dlarrf-f(3)

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 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

 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 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.

Author

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