%                                           y = asmDxq(d, x, K [, ddotx])
% ASMDXQ  Assemble y = D(d)x for x in Lorentz part of K.
% [y,t] = AasmDxq(d, x, K [, ddotx]) then y[k]+t(k)*d[k] = D(dk)xk.
%
% SEE ALSO sedumi
% **********  INTERNAL FUNCTION OF SEDUMI **********
function [y,t] = asmDxq(d, x, K, ddotx)
 %  
 %   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
   y = zeros(0,1);
   t = zeros(0,1);
 else
% ------------------------------------------------------------
% Let i1, i2 such that x(i1:i2-1) = "x1", i.e. Lorentz trace part.
% ------------------------------------------------------------
   if length(x) >= K.lq
     i1 = K.mainblks(1); i2 = K.mainblks(2);
   else
     i1 = 1; i2 = length(K.q)+1;
   end
   t = x(i1:i2-1);
   if nargin < 4
     ddotx = d.q1.*t + ddot(d.q2,x,K.qblkstart);
   end
% --------------------------------------------------
% Since d^{1/2} = (d+sqrt(det d)*iota) / trace(d^{1/2}),
% and d.auxtr = trace(d^{1/2})^2, d.auxdet = sqrt(2*det d),
% We have P(d)^{1/2}x = t*d + t*auxdet*e_1 - sqrt(det d)*Jx,
% where t = (d'*x + x(1)*auxdet)/auxtr.
% --------------------------------------------------
   t = (ddotx + t.* d.auxdet) ./ d.auxtr;      % old t = x1
   sdet = sqrt(d.det);
   y = [t.*(d.auxdet) - sdet .* x(i1:i2-1); qblkmul(sdet,x,K.qblkstart)];
   if nargout < 2
     y = y + [t.*d.q1; qblkmul(t,d.q2,K.qblkstart)];
   end
 end
