SRC/dlarrf.f(3)

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

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 split).
    !>

    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.

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 dlarrf.f.

Author

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