dlarrb.f - Man Page

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.

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 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.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:

June 2017

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 198 of file dlarrb.f.