# dlarrf.f(3) [centos man page]

dlarrf.f(3) LAPACK dlarrf.f(3)NAME

dlarrf.f-SYNOPSIS

Functions/Subroutines subroutine dlarrf (N, D, L, LD, CLSTRT, CLEND, W, WGAP, WERR, SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA, DPLUS, LPLUS, WORK, INFO) DLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.Function/Subroutine Documentation subroutine dlarrf (integerN, double precision, dimension( * )D, double precision, dimension( * )L, double precision, dimension( * )LD, integerCLSTRT, integerCLEND, double precision, dimension( * )W, double precision, dimension( * )WGAP, double precision, dimension( * )WERR, double precisionSPDIAM, double precisionCLGAPL, double precisionCLGAPR, double precisionPIVMIN, double precisionSIGMA, double precision, dimension( * )DPLUS, double precision, dimension( * )LPLUS, double precision, dimension( * )WORK, integerINFO) DLARRF 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 ), 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. Parameters: N N is INTEGER The order of the matrix (subblock, if the matrix splitted). D D is DOUBLE PRECISION array, dimension (N) The N diagonal elements of the diagonal matrix D. L L is DOUBLE PRECISION array, dimension (N-1) The (N-1) subdiagonal elements of the unit bidiagonal matrix L. LD LD is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension dimension is >= (CLEND-CLSTRT+1) The separation from the right neighbor eigenvalue in W. WERR WERR is DOUBLE PRECISION 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 DOUBLE PRECISION estimate of the spectral diameter obtained from the Gerschgorin intervals CLGAPL CLGAPL is DOUBLE PRECISION CLGAPR CLGAPR is DOUBLE PRECISION 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 DOUBLE PRECISION The minimum pivot allowed in the Sturm sequence. SIGMA SIGMA is DOUBLE PRECISION The shift used to form L(+) D(+) L(+)^T. DPLUS DPLUS is DOUBLE PRECISION array, dimension (N) The N diagonal elements of the diagonal matrix D(+). LPLUS LPLUS is DOUBLE PRECISION array, dimension (N-1) The first (N-1) elements of LPLUS contain the subdiagonal elements of the unit bidiagonal matrix L(+). WORK WORK is DOUBLE PRECISION 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 dlarrf.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 dlarrf.f(3)