SRC/dlarrj.f(3)

NAME
SRC/dlarrj.f

SYNOPSIS

  Functions/Subroutines
subroutine dlarrj (n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info)
DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

Function/Subroutine Documentation

  subroutine dlarrj (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e2, integer ifirst, integer ilast, double precision rtol, integer offset, double precision, dimension( * ) w, double precision, dimension( * ) werr, double precision, dimension( * ) work, integer, dimension( * ) iwork, double precision pivmin, double precision spdiam, integer info)

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

Purpose:

     Given the initial eigenvalue approximations of T, DLARRJ
     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 DOUBLE PRECISION array, dimension (N)
              The N diagonal elements of T.

    E2

              E2 is DOUBLE PRECISION 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 DOUBLE PRECISION
              Tolerance for the convergence of the bisection intervals.
              An interval [LEFT,RIGHT] has converged if
              RIGHT-LEFT < 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 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.

    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 for T.

    SPDIAM

              SPDIAM is DOUBLE PRECISION
              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.

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 165 of file dlarrj.f.

Author

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