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 eigenval
ues of L D L^T, W( IFIRST ) thru' W( ILAST ), to more
accuracy. Intervals [left, right] are maintained by stor
ing 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 bidiago
nal 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).
The relative tolerance.
W (input/output) REAL array, dimension (N)
On input, W( IFIRST ) thru' W( ILAST ) are esti
mates of the corresponding eigenvalues of L D L^T.
On output, these estimates 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
Man(1) output converted with
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