function p = predict(Theta1, Theta2, X)
%PREDICT Predict the label of an input given a trained neural network
%   p = PREDICT(Theta1, Theta2, X) outputs the predicted label of X given the
%   trained weights of a neural network (Theta1, Theta2)

% Useful values
m = size(X, 1);
num_labels = size(Theta2, 1);

% You need to return the following variables correctly
p = zeros(size(X, 1), 1);

% ====================== YOUR CODE HERE ======================
% Instructions: Complete the following code to make predictions using
%               your learned neural network. You should set p to a
%               vector containing labels between 1 to num_labels.
%
% Hint: The max function might come in useful. In particular, the max
%       function can also return the index of the max element, for more
%       information see 'help max'. If your examples are in rows, then, you
%       can use max(A, [], 2) to obtain the max for each row.
%

% Theta1 has size 25x401
% Theta2 has size 10x26

a1 = [ones(m, 1) X];
% a1 has size mx401

a2_tmp = sigmoid(a1 * Theta1');
% a2_tmp has size m x 401 * 401 x 25 = m x 25
a2 = [ones(m, 1) a2_tmp];
% a2 has size m x 26

a3 = sigmoid(a2 * Theta2');
% a3 has size m x 26 * 26 x 10 = m x 10
% note: sigmoid not actually neded here (arg max(sigmoid(z)) = arg max(z))

[~, p] = max(a3, [], 2);

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


end