Mixed-mode Jacobian failed when Tracker as the reverse mode backend

[ErikQQY]

Mixed-mode Jacobian works great when we chose Enzyme or Zygote as the reverse mode backend, however, there seems to be some problems with Tracker.jl when it was chosen as the backend.

using ADTypes
using ForwardDiff
using Tracker
using Random
using StableRNGs
using DifferentiationInterface
using SparseConnectivityTracer
using SparseMatrixColorings
const DI = DifferentiationInterface
xbig = rand(1000)
sparse_mixed_backend = AutoSparse(
    MixedMode(AutoForwardDiff(), AutoTracker()),
    sparsity_detector=TracerSparsityDetector(),
    coloring_algorithm=GreedyColoringAlgorithm(RandomOrder(MersenneTwister(0)))
)
arrowhead(x) = x .+ x[1] .+ vcat(sum(x), zeros(eltype(x), length(x)-1))
prep=prepare_jacobian(arrowhead, sparse_mixed_backend, xbig)
DI.jacobian(arrowhead, prep, sparse_mixed_backend, xbig)

Error

ERROR: MethodError: no method matching Float64(::Tracker.TrackedReal{Float64})
The type `Float64` exists, but no method is defined for this combination of argument types when trying to construct it.

Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
   @ Base rounding.jl:265
  (::Type{T})(::T) where T<:Number
   @ Core boot.jl:900
  Float64(::IrrationalConstants.Invsqrtπ)
   @ IrrationalConstants ~/.julia/packages/IrrationalConstants/vp5v4/src/macro.jl:112
  ...

Stacktrace:
  [1] convert(::Type{Float64}, x::Tracker.TrackedReal{Float64})
    @ Base ./number.jl:7
  [2] setindex!(A::Vector{Float64}, x::Tracker.TrackedReal{Float64}, i::Int64)
    @ Base ./array.jl:976
  [3] (::Tracker.var"#506#508"{@Kwargs{}, TrackedVector{Float64, Vector{Float64}}, Tuple{Int64}})(Δ::Tracker.TrackedReal{Tracker.TrackedReal{Float64}})
    @ Tracker ~/.julia/packages/Tracker/6rnwO/src/lib/array.jl:103
  [4] back_(g::Tracker.Grads, c::Tracker.Call{Tracker.var"#506#508"{…}, Tuple{…}}, Δ::Tracker.TrackedReal{Tracker.TrackedReal{…}})
    @ Tracker ~/.julia/packages/Tracker/6rnwO/src/back.jl:110
  [5] back(g::Tracker.Grads, x::Tracker.Tracked{Float64}, Δ::Tracker.TrackedReal{Tracker.TrackedReal{Float64}})
    @ Tracker ~/.julia/packages/Tracker/6rnwO/src/back.jl:125
  [6] #710
    @ ~/.julia/packages/Tracker/6rnwO/src/back.jl:113 [inlined]
  [7] #72
    @ ./tuple.jl:693 [inlined]
  [8] BottomRF
    @ ./reduce.jl:86 [inlined]
  [9] _foldl_impl(op::Base.BottomRF{Base.var"#72#73"{Tracker.var"#710#711"{…}}}, init::Nothing, itr::Base.Iterators.Zip{Tuple{Tuple{…}, Tuple{…}}})
    @ Base ./reduce.jl:62
 [10] foldl_impl
    @ ./reduce.jl:48 [inlined]
 [11] mapfoldl_impl
    @ ./reduce.jl:44 [inlined]
 [12] mapfoldl
    @ ./reduce.jl:175 [inlined]
 [13] foldl
    @ ./reduce.jl:198 [inlined]
 [14] foreach
    @ ./tuple.jl:693 [inlined]
 [15] back_(g::Tracker.Grads, c::Tracker.Call{Tracker.var"#back#703"{…}, Tuple{…}}, Δ::Vector{Float64})
    @ Tracker ~/.julia/packages/Tracker/6rnwO/src/back.jl:113
 [16] back(g::Tracker.Grads, x::Tracker.Tracked{Vector{Tracker.TrackedReal{Float64}}}, Δ::Vector{Float64})
    @ Tracker ~/.julia/packages/Tracker/6rnwO/src/back.jl:125
 [17] #712
    @ ~/.julia/packages/Tracker/6rnwO/src/back.jl:140 [inlined]
 [18] #715
    @ ~/.julia/packages/Tracker/6rnwO/src/back.jl:149 [inlined]
 [19] (::DifferentiationInterfaceTrackerExt.var"#3#4"{Tracker.var"#715#717"{Tuple{TrackedVector{…}}, Tracker.var"#712#713"{Params, TrackedVector{…}}}})(dy::Vector{Float64})
    @ DifferentiationInterfaceTrackerExt ~/.julia/packages/DifferentiationInterface/S3Qp3/ext/DifferentiationInterfaceTrackerExt/DifferentiationInterfaceTrackerExt.jl:60
 [20] map
    @ ./tuple.jl:355 [inlined]
 [21] value_and_pullback
    @ ~/.julia/packages/DifferentiationInterface/S3Qp3/ext/DifferentiationInterfaceTrackerExt/DifferentiationInterfaceTrackerExt.jl:59 [inlined]
 [22] value_and_pullback!(::typeof(arrowhead), ::Tuple{…}, ::DifferentiationInterfaceTrackerExt.TrackerPullbackPrepSamePoint{…}, ::AutoTracker, ::Vector{…}, ::Tuple{…})
    @ DifferentiationInterface ~/.julia/packages/DifferentiationInterface/S3Qp3/src/first_order/pullback.jl:204
 [23] pullback!
    @ ~/.julia/packages/DifferentiationInterface/S3Qp3/src/first_order/pullback.jl:229 [inlined]
 [24] _sparse_jacobian_aux!(::Tuple{…}, ::SparseArrays.SparseMatrixCSC{…}, ::DifferentiationInterfaceSparseMatrixColoringsExt.MixedModeSparseJacobianPrep{…}, ::AutoSparse{…}, ::Vector{…})
    @ DifferentiationInterfaceSparseMatrixColoringsExt ~/.julia/packages/DifferentiationInterface/S3Qp3/ext/DifferentiationInterfaceSparseMatrixColoringsExt/jacobian_mixed.jl:208
 [25] jacobian!
    @ ~/.julia/packages/DifferentiationInterface/S3Qp3/ext/DifferentiationInterfaceSparseMatrixColoringsExt/jacobian.jl:158 [inlined]
 [26] jacobian(::typeof(arrowhead), ::DifferentiationInterfaceSparseMatrixColoringsExt.MixedModeSparseJacobianPrep{…}, ::AutoSparse{…}, ::Vector{…})
    @ DifferentiationInterfaceSparseMatrixColoringsExt ~/.julia/packages/DifferentiationInterface/S3Qp3/ext/DifferentiationInterfaceSparseMatrixColoringsExt/jacobian.jl:165
 [27] top-level scope
    @ REPL[15]:1
Some type information was truncated. Use `show(err)` to see complete types.