Library Functions Manual

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 is INTEGER
!>          The order of the matrix (subblock, if the matrix split).
!>

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

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

!>          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 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.

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.