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

NAME

       LAPACK-3 - routine i deprecated and has been replaced by routine ZGGES

SYNOPSIS

       SUBROUTINE ZGEGS( JOBVSL,  JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR,
                         WORK, LWORK, RWORK, INFO )

           CHARACTER     JOBVSL, JOBVSR

           INTEGER       INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N

           DOUBLE        PRECISION RWORK( * )

           COMPLEX*16    A( LDA, * ), ALPHA( * ), B( LDB, * ), BETA( * ), VSL( LDVSL, *  ),  VSR(
                         LDVSR, * ), WORK( * )

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       This routine is deprecated and has been replaced by routine ZGGES.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

ARGUMENTS

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

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

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

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

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

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

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

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

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

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

        LDVSR   (input) INTEGER
                The leading dimension of the matrix VSR. LDVSR >= 1, and
                if JOBVSR = 'V', LDVSR >= N.

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

        LWORK   (input) 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   (workspace) DOUBLE PRECISION array, dimension (3*N)

        INFO    (output) 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)

 LAPACK driver routine (version 3.2)        April 2011                             ZGEGS(3lapack)