import numpy as np
from scipy.optimize import leastsq
import matplotlib.pyplot as plt

# 定义待拟合的函数形式
def func(x, coeffs):
    return coeffs[0] * np.sin(coeffs[1] * x) + coeffs[2]

# 定义目标函数，即待拟合数据
def target_func(x):
    return 2.5 * np.sin(0.7 * x) + 1.2

# 生成带噪声的待拟合数据
np.random.seed(0)
x_data = np.linspace(-10, 10, 100)
y_data = target_func(x_data) + np.random.normal(0, 0.5, 100)

# 定义误差函数，即最小二乘法的目标函数
def residuals(coeffs, y, x):
    return y - func(x, coeffs)

# 初始参数的估计值
initial_coeffs = [1, 1, 1]

# 使用最小二乘法拟合函数
result = leastsq(residuals, initial_coeffs, args=(y_data, x_data))
best_coeffs = result[0]

# 打印拟合得到的系数
print("拟合得到的系数：", best_coeffs)

# 绘制拟合结果
x_fit = np.linspace(-10, 10, 100)
y_fit = func(x_fit, best_coeffs)

plt.plot(x_data, y_data, 'bo', label='原始数据')
plt.plot(x_fit, y_fit, 'r-', label='拟合曲线')
plt.legend()
plt.xlabel('x')
plt.ylabel('y')
plt.show()