linear_least_squares_fitting_procedure.cpp

最小二乘法的拟合直线的C++源代码

//原理部分请参考有关资料，这里只给出c++程序。
//point.h
class Point //Point类的声明
{
 public: //外部接口
     Point(float xx=0, float yy=0) {X=xx;Y=yy;}
     float GetX() {return X;}
     float GetY() {return Y;}
     friend float linefit(Point l_point[], int n_point); //友元函数
//int型变量为点数
 private: //私有数据成员
     float X,Y;
};
//End of point.h

//main.cpp
#include<iostream>
#include<cmath>
#include "point.h"
using namespace std;
float linefit(Point l_point[], int n_point) //友元函数体
{
     float av_x,av_y; //声明变量
     float L_xx,L_yy,L_xy;
      //变量初始化
     av_x=0; //X的平均值
     av_y=0; //Y的平均值
     L_xx=0; //Lxx
     L_yy=0; //Lyy
     L_xy=0; //Lxy
     for(int i=0;i<n_point;i++) //计算X、Y的平均值
     {
         av_x+=l_point[i].X/n_point;
         av_y+=l_point[i].Y/n_point;
     }
     for(i=0;i<n_point;i++) //计算Lxx、Lyy和Lxy
     {
         L_xx+=(l_point[i].X-av_x)*(l_point[i].X-av_x);
         L_yy+=(l_point[i].Y-av_y)*(l_point[i].Y-av_y);
         L_xy+=(l_point[i].X-av_x)*(l_point[i].Y-av_y);
     }
     cout<<"This line can be fitted by y=ax+b."<<endl;
     cout<<"a="<<L_xy/L_xx; //输出回归系数a
     cout<<" b="<<av_y-L_xy*av_x/L_xx<<endl; //输出回归系数b
     return float(L_xy/sqrt(L_xx*L_yy)); //返回相关系数r
}

int main()
{
     Point l_p[10]={Point(6,10),Point(14,20),Point(26,30),
     Point(33,40),Point(46,50),Point(54,60),Point(67,70),
     Point(75,80),Point(84,90),Point(100,100)}; //初始化数据点
     float r=linefit(l_p,10); //进行线性回归计算
     cout<<"Line coefficient r="<<r<<endl; //输出相关系数
}