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CLAEIN(3F)							    CLAEIN(3F)

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

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

	 LOGICAL	NOINIT, RIGHTV

	 INTEGER	INFO, LDB, LDH, N

	 REAL		EPS3, SMLNUM

	 COMPLEX	W

	 REAL		RWORK( * )

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

PURPOSE
     CLAEIN 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 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
	     The eigenvalue of H whose corresponding right or left eigenvector
	     is to be computed.

     V	     (input/output) COMPLEX 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

									Page 1

CLAEIN(3F)							    CLAEIN(3F)

	     magnitude of a complex number (x,y) is taken to be |x| + |y|.

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

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

     RWORK   (workspace) REAL array, dimension (N)

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

     SMLNUM  (input) REAL
	     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.

									Page 2

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