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RedHat 9 (Linux i386) - man page for cgees (redhat section l)

CGEES(l)					)					 CGEES(l)

NAME
       CGEES  -  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 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 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 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  eigenvalues  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  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 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 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.

LAPACK version 3.0			   15 June 2000 				 CGEES(l)


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