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slarrf.f(3)				      LAPACK				      slarrf.f(3)

NAME
       slarrf.f -

SYNOPSIS
   Functions/Subroutines
       subroutine slarrf (N, D, L, LD, CLSTRT, CLEND, W, WGAP, WERR, SPDIAM, CLGAPL, CLGAPR,
	   PIVMIN, SIGMA, DPLUS, LPLUS, WORK, INFO)
	   SLARRF finds a new relatively robust representation such that at least one of the
	   eigenvalues is relatively isolated.

Function/Subroutine Documentation
   subroutine slarrf (integerN, real, dimension( * )D, real, dimension( * )L, real, dimension( *
       )LD, integerCLSTRT, integerCLEND, real, dimension( * )W, real, dimension( * )WGAP, real,
       dimension( * )WERR, realSPDIAM, realCLGAPL, realCLGAPR, realPIVMIN, realSIGMA, real,
       dimension( * )DPLUS, real, dimension( * )LPLUS, real, dimension( * )WORK, integerINFO)
       SLARRF finds a new relatively robust representation such that at least one of the
       eigenvalues is relatively isolated.

       Purpose:

	    Given the initial representation L D L^T and its cluster of close
	    eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ...
	    W( CLEND ), SLARRF finds a new relatively 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.

       Parameters:
	   N

		     N is INTEGER
		     The order of the matrix (subblock, if the matrix splitted).

	   D

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

	   L

		     L is REAL array, dimension (N-1)
		     The (N-1) subdiagonal elements of the unit bidiagonal
		     matrix L.

	   LD

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

	   CLSTRT

		     CLSTRT is INTEGER
		     The index of the first eigenvalue in the cluster.

	   CLEND

		     CLEND is INTEGER
		     The index of the last eigenvalue in the cluster.

	   W

		     W is REAL array, dimension
		     dimension is >=  (CLEND-CLSTRT+1)
		     The eigenvalue APPROXIMATIONS of L D L^T in ascending order.
		     W( CLSTRT ) through W( CLEND ) form the cluster of relatively
		     close eigenalues.

	   WGAP

		     WGAP is REAL array, dimension
		     dimension is >=  (CLEND-CLSTRT+1)
		     The separation from the right neighbor eigenvalue in W.

	   WERR

		     WERR is REAL array, dimension
		     dimension is >=  (CLEND-CLSTRT+1)
		     WERR contain the semiwidth of the uncertainty
		     interval of the corresponding eigenvalue APPROXIMATION in W

	   SPDIAM

		     SPDIAM is REAL
		     estimate of the spectral diameter obtained from the
		     Gerschgorin intervals

	   CLGAPL

		     CLGAPL is REAL

	   CLGAPR

		     CLGAPR is REAL
		     absolute gap on each end of the cluster.
		     Set by the calling routine to protect against shifts too close
		     to eigenvalues outside the cluster.

	   PIVMIN

		     PIVMIN is REAL
		     The minimum pivot allowed in the Sturm sequence.

	   SIGMA

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

	   DPLUS

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

	   LPLUS

		     LPLUS is REAL array, dimension (N-1)
		     The first (N-1) elements of LPLUS contain the subdiagonal
		     elements of the unit bidiagonal matrix L(+).

	   WORK

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

	   INFO

		     INFO is INTEGER
		     Signals processing OK (=0) or failure (=1)

       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 191 of file slarrf.f.

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

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