# Accessing variables in a ModelingToolkit system

**URL:** <https://discourse.julialang.org/t/accessing-variables-in-a-modelingtoolkit-system/57249>\
**Category:** Modelling & Simulations\
**Created:** [March 15, 2021, 11:13pm UTC](https://discourse.julialang.org/t/accessing-variables-in-a-modelingtoolkit-system/57249 "2021-03-15T23:13:26Z")\
**Posts on this page:** 10\
**Page:** 1

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**Author:** ![Dhruva2](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dhruva2/32/18475_2.png) [@Dhruva2](https://discourse.julialang.org/u/Dhruva2)\
**Post date:** [March 15, 2021, 11:13pm UTC](https://discourse.julialang.org/t/accessing-variables-in-a-modelingtoolkit-system/57249/1 "2021-03-15T23:13:26Z")

</div>

First off, the new functionality for connecting systems in ModelingToolkit is really powerful, awesome job!

I have a few issues with it that I can’t solve, however…

Suppose I have a ModelingToolkit ODESystem

```julia
od::ODESystem

```

To interactively access a state V(t) or a state W(t) in the subsystem sub, I need only write the following code

```julia
od.V
od.sub.W

```

How should I non-interactively access these variables? IE I want to build functions of the form

```julia
return_state(od, "V")
## gives od.V(t)

return substate(od, "sub", "W")
## gives od.sub.W(t) and not sub.W(t). 

```

The difference between od.sub.W(t) and sub.W(t) seems to be important when connecting subsubsystems to other ODESystems.

Struggling to build such functions.

Thanks a lot in advance!

_Also, to be a bit more informative as to why this is useful, I have a system with states x\_1(t) … x\_N(t). These are a subset of all the system states, and their position in the system.states array is variable. I need a function which takes in an integer i, and returns od.x\_i(t)_

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<div class="post-metadata">

**Author:** ![lungd](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lungd/32/10913_2.png) [@lungd](https://discourse.julialang.org/u/lungd)\
**Post date:** [March 16, 2021, 1:37am UTC](https://discourse.julialang.org/t/accessing-variables-in-a-modelingtoolkit-system/57249/2 "2021-03-16T01:37:29Z")

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You can use the very new `@nonamespace`

```julia
using ModelingToolkit
@parameters v, t
@named d = ODESystem(Equation[],t,[],[v])
@named c = ODESystem(Equation[],t,[],[v],systems=[d])
@named b = ODESystem(Equation[],t,[],[v],systems=[c])
@named a = ODESystem(Equation[],t,[],[v],systems=[b])

a.b.c.d.v # a₊b₊c₊d₊v

@nonamespace a.b.c.d.v # v
@nonamespace tmp = a.b.c.d # Model d with 0 equations
tmp.v # d₊v

@nonamespace tmp = a.b # Model b with 0 equations
tmp.c.d.v # b.c.d.v 

```

or getproperty(…; namepsace=false)

```julia
@parameters V, W
@named sub = ODESystem(Equation[],t,[],[V,W])
@named od = ODESystem(Equation[],t,[],[V,W],systems=[sub])

substate(sys,sub,state) = getproperty(getproperty(sys,Symbol(sub),namespace=false), Symbol(state))
substate(od, "sub", "W") # sub₊W

@variables V[1:3], W[1:3]
@named sub = ODESystem(Equation[],t,[V...,W...],[])
@named od = ODESystem(Equation[],t,[V...,W...],[],systems=[sub])
substate(sys,sub,state,i) = getproperty(getproperty(sys,Symbol(sub),namespace=false), Symbol("$(state)$(join('₀'+d for d in reverse(digits(i))))"))
substate(od,"sub","W",1) # sub₊W₁

```

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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 16, 2021, 3:12pm UTC](https://discourse.julialang.org/t/accessing-variables-in-a-modelingtoolkit-system/57249/3 "2021-03-16T15:12:17Z")

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We should probably document the programmatic ways to generate the namespaced names. Open an issue?

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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 16, 2021, 3:12pm UTC](https://discourse.julialang.org/t/accessing-variables-in-a-modelingtoolkit-system/57249/4 "2021-03-16T15:12:30Z")

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Maybe @pepijndevos has some ideas here/

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<div class="post-metadata">

**Author:** ![Dhruva2](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dhruva2/32/18475_2.png) [@Dhruva2](https://discourse.julialang.org/u/Dhruva2)\
**Post date:** [March 16, 2021, 3:28pm UTC](https://discourse.julialang.org/t/accessing-variables-in-a-modelingtoolkit-system/57249/5 "2021-03-16T15:28:11Z")

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works perfectly. thanks @lungd!

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<div class="post-metadata">

**Author:** ![Dhruva2](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dhruva2/32/18475_2.png) [@Dhruva2](https://discourse.julialang.org/u/Dhruva2)\
**Post date:** [March 16, 2021, 3:35pm UTC](https://discourse.julialang.org/t/accessing-variables-in-a-modelingtoolkit-system/57249/6 "2021-03-16T15:35:54Z")

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will do!

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**Author:** ![pepijndevos](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pepijndevos/32/20550_2.png) [@pepijndevos](https://discourse.julialang.org/u/pepijndevos)\
**Post date:** [March 17, 2021, 9:24am UTC](https://discourse.julialang.org/t/accessing-variables-in-a-modelingtoolkit-system/57249/7 "2021-03-17T09:24:46Z")

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The nonamespace solution is ok, but I think there might be an underlying behavior that could be improved.

I think part of this is due to how namespacing of the toplevel system works currently.  
Consider a flat system, if you do `equations(sys)` you get the toplevel equations without any namespacing, but if you do `sys.var` you get a namespaced variable. This then causes issues when connecting variables at the top level.

I’m not sure which way the solution would go, but if the namespacing on `states(sys)` and `sys.var` match, it’d avoid a lot of these challenges I think.

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<div class="post-metadata">

**Author:** ![baggepinnen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/baggepinnen/32/693_2.png) [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)\
**Post date:** [March 17, 2021, 5:49pm UTC](https://discourse.julialang.org/t/accessing-variables-in-a-modelingtoolkit-system/57249/8 "2021-03-17T17:49:05Z")

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I’m also strugglig with this. Consider trying to supply initial conditions for the state `P.x₁` in the following system

```julia
julia> fb
Model fb with 13 equations
States (13):
  u(t)
  loopgain₊y(t)
  loopgain₊u(t)
  y(t)
  loopgain₊C₊u(t)
  loopgain₊C₊y(t)
  loopgain₊nonlinear_P₊u(t)
  loopgain₊nonlinear_P₊y(t)
  loopgain₊C₊x₁(t) [defaults to 0.0]
  loopgain₊C₊x₂(t) [defaults to 0.0]
  loopgain₊nonlinear_P₊P₊u(t)
  loopgain₊nonlinear_P₊P₊y(t)
⋮
Parameters (0):

```

```julia
x0 = Pair[
    # fb.loopgain.nonlinear_P.P.x₁ => 1 # does not work
    loopgain.nonlinear_P.P.x₁ => 1 # works 
    # P.x₁ => 1 # does not work
]

```

It’s not clear to me why I cannot use the last one, i.e., `P.x₁ => 1`. If I inspect the available states after structural simplification, I learn that the only remaining states are

```julia
julia> simplified_sys
Model fb with 3 equations
States (3):
  loopgain₊C₊x₁(t) [defaults to 0.0]
  loopgain₊C₊x₂(t) [defaults to 0.0]
  loopgain₊nonlinear_P₊P₊x₁(t) [defaults to 0.0]
Parameters (0):
Incidence matrix:
⠼⠎⠢

```

I wonder if it could be made smoother to supply the initial state for `P₊x₁(t)` here. If I have passed a system `P` into a function that returns something where I can only access the state as `loopgain₊nonlinear_P₊P₊x₁(t)` it feels like I can easily get lost.

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<div class="post-metadata">

**Author:** ![lungd](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lungd/32/10913_2.png) [@lungd](https://discourse.julialang.org/u/lungd)\
**Post date:** [March 17, 2021, 9:54pm UTC](https://discourse.julialang.org/t/accessing-variables-in-a-modelingtoolkit-system/57249/9 "2021-03-17T21:54:01Z")

</div>

@pepijndevos, Can you show a concrete example where you would face such an issue?  
Maybe I already got used to the connector system you can see in the tutorials where you would define “flat” as a subsystem of a “full” system. By doing so, you connect the var with e.g. `flat.var ~ 1` and there you need the namespacing.

@baggepinnen, I think you want to define default values while creating the subsystems.  
`P = ..System(..., defaults=[x₁ => 1])` or something like `PSys(u0_x₁=1) = ..System(..., defaults=[x₁ => u0_x₁])`.  
If you add P to nonlinear\_P’s subsystems you can later use `defaults(simplified_sys)` to get the namespaced initial states like `loopgain₊nonlinear_P₊P₊x₁(t) => 1`  
If you want to change the initial state of the subsystem after simplifying “fb”, you must use the full name including namespaces.  
Your system only contains one “P” sys. But how to select the correct state if there is another subsystem with P.x₁?

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<div class="post-metadata">

**Author:** ![baggepinnen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/baggepinnen/32/693_2.png) [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)\
**Post date:** [March 18, 2021, 5:59am UTC](https://discourse.julialang.org/t/accessing-variables-in-a-modelingtoolkit-system/57249/10 "2021-03-18T05:59:12Z")

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> [@lungd](#):
>
> Your system only contains one “P” sys. But how to select the correct state if there is another subsystem with P.x₁?

I think my confusion comes partly from the fact that I do not consider `P` the name of a system here, I have a Julia object `P` that happens to also have the name (in MTK sense) `P`. If I refer to `P.x`, my intuition says that it should be the same as `loopgain₊nonlinear_P₊P₊x` since the innermost `P` there came from the `P` I’m holding in my hand. To make it more concrete, I expected something like

```julia
julia> struct Bar a end

julia> a = [0]
1-element Vector{Int64}:
 0

julia> bar = Bar(a)
Bar([0])

julia> bar.a === a
true

```

which does not appear to hold for MTK systems.