For several hours now, I have been trying to fit a model to a (generated) dataset as a casus for a problem I've been struggling with. I generated datapoints for the function f(x) = A*cos^n(x)+b, and added some noise. When I try to fit the dataset with this function and curve_fit, I get the error
./tester.py:10: RuntimeWarning: invalid value encountered in power
return Amp*(np.cos(x))**n + b
/usr/lib/python2.7/dist-packages/scipy/optimize/minpack.py:690: OptimizeWarning: Covariance of the parameters could not be estimated category=OptimizeWarning)
The code I'm using to generate the datapoints and fit the model is the following:
#!/usr/bin/env python
from __future__ import print_function
import numpy as np
from scipy.optimize import curve_fit
from matplotlib.pyplot import figure, show, rc, plot
def f(x, Amp, n, b):
return np.real(Amp*(np.cos(x))**n + b)
x = np.arange(0, 6.28, 0.01)
randomPart = np.random.rand(len(x))-0.5
fig = figure()
sample = f(x, 5, 2, 5)+randomPart
frame = fig.add_subplot(1,1,1)
frame.plot(x, sample, label="Sample measurements")
popt, pcov = curve_fit(f, x, sample, p0=(1,1,1))
modeldata = f(x, popt[0], popt[1], popt[2])
print(modeldata)
frame.plot(x, modeldata, label="Best fit")
frame.legend()
frame.set_xlabel("x")
frame.set_ylabel("y")
show()
The noisy data is shown - see the image below.
Does any of you have a clue of what's going on? I suspect it has something to do with the power law going into the complex domain, as the real part of the function is nowhere divergent. I have tried returning only the real part of the function, setting realistic bounds in curve_fit and using a numpy array instead of a python list for p0 already as well. I'm running the latest version of scipy available to me, scipy 0.17.0-1.