# Indexing symbolic arrays inside Differential Equation solution

**URL:** <https://discourse.julialang.org/t/indexing-symbolic-arrays-inside-differential-equation-solution/96764>\
**Category:** Modelling & Simulations\
**Tags:** question\
**Created:** [March 29, 2023, 9:16am UTC](https://discourse.julialang.org/t/indexing-symbolic-arrays-inside-differential-equation-solution/96764 "2023-03-29T09:16:48Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Daniel\_Doyle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/daniel_doyle/32/48125_2.png) [@Daniel\_Doyle](https://discourse.julialang.org/u/Daniel_Doyle)\
**Post date:** [March 29, 2023, 9:16am UTC](https://discourse.julialang.org/t/indexing-symbolic-arrays-inside-differential-equation-solution/96764/1 "2023-03-29T09:16:48Z")

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Hello,

I was running into an issue with indexing symbolic arrays from a solution and was wondering if anyone had some insight. Below is a simplified example:

```julia
using ModelingToolkit, StochasticDiffEq
using Plots

@variables t1 x(t1)[1:10]
@parameters μ σ
Dx = Differential(t1)
x_eq = Symbolics.scalarize(Dx.(x) .~ 1)
x_noise_eq = Symbolics.scalarize(x .* σ)
@named sde_sys = SDESystem(x_eq,
                           x_noise_eq, t1,
                           [x...],
                           [μ, σ]; tspan=(0, 10.0))
sde_prob = SDEProblem(sde_sys, Symbolics.scalarize(x .=> 1), (0.0, 10.0),
                      [μ => 1, σ => 0.2])
sde_sol = solve(sde_prob, SOSRI())
sde_sol(0; idxs=x[1:2]) # leads to an error
plot(sde_sol; idxs=x[1:2]) # does not lead to an error

```

Does anyone know why the plot line works but the direct indexing does not?

Thanks!

Edit:  
This does the trick for retrieving the integer indices in the above and appears to also work with multi-D arrays on a separate example I was working on:

```julia
indices = []
for i in 1:2
    push!(indices,SciMLBase.sym_to_index(x[i], SciMLBase.getsyms(sde_sol)))
end
sde_sol(0.5; idxs=indices)

```

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<div class="post-metadata">

**Author:** ![DanielVandH](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/danielvandh/32/31134_2.png) [@DanielVandH](https://discourse.julialang.org/u/DanielVandH)\
**Post date:** [March 29, 2023, 9:38am UTC](https://discourse.julialang.org/t/indexing-symbolic-arrays-inside-differential-equation-solution/96764/2 "2023-03-29T09:38:00Z")

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It’s not an issue with `x[1:2]`, you get the same issue without indexing:

```julia
julia> sde_sol(0; idxs=x) 
ERROR: TypeError: non-boolean (Num) used in boolean context
Stacktrace:
 [1] checkbounds
   @ .\abstractarray.jl:668 [inlined]
 [2] view
   @ .\subarray.jl:177 [inlined]
 [3] maybeview
   @ .\views.jl:146 [inlined]
 [4] dotview
   @ .\broadcast.jl:1201 [inlined]
 [5] sde_interpolant(Θ::Float64, dt::Float64, u0::Vector{Float64}, u1::Vector{Float64}, idxs::Symbolics.Arr{Num, 1}, deriv::Type{Val{0}})
   @ StochasticDiffEq C:\Users\User\.julia\packages\StochasticDiffEq\rZj4R\src\dense.jl:32
 [6] sde_interpolation(tval::Int64, id::StochasticDiffEq.LinearInterpolationData{Vector{Vector{Float64}}, Vector{Float64}}, idxs::Symbolics.Arr{Num, 1}, deriv::Type, p::Vector{Float64}, continuity::Symbol)
   @ StochasticDiffEq C:\Users\User\.julia\packages\StochasticDiffEq\rZj4R\src\dense.jl:169
 [7] LinearInterpolationData
   @ C:\Users\User\.julia\packages\StochasticDiffEq\rZj4R\src\interp_func.jl:7 [inlined]
 [8] #_#420
   @ C:\Users\User\.julia\packages\SciMLBase\o0qGB\src\solutions\rode_solutions.jl:66 [inlined]
 [9] top-level scope
   @ Untitled-1:16

julia> plot(sde_sol; idxs=x) 

```

When you put in this form of `idxs` into `sde_sol(0; idxs = x)`, the underlying interpolant in `sde_sol` is trying to use it, but I guess it hasn’t been implemented to interpret it correctly (you can see how it interprets it by looking at the functions in the stacktrace).

It works for the `plot` call because it gets interpreted correctly in the call which you can see here [SciMLBase.jl/solution\_interface.jl at 9e5f84dd748f462266d52927f1b5dd7202e40064 · SciML/SciMLBase.jl · GitHub](https://github.com/SciML/SciMLBase.jl/blob/9e5f84dd748f462266d52927f1b5dd7202e40064/src/solutions/solution_interface.jl#L233-L438), e.g. with `SciMLBase.interpret_vars(x[1:2], sde_sol, SciMLBase.getsyms(sde_sol))`.

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<div class="post-metadata">

**Author:** ![DanielVandH](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/danielvandh/32/31134_2.png) [@DanielVandH](https://discourse.julialang.org/u/DanielVandH)\
**Post date:** [March 29, 2023, 9:45am UTC](https://discourse.julialang.org/t/indexing-symbolic-arrays-inside-differential-equation-solution/96764/3 "2023-03-29T09:45:12Z")

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The issue causing the error is an expression like `checkbounds(A, x)` for an array `A` when doing `A[x]` in `StochasticDiffEq.sde_interpolant(0.0,0.0,zeros(10),zeros(10),x,Val{0})` when evaluating the interpolant (the arrays here are just for example). e.g.

```julia
julia> @inbounds checkbounds([], x)
ERROR: TypeError: non-boolean (Num) used in boolean context
Stacktrace:
 [1] checkbounds(A::Vector{Any}, I::Symbolics.Arr{Num, 1})
   @ Base .\abstractarray.jl:668
 [2] top-level scope
   @ REPL[82]:1

```

I guess there could be a better way to handle this array access by converting somewhere along the way.

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<div class="post-metadata">

**Author:** ![Daniel\_Doyle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/daniel_doyle/32/48125_2.png) [@Daniel\_Doyle](https://discourse.julialang.org/u/Daniel_Doyle)\
**Post date:** [March 29, 2023, 10:25am UTC](https://discourse.julialang.org/t/indexing-symbolic-arrays-inside-differential-equation-solution/96764/4 "2023-03-29T10:25:13Z")

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Sorry. I should have been clearer. My issue is not with indexing as x[1:2] but generally trying to index a solution’s results by using the variable names and indices as opposed to figuring out the integer slices for each variable. The issue is one of both readability (since I think it is clearer to index by variable names) and for working with multi-D arrays where it can be a bit harder to tell how Julia flattens it out.

Thanks for pointing to SciMLBase docs! I think the sym\_to\_index does the trick for what I am looking for here

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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:** [March 29, 2023, 2:34pm UTC](https://discourse.julialang.org/t/indexing-symbolic-arrays-inside-differential-equation-solution/96764/5 "2023-03-29T14:34:43Z")

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I think this is a case we haven’t handled well yet. In the near future it should be automatic but not all of the interpolation cases seem to be handled with SDEs.