clc
clear
close all

%% Exercise 2.1

syms x1 x2
c1 = 2 * x1 + 3 * x2 - 6;
c2 = -3 * x1 + 2 * x2 - 3;
c3 = 2 * x2 - 5;
c4 = 2 * x1 + x2 - 4;

c1 = solve(c1 == 0, x2, 'Real', true);
c2 = solve(c2 == 0, x2, 'Real', true);
c3 = solve(c3 == 0, x2, 'Real', true);
c4 = solve(c4 == 0, x2, 'Real', true);

i1 = solve(c1 == c2, x1, 'Real', true);
i2 = solve(c1 == c4, x1, 'Real', true);
i3 = solve(c4 == 0, x1, 'Real', true);

px = double([0 0 i1 i2 i3]);
py = double([0 subs(c2, x1, 0) subs(c1, x1, i1) subs(c4, x1, i2) subs(c4, x1, i3)]); 

xl = -0.05;
xh = 2.05;

colors = [224/255 6/255 191/255; 0 0 1; 1 0 0; 0 1 0];

axis([-0.05 2.05 -0.15 5.15])
i = 1;
hold on
for c = [c1 c2 c3 c4]
    %plot([xl, xh], [subs(c, x1, xl), subs(c, x1, xh)]);
    hatchfill(patch([xl, xl, xh, xh], ...
              double([-0.15, subs(c, x1, xl), subs(c, x1, xh), -0.15]), ...
              colors(i, :)), ...
        'HatchColor', colors(i, :), 'HatchOffset', (i-1)/5, 'HatchAngle', 45);
    i = i + 1;
end
%xline(0);
hatchfill(patch([0, 0, xh, xh], ...
              double([0, 5.15, 5.15, 0]), ...
              'white'), ...
        'HatchColor', [249/255 216/255 49/255], 'HatchOffset', 4/5, 'HatchAngle', 45);
%plot([xl, xh], [0, 0]);
hatchfill(patch(px, py, 'black'),'HatchColor', 'black', 'HatchAngle', 90);
alpha(.02)
legend('','2x1 + 3x2 <= 6', '', '-3x1 + 2x2 <= 3', '', '2x2 <= 5', ...
    '', '2x1 + x2 <= 4', '', 'x1 > 0 and x2 > 0', '', 'feasible region');
hold off

%% Exercise 3.2

G = [6 2 1; 2 5 2; 1 2 4];
c = [-8; -3; -3];
A = [1 0 1; 0 1 1];
b = [3; 0];

[x, lambda] = uzawa(G, c, A, b, [0;0;0], [0;0], 1e-8, 100);
display(x);
display(lambda);