NAME

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

SYNOPSIS

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( ∗ )

PURPOSE

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.

  —  LAPACK version 2.0  —  08 October 1994