Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - the initial eigenvalue approximations of T, DLARRJ does bisection to refine the
       eigenvalues of T,

SYNOPSIS

       SUBROUTINE DLARRJ( N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR,  WORK,  IWORK,  PIVMIN,
                          SPDIAM, INFO )

           INTEGER        IFIRST, ILAST, INFO, N, OFFSET

           DOUBLE         PRECISION PIVMIN, RTOL, SPDIAM

           INTEGER        IWORK( * )

           DOUBLE         PRECISION D( * ), E2( * ), W( * ), WERR( * ), WORK( * )

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.

ARGUMENTS

        N       (input) INTEGER
                The order of the matrix.

        D       (input) DOUBLE PRECISION array, dimension (N)
                The N diagonal elements of T.

        E2      (input) DOUBLE PRECISION array, dimension (N-1)
                The Squares of the (N-1) subdiagonal elements of T.

        IFIRST  (input) INTEGER
                The index of the first eigenvalue to be computed.

        ILAST   (input) INTEGER
                The index of the last eigenvalue to be computed.

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

        OFFSET  (input) 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       (input/output) 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    (input/output) 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    (workspace) DOUBLE PRECISION array, dimension (2*N)
                Workspace.

        IWORK   (workspace) INTEGER array, dimension (2*N)
                Workspace.

        PIVMIN  (input) DOUBLE PRECISION
                The minimum pivot in the Sturm sequence for T.

        SPDIAM  (input) DOUBLE PRECISION
                The spectral diameter of T.

        INFO    (output) INTEGER
                Error flag.

FURTHER DETAILS

        Based on contributions by
           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

 LAPACK auxiliary routine (version 3.2.2)   April 2011                            DLARRJ(3lapack)