最小二乘法曲线拟合+C代码

最小二乘法曲线的系数求解过程是解一个正规方程组的解的过程，下图是数值分析课本上，最小二乘法拟合的原理：

课本中的例子如下：

c代码如下：

#include "stdio.h"
#include "stdlib.h"
#include "math.h"
#include "vector"
using namespace std;


struct point
{
double x;
double y;
};


typedef vector doubleVector;


vector getFileInf(char *File);  //获取文件数据
doubleVector getCoeff(vector sample, int n);   //矩阵方程


void main()
{
int i, n;
char *File = "样本.txt";
vector sample;
doubleVector Coef;


sample = getFileInf(File);


printf("拟合阶数n：");
scanf("%d", &n);


Coef = getCoeff(sample, n);


printf("\n拟合矩阵的系数为：\n");
for(i=0; iprintf("a%d = %lf\n", i, Coef[i]);


}




//矩阵方程
doubleVector getCoeff(vector sample, int n)
{
vector matFunX;  //矩阵方程
vector matFunY;  //矩阵方程
doubleVector temp;
double sum;
int i, j, k;


//正规方程X
for(i=0; i<=n; i++)
{
temp.clear();
for(j=0; j<=n; j++)
{
sum = 0;
for(k=0; ksum += pow(sample[k].x, j+i);
temp.push_back(sum);
}

matFunX.push_back(temp);
}




//正规方程Y
for(i=0; i<=n; i++)
{
temp.clear();
sum = 0;
for(k=0; ksum += sample[k].y*pow(sample[k].x, i);
temp.push_back(sum);

matFunY.push_back(temp);
}




//矩阵行列式变换
double num1, num2, ratio;


for(i=0; i{
num1 = matFunX[i][i];
for(j=i+1; j{
num2 = matFunX[j][i];
ratio = num2/num1;


for(k=0; kmatFunX[j][k] = matFunX[j][k]-matFunX[i][k]*ratio;


matFunY[j][0] = matFunY[j][0]-matFunY[i][0]*ratio;
}


}




//计算拟合曲线的系数
doubleVector coeff(matFunX.size(), 0);
for(i=matFunX.size()-1; i>=0; i--)
{
if(i==matFunX.size()-1)
coeff[i] = matFunY[i][0]/matFunX[i][i];

else
{
for(j=i+1; jmatFunY[i][0] = matFunY[i][0]-coeff[j]*matFunX[i][j];
coeff[i] = matFunY[i][0]/matFunX[i][i];
}
}




return coeff;
}




//获取文件数据
vector getFileInf(char *File)
{
int i=1;
vector dst;


FILE *fp = fopen(File, "r");


if(fp==NULL)
{
printf("Open file error!!!\n");
exit(0);
}


point temp;
double num;


while(fscanf(fp, "%lf", &num)!=EOF)
{
if(i%2==0)
{
temp.y = num;
dst.push_back(temp);
}
else
temp.x = num;
i++;
}


fclose(fp);


return dst;
}

运行结果如下：