Asymptotic regression in Python

Question

I have this portion of a data-set, where the y values eventually must reach an asymptotic limit. Here is a plot of the first 300 entries:

I have seen asymptotic regression (of the form y = b0 + b1*(1-exp(-exp(lrc) * x)) and I think it would be the best model to fit this data. R seemingly already has the function in its libraries, but I cannot find one in Python.

(1) Is there any library function for asymptotic regression or relevant saturation dynamics models as answered by Cleb below? If not, how to model it using scipy.optimize.curve_fit?

(2) Also how to predict the maximum integer value of the curve? Example, If y=2454.1234 is the value at X=10**20 and y=2545.5678 at X=10**50, for a certain model, I want to obtain 2454. Is there any one-shot way, other than linear search?

Answer 1

If the problem persists, try using a checkpoints file that has been updated with the newest code.

The output will be like this:

The Code is given below:

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

def fun(x, a, b, n):    
   return a * x ** n / (x ** n + b) 

df = pd.read_csv('data.txt.txt', sep='\t') 
y = df['y'].astype(float) 
x = df['X'].astype(float) 
popt, pcov = curve_fit(f, x, y, p0=[1800., 20., 1.]) 
plt.scatter(x, y) 
plt.plot(x, f(x, *popt), 'r-')
plt.show()