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% ------ Question 2 Script ------ %
clc;
clear;
oring = [
1.00000 53.00000 1.00000
2.00000 57.00000 1.00000
3.00000 58.00000 1.00000
4.00000 63.00000 1.00000
5.00000 66.00000 0.00000
6.00000 66.80000 0.00000
7.00000 67.00000 0.00000
8.00000 67.20000 0.00000
9.00000 68.00000 0.00000
10.00000 69.00000 0.00000
11.00000 69.80000 1.00000
12.00000 69.80000 0.00000
13.00000 70.20000 1.00000
14.00000 70.20000 0.00000
15.00000 72.00000 0.00000
16.00000 73.00000 0.00000
17.00000 75.00000 0.00000
18.00000 75.00000 1.00000
19.00000 75.80000 0.00000
20.00000 76.20000 0.00000
21.00000 78.00000 0.00000
22.00000 79.00000 0.00000
23.00000 81.00000 0.00000 ];
% Set options for fminunc
options = optimset('GradObj', 'on', 'MaxIter', 400);
temp = oring(:,2);
o_ringTF = oring(:,3);
% Run fminunc to obtain the optimal theta
% This function will return theta and the cost
[theta, cost] = fminunc(@(a)(cost_logistic(a, temp, o_ringTF)), [80 -1], options)
% part c'
e = exp(1);
sigma = @(t) 1./(1 + e.^(-t));
plot(temp,o_ringTF,'o',temp,sigma(theta(1) + theta(2).*temp))