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 
z = hypothesis(theta, X);
t = lambda*(sum(theta .^ 2)-theta(1)^2)/2/m;
J = mean(- y .* log(z) + (y - 1) .* log(1 - z)) + t;

grad = mean((z - y) .* X)' + lambda /m * theta;
grad(1) = grad(1) - lambda /m * theta(1);
% ====================== 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






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

end