DLARRB (3)  Linux Man Pages
NAME
dlarrb.f 
SYNOPSIS
Functions/Subroutines
subroutine dlarrb (N, D, LLD, IFIRST, ILAST, RTOL1, RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, PIVMIN, SPDIAM, TWIST, INFO)
DLARRB provides limited bisection to locate eigenvalues for more accuracy.
Function/Subroutine Documentation
subroutine dlarrb (integerN, double precision, dimension( * )D, double precision, dimension( * )LLD, integerIFIRST, integerILAST, double precisionRTOL1, double precisionRTOL2, integerOFFSET, double precision, dimension( * )W, double precision, dimension( * )WGAP, double precision, dimension( * )WERR, double precision, dimension( * )WORK, integer, dimension( * )IWORK, double precisionPIVMIN, double precisionSPDIAM, integerTWIST, integerINFO)
DLARRB provides limited bisection to locate eigenvalues for more accuracy.
Purpose:

Given the relatively robust representation(RRR) L D L^T, DLARRB does "limited" bisection to refine the eigenvalues of L D L^T, W( IFIRSTOFFSET ) through W( ILASTOFFSET ), to more accuracy. Initial guesses for these eigenvalues are input in W, the corresponding estimate of the error in these guesses and their gaps are input in WERR and WGAP, respectively. During bisection, intervals [left, right] are maintained by storing their midpoints and semiwidths in the arrays W and WERR respectively.
Parameters:

N
N is INTEGER The order of the matrix.
DD is DOUBLE PRECISION array, dimension (N) The N diagonal elements of the diagonal matrix D.
LLDLLD is DOUBLE PRECISION array, dimension (N1) The (N1) elements L(i)*L(i)*D(i).
IFIRSTIFIRST is INTEGER The index of the first eigenvalue to be computed.
ILASTILAST is INTEGER The index of the last eigenvalue to be computed.
RTOL1RTOL1 is DOUBLE PRECISION
RTOL2RTOL2 is DOUBLE PRECISION Tolerance for the convergence of the bisection intervals. An interval [LEFT,RIGHT] has converged if RIGHTLEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(LEFT,RIGHT) ) where GAP is the (estimated) distance to the nearest eigenvalue.
OFFSETOFFSET is INTEGER Offset for the arrays W, WGAP and WERR, i.e., the IFIRSTOFFSET through ILASTOFFSET elements of these arrays are to be used.
WW is DOUBLE PRECISION array, dimension (N) On input, W( IFIRSTOFFSET ) through W( ILASTOFFSET ) are estimates of the eigenvalues of L D L^T indexed IFIRST throug ILAST. On output, these estimates are refined.
WGAPWGAP is DOUBLE PRECISION array, dimension (N1) On input, the (estimated) gaps between consecutive eigenvalues of L D L^T, i.e., WGAP(IOFFSET) is the gap between eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST then WGAP(IFIRSTOFFSET) must be set to ZERO. On output, these gaps are refined.
WERRWERR is DOUBLE PRECISION array, dimension (N) On input, WERR( IFIRSTOFFSET ) through WERR( ILASTOFFSET ) are the errors in the estimates of the corresponding elements in W. On output, these errors are refined.
WORKWORK is DOUBLE PRECISION array, dimension (2*N) Workspace.
IWORKIWORK is INTEGER array, dimension (2*N) Workspace.
PIVMINPIVMIN is DOUBLE PRECISION The minimum pivot in the Sturm sequence.
SPDIAMSPDIAM is DOUBLE PRECISION The spectral diameter of the matrix.
TWISTTWIST is INTEGER The twist index for the twisted factorization that is used for the negcount. TWIST = N: Compute negcount from L D L^T  LAMBDA I = L+ D+ L+^T TWIST = 1: Compute negcount from L D L^T  LAMBDA I = U D U^T TWIST = R: Compute negcount from L D L^T  LAMBDA I = N(r) D(r) N(r)
INFOINFO is INTEGER Error flag.
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 195 of file dlarrb.f.
Author
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