SRC/dlarrb.f(3)

NAME
SRC/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 (integer n, double precision, dimension( * ) d, double precision, dimension( * ) lld, integer ifirst, integer ilast, double precision rtol1, double precision rtol2, integer offset, double precision, dimension( * ) w, double precision, dimension( * ) wgap, double precision, dimension( * ) werr, double precision, dimension( * ) work, integer, dimension( * ) iwork, double precision pivmin, double precision spdiam, integer twist, integer info)

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 < 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 through
              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 = 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.

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 193 of file dlarrb.f.

Author

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