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dlarrj.f(3)				      LAPACK				      dlarrj.f(3)

NAME
       dlarrj.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlarrj (N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR, WORK, IWORK, PIVMIN,
	   SPDIAM, INFO)
	   DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix
	   T.

Function/Subroutine Documentation
   subroutine dlarrj (integerN, double precision, dimension( * )D, double precision, dimension( *
       )E2, integerIFIRST, integerILAST, double precisionRTOL, integerOFFSET, double precision,
       dimension( * )W, double precision, dimension( * )WERR, double precision, dimension( *
       )WORK, integer, dimension( * )IWORK, double precisionPIVMIN, double precisionSPDIAM,
       integerINFO)
       DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

       Purpose:

	    Given the initial eigenvalue approximations of T, DLARRJ
	    does  bisection to refine the eigenvalues of T,
	    W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial
	    guesses for these eigenvalues are input in W, the corresponding estimate
	    of the error in these guesses in WERR. During bisection, intervals
	    [left, right] are maintained by storing their mid-points and
	    semi-widths in the arrays W and WERR respectively.

       Parameters:
	   N

		     N is INTEGER
		     The order of the matrix.

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		     The N diagonal elements of T.

	   E2

		     E2 is DOUBLE PRECISION array, dimension (N-1)
		     The Squares of the (N-1) subdiagonal elements of T.

	   IFIRST

		     IFIRST is INTEGER
		     The index of the first eigenvalue to be computed.

	   ILAST

		     ILAST is INTEGER
		     The index of the last eigenvalue to be computed.

	   RTOL

		     RTOL is DOUBLE PRECISION
		     Tolerance for the convergence of the bisection intervals.
		     An interval [LEFT,RIGHT] has converged if
		     RIGHT-LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|).

	   OFFSET

		     OFFSET is INTEGER
		     Offset for the arrays W and WERR, i.e., the IFIRST-OFFSET
		     through ILAST-OFFSET elements of these arrays are to be used.

	   W

		     W is DOUBLE PRECISION array, dimension (N)
		     On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are
		     estimates of the eigenvalues of L D L^T indexed IFIRST through
		     ILAST.
		     On output, these estimates are refined.

	   WERR

		     WERR is DOUBLE PRECISION array, dimension (N)
		     On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are
		     the errors in the estimates of the corresponding elements in W.
		     On output, these errors are refined.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (2*N)
		     Workspace.

	   IWORK

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

	   PIVMIN

		     PIVMIN is DOUBLE PRECISION
		     The minimum pivot in the Sturm sequence for T.

	   SPDIAM

		     SPDIAM is DOUBLE PRECISION
		     The spectral diameter of T.

	   INFO

		     INFO is INTEGER
		     Error flag.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       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 167 of file dlarrj.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dlarrj.f(3)
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