Support Enzyme through EnzymeRules

[vchuravy]

Took a stab at defining a rule for Enzyme, still need to port the reverse rule

[gdalle]

Hi, thanks for the contribution! I didn't think anyone was actually using this package. Are you sure you pushed all the commits?

[vchuravy]

sigh missed the extension itself.

I was looking at ImplicitDifferentiation for AD through non linear problems and adjoint models for implicit time integration.

[gdalle]

I was looking at ImplicitDifferentiation for AD through non linear problems and adjoint models for implicit time integration.

Feel free to suggest any improvements! Right now the biggest limitations are

• the out-of-place linear operator
• the allocating linear solver of KrylovKit (but it was the one that came closest to idiomatic Julia without type restrictions, as opposed to Krylov which has lots of weird conversions)

[gdalle]

Thanks for the contribution! Before I review, can you add Enzyme to the systematic tests, both as an inner and as an outer backend, to see if they run?