Slarrb.f -
subroutine slarrb (N, D, LLD, IFIRST, ILAST, RTOL1, RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, PIVMIN, SPDIAM, TWIST, INFO)
SLARRB provides limited bisection to locate eigenvalues for more accuracy.
SLARRB provides limited bisection to locate eigenvalues for more accuracy.
Purpose:
Given the relatively robust representation(RRR) L D L^T, SLARRB does "limited" bisection to refine the eigenvalues of L D L^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 and their gaps are input in WERR and WGAP, respectively. During bisection, intervals [left, right] are maintained by storing their mid-points and semi-widths in the arrays W and WERR respectively.
Parameters:
N
N is INTEGER
The order of the matrix.
D
D is REAL array, dimension (N)
The N diagonal elements of the diagonal matrix D.
LLD
LLD is REAL array, dimension (N-1)
The (N-1) elements L(i)*L(i)*D(i).
IFIRST
IFIRST is INTEGER
The index of the first eigenvalue to be computed.
ILAST
ILAST is INTEGER
The index of the last eigenvalue to be computed.
RTOL1
RTOL1 is REAL
RTOL2
RTOL2 is REAL
Tolerance for the convergence of the bisection intervals.
An interval [LEFT,RIGHT] has converged if
RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )
where GAP is the (estimated) distance to the nearest
eigenvalue.
OFFSET
OFFSET is INTEGER
Offset for the arrays W, WGAP and WERR, i.e., the IFIRST-OFFSET
through ILAST-OFFSET elements of these arrays are to be used.
W
W is 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 throug
ILAST.
On output, these estimates are refined.
WGAP
WGAP is REAL array, dimension (N-1)
On input, the (estimated) gaps between consecutive
eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between
eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST
then WGAP(IFIRST-OFFSET) must be set to ZERO.
On output, these gaps are refined.
WERR
WERR is 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
WORK is REAL array, dimension (2*N)
Workspace.
IWORK
IWORK is INTEGER array, dimension (2*N)
Workspace.
PIVMIN
PIVMIN is REAL
The minimum pivot in the Sturm sequence.
SPDIAM
SPDIAM is REAL
The spectral diameter of the matrix.
TWIST
TWIST is INTEGER
The twist index for the twisted factorization that is used
for the negcount.
TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T
TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T
TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r)
INFO
INFO is INTEGER
Error flag.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Contributors:
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
Definition at line 195 of file slarrb.f.
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