DLARRF - the initial representation L D L^T and its clus
ter of close eigenvalues (in a relative measure), W(
IFIRST ), W( IFIRST+1 ), ..
SYNOPSIS
SUBROUTINE DLARRF( N, D, L, LD, LLD, IFIRST, ILAST, W,
DPLUS, LPLUS, WORK, IWORK, INFO )
INTEGER IFIRST, ILAST, INFO, N
INTEGER IWORK( * )
DOUBLE PRECISION D( * ), DPLUS( * ), L( * ),
LD( * ), LLD( * ), LPLUS( * ), W( * ),
WORK( * )
PURPOSE
Given the initial representation L D L^T and its cluster
of close eigenvalues (in a relative measure), W( IFIRST ),
W( IFIRST+1 ), ... W( ILAST ), DLARRF finds a new rela
tively robust representation L D L^T - SIGMA I = L(+) D(+)
L(+)^T such that at least one of the eigenvalues of L(+)
D(+) L(+)^T is relatively isolated.
ARGUMENTS
N (input) INTEGER
The order of the matrix.
D (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D.
L (input) DOUBLE PRECISION array, dimension (N-1)
The (n-1) subdiagonal elements of the unit bidiag
onal matrix L.
LD (input) DOUBLE PRECISION array, dimension (N-1)
The n-1 elements L(i)*D(i).
LLD (input) DOUBLE PRECISION array, dimension (N-1)
The n-1 elements L(i)*L(i)*D(i).
IFIRST (input) INTEGER
The index of the first eigenvalue in the cluster.
ILAST (input) INTEGER
The index of the last eigenvalue in the cluster.
W (input/output) DOUBLE PRECISION array, dimension
(N)
On input, the eigenvalues of L D L^T in ascending
order. W( IFIRST ) through W( ILAST ) form the
cluster of relatively close eigenalues. On
of the corresponding eigenvalues of L(+) D(+)
L(+)^T.
SIGMA (input) DOUBLE PRECISION
The shift used to form L(+) D(+) L(+)^T.
DPLUS (output) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix
D(+).
LPLUS (output) DOUBLE PRECISION array, dimension (N)
The first (n-1) elements of LPLUS contain the sub
diagonal elements of the unit bidiagonal matrix
L(+). LPLUS( N ) is set to SIGMA.
WORK (input) DOUBLE PRECISION array, dimension (???)
Workspace.
FURTHER DETAILS
Based on contributions by
Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA
Man(1) output converted with
man2html