coursera_machine_learning_ex/ex4/nnCostFunction.m

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

m = size(X, 1);
% You need to return the following variables correctly 
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));
           
ThetaGrad1 = zeros(size(Theta1));
ThetaGrad2 = zeros(size(Theta2));

a1 = [ones(size(X, 1),1) X]';
z2 = Theta1 * a1;
a2 = [ones(1, size(z2,2)); sigmoid(z2)];
z3 = Theta2 * a2;
a3 = sigmoid(z3);
y_map = zeros(length(y), num_labels);
for i = 1:length(y_map)
    y_map(i, y(i)) = 1;
end

d3 = a3 - y_map';
t = Theta2' * d3;


d2 = t(2:end,:) .* sigmoidGradient(z2);
ThetaGrad2 = ThetaGrad2 + d3 * a2';
ThetaGrad1 = ThetaGrad1 + d2 * a1';


ThetaGrad1 = ThetaGrad1 + lambda * [zeros(size(Theta1,1),1) Theta1(:,2:end)];
ThetaGrad2 = ThetaGrad2 + lambda * [zeros(size(Theta2,1),1) Theta2(:,2:end)];

grad = [ThetaGrad1(:); ThetaGrad2(:)];
grad = grad / m;
J = mean(sum( - y_map' .* log(a3) + (y_map' -1) .* log(1 - a3)));
J = J + lambda * 0.5 / size(X, 1) * (sum(sum(Theta1(:,2:end) .^2)) + sum(sum(Theta2(:,2:end) .^2)));
% ====================== 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.
%



















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

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

% Unroll gradients



end