# How to make ODESystem with DataInterpolations latex output more readable?
**URL:** https://discourse.julialang.org/t/how-to-make-odesystem-with-datainterpolations-latex-output-more-readable/120700
**Category:** Modelling & Simulations
**Tags:** question
**Created:** [September 29, 2024, 11:19pm UTC](https://discourse.julialang.org/t/how-to-make-odesystem-with-datainterpolations-latex-output-more-readable/120700 "2024-09-29T23:19:47Z")
**Posts on this page:** 8
**Page:** 1
### Author:  [@langestefan](https://discourse.julialang.org/u/langestefan)
#### Post date: [September 29, 2024, 11:19pm UTC](https://discourse.julialang.org/t/how-to-make-odesystem-with-datainterpolations-latex-output-more-readable/120700/1 "2024-09-29T23:19:47Z")
I have defined my model in ModelingToolkit.jl as such:
```julia
# define model parameters
@parameters Ci Ria Aw
# define sub-model components
@named C_i = Capacitor(C=Ci) # thermal capacity of interior
@named R_ia = Resistor(R=Ria) # thermal resistance between interior and ambient
@named T_a = Voltage() # ambient temperature
@named P_h = Current() # thermal power in kW
@named P_s = Current() # solar power in kW
@named A_w = Gain(k=Aw) # dimensionless window area gain (SHGC*Area)
@named gnd = Ground() # ground node
# input functions
@named T_a_f = TimeVaryingFunction(input_funcs[:T_a])
@named P_h_f = TimeVaryingFunction(input_funcs[:P_h])
@named P_s_f = TimeVaryingFunction(input_funcs[:P_s])
# collect all components in a vector
components = [C_i, R_ia, T_a, P_h, P_s, A_w, T_a_f, P_h_f, P_s_f, gnd]
# make component connections
conn = [
connect(C_i.p, R_ia.p),
connect(R_ia.n, T_a.p),
connect(C_i.n, gnd.g),
# ambient temperature input
connect(T_a.p, R_ia.n),
connect(T_a.V, T_a_f.output),
connect(T_a.n, gnd.g),
# solar power input: A_w * P_s
connect(A_w.output, P_s.I),
connect(A_w.input, P_s_f.output),
connect(P_s.n, C_i.p),
connect(P_s.p, gnd.g),
# thermal power input
connect(P_h.n, C_i.n),
connect(P_h.I, P_h_f.output),
connect(P_h.p, gnd.g)
]
```
The input functions are given by DataInterpolations.jl:
```julia
# define interpolated input functions of sampled data
T_a_interp = AkimaInterpolation(df.T_a, df.t_hour)
P_s_interp = AkimaInterpolation(df.P_s, df.t_hour)
P_h_interp = AkimaInterpolation(df.P_h, df.t_hour)
input_funcs = Dict(:T_a => T_a_interp, :P_s => P_s_interp, :P_h => P_h_interp)
```
Now when I display the equations of this model (after calling `structural_simplify(sys)` I get the following LaTeX output, which is not very readable:
I would like this more readable so I can inspect the equations.
Related question: can I make outputs / inputs such as C\_{i\_+ v}(t) display something else as well which makes more sense to me? For example, change C\_{i\_+ v}(t) to V\_{C}(t).
ps. I am on ModelingToolkit v8.75 due to requirements of a package I am using.
Thanks a lot 🙂
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [September 29, 2024, 11:25pm UTC](https://discourse.julialang.org/t/how-to-make-odesystem-with-datainterpolations-latex-output-more-readable/120700/2 "2024-09-29T23:25:18Z")
This is changed a bit in ModelingToolkit v9. With the latest versions, you can have a parameter that is a callable function. This is much better because you can see here that every `f` call constructs the interpolation and then calls it, while the parameter form will cache it and then reuse it. So the v9 form both makes the printout simpler (just a p(t)) and improves the performance.
That said, you can somewhat simulate it on v8 by building a function with the interpolation enclosed and then registering the enclosed function.
---
### Author:  [@langestefan](https://discourse.julialang.org/u/langestefan)
#### Post date: [September 29, 2024, 11:28pm UTC](https://discourse.julialang.org/t/how-to-make-odesystem-with-datainterpolations-latex-output-more-readable/120700/3 "2024-09-29T23:28:50Z")
Ah okay great. By registering do you mean as it’s done in this post from a while back? [Interpolation within ModelingToolkit framework - #6 by jairorua](https://discourse.julialang.org/t/interpolation-within-modelingtoolkit-framework/59432/6)
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [September 29, 2024, 11:35pm UTC](https://discourse.julialang.org/t/how-to-make-odesystem-with-datainterpolations-latex-output-more-readable/120700/4 "2024-09-29T23:35:06Z")
Kind of, that’s not the enclosed form and will allocate the vectors, though that form will still work.
---
### Author:  [@langestefan](https://discourse.julialang.org/u/langestefan)
#### Post date: [September 29, 2024, 11:42pm UTC](https://discourse.julialang.org/t/how-to-make-odesystem-with-datainterpolations-latex-output-more-readable/120700/5 "2024-09-29T23:42:11Z")
I see. By enclosed do you mean:
```julia
@register f_interpolate(t)
```
instead of:
```julia
@register f_interpolate(t, table_t::AbstractVector, table_u::AbstractVector)
```
Where the data has already been defined in `f_interpolate(t)`
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [September 29, 2024, 11:43pm UTC](https://discourse.julialang.org/t/how-to-make-odesystem-with-datainterpolations-latex-output-more-readable/120700/6 "2024-09-29T23:43:22Z")
Yes exactly.
---
### Author:  [@langestefan](https://discourse.julialang.org/u/langestefan)
#### Post date: [September 30, 2024, 12:20am UTC](https://discourse.julialang.org/t/how-to-make-odesystem-with-datainterpolations-latex-output-more-readable/120700/7 "2024-09-30T00:20:09Z")
I must still not be doing something right then, this leads to the same result as before:
```julia
# time variable
@variables t
# define interpolated input functions of sampled data
function T_a(t)
y = df.T_a
x = df.t_hour
int = AkimaInterpolation(y, x)
out = int(t)
end
function P_s(t)
y = df.P_s
x = df.t_hour
int = AkimaInterpolation(y, x)
out = int(t)
end
function P_h(t)
y = df.P_h
x = df.t_hour
int = AkimaInterpolation(y, x)
out = int(t)
end
@eval @register_symbolic P_h(t)
@eval @register_symbolic P_s(t)
@eval @register_symbolic T_a(t)
input_funcs = Dict(:T_a => T_a, :P_s => P_s, :P_h => P_h)
```
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [September 30, 2024, 9:57am UTC](https://discourse.julialang.org/t/how-to-make-odesystem-with-datainterpolations-latex-output-more-readable/120700/8 "2024-09-30T09:57:03Z")
You can’t eval it if it’s in a function since that would be in the wrong world age