WIP: GPU-compatibility of Jacobians

[ChrisRackauckas]

MWE:

using ForwardDiff
A =cu(-rand(3,3))
u =cu([1.0;0.0;0.0])
du =similar(u)
f(du,u) =mul!(du,A,u)
ForwardDiff.jacobian(f,du,u)

[ChrisRackauckas]

@vchuravy any idea why this would fallback to the Base broadcasting?

using ForwardDiff, CuArrays
x =CuArray([ForwardDiff.Dual(1.0f0,(0.0f0,0.0f0)) for i in1:10])
CuArrays.allowscalar(false)
ForwardDiff.partials.(Float32,x,1)

[KristofferC]

#351

The reason that PR got reverted needs to be checked here.

[ChrisRackauckas]

I see. As a continuation of #353@maleadt . The routes I'm thinking of are:

1. Requires.jl, add overloads for CuArrays. Would you accept that?
2. We may just add overloads for this in Requires of DiffEqBase. DiffEqBase has a faster @.. broadcast which gets rid of the timing issues of changing to broadcast (Julia v1.0 broadcast is quite slow :( ), and I'm not sure we could have no performance loss without using this.
3. We may just make sure the color-autodiff form of this into SparseDiffTools.jl.

Of course, not having it in ForwardDiff.jl is a hassle, and having the piracy version in DiffEqBase is a little awkward, but my main priority is to get it working for DiffEq and then find out where to put the code later.

[KristofferC]

Perhaps these @views could be reduced in "strength" by putting them where they are needed, e.g. only on the x[i]? And could the usage of @. be consistent among the changes (it's not used here, but used in other places).

[charleskawczynski]

I think we can close this now that #472 has merged.