cgees.f(3)							      LAPACK								cgees.f(3)

NAME

       cgees.f -

SYNOPSIS

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

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

       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.

       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 a 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

		     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 has been 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; if
		     JOBVS = 'V', LDVS >= N.

	   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).
		     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

		     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 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 197 of file cgees.f.

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

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