subroutine dlaein (RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO)
DLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.
DLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.
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.
Parameters:
RIGHTV is LOGICAL
= .TRUE. : compute right eigenvector;
= .FALSE.: compute left eigenvector.
NOINIT
NOINIT is LOGICAL
= .TRUE. : no initial vector supplied in (VR,VI).
= .FALSE.: initial vector supplied in (VR,VI).
N
N is INTEGER
The order of the matrix H. N >= 0.
H
H is DOUBLE PRECISION array, dimension (LDH,N)
The upper Hessenberg matrix H.
LDH
LDH is INTEGER
The leading dimension of the array H. LDH >= max(1,N).
WR
WR is DOUBLE PRECISION
WI
WI is DOUBLE PRECISION
The real and imaginary parts of the eigenvalue of H whose
corresponding right or left eigenvector is to be computed.
VR
VR is DOUBLE PRECISION array, dimension (N)
VI
VI is DOUBLE PRECISION 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
B is DOUBLE PRECISION array, dimension (LDB,N)
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= N+1.
WORK
WORK is DOUBLE PRECISION array, dimension (N)
EPS3
EPS3 is DOUBLE PRECISION
A small machine-dependent value which is used to perturb
close eigenvalues, and to replace zero pivots.
SMLNUM
SMLNUM is DOUBLE PRECISION
A machine-dependent value close to the underflow threshold.
BIGNUM
BIGNUM is DOUBLE PRECISION
A machine-dependent value close to the overflow threshold.
INFO
INFO is 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.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 174 of file dlaein.f.
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