Lagrange Interpolation using a closure and a namedtuple vs a class and a dataclass

lagrange_interp.py

from collections import namedtuple

Point = namedtuple('Point', ['x', 'y'])

def lagrange_interp(points):
    def interp(x):
        y = 0
        for pj in points:
            l = 1
            xj = pj.x
            for pi in points:
                xi = pi.x
                if xi == xj:
                    continue
                l *= (x - xi) / (xj - xi)
            y += pj.y * l
        return y
    return interp

f = lagrange_interp( [Point(0,0), Point(1,1)] )
f(19) # => 19



## Class style:

from dataclasses import dataclass

@dataclass
class Point:
    x: float
    y: float

class lagrange_interp:
    def __init__(self, points):
        self.points = points
    def __call__(self, x):
        y = 0
        for pj in self.points:
            l = 1
            xj = pj.x
            for pi in self.points:
                xi = pi.x
                if xi == xj:
                    continue
                l *= (x - xi) / (xj - xi)
            y += pj.y * l
        return y
    
f = lagrange_interp( [Point(0,0), Point(1,1)] )
f(19) # => 19