%                                                 z = qjmul(x,y,K)
% QJMUL  Implements Jordan product for Lorentz cones
%
% SEE ALSO sedumi
% **********  INTERNAL FUNCTION OF SEDUMI **********
function z = qjmul(x,y,K)
 %  
 %   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.
 %
 if length(K.q) == 0
   z = zeros(0,1);
 else
% ------------------------------------------------------------
% Let i1, i2 such that x(i1:i2-1) = "x1", i.e. Lorentz trace part.
% ------------------------------------------------------------
   if length(x) ~= length(y)
     error('x,y size mismatch');
   end
   ix = K.mainblks;
   if length(x) < K.lq        % Only q-part given?
     ix = (1-ix(1)) + ix;
     if length(x) ~= length(y)
       error('x, y size mismatch')
     end
   end
% ------------------------------------------------------------
% Let z1 = x'*y/sqrt2, z2 = (x1*y2+y1*x2)/sqrt2
% ------------------------------------------------------------
   z1 = x(ix(1):ix(2)-1).*y(ix(1):ix(2)-1)...
       + ddot(x(ix(2):ix(3)-1),y,K.qblkstart);
   z = [z1; qblkmul(x(ix(1):ix(2)-1),y,K.qblkstart)...
	   + qblkmul(y(ix(1):ix(2)-1),x,K.qblkstart)] / sqrt(2);
 end
