[Python] scipy curve_fit raises "OptimizeWarning: Covariance of the parameters could not be...

I am trying to fit this function to some data:



But when I use my code

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

def f(x, start, end):
res = np.empty_like(x)
res[x < start] =-1
res[x > end] = 1
linear = np.all([[start <= x], [x <= end]], axis=0)[0]
res[linear] = np.linspace(-1., 1., num=np.sum(linear))
return res

if __name__ == '__main__':

xdata = np.linspace(0., 1000., 1000)
ydata = -np.ones(1000)
ydata[500:1000] = 1.
ydata = ydata + np.random.normal(0., 0.25, len(ydata))

popt, pcov = curve_fit(f, xdata, ydata, p0=[495., 505.])
print(popt, pcov)
plt.figure()
plt.plot(xdata, f(xdata, *popt), 'r-', label='fit')
plt.plot(xdata, ydata, 'b-', label='data')
plt.show()


I get the warning

OptimizeWarning: Covariance of the parameters could not be estimated


Output:



In this example start and end should be closer to 500, but they don't change at all from my initial guess.

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