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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)
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 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.
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 DOUBLE PRECISION array, dimension (N) The N diagonal elements of the diagonal matrix D.
L is DOUBLE PRECISION array, dimension (N-1) The (N-1) subdiagonal elements of the unit bidiagonal matrix L.
LD is DOUBLE PRECISION 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 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 is DOUBLE PRECISION array, dimension dimension is >= (CLEND-CLSTRT+1) The separation from the right neighbor eigenvalue in W.
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 is DOUBLE PRECISION estimate of the spectral diameter obtained from the Gerschgorin intervals
CLGAPL is DOUBLE PRECISION
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 is DOUBLE PRECISION The minimum pivot allowed in the Sturm sequence.
SIGMA is DOUBLE PRECISION The shift used to form L(+) D(+) L(+)^T.
DPLUS is DOUBLE PRECISION array, dimension (N) The N diagonal elements of the diagonal matrix D(+).
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 is DOUBLE PRECISION 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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