ZGEEV  - compute for an N-by-N complex nonsymmetric matrix
       A, the eigenvalues and, optionally, the left and/or  right
       eigenvectors


SYNOPSIS

       SUBROUTINE ZGEEV( JOBVL,  JOBVR,  N,  A, LDA, W, VL, LDVL,
                         VR, LDVR, WORK, LWORK, RWORK, INFO )

           CHARACTER     JOBVL, JOBVR

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

           DOUBLE        PRECISION RWORK( * )

           COMPLEX*16    A( LDA, * ), VL( LDVL, * ), VR( LDVR,  *
                         ), W( * ), WORK( * )


PURPOSE

       ZGEEV  computes  for an N-by-N complex nonsymmetric matrix
       A, the eigenvalues and, optionally, the left and/or  right
       eigenvectors.  The right eigenvector v(j) of A satisfies
                        A * v(j) = lambda(j) * v(j)
       where lambda(j) is its eigenvalue.
       The left eigenvector u(j) of A satisfies
                     u(j)**H * A = lambda(j) * u(j)**H
       where u(j)**H denotes the conjugate transpose of u(j).

       The computed eigenvectors are normalized to have Euclidean
       norm equal to 1 and largest component real.


ARGUMENTS

       JOBVL   (input) CHARACTER*1
               = 'N': left eigenvectors of A are not computed;
               = 'V': left eigenvectors of are computed.

       JOBVR   (input) CHARACTER*1
               = 'N': right eigenvectors of A are not computed;
               = 'V': right eigenvectors of A are computed.

       N       (input) INTEGER
               The order of the matrix A. N >= 0.

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

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

       W       (output) COMPLEX*16 array, dimension (N)
               W contains the computed eigenvalues.

               If  JOBVL  =  'V',  the left eigenvectors u(j) are
               stored one after another in the columns of VL,  in
               the  same  order as their eigenvalues.  If JOBVL =
               'N', VL is not referenced.  u(j) = VL(:,j), the j-
               th column of VL.

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

       VR      (output) COMPLEX*16 array, dimension (LDVR,N)
               If JOBVR = 'V', the right  eigenvectors  v(j)  are
               stored  one after another in the columns of VR, in
               the same order as their eigenvalues.  If  JOBVR  =
               'N', VR is not referenced.  v(j) = VR(:,j), the j-
               th column of VR.

       LDVR    (input) INTEGER
               The leading dimension of the array VR.  LDVR >= 1;
               if JOBVR = 'V', LDVR >= N.

       WORK    (workspace/output) COMPLEX*16 array, dimension
               (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 gen­
               erally 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) DOUBLE PRECISION array, dimension
               (2*N)

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value.
               > 0:  if INFO = i, the QR algorithm failed to com­
               pute all the eigenvalues, and no eigenvectors have
               been  computed;  elements  and  i+1:N of W contain
               eigenvalues which have converged.


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