slarrf (3)  Linux Manuals
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).
DD is REAL array, dimension (N) The N diagonal elements of the diagonal matrix D.
LL is REAL array, dimension (N1) The (N1) subdiagonal elements of the unit bidiagonal matrix L.
LDLD is REAL 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 REAL 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 REAL array, dimension dimension is >= (CLENDCLSTRT+1) The separation from the right neighbor eigenvalue in W.
WERRWERR is REAL array, dimension dimension is >= (CLENDCLSTRT+1) WERR contain the semiwidth of the uncertainty interval of the corresponding eigenvalue APPROXIMATION in W
SPDIAMSPDIAM is REAL estimate of the spectral diameter obtained from the Gerschgorin intervals
CLGAPLCLGAPL is REAL
CLGAPRCLGAPR 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.
PIVMINPIVMIN is REAL The minimum pivot allowed in the Sturm sequence.
SIGMASIGMA is REAL The shift used to form L(+) D(+) L(+)^T.
DPLUSDPLUS is REAL array, dimension (N) The N diagonal elements of the diagonal matrix D(+).
LPLUSLPLUS is REAL array, dimension (N1) The first (N1) elements of LPLUS contain the subdiagonal elements of the unit bidiagonal matrix L(+).
WORKWORK is REAL 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 slarrf.f.
Author
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