NAME

       dlarrf.f -

SYNOPSIS

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

Function/Subroutine Documentation

   subroutine dlarrf (integerN, double precision, dimension( * )D, double precision, dimension( *
       )L, double precision, dimension( * )LD, integerCLSTRT, integerCLEND, double precision,
       dimension( * )W, double precision, dimension( * )WGAP, double precision, dimension( *
       )WERR, double precisionSPDIAM, double precisionCLGAPL, double precisionCLGAPR, double
       precisionPIVMIN, double precisionSIGMA, double precision, dimension( * )DPLUS, double
       precision, dimension( * )LPLUS, double precision, dimension( * )WORK, integerINFO)
       DLARRF 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 ), DLARRF 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 DOUBLE PRECISION array, dimension (N)
                     The N diagonal elements of the diagonal matrix D.

           L

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

           LD

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

           WERR

                     WERR is DOUBLE PRECISION 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 DOUBLE PRECISION
                     estimate of the spectral diameter obtained from the
                     Gerschgorin intervals

           CLGAPL

                     CLGAPL is DOUBLE PRECISION

           CLGAPR

                     CLGAPR is DOUBLE PRECISION
                     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 DOUBLE PRECISION
                     The minimum pivot allowed in the Sturm sequence.

           SIGMA

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

           DPLUS

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

           LPLUS

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

           WORK

                     WORK is DOUBLE PRECISION 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 dlarrf.f.

Author

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