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cgeesx.f(3)				      LAPACK				      cgeesx.f(3)

NAME
       cgeesx.f -

SYNOPSIS
   Functions/Subroutines
       subroutine cgeesx (JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W, VS, LDVS, RCONDE,
	   RCONDV, WORK, LWORK, RWORK, BWORK, INFO)
	    CGEESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur
	   vectors for GE matrices

Function/Subroutine Documentation
   subroutine cgeesx (characterJOBVS, characterSORT, logical, externalSELECT, characterSENSE,
       integerN, complex, dimension( lda, * )A, integerLDA, integerSDIM, complex, dimension( *
       )W, complex, dimension( ldvs, * )VS, integerLDVS, realRCONDE, realRCONDV, complex,
       dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, logical, dimension( * )BWORK,
       integerINFO)
	CGEESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur
       vectors for GE matrices

       Purpose:

	    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.

       Parameters:
	   JOBVS

		     JOBVS is CHARACTER*1
		     = 'N': Schur vectors are not computed;
		     = 'V': Schur vectors are computed.

	   SORT

		     SORT is 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

		     SELECT is procedure) 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

		     SENSE is 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

		     N is INTEGER
		     The order of the matrix A. N >= 0.

	   A

		     A is COMPLEX array, dimension (LDA, N)
		     On entry, the N-by-N matrix A.
		     On exit, A is overwritten by its Schur form T.

	   LDA

		     LDA is INTEGER
		     The leading dimension of the array A.  LDA >= max(1,N).

	   SDIM

		     SDIM is INTEGER
		     If SORT = 'N', SDIM = 0.
		     If SORT = 'S', SDIM = number of eigenvalues for which
				    SELECT is true.

	   W

		     W is 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

		     VS is 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

		     LDVS is INTEGER
		     The leading dimension of the array VS.  LDVS >= 1, and if
		     JOBVS = 'V', LDVS >= N.

	   RCONDE

		     RCONDE is 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

		     RCONDV is 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

		     WORK is COMPLEX array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

		     LWORK is 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. Note also
		     that an error is only returned if LWORK < max(1,2*N), but if
		     SENSE = 'E' or 'V' or 'B' this may not be large enough.
		     For good performance, LWORK must generally be larger.

		     If LWORK = -1, then a workspace query is assumed; the routine
		     only calculates upper bound on the optimal size of the
		     array WORK, returns this value as the first entry of the WORK
		     array, and no error message related to LWORK is issued by
		     XERBLA.

	   RWORK

		     RWORK is REAL array, dimension (N)

	   BWORK

		     BWORK is LOGICAL array, dimension (N)
		     Not referenced if SORT = 'N'.

	   INFO

		     INFO is 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 238 of file cgeesx.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      cgeesx.f(3)
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