% Computer lab 2 & 3
% Johan Larsson
% Max Niia

function [ alpha, alphas ] = super_linearity(xi, r)
    syms x;

    % The first and second derivate of the polynomial
    xprim = diff(54*x^6 + 45*x^5 - 102*x^4 - 69*x^3 + 35*x^2 + 16*x - 4, x, 1);
    xbis  = diff(54*x^6 + 45*x^5 - 102*x^4 - 69*x^3 + 35*x^2 + 16*x - 4, x, 2);

    % The value of the first and second derivative f'(r) and f''(r)
    first = vpa(subs(xprim, x, r));
    second = vpa(subs(xbis, x, r));
    index = size(xi, 2) - 1;
    index2 = index - 1;
    e = abs(xi(index) - r);
    e1 = abs(xi(index2) - r);
    alphas = [];
    for i = 1:size(xi, 2) - 2
        e_i = abs(xi(i) - r);
        e_i1 = abs(xi(i + 1) - r);
        t_1 = (log(e_i1) + log(abs(second/(2*first))));
        n_1 = (log(e_i) + log(abs(second/(2*first))));
        alphas(i) = t_1/n_1;
    end

    t = (log(e) + log(abs(second/(2*first))));
    n = (log(e1) + log(abs(second/(2*first))));

    alpha = t/n;
end