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


pred = sigmoid(X*theta);

J = 1./m .* sum(-y .* log(pred) - (1-y) .* log(1-pred)) + lambda ./ 2 ./ m .* sum(theta.^2);


reg = lambda .* theta ./ m;
reg(1) = 0;
grad = 1 / m .* (X' * (pred - y)) + reg;



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

end