close all;
clear;
X = load('ex2x.dat');
Y = load('ex2y.dat');
plot(X, Y, 'o');
ylabel('Height in meters')
xlabel('Age in years')
% store the number of training examples 训练样列的数目
m = length(Y);
% Add a column of ones to X 考虑到偏置项,加上一列ones(m,1),即m行1列的单位矩阵
X = [ones(m, 1), X];
%X m行2列 [mx2] the dimensions of the matrix X
theta = zeros(size(X(1,:)));
% theta <= theta 的转置
theta = theta';
%theta 2行1列 [2X1] the dimensions of the matrix theta
MAX_ITR = 1500;
alpha = 0.07;
for num_iterations = 1:MAX_ITR
grand = (1/m)*X'*(X*theta-Y);
theta = theta-alpha*grand;
end
theta
%%
% Plot the linear fit
% keep previous plot visible
hold on;
%X*theta = X0*theta0+X1*theta1+...+Xj*thetaj+...+Xm*thetam
plot(X(:,2), X*theta, '-')
legend('Training data', 'Linear regression')
% don't overlay any more plots on this figure
hold off
%%
% the predicted height
%the predicted height for age 3.5 predict1 : 年龄3.5的预测身高值
predict1= [1,3.5]*theta
%the predicted height for age 7 predict2 : 年龄7的预测身高值
predict2=[1,7]*theta
%%
% Calculate J matrix
% Grid over which we will calculate J
%-3到3之间的数值被100等分
theta0_vals = linspace(-3, 3, 100);
%-1到1之间的数值被100等分
theta1_vals = linspace(-1, 1, 100);
% initialize J_vals to a matrix of 0's
J_vals = zeros(length(theta0_vals), length(theta1_vals));
for i = 1:length(theta0_vals)
for j = 1:length(theta1_vals)
%T:[2X1] T=[-3;-1] or [-3;-0.979798] or ......[3;1] 等有100x100种取值；
T = [theta0_vals(i); theta1_vals(j)];
% J_vals:[100X100]
J_vals(i,j) = (0.5/m) * (X *T- Y)'* (X * T - Y);
end
end
J_vals = J_vals';
% Plot the surface plot
% 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
% Surface plot
figure;
surf(theta0_vals, theta1_vals, J_vals)
xlabel('\theta_0'); ylabel('\theta_1');
figure;
% Plot the cost function with 15 contours spaced logarithmically
% between 0.01 and 100
%x=logspace(a,b,n)生成有n个元素的对数等分行向量x，且x(1)=10的a次方，x(n)=10的b次方；
%生成从10的a次方到10的b次方之间按对数等分的n个元素的行向量。n如果省略，则默认值为50
contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 2, 15))
xlabel('\theta_0'); ylabel('\theta_1')
%{
X : [50x1] double
2.3684
2.5400
2.5421
2.5491
2.7867
2.9117
3.0356
3.1147
3.1582
3.3276
3.3793
3.4122
3.4216
3.5316
3.6393
3.6733
3.9256
4.0499
4.2483
4.3440
4.3827
4.4231
4.6102
4.6881
4.9777
5.0360
5.0685
5.4161
5.4396
5.4563
5.5698
5.6016
5.6878
5.7216
5.8539
6.1978
6.3511
6.4797
6.7384
6.8638
7.0223
7.0782
7.1514
7.4664
7.5974
7.7441
7.7730
7.8265
7.9306
Y : [50x1] double
0.7792
0.9160
0.9054
0.9057
0.9390
0.9668
0.9644
0.9145
0.9393
0.9607
0.8984
0.9121
0.9424
0.9662
1.0527
1.0144
0.9597
0.9685
1.0766
1.1455
1.0341
1.0070
0.9668
1.0896
1.0634
1.1237
1.0323
1.0874
1.0703
1.1606
1.0778
1.1070
1.0972
1.1649
1.1412
1.0844
1.1252
1.1168
1.1971
1.2069
1.1251
1.1236
1.2133
1.2523
1.2497
1.1800
1.1897
1.3030
1.2601
1.2562
%}
clear;
clc;
clf;
%该脚本尾部有原数据
% /media/heliheng/Resource/deep_learning/matMLLRexX = load('ex2x.dat');
Y = load('ex2y.dat');
plot(X, Y, 'o');
ylabel('Height in meters')
xlabel('Age in years')
% store the number of training examples 训练样列的数目
m = length(Y);
% Add a column of ones to X 考虑到偏置项,加上一列ones(m,1),即m行1列的单位矩阵
X = [ones(m, 1), X];
%X m行2列 [mx2] the dimensions of the matrix X
theta = zeros(size(X(1,:)));
% theta <= theta 的转置
theta = theta';
%theta 2行1列 [2X1] the dimensions of the matrix theta
MAX_ITR = 1500;
alpha = 0.07;
for num_iterations = 1:MAX_ITR
grand = (1/m)*X'*(X*theta-Y);
theta = theta-alpha*grand;
end
theta
%%
% Plot the linear fit
% keep previous plot visible
hold on;
%X*theta = X0*theta0+X1*theta1+...+Xj*thetaj+...+Xm*thetam
plot(X(:,2), X*theta, '-')
legend('Training data', 'Linear regression')
% don't overlay any more plots on this figure
hold off
%%
% the predicted height
%the predicted height for age 3.5 predict1 : 年龄3.5的预测身高值
predict1= [1,3.5]*theta
%the predicted height for age 7 predict2 : 年龄7的预测身高值
predict2=[1,7]*theta
%%
% Calculate J matrix
% Grid over which we will calculate J
%-3到3之间的数值被100等分
theta0_vals = linspace(-3, 3, 100);
%-1到1之间的数值被100等分
theta1_vals = linspace(-1, 1, 100);
% initialize J_vals to a matrix of 0's
J_vals = zeros(length(theta0_vals), length(theta1_vals));
for i = 1:length(theta0_vals)
for j = 1:length(theta1_vals)
%T:[2X1] T=[-3;-1] or [-3;-0.979798] or ......[3;1] 等有100x100种取值；
T = [theta0_vals(i); theta1_vals(j)];
% J_vals:[100X100]
J_vals(i,j) = (0.5/m) * (X *T- Y)'* (X * T - Y);
end
end
J_vals = J_vals';
% Plot the surface plot
% 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
% Surface plot
figure;
surf(theta0_vals, theta1_vals, J_vals)
xlabel('\theta_0'); ylabel('\theta_1');
figure;
% Plot the cost function with 15 contours spaced logarithmically
% between 0.01 and 100
%x=logspace(a,b,n)生成有n个元素的对数等分行向量x，且x(1)=10的a次方，x(n)=10的b次方；
%生成从10的a次方到10的b次方之间按对数等分的n个元素的行向量。n如果省略，则默认值为50
contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 2, 15))
xlabel('\theta_0'); ylabel('\theta_1')
%{
X : [50x1] double
2.3684
2.5400
2.5421
2.5491
2.7867
2.9117
3.0356
3.1147
3.1582
3.3276
3.3793
3.4122
3.4216
3.5316
3.6393
3.6733
3.9256
4.0499
4.2483
4.3440
4.3827
4.4231
4.6102
4.6881
4.9777
5.0360
5.0685
5.4161
5.4396
5.4563
5.5698
5.6016
5.6878
5.7216
5.8539
6.1978
6.3511
6.4797
6.7384
6.8638
7.0223
7.0782
7.1514
7.4664
7.5974
7.7441
7.7730
7.8265
7.9306
Y : [50x1] double
0.7792
0.9160
0.9054
0.9057
0.9390
0.9668
0.9644
0.9145
0.9393
0.9607
0.8984
0.9121
0.9424
0.9662
1.0527
1.0144
0.9597
0.9685
1.0766
1.1455
1.0341
1.0070
0.9668
1.0896
1.0634
1.1237
1.0323
1.0874
1.0703
1.1606
1.0778
1.1070
1.0972
1.1649
1.1412
1.0844
1.1252
1.1168
1.1971
1.2069
1.1251
1.1236
1.2133
1.2523
1.2497
1.1800
1.1897
1.3030
1.2601
1.2562
%}