clc;
clear all;
close all;

load('lab8_4.mat');

yid = id.Y;
uid = id.U;

plot(id)

counter = 1;
theta(:,counter) = [.20; 1];

alpha = 0.00001;
N = length(yid);

[E,e]=epsilon(theta,uid,yid,N);
V=gradient(E,e,N);
H=hessian(e,N);
theta(:, counter+1) = theta(:,counter) - alpha*inv(H)*V;
counter = counter + 1;

while (counter <= N || norm(theta(:,counter) - theta(:,counter-1)) >= 1e-6)
    [E,e]=epsilon(theta,uid,yid,N);
    V=gradient(E,e,N);
    H=hessian(e,N);
    theta(:, counter+1) = theta(:,counter) - alpha*inv(H)*V;
    counter = counter+1;
end

thetap = theta(:, counter);
B=[0 thetap(2,1)];
F=[1 thetap(1,1)];
model = idpoly(1,B,1,1,F,0,id.Ts);
figure;
compare(model, val);