How to fix “polyfit maybe poorly conditioned” in numpy?

Question

I am trying to do a polyfit on a set of data using numpy package.

The following is the code, it can run successfully. The fitted line seems to fit the data when the o

Answer 1

You will get a better fit if you use the Polynomial class, although if you go past the ends of the data with a high order fit you will see the fast divergence shown above because you are extrapolating. To use the Polynomial class

from numpy.polynomial import Polynomial as P
p = P.fit(x, y, order)

You can also experiment with more stable polynomial basis that will be better conditioned at high orders, say 100+, although that is hardly justified with noisy data like you are playing with.

from numpy.polynomial import Chebyshev as T
p = T.fit(x, y, order)

You can get in bounds plotting points x, y from the fits like so:

plot(*p.linspace(500))