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

NAME

       LAPACK-3  -  computes  for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real
       Schur form T, and, optionally, the matrix of Schur vectors Z

SYNOPSIS

       SUBROUTINE DGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, WR, WI,  VS,  LDVS,  WORK,  LWORK,
                         BWORK, INFO )

           CHARACTER     JOBVS, SORT

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

           LOGICAL       BWORK( * )

           DOUBLE        PRECISION A( LDA, * ), VS( LDVS, * ), WI( * ), WORK( * ), WR( * )

           LOGICAL       SELECT

           EXTERNAL      SELECT

PURPOSE

       DGEES  computes  for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur
       form  T,  and,  optionally,  the  matrix  of  Schur  vectors  Z.   This  gives  the  Schur
       factorization A = Z*T*(Z**T).
        Optionally, it also orders the eigenvalues on the diagonal of the
        real 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 matrix is in real Schur form if it is upper quasi-triangular with
        1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the
        form
                [  a  b  ]
                [  c  a  ]
        where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).

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 two DOUBLE PRECISION arguments
                SELECT must be declared EXTERNAL in the calling subroutine.
                If SORT = 'S', SELECT is used to select eigenvalues to sort
                to the top left of the Schur form.
                If SORT = 'N', SELECT is not referenced.
                An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if
                SELECT(WR(j),WI(j)) is true; i.e., if either one of a complex
                conjugate pair of eigenvalues is selected, then both complex
                eigenvalues are selected.
                Note that a selected complex eigenvalue may no longer
                satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since
                ordering may change the value of complex eigenvalues
                (especially if the eigenvalue is ill-conditioned); in this
                case INFO is set to N+2 (see INFO below).

        N       (input) INTEGER
                The order of the matrix A. N >= 0.

        A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
                On entry, the N-by-N matrix A.
                On exit, A has been overwritten by its real 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 (after sorting)
                for which SELECT is true. (Complex conjugate
                pairs for which SELECT is true for either
                eigenvalue count as 2.)

        WR      (output) DOUBLE PRECISION array, dimension (N)
                WI      (output) DOUBLE PRECISION array, dimension (N)
                WR and WI contain the real and imaginary parts,
                respectively, of the computed eigenvalues in the same order
                that they appear on the diagonal of the output Schur form T.
                Complex conjugate pairs of eigenvalues will appear
                consecutively with the eigenvalue having the positive
                imaginary part first.

        VS      (output) DOUBLE PRECISION array, dimension (LDVS,N)
                If JOBVS = 'V', VS contains the orthogonal 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) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                On exit, if INFO = 0, WORK(1) contains the optimal LWORK.

        LWORK   (input) INTEGER
                The dimension of the array WORK.  LWORK >= max(1,3*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.

        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 WR and WI
                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                             DGEES(3lapack)