slarrj.f(3)

NAME
slarrj.f -

SYNOPSIS

  Functions/Subroutines

subroutine slarrj (N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR, WORK, IWORK, PIVMIN, SPDIAM, INFO)
SLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

Function/Subroutine Documentation

  subroutine slarrj (integerN, real, dimension( * )D, real, dimension( * )E2, integerIFIRST, integerILAST, realRTOL, integerOFFSET, real, dimension( * )W, real, dimension( * )WERR, real, dimension( * )WORK, integer, dimension( * )IWORK, realPIVMIN, realSPDIAM, integerINFO)

SLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

Purpose:

     Given the initial eigenvalue approximations of T, SLARRJ
     does  bisection to refine the eigenvalues of 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 in WERR. 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 T.

    E2

              E2 is REAL array, dimension (N-1)
              The Squares of the (N-1) subdiagonal elements of T.

    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.

    RTOL

              RTOL is REAL
              Tolerance for the convergence of the bisection intervals.
              An interval [LEFT,RIGHT] has converged if
              RIGHT-LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|).

    OFFSET

              OFFSET is INTEGER
              Offset for the arrays W 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 through
              ILAST.
              On output, these estimates 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 for T.

    SPDIAM

              SPDIAM is REAL
              The spectral diameter of T.

    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 167 of file slarrj.f.

Author

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