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.

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

June 2017

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