dlarrb(l) [redhat man page]
DLARRB(l) ) DLARRB(l) NAME
DLARRB - the relatively robust representation(RRR) L D L^T, DLARRB does ``limited'' bisection to locate the eigenvalues of L D L^T, SYNOPSIS
SUBROUTINE DLARRB( N, D, L, LD, LLD, IFIRST, ILAST, SIGMA, RELTOL, W, WGAP, WERR, WORK, IWORK, INFO ) INTEGER IFIRST, ILAST, INFO, N DOUBLE PRECISION RELTOL, SIGMA INTEGER IWORK( * ) DOUBLE PRECISION D( * ), L( * ), LD( * ), LLD( * ), W( * ), WERR( * ), WGAP( * ), WORK( * ) PURPOSE
Given the relatively robust representation(RRR) L D L^T, DLARRB does ``limited'' bisection to locate the eigenvalues of L D L^T, W( IFIRST ) thru' W( ILAST ), to more accuracy. Intervals [left, right] are maintained 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) 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. SIGMA (input) DOUBLE PRECISION The shift used to form L D L^T (see DLARRF). RELTOL (input) DOUBLE PRECISION The relative tolerance. W (input/output) DOUBLE PRECISION array, dimension (N) On input, W( IFIRST ) thru' W( ILAST ) are estimates of the corresponding eigenvalues of L D L^T. On output, these estimates are ``refined''. WGAP (input/output) DOUBLE PRECISION array, dimension (N) The gaps between the eigenvalues of L D L^T. Very small gaps are changed on output. WERR (input/output) DOUBLE PRECISION array, dimension (N) On input, WERR( IFIRST ) thru' WERR( ILAST ) are the errors in the estimates W( IFIRST ) thru' W( ILAST ). On output, these are the ``refined'' errors. WORK (input) DOUBLE PRECISION array, dimension (???) Workspace. IWORK (input) INTEGER array, dimension (2*N) Workspace. INFO (output) INTEGER Error flag. FURTHER DETAILS
Based on contributions by Inderjit Dhillon, IBM Almaden, USA Osni Marques, LBNL/NERSC, USA LAPACK version 3.0 15 June 2000 DLARRB(l)
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dlarrb.f(3) LAPACK dlarrb.f(3) NAME
dlarrb.f - SYNOPSIS
Functions/Subroutines subroutine dlarrb (N, D, LLD, IFIRST, ILAST, RTOL1, RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, PIVMIN, SPDIAM, TWIST, INFO) DLARRB Function/Subroutine Documentation subroutine dlarrb (integerN, double precision, dimension( * )D, double precision, dimension( * )LLD, integerIFIRST, integerILAST, double precisionRTOL1, double precisionRTOL2, integerOFFSET, double precision, dimension( * )W, double precision, dimension( * )WGAP, double precision, dimension( * )WERR, double precision, dimension( * )WORK, integer, dimension( * )IWORK, double precisionPIVMIN, double precisionSPDIAM, integerTWIST, integerINFO) DLARRB 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( 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 DOUBLE PRECISION array, dimension (N) The N diagonal elements of the diagonal matrix D. LLD LLD is DOUBLE PRECISION 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 DOUBLE PRECISION RTOL2 RTOL2 is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (2*N) Workspace. IWORK IWORK is INTEGER array, dimension (2*N) Workspace. PIVMIN PIVMIN is DOUBLE PRECISION The minimum pivot in the Sturm sequence. SPDIAM SPDIAM is DOUBLE PRECISION 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: November 2011 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 dlarrb.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 dlarrb.f(3)