JuliaDiff
Jacobians
Sometimes you actually do want the jacobian of a function. If this function is a vector->vector function, the Jacobian is a matrix. It's not immediately obvious how to define the jacobian for, say, a function that accepts a struct and returns a struct. It would be nice to figure out some sensible conventions here.
Somewhere on Zygote there was an issue about this written up by @Roger-luo I am going to end up solving this in the next few weeks. It will be interesting to look back at the solution I end up with and what our past thoughts were.
A Wirtinger is a flavour of Jacobian, no?
It's the Jacobian with a change of basis (under the constraint that the function is holomorphic).
There are so many examples on here, discourse, and Zygote docs where someone writes the Wirtinger derivative in terms of frule and rrule (e.g. https://fluxml.ai/Zygote.jl/stable/complex/). Might be worth including it for completeness in https://juliadiff.org/ChainRulesCore.jl/dev/maths/complex.html