clear  all; 
clc;
data = load('ex1data1.txt');
X = data(:, 1); y = data(:, 2);
m = length(y); % number of training examples
plot(X,y,'rx');

%% =================== Part 3: Gradient descent ===================
fprintf('Running Gradient Descent ...\n')

%为什么加上一列1，为了算J时候，theta0 乘以1
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;

% compute and display initial cost
computeCost(X, y, theta)

% run gradient descent
[theta, J_history]= gradientDescent(X, y, theta, alpha, iterations);

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 %f\n',...
    predict1*10000);
predict2 = [1, 7] * theta;
fprintf('For population = 70,000, we predict a profit of %f\n',...
    predict2*10000);

% 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
%以10为底的指数 logspace(-2, 3, 20)坐标值标注范围以及间距
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);

function J = computeCost(X, y, theta)

m = length(y); % number of training examples 
J = 0;

for i=1:m
    J = J +(theta(1)*X(i,1) + theta(2)*X(i,2) - y(i))^2;  
end
% 除以2m是为了在更新参数的时候 好算   2因为J是二次，求骗到后产生系数2，
%m是为了不让J 过大（i=1:m已经是求偏导第二部的m、项了）
J = J/(m*2);
end

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)

m = length(y); % number of training examples
J_history = zeros(num_iters, 1);
J_1 = 0;% 偏导数J_1, J_2
J_2 = 0;
for iter = 1:num_iters
    for i = 1:m
        J_1 = J_1 + theta(1)*X(i,1) + theta(2)*X(i,2) - y(i);
        J_2 = J_2 + (theta(1)*X(i,1) + theta(2)*X(i,2) - y(i)) * X(i,2);
    end
    %J中的m 没有在上面的for内除，因为只除以一次就够了
    J_1 = J_1/m;
    J_2 = J_2/m;
%     temp1 = theta(1) - alpha * J_1;
%     temp2 = theta(2) - alpha * J_2;
%     theta(1) = temp1;
%     theta(2) = temp2;
    theta(1) = theta(1) - alpha * J_1;
    theta(2) = theta(2) - alpha * J_2;
    J_history(iter) = computeCost(X, y, theta);  
%     save J_history J_history
end
end