吴恩达机器学习ex1（第一次练习）

linear regression

%cost function
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;
  J1 = 0;

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta
%               You should set J to the cost.

  for i = 1:m
    J1=J1+((theta(1)+theta(2)*X(i,2))-y(i))^2;
  endfor
  
  J=J1/(2*m);


% =========================================================================

endfunction
 

%gradient descent algorithm
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);%初始化，用於記錄cost function的歷史數據
  
  

  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.
    %
    temp1=0;
    temp2=0;
    
    for j=1:m
      temp1=temp1+((theta(1)+theta(2)*X(j,2))-y(j));%注意：主函數裏面的X設計的是兩列第一列為X0，即第一列皆爲1
      temp2=temp2+(((theta(1)+theta(2)*X(j,2))-y(j))*X(j,2));
    endfor
    
    theta(1)=theta(1)-(alpha/m)*temp1;
    theta(2)=theta(2)-(alpha/m)*temp2;

    % ============================================================

    % Save the cost J in every iteration    
      J_history(iter) = computeCost(X, y, theta);

  endfor

endfunction

%data1.txt
6.1101,17.592
5.5277,9.1302
8.5186,13.662
7.0032,11.854
5.8598,6.8233
8.3829,11.886
7.4764,4.3483
8.5781,12
6.4862,6.5987
5.0546,3.8166
5.7107,3.2522
14.164,15.505
5.734,3.1551
8.4084,7.2258
5.6407,0.71618
5.3794,3.5129
6.3654,5.3048
5.1301,0.56077
6.4296,3.6518
7.0708,5.3893
6.1891,3.1386
20.27,21.767
5.4901,4.263
6.3261,5.1875
5.5649,3.0825
18.945,22.638
12.828,13.501
10.957,7.0467
13.176,14.692
22.203,24.147
5.2524,-1.22
6.5894,5.9966
9.2482,12.134
5.8918,1.8495
8.2111,6.5426
7.9334,4.5623
8.0959,4.1164
5.6063,3.3928
12.836,10.117
6.3534,5.4974
5.4069,0.55657
6.8825,3.9115
11.708,5.3854
5.7737,2.4406
7.8247,6.7318
7.0931,1.0463
5.0702,5.1337
5.8014,1.844
11.7,8.0043
5.5416,1.0179
7.5402,6.7504
5.3077,1.8396
7.4239,4.2885
7.6031,4.9981
6.3328,1.4233
6.3589,-1.4211
6.2742,2.4756
5.6397,4.6042
9.3102,3.9624
9.4536,5.4141
8.8254,5.1694
5.1793,-0.74279
21.279,17.929
14.908,12.054
18.959,17.054
7.2182,4.8852
8.2951,5.7442
10.236,7.7754
5.4994,1.0173
20.341,20.992
10.136,6.6799
7.3345,4.0259
6.0062,1.2784
7.2259,3.3411
5.0269,-2.6807
6.5479,0.29678
7.5386,3.8845
5.0365,5.7014
10.274,6.7526
5.1077,2.0576
5.7292,0.47953
5.1884,0.20421
6.3557,0.67861
9.7687,7.5435
6.5159,5.3436
8.5172,4.2415
9.1802,6.7981
6.002,0.92695
5.5204,0.152
5.0594,2.8214
5.7077,1.8451
7.6366,4.2959
5.8707,7.2029
5.3054,1.9869
8.2934,0.14454
13.394,9.0551
5.4369,0.61705

multipul feature

%cost function
function J = computeCostMulti(X, y, theta)
%COMPUTECOSTMULTI Compute cost for linear regression with multiple variables
%   J = COMPUTECOSTMULTI(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;
  J1 = 0;

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta
%               You should set J to the cost.
  for i = 1:m
    J1=J1+((theta(1)+theta(2)*X(i,2)+theta(3)*X(i,3))-y(i))^2;
  endfor
  
  J = J1/(2*m);





% =========================================================================

endfunction

% gradientDescent
function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)
%GRADIENTDESCENTMULTI Performs gradient descent to learn theta
%   theta = GRADIENTDESCENTMULTI(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 (computeCostMulti) and gradient here.
    %
    temp1=0;
    temp2=0;
    temp3=0;
    for j = 1:m
      temp1=temp1+((theta(1)+theta(2)*X(j,2)+theta(3)*X(j,3))-y(j));
      temp2=temp2+((theta(1)+theta(2)*X(j,2)+theta(3)*X(j,3))-y(j))*X(j,2);
      temp3=temp3+((theta(1)+theta(2)*X(j,2)+theta(3)*X(j,3))-y(j))*X(j,3);
    endfor
    
    theta(1)=theta(1)-(alpha/m)*temp1;
    theta(2)=theta(2)-(alpha/m)*temp2;
    theta(3)=theta(3)-(alpha/m)*temp3;

    % ============================================================

    % Save the cost J in every iteration    
    J_history(iter) = computeCostMulti(X, y, theta);

  endfor

endfunction

%特征缩放 分为三种类型，此为其中一种
function [theta] = normalEqn(X, y)
%NORMALEQN Computes the closed-form solution to linear regression 
%   NORMALEQN(X,y) computes the closed-form solution to linear 
%   regression using the normal equations.
% 標準方程法求解theta
  theta = zeros(size(X, 2), 1);

% ====================== YOUR CODE HERE ======================
% Instructions: Complete the code to compute the closed form solution
%               to linear regression and put the result in theta.
%

% ---------------------- Sample Solution ----------------------

  theta=pinv(X'*X)*X'*y;


% -------------------------------------------------------------


% ============================================================

endfunction

标准方程法

function [theta] = normalEqn(X, y)
%NORMALEQN Computes the closed-form solution to linear regression 
%   NORMALEQN(X,y) computes the closed-form solution to linear 
%   regression using the normal equations.
% 標準方程法求解theta
  theta = zeros(size(X, 2), 1);

% ====================== YOUR CODE HERE ======================
% Instructions: Complete the code to compute the closed form solution
%               to linear regression and put the result in theta.
%

% ---------------------- Sample Solution ----------------------

  theta=pinv(X'*X)*X'*y;


% -------------------------------------------------------------


% ============================================================

endfunction