% This is a single input (x) normalized Radial-Basis Neural Network
% The parameter vector theta is used to define the value of the
% output.  range = [x1, x2] where x1 is the minimum input value and x2 is
% the max input.  sig is used to describe the width of the basis function

function [y, mu] = rbnn(x, range, sig, theta);

p = length(theta);
theta = theta(:);
x1 = range(1);
x2 = range(2);

% define the centers of the basis functions
d = (x2 - x1)/(p-1);
xc = (0:(p-1))*d + x1;
xc = xc(:);  % make sure its a column-vector

% define the basis functions
dist = (x - xc).^2;
mu = exp(-dist/sig^2);
mu = mu(:)/sum(mu);      % normalize it

% define the output of the neural networ
y = mu'*theta;