SLARRF(l) ) SLARRF(l)NAME
SLARRF - the initial representation L D L^T and its cluster of close
eigenvalues (in a relative measure), W( IFIRST ), W( IFIRST+1 ), ..
SYNOPSIS
SUBROUTINE SLARRF( N, D, L, LD, LLD, IFIRST, ILAST, W, DPLUS, LPLUS,
WORK, IWORK, INFO )
INTEGER IFIRST, ILAST, INFO, N
INTEGER IWORK( * )
REAL D( * ), DPLUS( * ), L( * ), LD( * ), LLD( * ),
LPLUS( * ), W( * ), WORK( * )
PURPOSE
Given the initial representation L D L^T and its cluster of close ei‐
genvalues (in a relative measure), W( IFIRST ), W( IFIRST+1 ), ... W(
ILAST ), SLARRF finds a new relatively 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) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D.
L (input) REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the unit bidiagonal matrix L.
LD (input) REAL array, dimension (N-1)
The n-1 elements L(i)*D(i).
LLD (input) REAL 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) REAL 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 output, W( IFIRST ) thru' W( ILAST ) are
estimates of the corresponding eigenvalues of L(+) D(+) L(+)^T.
SIGMA (input) REAL
The shift used to form L(+) D(+) L(+)^T.
DPLUS (output) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D(+).
LPLUS (output) REAL array, dimension (N)
The first (n-1) elements of LPLUS contain the subdiagonal ele‐
ments of the unit bidiagonal matrix L(+). LPLUS( N ) is set to
SIGMA.
WORK (input) REAL array, dimension (???)
Workspace.
FURTHER DETAILS
Based on contributions by
Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA
LAPACK version 3.0 15 June 2000 SLARRF(l)
