SRC/slarrf.f(3)            Library Functions Manual            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
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/slarrf.f(3)