NAME

       slarrf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slarrf (N, D, L, LD, CLSTRT, CLEND, W, WGAP, WERR, SPDIAM, CLGAPL, CLGAPR,
           PIVMIN, SIGMA, DPLUS, LPLUS, WORK, INFO)
           SLARRF finds a new relatively robust representation such that at least one of the
           eigenvalues is relatively isolated.

Function/Subroutine Documentation

   subroutine slarrf (integerN, real, dimension( * )D, real, dimension( * )L, real, dimension( *
       )LD, integerCLSTRT, integerCLEND, real, dimension( * )W, real, dimension( * )WGAP, real,
       dimension( * )WERR, realSPDIAM, realCLGAPL, realCLGAPR, realPIVMIN, realSIGMA, real,
       dimension( * )DPLUS, real, dimension( * )LPLUS, real, dimension( * )WORK, integerINFO)
       SLARRF finds a new relatively robust representation such that at least one of the
       eigenvalues is relatively isolated.

       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.

       Parameters:
           N

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

           D

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

           L

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

           LD

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

           CLSTRT

                     CLSTRT is INTEGER
                     The index of the first eigenvalue in the cluster.

           CLEND

                     CLEND is INTEGER
                     The index of the last eigenvalue in the cluster.

           W

                     W is 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

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

           WERR

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

           SPDIAM

                     SPDIAM is REAL
                     estimate of the spectral diameter obtained from the
                     Gerschgorin intervals

           CLGAPL

                     CLGAPL is REAL

           CLGAPR

                     CLGAPR is 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

                     PIVMIN is REAL
                     The minimum pivot allowed in the Sturm sequence.

           SIGMA

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

           DPLUS

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

           LPLUS

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

           WORK

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

           INFO

                     INFO is INTEGER
                     Signals processing OK (=0) or failure (=1)

       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 191 of file slarrf.f.

Author

       Generated automatically by Doxygen for LAPACK from the source code.