DGEEV(l)	     LAPACK driver routine (version 1.1)	     DGEEV(l)

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(	* )

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

  The left eigenvectors	of A are the same as the right eigenvectors of A**T.
  If u(j) and v(j) are the left	and right eigenvectors,	respectively,
  corresponding	to the eigenvalue lambda(j), then (u(j)**T)*A =
  lambda(j)*(u(j)**T) and A*v(j) = lambda(j) * v(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 eigen-
	  values.  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 eigen-
	  values.  If JOBVR = 'N', VR is not referenced.  If the j-th eigen-
	  value	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, 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 illegal value.
	  > 0:	if INFO	= i, the QR algorithm failed to	compute	all the
	  eigenvalues, and no eigenvectors have	been computed; elements	i+1:N
	  of WR	and WI contain eigenvalues which have converged.