%% Exercise 3.1

% f(x1, x2) = x1^2 + u * x2^2;

% [x1 x2] [1 0] [x1] + [0][x1]
%         [0 u] [x2] + [0][x2]

% A = [1 0; 0 u]; b = [0; 0]

%% Exercise 3.2


for u = 1:10
    A = [1 0; 0 u];

    xs = -10:1:10;
    ys = xs;

    Z = zeros(size(xs, 2), size(ys, 2));

    for i = 1:size(xs, 2)
        for j = 1:size(ys, 2)
            vec = [xs(i); ys(j)];
            Z(i, j) = vec' * A * vec;
        end
    end

    if u <= 5
        fig = u;
        con = 5 + u;
    else
        fig = 10 + u - 5;
        con = 15 + u - 5;
    end
    
    subplot(4, 5, fig);
    h = surf(xs, ys, Z);
    set(h,'LineStyle','none');
    title(sprintf("Surf for u=%d", u));
    subplot(4, 5, con);
    contour(xs, ys, Z, 20);
    title(sprintf("Contour for u=%d", u));
end