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.