%            [Lden, Ld] = deninfac(symLden, L,dense,DAt, d, absd, qblkstart,pars)
% DENINFAC
% Uses pars.maxuden as max. allowable |L(i,k)|. Otherwise num. reordering.
%
% SEE ALSO sedumi
% ******************** INTERNAL FUNCTION OF SEDUMI ********************
function [Lden, Ld] = deninfac(symLden, L,dense,DAt, d, absd, qblkstart,pars)
 %  
 %   This file is part of SeDuMi 1.05
 %   Copyright (C) 2001 Jos F. Sturm
 %     Dept. Econometrics & O.R., Tilburg University, the Netherlands.
 %     Supported by the Netherlands Organization for Scientific Research (NWO).
 %   Affiliation SeDuMi 1.03 and 1.04Beta (2000):
 %     Dept. Quantitative Economics, Maastricht University, the Netherlands.
 %   Affiliations up to SeDuMi 1.02 (AUG1998):
 %     CRL, McMaster University, Canada.
 %     Supported by the Netherlands Organization for Scientific Research (NWO).
 % 
 %   This program is free software; you can redistribute it and/or modify
 %   it under the terms of the GNU General Public License as published by
 %   the Free Software Foundation; either version 2 of the License, or
 %   (at your option) any later version.
 % 
 %   This program is distributed in the hope that it will be useful,
 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 %   GNU General Public License for more details.
 % 
 %   You should have received a copy of the GNU General Public License
 %   along with this program; if not, write to the Free Software
 %   Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 %

% ------------------------------------------------------------
% INITIALIZE: check the numerical tolerance parameters in "pars",
%   and supply with defaults if necessary.
% ------------------------------------------------------------
 if nargin < 7
   pars.maxuden = 10;                  % Stability of product-form factors
 else
   if ~isfield(pars,'maxuden')
     pars.maxuden = 10;                % Stability of product-form factors
   end
 end
% --------------------------------------------------
% Scaling: let Ad = Aden * Dden, as [LP, QBLK, QNORM, QTR]
% with QBLK=DAt.denq, and the others dense.A(:,j)*dj,
% with dj = sqrt(d.l(k)) or dj=sqrt(d.det(k)).
% NOTE that A*P(d)*A' = ADA + Ad * Ad'.
% --------------------------------------------------
 if length(dense.cols) > 0
   i1 = dense.l+1; i2 = i1 + length(dense.q);
   Ad = [dense.A(:,1:i1-1), DAt.denq, dense.A(:,i2:end), dense.A(:,i1:i2-1)];
   smult = [d.l(dense.cols(1:dense.l)); ones(length(dense.q),1); ...
	   adenscale(dense,d,qblkstart); -d.det(dense.q)];
% --------------------------------------------------
% Correct for sparse part, i.e. let LAD = L\Ad
% (this also handles L.perm)
% --------------------------------------------------
   LAD = sparfwslv(L,Ad, symLden.LAD);
   clear Ad;
% --------------------------------------------------
% Factor the dense columns as "diag+rank-1"=diag(L.d)+LAD(:,k)*LAD(:,k)'
% --------------------------------------------------'
   [Lden, Ld] = dpr1fact(LAD, L.d, symLden, smult, pars.maxuden);
   Lden.dz = symLden.dz;
   Lden.first = symLden.first;
   Lden.perm = symLden.perm;
   clear LAD;
 else
% --------------------------------------------------
% If no dense columns
% --------------------------------------------------
   Lden.betajc = [0];
   Ld = L.d;
   Lden.rowperm = 1:length(L.d);
 end
% ------------------------------------------------------------
% If still Ld(i) = 0, then set to something positive. Otherwise
% we cannot do PCG.
% ------------------------------------------------------------
 skip = find(L.skip);
 if length(skip) > 0
   dtol = pars.canceltol * absd(L.perm(skip));
   dtol = max(dtol, pars.abstol);
   Ld(skip(find(Ld(skip) <= dtol))) = 1;
 end
