s7_p2_optilab

clear; close all; clc;

load data_l1_trend_filtering.mat;

N = length(yti);

% your solution here %
figure();
plot(yti); hold on
%% variables

% Creating A
A= zeros(N-1, N);

for i = 1:N-1
    A(i, i)=-1;
    A(i, i+1) = 1;
end

%creating gamma
gamma = 5;
gammas = linspace(1, 40, 20);

trade_off = zeros(2, 20);

%% CVX

for gamma = 1 : size(gammas, 2)
    cvx_begin
        variable x_head(N);
        %minimize( sqrt( (yti - x_head)'*(yti - x_head) )  +  gamma * sqrt( (A*x_head)'*(A*x_head) )  );
        %minimize( (yti - x_head)'*(yti - x_head)  +  gamma * (A*x_head)'*(A*x_head)   );
        minimize( norm( (yti - x_head) )  +  gamma * norm( (A*x_head) )  );

    cvx_end

    trade_off(1, gamma) = norm( (A*x_head) );
    trade_off(2, gamma) = norm( (yti - x_head) );

end
figure();
plot(trade_off(2, :),trade_off(1, :) );