SRC/slarrf.f(3)

NAME
SRC/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 (integer n, real, dimension( * ) d, real, dimension( * ) l, real, dimension( * ) ld, integer clstrt, integer clend, real, dimension( * ) w, real, dimension( * ) wgap, real, dimension( * ) werr, real spdiam, real clgapl, real clgapr, real pivmin, real sigma, real, dimension( * ) dplus, real, dimension( * ) lplus, real, dimension( * ) work, integer info)

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 split).

    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.

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 189 of file slarrf.f.

Author

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