如何使用 Scipy curve_fit 获取日志 function 拟合数据

Question

I am trying to get a*log(b/x)^c type fit for the following data (simplified for 10 data points)

I have tried methods described in some other questions like this one using both curve_fit and lmfit but the solution never converges. My guess is that my initial conditions are bad. I was able to get the other exponential function commented out fit but the application requires a log fit of the form given. The data with the fit that works is attached for reference.

import numpy as np
from scipy.optimize import curve_fit


x=[0, 0.89790454, 1.79580908, 2.69371362, 3.59161816, 4.48952269, 5.38742723, 6.28533177, 7.18323631, 8.08114085]
y=[0.39599324, 0.10255828, 0.07094521, 0.05500624, 0.04636146, 0.04585985,  0.0398909,  0.03340628, 0.03041699, 0.02498938]
x = np.array(x,dtype=float) 
y = np.array(y,dtype=float)


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

    return a*(np.log(b/x)**c)

popt, pcov = curve_fit(func, x, y, p0=[.5,.5,1],maxfev=10000)

print(popt)

a,b ,c = np.asarray(popt)

Answer 1

Replace your function with,

def func(x, a, b, c):
    #return a*np.exp(-c*(x*b))+d
    t1 = np.log(b/x)
    t2 = a*t1**c
    print(a,b,c,t1, t2)
    return t;

Yow will rapidly see that t1 = np.log(b / x) may be negative (this happens whenever b < x). A power of a negative number to a non-integer power is not a real number, and here numpy is producing nan results.

Answer 2

I have no difficukty with my fitting software (result below).

Often a cause of difficulty with non-linear fitting using iterative method of regression is the setting of initial values of the parameters to start the iterative process.