undef appeared during prepre_jacobian for Dual of BigFloat

[ErikQQY]

Also, find this issue while implementing SciML/BoundaryValueDiffEq.jl#258

Actually, I narrowed this down from BoundaryValueDiffEq.jl to NonlinearSolve.jl, and finally to DI, so this may affect NonlinearSolve as well. This MWE is just proof of the idea and may be not meaningful, but can still represent the issue here. When the x in prepare_jacobian is a Dual number of BigFloat, there would be undef in the output.

using ForwardDiff, DifferentiationInterface, SparseMatrixColorings, ADTypes
const DI = DifferentiationInterface

backend = AutoSparse(
    AutoForwardDiff(),
    sparsity_detector = ADTypes.KnownJacobianSparsityDetector(ones(3, 3)),
    coloring_algorithm = ConstantColoringAlgorithm(ones(3, 3), ones(Int64, 3))
)
a = ForwardDiff.Dual{:tag}(BigFloat(1.0), BigFloat(1.0))
u0 = [a for _ in 1:3]
jac_cache = DI.prepare_jacobian(nothing, BigFloat.([1.0,1.0,1.0]), backend, u0)

DifferentiationInterfaceSparseMatrixColoringsExt.PushforwardSparseJacobianPrep{DifferentiationInterface.BatchSizeSettings{1, true, true}, SparseMatrixColorings.ColumnColoringResult{Matrix{Float64}, SparseMatrixColorings.BipartiteGraph{Int64}, Vector{SubArray{Int64, 1, Vector{Int64}, Tuple{UnitRange{Int64}}, true}}}, Matrix{BigFloat}, Vector{Tuple{Vector{ForwardDiff.Dual{:tag, BigFloat, 1}}}}, Vector{Tuple{Vector{BigFloat}}}, DifferentiationInterfaceForwardDiffExt.ForwardDiffTwoArgPushforwardPrep{Nothing, Vector{ForwardDiff.Dual{Nothing, ForwardDiff.Dual{:tag, BigFloat, 1}, 1}}, Vector{ForwardDiff.Dual{Nothing, BigFloat, 1}}}}(DifferentiationInterface.BatchSizeSettings{1, true, true}(1, 1, 0), SparseMatrixColorings.ColumnColoringResult{Matrix{Float64}, SparseMatrixColorings.BipartiteGraph{Int64}, Vector{SubArray{Int64, 1, Vector{Int64}, Tuple{UnitRange{Int64}}, true}}}([1.0 1.0 1.0; 1.0 1.0 1.0; 1.0 1.0 1.0], SparseMatrixColorings.BipartiteGraph{Int64}(SparseMatrixColorings.SparsityPatternCSC{Int64}(3, 3, [1, 4, 7, 10], [1, 2, 3, 1, 2, 3, 1, 2, 3]), SparseMatrixColorings.SparsityPatternCSC{Int64}(3, 3, [1, 4, 7, 10], [1, 2, 3, 1, 2, 3, 1, 2, 3])), [1, 1, 1], SubArray{Int64, 1, Vector{Int64}, Tuple{UnitRange{Int64}}, true}[[1, 2, 3]], [1, 2, 3, 1, 2, 3, 1, 2, 3]), BigFloat[#undef; #undef; #undef;;], Tuple{Vector{ForwardDiff.Dual{:tag, BigFloat, 1}}}[([Dual{:tag}(1.0,0.0), Dual{:tag}(1.0,0.0), Dual{:tag}(1.0,0.0)],)], Tuple{Vector{BigFloat}}[([#undef, #undef, #undef],)], DifferentiationInterfaceForwardDiffExt.ForwardDiffTwoArgPushforwardPrep{Nothing, Vector{ForwardDiff.Dual{Nothing, ForwardDiff.Dual{:tag, BigFloat, 1}, 1}}, Vector{ForwardDiff.Dual{Nothing, BigFloat, 1}}}(ForwardDiff.Dual{Nothing, ForwardDiff.Dual{:tag, BigFloat, 1}, 1}[#undef, #undef, #undef], ForwardDiff.Dual{Nothing, BigFloat, 1}[#undef, #undef, #undef]))

These undef make the afterward Jacobian computation throw errors.

[gdalle]

Hi @ErikQQY! Thanks for reporting this.
I think these #undefs are supposed to be there, because the Jacobian preparation initializes some storage with similar , and BigFloat is not a bitstype so #undef is what you get as elements of an uninitialized array.
Can you give me an example where the Jacobian itself errors? I tried the following and it works:

DI.jacobian(copyto!, similar(u0), backend, u0)

Note that your version would fail

DI.jacobian(copyto!, BigFloat.([1.0, 1.0, 1.0]), backend, u0)

but that's only because you initialize y with the wrong type (BigFloat instead of Dual{BigFloat}). Does that make sense?

[gdalle]

Also note that the constant coloring you give in your example is not correct. With a dense Jacobian sparsity pattern like ones(3, 3), you need to give each column a different color to be able to recover all values.

[ErikQQY]

Oh, after further investigation, it turns out that the error is on the NonlinearSolve side, which initializes the storage with similar on u0(direct similar on Dual of BigFloat would be undef), and passes the undef y with u0 to prepare_jacobian, sorry for the false alarm and thank you for your patient response🙂