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 = sigmoid( X*theta );
o = ones(size(y));
reg = theta;
reg(1) = 0;
J = sum( y .* log(h) + (o-y) .* log(o-h) ) / (-m) + (lambda/(2*m))*sum(reg.^2);
grad = (X'*(h - y)) / m + (lambda/m) * reg;

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

end
