 SLAEIN(3) uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H

## SYNOPSIS

SUBROUTINE SLAEIN(
RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO )

LOGICAL NOINIT, RIGHTV

INTEGER INFO, LDB, LDH, N

REAL BIGNUM, EPS3, SMLNUM, WI, WR

REAL B( LDB, * ), H( LDH, * ), VI( * ), VR( * ), WORK( * )

## PURPOSE

SLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real 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 (VR,VI).
= .FALSE.: initial vector supplied in (VR,VI).
N (input) INTEGER
The order of the matrix H. N >= 0.
H (input) REAL array, dimension (LDH,N)
The upper Hessenberg matrix H.
LDH (input) INTEGER
The leading dimension of the array H. LDH >= max(1,N).
WR (input) REAL
WI (input) REAL The real and imaginary parts of the eigenvalue of H whose corresponding right or left eigenvector is to be computed.
VR (input/output) REAL array, dimension (N)
VI (input/output) REAL array, dimension (N) On entry, if NOINIT = .FALSE. and WI = 0.0, VR must contain a real starting vector for inverse iteration using the real eigenvalue WR; if NOINIT = .FALSE. and WI.ne.0.0, VR and VI must contain the real and imaginary parts of a complex starting vector for inverse iteration using the complex eigenvalue (WR,WI); otherwise VR and VI need not be set. On exit, if WI = 0.0 (real eigenvalue), VR contains the computed real eigenvector; if WI.ne.0.0 (complex eigenvalue), VR and VI contain the real and imaginary parts of the computed complex eigenvector. The eigenvector is 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|. VI is not referenced if WI = 0.0.
B (workspace) REAL array, dimension (LDB,N)
LDB (input) INTEGER
The leading dimension of the array B. LDB >= N+1.
WORK (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.
BIGNUM (input) REAL
A machine-dependent value close to the overflow threshold.
INFO (output) INTEGER
= 0: successful exit
= 1: inverse iteration did not converge; VR is set to the last iterate, and so is VI if WI.ne.0.0.