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.
%

% Add ones to the X data matrix
X = [ones(m, 1) X];


%get the first layer vals...
z2 = X*Theta1';
a2 = sigmoid(z2);

%next layer vals...
a2b = [ones(size(a2,1), 1) a2];

z3 = a2b*Theta2';

a3 = sigmoid(z3);

%[maxval, index] = max(a3, [], 2);

%set y to the number of labels...
y_temp=eye(num_labels)(y,:);

%no reg...
J = 1/m * sum(sum(-1 * y_temp .* log(a3)-(1-y_temp) .* log(1-a3)));

%with reg...
%reg = (lambda / (2*m)) * Theta1(2:end,:)' * Theta2(2:end,:);


%blarg! i forgot i need square sums...
reg = (lambda / (2*m)) *(sum(sumsq(Theta1(:,2:end)))+sum(sumsq(Theta2(:,2:end))));

J = J + reg;

%reg = (lambda / (2*m)) * Theta1(2:end,:)' * Theta1(2:end,:);
%J = (1/m) * (-y' * log(sigmoid(X * theta)) - ((1 - y)' * log(1 -sigmoid(X * theta)))) + reg;
%%do this for the rest of the terms...
%grad = (1/m) * (X' * (sigmoid(X * theta) - y)) + (lambda / m * theta);
%%do this for theta 0
%grad(1) = (1/m) * (X(:,1)' * (sigmoid(X * theta(:,1)) - y));



%WOOO here we go...
%let's try vector version
%delta3
d3 = a3 - y_temp;

%delta2
d2a = [ones(size(z2, 1), 1) sigmoidGradient(z2)];
d2b = (d3 * Theta2);

d2 = d2b .* d2a;
 
%strip the extra
d2 = d2(:, 2:end); 

Theta1_grad = Theta1_grad + d2' * X; 
Theta2_grad = Theta2_grad + d3' * a2b;

%no reg...
Theta1_grad = (1/m) * Theta1_grad; 
Theta2_grad = (1/m) * Theta2_grad;

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










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

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

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


end
