Query: slarrb
OS: redhat
Section: l
Format: Original Unix Latex Style Formatted with HTML and a Horizontal Scroll Bar
SLARRB(l) ) SLARRB(l)NAMESLARRB - the relatively robust representation(RRR) L D L^T, SLARRB does ``limited'' bisection to locate the eigenvalues of L D L^T,SYNOPSISSUBROUTINE SLARRB( N, D, L, LD, LLD, IFIRST, ILAST, SIGMA, RELTOL, W, WGAP, WERR, WORK, IWORK, INFO ) INTEGER IFIRST, ILAST, INFO, N REAL RELTOL, SIGMA INTEGER IWORK( * ) REAL D( * ), L( * ), LD( * ), LLD( * ), W( * ), WERR( * ), WGAP( * ), WORK( * )PURPOSEGiven the relatively robust representation(RRR) L D L^T, SLARRB 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.ARGUMENTSN (input) INTEGER The order of the matrix. D (input) REAL array, dimension (N) The n diagonal elements of the diagonal matrix D. L (input) REAL array, dimension (N-1) The n-1 subdiagonal elements of the unit bidiagonal matrix L. LD (input) REAL array, dimension (N-1) The n-1 elements L(i)*D(i). LLD (input) REAL 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) REAL The shift used to form L D L^T (see SLARRF). RELTOL (input) REAL The relative tolerance. W (input/output) REAL 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) REAL array, dimension (N) The gaps between the eigenvalues of L D L^T. Very small gaps are changed on output. WERR (input/output) REAL 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) REAL array, dimension (???) Workspace. IWORK (input) INTEGER array, dimension (2*N) Workspace. INFO (output) INTEGER Error flag.FURTHER DETAILSBased on contributions by Inderjit Dhillon, IBM Almaden, USA Osni Marques, LBNL/NERSC, USA LAPACK version 3.0 15 June 2000 SLARRB(l)
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