ZGEES(l)	     LAPACK driver routine (version 1.1)	     ZGEES(l)

NAME
  ZGEES	- compute for an N-by-N	complex	nonsymmetric matrix A, the eigen-
  values, 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 eigen-
  values, 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 correspond-
  ing 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 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 eigen-
	  values 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 eigen-
	  values 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 eigen-
	  values so that leading eigenvalues in	the Schur form no longer
	  satisfy SELECT = .TRUE..  This could also be caused by underflow
	  due to scaling.