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DLARRB(l)					)					DLARRB(l)

NAME
       DLARRB - the relatively robust representation(RRR) L D L^T, DLARRB does ``limited'' bisec-
       tion to locate the eigenvalues of L D L^T,

SYNOPSIS
       SUBROUTINE DLARRB( N, D, L, LD, LLD, IFIRST, ILAST, SIGMA, RELTOL, W,  WGAP,  WERR,  WORK,
			  IWORK, INFO )

	   INTEGER	  IFIRST, ILAST, INFO, N

	   DOUBLE	  PRECISION RELTOL, SIGMA

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION D( * ), L( * ), LD( * ), LLD( * ), W( * ), WERR( * ), WGAP( *
			  ), WORK( * )

PURPOSE
       Given the relatively robust representation(RRR) L D L^T, DLARRB does ``limited'' bisection
       to  locate  the	eigenvalues  of  L D L^T, W( IFIRST ) thru' W( ILAST ), to more accuracy.
       Intervals [left, right] are maintained by storing their mid-points and semi-widths in  the
       arrays W and WERR respectively.

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 bidiagonal 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.

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

       RELTOL  (input) DOUBLE PRECISION
	       The relative tolerance.

       W       (input/output) DOUBLE PRECISION array, dimension (N)
	       On  input,  W( IFIRST ) thru' W( ILAST ) are estimates of the corresponding eigen-
	       values of L D L^T.  On output, these estimates are ``refined''.

       WGAP    (input/output) DOUBLE PRECISION array, dimension (N)
	       The gaps between the eigenvalues of L D L^T. Very small gaps are changed  on  out-
	       put.

       WERR    (input/output) DOUBLE PRECISION array, dimension (N)
	       On  input,  WERR(  IFIRST ) thru' WERR( ILAST ) are the errors in the estimates W(
	       IFIRST ) thru' W( ILAST ).  On output, these are the ``refined'' errors.

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

       IWORK   (input) INTEGER array, dimension (2*N)
	       Workspace.

       INFO    (output) INTEGER
	       Error flag.

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

LAPACK version 3.0			   15 June 2000 				DLARRB(l)
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