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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)
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 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.
N
D
L
LD
CLSTRT
CLEND
W
WGAP
WERR
SPDIAM
CLGAPL
CLGAPR
PIVMIN
SIGMA
DPLUS
LPLUS
WORK
INFO
Author:
N is INTEGER The order of the matrix (subblock, if the matrix splitted).
D is REAL array, dimension (N) The N diagonal elements of the diagonal matrix D.
L is REAL array, dimension (N-1) The (N-1) subdiagonal elements of the unit bidiagonal matrix L.
LD is REAL array, dimension (N-1) The (N-1) elements L(i)*D(i).
CLSTRT is INTEGER The index of the first eigenvalue in the cluster.
CLEND is INTEGER The index of the last eigenvalue in the cluster.
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 is REAL array, dimension dimension is >= (CLEND-CLSTRT+1) The separation from the right neighbor eigenvalue in W.
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 is REAL estimate of the spectral diameter obtained from the Gerschgorin intervals
CLGAPL is REAL
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 is REAL The minimum pivot allowed in the Sturm sequence.
SIGMA is REAL The shift used to form L(+) D(+) L(+)^T.
DPLUS is REAL array, dimension (N) The N diagonal elements of the diagonal matrix D(+).
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 is REAL array, dimension (2*N) Workspace.
INFO is INTEGER Signals processing OK (=0) or failure (=1)
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
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
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
Author¶
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