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 = size(X, 2); % number of features

% 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

% ==== Evaluating the cost ====
%First part, without Regularization
for i = 1:m
    hypothesis = sigmoid(theta' * X(i, :)');
    J += y(i) * log(hypothesis) + (1 - y(i)) * log(1 - hypothesis);
end;
J *= -1 / m;

%Regularization (penalizing the parameters)
secondPart = 0;
for j = 2:n
    secondPart += theta(j) ^ 2;
end;
secondPart *= lambda / (2 * m);
J += secondPart;

% ==== Evaluating the gradient ====
for i = 1:m
    hypothesis = sigmoid(theta' * X(i, :)');
    grad(1) += (hypothesis - y(i)) * X(i, 1);
end;
grad(1) *= 1 / m;

for j = 2:n
    for i = 1:m
        hypothesis = sigmoid(theta' * X(i, :)');
        grad(j) += (hypothesis - y(i)) * X(i, j);
    end;
    grad(j) *= 1 / m;
    grad(j) += (lambda * theta(j)) / m;
end;

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

end