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CGEES(l)			       )			      CGEES(l)

NAME
       CGEES - 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 CGEES( 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( * )

	   REAL		 RWORK( * )

	   COMPLEX	 A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * )

	   LOGICAL	 SELECT

	   EXTERNAL	 SELECT

PURPOSE
       CGEES 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 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 diago‐
	       nal of the Schur form.  = 'N': Eigenvalues are not ordered:
	       = 'S': Eigenvalues are ordered (see SELECT).

       SELECT  (input) LOGICAL FUNCTION of one COMPLEX 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 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  ei‐
	       genvalues for which SELECT is true.

       W       (output) COMPLEX 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 array, dimension (LDVS,N)
	       If JOBVS = 'V', VS contains the unitary matrix Z of Schur  vec‐
	       tors.  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 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) REAL 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  ei‐
	       genvalues 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 ei‐
	       genvalues 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.

LAPACK version 3.0		 15 June 2000			      CGEES(l)
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