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 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

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.

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.
                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 (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).
                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   (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.

 LAPACK driver routine (version 3.2.2)      April 2011                            CGEESX(3lapack)