CXML
        	    
LAPACK version 3.0
zgeev(3)

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

SYNTAX
  SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK,
		    LWORK, RWORK, INFO )

      CHARACTER	    JOBVL, JOBVR

      INTEGER	    INFO, LDA, LDVL, LDVR, LWORK, N

      DOUBLE	    PRECISION RWORK( * )

      COMPLEX*16    A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), W( * ), WORK(
		    * )

DESCRIPTION
  ZGEEV 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*16 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*16 array, dimension (N)
	  W contains the computed eigenvalues.

  VL	  (output) COMPLEX*16 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*16 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*16 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) DOUBLE PRECISION 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.