dlarrb(3)

NAME

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 eigenvalues of L

D L^T, W( IFIRST ) thru' W( ILAST ), to more accuracy. Intervals

[left, right] are maintained by storing their mid-points and se

mi-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).

RELTOL (input) DOUBLE PRECISION

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

LAPACK version 3.0 15 June 2000

DLARRB(3)