Numerical differentiation and Integration

Hi folks,
I was wondering if somebody could recommend the best(?) package for numerical differentiation and integration. I’m mostly interested in numerics, which means that I usually have a set of points on a grid and wnat to perform the first and second derivative. What I mean to say is that it is not an analytic form what I have, it is just a collection of numbers of f(x) for a grid of points x.
Thx in advance,
Ferran.

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A small example with representative inputs would help give more detailed suggestions. The “goto” AD-packages are

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Maybe https://julialang.org/blog/2017/09/gsoc-derivative_operators

Is your function ‘f’ a black box (e.g coming from real-world measurements)? If so, ForwardDiff and ReverseDiff are not what you need.

If you have the original function, the recommendations to use automatic-differentiation are worth paying attention to. But if you have a grid of values, Interpolations may be closer to what you’re looking for. (It can compute both gradient and hessian.)

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