computeNumericalGradient.m

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;
for i=1:length(theta)
    basis = zeros(size(theta)); basis(i)=1;
%{
    lj = J(theta+epsilon*basis)
    rj = J(theta-epsilon*basis)
    numgrad(i) = (lj - rj)/(2*epsilon)
    pause
%}
    numgrad(i) = gather((J(theta + epsilon*basis) - J(theta - epsilon*basis)) / (2*epsilon));
end


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