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NAME
     dgeev - compute for an N-by-N real  nonsymmetric  matrix  A,
     the  eigenvalues  and,  optionally,  the  left  and/or right
     eigenvectors

SYNOPSIS
     SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL,
               VR, LDVR, WORK, LWORK, INFO )

     CHARACTER JOBVL, JOBVR

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

     DOUBLE PRECISION A( LDA, * ), VL( LDVL, * ), VR( LDVR, *  ),
               WI( * ), WORK( * ), WR( * )



     #include <sunperf.h>

     void dgeev(char jobvl, char jobvr, int n,  double  *da,  int
               lda, double *wr, double *wi, double *vl, int ldvl,
               double *vr, int ldvr, int *info) ;

PURPOSE
     DGEEV computes for an N-by-N real nonsymmetric matrix A, the
     eigenvalues and, optionally, the left and/or right eigenvec-
     tors.

     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 A 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) DOUBLE PRECISION  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).

     WR        (output) DOUBLE PRECISION array, dimension (N)
               WI      (output) DOUBLE PRECISION array, dimension
               (N)  WR  and  WI  contain  the  real and imaginary
               parts, respectively, of the computed  eigenvalues.
               Complex conjugate pairs of eigenvalues appear con-
               secutively with the eigenvalue having the positive
               imaginary part first.

     VL        (output)   DOUBLE   PRECISION   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.  If the j-th eigenvalue
               is real, then u(j) = VL(:,j), the j-th  column  of
               VL.   If  the j-th and (j+1)-st eigenvalues form a
               complex conjugate pair,  then  u(j)  =  VL(:,j)  +
               i*VL(:,j+1) and
               u(j+1) = VL(:,j) - i*VL(:,j+1).

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

     VR        (output)   DOUBLE   PRECISION   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.  If the j-th eigenvalue
               is real, then v(j) = VR(:,j), the j-th  column  of
               VR.   If  the j-th and (j+1)-st eigenvalues form a
               complex conjugate pair,  then  v(j)  =  VR(:,j)  +
               i*VR(:,j+1) and
               v(j+1) = VR(:,j) - i*VR(:,j+1).

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

     WORK      (workspace/output) DOUBLE PRECISION array,  dimen-
               sion (LWORK)
               On exit, if INFO = 0, WORK(1) returns the  optimal
               LWORK.

     LWORK     (input) INTEGER
               The  dimension  of  the  array  WORK.   LWORK   >=
               max(1,3*N),  and  if  JOBVL  = 'V' or JOBVR = 'V',
               LWORK >= 4*N.  For good  performance,  LWORK  must
               generally be larger.

     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 i+1:N of WR and WI contain
               eigenvalues which have converged.

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