clear all; close all; clcx = load(‘ex4x.dat‘); y = load(‘ex4y.dat‘);[m, n] = size(x);% Add intercept term to xx = [ones(m, 1), x]; % Plot the training data% Use different markers for positives and negativesfigurepos = find(y); neg = find(y == 0);plot(x(pos, 2), x(pos,3), ‘+‘)hold onplot(x(neg, 2), x(neg, 3), ‘o‘)hold onxlabel(‘Exam 1 score‘)ylabel(‘Exam 2 score‘)% Initialize fitting parameterstheta = zeros(n+1, 1);% Define the sigmoid functiong = inline(‘1.0 ./ (1.0 + exp(-z))‘); % Newton‘s methodMAX_ITR = 7;J = zeros(MAX_ITR, 1);for i = 1:MAX_ITR    % Calculate the hypothesis function    z = x * theta;    h = g(z);        % Calculate gradient and hessian.    % The formulas below are equivalent to the summation formulas    % given in the lecture videos.    grad = (1/m).*x‘ * (h-y);    H = (1/m).*x‘ * diag(h) * diag(1-h) * x;        % Calculate J (for testing convergence)    J(i) =(1/m)*sum(-y.*log(h) - (1-y).*log(1-h));        theta = theta - H\grad;end% Display thetatheta% Calculate the probability that a student with% Score 20 on exam 1 and score 80 on exam 2 % will not be admittedprob = 1 - g([1, 20, 80]*theta)% Plot Newton‘s method result% Only need 2 points to define a line, so choose two endpointsplot_x = [min(x(:,2))-2,  max(x(:,2))+2];% Calculate the decision boundary lineplot_y = (-1./theta(3)).*(theta(2).*plot_x +theta(1));plot(plot_x, plot_y)legend(‘Admitted‘, ‘Not admitted‘, ‘Decision Boundary‘)hold off% Plot Jfigureplot(0:MAX_ITR-1, J, ‘o--‘, ‘MarkerFaceColor‘, ‘r‘, ‘MarkerSize‘, 8)xlabel(‘Iteration‘); ylabel(‘J‘)% Display JJ