Why doesn't use the variable value inside the function in python

Question

Why doesn't the following function take the inner h value that is defined in the function body and gives weird results (arbitrary h value)?

def diff(f): # def not define
       h = 0.001
       return (lambda x: (f(x+h) - f(x)) / h) 
def sin_by_million (x):
    return math.sin( 10 ** 6 *x)
>>> diff(sin_by_million) (0)
826.8795405320026

Instead of 1000000?

Because your h is much too large to have a correct approximation of the derivative in 0. — Thierry Lathuille
– Thierry Lathuille, Commented Jan 23, 2021 at 17:47
also your code is badly formatted (define doesn't exist, extra paren before lamba) — Pierre D
– Pierre D, Commented Jan 23, 2021 at 17:49

Pierre D · Accepted Answer · 2021-01-23 18:04:35Z

1

As per @ThierryLathuille comment, your step h is too big. In real life, you should adapt it based on the function and value at which you want the derivative.

Check out jax instead:

import jax
import jax.numpy as np

def sin_by_million(x):
    return np.sin(1e6 * x)

Then:

>>> g = jax.grad(sin_by_million)
... g(0.0)
DeviceArray(1000000., dtype=float32)

The beauty of jax is that it actually compiles your call tree using chain rule, and produces some code (the calls after the first one are much, much faster). It also works on multivariate functions and complex code (with some rules though). And it works wonderfully well & fast on GPUs.

edited Jan 23, 2021 at 18:04

answered Jan 23, 2021 at 17:57

Pierre D

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