CXML
        	    
LAPACK version 3.0
zlaein(3)

PURPOSE
  ZLAEIN - use inverse iteration to find a right or left eigenvector
  corresponding to the eigenvalue W of a complex upper Hessenberg matrix H

SYNTAX
  SUBROUTINE ZLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3,
		     SMLNUM, INFO )

      LOGICAL	     NOINIT, RIGHTV

      INTEGER	     INFO, LDB, LDH, N

      DOUBLE	     PRECISION EPS3, SMLNUM

      COMPLEX*16     W

      DOUBLE	     PRECISION RWORK( * )

      COMPLEX*16     B( LDB, * ), H( LDH, * ), V( * )

DESCRIPTION
  ZLAEIN uses inverse iteration to find a right or left eigenvector
  corresponding to the eigenvalue W of a complex upper Hessenberg matrix H.

ARGUMENTS
  RIGHTV   (input) LOGICAL
	   = .TRUE. : compute right eigenvector;
	   = .FALSE.: compute left eigenvector.

  NOINIT   (input) LOGICAL
	   = .TRUE. : no initial vector supplied in V
	   = .FALSE.: initial vector supplied in V.

  N	  (input) INTEGER
	  The order of the matrix H.  N >= 0.

  H	  (input) COMPLEX*16 array, dimension (LDH,N)
	  The upper Hessenberg matrix H.

  LDH	  (input) INTEGER
	  The leading dimension of the array H.	 LDH >= max(1,N).

  W	  (input) COMPLEX*16
	  The eigenvalue of H whose corresponding right or left eigenvector
	  is to be computed.

  V	  (input/output) COMPLEX*16 array, dimension (N)
	  On entry, if NOINIT = .FALSE., V must contain a starting vector for
	  inverse iteration; otherwise V need not be set.  On exit, V
	  contains the computed eigenvector, normalized so that the component
	  of largest magnitude has magnitude 1; here the magnitude of a
	  complex number (x,y) is taken to be |x| + |y|.

  B	  (workspace) COMPLEX*16 array, dimension (LDB,N)

  LDB	  (input) INTEGER
	  The leading dimension of the array B.	 LDB >= max(1,N).

  RWORK	  (workspace) DOUBLE PRECISION array, dimension (N)

  EPS3	  (input) DOUBLE PRECISION
	  A small machine-dependent value which is used to perturb close
	  eigenvalues, and to replace zero pivots.

  SMLNUM  (input) DOUBLE PRECISION
	  A machine-dependent value close to the underflow threshold.

  INFO	  (output) INTEGER
	  = 0:	successful exit
	  = 1:	inverse iteration did not converge; V is set to the last
	  iterate.