CGEEV(l)								 )								  CGEEV(l)

NAME

       CGEEV - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, 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, 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 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  eigenval-
	       ues.  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 eigenval-
	       ues.  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)