.TH  DLARRF 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " 
.SH NAME
DLARRF - initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ..
.SH SYNOPSIS
.TP 19
SUBROUTINE DLARRF(
N, D, L, LD, CLSTRT, CLEND,
W, WGAP, WERR,
SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA,
DPLUS, LPLUS, WORK, INFO )
.TP 19
.ti +4
INTEGER
CLSTRT, CLEND, INFO, N
.TP 19
.ti +4
DOUBLE
PRECISION CLGAPL, CLGAPR, PIVMIN, SIGMA, SPDIAM
.TP 19
.ti +4
DOUBLE
PRECISION D( * ), DPLUS( * ), L( * ), LD( * ),
LPLUS( * ), W( * ), WGAP( * ), WERR( * ), WORK( * )
.SH PURPOSE
Given the initial representation L D L^T and its cluster of close
eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ...
W( CLEND ), 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.
.br

.SH ARGUMENTS
.TP 8
N       (input) INTEGER
The order of the matrix (subblock, if the matrix splitted).
.TP 8
D       (input) DOUBLE PRECISION array, dimension (N)
The N diagonal elements of the diagonal matrix D.
.TP 8
L       (input) DOUBLE PRECISION array, dimension (N-1)
The (N-1) subdiagonal elements of the unit bidiagonal
matrix L.
.TP 8
LD      (input) DOUBLE PRECISION array, dimension (N-1)
The (N-1) elements L(i)*D(i).
.TP 8
CLSTRT  (input) INTEGER
The index of the first eigenvalue in the cluster.
.TP 8
CLEND   (input) INTEGER
The index of the last eigenvalue in the cluster.
.TP 8
W       (input) DOUBLE PRECISION array, dimension >=  (CLEND-CLSTRT+1)
The eigenvalue APPROXIMATIONS of L D L^T in ascending order.
W( CLSTRT ) through W( CLEND ) form the cluster of relatively
close eigenalues.
.TP 8
WGAP    (input/output) DOUBLE PRECISION array, dimension >=  (CLEND-CLSTRT+1)
The separation from the right neighbor eigenvalue in W.
.TP 8
WERR    (input) DOUBLE PRECISION array, dimension >=  (CLEND-CLSTRT+1)
WERR contain the semiwidth of the uncertainty
interval of the corresponding eigenvalue APPROXIMATION in W

SPDIAM (input) estimate of the spectral diameter obtained from the
Gerschgorin intervals

CLGAPL, CLGAPR (input) absolute gap on each end of the cluster.
Set by the calling routine to protect against shifts too close
to eigenvalues outside the cluster.
.TP 8
PIVMIN  (input) DOUBLE PRECISION
The minimum pivot allowed in the Sturm sequence.
.TP 8
SIGMA   (output) DOUBLE PRECISION
The shift used to form L(+) D(+) L(+)^T.
.TP 8
DPLUS   (output) DOUBLE PRECISION array, dimension (N)
The N diagonal elements of the diagonal matrix D(+).
.TP 8
LPLUS   (output) DOUBLE PRECISION array, dimension (N-1)
The first (N-1) elements of LPLUS contain the subdiagonal
elements of the unit bidiagonal matrix L(+).
.TP 8
WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)
Workspace.
.SH FURTHER DETAILS
Based on contributions by
.br
   Beresford Parlett, University of California, Berkeley, USA
   Jim Demmel, University of California, Berkeley, USA
.br
   Inderjit Dhillon, University of Texas, Austin, USA
.br
   Osni Marques, LBNL/NERSC, USA
.br
   Christof Voemel, University of California, Berkeley, USA

