# Interpolation with ModelingToolkit.jl

**URL:** <https://discourse.julialang.org/t/interpolation-with-modelingtoolkit-jl/79867>\
**Category:** General Usage\
**Created:** [April 22, 2022, 10:56pm UTC](https://discourse.julialang.org/t/interpolation-with-modelingtoolkit-jl/79867 "2022-04-22T22:56:28Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![astrobc1](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/astrobc1/32/45632_2.png) [@astrobc1](https://discourse.julialang.org/u/astrobc1)\
**Post date:** [April 22, 2022, 10:56pm UTC](https://discourse.julialang.org/t/interpolation-with-modelingtoolkit-jl/79867/1 "2022-04-22T22:56:29Z")

</div>

I’m trying to use cubic spline interpolation from DataInterpolations.jl in my loss function with ModelingToolkit.jl. There’s an older thread that seems to discuss this [here](https://discourse.julialang.org/t/interpolation-within-modelingtoolkit-framework/59432) but I have’t been able to get that working, and it hasn’t seen traffic in some time, but please let me know if I should continue with that thread.

I’ve tried with and without the various collect’s but I think my problem is my lack of understanding of how `@register` works.

```julia
julia> using ModelingToolkit, DataInterpolations

julia> n=10
10

julia> @parameters x[1:n] data[1:n]
2-element Vector{Symbolics.Arr{Num, 1}}:
 x[1:10]
 data[1:10]

julia> function interp(x, y, xnew)
           itp = CubicSpline(y, x)
           return itp.(xnew)
       end
interp (generic function with 1 method)

julia> @register interp(a, b, c)

julia> rms(x, y) = sqrt(sum((x .- y).^2) / length(x))
rms (generic function with 1 method)

julia> @variables c0 c1
2-element Vector{Num}:
 c0
 c1

julia> model(x, c0, c1) = @. c0 + c1 * x
model (generic function with 1 method)

julia> loss = rms(collect(data), interp(collect(x), model(collect(x), c0, c1), collect(x)))
ERROR: TypeError: non-boolean (Num) used in boolean context
Stacktrace:
 [1] lu!(A::LinearAlgebra.Tridiagonal{Num, Vector{Num}}, pivot::LinearAlgebra.RowMaximum; check::Bool)
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/lu.jl:515
 [2] lu(A::LinearAlgebra.Tridiagonal{Num, Vector{Num}}, pivot::LinearAlgebra.RowMaximum; check::Bool)
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/lu.jl:279
 [3] lu (repeats 2 times)
   @ /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/lu.jl:278 [inlined]
 [4] \(A::LinearAlgebra.Tridiagonal{Num, Vector{Num}}, B::Vector{Real})
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/generic.jl:1142
 [5] CubicSpline(u::Vector{Num}, t::Vector{Num})
   @ DataInterpolations ~/.julia/packages/DataInterpolations/HJsu4/src/interpolation_caches.jl:156
 [6] interp(x::Vector{Num}, y::Vector{Num}, xnew::Vector{Num})
   @ Main ./REPL[8]:2
 [7] top-level scope
   @ REPL[15]:1

```

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<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:** [April 22, 2022, 11:54pm UTC](https://discourse.julialang.org/t/interpolation-with-modelingtoolkit-jl/79867/2 "2022-04-22T23:54:22Z")

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Open an issue. DataInterpolations is already registered so it should just work?

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<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:** [April 23, 2022, 12:08am UTC](https://discourse.julialang.org/t/interpolation-with-modelingtoolkit-jl/79867/3 "2022-04-23T00:08:33Z")

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I think `@register` and symbolic arrays don’t get along:

```julia
 julia> @variables x[1:10] y[1:10] a b
4-element Vector{Any}:
  x[1:10]
  y[1:10]
 a
 b

julia> h(x, y) = x.^2 .+ y
h (generic function with 9 methods)

julia> @register h(x, y)

julia> h(a, b)
h(a, b)

julia> h(x, y)
(broadcast(+, broadcast(literal_pow, Base.RefValue{typeof(^)}(^), x, Base.RefValue{Val{2}}(Val{2}())), y))[1:10]

julia> h.(x, y)
(broadcast(h, x, y))[1:10]

```

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<div class="post-metadata">

**Author:** ![astrobc1](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/astrobc1/32/45632_2.png) [@astrobc1](https://discourse.julialang.org/u/astrobc1)\
**Post date:** [April 23, 2022, 2:13am UTC](https://discourse.julialang.org/t/interpolation-with-modelingtoolkit-jl/79867/4 "2022-04-23T02:13:05Z")

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I believe your example checks out fine, but when you actually utilize the loss function you may need to collect some symbolic arrays. I also don’t think you need to register your function h here.

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<div class="post-metadata">

**Author:** ![astrobc1](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/astrobc1/32/45632_2.png) [@astrobc1](https://discourse.julialang.org/u/astrobc1)\
**Post date:** [April 23, 2022, 8:06pm UTC](https://discourse.julialang.org/t/interpolation-with-modelingtoolkit-jl/79867/5 "2022-04-23T20:06:05Z")

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Should I open the issue on DataInterpolations, Symbolics, or ModelingToolkit?

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<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:** [April 23, 2022, 10:32pm UTC](https://discourse.julialang.org/t/interpolation-with-modelingtoolkit-jl/79867/6 "2022-04-23T22:32:38Z")

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ModelingToolkit.jl