man slarrf (Fonctions bibliothèques) - the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( IFIRST ), W( IFIRST+1 ), ..

NAME

SLARRF - the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( IFIRST ), W( IFIRST+1 ), ..

SYNOPSIS

SUBROUTINE SLARRF(
N, D, L, LD, LLD, IFIRST, ILAST, W, DPLUS, LPLUS, WORK, IWORK, INFO )
INTEGER IFIRST, ILAST, INFO, N
INTEGER IWORK( * )
REAL D( * ), DPLUS( * ), L( * ), LD( * ), LLD( * ), LPLUS( * ), W( * ), WORK( * )

PURPOSE

Given the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( IFIRST ), W( IFIRST+1 ), ... W( ILAST ), SLARRF finds a new relatively robust representation L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the eigenvalues of L(+) D(+) L(+)^T is relatively isolated.

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.
W (input/output) REAL array, dimension (N)
On input, the eigenvalues of L D L^T in ascending order. W( IFIRST ) through W( ILAST ) form the cluster of relatively close eigenalues. On output, W( IFIRST ) thru' W( ILAST ) are estimates of the corresponding eigenvalues of L(+) D(+) L(+)^T.
SIGMA (input) REAL
The shift used to form L(+) D(+) L(+)^T.
DPLUS (output) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D(+).
LPLUS (output) REAL array, dimension (N)
The first (n-1) elements of LPLUS contain the subdiagonal elements of the unit bidiagonal matrix L(+). LPLUS( N ) is set to SIGMA.
WORK (input) REAL array, dimension (???)
Workspace.

FURTHER DETAILS

Based on contributions by

Inderjit Dhillon, IBM Almaden, USA

Osni Marques, LBNL/NERSC, USA