Numerical Differentiation ++ - Ian Bell [CppNow 2021]

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Numerical differentiation with automatic differentiation or complex mathematics allows finite differentiation to numerical precision with a quite reasonable computational overhead. But doing this generically is non-trivial indeed. The core code is working great and has Python wrappers, but some design goals seem impossible to achieve in C++. I hope to explain my challenges and hope to engage the community to help me out.
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Ian Bell is a Mechanical Engineer at the National Institute of Standards and Technology and has written a number of C++ libraries to do useful things in numerics, optimization, and thermophysics.
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May 1, 2022 - May 6, 2022 - Aspen, Colorado
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[christophclear]

For the most part, managing variants directly is somewhat of a nuisance. What we do is have a macro (yeah) handling reasonable enums, create an enum E with it, and then have a template V<T> with template template parameter T that creates a variant that contains all T<e> for all enum values e of E. That way adding a value to E is sufficient to expand everything, and you can then specialize the template T if you want to.

Great lightning talk! Would love to see a full length talk based on this. Also curious to hear about your experiences with symbolic differentiation (and code generation), and how you view the pro's and con's.

[MusicEngineeer]

is there some code available that demonstrates the proposed solution? i must admit that i'm not able to immediately fill in the details from just being told that the solution is to "use std::vector<std::variant> + visitors + concepts" even though i do know what all these things are in isolation

[csokkerzon]

About the compile time issue: what if you put the rarely changing part of the template code and the explicit insantiations in a precompiled header?

[JohnDlugosz]

Help Requested bullet 2, at the very end:
Look at the talk here about Circle.

[quentinquadrat]

I'm big fan of C++ but for some problems that cannot be easily done with it, people should stop losing effort on it and use instead a better language that can solve easily by design (i.e Julia, Lisp ...)