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.
%
%
%X = [ones(size(X, 1), 1) X];

p = zeros(size(X, 1), 1);

h1 = sigmoid([ones(m, 1) X] * Theta1');
h2 = sigmoid([ones(m, 1) h1] * Theta2');

tempy = zeros(m, num_labels);

for k = 1:num_labels
    tempy(:, k) = (y == k);
endfor

K = num_labels;
for i = 1:m
    % iterativ
    %for k = 1:K
    %   temp_y = (y == k);
    %   J += -temp_y(i) * log(h2(i,k)) - (1 - temp_y(i)) * log(1 - h2(i,k));
    %endfor

    %vectorizat
    J += sum(-tempy(i, :) * log(h2(i, :)') - (1 - tempy(i, :)) * log(1 - h2(i, :)'));
endfor
J = J/m;

%vectorizat
J += lambda/(2*m) * (sum(sum(Theta1(:, 2:end) .* Theta1(:, 2:end)), 2) + sum(sum(Theta2(:, 2:end) .* Theta2(:, 2:end)), 2));

JCost = 0;
%for j = 1:25
    % iterativ
    %for k = 2:401
    %JCost += Theta1(j,k)*Theta1(j,k);
    %endfor
    %vectorized
%    JCost += sum(Theta1(j, 2:end) .* Theta1(j, 2:end));
%endfor

%for j = 1:10
    %iterativ
    %for k = 2:26
    %JCost += Theta2(j,k)*Theta2(j,k);
    %endfor
    %vectorized
%    JCost += sum(Theta2(j, 2:end) .* Theta2(j, 2:end));
%endfor



% -------------------------------------------------------------
Delta_1 = zeros(size(Theta1));
Delta_2 = zeros(size(Theta2));

for t = 1:m
    % Pasul 1
    a_1 = [1 ; X(t, :)'];
    z_2 = Theta1 * a_1;
    a_2 = [1 ; sigmoid(z_2)];
    z_3 = Theta2 * a_2;
    a_3 = sigmoid(z_3);

    % Pasul 2
    delta_3 = zeros(num_labels, 1);
    for k = 1:num_labels
        delta_3(k) = a_3(k) - (y == k)(t);
    endfor

    % Pasul 3
    delta_2 = (Theta2)' * delta_3 .* sigmoidGradient([1; z_2]);
    delta_2 = delta_2(2:end);

    Delta_1 = Delta_1 + delta_2 * (a_1');
    Delta_2 = Delta_2 + delta_3 * (a_2');
endfor

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

Theta1_grad(:, 1) = Delta_1(:, 1) ./ m;
Theta2_grad(:, 1) = Delta_2(:, 1) ./ m;

Theta1_grad(:, 2:end) = Delta_1(:, 2:end) ./ m + lambda/m .* Theta1(:, 2:end);
Theta2_grad(:, 2:end) = Delta_2(:, 2:end) ./ m + lambda/m .* Theta2(:, 2:end);
% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


end