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Complex Differentiation #1

@jrevels

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@jrevels

Complex differentiation is one of those features that I had always planned on officially supporting in previous packages, but I never got around to grinding out the details/API consequences.

Since I see Capstan as my "fresh start" to AD now that Cassette is on the table, maybe it's time to dive into complex AD for real (pun intended).

Ideally, Capstan could eventually provide an API that supports differentiating:

  • non-holomorphic functions
  • C^N -> C^M functions
  • R^N -> C^M functions
  • C^N -> R^M functions

Relevant resources include https://arxiv.org/abs/0906.4835 (thanks for introducing me to this material, @ssfrr).

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