Problems with StaticArrays with Dual elements should NOT go through Dual number overloads

[jClugstor]

As noted in the discourse thread: https://discourse.julialang.org/t/differentiationinterface-forwarddiff-unable-to-diff-ldiv-any-other-options-to-solve-linear-system-w-o-allocations-and-differentiate/131076/21

we should add some tests to make sure the recent ForwardDiff overloads work in the context of StaticArrays.

[jClugstor]

Currently they don't, while any StaticLinearProblem with Dual elements is also a DualAbstractLinearProblem, the definition for a StaticLinearProblem is more specific, so it goes through those dispatches instead.

const StaticLinearProblem = LinearProblem{uType, iip, <:SMatrix,
    <:Union{<:SMatrix, <:SVector}} where {uType, iip}

[jClugstor]

@oscardssmith I'm having trouble matching the types here. I want it so that StaticArrays with Dual elements are recognized as a StaticDualLinearProblem, but I can't figure out why what I have is incorrect.

infil> typeof(prob)
LinearProblem{Nothing, true, SMatrix{3, 3, ForwardDiff.Dual{ForwardDiff.Tag{typeof(static_linsolve), Float64}, Float64, 2}, 9}, SVector{3, ForwardDiff.Dual{ForwardDiff.Tag{typeof(static_linsolve), Float64}, Float64, 2}}, SciMLBase.NullParameters, Nothing, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}}

infil> DualStaticLinearProblem = LinearProblem{
           <:Union{Number, <:AbstractArray, Nothing}, iip,
           <:StaticArray{Size, <:Dual{T, V, P}, N},
           <:StaticArray{Size, <:Dual{T, V, P}, N},
           <:Any
       } where {iip, T, V, P, N, Size}
LinearProblem{<:Union{Nothing, Number, var"#s408"} where var"#s408"<:AbstractArray, iip, <:StaticArray{Size, <:ForwardDiff.Dual{T, V, P}, N}, <:StaticArray{Size, <:ForwardDiff.Dual{T, V, P}, N}} where {iip, T, V, P, N, Size}

infil> prob isa DualStaticLinearProblem
false

The types for A and b should match, prob.A isa <:StaticArray{Size, <:Dual{T,V,P},N} where {Size, T, V, P, N} and same for prob.b. Any clue where the problem is?

[oscardssmith]

why do these need a separate codepath?

[ChrisRackauckas]

It should just direct differentiate the static array code, no overload required for those

[jClugstor]

Oh ok, then there's no issue then, since that's what happens currently.

[jClugstor]

Nevermind, I must have had a weird environment or something, these problems do end up going through the overload. I'm not sure why it wasn't doing that for me before.

I'm confused though, I thought that const StaticLinearProblem = LinearProblem{uType, iip, <:SMatrix, <:Union{<:SMatrix, <:SVector}} where {uType, iip} would be more specific than the definitions for the DualLinearProblems?

[jClugstor]

Oh, what's happening is that for solve it goes through the StaticLinearProblem dispatch, but if I try to create a cache through init it ends up as a DualLinearCache, because there's no special init for StaticLinearProblem.