Example integration with DI

[gdalle]

Setup

using Pkg
Pkg.activate(temp=true)
Pkg.add(url="https://github.com/SciML/ADTypes.jl", rev="gd/sparsity_detector")
Pkg.add(url="https://github.com/gdalle/DifferentiationInterface.jl", subdir="DifferentiationInterface", rev="gd/sparsity_detector")
Pkg.add(url="https://github.com/gdalle/DifferentiationInterface.jl", subdir="DifferentiationInterfaceTest")
Pkg.add(url="https://github.com/gdalle/SparseConnectivityTracer.jl", rev="main")
Pkg.add(["BenchmarkTools", "ForwardDiff", "SparseDiffTools", "Symbolics"])

using BenchmarkTools
using DifferentiationInterface
import ForwardDiff, SparseConnectivityTracer, SparseDiffTools, Symbolics

b1 = AutoSparseForwardDiff(; sparsity_detector=SparseDiffTools.SymbolicsSparsityDetection())

b2 = AutoSparseForwardDiff(;
    sparsity_detector=Base.get_extension(
        SparseConnectivityTracer,
        :SparseConnectivityTracerSparseDiffToolsExt
    ).ConnectivityTracerSparsityDetection()
)

Results:

julia> @btime prepare_jacobian($diff, $b1, $(rand(100)));
  1.271 ms (15662 allocations: 1.10 MiB)

julia> @btime prepare_jacobian($diff, $b2, $(rand(100)));
  84.229 μs (1964 allocations: 213.94 KiB)

[gdalle]

This relies on #9