numpy.polynomial.polynomial.polyfit and numpy.polyfit return coefficients in different order

[astrofrog]

Summary

This may be a 'historical reasons' issue, but it looks like numpy.polynomial.polynomial.polyfit and numpy.polyfit return coefficients in reverse order from each other. I wonder if one of the functions should be deprecated from the public API in future, as having two functions with the same name in the same package that operate differently can lead to confusion?

Reproducing code example:

import numpy as np
from numpy.polynomial.polynomial import polyfit

x = np.linspace(0, 1, 100)
y = x ** 3

p1 = np.polyfit(x, y, 3)
p2 = polyfit(x, y, 3)

print('p1', p1)
print('p2', p2)

Result

p1 [ 1.00000000e+00  4.64782291e-16 -7.05817953e-16 -1.47054969e-17]
p2 [-1.93895090e-16  8.46391197e-16 -7.28660556e-16  1.00000000e+00]

Numpy/Python version information:

Python 3.6, Numpy 1.15.0, installed with conda.

[charris]

It was the original intention to deprecate the old, but that did not fly due to its wide use. We should probably add a note to polyfit promoting the new function. BTW, numpy.polynomial.polynomial.polyfit is intended as a building block, users should be using numpy.polynomial.Polynomial.fit, i.e., the Polynomial class function.