CXML
        	    
LAPACK version 3.0
dgeev(3)

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

SYNTAX
  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( * )

DESCRIPTION
  DGEEV computes for an N-by-N real 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 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
	  consecutively 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, 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.

	  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.

  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.