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:length(theta))'*theta(2:length(theta));

grad = X'*(sigmoid(X*theta)-y)/m;
grad(2:length(theta)) = grad(2:length(theta)) + theta(2:length(theta))*lambda/m;



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

end

% ======weights can be found using the following code=====
%  Set options for fminunc
%options = optimset('GradObj', 'on', 'MaxIter', 400);

%  Run fminunc to obtain the optimal theta
%  This function will return theta and the cost 
%[theta, cost] = fminunc(@(t)costFunction(t, X, y), initial_theta, options);