SLARRB(l) ) SLARRB(l)NAME
SLARRB - the relatively robust representation(RRR) L D L^T, SLARRB does
``limited'' bisection to locate the eigenvalues of L D L^T,
SYNOPSIS
SUBROUTINE SLARRB( N, D, L, LD, LLD, IFIRST, ILAST, SIGMA, RELTOL, W,
WGAP, WERR, WORK, IWORK, INFO )
INTEGER IFIRST, ILAST, INFO, N
REAL RELTOL, SIGMA
INTEGER IWORK( * )
REAL D( * ), L( * ), LD( * ), LLD( * ), W( * ), WERR( *
), WGAP( * ), WORK( * )
PURPOSE
Given the relatively robust representation(RRR) L D L^T, SLARRB does
``limited'' bisection to locate the eigenvalues of L D L^T, W( IFIRST )
thru' W( ILAST ), to more accuracy. Intervals [left, right] are main‐
tained by storing their mid-points and semi-widths in the arrays W and
WERR respectively.
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.
SIGMA (input) REAL
The shift used to form L D L^T (see SLARRF).
RELTOL (input) REAL
The relative tolerance.
W (input/output) REAL array, dimension (N)
On input, W( IFIRST ) thru' W( ILAST ) are estimates of the
corresponding eigenvalues of L D L^T. On output, these esti‐
mates are ``refined''.
WGAP (input/output) REAL array, dimension (N)
The gaps between the eigenvalues of L D L^T. Very small gaps
are changed on output.
WERR (input/output) REAL array, dimension (N)
On input, WERR( IFIRST ) thru' WERR( ILAST ) are the errors in
the estimates W( IFIRST ) thru' W( ILAST ). On output, these
are the ``refined'' errors.
WORK (input) REAL array, dimension (???)
Workspace.
IWORK (input) INTEGER array, dimension (2*N)
Workspace.
INFO (output) INTEGER
Error flag.
FURTHER DETAILS
Based on contributions by
Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA
LAPACK version 3.0 15 June 2000 SLARRB(l)
