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CGEEV(l)					)					 CGEEV(l)

NAME
       CGEEV  - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, option-
       ally, 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( * )

PURPOSE
       CGEEV  computes	for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, option-
       ally, 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 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.

       RWORK   (workspace) REAL array, dimension (2*N)

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

LAPACK version 3.0			   15 June 2000 				 CGEEV(l)
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