Can't compute ForwardDiff hessian #627
Description
I was testing the master version of Interpolations.jl on my code and ran into an error inside of an optimizer with autodifferentiation. It looks like I can't take the ForwardDiff.hessian of a 2D cubic spline interpolation any more. Below is a minimal example, which works fine on Interpolations.jl v0.15 but fails on master (for either ForwardDiff v0.10 or v1). It looks like some issue with nested Duals.
import Pkg; Pkg.activate(temp=true)
Pkg.add(name="Interpolations", rev="master")
Pkg.add(name="ForwardDiff")
import Interpolations, ForwardDiff
N = 11
x = range(1.0, 3.0, N)
y = range(-3.0, 3.0, N)
u = rand(N, N)
uitp = Interpolations.cubic_spline_interpolation((x, y), u; extrapolation_bc=Interpolations.Line())
f = x -> uitp(x[1], x[2])
x = [π/3, -π/2]
ForwardDiff.hessian(f, x)
which gives:
Activating new project at `[/var/folders/nt/ct_lf2n94_1c21908mmbx55w0000gq/T/jl_n8v5VV](http://localhost:8888/var/folders/nt/ct_lf2n94_1c21908mmbx55w0000gq/T/jl_n8v5VV)`
Updating git-repo `[https://github.com/JuliaMath/Interpolations.jl.git`](https://github.com/JuliaMath/Interpolations.jl.git%60)
Resolving package versions...
Updating `[/private/var/folders/nt/ct_lf2n94_1c21908mmbx55w0000gq/T/jl_n8v5VV/Project.toml](http://localhost:8888/private/var/folders/nt/ct_lf2n94_1c21908mmbx55w0000gq/T/jl_n8v5VV/Project.toml)`
[a98d9a8b] + Interpolations v0.16.0 `[https://github.com/JuliaMath/Interpolations.jl.git#master`](https://github.com/JuliaMath/Interpolations.jl.git#master%60)
Updating `[/private/var/folders/nt/ct_lf2n94_1c21908mmbx55w0000gq/T/jl_n8v5VV/Manifest.toml](http://localhost:8888/private/var/folders/nt/ct_lf2n94_1c21908mmbx55w0000gq/T/jl_n8v5VV/Manifest.toml)`
[79e6a3ab] + Adapt v4.3.0
[13072b0f] + AxisAlgorithms v1.1.0
[d360d2e6] + ChainRulesCore v1.25.1
[34da2185] + Compat v4.16.0
[a98d9a8b] + Interpolations v0.16.0 `[https://github.com/JuliaMath/Interpolations.jl.git#master`](https://github.com/JuliaMath/Interpolations.jl.git#master%60)
[6fe1bfb0] + OffsetArrays v1.17.0
⌅ [aea7be01] + PrecompileTools v1.2.1
[21216c6a] + Preferences v1.4.3
[c84ed2f1] + Ratios v0.4.5
[ae029012] + Requires v1.3.1
[90137ffa] + StaticArrays v1.9.13
[1e83bf80] + StaticArraysCore v1.4.3
[efce3f68] + WoodburyMatrices v1.0.0
[56f22d72] + Artifacts v1.11.0
[ade2ca70] + Dates v1.11.0
[8ba89e20] + Distributed v1.11.0
[8f399da3] + Libdl v1.11.0
[37e2e46d] + LinearAlgebra v1.11.0
[a63ad114] + Mmap v1.11.0
[de0858da] + Printf v1.11.0
[9a3f8284] + Random v1.11.0
[ea8e919c] + SHA v0.7.0
[9e88b42a] + Serialization v1.11.0
[1a1011a3] + SharedArrays v1.11.0
[6462fe0b] + Sockets v1.11.0
[2f01184e] + SparseArrays v1.11.0
[fa267f1f] + TOML v1.0.3
[cf7118a7] + UUIDs v1.11.0
[4ec0a83e] + Unicode v1.11.0
[e66e0078] + CompilerSupportLibraries_jll v1.1.1+0
[4536629a] + OpenBLAS_jll v0.3.27+1
[bea87d4a] + SuiteSparse_jll v7.7.0+0
[8e850b90] + libblastrampoline_jll v5.11.0+0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`
Resolving package versions...
Updating `[/private/var/folders/nt/ct_lf2n94_1c21908mmbx55w0000gq/T/jl_n8v5VV/Project.toml](http://localhost:8888/private/var/folders/nt/ct_lf2n94_1c21908mmbx55w0000gq/T/jl_n8v5VV/Project.toml)`
[f6369f11] + ForwardDiff v1.0.1
Updating `[/private/var/folders/nt/ct_lf2n94_1c21908mmbx55w0000gq/T/jl_n8v5VV/Manifest.toml](http://localhost:8888/private/var/folders/nt/ct_lf2n94_1c21908mmbx55w0000gq/T/jl_n8v5VV/Manifest.toml)`
[bbf7d656] + CommonSubexpressions v0.3.1
[163ba53b] + DiffResults v1.1.0
[b552c78f] + DiffRules v1.15.1
[ffbed154] + DocStringExtensions v0.9.4
[f6369f11] + ForwardDiff v1.0.1
[92d709cd] + IrrationalConstants v0.2.4
[692b3bcd] + JLLWrappers v1.7.0
[2ab3a3ac] + LogExpFunctions v0.3.29
[1914dd2f] + MacroTools v0.5.16
[77ba4419] + NaNMath v1.1.3
[276daf66] + SpecialFunctions v2.5.1
[efe28fd5] + OpenSpecFun_jll v0.5.6+0
[05823500] + OpenLibm_jll v0.8.5+0
MethodError: no method matching ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}(::Float64, ::ForwardDiff.Partials{2, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}})
The type `ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}` exists, but no method is defined for this combination of argument types when trying to construct it.
Closest candidates are:
ForwardDiff.Dual{T, V, N}(::Number) where {T, V, N}
@ ForwardDiff [~/.julia/packages/ForwardDiff/Wq9Wb/src/dual.jl:78](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/dual.jl#line=77)
ForwardDiff.Dual{T, V, N}(::Any) where {T, V, N}
@ ForwardDiff [~/.julia/packages/ForwardDiff/Wq9Wb/src/dual.jl:77](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/dual.jl#line=76)
ForwardDiff.Dual{T, V, N}(::V, ::ForwardDiff.Partials{N, V}) where {T, V, N}
@ ForwardDiff [~/.julia/packages/ForwardDiff/Wq9Wb/src/dual.jl:17](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/dual.jl#line=16)
...
Stacktrace:
[1] apply_partials(x_dual::ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}, val::Float64)
@ InterpolationsForwardDiffExt [~/.julia/packages/Interpolations/5GvP0/ext/InterpolationsForwardDiffExt.jl:19](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/Interpolations/5GvP0/ext/InterpolationsForwardDiffExt.jl#line=18)
[2] _broadcast_getindex_evalf
@ ./broadcast.jl:678 [inlined]
[3] _broadcast_getindex
@ ./broadcast.jl:651 [inlined]
[4] (::Base.Broadcast.var"#17#18"{Base.Broadcast.Broadcasted{Base.Broadcast.Style{Tuple}, Nothing, typeof(InterpolationsForwardDiffExt.apply_partials), Tuple{Tuple{ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}}, Tuple{Float64, Float64}}}})(k::Int64)
@ Base.Broadcast ./broadcast.jl:1102
[5] ntuple
@ ./ntuple.jl:49 [inlined]
[6] copy
@ ./broadcast.jl:1102 [inlined]
[7] materialize
@ ./broadcast.jl:872 [inlined]
[8] maybe_clamp(::Interpolations.NeedsCheck, itp::Interpolations.BSplineInterpolation{Float64, 2, OffsetArrays.OffsetMatrix{Float64, Matrix{Float64}}, Interpolations.BSpline{Interpolations.Cubic{Interpolations.Line{Interpolations.OnGrid}}}, Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}}, xs::Tuple{ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}})
@ InterpolationsForwardDiffExt [~/.julia/packages/Interpolations/5GvP0/ext/InterpolationsForwardDiffExt.jl:12](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/Interpolations/5GvP0/ext/InterpolationsForwardDiffExt.jl#line=11)
[9] maybe_clamp(itp::Interpolations.BSplineInterpolation{Float64, 2, OffsetArrays.OffsetMatrix{Float64, Matrix{Float64}}, Interpolations.BSpline{Interpolations.Cubic{Interpolations.Line{Interpolations.OnGrid}}}, Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}}, xs::Tuple{ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}})
@ Interpolations [~/.julia/packages/Interpolations/5GvP0/src/Interpolations.jl:450](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/Interpolations/5GvP0/src/Interpolations.jl#line=449)
[10] ScaledInterpolation
@ [~/.julia/packages/Interpolations/5GvP0/src/scaling/scaling.jl:81](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/Interpolations/5GvP0/src/scaling/scaling.jl#line=80) [inlined]
[11] (::Interpolations.Extrapolation{Float64, 2, Interpolations.ScaledInterpolation{Float64, 2, Interpolations.BSplineInterpolation{Float64, 2, OffsetArrays.OffsetMatrix{Float64, Matrix{Float64}}, Interpolations.BSpline{Interpolations.Cubic{Interpolations.Line{Interpolations.OnGrid}}}, Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}}, Interpolations.BSpline{Interpolations.Cubic{Interpolations.Line{Interpolations.OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}, Interpolations.BSpline{Interpolations.Cubic{Interpolations.Line{Interpolations.OnGrid}}}, Interpolations.Line{Nothing}})(::ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}, ::ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2})
@ Interpolations [~/.julia/packages/Interpolations/5GvP0/src/extrapolation/extrapolation.jl:54](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/Interpolations/5GvP0/src/extrapolation/extrapolation.jl#line=53)
[12] (::var"#1#2")(x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}})
@ Main ./In[1]:12
[13] vector_mode_dual_eval!
@ [~/.julia/packages/ForwardDiff/Wq9Wb/src/apiutils.jl:24](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/apiutils.jl#line=23) [inlined]
[14] vector_mode_gradient(f::var"#1#2", x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}}})
@ ForwardDiff [~/.julia/packages/ForwardDiff/Wq9Wb/src/gradient.jl:98](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/gradient.jl#line=97)
[15] gradient
@ [~/.julia/packages/ForwardDiff/Wq9Wb/src/gradient.jl:20](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/gradient.jl#line=19) [inlined]
[16] #107
@ [~/.julia/packages/ForwardDiff/Wq9Wb/src/hessian.jl:17](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/hessian.jl#line=16) [inlined]
[17] vector_mode_dual_eval!
@ [~/.julia/packages/ForwardDiff/Wq9Wb/src/apiutils.jl:24](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/apiutils.jl#line=23) [inlined]
[18] vector_mode_jacobian(f::ForwardDiff.var"#107#108"{var"#1#2", ForwardDiff.HessianConfig{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}}}}, x::Vector{Float64}, cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}}})
@ ForwardDiff [~/.julia/packages/ForwardDiff/Wq9Wb/src/jacobian.jl:129](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/jacobian.jl#line=128)
[19] jacobian
@ [~/.julia/packages/ForwardDiff/Wq9Wb/src/jacobian.jl:22](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/jacobian.jl#line=21) [inlined]
[20] hessian
@ [~/.julia/packages/ForwardDiff/Wq9Wb/src/hessian.jl:18](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/hessian.jl#line=17) [inlined]
[21] hessian(f::var"#1#2", x::Vector{Float64}, cfg::ForwardDiff.HessianConfig{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}, 2}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#1#2", Float64}, Float64, 2}}})
@ ForwardDiff [~/.julia/packages/ForwardDiff/Wq9Wb/src/hessian.jl:15](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/hessian.jl#line=14)
[22] hessian(f::var"#1#2", x::Vector{Float64})
@ ForwardDiff [~/.julia/packages/ForwardDiff/Wq9Wb/src/hessian.jl:15](http://localhost:8888/lab/tree/FUSE/playground/~/.julia/packages/ForwardDiff/Wq9Wb/src/hessian.jl#line=14)
[23] top-level scope
@ In[1]:15