cache = true;

if cache
    load("I.mat");
else
    tau_min = 0;
    tau_max = 10;
    tau_interval = 0.1;
    tau_range = tau_min:tau_interval:tau_max;

    s_b_min = 1;
    s_b_max = 32;
    s_b_range = s_b_min:s_b_max;

    result = zeros(1, 32);

    m = 4;

    I = zeros(length(tau_range), 0);

    for tau_idx = 1:length(tau_range)
        tau = tau_range(tau_idx);
        I(tau_idx) = calc_int(tau, m);
    end

end

%%

for s_b_idx = 1:length(s_b_range)
    s_b = s_b_range(s_b_idx);
    f_set = zeros(length(tau_range), 1);

    for tau_idx = 1:length(tau_range)
        tau = tau_range(tau_idx);
        f_set(tau_idx) = s_b * (1 + tau ^ 2) + (100 - s_b) * I(tau_idx);
    end

    t = min(f_set);
    result(s_b_idx) = t;
end

plot(s_b_range, result);