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

NAME

       LAPACK-3  -  computes  for  a  pair  of  N-by-N  complex  nonsymmetric matrices (A,B), the
       generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors

SYNOPSIS

       SUBROUTINE ZGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL, VR, LDVR,  WORK,
                         LWORK, RWORK, INFO )

           CHARACTER     JOBVL, JOBVR

           INTEGER       INFO, LDA, LDB, LDVL, LDVR, LWORK, N

           DOUBLE        PRECISION RWORK( * )

           COMPLEX*16    A(  LDA,  *  ),  ALPHA(  * ), B( LDB, * ), BETA( * ), VL( LDVL, * ), VR(
                         LDVR, * ), WORK( * )

PURPOSE

       ZGGEV computes for a pair of N-by-N complex nonsymmetric matrices (A,B),  the  generalized
       eigenvalues, and optionally, the left and/or right generalized eigenvectors.
        A generalized eigenvalue for a pair of matrices (A,B) is a scalar
        lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
        singular. It is usually represented as the pair (alpha,beta), as
        there is a reasonable interpretation for beta=0, and even for both
        being zero.
        The right generalized eigenvector v(j) corresponding to the
        generalized eigenvalue lambda(j) of (A,B) satisfies
                     A * v(j) = lambda(j) * B * v(j).
        The left generalized eigenvector u(j) corresponding to the
        generalized eigenvalues lambda(j) of (A,B) satisfies
                     u(j)**H * A = lambda(j) * u(j)**H * B
        where u(j)**H is the conjugate-transpose of u(j).

ARGUMENTS

        JOBVL   (input) CHARACTER*1
                = 'N':  do not compute the left generalized eigenvectors;
                = 'V':  compute the left generalized eigenvectors.

        JOBVR   (input) CHARACTER*1
                = 'N':  do not compute the right generalized eigenvectors;
                = 'V':  compute the right generalized eigenvectors.

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

        A       (input/output) COMPLEX*16 array, dimension (LDA, N)
                On entry, the matrix A in the pair (A,B).
                On exit, A has been overwritten.

        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 in the pair (A,B).
                On exit, B has been overwritten.

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

        ALPHA   (output) COMPLEX*16 array, dimension (N)
                BETA    (output) COMPLEX*16 array, dimension (N)
                On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
                generalized eigenvalues.
                Note: the quotients ALPHA(j)/BETA(j) may easily over- or
                underflow, and BETA(j) may even be zero.  Thus, the user
                should avoid naively computing the ratio alpha/beta.
                However, ALPHA will be always less than and usually
                comparable with norm(A) in magnitude, and BETA always less
                than and usually comparable with norm(B).

        VL      (output) COMPLEX*16 array, dimension (LDVL,N)
                If JOBVL = 'V', the left generalized eigenvectors u(j) are
                stored one after another in the columns of VL, in the same
                order as their eigenvalues.
                Each eigenvector is scaled so the largest component has
                abs(real part) + abs(imag. part) = 1.
                Not referenced if JOBVL = 'N'.

        LDVL    (input) INTEGER
                The leading dimension of the matrix VL. LDVL >= 1, and
                if JOBVL = 'V', LDVL >= N.

        VR      (output) COMPLEX*16 array, dimension (LDVR,N)
                If JOBVR = 'V', the right generalized eigenvectors v(j) are
                stored one after another in the columns of VR, in the same
                order as their eigenvalues.
                Each eigenvector is scaled so the largest component has
                abs(real part) + abs(imag. part) = 1.
                Not referenced if JOBVR = 'N'.

        LDVR    (input) INTEGER
                The leading dimension of the matrix VR. LDVR >= 1, and
                if JOBVR = 'V', LDVR >= 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.
                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/output) DOUBLE PRECISION array, dimension (8*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.  No eigenvectors have been
                calculated, but ALPHA(j) and BETA(j) should be
                correct for j=INFO+1,...,N.
                > N:  =N+1: other then QZ iteration failed in DHGEQZ,
                =N+2: error return from DTGEVC.

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