% This program calls the BackpropCE and the BackpropXOR functions and
%trains the neural networks max_epoch times each. The squared sum of the output
%error (es1 and es2) is calculated at every epoch for each neural network, 
%and their average (E1 and E2) is calculated.

% W11 and W12: weights adjusted by the BackpropCE.m function.
% W21 and W22: weights adjusted by the BackproXOR.m function.

clear all
close all
clc

% Inputs:
X = [0 0 1;
     0 1 1;
     1 0 1;
     1 1 1];

% Desired outputs:
D = [0; 0; 1; 1];

Ne = 500;

% Average and weights initialization:
E1 = zeros(Ne, 1);
E2 = zeros(Ne, 1);
W11 = 2*rand(4, 3) - 1; % Cross entropy
W12 = 2*rand(1, 4) - 1; % Cross entropy
W21 = W11; % Sum of squared error
W22 = W12; % Sum of squared error

%Training processes:
max_epoch = Ne;
for epoch = 1:max_epoch
    [W11, W12] = BackpropCE(W11, W12, X, D);
    [W21, W22] = BackpropXOR(W21, W22, X, D);
    
    es1 = 0;
    es2 = 0;
    
    N = size(X,1);
    for k = 1:N
        x = X(k, :)';
        d = D(k);
        
        v1 = W11*x;
        y1 = Sigmoid(v1);
        v = W12*y1;
        y = Sigmoid(v);
        es1 = es1 + (d - y)^2;
        
        v1 = W21*x;
        y1 = Sigmoid(v1);
        v = W22*y1;
        y = Sigmoid(v);
        es2 = es2 + (d - y)^2;
    end
    E1(epoch) = es1/N;
    E2(epoch) = es2/N;
end

% Figure position and size
Figure_config = struct('PaperPositionMode','auto', ...
                       'Units','centimeters', ...
                       'Position',[5 9 30 20]); 
CEvsSSE_figure = figure();
set(CEvsSSE_figure, Figure_config);
plot(1:max_epoch, E1, 'r', 1:max_epoch, E2, 'b:', 'LineWidth', 2.5)
ax = gca;
ax.YGrid = 'on';
ax.FontSize = 20;
xlabel('Epoch')
ylabel('Average of Training error')
legend('Cross Entropy', 'Sum of Squared Errors')