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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