ex1.m
代码语言：javascript复制%% Machine Learning Online Class - Exercise 1: Linear Regression
% Instructions
% ------------
%
% This file contains code that helps you get started on the
% linear exercise. You will need to complete the following functions
% in this exericse:
%
% warmUpExercise.m
% plotData.m
% gradientDescent.m
% computeCost.m
% gradientDescentMulti.m
% computeCostMulti.m
% featureNormalize.m
% normalEqn.m
%
% For this exercise, you will not need to change any code in this file,
% or any other files other than those mentioned above.
%
% x refers to the population size in 10,000s
% y refers to the profit in $10,000s
%
%% Initialization
clear ; close all; clc
%% ==================== Part 1: Basic Function ====================
% Complete warmUpExercise.m
fprintf('Running warmUpExercise ... n');
fprintf('5x5 Identity Matrix: n');
warmUpExercise()
fprintf('Program paused. Press enter to continue.n');
pause;
%% ======================= Part 2: Plotting =======================
fprintf('Plotting Data ...n')
data = load('ex1data1.txt');
X = data(:, 1); y = data(:, 2);
m = length(y); % number of training examples
% Plot Data
% Note: You have to complete the code in plotData.m
plot(X, y, 'rx','MarkerSize', 10);
ylabel('Profit in $10,000s');
xlabel('Population of City in 10,000s');
fprintf('Program paused. Press enter to continue.n');
pause;
%% =================== Part 3: Cost and Gradient descent ===================
X = [ones(m, 1), data(:,1)]; % Add a column of ones to x
theta = zeros(2, 1); % initialize fitting parameters
% Some gradient descent settings
iterations = 1500;
alpha = 0.01;
fprintf('nTesting the cost function ...n')
% compute and display initial cost
J = computeCost(X, y, theta);
fprintf('With theta = [0 ; 0]nCost computed = %fn', J);
fprintf('Expected cost value (approx) 32.07n');
% further testing of the cost function
J = computeCost(X, y, [-1 ; 2]);
fprintf('nWith theta = [-1 ; 2]nCost computed = %fn', J);
fprintf('Expected cost value (approx) 54.24n');
fprintf('Program paused. Press enter to continue.n');
pause;
fprintf('nRunning Gradient Descent ...n')
% run gradient descent
theta = gradientDescent(X, y, theta, alpha, iterations);
% print theta to screen
fprintf('Theta found by gradient descent:n');
fprintf('%fn', theta);
fprintf('Expected theta values (approx)n');
fprintf(' -3.6303n 1.1664nn');
% Plot the linear fit
hold on; % keep previous plot visible
plot(X(:,2), X*theta, '-')
legend('Training data', 'Linear regression')
hold off % don't overlay any more plots on this figure
% Predict values for population sizes of 35,000 and 70,000
predict1 = [1, 3.5] *theta;
fprintf('For population = 35,000, we predict a profit of %fn',predict1*10000);
predict2 = [1, 7] * theta;
fprintf('For population = 70,000, we predict a profit of %fn',predict2*10000);
fprintf('Program paused. Press enter to continue.n');
pause;
%% ============= Part 4: Visualizing J(theta_0, theta_1) =============
fprintf('Visualizing J(theta_0, theta_1) ...n')
% Grid over which we will calculate J
theta0_vals = linspace(-10, 10, 100);
theta1_vals = linspace(-1, 4, 100);
% initialize J_vals to a matrix of 0's
J_vals = zeros(length(theta0_vals), length(theta1_vals));
% Fill out J_vals
for i = 1:length(theta0_vals)
for j = 1:length(theta1_vals)
t = [theta0_vals(i); theta1_vals(j)];
J_vals(i,j) = computeCost(X, y, t);
end
end
% Because of the way meshgrids work in the surf command, we need to
% transpose J_vals before calling surf, or else the axes will be flipped
J_vals = J_vals';
% Surface plot
figure;
surf(theta0_vals, theta1_vals, J_vals)
xlabel('theta_0'); ylabel('theta_1');
% Contour plot
figure;
% Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100
contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 3, 20))
xlabel('theta_0'); ylabel('theta_1');
hold on;
plot(theta(1), theta(2), 'rx', 'MarkerSize', 10, 'LineWidth', 2);
