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NAME
     zgees - compute for an N-by-N complex nonsymmetric matrix A,
     the  eigenvalues,  the  Schur  form  T, and, optionally, the
     matrix of Schur vectors Z

SYNOPSIS
     SUBROUTINE ZGEES( JOBVS, SORT, SELECT, N, A, LDA,  SDIM,  W,
               VS, LDVS, WORK, LWORK, RWORK, BWORK, INFO )

     CHARACTER JOBVS, SORT

     INTEGER INFO, LDA, LDVS, LWORK, N, SDIM

     LOGICAL BWORK( * )

     DOUBLE PRECISION RWORK( * )

     COMPLEX*16 A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * )

     LOGICAL SELECT

     EXTERNAL SELECT



     #include <sunperf.h>

     void zgees(char jobvs, char sort, int  (*select)(),  int  n,
               doublecomplex  *za, int lda, int *sdim, doublecom-
               plex *w, doublecomplex *vs, int ldvs, int *info) ;

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  factoriza-
     tion 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': Eigen-
               values are not ordered:
               = 'S': Eigenvalues are ordered (see SELECT).

     SELECT    (input) LOGICAL FUNCTION of one  COMPLEX*16  argu-
               ment
               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 refer-
               enced.   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 out-
               put 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
               (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 gen-
               erally be larger.

     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  ille-
               gal 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  con-
               tain  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 com-
               plex eigenvalues so that  leading  eigenvalues  in
               the  Schur form no longer satisfy SELECT = .TRUE..
               This could also be  caused  by  underflow  due  to
               scaling.

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