How to fit data to a given theoretical model in octave/python?

Question

I have file with a column of numerical data and I would like to fit this data to a theoretical function that should described them. The function i want to fin the data on is:

The parameter to fit are the (n,a) is there a way to fit a set of data, using octave or python, to a defined function?
Usually I do it using gnuplot but since I have to do a bit more data analysis I would like to learn ho to do it with a programming language. Thank you.

Answer 1

You definitely can. There’s many possibilities, one of the easiest one I can think of is to use a least squares approach (assuming n and a are floating point numbers and not integers). Like this more or less:

from scipy.optimize import curve_fit

def func(x, n, a):
    return x**n / (x**n + a**n)

popt, pcov = curve_fit(func, xdata, ydata)

Where”popt “ contains your optimized n, a parameters. I strongly suggest you plot your xdata, ydata and your fitted function after: depending on the noise on your xdata, ydata sometimes curve_fir can go ballistic.

https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html

Answer 2

Octave

Octave has several fitting functions. Just do a search on https://octave.sourceforge.io/docs.php for the word 'fit'.

Here's one that looks relevant to your problem, from the optim package: https://octave.sourceforge.io/optim/function/nonlin_curvefit.html