function [J] = genetic_ode_function(x, t_truth, x_truth, x0)
%
% x is a matrix of size [ N_pop x N_vars ] 
%   
% 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.
% 
%-----

[ N_pop, N_vars ] = size(x);
x_dim = size(x0,1);

power_of_pointwise_error = 3.; % maybe a power > 1 would do a better job selecting optimal population members

J = zeros(N_pop,1);
for pi=1:N_pop,
  
  % From the sample x, extract the matrix A:
  % 
  A = reshape( x(pi,:), [x_dim,x_dim] );
  
  % Solve an ode with these coefficient matrices:  
  [t_sample,x_sample] = ode45( @(t,x) linear_ode_function( x, A ), t_truth, x0 );
  
  % compute the norm between the truth and what we found when we solved the ODE with our given A and b:
  J(pi) = mean( abs(x_sample(:) - x_truth(:)).^power_of_pointwise_error );
  
end