用python进行线性/非线性拟合的三种方法

import numpy as np
import matplotlib.pyplot as plt

x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
y = np.array([2.5, 4.5, 4.8, 5.5, 6.0, 7.0, 7.8, 8.0, 9.0, 9.5])

# 计算回归系数
slope, intercept = np.polyfit(x, y, 1)

# 绘制拟合曲线
plt.scatter(x, y)
plt.plot(x, slope * x + intercept, color='red')

plt.show()

import numpy as np
import matplotlib.pyplot as plt

x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
y = np.array([2.5, 4.5, 4.8, 5.5, 6.0, 7.0, 7.8, 8.0, 9.0, 9.5])

# 计算多项式回归系数
coefs = np.polyfit(x, y, 3)

# 使用np.poly1d函数来生成一个多项式拟合对象
poly = np.poly1d(coefs)

# 生成新的横坐标，使得拟合曲线更加平滑
new_x = np.linspace(min(x), max(x), 1000)

# 绘制拟合曲线
plt.scatter(x, y)
plt.plot(new_x, poly(new_x), color='red')

plt.show()

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

def func(x, a, b, c):
    return a * np.exp(-b * x) + c

# 生成模拟数据
x_data = np.linspace(0, 4, 50)
y_data = func(x_data, 2.5, 1.3, 0.5) + 0.2 * np.random.normal(size=len(x_data))

# 使用curve_fit函数来拟合非线性数据
popt, pcov = curve_fit(func, x_data, y_data)

# 画出原始数据和拟合曲线
plt.scatter(x_data, y_data, label="Data")
plt.plot(x_data, func(x_data, *popt), color='red', label="Fitted curve")
plt.legend()
plt.show()