NAME

       zgees.f -

SYNOPSIS

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

Function/Subroutine Documentation

   subroutine zgees (characterJOBVS, characterSORT, logical, externalSELECT, integerN,
       complex*16, dimension( lda, * )A, integerLDA, integerSDIM, complex*16, dimension( * )W,
       complex*16, dimension( ldvs, * )VS, integerLDVS, complex*16, dimension( * )WORK,
       integerLWORK, double precision, dimension( * )RWORK, logical, dimension( * )BWORK,
       integerINFO)
        ZGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur
       vectors for GE matrices

       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.

       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*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

                     N is INTEGER
                     The order of the matrix A. N >= 0.

           A

                     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

                     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*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

                     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

                     LDVS is INTEGER
                     The leading dimension of the array VS.  LDVS >= 1; if
                     JOBVS = 'V', LDVS >= N.

           WORK

                     WORK is COMPLEX*16 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 DOUBLE PRECISION 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 zgees.f.

Author

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