function [x_bin] = var_encode(x, bounds, N_gene)
% VAR_ENCODE - Encodes the variables x in a binary representation
% 
% Inputs: 
%   x = [ number_of_samples x number_of_variables ] input matrix of variables to be encoded
%   bounds = [ number_of_variables x 2 ] input matrix where the ith row is the valid bounds for the ith variable
%   N_gene = number of bits used to encode a scalar representation 
%   
% Outputs:
%   x_bin = [ number_of_samples x N_var * N_gene ] binary encoding of each variable in x
% 
% 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.
% 
%-----

% Check inputs:
[N_samples,N_var] = size(x);
assert( size(bounds,1)==N_var, 'bounds input must have N_var rows' );
assert( size(bounds,2)==2, 'bounds input must have two columns' );

% make sure all our initial input variables are within the required variables bounds before we encode them in binary: 
% 
x = enforce_bounds(x,bounds);

% Compute the normalized variable values: 
% 
x_low  = repmat( bounds(:,1), [1,N_samples] ).';
x_len  = repmat( bounds(:,2) - bounds(:,1), [1,N_samples] ).';
x_norm = ( x - x_low ) ./ x_len;

x_bin = []; 
for ii=1:N_var
  vars     = x_norm(:,ii); % convert a column of variables at a time 
  vars_bin = zeros(N_samples,N_gene);
  for mm=1:N_gene
    if( mm==1 )
      vars_bin(:,mm) = ceil( x_norm(:,ii) - 2^(-mm) ); % 0 => means to the left of the boundary; 1 => to the right
    else
      Qm = ( 2.^( -(1:(mm-1)) ) ).';
      vars_bin(:,mm) = ceil( x_norm(:,ii) - 2^(-mm) - vars_bin( :, 1:(mm-1) ) * Qm );
    end
  end
  x_bin = [ x_bin, vars_bin ]; 
end