Makie recipe to plot ODESolution of DifferentialEquations.jl?

Specific Domains Visualization
, , ,
1

Related to this question.

Is there a recipe to plot the DiffEq solution components against time?

I tried

Makie.convert_arguments(sol::ODESolution) = (sol.t, [[v[1] for v in sol.u], [[v[2] for v in sol.u]]])

but it plots solution components against each other.

2

There is none that is shipped in the package.

3

As there is none, I would really appreciate advice how to implement one, because the Makie docs on recipes are a bit confusing.

4

Maybe this GMT example is similar to what you want?

5

Is there a recipe to plot the DiffEq solution components against time?

unsure is this what you want, here’s how I plotted for 4 degree of freedom system - the function rotor in mine returns SVector{4}(du1,du2,du3,du4)

prob = ODEProblem(rotor, u0, times, params)
sol1 = solve(prob, AutoVern7(Rodas5()), dt = .005)
T = range(0,8000,length=500)  
# for plotting time series for 3rd variable
GLMakie.plot(T, sol1(T)[3,:], xlim=(0,8000))

you also can try DynamicalSystems.ji’s trajectory function example
and interactive trajectory

6

I’m still confused how to pack it into a recipe.

7

You need something like this:
Makie.convert_arguments(p::Makie.PointBased, sol::ODESolution) = convert_arguments(p, sol.t, [[v[1] for v in sol.u], [[v[2] for v in sol.u]]])
Not sure if this will work, you have to supply a minimal working example.

We’re pretty close to pin down how Makie should do recipes in the future and then revamp the docs accordingly.

8

I’m also confused how recipes and argument conversion work and would be happy to see some more examples and detailed explanations in the Docs.
However, for plotting multidimensional solutions, I find it convenient to use series. Here is a MWE with what I use:

using DifferentialEquations
using GLMakie

function f!(du, u, p, t)
  x, y = u
  α, β, γ, δ = p
  du .= [α*x - β*x*y, δ*x*y - γ*y]
  nothing
end

prob = ODEProblem(f!, [0.1, 0.1], (0.0, 25.0), (α = 1, β = 1.5, γ = 1, δ = 2))
sol = solve(prob, saveat=0.1)

# plot solution using series 
# 1: manually
GLMakie.series(sol.t, hcat(sol.u...); labels=["x", "y"])
axislegend()

# 2: convert arguments
Makie.convert_arguments(T::Type{<: Series}, sol::ODESolution) =  Makie.convert_arguments(T, sol.t, hcat(sol.u...))
GLMakie.series(sol; labels=["x", "y"])
axislegend()
9

How wide is the makie support in SciML now? Is there an overview?

10

There is now a recipe in there but it’s not the most widely used. It needs some docs and some battle testing.

11

Can you point to some minimal instructions for battle testing? Or is it simply

using CairoMakie

plot(u)

?

12

Minimal and battle testing are exact opposites… the whole point is to try everything. Plot the solution with bigfloats, taylordiff, phase plots, complex numbers, … just everything.