# Plotting observed of DiscreteSystem
**URL:** https://discourse.julialang.org/t/plotting-observed-of-discretesystem/117620
**Category:** Modelling & Simulations
**Tags:** question, plotting, sciml
**Created:** [July 30, 2024, 3:26am UTC](https://discourse.julialang.org/t/plotting-observed-of-discretesystem/117620 "2024-07-30T03:26:23Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@binnisb](https://discourse.julialang.org/u/binnisb)
#### Post date: [July 30, 2024, 3:26am UTC](https://discourse.julialang.org/t/plotting-observed-of-discretesystem/117620/1 "2024-07-30T03:26:23Z")
Hey.
I wanted to try out MTK so I am moving an Excel calculation I had set up for calculating monthly repayments of a inflation linked loan to MTK.
I got the model running. My issue is how to plot the observed values, not just the unknowns.
From what I can see, the `observed(sys)` returns the values I want to plot, but in the `sol` it only contains `N, ind, P, amortization`
I would like to plot the `pmt_c, ipmt_c and ppmt_c` as well.
I am using MTK v9.26.0
---
### Author:  [@binnisb](https://discourse.julialang.org/u/binnisb)
#### Post date: [July 30, 2024, 3:30am UTC](https://discourse.julialang.org/t/plotting-observed-of-discretesystem/117620/2 "2024-07-30T03:30:38Z")
```julia
using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
using OrdinaryDiffEq: solve, FunctionMap
using PlutoPlotly
@inline function if_else(
@nospecialize(condition),
@nospecialize(trueval),
@nospecialize(falseval)
)
return ifelse(condition, trueval, falseval)
end
k = ShiftIndex(t)
@parameters r infl yr yr_periods cost total_payment
@variables P(t) ind(t) N(t) pmt_c(t) ipmt_c(t) ppmt_c(t) amortization(t)
periods = yr*yr_periods
rᵢ = r/yr_periods
eqs = [
N(k) ~ N(k-1) + 1
ind(k) ~ ind(k - 1) * (1 + infl)^(1/yr_periods)
P(k) ~ max((P(k - 1) - amortization(k - 1))*ind(k)/ind(k - 1), 0)
pmt_c(k) ~ -P(k) * rᵢ / (1 - (1 + rᵢ)^(-periods+N(k-1)))
ipmt_c(k) ~ -P(k) * rᵢ
ppmt_c(k) ~ pmt_c(k) - ipmt_c(k)
amortization(k) ~ if_else(P(k)>0, if_else(total_payment + pmt_c(k) >0, total_payment + pmt_c(k), -ppmt_c(k)), 0)
]
@mtkbuild sys = DiscreteSystem(eqs, t)
u0 = [
P(k-1) => 10_000_000,
ind(k-1) => 100,
N(k-1) => 0,
amortization(k-1) => 0
]
p = [
r => 0.0375,
infl => 0.0621,
yr => 30,
yr_periods => 12,
cost => 520,
total_payment => 110_000
]
tspan = (1, 360 + 1)
prob = DiscreteProblem(sys, u0, tspan, p)
sol = solve(prob, FunctionMap())
p1 = plot(sol[:N], sol[:amortization])
p2 = plot(sol[:N], sol[:P])
p0 = hcat(p1, p2)
relayout!(p0, title_text="Loan")
p0
```
---
### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [July 30, 2024, 8:29am UTC](https://discourse.julialang.org/t/plotting-observed-of-discretesystem/117620/3 "2024-07-30T08:29:24Z")
Hello and welcome to the community! 👋
This feature was actually merged as late as yesterday!
>
>
> Requires:
> \- https://github.com/SciML/SymbolicIndexingInterface.jl/pull/75
> \- ht…tps://github.com/SciML/RecursiveArrayTools.jl/pull/372
> \- https://github.com/SciML/SciMLBase.jl/pull/645
> \- https://github.com/SciML/ModelingToolkit.jl/pull/2676
> - ~PR is based off of this branch right now, will rebase on \`master\` once the above PR is merged~ Rebased
>
> \## Checklist
>
> \- \[\] Appropriate tests were added
> \- \[\] Any code changes were done in a way that does not break public API
> \- \[\] All documentation related to code changes were updated
> \- \[\] The new code follows the
> \[contributor guidelines\](https://github.com/SciML/.github/blob/master/CONTRIBUTING.md), in particular the \[SciML Style Guide\](https://github.com/SciML/SciMLStyle) and
> \[COLPRAC\](https://github.com/SciML/COLPRAC).
> \- \[\] Any new documentation only uses public API
>
> \## Additional context
>
> Add any other context about the problem here.
It hasn’t yet made it’s way into a release. Expect it to be available within a few days.
---
### Author:  [@binnisb](https://discourse.julialang.org/u/binnisb)
#### Post date: [July 30, 2024, 8:38am UTC](https://discourse.julialang.org/t/plotting-observed-of-discretesystem/117620/4 "2024-07-30T08:38:03Z")
Thanks! I suspected it 😅 Always fun to live on the edge!
---
### Author:  [@binnisb](https://discourse.julialang.org/u/binnisb)
#### Post date: [July 30, 2024, 10:52am UTC](https://discourse.julialang.org/t/plotting-observed-of-discretesystem/117620/5 "2024-07-30T10:52:47Z")
And for others, now I found this regarding the variable elimination and the simplification process:
> **[Internal Details · ModelingToolkit.jl](https://docs.sciml.ai/ModelingToolkit/dev/internals/)**
>
> Documentation for ModelingToolkit.jl.