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
%
% 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.
%
temp = zeros(m,num_labels);
for j = 1:size(y,1)
temp(j,y(j)) = 1;
endfor
y = temp;
X = [ones(m,1) X];
a2 = sigmoid(X * Theta1');
a3 = sigmoid([ones(size(a2,1),1) a2] * Theta2');
J = 1/m * sum(sum((-y).*log(a3) - (1-y).*log(1-a3)))+ lambda/(2*m)*...
(sum(sum(Theta1(:,2:input_layer_size+1).^2)) + sum(sum(Theta2(:,2:hidden_layer_size+1).^2)));
Error_3 = a3 - y;
sigmoidgrad1 = sigmoidGradient(X * Theta1');
Error_2 = Error_3 * Theta2 .* [ones(size(sigmoidgrad1,1),1) sigmoidgrad1];
Theta1_grad =1/m * Error_2(:,2:end)' * X + lambda/m * [zeros(size(Theta1,1),1) Theta1(:,2:end)];
Theta2_grad =1/m * Error_3' * [ones(size(a2,1),1) a2] + lambda/m * [zeros(size(Theta2,1),1) Theta2(:,2:end)];
% -------------------------------------------------------------
% =========================================================================
% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];
end
