Jacobians

[willtebbutt]

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.

[oxinabox]

A Wirtinger is a flavour of Jacobian, no?

[oxinabox]

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.

[sethaxen]

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).

[sethaxen]

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