Lagrange Interpolation and Gregory-Newton Interpolation

Gino Prasad

09/18/2022

def delta(k, delta_cache):
    if len(delta_cache) <= k:
        for _ in range(k - len(delta_cache) + 1):
            delta_cache.append([])
            for i, val in enumerate(delta_cache[-2][:-1]):
                delta_cache[-1].append(delta_cache[-2][i+1] - val)
    return delta_cache[k]

def gregory_newton_interpolation(inps, vals, x):
    delta_cache = [vals]

    assert not any(delta(2, [inps]))
    
    print(delta(0, [[4, 5, 6]]))

gregory_newton_interpolation([1, 2, 3], [2, 3, 4], 1.5)

[4, 5, 6]

def lagrange_interpolation(inps, vals, x):
    assert len(inps) == len(vals)
    sums = 0
    for i, (inp1, val) in enumerate(zip(inps, vals)):
        term = 0
        num = den = 1
        for j, inp2 in enumerate(inps):
            if i == j:
                continue
            num *= (x - inp2)
            den *= (inp1 - inp2)
        sums += (num / den) * val
    return sums

input_arr = [1, 1.2, 1.3, 1.5]
value_arr = [0.368, 0.301, 0.273, 0.223]

lagrange_interpolation(input_arr, value_arr, 1.4)

0.24733333333333346