s2p2d - Optilab

clear; clc; close all;

% Dimension of A and b
n = 2;

% Generate all vectors x of dimension d with coordinates between -range and +range
step  = 1;
range = 20;
interval = -range:step:range; % the window of x to be observed regarding the set 'C'

% Generate all combinations in the defined range
x = combn(interval, n); x = x';

% your solution here

A = diag([-2 -3]); % A is Negative semi-definite
b = zeros(2,1);
c1 = -sqrt(2);
c2 = 100;

eig_A = eig(A);
eig_A(eig_A >= 0);
if numel(eig_A(eig_A >= 0)) == n
    disp('A is Positive semi-definite')
elseif numel(eig_A(eig_A <= 0)) == n
    disp('A is Negative semi-definite')
else
    disp('A is neither Positive nor Negative semi-definite')
end


% Plot the set C using the sign function
% the points inside the set 'C' should get the value (+1) and the points outside the set should get the value (-1).

Q = diag(x'*A*x) + (b'*x)'+ c1*ones(size(x,2),1);
Q_sign = -1*sign(Q);


figure();

surf(interval, interval, reshape(Q, [41, 41]));
title('c = -sqrt(2)');



Q = diag(x'*A*x) + (b'*x)'+ c2*ones(size(x,2),1);
Q_sign = -1*sign(Q);


figure();
surf(interval, interval, reshape(Q, [41, 41]));
title('c = 100');