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dlarrf

NAME

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

SYNOPSIS

SUBROUTINE DLARRF(

N, D, L, LD, LLD, IFIRST, ILAST, W, DPLUS, LPLUS, WORK, IWORK, INFO )

    

INTEGER IFIRST, ILAST, INFO, N

    

INTEGER IWORK( * )

    

DOUBLE PRECISION 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 ), DLARRF 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) 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.

W (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION

The shift used to form L(+) D(+) L(+)^T.

DPLUS (output) DOUBLE PRECISION array, dimension (N)

The n diagonal elements of the diagonal matrix D(+).

LPLUS (output) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (???)

Workspace.

FURTHER DETAILS

Based on contributions by

   Inderjit Dhillon, IBM Almaden, USA

   Osni Marques, LBNL/NERSC, USA