function A = warmUpExercise()

A = [];

A = eye(5);

end

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);

function plotData(x, y)

figure;

plot(x,y,'rx','MarkerSize',10);

ylabel('Profit in $10,000s');

xlabel('Population of City in 10,000s');

end　

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;

% run gradient descent

theta = gradientDescent(X, y, theta, alpha, iterations);

% print theta to screen

fprintf('Theta found by gradient descent:\n');

fprintf('%f\n', theta);

% 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　　

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

% Initialize some useful values

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

J_history = zeros(num_iters, 1);

for iter = 1:num_iters

    theta = theta - alpha/length(y)*(X'*(X*theta-y))；

    % Save the cost J in every iteration

    J_history(iter) = computeCost(X, y, theta);

end

end

function J = computeCost(X, y, theta)

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

J = 1/(2*m)*sum((X*theta-y).^2)；

end

% 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);

data = load('ex1data2.txt');

X = data(:, 1:2);

y = data(:, 3);

m = length(y);

[X mu sigma] = featureNormalize(X);

% Add intercept term to X

X = [ones(m, 1) X];

function [X_norm, mu, sigma] = featureNormalize(X)

X_norm = X;

mu = zeros(1, size(X, 2));

sigma = zeros(1, size(X, 2));

mu = mean(X,1)；

sigma = std(X,0,1)；

X_norm = (X_norm-mu)./sigma；

end

% Choose some alpha value

alpha = 0.05;

num_iters = 100;

% Init Theta and Run Gradient Descent

theta = zeros(3, 1);

[theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters);

% Plot the convergence graph

figure;

plot(1:numel(J_history), J_history, '-b', 'LineWidth', 2);

xlabel('Number of iterations');

ylabel('Cost J');

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

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

J_history = zeros(num_iters, 1);

for iter = 1:num_iters

    theta = theta - alpha/m*(X'*(X*theta-y));

    % Save the cost J in every iteration

    J_history(iter) = computeCostMulti(X, y, theta);

end

end

function J = computeCostMulti(X, y, theta)

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

J = 1/(2*m)*sum((X*theta-y).^2)；%J=(X*theta-y)'*(X*theta-y)/(2*m);

end

X1 = [1,1650,3];

X1(2:3) = (X1(2:3)-mu)./sigma;

price = X1*theta;

%%Load Data

data = csvread('ex1data2.txt');

X = data(:, 1:2);

y = data(:, 3);

m = length(y);

% Add intercept term to X

X = [ones(m, 1) X];

% Calculate the parameters from the normal equation

theta = normalEqn(X, y);

function [theta] = normalEqn(X, y)

theta = zeros(size(X, 2), 1);

theta = (X'*X)^(-1)*X'*y；

end

price = [1,1650,3]*theta；