A = eye(5,5)

data = load('ex1data1.txt');  %加载ex1data1.txt数据
X = data(:, 1); y = data(:, 2);  %取第一列的全部数据为X，第二列为y
m = length(y);   %m等于训练样本个数

plot(x, y, 'rx', 'MarkerSize', 10);
ylabel('Profit in $10,000s');       %设定y轴标题
xlabel('Population of City in 10,000s');   %设定x轴标题

X = [ones(m, 1), data(:,1)]; % 在x中添加一列
theta = zeros(2, 1); % 初始化拟合参数
iterations = 1500;
alpha = 0.01;

function J = computeCost(X, y, theta)
%COMPUTECOST Compute cost for linear regression
%   J = COMPUTECOST(X, y, theta) computes the cost of using theta as the
%   parameter for linear regression to fit the data points in X and y% Initialize some useful values
m = length(y); % number of training examples% You need to return the following variables correctly
J = 0;% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta
%               You should set J to the cost.J = (1/(2*m)) *((X * theta-y)'*(X*theta-y));% ============================================================
end

predict1 = [1, 3.5] * theta;
predict2 = [1, 7] * theta;
function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
%   theta = GRADIENTDESCENT(X, y, theta, alpha, num_iters) updates theta by
%   taking num_iters gradient steps with learning rate alpha% Initialize some useful values
m = length(y); % number of training examples
J_history = zeros(num_iters, 1);for iter = 1:num_iters% ====================== YOUR CODE HERE ==================% Instructions: Perform a single gradient step on the parameter vector%               theta. %% Hint: While debugging, it can be useful to print out the values%       of the cost function (computeCost) and gradient here.%theta = theta - (alpha/m) * (X'*(X*theta-y));% ========================================================% Save the cost J in every iteration    J_history(iter) = computeCost(X, y, theta);
end
end