ZGEES(3)       LAPACK routine of NEC Numeric Library Collection       ZGEES(3)



NAME
       ZGEES

SYNOPSIS
       SUBROUTINE ZGEES (JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS, LDVS,
           WORK, LWORK, RWORK, BWORK, INFO)



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

           SORT      (input)
                     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    (input)
                     SELECT is a LOGICAL FUNCTION of one COMPLEX*16 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)
                     N is INTEGER
                     The order of the matrix A. N >= 0.

           A         (input/output)
                     A is COMPLEX*16 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)
                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,N).

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

           W         (output)
                     W is COMPLEX*16 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)
                     VS is COMPLEX*16 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)
                     LDVS is INTEGER
                     The leading dimension of the array VS.  LDVS >= 1; if
                     JOBVS = 'V', LDVS >= N.

           WORK      (output)
                     WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK     (input)
                     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     (output)
                     RWORK is DOUBLE PRECISION array, dimension (N)

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

           INFO      (output)
                     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.



LAPACK routine                  31 October 2017                       ZGEES(3)