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NAME
     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( * )



     #include <sunperf.h>

     void cgeev(char jobvl, char jobvr, int n, complex  *ca,  int
               lda,  complex  *w,  complex *vl, int ldvl, complex
               *vr, int ldvr, int *info) ;

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.

     VL        (output) COMPLEX array, dimension (LDVL,N)
               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.

     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
               compute  all  the eigenvalues, and no eigenvectors
               have been computed; elements and i+1:N of  W  con-
               tain eigenvalues which have converged.

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