/
run.m
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run.m
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%% Initialization
clear ; close all; clc
%% ======================= 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
plotData(X, y);
fprintf('Program paused. Press enter to continue.\n');
pause;
%% =================== Part 3: Gradient descent ===================
fprintf('Running Gradient Descent ...\n')
X = [ones(m, 1), data(:,1)]; % Add a column of ones to x
theta = zeros(2, 1); % initialize fitting parameters [theta_0; theta_1]
% Some gradient descent settings
iterations = 15;
alpha = 0.01;
% compute and display initial cost
computeCost(X, y, theta)
% run gradient descent
[theta, J] = stochasticDescent(X, y, theta, alpha, iterations);
% print theta to screen
fprintf('Theta found by gradient descent: ');
fprintf('%f %f \n', theta(1), theta(2));
% 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
figure
plot(J);
hold on
legend('J_{train} averaged every 1000 grad calculations')
xlabel('Number of Steps');
ylabel('Log of the Training Cost (L2 norm of difference)');
hold off
% 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 %f\n',...
% predict1*10000);
% predict2 = [1, 7] * theta;
% fprintf('For population = 70,000, we predict a profit of %f\n',...
% 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);