DLARRF  - the initial representation L D L^T and its clus­
       ter of close  eigenvalues  (in  a  relative  measure),  W(
       IFIRST ), W( IFIRST+1 ), ..


SYNOPSIS

       SUBROUTINE DLARRF( N,  D,  L,  LD,  LLD, IFIRST, ILAST, W,
                          DPLUS, LPLUS, WORK, IWORK, INFO )

           INTEGER        IFIRST, ILAST, INFO, N

           INTEGER        IWORK( * )

           DOUBLE         PRECISION D( * ), DPLUS( * ), L(  *  ),
                          LD(  * ), LLD( * ), LPLUS( * ), W( * ),
                          WORK( * )


PURPOSE

       Given the initial representation L D L^T and  its  cluster
       of close eigenvalues (in a relative measure), W( IFIRST ),
       W( IFIRST+1 ), ... W( ILAST ), DLARRF finds  a  new  rela­
       tively 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.


ARGUMENTS

       N       (input) INTEGER
               The order of the matrix.

       D       (input) DOUBLE PRECISION array, dimension (N)
               The  n diagonal elements of the diagonal matrix D.

       L       (input) DOUBLE PRECISION array, dimension (N-1)
               The (n-1) subdiagonal elements of the unit bidiag­
               onal matrix L.

       LD      (input) DOUBLE PRECISION array, dimension (N-1)
               The n-1 elements L(i)*D(i).

       LLD     (input) DOUBLE PRECISION array, dimension (N-1)
               The n-1 elements L(i)*L(i)*D(i).

       IFIRST  (input) INTEGER
               The  index of the first eigenvalue in the cluster.

       ILAST   (input) INTEGER
               The index of the last eigenvalue in the cluster.

       W       (input/output) DOUBLE PRECISION array, dimension
               (N)
               On  input, the eigenvalues of L D L^T in ascending
               order.  W( IFIRST ) through W( ILAST  )  form  the
               cluster   of   relatively  close  eigenalues.   On

               of  the  corresponding  eigenvalues  of  L(+) D(+)
               L(+)^T.

       SIGMA   (input) DOUBLE PRECISION
               The shift used to form L(+) D(+) L(+)^T.

       DPLUS   (output) DOUBLE PRECISION array, dimension (N)
               The n diagonal elements  of  the  diagonal  matrix
               D(+).

       LPLUS   (output) DOUBLE PRECISION array, dimension (N)
               The first (n-1) elements of LPLUS contain the sub­
               diagonal elements of the  unit  bidiagonal  matrix
               L(+). LPLUS( N ) is set to SIGMA.

       WORK    (input) DOUBLE PRECISION array, dimension (???)
               Workspace.


FURTHER DETAILS

       Based on contributions by
          Inderjit Dhillon, IBM Almaden, USA
          Osni Marques, LBNL/NERSC, USA


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