Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes  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  (external 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.
                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 (MAX(1,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 driver routine (version 3.2)        April 2011                             CGEES(3lapack)