Lagrange polynomials and numpy Polynomials

My issue is about the documentation of lagrange interpolation here: https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.lagrange.html lagrange returns a numpy.poly1d that contains “The polynomial’s coefficients, in decreasing powers”

Then, the documentation shows to pass this result to numpy Polynomials. But this class accepts as parameters “Polynomial coefficients in order of increasing degree” https://numpy.org/doc/stable/reference/generated/numpy.polynomial.polynomial.Polynomial.html

Does it seem like a conceptual error? Coefficients are the same, but the order is reversed so when you want to interpolate things do not work well

Reproducing code example:

from numpy.polynomial.polynomial import Polynomial
from scipy.interpolate import lagrange
x = np.array([0, 1, 2])
y = x**3
poly = lagrange(x, y)

poly1d([ 3., -2.,  0.]) #3x^2 -2x

Polynomial(poly).coef
array([ 3., -2.,  0.]) #-2x +3

Scipy/Numpy/Python version information:

import sys, scipy, numpy; print(scipy.__version__, numpy.__version__, sys.version_info)
1.7.0 1.20.3 sys.version_info(major=3, minor=7, micro=3, releaselevel='final', serial=0)

[ev-br]

poly1d is considered legacy and its use in new code is discouraged. This function predates numpy Polynomial, so we cannot just change its return type. All in all, best is to show the recommended usage — which this example tried to do 😃.

[charris]

are there any plans w. r. t. np.poly1d

Nothing planned that I am aware of. The Chebyshev polynomials have the advantage that the coefficients are easy to compute from values sampled at the Chebyshev points, so would work well with the scipy functions that just compute the polynomial values.