# ModellingToolkit ODESystem definition throwing error

**URL:** <https://discourse.julialang.org/t/modellingtoolkit-odesystem-definition-throwing-error/63002>\
**Category:** Numerics\
**Tags:** diffeq, error-message\
**Created:** [June 16, 2021, 12:23pm UTC](https://discourse.julialang.org/t/modellingtoolkit-odesystem-definition-throwing-error/63002 "2021-06-16T12:23:51Z")\
**Posts on this page:** 6\
**Page:** 1

<div class="post-metadata">

**Author:** ![ap2013](https://avatars.discourse-cdn.com/v4/letter/a/4491bb/32.png) [@ap2013](https://discourse.julialang.org/u/ap2013)\
**Post date:** [June 16, 2021, 12:23pm UTC](https://discourse.julialang.org/t/modellingtoolkit-odesystem-definition-throwing-error/63002/1 "2021-06-16T12:23:51Z")

</div>

I am defining and ODESystem using ModellingToolkit and I am running into a problem in the definition of the equations.

The code below is the function to define the ODESystem

```julia
function connectFFFB_Grad(plant, ref, pid, mlp,lookahead_times,N,plantMatrices;name=:FF_FB_G)   
    @parameters t 
    dt = Differential(t)
    @variables intError(t)
    # @variables dydw[1:N](t) #grad output wrt weights
    @variables dx1dw[1:N](t) #grad 4th plant state wrt weights
    @variables dx2dw[1:N](t) #grad 4th plant state wrt weights
    @variables dx3dw[1:N](t) #grad 4th plant state wrt weights
    @variables dx4dw[1:N](t) #grad 4th plant state wrt weights
    A,B,C,D = plantMatrices
    # @variables e(t)
    eqs = vcat(
            get_input(pid,1) ~ get_output(ref, 1) - get_output(plant,1),
            get_output(pid,1) ~ get_input(plant, 1),
            get_output.((ref,), 2:length(lookahead_times)+1) .~ get_inputs(mlp,length(lookahead_times)),
            get_output(mlp,1) ~ get_input(plant,2),
            dt(intError) ~ abs2(get_output(ref,1) - get_output(plant,1)),

            dt.(dx1dw) .~ A[1,:]*vcat(dx1dw,dx2dw,dx3dw,dx4dw), 
            dt.(dx2dw) .~ A[2,:]*vcat(dx1dw,dx2dw,dx3dw,dx4dw),
            dt.(dx3dw) .~ A[3,:]*vcat(dx1dw,dx2dw,dx3dw,dx4dw), 
            dt.(dx4dw) .~ A[4,:]*vcat(dx1dw,dx2dw,dx3dw,dx4dw), 
            # dt.(dydw) .~ C*[A*vcat(dx1dw,dx2dw,dx3dw,dx4dw).+B[:,2]*get_hiddens(mlp,N)], 
            # # e ~ abs2(get_output(ref,1) - get_output(plant,1)),
    ) 
    return ODESystem(eqs; systems=[plant,ref,pid,mlp],name=name)
end

```

I am getting the following error

```julia
ERROR: MethodError: no method matching *(::Vector{Int64}, ::Vector{Num})
Closest candidates are:
  *(::Any, ::Any, ::Any, ::Any...) at operators.jl:560
  *(::StridedMatrix{T}, ::StridedVector{S}) where {T<:Union{Float32, Float64, ComplexF32, ComplexF64}, S<:Real} at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/matmul.jl:44
  *(::StridedVecOrMat{T} where T, ::LinearAlgebra.LQPackedQ) at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/lq.jl:278
  ...
Stacktrace:
 [1] connectFFFB_Grad(plant::ODESystem, ref::ODESystem, pid::ODESystem, mlp::ODESystem, lookahead_times::StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}}, N::Int64, plantMatrices::NTuple{4, Matrix{Int64}}; name::Symbol)

```

I know that the error is in the te last four equations as I had previously function defining the same system excluding those four variables and it worked well.

It seems that the multiplication between the matrix column and the vector with the variables is not defined but I don’t understand why. Especially as I have another ODESystem defined by the following function that doesn’t pose any problems.

```julia
function linear_plant(A,B,C,D; name=:lp)
    
    num_inputs = size(B,2)
    num_states = size(A,1)
    num_outputs = size(C,1)

    @parameters t
    dt = Differential(t)

    @variables x[1:num_states](t)
    @variables u[1:num_inputs](t)
    @variables o[1:num_outputs](t)
    
    eqs = vcat(
                dt.(x) .~ A*x .+ B*u,
                o .~ C*x .+ D*u
    )    
    return ODESystem(eqs;name=name)   
end

```

A is a 4x4 matrix defined as follows

```julia
A = [0 1 0 0; -2 -2 1 0; 0 0 0 1; 0 0 -2 -2];

```

I would appreciate any help understanding this error.

---

<div class="post-metadata">

**Author:** ![contradict](https://avatars.discourse-cdn.com/v4/letter/c/ac91a4/32.png) [@contradict](https://discourse.julialang.org/u/contradict)\
**Post date:** [June 16, 2021, 4:19pm UTC](https://discourse.julialang.org/t/modellingtoolkit-odesystem-definition-throwing-error/63002/2 "2021-06-16T16:19:29Z")

</div>

I think you need a broadcast in there:

```julia
A[1,:] .* vcat(dx1dw,dx2dw,dx3dw,dx4dw)

```

---

<div class="post-metadata">

**Author:** ![ap2013](https://avatars.discourse-cdn.com/v4/letter/a/4491bb/32.png) [@ap2013](https://discourse.julialang.org/u/ap2013)\
**Post date:** [June 16, 2021, 4:24pm UTC](https://discourse.julialang.org/t/modellingtoolkit-odesystem-definition-throwing-error/63002/3 "2021-06-16T16:24:19Z")

</div>

> [@contradict](#):
>
> `vcat`

Thanks for the suggestion contradict. I tried that and I get an error

```julia
julia> ERROR: DimensionMismatch("arrays could not be broadcast to a common size; got a dimension with lengths 4 and 40")
Stacktrace:
  [1] _bcs1
    @ ./broadcast.jl:501 [inlined]
  [2] _bcs
    @ ./broadcast.jl:495 [inlined]
  [3] broadcast_shape
    @ ./broadcast.jl:489 [inlined]
  [4] combine_axes
    @ ./broadcast.jl:484 [inlined]
  [5] _axes
    @ ./broadcast.jl:209 [inlined]
  [6] axes
    @ ./broadcast.jl:207 [inlined]
  [7] combine_axes
    @ ./broadcast.jl:484 [inlined]
  [8] instantiate
    @ ./broadcast.jl:266 [inlined]
  [9] materialize
    @ ./broadcast.jl:883 [inlined]
 [10] connectFFFB_Grad(plant::ODESystem, ref::ODESystem, pid::ODESystem, mlp::ODESystem, lookahead_times::StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}}, N::Int64, plantMatrices::NTuple{4, Matrix{Int64}}; name::Symbol)

```

I think A[1,:] is a vector of length 4 and vcat(dx1dw,dx2dw,dx3dw,dx4dw) is 4xN in this case N=10.

---

<div class="post-metadata">

**Author:** ![contradict](https://avatars.discourse-cdn.com/v4/letter/c/ac91a4/32.png) [@contradict](https://discourse.julialang.org/u/contradict)\
**Post date:** [June 16, 2021, 4:38pm UTC](https://discourse.julialang.org/t/modellingtoolkit-odesystem-definition-throwing-error/63002/4 "2021-06-16T16:38:18Z")

</div>

Oh, I see, I misunderstood. It looks like there is no vector-matrix product defined for the `Num` type, I think the proposed solution for this is support for Symbolic Arrays: [https://github.com/JuliaSymbolics/SymbolicUtils.jl/pull/123](https://github.com/JuliaSymbolics/SymbolicUtils.jl/pull/123)

I suppose you could write it out manually, but I don’t know of a nice solution to this.

---

<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:** [June 16, 2021, 6:21pm UTC](https://discourse.julialang.org/t/modellingtoolkit-odesystem-definition-throwing-error/63002/5 "2021-06-16T18:21:39Z")

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This is all undergoing major changes with symbolic arrays:

[https://symbolics.juliasymbolics.org/dev/manual/arrays/](https://symbolics.juliasymbolics.org/dev/manual/arrays/)

merged like yesterday, and it’s getting to ModelingToolkit:

[https://github.com/SciML/ModelingToolkit.jl/pull/989](https://github.com/SciML/ModelingToolkit.jl/pull/989)

This kind of thing will make it so you can say “this is an array operation” as a single symbolic command, and should help in these cases. I’ll just say, let’s get the major thrust of this work done and then open an issue if you still have some problems are moving to the new form.

---

<div class="post-metadata">

**Author:** ![ap2013](https://avatars.discourse-cdn.com/v4/letter/a/4491bb/32.png) [@ap2013](https://discourse.julialang.org/u/ap2013)\
**Post date:** [June 17, 2021, 8:45am UTC](https://discourse.julialang.org/t/modellingtoolkit-odesystem-definition-throwing-error/63002/6 "2021-06-17T08:45:14Z")

</div>

Thanks Chris!