function numgrad = computeNumericalGradient(J, theta)
% numgrad = computeNumericalGradient(J, theta)
% theta: a vector of parameters
% J: a function that outputs a real-number. Calling y = J(theta) will return the
% function value at theta. 
  
% Initialize numgrad with zeros
numgrad = zeros(size(theta));

%% ---------- YOUR CODE HERE --------------------------------------
% Instructions: 
% Implement numerical gradient checking, and return the result in numgrad.  
% (See Section 2.3 of the lecture notes.)
% You should write code so that numgrad(i) is (the numerical approximation to) the 
% partial derivative of J with respect to the i-th input argument, evaluated at theta.  
% I.e., numgrad(i) should be the (approximately) the partial derivative of J with 
% respect to theta(i).
%                
% Hint: You will probably want to compute the elements of numgrad one at a time. 

EPSILON=1e-4;
N=length(theta);
In=eye(N);
for k=1:N
    if mod(k,100)==0
        k 
    end;
    e_i=In(:,k);
    theta_ip=theta+EPSILON*e_i;
    theta_im=theta-EPSILON*e_i;
    numgrad(k)=(J(theta_ip)-J(theta_im))/(2*EPSILON);
end

%% ---------------------------------------------------------------
end