Python中的非线性曲线拟合程序

我想找到并绘制一个函数f,该函数表示拟合在我已经知道的一些设定点x和y上的曲线.

经过一番研究后,我开始尝试scipy.optimize和curve_fit,但在参考指南上我发现该程序改用函数来拟合数据,并且假设ydata = f(xdata,* params)eps.

所以我的问题是：我必须在代码中进行哪些更改才能使用curve_fit或其他任何库来使用设定点查找曲线的功能？ (注意：我也想知道该函数,以便以后可以为我的项目进行集成并对其进行绘制).我知道它将是一个衰减的指数函数,但不知道确切的参数.这是我在程序中尝试过的：

    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

    xdata = np.array([0.2, 0.5, 0.8, 1])
    ydata = np.array([6, 1, 0.5, 0.2])
    plt.plot(xdata, ydata, 'b-', label='data')
    popt, pcov = curve_fit(func, xdata, ydata)
    plt.plot(xdata, func(xdata, *popt), 'r-', label='fit')

    plt.xlabel('x')
    plt.ylabel('y')
    plt.legend()
    plt.show()

如果有任何更改,目前正在Raspberry Pi上开发此项目.并希望使用最小二乘法,因为它既精确又好,但是任何其他效果很好的方法都值得欢迎.
同样,这是基于scipy库的参考指南.另外,我得到以下图形,甚至不是曲线：基于设定点的图形和曲线

解决方法:

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

#c is a constant so taking the derivative makes it go to zero
def deriv(x, a, b, c):
    return -a * b * np.exp(-b * x)

#Integrating gives you another c coefficient (offset) let's call it c1 and set it equal to zero by default
def integ(x, a, b, c, c1 = 0):
    return -a/b * np.exp(-b * x) + c*x + c1

#There are only 4 (x,y) points here
xdata = np.array([0.2, 0.5, 0.8, 1])
ydata = np.array([6, 1, 0.5, 0.2])

#curve_fit already uses "non-linear least squares to fit a function, f, to data"
popt, pcov = curve_fit(func, xdata, ydata)
a,b,c = popt #these are the optimal parameters for fitting your 4 data points

#Now get more x values to plot the curve along so it looks like a curve
step = 0.01
fit_xs = np.arange(min(xdata),max(xdata),step)

#Plot the results
plt.plot(xdata, ydata, 'bx', label='data')
plt.plot(fit_xs, func(fit_xs,a,b,c), 'r-', label='fit')
plt.plot(fit_xs, deriv(fit_xs,a,b,c), 'g-', label='deriv')
plt.plot(fit_xs, integ(fit_xs,a,b,c), 'm-', label='integ')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()

标签：raspberry-pi,curve-fitting,non-linear-regression,python
来源： https://codeday.me/bug/20191111/2018006.html