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       X            W     pred    y
5.1 3.5 1.4 0.2    0.5    0.00    0
4.9 3.0 1.4 0.2    0.5    0.00    0
6.2 3.4 5.4 2.3    0.5    0.99    1
5.9 3.0 5.1 1.8    0.5    0.99    1

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vector pred = sigmoid(dot(X, W, 4, 4, 1 ) );

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vector <float> dot (const vector <float>& m1, const vector <float>& m2, 
                    const int m1_rows, const int m1_columns, const int m2_columns) {
    
    /*  Returns the product of two matrices: m1 x m2.
        Inputs:
            m1: vector, left matrix of size m1_rows x m1_columns
            m2: vector, right matrix of size m1_columns x m2_columns 
                (the number of rows in the right matrix must be equal 
                to the number of the columns in the left one)
            m1_rows: int, number of rows in the left matrix m1

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vector<float> pred_error = y - pred;

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vector<float> pred_delta = pred_error * sigmoid_d(pred);

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vector W_delta = dot(transpose( &X[0], 4, 4 ), pred_delta, 4, 4, 1);

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W = W + W_delta;

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vector<float> X {
    5.1, 3.5, 1.4, 0.2,
    4.9, 3.0, 1.4, 0.2,
    6.2, 3.4, 5.4, 2.3,
    5.9, 3.0, 5.1, 1.8
};

vector<float> y {
    0,
    0,

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vector <float> operator-(const vector <float>& m1, const vector <float>& m2){
    
    /*  Returns the difference between two vectors.
        Inputs:
            m1: vector
            m2: vector
        Output: vector, m1 - m2, difference between two vectors m1 and m2.
    */
    
    const unsigned long VECTOR_SIZE = m1.size();

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vector <float> sigmoid_d (const vector <float>& m1) {
    
    /*  Returns the value of the sigmoid function derivative f'(x) = f(x)(1 - f(x)), 
        where f(x) is sigmoid function.
        Input: m1, a vector.
        Output: x(1 - x) for every element of the input matrix m1.
    */
    
    const unsigned long VECTOR_SIZE = m1.size();
    vector <float> output (VECTOR_SIZE);