%                                                      L = sparchol(L,X,pars,absd)
% SPARCHOL Fast block sparse Cholesky factorization.
%    L = sparchol(L,X,pars) uses only tril(X); triu(X) is assumed
%    to be its transpose. The sparse Cholesky factor will be
%    placed in the fields L.L, L.d; the symbolic factorization fields
%    remain unchanged.
%    On input, L should be the symbolic factorization structure of X,
%    as created by SYMBCHOL.
%    Performs LDL' factorization of X(L.perm,L.perm).
%
%   There are important differences with CHOL(X(L.perm,L.perm))':
%
%   -  SPARCHOL uses the supernodal partition L.XSUPER,
%    to use dense linear algebra on dense subblocks.
%    This explains the performance benefit of SPARCHOL over CHOL.
%
%   -  SPARCHOL never fails.
%
%   - To solve "X*y = b", use
%    >> L = sparchol(symbchol(X),X);
%    >> L.d(find(L.skip)) = inf;
%    >> y = sparbwslv(L, sparfwslv(L,b) ./ L.d);
%
% SEE ALSO symbchol, sparfwslv, sparbwslv, [symbfact, symmmd, chol].
function L = sparchol(L,X,pars,absd)

 %  
 %   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.
 %

% ----------------------------------------
% Numerical block sparse Cholesky of X
% ----------------------------------------
 if nargin > 3
   [L.L,L.d,L.skip,L.add] = blkchol(L,X,pars,absd);
 else
   [L.L,L.d,L.skip,L.add] = blkchol(L,X,pars);
 end
% ------------------------------------------------------------
% For numerical reasons, "blkchol" may skip instable pivots,
% or add on the diagonal. Such pivots are then listed in L.{skip,add}.
% ------------------------------------------------------------
