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

NAME

       LAPACK-3  -  the initial representation L D L^T and its cluster of close eigenvalues (in a
       relative measure), W( CLSTRT ), W( CLSTRT+1 ), ..

SYNOPSIS

       SUBROUTINE SLARRF( N, D, L, LD, CLSTRT, CLEND, W,  WGAP,  WERR,  SPDIAM,  CLGAPL,  CLGAPR,
                          PIVMIN, SIGMA, DPLUS, LPLUS, WORK, INFO )

           INTEGER        CLSTRT, CLEND, INFO, N

           REAL           CLGAPL, CLGAPR, PIVMIN, SIGMA, SPDIAM

           REAL           D(  *  ),  DPLUS(  * ), L( * ), LD( * ), LPLUS( * ), W( * ), WGAP( * ),
                          WERR( * ), WORK( * )

PURPOSE

       Given the initial representation L D L^T and  its  cluster  of  close  eigenvalues  (in  a
       relative measure), W( CLSTRT ), W( CLSTRT+1 ), ...
        W( CLEND ), SLARRF finds a new relatively robust representation
        L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the
        eigenvalues of L(+) D(+) L(+)^T is relatively isolated.

ARGUMENTS

        N       (input) INTEGER
                The order of the matrix (subblock, if the matrix splitted).

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

        L       (input) REAL array, dimension (N-1)
                The (N-1) subdiagonal elements of the unit bidiagonal
                matrix L.

        LD      (input) REAL array, dimension (N-1)
                The (N-1) elements L(i)*D(i).

        CLSTRT  (input) INTEGER
                The index of the first eigenvalue in the cluster.

        CLEND   (input) INTEGER
                The index of the last eigenvalue in the cluster.

        W       (input) REAL array, dimension
                dimension is >=  (CLEND-CLSTRT+1)
                The eigenvalue APPROXIMATIONS of L D L^T in ascending order.
                W( CLSTRT ) through W( CLEND ) form the cluster of relatively
                close eigenalues.

        WGAP    (input/output) REAL array, dimension
                dimension is >=  (CLEND-CLSTRT+1)
                The separation from the right neighbor eigenvalue in W.

        WERR    (input) REAL array, dimension
                dimension is >=  (CLEND-CLSTRT+1)
                WERR contain the semiwidth of the uncertainty
                interval of the corresponding eigenvalue APPROXIMATION in W

        SPDIAM  (input) REAL
                estimate of the spectral diameter obtained from the
                Gerschgorin intervals

        CLGAPL  (input) REAL

        CLGAPR  (input) REAL
                absolute gap on each end of the cluster.
                Set by the calling routine to protect against shifts too close
                to eigenvalues outside the cluster.

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

        SIGMA   (output) REAL
                The shift used to form L(+) D(+) L(+)^T.

        DPLUS   (output) REAL             array, dimension (N)
                The N diagonal elements of the diagonal matrix D(+).

        LPLUS   (output) REAL             array, dimension (N-1)
                The first (N-1) elements of LPLUS contain the subdiagonal
                elements of the unit bidiagonal matrix L(+).

        WORK    (workspace) REAL array, dimension (2*N)
                Workspace.

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                            SLARRF(3lapack)