用python中的多元曲线拟合估计椭圆状形状的参数和阶数

import numpy as np
from scipy.optimize import curve_fit

def ellipse_func(x, a, b, h, k, theta):
    """
    椭圆函数
    x: 输入变量
    a: 长轴半径
    b: 短轴半径
    h: 椭圆中心x坐标
    k: 椭圆中心y坐标
    theta: 椭圆旋转角度
    """
    cos_theta = np.cos(theta)
    sin_theta = np.sin(theta)
    x_hat = (x[0] - h) * cos_theta + (x[1] - k) * sin_theta
    y_hat = (x[1] - k) * cos_theta - (x[0] - h) * sin_theta
    return (x_hat / a) ** 2 + (y_hat / b) ** 2 - 1

# 准备数据点
x_data = np.array([x1, x2, x3, ...])
y_data = np.array([y1, y2, y3, ...])

# 初始参数的猜测值
initial_guess = [a_guess, b_guess, h_guess, k_guess, theta_guess]

# 进行拟合
params, params_covariance = curve_fit(ellipse_func, (x_data, y_data), z_data, p0=initial_guess)

a_fit, b_fit, h_fit, k_fit, theta_fit = params