%      [Lsd,Rscl] = sdfactor(L,Lden, dense,DAt, d,v,y, At,K,R,y0,pars)
% SDFACTOR  Factor self-dual embedding
%
% SEE ALSO sedumi
% ******************** INTERNAL FUNCTION OF SEDUMI ********************
function Lsd = sdfactor(L,Lden, dense,DAt, d,v,y, At,c,K,R,y0,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.
 %

% ------------------------------------------------------------
% Compute D*Rc
% ------------------------------------------------------------
 Lsd.DRc = [sqrt(d.l).*R.c(1:K.l); asmDxq(d,R.c,K); psdscale(d,R.c,K)];
% ------------------------------------------------------------
% Solve AP(d)A' * ysd = y0*Rb + AD(y0*DRc-2v)
% and let xsd = (y0*DRc-2v) - DA'*ysd.
% ------------------------------------------------------------
 [Lsd.y,Lsd.x,Lsd.kcg,Lsd.b] = wrapPcg(L,Lden,At,dense,d, DAt,K, y0*R.b,...
    y0*Lsd.DRc - 2*v, pars.cg, min(1,y0)*R.maxRb);
% ------------------------------------------------------------
% Now let ysd -= y and xsd += v.
% It follows then that AD*xsd = x0 * b + Lsd.b, where Lsd.b = numerical error.
% ------------------------------------------------------------
 Lsd.y = Lsd.y - y;
 Lsd.x = Lsd.x + v;
% ------------------------------------------------------------
% Compute denom = norm(xsd)^2
% ------------------------------------------------------------
 Lsd.denom = norm(Lsd.x)^2 + Lsd.b'*Lsd.y;


