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