CXML
        	    
LAPACK version 3.0
zgees(3)

PURPOSE
  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

SYNTAX
  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

DESCRIPTION
  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.

	  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.