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

h = sigmoid(X*theta);
J = (-1/m*sum((y.*log(h))+((1-y).*log(1-h))))+((lambda/(2*m))*(sum(power(theta,2))-power(theta(1),2)));

grad(1) = (1/m).*sum((h-y).*X(:,1));

for i = 2:numel(theta)
    grad(i) = ((1/m).*sum((h - y).*X(:,i)))+(lambda/m)*theta(i);
end


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

end