DLAEIN - use inverse iteration to find a right or left
eigenvector corresponding to the eigenvalue (WR,WI) of a
real upper Hessenberg matrix H
SYNOPSIS
SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR,
VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM,
INFO )
LOGICAL NOINIT, RIGHTV
INTEGER INFO, LDB, LDH, N
DOUBLE PRECISION BIGNUM, EPS3, SMLNUM, WI, WR
DOUBLE PRECISION B( LDB, * ), H( LDH, * ), VI(
* ), VR( * ), WORK( * )
PURPOSE
DLAEIN 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) DOUBLE PRECISION 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) DOUBLE PRECISION
WI (input) DOUBLE PRECISION The real and
imaginary parts of the eigenvalue of H whose cor
responding right or left eigenvector is to be com
puted.
VR (input/output) DOUBLE PRECISION array, dimension
(N)
VI (input/output) DOUBLE PRECISION array,
dimension (N) On entry, if NOINIT = .FALSE. and WI
= 0.0, VR must contain a real starting vector for
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 eigen
vector; 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 magni
tude has magnitude 1; here the magnitude of a com
plex number (x,y) is taken to be |x| + |y|. VI is
not referenced if WI = 0.0.
B (workspace) DOUBLE PRECISION array, dimension
(LDB,N)
LDB (input) INTEGER
The leading dimension of the array B. LDB >= N+1.
WORK (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.
BIGNUM (input) DOUBLE PRECISION
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.
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