scipy - Python curve fit library that allows me to assign bounds to parameters

Question

I'd like to be able to perform fits that allows me to fit an arbitrary curve function to data, and allows me to set arbitrary bounds on parameters, for example I want to fit function:

f(x) = a1(x-a2)^a3cdotexp(-a4*x^a5)

and say:

• a2 is in following range: (-1, 1)
• a3 and a5 are positive

There is nice scipy curve_fit function, but it doesn't allow to specify parameter bounds. There also is nice http://code.google.com/p/pyminuit/ library that does generic minimalization, and it allows to set bounds on parameters, but in my case it did not coverge.

Answer 1

Note: New in version 0.17 of SciPy

Let's suppose you want to fit a model to the data which looks like this:

y=a*t**alpha+b

and with the constraint on alpha

0<alpha<2

while other parameters a and b remains free. Then we should use the bounds option of curve_fit in the following fashion:

import numpy as np
from scipy.optimize import curve_fit
def func(t, a,alpha,b):
     return a*t**alpha+b
param_bounds=([-np.inf,0,-np.inf],[np.inf,2,np.inf])
popt, pcov = curve_fit(func, xdata, ydata,bounds=param_bounds)

Source is here.