smooth-approx.py

from dataclasses import dataclass
from random import random

@dataclass
class Vector:
    x : float
    y : float

    def __sub__(v1, v2):
        return Vector(v1.x - v2.x, v1.y - v2.y)

    def norm(v):
        return v.x * v.x + v.y * v.y

N = 5
params, vs = [], []

for idx in range(N):
    vs.append(Vector(random(), random()))
    params.append(random())

def g(n, v0):
    z = 1
    for (k, v) in enumerate(vs):
        if k != n:
            z *= (v - v0).norm() / (v - vs[n]).norm()

    return z

f = lambda v: sum(map(lambda k: params[k] * g(k, v), range(N)))