dlarrb (l)  Linux Man Pages
dlarrb: the relatively robust representation(RRR) L D L^T, DLARRB does "limited" bisection to refine the eigenvalues of L D L^T,
NAME
DLARRB  the relatively robust representation(RRR) L D L^T, DLARRB does "limited" bisection to refine the eigenvalues of L D L^T,SYNOPSIS
 SUBROUTINE DLARRB(
 N, D, LLD, IFIRST, ILAST, RTOL1, RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, PIVMIN, SPDIAM, TWIST, INFO )
 INTEGER IFIRST, ILAST, INFO, N, OFFSET, TWIST
 DOUBLE PRECISION PIVMIN, RTOL1, RTOL2, SPDIAM
 INTEGER IWORK( * )
 DOUBLE PRECISION D( * ), LLD( * ), W( * ), WERR( * ), WGAP( * ), WORK( * )
PURPOSE
Given the relatively robust representation(RRR) L D L^T, DLARRB does "limited" bisection to refine the eigenvalues of L D L^T, W( IFIRSTOFFSET ) through W( ILASTOFFSET ), 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 midpoints and semiwidths in the arrays W and WERR respectively.
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.
 LLD (input) DOUBLE PRECISION array, dimension (N1)
 The (N1) elements L(i)*L(i)*D(i).
 IFIRST (input) INTEGER
 The index of the first eigenvalue to be computed.
 ILAST (input) INTEGER
 The index of the last eigenvalue to be computed.
 RTOL1 (input) DOUBLE PRECISION
 RTOL2 (input) DOUBLE PRECISION Tolerance for the convergence of the bisection intervals. An interval [LEFT,RIGHT] has converged if RIGHTLEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(LEFT,RIGHT) ) where GAP is the (estimated) distance to the nearest eigenvalue.
 OFFSET (input) INTEGER
 Offset for the arrays W, WGAP and WERR, i.e., the IFIRSTOFFSET through ILASTOFFSET elements of these arrays are to be used.
 W (input/output) DOUBLE PRECISION array, dimension (N)
 On input, W( IFIRSTOFFSET ) through W( ILASTOFFSET ) are estimates of the eigenvalues of L D L^T indexed IFIRST throug ILAST. On output, these estimates are refined.
 WGAP (input/output) DOUBLE PRECISION array, dimension (N1)
 On input, the (estimated) gaps between consecutive eigenvalues of L D L^T, i.e., WGAP(IOFFSET) is the gap between eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST then WGAP(IFIRSTOFFSET) must be set to ZERO. On output, these gaps are refined.
 WERR (input/output) DOUBLE PRECISION array, dimension (N)
 On input, WERR( IFIRSTOFFSET ) through WERR( ILASTOFFSET ) are the errors in the estimates of the corresponding elements in W. On output, these errors are refined.
 WORK (workspace) DOUBLE PRECISION array, dimension (2*N)
 Workspace.
 IWORK (workspace) INTEGER array, dimension (2*N)
 Workspace.
 PIVMIN (input) DOUBLE PRECISION
 The minimum pivot in the Sturm sequence.
 SPDIAM (input) DOUBLE PRECISION
 The spectral diameter of the matrix.
 TWIST (input) 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 (output) INTEGER
 Error flag.
FURTHER DETAILS
Based on contributions byBeresford 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