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dlarrb.f(3)				      LAPACK				      dlarrb.f(3)

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( IFIRST-OFFSET ) through W( ILAST-OFFSET ), 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 mid-points and
	    semi-widths in the arrays W and WERR respectively.

       Parameters:
	   N

		     N is INTEGER
		     The order of the matrix.

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		     The N diagonal elements of the diagonal matrix D.

	   LLD

		     LLD is DOUBLE PRECISION array, dimension (N-1)
		     The (N-1) elements L(i)*L(i)*D(i).

	   IFIRST

		     IFIRST is INTEGER
		     The index of the first eigenvalue to be computed.

	   ILAST

		     ILAST is INTEGER
		     The index of the last eigenvalue to be computed.

	   RTOL1

		     RTOL1 is DOUBLE PRECISION

	   RTOL2

		     RTOL2 is DOUBLE PRECISION
		     Tolerance for the convergence of the bisection intervals.
		     An interval [LEFT,RIGHT] has converged if
		     RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )
		     where GAP is the (estimated) distance to the nearest
		     eigenvalue.

	   OFFSET

		     OFFSET is INTEGER
		     Offset for the arrays W, WGAP and WERR, i.e., the IFIRST-OFFSET
		     through ILAST-OFFSET elements of these arrays are to be used.

	   W

		     W is DOUBLE PRECISION array, dimension (N)
		     On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are
		     estimates of the eigenvalues of L D L^T indexed IFIRST throug
		     ILAST.
		     On output, these estimates are refined.

	   WGAP

		     WGAP is DOUBLE PRECISION array, dimension (N-1)
		     On input, the (estimated) gaps between consecutive
		     eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between
		     eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST
		     then WGAP(IFIRST-OFFSET) must be set to ZERO.
		     On output, these gaps are refined.

	   WERR

		     WERR is DOUBLE PRECISION array, dimension (N)
		     On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are
		     the errors in the estimates of the corresponding elements in W.
		     On output, these errors are refined.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (2*N)
		     Workspace.

	   IWORK

		     IWORK is INTEGER array, dimension (2*N)
		     Workspace.

	   PIVMIN

		     PIVMIN is DOUBLE PRECISION
		     The minimum pivot in the Sturm sequence.

	   SPDIAM

		     SPDIAM is DOUBLE PRECISION
		     The spectral diameter of the matrix.

	   TWIST

		     TWIST 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)

	   INFO

		     INFO 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
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dlarrb.f(3)
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