function [W1, W2, W3, W4] = DeepReLU(W1, W2, W3, W4, X, D)

%The function DeepReLU trains the given deep neural network using the 
%back-propagation algorithm. It takes the weights of the network and 
%training data and returns the trained weights.

    alpha = 0.01;
    
    N = size(X,3); %number of samples
    for k = 1:N
        x = reshape(X(:, :, k), 25, 1);  %reorganizes the k-th sample into a 25x1 vector
        d = D(k, :)';   %desired output
        
        v1 = W1*x;
        y1 = ReLU(v1);
        
        v2 = W2*y1;
        y2 = ReLU(v2);
        
        v3 = W3*y2;
        y3 = ReLU(v3);
        
        v = W4*y3;
        y = Softmax(v);
        
        e = d - y;
        delta = e;
        
        e3 = W4'*delta;
        delta3 = (v3 > 0).*e3;
        
        e2 = W3'*delta3;
        delta2 = (v2 > 0).*e2;
        
        e1 = W2'*delta2;
        delta1 = (v1 > 0).*e1;
        
        dW4 = alpha*delta*y3';
        W4 = W4 + dW4;
        
        dW3 = alpha*delta3*y2';
        W3 = W3 + dW3;
        
        dW2 = alpha*delta2*y1';
        W2 = W2 + dW2;
        
        dW1 = alpha*delta1*x';
        W1 = W1 + dW1;
    end
end