Model linearization fails when no parameter is used

[BambOoxX]

Describe the bug 🐞

When attempting linearization of a MTK model without parameters, the linearize call fails with

ERROR: MethodError: no method matching similar(::SciMLBase.NullParameters, ::Type{ForwardDiff.Dual{ForwardDiff.Tag{…}, Any, 0}})
An arithmetic operation was performed on a NullParameters object. This means no parameters were passed
into the AbstractSciMLProblem (e.x.: ODEProblem) but the parameters object `p` was used in an arithmetic
expression. Two common reasons for this issue are:

1. Forgetting to pass parameters into the problem constructor. For example, `ODEProblem(f,u0,tspan)` should
be `ODEProblem(f,u0,tspan,p)` in order to use parameters.

2. Using the wrong function signature. For example, with `ODEProblem`s the function signature is always
`f(du,u,p,t)` for the in-place form or `f(u,p,t)` for the out-of-place form. Note that the `p` argument
will always be in the function signature regardless of if the problem is defined with parameters!



Closest candidates are:
  similar(::VSCodeServer.JuliaInterpreter.Compiled, ::Any)
   @ VSCodeServer d:\user\.vscode\extensions\julialang.language-julia-1.65.2\scripts\packages\JuliaInterpreter\src\types.jl:7
  similar(::Type{A}, ::Type{T}, ::StaticArraysCore.Size{S}) where {A<:Array, T, S}
   @ StaticArrays D:\user\.julia\packages\StaticArrays\Uc4hE\src\abstractarray.jl:136
  similar(::Type{SA}, ::Type{T}, ::StaticArraysCore.Size{S}) where {SA<:StaticArraysCore.SizedArray, T, S}
   @ StaticArrays D:\user\.julia\packages\StaticArrays\Uc4hE\src\abstractarray.jl:135
  ...

Stacktrace:
 [1] jacobian_wrt_vars(pf::SciMLBase.ParamJacobianWrapper{…}, p::SciMLBase.NullParameters, input_idxs::UnitRange{…}, chunk::ForwardDiff.Chunk{…})
   @ ModelingToolkit D:\user\.julia\packages\ModelingToolkit\arrCl\src\utils.jl:809
 [2] (::ModelingToolkit.var"#144#148"{…})(u::Vector{…}, p::SciMLBase.NullParameters, t::Float64)
   @ ModelingToolkit D:\user\.julia\packages\ModelingToolkit\arrCl\src\systems\abstractsystem.jl:1442
 [3] linearize(sys::ODESystem, lin_fun::ModelingToolkit.var"#144#148"{…}; t::Float64, op::Dict{…}, allow_input_derivatives::Bool, p::SciMLBase.NullParameters)
   @ ModelingToolkit D:\user\.julia\packages\ModelingToolkit\arrCl\src\systems\abstractsystem.jl:1694
 [4] linearize(sys::ODESystem, inputs::Vector{…}, outputs::Vector{…}; op::Dict{…}, t::Float64, allow_input_derivatives::Bool, zero_dummy_der::Bool, kwargs::@Kwargs{})
   @ ModelingToolkit D:\user\.julia\packages\ModelingToolkit\arrCl\src\systems\abstractsystem.jl:1745
 [5] top-level scope
   @ Untitled-1:26
Some type information was truncated. Use `show(err)` to see complete types.

Expected behavior

Linearization of MTK models should work even in the absence of additional parameters

Minimal Reproducible Example 👇

parameter-less version of the example provided in https://discourse.julialang.org/t/differential-equation-with-periodic-orbit-can-diffeq-jl-determine-the-period/107982/8

using ModelingToolkit
using DifferentialEquations, ControlSystemsBase

@variables begin
    t
    x(t)
    y(t)
end

D = Differential(t)

eqs = [
    D(x) ~ -y
    D(y) ~ x
]

@named model = ODESystem(eqs, t, [x, y], [])
sys = structural_simplify(model)

tspan = (0.0, 2π)
@nonamespace initial_conditions = Dict([x => 1.0, y => 0.0])

prob = ODEProblem(sys, initial_conditions, tspan)
sol = solve(prob, Tsit5(), reltol=1e-8, abstol=1e-8)

(; A, B, C, D), simplified_sys = linearize(sys, [], [x, y], op=initial_conditions)

Error & Stacktrace ⚠️

Already provided

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

  [aaaaaaaa] ControlSystemsBase v1.10.1
  [0c46a032] DifferentialEquations v7.12.0
  [e9467ef8] GLMakie v0.9.4
  [5c1252a2] GeometryBasics v0.4.9
  [961ee093] ModelingToolkit v8.74.1
  [16a59e39] ModelingToolkitStandardLibrary v2.3.4
  [37e2e46d] LinearAlgebra

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

  [47edcb42] ADTypes v0.2.6
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⌅ [79e6a3ab] Adapt v3.7.2
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⌃ [764a87c0] BoundaryValueDiffEq v5.6.0
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  [f27f6e37] libvorbis_jll v1.3.7+1
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [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
  [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

• Output of versioninfo()

Julia Version 1.10.0
Commit 3120989f39 (2023-12-25 18:01 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 8 × 11th Gen Intel(R) Core(TM) i7-1185G7 @ 3.00GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, tigerlake)
  Threads: 11 on 8 virtual cores
Environment:
  JULIA_EDITOR = code

Additional context

Add any other context about the problem here.

[baggepinnen]

The problem here is not the lack of parameters, it's the lack of inputs. If you are only after the state jacobian (the A matrix), see calculate_jacobian instead.

julia> calculate_jacobian(model)
2×2 Matrix{Num}:
 0  -1
 1   0

A side note, linearize expects model and not sys, i.e., you may not call structural_simplify on the system before calling linearize

[BambOoxX]

Thanks for the tips @baggepinnen. However, given what you say, can you explain why the linearizarion works (understand does not error) if a dummy parameter is passed, even on a structurally simplified model?

[baggepinnen]

Probably a coincidence since the example is very small and simple. It will not work in general.

[BambOoxX]

@baggepinnen OK. Should there be some documentation or more explicit error in case of absence of input? Or a generic fallback returning empty B, C, D matrices ?

[BambOoxX]

I'll close this for now as the use case seems a bit different now with v9