Fitted Exponential Curve Error

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

x =  [333,500,1000,2000,5000,10000]

y = [195.3267, 233.0235, 264.5914,294.8728, 328.3523,345.4688]

popt, pcov = curve_fit(func, x, y)

plt.figure()
plt.plot(x, y, 'ko', label="Original Noised Data")
plt.plot(x, func(x, *popt), 'r-', label="Fitted Curve")
plt.legend()
plt.show()

Error: C:\Users\Aidan\Anaconda3\lib\site-packages\scipy\optimize\minpack.py:794: OptimizeWarning: Covariance of the parameters could not be estimated
category=OptimizeWarning)

--------------------------------------------------------------------------- TypeError Traceback (most recent call last) in () 14 plt.figure() 15 plt.plot(x, y, 'ko', label="Original Noised Data") ---> 16 plt.plot(x, func(x, *popt), 'r-', label="Fitted Curve") 17 plt.legend() 18 plt.show()

in func(x, a, b, c) 4 5 def func(x, a, b, c): ----> 6 return a * np.exp(-b * x) + c 7 8 x = [333,500,1000,2000,5000,10000]

TypeError: 'numpy.float64' object cannot be interpreted as an integer

For some reason I am not able to get a curve fit based on my data. I am following the exponential example from here: How to do exponential and logarithmic curve fitting in Python? I found only polynomial fitting

But I am using an two arrays rather than made up random data. I am new to python!

Solution

There are a few issues with your code.

You use lists instead of numpy.ndarray: the numpy and scipy routines are meant to work with numpy.ndarray and they use them internally. You should use them as well.
You are likely to get overflow issues with your data and your function, e.g. np.exp(-1000) is already approximated to zero in Python3
You are trying to fit a function that it is unlikely to fit your data. It looks more like an exponential recovery than a decay.

The following code tentatively address all these issues:

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

def func(x, a, b, c):
    return a * (1 - np.exp(-b * x)) + c

x =  np.array([333.0,500.0,1000.0,2000.0,5000.0,10000.0]) / 1000
y = np.array([195.3267, 233.0235, 264.5914,294.8728, 328.3523,345.4688]) / 10

popt, pcov = curve_fit(func, x, y)
print(popt)

plt.figure()
plt.plot(x, y, 'ko', label="Original Noised Data")
plt.plot(x, func(x, *popt), 'r-', label="Fitted Curve")
plt.legend()
plt.show()