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slarrb

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 maintained 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 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