最小二乘拟合圆C语言

在 C 语言中，可以使用最小二乘法来拟合一个圆。最小二乘法是一种常用的数值分析方法，可以通过最小化实际观测数据与拟合函数之间的残差平方和来找到最优的拟合参数。

以下是一个用 C 语言实现最小二乘拟合圆的示例代码：

#include <stdio.h>
#include <math.h>

void fitCircle(double x[], double y[], int n, double *centerX, double *centerY, double *radius) {
    double sumX = 0.0, sumY = 0.0, sumX2 = 0.0, sumY2 = 0.0, sumXY = 0.0;
    for (int i = 0; i < n; i++) {
        sumX += x[i];
        sumY += y[i];
        sumX2 += x[i] * x[i];
        sumY2 += y[i] * y[i];
        sumXY += x[i] * y[i];
    }

    double meanX = sumX / n;
    double meanY = sumY / n;

    double u1 = sumX2 - n * meanX * meanX;
    double u2 = sumXY - n * meanX * meanY;
    double v1 = sumXY - n * meanX * meanY;    double v2 = sumY2 - n * meanY * meanY;

    double centerX_temp = (v1 * sumX - u1 * sumY) / (2 * (v1 * meanX - u2 * meanY));
    double centerY_temp = (u2 * sumX - v2 * sumY) / (2 * (u2 * meanX - v2 * meanY));

    *centerX = centerX_temp;
    *centerY = centerY_temp;
    *radius = sqrt((centerX_temp - x[0]) * (centerX_temp - x[0]) + (centerY_temp - y[0]) * (centerY_temp - y[0]));
}

int main() {
    double x[] = {1.0, 2.0, 3.0, 4.0, 5.0};
    double y[] = {1.0, 3.0, 6.0