NAME

       cgeesx.f -

SYNOPSIS

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

Function/Subroutine Documentation

   subroutine cgeesx (characterJOBVS, characterSORT, logical, externalSELECT, characterSENSE,
       integerN, complex, dimension( lda, * )A, integerLDA, integerSDIM, complex, dimension( *
       )W, complex, dimension( ldvs, * )VS, integerLDVS, realRCONDE, realRCONDV, complex,
       dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, logical, dimension( * )BWORK,
       integerINFO)
        CGEESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur
       vectors for GE matrices

       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.

       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 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

                     SENSE is 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

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

           A

                     A is COMPLEX array, dimension (LDA, N)
                     On entry, the N-by-N matrix A.
                     On exit, A is 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 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 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, and if
                     JOBVS = 'V', LDVS >= N.

           RCONDE

                     RCONDE is 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

                     RCONDV is 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

                     WORK is COMPLEX 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).
                     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

                     RWORK is REAL 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 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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Definition at line 238 of file cgeesx.f.

Author

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