GetPOMDPAverageStatistics

   Averages statistics collected after an experiment.

   Experiments are repeated several times to get reliable statistics on
   the results. After each experiment, a file is generated with statistics
   on the results of the experiments. This function agregates those
   statistics computing their average value and their standard deviation.
   These are the values used to generate the plots in the paper.

   This function accepts two parameters
      - Prefix: First part of the name for the files with the results. All
                files are assumed to be in the Result directory (this part
                of the filename is automatically added) and filenames are
                supposed to be numbered consecutively. The number is added
                at the end of the file name, preceeded by a '-'.
      - n: Number of the first result file to be used. If not given 1 is
           assumed.
   This function reads as many available result files as available.
   The results are returned and also written down to a file with name
   'Results/Prefix-result.mat'.

   The outputs are
      tics: Time at which statistics where collected
      SM: Mean for 
           AV: Average value for all beliefs
           R: Average Discounted accumulated reward for several simulations
           nAlpha: Average number of alpha elements in the policy
           nChanges: Average number of changes of optimal action per
                     belief from one policy to the next.
      SD: The standard deviation for the previous data.

   Example of use 
    [tics SM SD]=GetPOMDPAverageStatistics('Test1-Figure1')

   See also TestRep, GetPOMDPSolutionStatistics.

0001 function [tics SM SD]=GetPOMDPAverageStatistics(prefix,varargin)
0002 %   Averages statistics collected after an experiment.
0003 %
0004 %   Experiments are repeated several times to get reliable statistics on
0005 %   the results. After each experiment, a file is generated with statistics
0006 %   on the results of the experiments. This function agregates those
0007 %   statistics computing their average value and their standard deviation.
0008 %   These are the values used to generate the plots in the paper.
0009 %
0010 %   This function accepts two parameters
0011 %      - Prefix: First part of the name for the files with the results. All
0012 %                files are assumed to be in the Result directory (this part
0013 %                of the filename is automatically added) and filenames are
0014 %                supposed to be numbered consecutively. The number is added
0015 %                at the end of the file name, preceeded by a '-'.
0016 %      - n: Number of the first result file to be used. If not given 1 is
0017 %           assumed.
0018 %   This function reads as many available result files as available.
0019 %   The results are returned and also written down to a file with name
0020 %   'Results/Prefix-result.mat'.
0021 %
0022 %   The outputs are
0023 %      tics: Time at which statistics where collected
0024 %      SM: Mean for
0025 %           AV: Average value for all beliefs
0026 %           R: Average Discounted accumulated reward for several simulations
0027 %           nAlpha: Average number of alpha elements in the policy
0028 %           nChanges: Average number of changes of optimal action per
0029 %                     belief from one policy to the next.
0030 %      SD: The standard deviation for the previous data.
0031 %
0032 %   Example of use
0033 %    [tics SM SD]=GetPOMDPAverageStatistics('Test1-Figure1')
0034 %
0035 %   See also TestRep, GetPOMDPSolutionStatistics.
0036   
0037   if nargin==1
0038     start=1;
0039   else
0040     start=varargin{1};
0041   end
0042   
0043   k=1;
0044   found=true;
0045   while found
0046     name=sprintf('Results/%s-%u.mat',prefix,start+k-1);
0047     fid=fopen(name);
0048     if (fid<0)
0049       found=false;
0050     else
0051       fprintf('Reading file: %s\n',name);
0052       fclose(fid);
0053 
0054       C=load(name);
0055         
0056       if k==1
0057         nSteps=size(C.aV,2);
0058         tics=C.tics;
0059         
0060         AV=zeros(10,nSteps);
0061         R=zeros(10,nSteps);
0062         nAlpha=zeros(10,nSteps);
0063         nChanges=zeros(10,nSteps);
0064       else
0065         if nSteps~=size(C.aV,2)
0066           error('Size missmatch between different results');
0067         end
0068       end
0069       
0070       AV(k,:)=C.aV;
0071       R(k,:)=C.aR;
0072       nAlpha(k,:)=C.nA;
0073       nChanges(k,:)=C.nC;
0074       
0075       k=k+1;
0076     end % end of if file can be openned
0077   end
0078   if k>1
0079     % Compute mean values
0080     r=1:(k-1);
0081     SM.AV=mean(AV(r,:),1);
0082     SD.AV=std(AV(r,:),1,1);
0083     
0084     SM.R=mean(R(r,:),1);
0085     SD.R=std(R(r,:),1,1);
0086     
0087     SM.nAlpha=mean(nAlpha(r,:),1);
0088     SD.nAlpha=std(nAlpha(r,:),1,1);
0089     
0090     SM.nChanges=mean(nChanges(r,:),1);
0091     SD.nChanges=std(nChanges(r,:),1,1);
0092   
0093     name=sprintf('Results/%s-results.mat',prefix);
0094     save(name,'tics','SM','SD');
0095   else
0096     error('No data available to compute the average results');
0097   end