python使用curve_fit拟合任意分布

curve_fit的文档：https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html

注意：拟合分布是 已知分布，拟合参数！

官方教程

"""拟合任意分布"""
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
import numpy as np


def func(x, a, b, c):  # 用来拟合的方程
    return a * np.exp(-b * x) + c


def get_xy():
    xdata: np.ndarray = np.linspace(0, 4, 50)  # x值
    y = func(xdata, 2.5, 1.3, 0.5)
    rng = np.random.default_rng()
    y_noise = 0.2 * rng.normal(size=xdata.size)
    ydata: np.ndarray = y + y_noise  # 拟合的数据 y
    return xdata, ydata


if __name__ == '__main__':
    x_value, y_value = get_xy()
    popt, pcov = curve_fit(func, x_value, y_value)
    # 绘图
    plt.plot(x_value, y_value, 'b-', label='data')
    plt.plot(x_value, func(x_value, *popt), 'r-',
             label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))
    # 这个写法是加一个限制：0 <= a <= 3, 0 <= b <= 1 and 0 <= c <= 0.5
    popt_2, pcov_2 = curve_fit(func, x_value, y_value, bounds=([0, 0, 0.5], [3., 1., 1]))
    plt.plot(x_value, func(x_value, *popt_2), 'g--',
             label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt_2))
    plt.xlabel('x')
    plt.ylabel('y')
    plt.legend()
    plt.show()

简易的用法

更换

from scipy.optimize import curve_fit
import numpy as np


def func(x, a, b, c):  # 用来拟合的方程
    return a * np.exp(-b * x) + c


def get_xy():
    xdata: np.ndarray = np.linspace(0, 4, 50)  # x值
    y = func(xdata, 2.5, 1.3, 0.5)
    rng = np.random.default_rng()
    y_noise = 0.2 * rng.normal(size=xdata.size)
    ydata: np.ndarray = y + y_noise  # 拟合的数据 y
    return xdata, ydata


if __name__ == '__main__':
    x_value, y_value = get_xy()
    popt, pcov = curve_fit(func, x_value, y_value)  # 拟合分布
    y_pred = func(x_value, *popt)  # 预测结果