CXML
        	    
LAPACK version 3.0
cgeesx(3)

PURPOSE
  CGEESX - 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 CGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W, VS,
		     LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK, BWORK, INFO )

      CHARACTER	     JOBVS, SENSE, SORT

      INTEGER	     INFO, LDA, LDVS, LWORK, N, SDIM

      REAL	     RCONDE, RCONDV

      LOGICAL	     BWORK( * )

      REAL	     RWORK( * )

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

      LOGICAL	     SELECT

      EXTERNAL	     SELECT

DESCRIPTION
  CGEESX 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; computes a reciprocal condition number for
  the average of the selected eigenvalues (RCONDE); and computes a reciprocal
  condition number for the right invariant subspace corresponding to the
  selected eigenvalues (RCONDV).  The leading columns of Z form an
  orthonormal basis for this invariant subspace.

  For further explanation of the reciprocal condition numbers RCONDE and
  RCONDV, see Section 4.10 of the LAPACK Users' Guide (where these quantities
  are called s and sep respectively).

  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.  An eigenvalue W(j) is selected if SELECT(W(j)) is
	  true.

  SENSE	  (input) CHARACTER*1
	  Determines which reciprocal condition numbers are computed.  = 'N':
	  None are computed;
	  = 'E': Computed for average of selected eigenvalues only;
	  = 'V': Computed for selected right invariant subspace only;
	  = 'B': Computed for both.  If SENSE = 'E', 'V' or 'B', SORT must
	  equal 'S'.

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

  RCONDE  (output) REAL
	  If SENSE = 'E' or 'B', RCONDE contains the reciprocal condition
	  number for the average of the selected eigenvalues.  Not referenced
	  if SENSE = 'N' or 'V'.

  RCONDV  (output) REAL
	  If SENSE = 'V' or 'B', RCONDV contains the reciprocal condition
	  number for the selected right invariant subspace.  Not referenced
	  if SENSE = 'N' or 'E'.

  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).  Also, if
	  SENSE = 'E' or 'V' or 'B', LWORK >= 2*SDIM*(N-SDIM), where SDIM is
	  the number of selected eigenvalues computed by this routine.	Note
	  that 2*SDIM*(N-SDIM) <= N*N/2.  For good performance, LWORK must
	  generally be larger.

  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
	  transformation 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.