function [x] = var_decode(x_bin, bounds)
% VAR_DECODE - Decodes the binary variables x_bin into a normal float representation
% 
% Inputs: 
%   x_bin = [ number_of_samples x N_var * N_gene binary zero and ones ] input matrix of variables to be decoded
%   bounds = [ number_of_variables x 2 ] input matrix where the ith row is the valid bounds for the ith variable
%   
% 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:
assert( size(bounds,2)==2, 'bounds input must have two columns' );
N_var     = size(bounds,1);
N_gene    = size(x_bin,2)/N_var;
N_samples = size(x_bin,1);

% Compute the decoded variables:
% 
x_low  = repmat( bounds(:,1), [1,N_samples] ).';
x_len  = repmat( bounds(:,2) - bounds(:,1), [1,N_samples] ).';

Qm = ( 2.^( -(1:N_gene)) ).';

x_quant = zeros(N_samples,N_var);
for ii=1:N_var
  inds     = ( N_gene*(ii-1) + 1 ) : ( N_gene*ii );
  vars_bin = x_bin(:,inds); % convert a single of variables at a time 
  x_quant(:,ii)  = vars_bin * Qm; % + 2^( -(N_gene+1) ); % I don't think that this term should be added 
end

x = x_quant .* x_len + x_low;