%
%                          Example 15_4.m 
%
  clear all
  
  q = 0:.01:1;
  a = 0.05;
  b = 0.05;

%
% Compute surrogate and high-fidelity model responses on the interval [0,1] and at the
% M=3 interpolation points q_interp and M=6 regression points q_regress
%

  q_interp = [0 0.5 1];
  q_regress = [0.1090 0.3404 0.4984 0.5853 0.7171 0.9407]';
  X = [ones(6,1) q_regress q_regress.^2];

  ys = (q-1/4).^2 + 1/2;
  ys_interp = (q_interp-1/4).^2 + 1/2;
  y = ys + a*(q+b).*sin(20*pi*q);
  y_regress = (q_regress - 1/4*ones(size(q_regress))).^2 + 1/2*ones(size(q_regress)) + a*(q_regress+b).*sin(20*pi*q_regress);
  w = X\y_regress;
  ys_regress = w(1)*ones(size(q)) + w(2)*q + w(3)*q.^2;

%
% Plot the solutions with M=3 interpolation points and M=6 regression points
%

  figure(1)
  plot(q,y,'-b',q,ys,'--k','linewidth',3)
  hold on
  plot(q_interp,ys_interp,'ro','linewidth',8)
  hold off
  set(gca,'Fontsize',[22]);
  xlabel('Parameter q')
  ylabel('Model Response')
  legend(' High-Fidelity Response f(q)',' Surrogate f_S(q)','Training Data','Location','Northwest')
  %print -depsc chpt12_fig1a 

  figure(2)
  plot(q,y,'-b',q,ys_regress,'--k','linewidth',3)
  hold on
  plot(q_regress,y_regress,'ro','linewidth',8)
  hold off 
  set(gca,'Fontsize',[22]);
  xlabel('Parameter q')
  ylabel('Model Response')
  legend(' High-Fidelity Response f(q)',' Surrogate f_S(q)','Training Data','Location','Northwest')
  %print -depsc chpt12_fig1b