So, I'm trying to fit a set of data with a power law of the following kind:
def f(x,N,a): # Power law fit
if a >0:
return N*x**(-a)
else:
return 10.**300
par,cov = scipy.optimize.curve_fit(f,data,time,array([10**(-7),1.2]))
where the else condition is just to force a to be positive. Using scipy.optimize.curve_fit yields an awful fit (green line), returning values of 1.2e+04 and 1.9e0-7 for N and a, respectively, with absolutely no intersection with the data. From fits I've put in manually, the values should land around 1e-07 and 1.2 for N and a, respectively, though putting those into curve_fit as initial parameters doesn't change the result. Removing the condition for a to be positive results in a worse fit, as it chooses a negative, which leads to a fit with the wrong sign slope.
I can't figure out how to get a believable, let alone reliable, fit out of this routine, but I can't find any other good Python curve fitting routines. Do I need to write my own least-squares algorithm or is there something I'm doing wrong here?