function [J] = genetic_ode_function_xt_minus_Ax(x, x_truth, xdot_truth)
%
% x is a population 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);
[ N_t, x_dim ] = size(x_truth); 

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] );
  
  xdot = ( A * x_truth.' ).'; 
  
  % compute the norm between the truth and what we found when we solved the ODE with our given A and b:
  J(pi) = mean( sum( abs( xdot_truth - xdot ).^power_of_pointwise_error, 2 ).^(1./power_of_pointwise_error) );
  
end