最小二乘法多项式拟合代码-最小二乘法多项式拟合python代码-最小二乘法多项式拟合C/C++代码

#include<stdio.h> #include<stdlib.h> #include<math.h> /*最小二乘法拟合n阶多项式*/ void fit(const float* x, const float* y, int num_point, int n, float* coeff, float* mse) { //判断拟合阶次是否合法 if (n >= num_point) { printf("多项式的阶次不能大于等于坐标点数！"); return; } //构造线性方程组Ax=b，为矩阵A 和b分配内存空间 float** A = (float**)malloc(sizeof(float*) * (n + 1)); for (int i = 0; i < n+1; i++) { A[i] = (float*)malloc(sizeof(float) * (n + 1)); } float* b = (float*)malloc(sizeof(float) * (n + 1)); //构造矩阵A和b for (int k = 0; k < n + 1; k++) { for (int j = 0; j <= n + 1; j++) { float sum1 = 0; for (int i = 0; i < num_point; i++) { sum1 += float(pow(x[i], k) * pow(x[i], j)); } A[k][j] = sum1; } float sum2 = 0; for (int i = 0; i < num_point; i++) { sum2 += float(pow(x[i], k) * y[i]); } b[k] = sum2; } //采用高斯消元法，将矩阵A变换为对角矩阵 for (int k = 0; k < n; k++) { for (int i = k + 1; i < n + 1; i++) { float m = A[i][k] / A[k][k]; for (int j = k + 1; j < n + 1; j++) { A[i][j] = A[i][j] - m * A[k][j]; } b[i] = b[i] - m * b[k]; } } //高斯消元法回代，求出多项式系数 coeff[n] = b[n] / A[n][n]; for (int i = n - 1; i >= 0; i--) { float sum3 = 0; for (int j = i + 1; j < n + 1; j++) { sum3 += A[i][j] * coeff[j]; } coeff[i] = (b[i] - sum3) / A[i][i]; } //求拟合的均方误差 float sum_sqr_err = 0; for (int i = 0; i < num_point; i++) { float fx = 0; for (int j = 0; j < n + 1; j++) { fx += coeff[j] * float(pow(x[i], j)); } sum_sqr_err += (y[i] - fx) * (y[i] - fx); } *mse = sum_sqr_err / num_point; //释放内存空间 /* for (int i = 0; i < n + 1; i++) { free(A[i]); }*/ free(A); free(b); } int main() { float x[6]{ 1,2,4,6,8,10 }; float y[6]{ 1.8,3.7,8.2,12.0,15.8,20.2 }; int n = 2;//预估方程是二阶的，y=a0+a1*x+a2*x^2 int num_point = 6; float coeff[3];//系数的个数为n+1,依次是a0,a1,a2 float mse; fit(x, y, num_point, n, coeff, &mse); printf("多项式系数："); for (int i = 0; i < n + 1; i++) { printf("%lf ", coeff[i]); } printf("\n拟合均方误差：%lf\n", mse); return 0; }