function [x_norm] = var_encode(x, bounds)
% VAR_ENCODE - Encodes the variables "x" in a normalized representation: 0 <= x_norm <= 1
% 
% 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
%   
% Outputs:
%   x_norm = [ number_of_samples x N_var ] 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:
% 
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;