How to print Gaussian curve fitting results?

Question

It took me some time but I have used the code below to create myself a Gaussian fit for my x,y data set.

import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit
def Gauss(x, a, x0, sigma, offset):
    return a * np.exp(-(x - x0)**2 / (2 * sigma**2)) + offset
x, y = np.random.random(100), np.random.random(100)
popt, pcov = curve_fit(Gauss, x, y, p0=[np.max(y), np.median(x), np.std(x), np.min(y)])
plt.plot(x, y, 'b+:', label='data')
x_fit = np.linspace(np.min(x), np.max(x), 1000)
plt.plot(x_fit, Gauss(x_fit, *popt), 'r-', label='fit')
plt.legend()
plt.title('Something')
plt.xlabel('Anotherthing')
plt.ylabel('Athing')
plt.show()

I can see my fit is well done and see the graph and everything.

What I would like to know now is how can I print out the results of this fit on my screen such as the max value at x on fit's max point, the estimated error and etc?

Is these information accessible? If so, is there a way to print out this information? If not, can someone point me to the right direction about finding the error of the fit please?

Answer 1

as tagoma pointed out, all the relevant information of your fit is self-contained in popt (optimal parameters) and pcov (covariance matrix). In this case, given your set of parameters (a, x0, sigma, offset) you can unpack them as:

a, x0, sigma, offset = popt;

To unpack their uncertainties, similarly:

ua, ux0, usigma, uoffset = np.sqrt(np.diag(pcov));

(as they are given by their own covariances).

As far as I know, further information like chi square or standard deviations are not provided by curve_fit, and I usually implement the needed calculation just after the fit is done, simply adding up all the square deviations and dividing by original value (but that's more a statistics thing).

Hope it helped.

Answer 2

Take a look here: https://lmfit.github.io/lmfit-py/model.html [see the function result.fit_report()]. You can also add the final parameters to the label of your plot How to return the fit error in Python curve_fit.

Answer 3

The relevant information is contained in your variables popt and pcov. See scipy doc. You will be returned an array for each of these variables.