function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)

Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
                 hidden_layer_size, (input_layer_size + 1));

Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
                 num_labels, (hidden_layer_size + 1));

% Setup some useful variables
m = size(X, 1);
X = [ones(m,1) X];
% You need to return the following variables correctly
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
%               following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
%         variable J. After implementing Part 1, you can verify that your
%         cost function computation is correct by verifying the cost
%         computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
%         Theta2_grad, respectively. After implementing Part 2, you can check
%         that your implementation is correct by running checkNNGradients
%
%         Note: The vector y passed into the function is a vector of labels
%               containing values from 1..K. You need to map this vector into a
%               binary vector of 1's and 0's to be used with the neural network
%               cost function.
%
%         Hint: We recommend implementing backpropagation using a for-loop
%               over the training examples if you are implementing it for the
%               first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
%         Hint: You can implement this around the code for
%               backpropagation. That is, you can compute the gradients for
%               the regularization separately and then add them to Theta1_grad
%               and Theta2_grad from Part 2.
%
h1_out = reshape([ones(m,1) sigmoid(X * Theta1')], m, size(Theta1,1) + 1);
h = sigmoid(h1_out * Theta2');
tmp_y = zeros(size(h));
for i = 1:m,
    tmp_y(i,y(i)) = 1;
end
y = tmp_y;
tmp_theta1 = Theta1;
tmp_theta2 = Theta2;
tmp_theta1(:,1) = 0;
tmp_theta2(:,1) = 0;

J = (-1/m)*sum(sum(y.*log(h)) + sum((1-y).*log(1 - h))) + ...
        (lambda/(2*m))*(sum(tmp_theta1(:) .^ 2) + sum(tmp_theta2(:) .^ 2));

a_1 = X;

z_2 = a_1 * Theta1';
a_2 = h1_out;

z_3 = h1_out * Theta2';
a_3 = h;

diff_3 = a_3 - y;
diff_2 = diff_3 * Theta2  .* sigmoidGradient([ones(size(z_2, 1), 1) z_2]);
diff_2 = diff_2(:,2:end);

delta_1 = diff_2' * a_1;
delta_2 =  diff_3' * a_2;

Theta1_grad = delta_1 ./ m + (lambda/m) .* tmp_theta1;
Theta2_grad = delta_2 ./ m + (lambda/m) .* tmp_theta2;

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

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


end