dlarrf(l) [redhat man page]
DLARRF(l) ) DLARRF(l) NAME
DLARRF - the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( IFIRST ), W( IFIRST+1 ), .. SYNOPSIS
SUBROUTINE DLARRF( N, D, L, LD, LLD, IFIRST, ILAST, W, DPLUS, LPLUS, WORK, IWORK, INFO ) INTEGER IFIRST, ILAST, INFO, N INTEGER IWORK( * ) DOUBLE PRECISION D( * ), DPLUS( * ), L( * ), LD( * ), LLD( * ), LPLUS( * ), W( * ), WORK( * ) PURPOSE
Given the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( IFIRST ), W( IFIRST+1 ), ... W( ILAST ), 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. 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. W (input/output) DOUBLE PRECISION array, dimension (N) On input, the eigenvalues of L D L^T in ascending order. W( IFIRST ) through W( ILAST ) form the cluster of relatively close eige- nalues. On output, W( IFIRST ) thru' W( ILAST ) are estimates of the corresponding eigenvalues of L(+) D(+) L(+)^T. SIGMA (input) DOUBLE PRECISION The shift used to form L(+) D(+) L(+)^T. DPLUS (output) DOUBLE PRECISION array, dimension (N) The n diagonal elements of the diagonal matrix D(+). LPLUS (output) DOUBLE PRECISION array, dimension (N) The first (n-1) elements of LPLUS contain the subdiagonal elements of the unit bidiagonal matrix L(+). LPLUS( N ) is set to SIGMA. WORK (input) DOUBLE PRECISION array, dimension (???) Workspace. FURTHER DETAILS
Based on contributions by Inderjit Dhillon, IBM Almaden, USA Osni Marques, LBNL/NERSC, USA LAPACK version 3.0 15 June 2000 DLARRF(l)
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dlarrj.f(3) LAPACK dlarrj.f(3) NAME
dlarrj.f - SYNOPSIS
Functions/Subroutines subroutine dlarrj (N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR, WORK, IWORK, PIVMIN, SPDIAM, INFO) DLARRJ Function/Subroutine Documentation subroutine dlarrj (integerN, double precision, dimension( * )D, double precision, dimension( * )E2, integerIFIRST, integerILAST, double precisionRTOL, integerOFFSET, double precision, dimension( * )W, double precision, dimension( * )WERR, double precision, dimension( * )WORK, integer, dimension( * )IWORK, double precisionPIVMIN, double precisionSPDIAM, integerINFO) DLARRJ Purpose: Given the initial eigenvalue approximations of T, DLARRJ does bisection 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 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 T. E2 E2 is DOUBLE PRECISION array, dimension (N-1) The Squares of the (N-1) subdiagonal elements of T. 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. RTOL RTOL is DOUBLE PRECISION Tolerance for the convergence of the bisection intervals. An interval [LEFT,RIGHT] has converged if RIGHT-LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|). OFFSET OFFSET is 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 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 through ILAST. On output, these estimates 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 for T. SPDIAM SPDIAM is DOUBLE PRECISION The spectral diameter of T. 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 167 of file dlarrj.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 dlarrj.f(3)