DLARRF (3)  Linux Manuals
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).
DD is DOUBLE PRECISION array, dimension (N) The N diagonal elements of the diagonal matrix D.
LL is DOUBLE PRECISION array, dimension (N1) The (N1) subdiagonal elements of the unit bidiagonal matrix L.
LDLD is DOUBLE PRECISION array, dimension (N1) The (N1) elements L(i)*D(i).
CLSTRTCLSTRT is INTEGER The index of the first eigenvalue in the cluster.
CLENDCLEND is INTEGER The index of the last eigenvalue in the cluster.
WW is DOUBLE PRECISION array, dimension dimension is >= (CLENDCLSTRT+1) The eigenvalue APPROXIMATIONS of L D L^T in ascending order. W( CLSTRT ) through W( CLEND ) form the cluster of relatively close eigenalues.
WGAPWGAP is DOUBLE PRECISION array, dimension dimension is >= (CLENDCLSTRT+1) The separation from the right neighbor eigenvalue in W.
WERRWERR is DOUBLE PRECISION array, dimension dimension is >= (CLENDCLSTRT+1) WERR contain the semiwidth of the uncertainty interval of the corresponding eigenvalue APPROXIMATION in W
SPDIAMSPDIAM is DOUBLE PRECISION estimate of the spectral diameter obtained from the Gerschgorin intervals
CLGAPLCLGAPL is DOUBLE PRECISION
CLGAPRCLGAPR 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.
PIVMINPIVMIN is DOUBLE PRECISION The minimum pivot allowed in the Sturm sequence.
SIGMASIGMA is DOUBLE PRECISION The shift used to form L(+) D(+) L(+)^T.
DPLUSDPLUS is DOUBLE PRECISION array, dimension (N) The N diagonal elements of the diagonal matrix D(+).
LPLUSLPLUS is DOUBLE PRECISION array, dimension (N1) The first (N1) elements of LPLUS contain the subdiagonal elements of the unit bidiagonal matrix L(+).
WORKWORK is DOUBLE PRECISION array, dimension (2*N) Workspace.
INFOINFO 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.
Author
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