% SPARFWSLV Solves block sparse upper-triangular system.
%    y = sparfwslv(L,b) yields the same result as
%              y = L.L\b(L.perm,:)
%    However, SPARFWSLV is faster than the built-in operator "\",
%    because it uses dense linear algebra and loop-unrolling on
%    supernodes.
%
%    For sparse b, one should use
%    y = sparfwslv(L,b,symbfwblk(L.L,L.xsuper, b));
%
%    Typical use, with X sparse m x m positive definite and b is m x n:
%            L = sparchol(symbchol(X),X);
%            L.d(L.dep) = inf;
%            y = sparbwslv(L,sparfwslv(L,b) ./ L.d);
%    Then y solves X*y=b.
%
% See also symbchol, sparchol, sparbwslv, mrdivide, mldivide.

function y = sparfwslv(L,b, ysymb)
%
% This file is part of SeDuMi 1.1 by Imre Polik and Oleksandr Romanko
% Copyright (C) 2005 McMaster University, Hamilton, CANADA  (since 1.1)
%
% Copyright (C) 2001 Jos F. Sturm (up to 1.05R5)
%   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.,  51 Franklin Street, Fifth Floor, Boston, MA
% 02110-1301, USA
%

% ----------------------------------------
% Solve L.L * y = b
% ----------------------------------------
if nargin > 2
    y = fwblkslv(L,b,ysymb);
else
    y = fwblkslv(L,b);
end
