NAME

       zgegs.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zgegs (JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR,
           WORK, LWORK, RWORK, INFO)
            ZGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors
           for GE matrices

Function/Subroutine Documentation

   subroutine zgegs (characterJOBVSL, characterJOBVSR, integerN, complex*16, dimension( lda, *
       )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( *
       )ALPHA, complex*16, dimension( * )BETA, complex*16, dimension( ldvsl, * )VSL,
       integerLDVSL, complex*16, dimension( ldvsr, * )VSR, integerLDVSR, complex*16, dimension( *
       )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)
        ZGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for
       GE matrices

       Purpose:

            This routine is deprecated and has been replaced by routine ZGGES.

            ZGEGS computes the eigenvalues, Schur form, and, optionally, the
            left and or/right Schur vectors of a complex matrix pair (A,B).
            Given two square matrices A and B, the generalized Schur
            factorization has the form

               A = Q*S*Z**H,  B = Q*T*Z**H

            where Q and Z are unitary matrices and S and T are upper triangular.
            The columns of Q are the left Schur vectors
            and the columns of Z are the right Schur vectors.

            If only the eigenvalues of (A,B) are needed, the driver routine
            ZGEGV should be used instead.  See ZGEGV for a description of the
            eigenvalues of the generalized nonsymmetric eigenvalue problem
            (GNEP).

       Parameters:
           JOBVSL

                     JOBVSL is CHARACTER*1
                     = 'N':  do not compute the left Schur vectors;
                     = 'V':  compute the left Schur vectors (returned in VSL).

           JOBVSR

                     JOBVSR is CHARACTER*1
                     = 'N':  do not compute the right Schur vectors;
                     = 'V':  compute the right Schur vectors (returned in VSR).

           N

                     N is INTEGER
                     The order of the matrices A, B, VSL, and VSR.  N >= 0.

           A

                     A is COMPLEX*16 array, dimension (LDA, N)
                     On entry, the matrix A.
                     On exit, the upper triangular matrix S from the generalized
                     Schur factorization.

           LDA

                     LDA is INTEGER
                     The leading dimension of A.  LDA >= max(1,N).

           B

                     B is COMPLEX*16 array, dimension (LDB, N)
                     On entry, the matrix B.
                     On exit, the upper triangular matrix T from the generalized
                     Schur factorization.

           LDB

                     LDB is INTEGER
                     The leading dimension of B.  LDB >= max(1,N).

           ALPHA

                     ALPHA is COMPLEX*16 array, dimension (N)
                     The complex scalars alpha that define the eigenvalues of
                     GNEP.  ALPHA(j) = S(j,j), the diagonal element of the Schur
                     form of A.

           BETA

                     BETA is COMPLEX*16 array, dimension (N)
                     The non-negative real scalars beta that define the
                     eigenvalues of GNEP.  BETA(j) = T(j,j), the diagonal element
                     of the triangular factor T.

                     Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
                     represent the j-th eigenvalue of the matrix pair (A,B), in
                     one of the forms lambda = alpha/beta or mu = beta/alpha.
                     Since either lambda or mu may overflow, they should not,
                     in general, be computed.

           VSL

                     VSL is COMPLEX*16 array, dimension (LDVSL,N)
                     If JOBVSL = 'V', the matrix of left Schur vectors Q.
                     Not referenced if JOBVSL = 'N'.

           LDVSL

                     LDVSL is INTEGER
                     The leading dimension of the matrix VSL. LDVSL >= 1, and
                     if JOBVSL = 'V', LDVSL >= N.

           VSR

                     VSR is COMPLEX*16 array, dimension (LDVSR,N)
                     If JOBVSR = 'V', the matrix of right Schur vectors Z.
                     Not referenced if JOBVSR = 'N'.

           LDVSR

                     LDVSR is INTEGER
                     The leading dimension of the matrix VSR. LDVSR >= 1, and
                     if JOBVSR = 'V', LDVSR >= 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.
                     To compute the optimal value of LWORK, call ILAENV to get
                     blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.)  Then compute:
                     NB  -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR;
                     the optimal LWORK is N*(NB+1).

                     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 (3*N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value.
                     =1,...,N:
                           The QZ iteration failed.  (A,B) are not in Schur
                           form, but ALPHA(j) and BETA(j) should be correct for
                           j=INFO+1,...,N.
                     > N:  errors that usually indicate LAPACK problems:
                           =N+1: error return from ZGGBAL
                           =N+2: error return from ZGEQRF
                           =N+3: error return from ZUNMQR
                           =N+4: error return from ZUNGQR
                           =N+5: error return from ZGGHRD
                           =N+6: error return from ZHGEQZ (other than failed
                                                          iteration)
                           =N+7: error return from ZGGBAK (computing VSL)
                           =N+8: error return from ZGGBAK (computing VSR)
                           =N+9: error return from ZLASCL (various places)

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Definition at line 224 of file zgegs.f.

Author

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