SLARRJ(1) LAPACK auxiliary routine (version 3.2) SLARRJ(1)NAME
SLARRJ - the initial eigenvalue approximations of T, SLARRJ does bisec‐
tion to refine the eigenvalues of T,
SYNOPSIS
SUBROUTINE SLARRJ( N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR,
WORK, IWORK, PIVMIN, SPDIAM, INFO )
INTEGER IFIRST, ILAST, INFO, N, OFFSET
REAL PIVMIN, RTOL, SPDIAM
INTEGER IWORK( * )
REAL D( * ), E2( * ), W( * ), WERR( * ), WORK( * )
PURPOSE
Given the initial eigenvalue approximations of T, SLARRJ does bisec‐
tion to refine the eigenvalues of T, W( IFIRST-OFFSET ) through W(
ILAST-OFFSET ), to more accuracy. Initial guesses for these eigenvalues
are input in W, the corresponding estimate of the error in these
guesses in WERR. During bisection, intervals [left, right] are main‐
tained 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 T.
E2 (input) REAL array, dimension (N-1)
The Squares of the (N-1) subdiagonal elements of T.
IFIRST (input) INTEGER
The index of the first eigenvalue to be computed.
ILAST (input) INTEGER
The index of the last eigenvalue to be computed.
RTOL (input) REAL
Tolerance for the convergence of the bisection intervals. An
interval [LEFT,RIGHT] has converged if RIGHT-
LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|).
OFFSET (input) INTEGER
Offset for the arrays W and WERR, i.e., the IFIRST-OFFSET
through ILAST-OFFSET elements of these arrays are to be used.
W (input/output) REAL array, dimension (N)
On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are
estimates of the eigenvalues of L D L^T indexed IFIRST through
ILAST. On output, these estimates are refined.
WERR (input/output) REAL array, dimension (N)
On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET )
are the errors in the estimates of the corresponding elements
in W. On output, these errors are refined.
WORK (workspace) REAL array, dimension (2*N)
Workspace.
IWORK (workspace) INTEGER array, dimension (2*N)
Workspace.
PIVMIN (input) DOUBLE PRECISION
The minimum pivot in the Sturm sequence for T.
SPDIAM (input) DOUBLE PRECISION
The spectral diameter of T.
INFO (output) INTEGER
Error flag.
FURTHER DETAILS
Based on contributions by
Beresford Parlett, University of California, Berkeley, USA
Jim Demmel, University of California, Berkeley, USA
Inderjit Dhillon, University of Texas, Austin, USA
Osni Marques, LBNL/NERSC, USA
Christof Voemel, University of California, Berkeley, USA
LAPACK auxiliary routine (versioNovember 2008 SLARRJ(1)
