%                   [t,wr,w] = trydif(t,wrIN,wIN, x,z, pars,K)
% TRYDIF  Tries feasibility of differentiated step length w.r.t.
%  wide region and its neighborhood.
%
% SEE ALSO sedumi, stepdif
% **********  INTERNAL FUNCTION OF SEDUMI **********
function [t,wr,w] = trydif(t,wrIN,wIN, x,z, pars,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.
 %

 thetaSQR = pars.theta^2;
 ix = K.mainblks;
% --------------------------------------------------
% Let w = D(xM)*zM, compute lambda(w).
% --------------------------------------------------
% LORENTZ
 w.tdetx = tdet(x,K);
 w.tdetz = tdet(z,K);
 detxz = w.tdetx .* w.tdetz / 4;
   if length(K.q) == 0
     lab2q = zeros(0,1);
   else
     halfxz = (x(ix(1):ix(2)-1).*z(ix(1):ix(2)-1)...
	 + ddot(x(ix(2):ix(3)-1),z,K.qblkstart)) / 2;
     lab2q = halfxz + sqrt(halfxz.^2 - detxz);
   end
% PSD
 w.ux = psdfactor(x,K);
 w.s = psdscale(w.ux,z,K);
% ALL:
 w.lab = [x(1:K.l).*z(1:K.l); detxz ./ lab2q; lab2q; psdeig(w.s,K)];
 [wr.delta,wr.h,wr.alpha] = iswnbr(w.lab, thetaSQR);
 wr.desc = wrIN.desc;       % always descent direction.
 if wr.delta > pars.beta
   t = 0; w = wIN; wr = wrIN;
 end
