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' * theta)-(theta(1)^2)));

grad = ((1/m)*(X' * (sigmoid(X*theta) - y)))+((lambda/m)*(theta));

grad(1) = grad(1) - ((lambda/m)*(theta(1)));

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

end
