[Machine Learning] Use the e^x function to fit data

Implemented using scipy.optimize.curve_fitfunctions.
curve_fitThe parameters are as follows:

scipy.optimize.curve_fit(f, xdata, ydata, p0=None, sigma=None, absolute_sigma=False, 
						 check_finite=True, bounds=(- inf, inf), method=None, jac=None, **kwargs)

Introduce the basic parameters required for use. Please refer to the official documentation for detailed parameters :

f：模型函数，ydata=f(xdata, *params)，其中param为xdata与ydata映射时的参数。
xdata：自变量
ydata：因变量

curve_fitThe function is to use the nonlinear least squares method to fit xdata, ydatain fthe form of a function.

# 定义xy之间的映射函数
def func(x, a, b, c):
    return a * np.exp(-b*x) + c

Before fitting the curve, declare a function func. The first parameter is the independent variable x, and the following parameters are all the parameters in the function *param. funcAssign the function curve_fitto the parameters in f. Here is an example.

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

# 声明待拟合的数据
xdata = np.linspace(0, 4, 50)
y = func(xdata, 2.5, 1.3, 0.5) # 使用func先生成ydata，a=2.5,b=1.3,c=0.5

# 给ydata添加随机噪声
rng = np.random.default_rng()
y_noise = 0.2 * rng.normal(size=xdata.size)
ydata = y + y_noise

# 展示数据
plt.scatter(xdata, ydata, label='data')

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# 拟合数据并展示曲线
popt, pcov = curve_fit(func, xdata, ydata)
plt.plot(xdata, func(xdata, *popt), 'r-',
         label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))

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# 强制参数 a/b/c 的取值范围为：[0,2]/[0,1]/[0,0.3]
popt, pcov = curve_fit(func, xdata, ydata, bounds=(0, [2., 1., 0.3]))
plt.plot(xdata, func(xdata, *popt), 'g--',
         label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))

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Reference: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html#scipy.optimize.curve_fit

[Machine Learning] Use the e^x function to fit data

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