使用csharp 实现最小二乘法法拟合椭圆的代码

using System;
using System.Collections.Generic;
using System.Linq;

namespace EllipseFitting
{
    class Program
    {
        static void Main(string[] args)
        {
            List<double> x = new List<double>() { 1, 2, 3, 4, 5 };
            List<double> y = new List<double>() { 2, 3, 4, 5, 6 };
            Tuple<double, double, double> ellipse = FitEllipse(x, y);
            Console.WriteLine($"Semi-major axis: {ellipse.Item1}");
            Console.WriteLine($"Semi-minor axis: {ellipse.Item2}");
            Console.WriteLine($"Orientation angle: {ellipse.Item3}");
        }

        static Tuple<double, double, double> FitEllipse(List<double> x, List<double> y)
        {
            // Compute the centroid of the points
            double xMean = x.Average();
            double yMean = y.Average();

            // Compute the covariance matrix of the points
            double covXX = x.Select(xi => (xi - xMean) * (xi - xMean)).Sum() / x.Count;
            double covYY = y.Select(yi => (yi - yMean) * (yi - yMean)).Sum() / y.Count;
            double covXY = x.Zip(y, (xi, yi) => (xi - xMean) * (yi - yMean)).Sum() / x.Count;
            double covYX = covXY;

            // Compute the eigenvalues and eigenvectors of the covariance matrix
            double lambda1 = (covXX + covYY + Math.Sqrt((covXX - covYY) * (covXX - covYY) + 4 * covXY * covYX)) / 2;
            double lambda2 = (covXX + covYY - Math.Sqrt((covXX - covYY) * (covXX - covYY) + 4 * covXY * covYX)) / 2;
            double angle = Math.Atan2(covXY, lambda1 - covXX);

            // Compute the semi-major and semi-minor axes
            double a = Math.Sqrt(lambda1);
            double b = Math.Sqrt(lambda2);

            return Tuple.Create(a, b, angle);
        }
    }
}