[eigen] cppduals - dual number implementation with Eigen specializations

[Michael Tesch <tesch1@xxxxxxxxx>]

Hello,

I've written (yet another!) Dual Number implementation for automatic differentiation.  It is meant to be used as the value-type in Eigen matrices, and has templates for vectorization (shockingly) similar to (and based on) Eigen's complex-type vectorizations.  It is quite fast for first-order forward diff, and imho pretty easy to use.  There are also SSE/SSE3/AVX vectorizations for std::complex<dual< float | double >> types.

The library is here: https://gitlab.com/tesch1/cppduals , and there's a small paper in JOSS too: https://doi.org/10.21105/joss.01487

I hope this could be useful for someone and would be glad for any feedback, improvements, etc..

It would be interesting to compare this approach to others, by hand-wavey arguments I believe it should ultimately be faster in certain cases.

Cheers,

Michael