clear ; close all; clc
data = load('ex2data1.txt');
X = data(:, [1, 2]); y = data(:, 3);
fprintf(['Plotting data with + indicating (y = 1) examples and o ' ...
         'indicating (y = 0) examples.\n']);
plotData(X, y);
hold on;
xlabel('Exam 1 score')
ylabel('Exam 2 score')
legend('Admitted', 'Not admitted')
hold off;
[m, n] = size(X);
X = [ones(m, 1) X];
initial_theta = zeros(n + 1, 1);
[cost, grad] = costFunction(initial_theta, X, y);
fprintf('Cost at initial theta (zeros): %f\n', cost);
fprintf(' %f \n', grad);
test_theta = [-24; 0.2; 0.2];
[cost, grad] = costFunction(test_theta, X, y);
fprintf('\nCost at test theta: %f\n', cost);
fprintf(' %f \n', grad);
options = optimset('GradObj', 'on', 'MaxIter', 400);%運用自動選擇α的函式的options
[theta, cost] = ...
fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
fprintf('Cost at theta found by fminunc: %f\n', cost);
fprintf('Expected cost (approx): 0.203\n');
fprintf('theta: \n');
fprintf(' %f \n', theta);
fprintf('Expected theta (approx):\n');
fprintf(' -25.161\n 0.206\n 0.201\n');
plotDecisionBoundary(theta, X, y);
hold on;
xlabel('Exam 1 score')
ylabel('Exam 2 score')
legend('Admitted', 'Not admitted')
hold off;
fprintf('\nProgram paused. Press enter to continue.\n');
pause;

prob = sigmoid([1 45 85] * theta);%預測考45和85分的同學能不能過，過的概率
fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
         'probability of %f\n'], prob);
% Compute accuracy on our training set
p = predict(theta, X);
fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
fprintf('Expected accuracy (approx): 89.0\n');

fprintf('\n');

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function plotData(X, y)
figure; hold on;
pos=find(y==1);
neg=find(y==0);
plot(X(pos,1),X(pos,2),'k+','LineWidth',2,'MarkerSize',7,'Color',[1 0 0]);
plot(X(neg,1),X(neg,2),'ko','LineWidth',2,'MarkerSize',7,'Color',[0.3 0.8 0.9]);
legend('pos','neg');
xlabel('exam 1 score');
ylabel('exam 2 score');

title('picture')

hold off;

end

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function [J, grad] = costFunction(theta, X, y)
m = length(y); % number of training examples
J = 0;
grad = zeros(size(theta));
J=((-y)'*log(sigmoid(X*theta))-(1-y)'*log(1-sigmoid(X*theta)))/m;
grad=((sigmoid(X*theta)-y)'*X)/m;

end

function g = sigmoid(z)
g=1./(1+exp(-z));
end

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function plotDecisionBoundary(theta, X, y)
%PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with
%the decision boundary defined by theta
%   PLOTDECISIONBOUNDARY(theta, X,y) plots the data points with + for the 
%   positive examples and o for the negative examples. X is assumed to be 
%   a either 
%   1) Mx3 matrix, where the first column is an all-ones column for the 
%      intercept.
%   2) MxN, N>3 matrix, where the first column is all-ones
% Plot Data
plotData(X(:,2:3), y);
hold on
if size(X, 2) <= 3
    % Only need 2 points to define a line, so choose two endpoints
    plot_x = [min(X(:,2))-2,  max(X(:,2))+2];
    % Calculate the decision boundary line
    plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));
    % Plot, and adjust axes for better viewing
    legend('Admitted', 'Not admitted', 'Decision Boundary')
    axis([30, 100, 30, 100])
else
    % Here is the grid range
    u = linspace(-1, 1.5, 50);
    v = linspace(-1, 1.5, 50);


    z = zeros(length(u), length(v));
    % Evaluate z = theta*x over the grid
    for i = 1:length(u)
        for j = 1:length(v)
            z(i,j) = mapFeature(u(i), v(j))*theta;
        end
    end
    z = z'; % important to transpose z before calling contour


    % Plot z = 0
    % Notice you need to specify the range [0, 0]
    contour(u, v, z, [0, 0], 'LineWidth', 2)
end
hold off


end

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function p = predict(theta, X)
m = size(X, 1); % Number of training examples
p = zeros(m, 1);
v=sigmoid(X*theta);
for i=1:m
    if v(i,1)>=0.5
        p(i,1)=1;
    else
        p(i,1)=0;
end
end