利用Python的scipy包實現曲線的擬合

調用scipy包中的curve_fit，可以根據指定的函數形式，對一組已知自變量和因變量的數據進行曲線擬合。

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


# 自定義函數
def func(x, a, b):
    return a*pow(x, b)


data = pd.read_excel(r'C:\Users\YBM\Desktop\data.xlsx')
x = data['x']
y = data['y']

popt, pcov = curve_fit(x, y)
a = popt[0]
b = popt[1]
yvals = func(x, a, b)

plot1 = plt.plot(x, y, 's', label='original values')
plot2 = plt.plot(x, yvals, 'r', label='polyfit values')
plt.xlabel('x')
plt.ylabel('y')
plt.legend(loc=4) # 指定legend的位置在右下角
plt.title('curve_fit')

 

也可以定義三個參數的函數：

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


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


xdata = np.linspace(0, 4, 50)
y = func(xdata, 2.5, 1.3, 0.5)
y_noise = 0.2 * np.random.normal(size=xdata.size)
ydata = y + y_noise
plt.plot(xdata, ydata, 'b-', label='data')

popt, pcov = curve_fit(func, xdata, ydata)
a = popt[0]
b = popt[1]
c = popt[2]
yvals = func(xdata, a, b, c)
plot1 = plt.plot(xdata, ydata, 's', label='original values')
plot2 = plt.plot(xdata, yvals, 'r', label='polyfit values')
# 或：
plt.plot(xdata, func(xdata, *popt), 'r-', label='fit')

# 限制參數范圍：0<a<3, 0<b<2， 0<c<1
popt, pcov = curve_fit(func, xdata, ydata, bounds=(0, [3., 2., 1.]))
plt.plot(xdata, func(xdata, *popt), 'r-', label='fit')