MakeFigure4

   Generates Figure 4.

   This figure displays the value for beliefs with only one component.
   Those beliefs only have two parameters (mean and covariance) and, thus,
   the value can be displayed as a 3d plot to show how that the value
   function is not convex in the parameter space.

   POMDP are sometimes addressed in the parameter space (see the paper by
   Brooks et al. 2006, cited in our paper) but then value iteration can
   not take advantage of the convexity of the value function.

   If the results for Figure 1 are not pre-computed we compute them on the
   fly (this can be quite time consuming). Even if they are pre-computed,
   this function takes some time since it computes the value for a large
   collection of beliefs.

0001 function MakeFigure4
0002 %   Generates Figure 4.
0003 %
0004 %   This figure displays the value for beliefs with only one component.
0005 %   Those beliefs only have two parameters (mean and covariance) and, thus,
0006 %   the value can be displayed as a 3d plot to show how that the value
0007 %   function is not convex in the parameter space.
0008 %
0009 %   POMDP are sometimes addressed in the parameter space (see the paper by
0010 %   Brooks et al. 2006, cited in our paper) but then value iteration can
0011 %   not take advantage of the convexity of the value function.
0012 %
0013 %   If the results for Figure 1 are not pre-computed we compute them on the
0014 %   fly (this can be quite time consuming). Even if they are pre-computed,
0015 %   this function takes some time since it computes the value for a large
0016 %   collection of beliefs.
0017 %
0018 
0019   % means and covariances to use in the plot
0020   mu=-20:0.5:20;
0021   sigma=0.5:0.5:7;
0022   
0023   % Nothing to be modified beyond this point
0024   
0025   fprintf('Loading/Generating the simulation results\n');
0026   GenData=@()(TestRep('Test1','Figure2',2));
0027   Results=GetData('Results/Test1-Figure2-2.mat',GenData);
0028   
0029   % Get the las policy of the simulation
0030   Policy=Results.V{end};
0031   
0032   fprintf('Computing the values for 1-Gaussian beliefs from the loaded data\n');
0033   fprintf('This can take some time....\n');
0034   
0035   nMu=size(mu,2);
0036   nSigma=size(sigma,2);
0037   v=zeros(nSigma,nMu);
0038   a=zeros(nSigma,nMu);
0039   for i=1:nSigma
0040     for j=1:nMu
0041       b=GBelief(GMixture(1,{Gaussian(mu(j),sigma(i)^2)}));
0042       [a(i,j) v(i,j)]=OptimalAction(Policy,b);
0043     end
0044   end
0045   fprintf('....plotting the results\n');
0046   
0047     
0048   h=clf;
0049   set(h,'name','C-POMDP Figure 4','numbertitle','off');
0050   
0051   surf(mu,sigma,v,a);
0052   xlabel('\mu');
0053   ylabel('\sigma');
0054   zlabel('Value');
0055   
0056