# Indexing of Symbolic Arrays (Arr{Num,3}) not working when a guess is provided in MTK

**URL:** <https://discourse.julialang.org/t/indexing-of-symbolic-arrays-arr-num-3-not-working-when-a-guess-is-provided-in-mtk/128631>\
**Category:** Modelling & Simulations\
**Tags:** modelingtoolkit, symbolics\
**Created:** [May 2, 2025, 2:43pm UTC](https://discourse.julialang.org/t/indexing-of-symbolic-arrays-arr-num-3-not-working-when-a-guess-is-provided-in-mtk/128631 "2025-05-02T14:43:44Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![sass-jacob](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sass-jacob/32/215582_2.png) [@sass-jacob](https://discourse.julialang.org/u/sass-jacob)\
**Post date:** [May 2, 2025, 2:43pm UTC](https://discourse.julialang.org/t/indexing-of-symbolic-arrays-arr-num-3-not-working-when-a-guess-is-provided-in-mtk/128631/1 "2025-05-02T14:43:44Z")

</div>

Hello,

I have created a MWE where the indexing of symbolic arrays begins to fail when I provide an initial guess for the variables as data for MTK. If I remove the guess, the indexing works fine.  
Edit, more info: if the guess is provided as a scalar this works properly.

```julia
function testsymarray()
    @variables begin
        b(t)[1:10, 1:10, 1:10], [guess = fill(0.0, 10, 10, 10), irreducible=true]
    end 

    var_tuple = (b = b,)

    eqs = Equation[]

    append!(eqs, somefunction(var_tuple))
end

function somefunction(var_tuple)
    (; b) = var_tuple

    b_first = b[1:end,1,1]

    return Symbolics.scalarize(b_first .~ 0.0)
end

testsymarray()

```

```julia
ERROR: ArgumentError: invalid index: i of type SymbolicUtils.BasicSymbolic{Int64}
Stacktrace:
  [1] to_index(i::SymbolicUtils.BasicSymbolic{Int64})
    @ Base ./indices.jl:315
  [2] to_index(A::Array{Float64, 3}, i::SymbolicUtils.BasicSymbolic{Int64})
    @ Base ./indices.jl:292
  [3] to_indices
    @ ./indices.jl:368 [inlined]
  [4] to_indices
    @ ./indices.jl:359 [inlined]
  [5] getindex(::Array{Float64, 3}, ::SymbolicUtils.BasicSymbolic{Int64}, ::Int64, ::Int64)
    @ Base ./abstractarray.jl:1312
  [6] (::Symbolics.var"#229#231"{…})(::SymbolicUtils.BasicSymbolic{…}, ::SymbolicUtils.BasicSymbolic{…}, ::SymbolicUtils.BasicSymbolic{…}, ::Vararg{…})
    @ Symbolics ~/.julia/packages/Symbolics/B6Z8m/src/variable.jl:39
  [7] (::Symbolics.var"#329#330"{…})(::SymbolicUtils.BasicSymbolic{…}, ::SymbolicUtils.BasicSymbolic{…}, ::Vararg{…})
    @ Symbolics ~/.julia/packages/Symbolics/B6Z8m/src/array-lib.jl:12
  [8] getindex(::SymbolicUtils.BasicSymbolic{Array{Real, 3}}, ::SymbolicUtils.BasicSymbolic{Int64}, ::Int64, ::Int64)
    @ Symbolics ~/.julia/packages/Symbolics/B6Z8m/src/array-lib.jl:86
  [9] getindex(::SymbolicUtils.BasicSymbolic{Array{Real, 3}}, ::UnitRange{Int64}, ::Int64, ::Int64)
    @ Symbolics ~/.julia/packages/Symbolics/B6Z8m/src/array-lib.jl:76
 [10] getindex(::Symbolics.Arr{Num, 3}, ::UnitRange{Int64}, ::Int64, ::Int64)
    @ Symbolics ~/.julia/packages/Symbolics/B6Z8m/src/array-lib.jl:94

```

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 3, 2025, 3:28am UTC](https://discourse.julialang.org/t/indexing-of-symbolic-arrays-arr-num-3-not-working-when-a-guess-is-provided-in-mtk/128631/2 "2025-05-03T03:28:07Z")

</div>

Open an issue. By eye it looks like it works, but it requires digging in so it should go into the issue tracker.

---

<div class="post-metadata">

**Author:** ![sass-jacob](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sass-jacob/32/215582_2.png) [@sass-jacob](https://discourse.julialang.org/u/sass-jacob)\
**Post date:** [May 4, 2025, 4:53pm UTC](https://discourse.julialang.org/t/indexing-of-symbolic-arrays-arr-num-3-not-working-when-a-guess-is-provided-in-mtk/128631/3 "2025-05-04T16:53:04Z")

</div>

Issue here:

> <https://github.com/SciML/ModelingToolkit.jl/issues/3598>
>
> \*\*Describe the bug 🐞\*\*
> 
> I have an array-valued variable that I want to provide a…n initial guess for via 'guess' specification in \`@variables\` macro. When providing this initial guess as a non-scalar, indexing issues arise for the array-valued variable.
> 
> \*\*Expected behavior\*\*
> 
> Providing an initial guess within the metadata that is array-valued should not affect the ability to index the variable associated with that initial guess.
> 
> \*\*Minimal Reproducible Example 👇\*\*
> 
> \`\`\`julia
> using ModelingToolkit
> 
> @variables begin
> a\[1:10, 1:10, 1:10\]
> b\[1:10, 1:10, 1:10\], \[guess = fill(0.0, 10, 10, 10)\]
> end 
> 
> eq\_a = a\[1:10, 1, 1:10\] .~ 1.0
> eq\_b = b\[1:10, 1, 1:10\] .~ 1.0 # errors here
> \`\`\`
> 
> \*\*Error & Stacktrace ⚠️\*\*
> 
> \`\`\`julia
> ERROR: ArgumentError: invalid index: i of type SymbolicUtils.BasicSymbolic{Int64}
> Stacktrace:
> \[1\] to\_index(i::SymbolicUtils.BasicSymbolic{Int64})
> @ Base ./indices.jl:315
> \[2\] to\_index(A::Array{Float64, 3}, i::SymbolicUtils.BasicSymbolic{Int64})
> @ Base ./indices.jl:292
> \[3\] to\_indices
> @ ./indices.jl:368 \[inlined\]
> \[4\] to\_indices
> @ ./indices.jl:359 \[inlined\]
> \[5\] getindex(::Array{Float64, 3}, ::SymbolicUtils.BasicSymbolic{Int64}, ::Int64, ::SymbolicUtils.BasicSymbolic{Int64})
> @ Base ./abstractarray.jl:1312
> \[6\] (::Symbolics.var"#229#231"{…})(::SymbolicUtils.BasicSymbolic{…}, ::SymbolicUtils.BasicSymbolic{…}, ::SymbolicUtils.BasicSymbolic{…}, ::Vararg{…})
> @ Symbolics ~/.julia/packages/Symbolics/B6Z8m/src/variable.jl:39
> \[7\] getindex(::SymbolicUtils.BasicSymbolic{…}, ::SymbolicUtils.BasicSymbolic{…}, ::Int64, ::SymbolicUtils.BasicSymbolic{…})
> @ Symbolics ~/.julia/packages/Symbolics/B6Z8m/src/array-lib.jl:86
> \[8\] getindex(::SymbolicUtils.BasicSymbolic{Array{Real, 3}}, ::UnitRange{Int64}, ::Int64, ::UnitRange{Int64})
> @ Symbolics ~/.julia/packages/Symbolics/B6Z8m/src/array-lib.jl:76
> \[9\] getindex(::Symbolics.Arr{Num, 3}, ::UnitRange{Int64}, ::Int64, ::UnitRange{Int64})
> @ Symbolics ~/.julia/packages/Symbolics/B6Z8m/src/array-lib.jl:94
> \[10\] top-level scope
> @ ~/.julia/dev/phase\_separation\_scripts/initial\_guess\_array\_indexing.jl:9
> Some type information was truncated. Use \`show(err)\` to see complete types.
> \`\`\`
> 
> \*\*Environment (please complete the following information):\*\*
> 
> \`\`\`julia
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> 
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> \[189a3867\] Reexport v1.2.2
> \[05181044\] RelocatableFolders v1.0.1
> \[ae029012\] Requires v1.3.1
> \[ae5879a3\] ResettableStacks v1.1.1
> \[79098fc4\] Rmath v0.8.0
> \[47965b36\] RootedTrees v2.23.1
> \[7e49a35a\] RuntimeGeneratedFunctions v0.5.14
> \[9dfe8606\] SCCNonlinearSolve v1.1.0
> \[94e857df\] SIMDTypes v0.1.0
> \[0bca4576\] SciMLBase v2.86.2
> \[19f34311\] SciMLJacobianOperators v0.1.3
> \[c0aeaf25\] SciMLOperators v0.3.14
> \[53ae85a6\] SciMLStructures v1.7.0
> \[7e506255\] ScopedValues v1.3.0
> \[6c6a2e73\] Scratch v1.2.1
> \[91c51154\] SentinelArrays v1.4.8
> \[efcf1570\] Setfield v1.1.2
> \[992d4aef\] Showoff v1.0.3
> \[777ac1f9\] SimpleBufferStream v1.2.0
> \[727e6d20\] SimpleNonlinearSolve v2.3.0
> \[699a6c99\] SimpleTraits v0.9.4
> \[ce78b400\] SimpleUnPack v1.1.0
> \[a2af1166\] SortingAlgorithms v1.2.1
> \[9f842d2f\] SparseConnectivityTracer v0.6.18
> \[47a9eef4\] SparseDiffTools v2.25.0
> \[0a514795\] SparseMatrixColorings v0.4.19
> \[276daf66\] SpecialFunctions v2.5.1
> \[860ef19b\] StableRNGs v1.0.2
> \[aedffcd0\] Static v1.2.0
> \[0d7ed370\] StaticArrayInterface v1.8.0
> \[90137ffa\] StaticArrays v1.9.13
> \[1e83bf80\] StaticArraysCore v1.4.3
> \[10745b16\] Statistics v1.11.1
> \[82ae8749\] StatsAPI v1.7.0
> \[2913bbd2\] StatsBase v0.34.4
> \[4c63d2b9\] StatsFuns v1.5.0
> \[9672c7b4\] SteadyStateDiffEq v2.5.0
> \[789caeaf\] StochasticDiffEq v6.76.0
> \[7792a7ef\] StrideArraysCore v0.5.7
> \[892a3eda\] StringManipulation v0.4.1
> \[09ab397b\] StructArrays v0.7.1
> \[c3572dad\] Sundials v4.28.0
> \[2efcf032\] SymbolicIndexingInterface v0.3.40
> \[19f23fe9\] SymbolicLimits v0.2.2
> \[d1185830\] SymbolicUtils v3.27.0
> \[0c5d862f\] Symbolics v6.38.0
> \[3783bdb8\] TableTraits v1.0.1
> \[bd369af6\] Tables v1.12.0
> \[ed4db957\] TaskLocalValues v0.1.2
> \[62fd8b95\] TensorCore v0.1.1
> \[8ea1fca8\] TermInterface v2.0.0
> \[1c621080\] TestItems v1.0.0
> \[8290d209\] ThreadingUtilities v0.5.3
> \[a759f4b9\] TimerOutputs v0.5.28
> \[e689c965\] Tracy v0.1.4
> \[3bb67fe8\] TranscodingStreams v0.11.3
> \[410a4b4d\] Tricks v0.1.10
> \[781d530d\] TruncatedStacktraces v1.4.0
> \[5c2747f8\] URIs v1.5.2
> \[3a884ed6\] UnPack v1.0.2
> \[1cfade01\] UnicodeFun v0.4.1
> \[1986cc42\] Unitful v1.22.0
> \[45397f5d\] UnitfulLatexify v1.6.4
> \[a7c27f48\] Unityper v0.1.6
> \[013be700\] UnsafeAtomics v0.3.0
> \[41fe7b60\] Unzip v0.2.0
> \[19fa3120\] VertexSafeGraphs v0.2.0
> \[897b6980\] WeakValueDicts v0.1.0
> \[efce3f68\] WoodburyMatrices v1.0.0
> \[6e34b625\] Bzip2\_jll v1.0.9+0
> \[4ee394cb\] CUDA\_Driver\_jll v0.12.1+1
> \[76a88914\] CUDA\_Runtime\_jll v0.16.1+0
> ⌃ \[83423d85\] Cairo\_jll v1.18.4+0
> \[ee1fde0b\] Dbus\_jll v1.16.2+0
> \[cd4c43a9\] Dierckx\_jll v0.2.0+0
> \[2702e6a9\] EpollShim\_jll v0.0.20230411+1
> \[2e619515\] Expat\_jll v2.6.5+0
> ⌅ \[b22a6f82\] FFMPEG\_jll v4.4.4+1
> \[f5851436\] FFTW\_jll v3.3.11+0
> \[a3f928ae\] Fontconfig\_jll v2.16.0+0
> \[d7e528f0\] FreeType2\_jll v2.13.4+0
> \[559328eb\] FriBidi\_jll v1.0.17+0
> \[0656b61e\] GLFW\_jll v3.4.0+2
> \[d2c73de3\] GR\_jll v0.73.14+0
> \[78b55507\] Gettext\_jll v0.21.0+0
> ⌃ \[7746bdde\] Glib\_jll v2.82.4+0
> \[3b182d85\] Graphite2\_jll v1.3.15+0
> \[2e76f6c2\] HarfBuzz\_jll v8.5.0+0
> \[1d5cc7b8\] IntelOpenMP\_jll v2025.0.4+0
> \[aacddb02\] JpegTurbo\_jll v3.1.1+0
> \[9c1d0b0a\] JuliaNVTXCallbacks\_jll v0.2.1+0
> \[c1c5ebd0\] LAME\_jll v3.100.2+0
> \[88015f11\] LERC\_jll v4.0.1+0
> \[dad2f222\] LLVMExtra\_jll v0.0.35+0
> \[1d63c593\] LLVMOpenMP\_jll v18.1.8+0
> \[dd4b983a\] LZO\_jll v2.10.3+0
> \[ad6e5548\] LibTracyClient\_jll v0.9.1+6
> ⌅ \[e9f186c6\] Libffi\_jll v3.2.2+2
> \[7e76a0d4\] Libglvnd\_jll v1.7.1+1
> \[94ce4f54\] Libiconv\_jll v1.18.0+0
> \[4b2f31a3\] Libmount\_jll v2.41.0+0
> \[89763e89\] Libtiff\_jll v4.7.1+0
> \[38a345b3\] Libuuid\_jll v2.41.0+0
> \[856f044c\] MKL\_jll v2025.0.1+1
> \[e98f9f5b\] NVTX\_jll v3.1.1+0
> \[e7412a2a\] Ogg\_jll v1.3.5+1
> \[458c3c95\] OpenSSL\_jll v3.5.0+0
> \[efe28fd5\] OpenSpecFun\_jll v0.5.6+0
> \[91d4177d\] Opus\_jll v1.3.3+0
> \[36c8627f\] Pango\_jll v1.56.1+0
> \[30392449\] Pixman\_jll v0.44.2+0
> ⌅ \[c0090381\] Qt6Base\_jll v6.7.1+1
> ⌅ \[629bc702\] Qt6Declarative\_jll v6.7.1+2
> ⌅ \[ce943373\] Qt6ShaderTools\_jll v6.7.1+1
> ⌃ \[e99dba38\] Qt6Wayland\_jll v6.7.1+1
> \[f50d1b31\] Rmath\_jll v0.5.1+0
> ⌅ \[fb77eaff\] Sundials\_jll v5.2.3+0
> \[a44049a8\] Vulkan\_Loader\_jll v1.3.243+0
> ⌃ \[a2964d1f\] Wayland\_jll v1.21.0+2
> \[2381bf8a\] Wayland\_protocols\_jll v1.36.0+0
> ⌅ \[02c8fc9c\] XML2\_jll v2.13.6+1
> \[ffd25f8a\] XZ\_jll v5.8.1+0
> \[f67eecfb\] Xorg\_libICE\_jll v1.1.2+0
> \[c834827a\] Xorg\_libSM\_jll v1.2.6+0
> \[4f6342f7\] Xorg\_libX11\_jll v1.8.12+0
> \[0c0b7dd1\] Xorg\_libXau\_jll v1.0.13+0
> \[935fb764\] Xorg\_libXcursor\_jll v1.2.4+0
> \[a3789734\] Xorg\_libXdmcp\_jll v1.1.6+0
> \[1082639a\] Xorg\_libXext\_jll v1.3.7+0
> \[d091e8ba\] Xorg\_libXfixes\_jll v6.0.1+0
> \[a51aa0fd\] Xorg\_libXi\_jll v1.8.3+0
> \[d1454406\] Xorg\_libXinerama\_jll v1.1.6+0
> \[ec84b674\] Xorg\_libXrandr\_jll v1.5.5+0
> \[ea2f1a96\] Xorg\_libXrender\_jll v0.9.12+0
> \[c7cfdc94\] Xorg\_libxcb\_jll v1.17.1+0
> \[cc61e674\] Xorg\_libxkbfile\_jll v1.1.3+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 v1.4.7+0
> \[33bec58e\] Xorg\_xkeyboard\_config\_jll v2.44.0+0
> \[c5fb5394\] Xorg\_xtrans\_jll v1.6.0+0
> \[3161d3a3\] Zstd\_jll v1.5.7+1
> \[1e29f10c\] demumble\_jll v1.3.0+0
> \[35ca27e7\] eudev\_jll v3.2.9+0
> \[214eeab7\] fzf\_jll v0.61.1+0
> \[1a1c6b14\] gperf\_jll v3.1.1+1
> \[a4ae2306\] libaom\_jll v3.11.0+0
> \[0ac62f75\] libass\_jll v0.15.2+0
> \[1183f4f0\] libdecor\_jll v0.2.2+0
> \[2db6ffa8\] libevdev\_jll v1.11.0+0
> \[f638f0a6\] libfdk\_aac\_jll v2.0.3+0
> \[36db933b\] libinput\_jll v1.18.0+0
> \[b53b4c65\] libpng\_jll v1.6.47+0
> \[f27f6e37\] libvorbis\_jll v1.3.7+2
> \[009596ad\] mtdev\_jll v1.1.6+0
> \[1317d2d5\] oneTBB\_jll v2022.0.0+0
> ⌅ \[1270edf5\] x264\_jll v2021.5.5+0
> ⌅ \[dfaa095f\] x265\_jll v3.5.0+0
> \[d8fb68d0\] xkbcommon\_jll v1.8.1+0
> \[0dad84c5\] ArgTools v1.1.2
> \[56f22d72\] Artifacts v1.11.0
> \[2a0f44e3\] Base64 v1.11.0
> \[ade2ca70\] Dates v1.11.0
> \[8ba89e20\] Distributed v1.11.0
> \[f43a241f\] Downloads v1.6.0
> \[7b1f6079\] FileWatching v1.11.0
> \[9fa8497b\] Future v1.11.0
> \[b77e0a4c\] InteractiveUtils v1.11.0
> \[4af54fe1\] LazyArtifacts v1.11.0
> \[b27032c2\] LibCURL v0.6.4
> \[76f85450\] LibGit2 v1.11.0
> \[8f399da3\] Libdl v1.11.0
> \[37e2e46d\] LinearAlgebra v1.11.0
> \[56ddb016\] Logging v1.11.0
> \[d6f4376e\] Markdown v1.11.0
> \[a63ad114\] Mmap v1.11.0
> \[ca575930\] NetworkOptions v1.2.0
> \[44cfe95a\] Pkg v1.11.0
> \[de0858da\] Printf v1.11.0
> \[9abbd945\] Profile v1.11.0
> \[3fa0cd96\] REPL 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
> \[f489334b\] StyledStrings v1.11.0
> \[4607b0f0\] SuiteSparse
> \[fa267f1f\] TOML v1.0.3
> \[a4e569a6\] Tar v1.10.0
> \[8dfed614\] Test v1.11.0
> \[cf7118a7\] UUIDs v1.11.0
> \[4ec0a83e\] Unicode v1.11.0
> \[e66e0078\] CompilerSupportLibraries\_jll v1.1.1+0
> \[deac9b47\] LibCURL\_jll v8.6.0+0
> \[e37daf67\] LibGit2\_jll v1.7.2+0
> \[29816b5a\] LibSSH2\_jll v1.11.0+1
> \[c8ffd9c3\] MbedTLS\_jll v2.28.6+0
> \[14a3606d\] MozillaCACerts\_jll v2023.12.12
> \[4536629a\] OpenBLAS\_jll v0.3.27+1
> \[05823500\] OpenLibm\_jll v0.8.1+2
> \[efcefdf7\] PCRE2\_jll v10.42.0+1
> \[bea87d4a\] SuiteSparse\_jll v7.7.0+0
> \[83775a58\] Zlib\_jll v1.2.13+1
> \[8e850b90\] libblastrampoline\_jll v5.11.0+0
> \[8e850ede\] nghttp2\_jll v1.59.0+0
> \[3f19e933\] p7zip\_jll v17.4.0+2
> \`\`\`
> 
> - Output of \`versioninfo()\`
> 
> \`\`\`julia
> Julia Version 1.11.3
> Commit d63adeda50d (2025-01-21 19:42 UTC)
> Build Info:
> Official https://julialang.org/ release
> Platform Info:
> OS: macOS (arm64-apple-darwin24.0.0)
> CPU: 10 × Apple M1 Pro
> WORD\_SIZE: 64
> LLVM: libLLVM-16.0.6 (ORCJIT, apple-m1)
> Threads: 8 default, 0 interactive, 4 GC (on 8 virtual cores)
> Environment:
> JULIA\_EDITOR = code
> JULIA\_NUM\_THREADS = 8
> \`\`\`