y = lineal_regress(V, b2f);
%y = kvadr_regress(V, b1f);
%y = stepen_poly(V, b1f);
k = plot_disp_loss(V, b2f, y);

function y=lineal_regress(V, bf)
    A = [sum(V) length(V);
        sum(V.^2) sum(V)];
    B = [sum(bf) sum(V .* bf)]';
    x = A\B;
    a = x(1);
    b = x(2);
    y = a*V + b;
end

function y = kvadr_regress(V, bf)
    A = [sum(V.^2) sum(V) length(V);
         sum(V.^3) sum(V.^2) sum(V);
         sum(V.^4) sum(V.^3) sum(V.^2)];
    B = [sum(bf) sum(V .* bf) sum(V.^2 .* bf)]';
    x = A\B;
    a = x(1);
    b = x(2);
    c = x(3);
    y = a * V.^2 + b * V + c;
end

function y = stepen_poly(V, bf)
    A = [length(V) sum(log(V));
        sum(log(V)) sum(log(V).^2)];
    B = [sum(log(bf)) sum(log(bf).*log(V))]';
    x = A\B;
    a = exp(x(1));
    b = x(2);
    y = a * V.^b;
end

function y = loss_fn(bf, res)
    y = 1/length(bf) * sum(abs((bf - res)./bf));
end

function loss = plot_disp_loss(V, bf, res)
    loss = loss_fn(bf, res);
    disp("loss is: " + loss * 100 + "%");
    figure('Color', 'w');
    plot(V, bf, 'r');
    hold on;
    plot(V, res, 'b');
end
///////////////////////////////////////////////////////////////////////////////////////////////////////////


%disp(V);
%disp(b1f);

%disp(a);
%disp(b);
y = regr_n_degree(tt(2:length(tt))', xx(2:length(tt))', 10);
k = build_plot_disp_loss(tt(2:end)', xx(2:end)', y);

function y=lineal_regress(V, bf)
    A = [sum(V) length(V);
        sum(V.^2) sum(V)];
    B = [sum(bf) sum(V .* bf)]';
    x = A\B;
    a = x(1);
    b = x(2);
    y = a*V + b;
end

function y = kvadr_regress(V, bf)
    A = [sum(V.^2) sum(V) length(V);
         sum(V.^3) sum(V.^2) sum(V);
         sum(V.^4) sum(V.^3) sum(V.^2)];
    B = [sum(bf) sum(V .* bf) sum(V.^2 .* bf)]';
    x = A\B;
    a = x(1);
    b = x(2);
    c = x(3);
    y = a * V.^2 + b * V + c;
end

function y = regr_n_degree(V, bf, degree)
    A = [];
    pow = [0:degree];
    for k=0:degree
        tmp = V' .^ pow;
        A = [sum(tmp, 1)' A];
        pow = pow + 1;
    end
    A(1, end) = length(V);
    pow = [0:degree];
    B = sum((V' .^ pow).* bf', 1)';
    pow = [degree:-1:0];
    coeffs = A\B;
    tmp = V' .^ pow;
    y = sum(tmp .* coeffs', 2)';
end


function y = stepen_poly(V, bf)
    A = [length(V) sum(log(V));
        sum(log(V)) sum(log(V).^2)];
    B = [sum(log(bf)) sum(log(bf).*log(V))]';
    x = A\B;
    a = exp(x(1));
    b = x(2);
    y = a * V.^b;
end

function y = loss_fn(bf, res)
    y = 1/length(bf) * sum(abs((bf - res)./(bf)));
    %disp(bf);
end

function loss = build_plot_disp_loss(V, bf, res)
    loss = loss_fn(bf, res);
    disp("loss is: " + loss * 100 + "%");
    figure('Color', 'w');
    plot(V, bf, 'r');
    hold on;
    plot(V, res, 'b');
end
///////////////////////////////////////////////////////////////////////////////////////////////////////////
x = tt(2:end);
y = xx(2:end);
A = [ (exp(-5*x).*cos(5*x)) (exp(-5*x).*sin(5*x)) ones(length(tt) - 1, 1)];
%disp(A);
res = A \ y;
%disp(res);
x1 = @(x) exp(-5*x).*cos(5*x).*res(1) + exp(-5*x).*sin(5*x).*res(2) + res(3);
%values1 = exp(-5*tt').*cos(5*tt').*res(1) + exp(-5*tt').*sin(5*tt').*res(2) + res(3);
values1 = x1(tt);
c4 = yy(3) - res(2).*exp(-5*tt(3)).*cos(5*tt(3)) + exp(-5*tt(3)).*res(1).*sin(5*tt(3));
x2 = @(x) -exp(-5*x).*sin(5*x).*res(1) + exp(-5*x).*cos(5*x).*res(2) + c4;
%values2 = -exp(-5*tt').*sin(5*tt').*res(1) + exp(-5*tt').*cos(5*tt').*res(2) + c4;
values2 = x2(tt);

plot(tt', values2, 'r');
hold on;
plot(tt', yy', 'b*');

%plot(x1(tt)', x2(x1(tt)), 'r');