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

                        WI, VS, LDVS, WORK, LWORK, BWORK, INFO )



          LOGICAL       BWORK( * )

          REAL          A( LDA, * ), VS( LDVS, * ), WI( * ), WORK(
                        * ), WR( * )

          LOGICAL       SELECT

          EXTERNAL      SELECT

      SGEES computes for an N-by-N real nonsymmetric matrix A, the
      eigenvalues, the real Schur form T, and, optionally, the
      matrix of Schur vectors Z.  This gives the Schur factoriza-
      tion A = Z*T*(Z**T).

      Optionally, it also orders the eigenvalues on the diagonal
      of the real Schur form so that selected eigenvalues are at
      the top left.  The leading columns of Z then form an ortho-
      normal basis for the invariant subspace corresponding to the
      selected eigenvalues.

      A matrix is in real Schur form if it is upper quasi-
      triangular with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will
      be standardized in the form
              [  a  b  ]
              [  c  a  ]

      where b*c < 0. The eigenvalues of such a block are a +-

      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 two REAL variables
              SELECT must be declared EXTERNAL in the calling sub-
              routine.  If SORT = 'S', SELECT is used to select
              eigenvalues to sort to the top left of the Schur
              form.  If SORT = 'N', SELECT is not referenced.  An
              eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if
              SELECT(WR(j),WI(j)) is true; i.e., if either one of
              a complex conjugate pair of eigenvalues is selected,
              then both complex eigenvalues are selected.  Note
              that a selected complex eigenvalue may no longer
              satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering,
              since ordering may change the value of complex
              eigenvalues (especially if the eigenvalue is ill-
              conditioned); in this case INFO is set to N+2 (see
              INFO below).

      N       (input) INTEGER
              The order of the matrix A. N >= 0.

      A       (input/output) REAL array, dimension (LDA,N)
              On entry, the N-by-N matrix A.  On exit, A has been
              overwritten by its real Schur form T.

      LDA     (input) INTEGER
              The leading dimension of the array A.  LDA >=

      SDIM    (output) INTEGER
              If SORT = 'N', SDIM = 0.  If SORT = 'S', SDIM =
              number of eigenvalues (after sorting) for which
              SELECT is true. (Complex conjugate pairs for which
              SELECT is true for either eigenvalue count as 2.)

      WR      (output) REAL array, dimension (N)
              WI      (output) REAL array, dimension (N) WR and WI
              contain the real and imaginary parts, respectively,
              of the computed eigenvalues in the same order that
              they appear on the diagonal of the output Schur form
              T.  Complex conjugate pairs of eigenvalues will
              appear consecutively with the eigenvalue having the
              positive imaginary part first.

      VS      (output) REAL array, dimension (LDVS,N)
              If JOBVS = 'V', VS contains the orthogonal matrix Z
              of Schur vectors.  If JOBVS = 'N', VS is not refer-

      LDVS    (input) INTEGER
              The leading dimension of the array VS.  LDVS >= 1;

              if JOBVS = 'V', LDVS >= N.

      WORK    (workspace/output) REAL array, dimension (LWORK)
              On exit, if INFO = 0, WORK(1) contains the optimal

      LWORK   (input) INTEGER
              The dimension of the array WORK.  LWORK >=
              max(1,3*N).  For good performance, LWORK must gen-
              erally be larger.

      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
              > 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 WR and WI
              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.