Update Cholesky and SVD to use Composite

[oxinabox]

Composite was made for this case,
but we haven't changed it over, and it still uses a hack.

• SVD
• Cholesky

[nickrobinson251]

definition of Composite in ChainRulesCore

• src https://github.com/JuliaDiff/ChainRulesCore.jl/blob/master/src/differentials/composite.jl
• test https://github.com/JuliaDiff/ChainRulesCore.jl/blob/master/test/differentials/composite.jl

[nickrobinson251]

I'd like to take a go at this, to understand better whatsup with Cmposite, but will probably need some guidance. Will try to open a PR this weekend.

For SVD, will we have svd_pullback(Ȳ::Composite{<:SVD}) and then in getproperty_svd_pullback change all uses of NamedTuples to Composites?

[oxinabox]

Will try to open a PR this weekend.

It's the weekend.

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For SVD, will we have svd_pullback(Ȳ::Composite{<:SVD}) and then in getproperty_svd_pullback change all uses of NamedTuples to Composites?

That sounds right.

The important part to remember about Composites in reverse mode,
is if your primal argument was a struct, then your pullback return is a Composite.
So that is your getproperty_svd_pullback

And conversely:
if the primal return value is a struct, your pullback argument is a Composite.
so that is your svd_pullback