DLARRB - the relatively robust representation(RRR) L D
L^T, DLARRB does ``limited'' bisection to locate the
eigenvalues of L D L^T,
SYNOPSIS
SUBROUTINE DLARRB( N, D, L, LD, LLD, IFIRST, ILAST, SIGMA,
RELTOL, W, WGAP, WERR, WORK, IWORK,
INFO )
INTEGER IFIRST, ILAST, INFO, N
DOUBLE PRECISION RELTOL, SIGMA
INTEGER IWORK( * )
DOUBLE PRECISION D( * ), L( * ), LD( * ), LLD(
* ), W( * ), WERR( * ), WGAP( * ),
WORK( * )
PURPOSE
Given the relatively robust representation(RRR) L D L^T,
DLARRB 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) 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 bidiago
nal 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.
SIGMA (input) DOUBLE PRECISION
The shift used to form L D L^T (see DLARRF).
The relative tolerance.
W (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension
(N)
The gaps between the eigenvalues of L D L^T. Very
small gaps are changed on output.
WERR (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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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