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slarrb.f(3) LAPACK slarrb.f(3)

NAME

slarrb.f -

SYNOPSIS

Functions/Subroutines


subroutine slarrb (N, D, LLD, IFIRST, ILAST, RTOL1, RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, PIVMIN, SPDIAM, TWIST, INFO)
 
SLARRB provides limited bisection to locate eigenvalues for more accuracy.

Function/Subroutine Documentation

subroutine slarrb (integerN, real, dimension( * )D, real, dimension( * )LLD, integerIFIRST, integerILAST, realRTOL1, realRTOL2, integerOFFSET, real, dimension( * )W, real, dimension( * )WGAP, real, dimension( * )WERR, real, dimension( * )WORK, integer, dimension( * )IWORK, realPIVMIN, realSPDIAM, integerTWIST, integerINFO)

SLARRB provides limited bisection to locate eigenvalues for more accuracy.
Purpose:
 Given the relatively robust representation(RRR) L D L^T, SLARRB
 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 REAL array, dimension (N)
          The N diagonal elements of the diagonal matrix D.
LLD
          LLD is REAL 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 REAL
RTOL2
          RTOL2 is REAL
          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 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 throug
          ILAST.
          On output, these estimates are refined.
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.EQ.ILAST
          then WGAP(IFIRST-OFFSET) must be set to ZERO.
          On output, these gaps are refined.
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.
WORK
          WORK is REAL array, dimension (2*N)
          Workspace.
IWORK
          IWORK is INTEGER array, dimension (2*N)
          Workspace.
PIVMIN
          PIVMIN is REAL
          The minimum pivot in the Sturm sequence.
SPDIAM
          SPDIAM is REAL
          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 slarrb.f.

Author

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