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

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

     CHARACTER JOBVL, JOBVR

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

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



     #include <sunperf.h>

     void sgeev(char jobvl, char jobvr, int  n,  float  *sa,  int
               lda,  float  *wr,  float *wi, float *vl, int ldvl,
               float *vr, int ldvr, int *info) ;

PURPOSE
     SGEEV 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) REAL 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) REAL array, dimension (N)
               WI      (output) REAL array, dimension (N) WR  and
               WI  contain  the real and imaginary parts, respec-
               tively, of the computed eigenvalues.  Complex con-
               jugate  pairs  of eigenvalues appear consecutively
               with the eigenvalue having the positive  imaginary
               part first.

     VL        (output) REAL 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) REAL 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) REAL 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(1,3*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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