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))-(ones(size(y))-y)'*log(ones(size(y))-sigmoid(X*theta)))+lambda/2/m*(theta'*theta-theta(1)^2);

grad(1)=1/m*(X(:,1))'*(sigmoid(X*theta)-y);

grad(2:size(theta))=1/m*(X(:,2:size(theta)))'*(sigmoid(X*theta)-y)+lambda/m*theta(2:size(theta));






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

end
