gaussian fit with scipy.optimize.curve_fit in python with wrong results

Question

I am having some trouble to fit a gaussian to data. I think the problem is that most of the elements are close to zero, and there not many points to actually be fitted. But

Answer 1

Your problem is with the initial parameters of the curve_fit. By default, if no other information is given, it will start with an array of 1, but this obviously lead to a radically wrong result. This can be corrected simply by giving a reasonable starting vector. To do this, I start from the estimated mean and standard deviation of your dataset

#estimate mean and standard deviation
meam = sum(x * y)
sigma = sum(y * (x - m)**2)
#do the fit!
popt, pcov = curve_fit(gauss_function, x, y, p0 = [1, mean, sigma])
#plot the fit results
plot(x,gauss_function(x, *popt))
#confront with the given data
plot(x,y,'ok')

This will perfectly approximate your results. Remember that curve fitting in general cannot work unless you start from a good point (inside the convergence basin, to be clear), and this doesn't depend on the implementation. Never do blind fit when you can use your knowledge!