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

           INTEGER        IFIRST, ILAST, INFO, N

           INTEGER        IWORK( * )

           REAL           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 ), SLARRF 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) REAL array, dimension (N)
               The  n diagonal elements of the diagonal matrix D.

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

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

       LLD     (input) REAL 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) REAL 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  out­
               put, W( IFIRST ) thru' W( ILAST ) are estimates of
               the corresponding eigenvalues of L(+) D(+) L(+)^T.

               The shift used to form L(+) D(+) L(+)^T.

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

       LPLUS   (output) REAL 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) REAL array, dimension (???)
               Workspace.


FURTHER DETAILS

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


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