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);
         
% 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
%
X = [ones([m,1]) X]; % Add column one to the left of matrix which is the bias unit.
a2 = sigmoid(X*Theta1') % Output of the hidden layer
a2 = [ones([size(a2,1),1]) a2] % The bias unit added
a3 = sigmoid(a2*Theta2') % Output of the NN.
y_t = zeros(size(y,2),m);
for n=1:m % Recoding the label 0~9 as vectors containing only values 0 or 1.
    if y(n)==0
        y_t(10,n)=1;
    else
        y_t(y(n),n)=1;
    end
end
y=y_t;
for n=1:m % Calculating cost function
    J = J + ((-1)*y(:,n)'*log(a3(n,:)')-(ones(size(y(:,n)))-y(:,n))'*log((ones(size(a3(n,:)))-a3(n,:))'))
end
J = J/m % Cost function without regularization

for n=2:size(Theta1,2)
    J=J+lambda/(2*m)*Theta1(:,n)'*Theta1(:,n);
end
for n=2:size(Theta2,2)
    J=J+lambda/(2*m)*Theta2(:,n)'*Theta2(:,n);
end % Regularized cost function

% 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.
%
tri1 = zeros(size(Theta1)); %Initialization
tri2 = zeros(size(Theta2));
for n=1:m
    delta3 = (a3(n,:)'-y(:,n)).*sigmoidGradient((a2(n,:)*Theta2')'); % Calculating the error of NN output 
    delta2 = Theta2'*delta3; % Calculating the error of the hidden layer output 
    delta2 = delta2(2:end);
    delta2 = delta2.*sigmoidGradient((X(n,:)*Theta1')');
    tri1=tri1+delta2*X(n,:);
    tri2=tri2+delta3*a2(n,:);
end
Theta1_grad = tri1/m;
Theta1_grad(:,2:end)=Theta1_grad(:,2:end)+lambda/m*Theta1(:,2:end); % Regularization added.
Theta2_grad = tri2/m;
Theta2_grad(:,2:end)=Theta2_grad(:,2:end)+lambda/m*Theta2(:,2:end); % Regularization added.
% 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.
%



















% -------------------------------------------------------------

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

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


end
