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

NAME

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

SYNOPSIS

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

           INTEGER        IFIRST, ILAST, INFO, N, OFFSET

           REAL           PIVMIN, RTOL, SPDIAM

           INTEGER        IWORK( * )

           REAL           D( * ), E2( * ), W( * ), WERR( * ), WORK( * )

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.

ARGUMENTS

        N       (input) INTEGER
                The order of the matrix.

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

        E2      (input) REAL             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) REAL
               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) 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    (input/output) 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    (workspace) REAL             array, dimension (2*N)
                Workspace.

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

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

        SPDIAM  (input) REAL
                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                            SLARRJ(3lapack)