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DLARRB(l)			       )			     DLARRB(l)

NAME
       DLARRB - the relatively robust representation(RRR) L D L^T, DLARRB does
       ``limited'' bisection 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	 main‐
       tained  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  eigenvalues  of L D L^T.	On output, these esti‐
	       mates 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 output.

       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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