Flashnux

GNU/Linux man pages

Livre :
Expressions régulières,
Syntaxe et mise en oeuvre :

ISBN : 978-2-7460-9712-4
EAN : 9782746097124
(Editions ENI)

GNU/Linux

CentOS 4.8

 i386

dlarrb(l)
DLARRB

DLARRB

NAME
SYNOPSIS
PURPOSE
ARGUMENTS
FURTHER DETAILS

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 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 bidiagonal 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 estimates 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

dlarrb(l)