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


SYNOPSIS

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

           CHARACTER     JOBVL, JOBVR

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

           REAL          RWORK( * )

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


PURPOSE

       CGEEV  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 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 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 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 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) REAL 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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