2D spline interpolation example using SciPy.

scipy-interpolate.py

import sys
from math import exp
import numpy as np
from scipy.interpolate import RectBivariateSpline
import random
from time import time


def f(x, y):
    return exp(-(2.0*x)**2.0 - (y/2.0)**2.0)


rmin, rmax = -1.0, 1.0

n = 500
num_samples = 10

r = [rmin + i*(rmax - rmin)/(n - 1) for i in range(n)]

z = []
for y in r:
    z.append([f(y, x) for x in r])
z = np.array(z)

print('num grid points', n*n)
t0 = time()
interp_spline = RectBivariateSpline(r, r, z)
print('time spent in setting up', time() - t0)

print('num samples', num_samples)

random.seed(0)
t0 = time()
for _ in range(num_samples):
    x, y = random.uniform(rmin, rmax), random.uniform(rmin, rmax)
    r = interp_spline(x, y)
print('time spent in interpolating', time() - t0)

Inspired by https://scipython.com/book/chapter-8-scipy/examples/two-dimensional-interpolation-with-scipyinterpolaterectbivariatespline/.