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
n = length(theta);

% 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
tempTheta = theta(1);
h = sigmoid(X*theta);
theta(1) = 0;
J = (1/m)*(-y'*log(h)-(1-y)'*log(1-h));
J = J + (lambda/(2*m))*sum(theta.^2);
theta(1) = tempTheta;
grad = (1/m)*X'*(sigmoid(X*theta)-y);
for i=2:n
  grad(i) = grad(i) + (lambda/m)*theta(i);
endfor



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

end
