (output) COMPLEX*16 array, dimension (LDVS,N)  
 *          If JOBVS = 'V', VS contains the unitary matrix Z of Schur  
 *          vectors.  
 *          If JOBVS = 'N', VS is not referenced.  
 *  
 *  LDVS    (input) INTEGER  
 *          The leading dimension of the array VS.  LDVS >= 1; if  
 *          JOBVS = 'V', LDVS >= N.  
 *  
 *  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 dimension of the array WORK.  LWORK >= max(1,2*N).  
 *          For good performance, LWORK must generally be larger.  
 *  
 *          If LWORK = -1, then a workspace query is assumed; the routine  
 *          only calculates the optimal size of the WORK array, returns  
 *          this value as the first entry of the WORK array, and no error  
 *          message related to LWORK is issued by XERBLA.  
 *  
 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)  
 *  
 *  BWORK   (workspace) LOGICAL array, dimension (N)  
 *          Not referenced if SORT = 'N'.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0: successful exit  
 *          < 0: if INFO = -i, the i-th argument had an illegal value.  
 *          > 0: if INFO = i, and i is  
 *               <= N:  the QR algorithm failed to compute all the  
 *                      eigenvalues; elements 1:ILO-1 and i+1:N of W  
 *                      contain those eigenvalues which have converged;  
 *                      if JOBVS = 'V', VS contains the matrix which  
 *                      reduces A to its partially converged Schur form.  
 *               = N+1: the eigenvalues could not be reordered because  
 *                      some eigenvalues were too close to separate (the  
 *                      problem is very ill-conditioned);  
 *               = N+2: after reordering, roundoff changed values of  
 *                      some complex eigenvalues so that leading  
 *                      eigenvalues in the Schur form no longer satisfy  
 *                      SELECT = .TRUE..  This could also be caused by  
 *                      underflow due to scaling.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.3  
changed lines
  Added in v.1.14

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