slarrb()

subroutine slarrb	(	integer	n,
		real, dimension( * )	d,
		real, dimension( * )	lld,
		integer	ifirst,
		integer	ilast,
		real	rtol1,
		real	rtol2,
		integer	offset,
		real, dimension( * )	w,
		real, dimension( * )	wgap,
		real, dimension( * )	werr,
		real, dimension( * )	work,
		integer, dimension( * )	iwork,
		real	pivmin,
		real	spdiam,
		integer	twist,
		integer	info )

SLARRB provides limited bisection to locate eigenvalues for more accuracy.

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Purpose:

!>
!> Given the relatively robust representation(RRR) L D L^T, SLARRB
!> does  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

[in]	N	!> N is INTEGER !> The order of the matrix. !>
[in]	D	!> D is REAL array, dimension (N) !> The N diagonal elements of the diagonal matrix D. !>
[in]	LLD	!> LLD is REAL array, dimension (N-1) !> The (N-1) elements L(i)*L(i)*D(i). !>
[in]	IFIRST	!> IFIRST is INTEGER !> The index of the first eigenvalue to be computed. !>
[in]	ILAST	!> ILAST is INTEGER !> The index of the last eigenvalue to be computed. !>
[in]	RTOL1	!> RTOL1 is REAL !>
[in]	RTOL2	!> RTOL2 is REAL !> 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. !>
[in]	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. !>
[in,out]	W	!> W is REAL 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. !>
[in,out]	WGAP	!> WGAP is REAL 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. !>
[in,out]	WERR	!> WERR is REAL 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. !>
[out]	WORK	!> WORK is REAL array, dimension (2*N) !> Workspace. !>
[out]	IWORK	!> IWORK is INTEGER array, dimension (2*N) !> Workspace. !>
[in]	PIVMIN	!> PIVMIN is REAL !> The minimum pivot in the Sturm sequence. !>
[in]	SPDIAM	!> SPDIAM is REAL !> The spectral diameter of the matrix. !>
[in]	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) !>
[out]	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