1. 原理

 

2. Octave

function theta = leastSquaresMethod(X, y)    theta = pinv(X' * X) * X' * y;

 

3. Python

# -*- coding:utf8 -*-import numpy as npdef lse(input_X, _y):    """    least squares method    :param input_X: np.matrix input X    :param _y: np.matrix y    """    return (input_X.T * input_X).I * input_X.T * _ydef test():    """    test    :return: None    """    m = np.loadtxt('linear_regression_using_gradient_descent.csv', delimiter=',')    input_X, y = np.asmatrix(m[:, :-1]), np.asmatrix(m[:, -1]).T    final_theta = lse(input_X, y)    t1, t2, t3 = np.array(final_theta).reshape(-1,).tolist()    print('对测试数据 y = 2 - 4x + 2x^2 求得的参数为: %.3f, %.3f, %.3f\n' % (t1, t2, t3))if __name__ == "__main__":    test()

 

4. C++

#include 
     
      #include 
      
       using namespace std;using namespace Eigen;MatrixXd les(MatrixXd &input_X, MatrixXd &y) {    return (input_X.transpose() * input_X).inverse() * input_X.transpose() * y;}void generate_data(MatrixXd &input_X, MatrixXd &y) {    ArrayXd v = ArrayXd::LinSpaced(50, 0, 2);    input_X.col(0) = VectorXd::Constant(50, 1, 1);    input_X.col(1) = v.matrix();    input_X.col(2) = v.square().matrix();    y.col(0) = 2 * input_X.col(0) - 4 * input_X.col(1) + 2 * input_X.col(2);    y.col(0) += VectorXd::Random(50) / 25;  }int main() {    MatrixXd input_X(50, 3), y(50, 1);    generate_data(input_X, y);    cout << "对测试数据 y = 2 - 4x + 2x^2 求得的参数为: " << les(input_X, y).transpose() << endl;}