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CGEEV(3F)							     CGEEV(3F)

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).

									Page 1

CGEEV(3F)							     CGEEV(3F)

     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.

     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.

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