function [J, grad] = costFunction(theta, X, y)
%COSTFUNCTION Compute cost and gradient for logistic regression
%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
%   parameter for logistic regression and the gradient of the cost
%   w.r.t. to the parameters.

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta
%
% Note: grad should have the same dimensions as theta
%


% refer to the vectorized function in Week 3|Logistic Regression Model|
% Simplified Cost Function and Gradient Descent
% h = g(X * theta)


J = 1 / m * (-1 .* y' * log(sigmoid(X*theta)) - (1 .- y)' * log(1 .- sigmoid(X*theta)));

% compute the gradient only

% 1. vector method
% grad = 1/m * X' * (sigmoid(X*theta) - y);

%
% 2. sum method
grad = 1/m * sum((sigmoid(X*theta) - y ).* X);






% =============================================================

end