function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized 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

H_theta = sigmoid(X * theta);

J = -1/m * sum(y .* log(H_theta) + (1 - y) .* log(1 - H_theta)) + ...
    lambda/(2 * m) * norm(theta([2:end]))^2;

% extra term for gradient
G = lambda/m .* theta;
G(1) = 0;

grad = 1/m .* X' * (H_theta - y) + G;

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

end
