function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
%   X, y, lambda) computes the cost and gradient of the neural network. The
%   parameters for the neural network are "unrolled" into the vector
%   nn_params and need to be converted back into the weight matrices. 
% 
%   The returned parameter grad should be a "unrolled" vector of the
%   partial derivatives of the neural network.
%

% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
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);
mn1 = size(Theta1,2);
mn2 = size(Theta2,2);
n = size(Theta2,1);         
% 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.
%
Y = zeros(m,n);
for i = 1:m
	Y(i,y(i)) = 1;
end;

a1 = [ones(m, 1) X];

z2 = a1*Theta1';
zz2 =[zeros(m,1), z2];
a2 = sigmoid(z2);
a2 = [ones(m,1) a2];

z3 = a2*Theta2';
a3 = sigmoid(z3);

J = sum(sum(-Y.*log(a3)-(1-Y).*log(1-a3)))/m;

J = J + (sum(sum(Theta1(:,2:mn1).^2))+sum(sum(Theta2(:,2:mn2).^2)))*lambda/2/m;

delta3 = a3 - Y;
delta2 = delta3*Theta2.*sigmoidGradient(zz2);
%delta2 = delta2(:,2:end);

Theta1_grad = Theta1_grad + (delta2(:,2:end))'*a1;
Theta2_grad = Theta2_grad + (delta3)'*a2;

Theta1_remove1 = [zeros(size(Theta1,1),1) Theta1(:,2:end)];
Theta2_remove2 = [zeros(size(Theta2,1),1) Theta2(:,2:end)];
Theta1_grad = Theta1_grad/m + lambda/m * Theta1_remove1;
Theta2_grad = Theta2_grad/m + lambda/m * Theta2_remove2;
% -------------------------------------------------------------

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

% Unroll gradients

grad = [Theta1_grad(:) ; Theta2_grad(:)];


end

%==========Find the optimal paramter for neural network by minimizing the cost function==
%  Change the MaxIter to a larger value to see how more training helps.
%initial_Theta1 = randInitializeWeights(input_layer_size, hidden_layer_size);
%initial_Theta2 = randInitializeWeights(hidden_layer_size, num_labels);

% Unroll parameters
%initial_nn_params = [initial_Theta1(:) ; initial_Theta2(:)];
%options = optimset('MaxIter', 50);

%  You should also try different values of lambda
%lambda = 1;

% Create "short hand" for the cost function to be minimized
%costFunction = @(p) nnCostFunction(p, ...
%                                   input_layer_size, ...
%                                   hidden_layer_size, ...
%                                   num_labels, X, y, lambda);

% Now, costFunction is a function that takes in only one argument (the
% neural network parameters)
%[nn_params, cost] = fmincg(costFunction, initial_nn_params, options);

% Obtain Theta1 and Theta2 back from nn_params
%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));