juliagni / geometricproblems.jl Goto Github PK

```@example
HTML("""<object type="image/svg+xml" class="display-light-only" data=$(joinpath(Main.buildpath, "images/coupled_harmonic_oscillator.png"))></object>""") # hide
```

```@example
HTML("""<object type="image/svg+xml" class="display-dark-only" data=$(joinpath(Main.buildpath, "images/coupled_harmonic_oscillator_dark.png"))></object>""") # hide
```

The following shows the ``q_1`` component of the system for different values of ``k``: 

```@example
using GeometricIntegrators: integrate, ImplicitMidpoint # hide
using GeometricProblems.CoupledHarmonicOscillator: hodeproblem, default_parameters, tspan, tstep, q₀, p₀ # hide
using GeometricEquations: EnsembleProblem # hide
using GeometricMachineLearning: DataLoader # hide
using Plots # hide
 # hide
const m₁ = default_parameters.m₁  # hide
const m₂ = default_parameters.m₂ # hide
const k₁ = default_parameters.k₁ # hide
const k₂ = default_parameters.k₂ # hide
const k = [0.0, 0.5, 0.75, 1.0, 2.0, 3.0, 4.0] # hide
 # hide
params_collection = [(m₁ = m₁, m₂ = m₂, k₁ = k₁, k₂ = k₂, k = k_val) for k_val in k] # hide
ensemble_problem = EnsembleProblem(hodeproblem().equation, tspan, tstep, (q = q₀, p = p₀), params_collection) # hide
ensemble_solution = integrate(ensemble_problem, ImplicitMidpoint()) # hide
 # hide
dl = DataLoader(ensemble_solution) # hide
q₁ = dl.input.q[1, :, :] # hide
h = tspan[2] / (size(q₁, 1) - 1) # hide
t = 0.0:h:tspan[2] # hide
n_param_sets = length(params_collection) #hide 
labels = reshape(["k = "*string(params.k) for params in params_collection], 1, n_param_sets) # hide
 # hide
const one_plot = false # hide
const psize = (900, 600) # hide
plot_q₁ = one_plot ? plot(t, q₁, size=psize) : plot(t, q₁, layout=(n_param_sets, 1), size=psize, label=labels, legend=:topright) # hide
```