Why doesn't Scipy's curve_fit give the correct result for the following problem(s)?

Question

Code:

from scipy.optimize import curve_fit
import numpy as np
from numpy import *


def func(x, a, b): 
    return ff(x,a,b) 


ff= lambda x,a,b: eval("1/(a*x+b)")

xdata = [1 ,2, 4, 6, 8, 10]
ydata = [0.22, 0.1, 0.06, 0.04, 0.03, 0.024]

popt, pcov = curve_fit(func, xdata, ydata)
print('\n', '[a b] for the best fit =    ', popt,'\n')

when this runs it gives

 [a b] for the best fit =     [ 4.62673137 -0.04794652]

Meanwhile according to my scientific calculator (or by solving this manually), the answer should be:

 [a b] for the best fit =     [ 0.9232 4.05396]

I tested the program repeatedly, this isn't the only example in which it doesn't provide correct results.

Answer 1

I've checked you calculations:

import matplotlib.pyplot as plt
plt.scatter(xdata, ydata)
plt.scatter(xdata, func(np.array(xdata), 4.62673137, -0.04794652), c='r')
plt.scatter(xdata, func(np.array(xdata), 0.9232, 4.05396), c='g')
plt.show()

and found that curve_fit() gave good well-fitting parameters. The problem is with your other solution.

Suggestions:

Don't use from X import * . It makes code extremely hard to manage in some cases.

Don't use eval() if you don't need it. In this case:

def func(x, a, b):
    return 1. / (a * x + b)

is shorter and clearer.