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zgees

 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 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': Eigenvalues
              are not ordered:
              = 'S': Eigenvalues are ordered (see SELECT).

      SELECT  (input) LOGICAL FUNCTION of one COMPLEX*16 variable

              SELECT must be declared EXTERNAL in the calling sub-
              routine.  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 refer-
              enced.

      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 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 eigen-
              values could not be reordered because some eigen-
              values 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.