SLARRJ(3)      LAPACK routine of NEC Numeric Library Collection      SLARRJ(3)



NAME
       SLARRJ

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



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)
                     N is INTEGER
                     The order of the matrix.

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

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

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

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

           RTOL      (input)
                     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    (input)
                     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         (input/output)
                     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      (input/output)
                     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      (output)
                     WORK is REAL array, dimension (2*N)
                     Workspace.

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

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

           SPDIAM    (input)
                     SPDIAM is REAL
                     The spectral diameter of T.

           INFO      (output)
                     INFO is INTEGER
                     Error flag.



LAPACK routine                  31 October 2017                      SLARRJ(3)