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from math import isinf
def product(xs):
p = 1
for x in xs:
p *= x
return p
# O(n) time per interpolation once the weights are computed for the sample points.
def interp(xs, ws, fs, x):
y, l = 0, 0
for xi, wi, fi in zip(xs, ws, fs):
if x == xi: return fi
li = wi/(x - xi)
yi = li*fi
if isinf(yi): return fi # Only check that should be needed, but Python raises div-by-zero FP exceptions.
y += yi
l += li
return y/l
# O(n^2) time, but only depends on sample points, not on function values.
def weights(xs):
return [1/product(xi - xj for j, xj in enumerate(xs) if i != j) for i, xi in enumerate(xs)]
xs = [-1, 0, 1]
ws = weights(xs)
r = 1e200
fs = [r, 0, r]
print([interp(xs, ws, fs, x) for x in (-3, -2, 1, 0, 1, 2, 3)])
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