ForwardDiff Vectorization with AkimaInterpolations doesn't work

Describe the bug 🐞

When trying to vectorize derivatives in ForwardDiff (i.e. compute derivatives for a vector), a MethodError is thrown instead of the expected behavior.

Expected behavior

That the derivative be computed for the entire vector.

Quick edit: I expected the result to be identical to the code here: map(x->ForwardDiff.derivative(test,x), [0.5,1.5])

Minimal Reproducible Example 👇

test = AkimaInterpolation([1,2,3], [1,2,3]; extrapolate = true)
ForwardDiff.derivative.(test,[0.5,1.5])

Error & Stacktrace ⚠️

MethodError: no method matching length(::AkimaInterpolation{Vector{Int64}, Vector{Int64}, Vector{Float64}, Vector{Float64}, Vector{Float64}, Int64})

Closest candidates are:
  length(!Matched::Base.MethodSpecializations)
   @ Base reflection.jl:1166
  length(!Matched::ExponentialBackOff)
   @ Base error.jl:267
  length(!Matched::Core.Compiler.InstructionStream)
   @ Base show.jl:2777
  ...

Stacktrace:
 [1] _similar_shape(itr::AkimaInterpolation{Vector{Int64}, Vector{Int64}, Vector{Float64}, Vector{Float64}, Vector{Float64}, Int64}, ::Base.HasLength)
   @ Base ./array.jl:710
 [2] _collect(cont::UnitRange{Int64}, itr::AkimaInterpolation{Vector{Int64}, Vector{Int64}, Vector{Float64}, Vector{Float64}, Vector{Float64}, Int64}, ::Base.HasEltype, isz::Base.HasLength)
   @ Base ./array.jl:765
 [3] collect(itr::AkimaInterpolation{Vector{Int64}, Vector{Int64}, Vector{Float64}, Vector{Float64}, Vector{Float64}, Int64})
   @ Base ./array.jl:759
 [4] broadcastable(x::AkimaInterpolation{Vector{Int64}, Vector{Int64}, Vector{Float64}, Vector{Float64}, Vector{Float64}, Int64})
   @ Base.Broadcast ./broadcast.jl:743
 [5] broadcasted(::typeof(ForwardDiff.derivative), ::AkimaInterpolation{Vector{Int64}, Vector{Int64}, Vector{Float64}, Vector{Float64}, Vector{Float64}, Int64}, ::Vector{Float64})
   @ Base.Broadcast ./broadcast.jl:1344
 [6] top-level scope
   @ ~/equil_model/test.ipynb:4

Environment (please complete the following information):

Output of using Pkg; Pkg.status()

Status `~/.julia/environments/v1.10/Project.toml`
  [80f14c24] AbstractMCMC v5.2.0
  [717c3277] AdaptiveMCMC v0.1.4
  [6e4b80f9] BenchmarkTools v1.5.0
  [a134a8b2] BlackBoxOptim v0.6.3
⌃ [336ed68f] CSV v0.10.13
  [5d742f6a] CSVFiles v1.0.2
⌅ [052768ef] CUDA v5.1.2
⌃ [13f3f980] CairoMakie v0.11.10
  [324d7699] CategoricalArrays v0.10.8
⌃ [082447d4] ChainRules v1.63.0
  [a93c6f00] DataFrames v1.6.1
  [82cc6244] DataInterpolations v5.2.0
  [8bb1440f] DelimitedFiles v1.9.1
⌃ [31c24e10] Distributions v0.25.107
  [bbc10e6e] DynamicHMC v3.4.7
  [5789e2e9] FileIO v1.16.3
⌃ [1a297f60] FillArrays v1.10.0
⌃ [587475ba] Flux v0.14.15
  [f6369f11] ForwardDiff v0.10.36
  [c27321d9] Glob v1.3.1
  [f67ccb44] HDF5 v0.17.2
⌃ [7073ff75] IJulia v1.24.2
⌃ [de52edbc] Integrals v4.1.0
  [a98d9a8b] Interpolations v0.15.1
  [c8e1da08] IterTools v1.10.0
⌃ [c3a54625] JET v0.8.29
⌃ [033835bb] JLD2 v0.4.46
  [9da8a3cd] JLSO v2.7.0
  [b964fa9f] LaTeXStrings v1.3.1
  [c7f686f2] MCMCChains v6.0.6
  [eff96d63] Measurements v2.11.0
  [0e6f8da7] NBodySimulator v1.10.0
  [429524aa] Optim v1.9.4
⌃ [7f7a1694] Optimization v3.19.3
⌃ [36348300] OptimizationOptimJL v0.1.14
  [90014a1f] PDMats v0.11.31
⌃ [43a3c2be] PairPlots v2.7.1
  [f0f68f2c] PlotlyJS v0.18.13
⌃ [91a5bcdd] Plots v1.40.3
  [27ebfcd6] Primes v0.5.6
  [49802e3a] ProgressBars v1.5.1
  [92933f4c] ProgressMeter v1.10.0
  [1fd47b50] QuadGK v2.9.4
⌃ [67601950] Quadrature v2.0.0
⌃ [37e2e3b7] ReverseDiff v1.15.1
  [b0e4dd01] RollingFunctions v0.8.0
⌃ [90137ffa] StaticArrays v1.9.3
  [2913bbd2] StatsBase v0.34.3
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  [ac1d9e8a] ThreadsX v0.1.12
⌃ [9e3dc215] TimeSeries v0.24.1
⌃ [fce5fe82] Turing v0.30.7
⌃ [1986cc42] Unitful v1.19.0
  [6112ee07] UnitfulAstro v1.2.1
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⌃ [02a925ec] cuDNN v1.3.0
  [37e2e46d] LinearAlgebra
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  [9e88b42a] Serialization
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Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated`

Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

Status `~/.julia/environments/v1.10/Manifest.toml`
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⌃ [587475ba] Flux v0.14.15
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⌅ [61eb1bfa] GPUCompiler v0.25.0
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⌅ [3955a311] GridLayoutBase v0.10.2
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⌃ [0bca4576] SciMLBase v2.10.0
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⌃ [727e6d20] SimpleNonlinearSolve v1.4.0
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⌃ [47a9eef4] SparseDiffTools v2.18.0
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⌅ [aedffcd0] Static v0.8.10
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⌃ [90137ffa] StaticArrays v1.9.3
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⌅ [2efcf032] SymbolicIndexingInterface v0.2.2
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  [5e66a065] TableShowUtils v0.2.6
  [3783bdb8] TableTraits v1.0.1
  [382cd787] TableTraitsUtils v1.0.2
  [bd369af6] Tables v1.11.1
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  [731e570b] TiffImages v0.10.0
⌃ [9e3dc215] TimeSeries v0.24.1
  [a759f4b9] TimerOutputs v0.5.24
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⌃ [28d57a85] Transducers v0.4.80
  [24ddb15e] TransmuteDims v0.1.16
  [d5829a12] TriangularSolve v0.2.0
  [410a4b4d] Tricks v0.1.8
  [981d1d27] TriplotBase v0.1.0
  [781d530d] TruncatedStacktraces v1.4.0
  [9d95972d] TupleTools v1.5.0
⌃ [fce5fe82] Turing v0.30.7
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
⌃ [1986cc42] Unitful v1.19.0
  [6fb2a4bd] UnitfulAngles v0.7.2
  [6112ee07] UnitfulAstro v1.2.1
  [45397f5d] UnitfulLatexify v1.6.3
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  [d80eeb9a] UnsafeAtomicsLLVM v0.1.5
  [41fe7b60] Unzip v0.2.0
  [770da0de] UpdateJulia v0.4.4
  [3d5dd08c] VectorizationBase v0.21.70
  [81def892] VersionParsing v1.3.0
  [19fa3120] VertexSafeGraphs v0.2.0
  [ea10d353] WeakRefStrings v1.4.2
  [0f1e0344] WebIO v0.8.21
  [104b5d7c] WebSockets v1.6.0
  [cc8bc4a8] Widgets v0.6.6
  [efce3f68] WoodburyMatrices v1.0.0
  [76eceee3] WorkerUtilities v1.6.1
  [c2297ded] ZMQ v1.2.6
  [e88e6eb3] Zygote v0.6.70
  [700de1a5] ZygoteRules v0.2.5
⌃ [02a925ec] cuDNN v1.3.0
⌅ [68821587] Arpack_jll v3.5.1+1
  [6e34b625] Bzip2_jll v1.0.8+1
  [4e9b3aee] CRlibm_jll v1.0.1+0
⌅ [4ee394cb] CUDA_Driver_jll v0.7.0+1
⌅ [76a88914] CUDA_Runtime_jll v0.10.1+0
⌅ [62b44479] CUDNN_jll v8.9.4+0
  [83423d85] Cairo_jll v1.18.0+2
  [5ae413db] EarCut_jll v2.2.4+0
  [2702e6a9] EpollShim_jll v0.0.20230411+0
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⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [f5851436] FFTW_jll v3.3.10+0
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  [559328eb] FriBidi_jll v1.0.14+0
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  [d2c73de3] GR_jll v0.73.6+0
  [78b55507] Gettext_jll v0.21.0+0
  [7746bdde] Glib_jll v2.80.2+0
  [3b182d85] Graphite2_jll v1.3.14+0
⌃ [0234f1f7] HDF5_jll v1.14.2+1
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
  [e33a78d0] Hwloc_jll v2.10.0+0
  [905a6f67] Imath_jll v3.1.11+0
  [1d5cc7b8] IntelOpenMP_jll v2024.1.0+0
  [aacddb02] JpegTurbo_jll v3.0.3+0
  [9c1d0b0a] JuliaNVTXCallbacks_jll v0.2.1+0
  [f7e6163d] Kaleido_jll v0.2.1+0
  [c1c5ebd0] LAME_jll v3.100.2+0
⌅ [88015f11] LERC_jll v3.0.0+1
⌅ [dad2f222] LLVMExtra_jll v0.0.29+0
  [1d63c593] LLVMOpenMP_jll v15.0.7+0
  [dd4b983a] LZO_jll v2.10.2+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.8.11+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.49.0+0
  [94ce4f54] Libiconv_jll v1.17.0+0
  [4b2f31a3] Libmount_jll v2.40.1+0
⌅ [89763e89] Libtiff_jll v4.5.1+1
  [38a345b3] Libuuid_jll v2.40.1+0
  [856f044c] MKL_jll v2024.1.0+0
  [7cb0a576] MPICH_jll v4.2.1+1
  [f1f71cc9] MPItrampoline_jll v5.4.0+0
  [9237b28f] MicrosoftMPI_jll v10.1.4+2
  [e98f9f5b] NVTX_jll v3.1.0+2
  [e7412a2a] Ogg_jll v1.3.5+1
  [18a262bb] OpenEXR_jll v3.2.4+0
  [fe0851c0] OpenMPI_jll v5.0.3+0
  [458c3c95] OpenSSL_jll v3.0.14+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [36c8627f] Pango_jll v1.52.2+0
  [30392449] Pixman_jll v0.43.4+0
  [c0090381] Qt6Base_jll v6.7.1+1
  [f50d1b31] Rmath_jll v0.4.2+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.31.0+0
  [02c8fc9c] XML2_jll v2.12.7+0
  [aed1982a] XSLT_jll v1.1.34+0
  [ffd25f8a] XZ_jll v5.4.6+0
  [f67eecfb] Xorg_libICE_jll v1.1.1+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.6+0
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+0
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [8f1865be] ZeroMQ_jll v4.3.5+0
  [3161d3a3] Zstd_jll v1.5.6+0
  [35ca27e7] eudev_jll v3.2.9+0
⌅ [214eeab7] fzf_jll v0.43.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [9a68df92] isoband_jll v0.2.3+0
  [477f73a3] libaec_jll v1.1.2+0
  [a4ae2306] libaom_jll v3.9.0+0
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  [f638f0a6] libfdk_aac_jll v2.0.2+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.43+1
  [075b6546] libsixel_jll v1.10.3+0
  [a9144af2] libsodium_jll v1.0.20+0
  [f27f6e37] libvorbis_jll v1.3.7+1
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [8bf52ea8] CRC32c
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [9abbd945] Profile
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.0.5+1
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+2
  [05823500] OpenLibm_jll v0.8.1+2
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

Output of versioninfo()

Julia Version 1.10.0
Commit 3120989f39b (2023-12-25 18:01 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 32 × Intel(R) Xeon(R) CPU E5-2630 v3 @ 2.40GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, haswell)
  Threads: 47 on 32 virtual cores

SciML / DataInterpolations.jl

ForwardDiff Vectorization with AkimaInterpolations doesn't work #278