SLAEIN(l) ) SLAEIN(l)NAME
SLAEIN - use inverse iteration to find a right or left eigenvector cor‐
responding 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 cor‐
responding 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 eigen‐
value 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 eigenval‐
ue), 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 mag‐
nitude 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.
LAPACK version 3.0 15 June 2000 SLAEIN(l)
