最小二乘法实现C++

来源：http://blog.csdn.net/qll125596718/article/details/8248249

     

求a、b的值：

1. // Ordinary Least Square.cpp : 定义控制台应用程序的入口点。
2. //
3.  
4. #include "stdafx.h"
5. #include <iostream>
6. #include <fstream>
7. #include <vector>
8. using namespace std;
9.  
10. class LeastSquare
11. {
12.    double a, b;
13. public:
14.    LeastSquare(const vector<double>& x, const vector<double>& y)//最小二乘法公式
15.    {
16.       double t1 = 0, t2 = 0, t3 = 0, t4 = 0;
17.       for (int i = 0; i < x.size(); ++i)
18.       {
19.          t1 += x[i] * x[i];
20.          t2 += x[i];
21.          t3 += x[i] * y[i];
22.          t4 += y[i];
23.       }
24.       a = (t3 * x.size() - t2 * t4) / (t1 * x.size() - t2 * t2);
25.       b = (t1 * t4 - t2 * t3) / (t1 * x.size() - t2 * t2);
26.    }
27.  
28.    double getY(const double x) const
29.    {
30.       return a * x + b;
31.    }
32.  
33.    void print() const
34.    {
35.       cout << "y = " << a << "x + " << b << endl;
36.    }
37.  
38. };
39.  
40.  
41. int _tmain(int argc, _TCHAR* argv[])
42. {
43.    if (argc != 2)
44.    {
45.       cout << "Usage: DataFile.txt" << endl;
46.       return -1;
47.    }
48.    else
49.    {
50.       vector<double> x;
51.       ifstream in(argv[1]);
52.       for (double d; in >> d;)//将读取出来的数值全部存入容器X中
53.       {
54.          x.push_back(d);//push_back()是把一个元素，放入这个容器的末尾，相当于末尾添加一个元素
55.  
56.       }
57.       int sz = x.size();
58.  
59.       vector<double> y(x.begin() + sz / 2, x.end());//把余下的容器Ｘ中的元素全部放进容器Y
60.       x.resize(sz / 2);//调整容器X的长度大小，超过当前size的元素删除
61.       LeastSquare ls(x, y);//调用最小二乘法求a和b
62.       ls.print();
63.  
64.       cout << "Input x:\n";
65.       double x0;
66.  
67.       while (cin >> x0)
68.       {
69.          cout << "y = " << ls.getY(x0) << endl;
70.          cout << "Input x:\n";
71.       }
72.    }
73.    return 0;
74. }

实验模拟数据：

10	15	20	25	30	35	40	45
2000.36	2000.50	2000.72	2000.80	2001.07	2001.25	2001.48	2001.60

实验结果：