SRC/dlaein.f(3) | Library Functions Manual | SRC/dlaein.f(3) |
NAME
SRC/dlaein.f
SYNOPSIS
Functions/Subroutines
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.
Function/Subroutine Documentation
subroutine dlaein (logical rightv, logical noinit, integer n, double precision, dimension( ldh, * ) h, integer ldh, double precision wr, double precision wi, double precision, dimension( * ) vr, double precision, dimension( * ) vi, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, double precision eps3, double precision smlnum, double precision bignum, integer info)
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
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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 170 of file dlaein.f.
Author
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