%
% Written by:
% -- 
% John L. Weatherwax                2006-08-28
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear; close all; clc; 

randn('seed',0);

N_var = 2; 
N_samples = 13;
bounds = [ -10, +10 ; -5, +5 ];

% do a single example to check the code: 
% 
x = 10*randn( N_samples, N_var );
x = enforce_bounds( x, bounds );
x % print x 

N_gene = 8; % larger values make the binary approximation more accurate
x_bin = var_encode(x, bounds, N_gene);
%x_bin % print x_bin 

x_encode_decode = var_decode(x_bin, bounds);
x_encode_decode % print x_encode_decode.  The larger the value of N_gene the closer this matrix equals the original x 
norm( x - x_encode_decode ) 

mean_error = [];
num_of_genes = 10:25;
for ng = num_of_genes, 
  N_gene = ng; 
  samples = [];
  for ii=1:100
    x = 10*randn( N_samples, N_var );
    x               = enforce_bounds( x, bounds );
    x_bin           = var_encode(x, bounds, N_gene); % transform 
    x_encode_decode = var_decode(x_bin, bounds); % transform back 
    samples = [ samples, norm( x - x_encode_decode ) ];
  end
  mean_error = [ mean_error, mean( samples ) ];
end

figure; plot( num_of_genes, mean_error, '-o' ); 
xlabel('number of genes to use in binary representation');
ylabel('average error over 100 discretizations');
%saveas( gcf, '../../WriteUp/Graphics/Chapter2/verification_of_binary_representation.eps', 'epsc' );