claein(3)

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

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.

LAPACK version 3.0 15 June 2000

CLAEIN(3)