cross-posted from niplav.github.io

I recently learned about the python function scipy.optimize.curve_fit, and I'm really happy I did.

It fulfills a need I didn't know I'd always had, but never fulfilled: I often have a dataset and a function with some parameters, and I just want the damn parameters to be fitted to that dataset, even if imperfectly. Please don't ask any more annoying questions like “Is the dataset generated by a Gaussian?” or “Is the underlying process ergodic?”, just fit the goddamn curve!

And scipy.optimize.curve_fit does exactly that!

You give it a function f with some parameters a, b, c, … and a dataset consisting of input values x and output values y, and it then optimizes a, b, c, … so that f(x, a, b, c, …) is as close as possible to y (where, of course, x and y can both be numpy arrays).

This is awesome! I have some datapoints x, y and I believe it's generated by some obscure function, let's say of the form $f(x,a,b,c)=a\cdot x\cdot sin(b\cdot x+c)$, but I don't know the exact values for a, b and c?

No problem! I just throw the whole thing into curve_fit (scipy.optimize.curve_fit(f, x, y)) and out comes an array of optimal values for a, b, c!

What if I then want c to be necessarily positive?

Trivial! curve_fit comes with an optional argument called bounds, since b is the second argument, I call scipy.optimize.curve_fit(f, x, y, bounds=([-numpy.inf, -numpy.inf, 0], numpy.inf)), which says that curve_fit should not make the second argument smaller than zero, but otherwise can do whatever it wants.

So far, I've already used this function two times, and I've only known about it for a week! A must for every wannabe data-scientist.

For more information about this amazing function, consult its documentation.