larrf(3)

NAME
larrf - larrf: step in stemr, find relative robust representation (RRR)

SYNOPSIS

  Functions

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.
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.

Detailed Description

Function 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

  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

Author

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