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

reg = (lambda / (2*m)) * theta(2:end,:)' * theta(2:end,:); 

J = (1/m) * (-y' * log(sigmoid(X * theta)) - ((1 - y)' * log(1 -sigmoid(X * theta)))) + reg;

%do this for the rest of the terms...
grad = (1/m) * (X' * (sigmoid(X * theta) - y)) + (lambda / m * theta);

%do this for theta 0
grad(1) = (1/m) * (X(:,1)' * (sigmoid(X * theta(:,1)) - y));

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

end
