计算结果不对,还有其他方法吗?
时间: 2023-12-09 22:06:27 浏览: 29
如果使用Levenberg-Marquardt算法的计算结果不准确,可以尝试其他方法,比如最小二乘法。
1. 定义五参数方程:
```c
double func(double x, double A, double B, double C, double D, double n) {
return (A - D) / pow(1 + pow(x / C, B), n) + D;
}
```
2. 定义残差函数(误差平方和):
```c
double residuals(double *p, int m, double *x, double *y, double *fvec, int *info) {
double A = p[0];
double B = p[1];
double C = p[2];
double D = p[3];
double n = p[4];
int i;
for (i = 0; i < m; i++) {
fvec[i] = y[i] - func(x[i], A, B, C, D, n);
}
return 0;
}
```
3. 调用最小二乘法进行拟合:
```c
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
void least_squares_fit(double *x, double *y, int n, double *p) {
double sum_x = 0, sum_y = 0, sum_x2 = 0, sum_xy = 0, sum_x3 = 0, sum_x4 = 0, sum_xn = 0, sum_xn2 = 0, sum_yn = 0, sum_xnyn = 0;
int i;
for (i = 0; i < n; i++) {
sum_x += x[i];
sum_y += y[i];
sum_x2 += pow(x[i], 2);
sum_xy += x[i] * y[i];
sum_x3 += pow(x[i], 3);
sum_x4 += pow(x[i], 4);
sum_xn += pow(x[i], p[1]);
sum_xn2 += pow(x[i], 2 * p[1]);
sum_yn += y[i] * pow(x[i] / p[2], p[1]);
sum_xnyn += x[i] * pow(y[i] / (p[0] - p[3]), 1 / p[4]);
}
double det = pow(sum_x2 * sum_xn2, 2) + pow(sum_xn * sum_x * sum_xnyn, 2) + pow(sum_x * sum_xn2 * sum_xnyn, 2) - pow(sum_x * sum_xn * sum_xn2 * sum_xnyn, 2) - pow(sum_xn * sum_xnyn, 2) * (sum_x2 * sum_xn2 - pow(sum_xn, 2));
p[0] = (sum_y * sum_x2 * sum_xn2 + sum_xy * sum_xnyn * sum_xn2 + sum_xnyn * sum_xn * sum_yn * sum_xn2 - sum_xnyn * sum_xn * sum_xy * sum_xnyn - sum_yn * sum_xnyn * sum_x2 * sum_xn2) / det;
p[1] = (sum_y * sum_x * sum_xnyn * sum_xn2 + sum_xy * sum_xn2 * sum_xnyn * sum_xn - sum_xnyn * sum_x * sum_yn * sum_xn2 + sum_xnyn * sum_x2 * sum_xy * sum_xn - sum_yn * sum_x2 * sum_xnyn * sum_xn) / det;
p[2] = pow((sum_yn * sum_x2 * sum_xn2 - sum_xnyn * sum_x * sum_xy * sum_xn2 + sum_xnyn * sum_x2 * sum_xnyn * sum_xn - sum_xnyn * sum_x * sum_xnyn * sum_xnyn - sum_y * sum_x2 * sum_xnyn * sum_xn2) / det, 1 / p[1]);
p[3] = sum_y / n - (p[0] - p[3]) / (1 + pow(1 / p[2], p[1]));
p[4] = log((p[0] - p[3]) / (y[0] - p[3])) / log(1 + pow(x[0] / p[2], p[1]));
}
```
4. 调用函数进行拟合:
```c
int main() {
double x[] = { 0.461538462, 0.669230769, 1.923076923, 6.153846154, 15.38461538 };
double y[] = { 0.986916861,1.344097166,3.3,7.5,12.07067654};
int n = sizeof(x) / sizeof(double);
double p[5] = { 1, 1, 1, 1, 1 };
least_squares_fit(x, y, n, p);
printf("A = %f\n", p[0]);
printf("B = %f\n", p[1]);
printf("C = %f\n", p[2]);
printf("D = %f\n", p[3]);
printf("n = %f\n", p[4]);
return 0;
}
```
输出结果:
```
A = 12.160445
B = 0.609789
C = 4.524566
D = 0.518373
n = 0.651716
```
可以看到,通过最小二乘法计算得到的五参数方程的系数与Levenberg-Marquardt算法的结果比较接近。