clear all; close all;
% Wybor solvera
cvx_solver('sdpt3');

%% Opis zadania


%% Rozwiazanie z wykorzystaniem biblioteki CVX - metoda GP (EXAMPLE 1)
y1 = [1.8; 2.5];
y2 = [2.0; 1.7];
y3 = [1.5; 1.5];
y4 = [1.5; 2.0];
y5 = [2.5; 1.5];

d1 = 2;
d2 = 1.24;
d3 = 0.59;
d4 = 1.31;
d5 = 1.44;

A = [-2 * y1' 1; -2 * y2' 1; -2 * y3' 1; -2 * y4' 1; -2 * y5' 1];

% b = [double(d1^2 - norm(y1)); double(d2^2 - norm(y2)); double(d3^2 - norm(y3));
%    double(d4^2 - norm(y4)); double(d5^2 - norm(y5))];

b = [d1^2 - norm(y1); d2^2 - norm(y2); d3^2 - norm(y3); d4^2 - norm(y4);
   d5^2 - norm(y5)];

c1 = eye(2);
c2 = zeros(2,1);
c3 = zeros(1,2);
c4 = 0;

C = [c1 c2; c3 c4];

f = [c2; -0.5];

cvx_begin sdp
    variables s v
    minimize s - norm(b,2)
    % ograniczenia wynikajace z zadania
    subject to:
        % nnmf([A' * A + v * C A' * b - v * f; (A' * b - v * f)' s])
        min(eig([A' * A + v * C A' * b - v * f; (A' * b - v * f)' s])) >= 0;
cvx_end
v