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

J = 1/m * (-y'*log(sigmoid(X*theta)) - (1-y)'*log(1-sigmoid(X*theta))) ...
    + lambda/(2*m) * theta(2:end)' * theta(2:end);

regularization_term = ...
  lambda/m * (theta .* prepad(ones(length(theta)-1, 1), length(theta), 0));
grad = 1/m * X' * (sigmoid(X*theta) - y) + regularization_term;

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

end