Access to vector of variables

[ValentinKaisermayer]

Consider a simple example, where I use a vector of variables.

function advection(;name, c=1, L=10, N=10, x0=0, xL=1)
    @parameters t
    @variables x[1:N](t)

    x0 = fill(x0, N)

    Δz = L / N
    Dt = Differential(t)
    eqs = [
        Dt(x[1]) ~ -c * (-xL + x[1]) / Δz
        [Dt(x[i]) ~ -c * (-x[i-1] + x[i]) / Δz for i in 2:N]...
    ]
    return ODESystem(eqs, t, [x], []; name=name, default_u0=[(x .=> x0)...])
end

@named model = advection()
sys = structural_simplify(model)
prob = ODAEProblem(sys, Pair[], (0, 50))
sol = solve(prob, Tsit5())
plot(sol)

If I try to access the variables like I would do for other models with scalar variables, I get:

julia> model.x
ERROR: MethodError: no method matching nameof(::Array{Num,1})
Closest candidates are:
  nameof(::VSCodeServer.JuliaInterpreter.Frame) at .vscode\extensions\julialang.language-julia-1.1.35\scripts\packages\JuliaInterpreter\src\utils.jl:17
  nameof(::JuliaInterpreter.Frame) at .julia\packages\JuliaInterpreter\lObtQ\src\utils.jl:17
  nameof(::Core.IntrinsicFunction) at reflection.jl:1194
  ...
Stacktrace:
 [1] getname(::Array{Num,1}) at .julia\packages\ModelingToolkit\9sIpH\src\systems\abstractsystem.jl:126
 [2] (::ModelingToolkit.var"#25#29"{Symbol})(::Array{Num,1}) at .julia\packages\ModelingToolkit\9sIpH\src\systems\abstractsystem.jl:223
 [3] findnext(::ModelingToolkit.var"#25#29"{Symbol}, ::Array{Array{Num,1},1}, ::Int64) at .\array.jl:1810
 [4] findfirst(::Function, ::Array{Array{Num,1},1}) at .\array.jl:1861
 [5] getproperty(::ODESystem, ::Symbol; namespace::Bool) at .julia\packages\ModelingToolkit\9sIpH\src\systems\abstractsystem.jl:223
 [6] getproperty(::ODESystem, ::Symbol) at .julia\packages\ModelingToolkit\9sIpH\src\systems\abstractsystem.jl:210
 [7] top-level scope at REPL[88]:1

The displayed information for the model is also not quite correct.

julia> model
Model model with 10 equations
States (1):
  Num[x₁(t), x₂(t), x₃(t), x₄(t), x₅(t), x₆(t), x₇(t), x₈(t), x₉(t), x₁₀(t)]
Parameters (0):

It should be 10 states - I think.

[baggepinnen]

Similar to #605
?

[YingboMa]

Since x is an array, you need to write

ODESystem(eqs, t, x, []; name=name, default_u0=[(x .=> x0)...])

[YingboMa]

I'll close this issue because it's a duplicate

[ValentinKaisermayer]

I tried that

function advection(;name, c=1, L=10, N=10, x0=0, xL=1)
    @parameters t
    @variables x[1:N](t)

    x0 = fill(x0, N)

    Δz = L / N
    Dt = Differential(t)
    eqs = [
        Dt(x[1]) ~ -c * (-xL + x[1]) / Δz
        [Dt(x[i]) ~ -c * (-x[i-1] + x[i]) / Δz for i in 2:N]...
    ]
    return ODESystem(eqs, t, x, []; name=name, defaults=[(x .=> x0)...])
end

@named model = advection()
sys = structural_simplify(model)
prob = ODAEProblem(sys, Pair[], (0, 50))
sol = solve(prob, Tsit5())

But something is still not correct

julia> model.x₁
model₊x₁(t)

julia> plot(sol; vars=[model.x₁])
ERROR: KeyError: key model₊x₁(t) not found

Also I have to say that I find the unicode variable names very inconvenient.

[ChrisRackauckas]

A user shouldn't ever have to write a unicode variable name. Each time you see that it's a current broken abstraction that is being worked on.