Bengt Fornbeg weights for finite difference

fornberg.py

import numpy as np

def weights(z, x, m=0):
    """
    Fornberg finite difference weights.
    F90: https://github.com/bjodah/finitediff/blob/master/src/finitediff_fort.f90

    Made this for Advent of Code 2023, Day 9.

    Arguments:
        z: location where approximations are to be accurate
        x: grid point locations, found in x(0:n)
        m: highest derivative for which weights are sought

    Returns:
        array

    References:
        B Fornberg (1988). Generation of Finite Difference Formulas on
            Arbitrarily Spaced Grids, Mathematics of Compuation 51 (184),
            p 699-706, doi: 10.1090/S0025-5718-1988-0935077-0.

    Example:
        >>> weights(6, range(6), 0)
        array([[ -1],
               [  6],
               [-15],
               [ 20],
               [-15],
               [  6]])
    """
    n = len(x) - 1
    c = np.zeros((n+1, m+1))
    c1 = 1
    c4 = x[0] - z
    c[0, 0] = 1

    for i in range(1, n+1):
        mn = min(i, m)
        c2 = 1
        c5 = c4
        c4 = x[i] - z
        for j in range(i):
            c3 = x[i] - x[j]
            c2 *= c3
            if j == i - 1:
                for k in range(mn, 0, -1):
                    c[i, k] = c1 * (k * c[i-1, k-1] - c5 * c[i-1, k]) / c2
                c[i, 0] = -c1 * c5 * c[i-1, 0] / c2
            for k in range(mn, 0, -1):
                c[j, k] = (c4 * c[j, k] - k * c[j, k-1]) / c3
            c[j, 0] = c4 * c[j, 0] / c3
        c1 = c2

    return c