zgees(3F)

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

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  (input) 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 (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.

     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.