# slarrf(3) [centos man page]

slarrf.f(3) LAPACK slarrf.f(3)NAME

slarrf.f-SYNOPSIS

Functions/Subroutines subroutine slarrf (N, D, L, LD, CLSTRT, CLEND, W, WGAP, WERR, SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA, DPLUS, LPLUS, WORK, INFO) SLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.Function/Subroutine Documentation subroutine slarrf (integerN, real, dimension( * )D, real, dimension( * )L, real, dimension( * )LD, integerCLSTRT, integerCLEND, real, dimension( * )W, real, dimension( * )WGAP, real, dimension( * )WERR, realSPDIAM, realCLGAPL, realCLGAPR, realPIVMIN, realSIGMA, real, dimension( * )DPLUS, real, dimension( * )LPLUS, real, dimension( * )WORK, integerINFO) SLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated. Purpose: Given the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ... W( CLEND ), SLARRF 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. Parameters: N N is INTEGER The order of the matrix (subblock, if the matrix splitted). D D is REAL array, dimension (N) The N diagonal elements of the diagonal matrix D. L L is REAL array, dimension (N-1) The (N-1) subdiagonal elements of the unit bidiagonal matrix L. LD LD is REAL array, dimension (N-1) The (N-1) elements L(i)*D(i). CLSTRT CLSTRT is INTEGER The index of the first eigenvalue in the cluster. CLEND CLEND is INTEGER The index of the last eigenvalue in the cluster. W W is REAL array, dimension dimension is >= (CLEND-CLSTRT+1) The eigenvalue APPROXIMATIONS of L D L^T in ascending order. W( CLSTRT ) through W( CLEND ) form the cluster of relatively close eigenalues. WGAP WGAP is REAL array, dimension dimension is >= (CLEND-CLSTRT+1) The separation from the right neighbor eigenvalue in W. WERR WERR is REAL array, dimension dimension is >= (CLEND-CLSTRT+1) WERR contain the semiwidth of the uncertainty interval of the corresponding eigenvalue APPROXIMATION in W SPDIAM SPDIAM is REAL estimate of the spectral diameter obtained from the Gerschgorin intervals CLGAPL CLGAPL is REAL CLGAPR CLGAPR is REAL absolute gap on each end of the cluster. Set by the calling routine to protect against shifts too close to eigenvalues outside the cluster. PIVMIN PIVMIN is REAL The minimum pivot allowed in the Sturm sequence. SIGMA SIGMA is REAL The shift used to form L(+) D(+) L(+)^T. DPLUS DPLUS is REAL array, dimension (N) The N diagonal elements of the diagonal matrix D(+). LPLUS LPLUS is REAL array, dimension (N-1) The first (N-1) elements of LPLUS contain the subdiagonal elements of the unit bidiagonal matrix L(+). WORK WORK is REAL array, dimension (2*N) Workspace. INFO INFO is INTEGER Signals processing OK (=0) or failure (=1) 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 191 of file slarrf.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 slarrf.f(3)