Plotting

When Plots is loaded, the CTModelsPlots extension adds a recipe so a Solution can be drawn directly with plot / plot!. The recipe lays out the state, control, costate (and, when present, path constraints and their duals) on a shared time axis.

using CTModels
using Plots      # activates the CTModelsPlots extension

pre = CTModels.PreModel()
CTModels.variable!(pre, 0)
CTModels.time!(pre; t0=0.0, tf=1.0)
CTModels.state!(pre, 2)
CTModels.control!(pre, 1)
CTModels.dynamics!(pre, (r, t, x, u, v) -> (r[1] = x[2]; r[2] = u[1]; nothing))
CTModels.objective!(pre, :min; lagrange=(t, x, u, v) -> u[1]^2)
CTModels.time_dependence!(pre; autonomous=true)
ocp = CTModels.build(pre)

N = 101
T = collect(range(0.0, 1.0; length=N))
sol = CTModels.build_solution(ocp, T, hcat(cos.(T), -sin.(T)),
    reshape(-cos.(T), N, 1), Float64[], zeros(N, 2);
    objective=0.5, iterations=10, constraints_violation=1e-9,
    message="ok", status=:optimal, successful=true)

Default plot

Plots.plot(sol)

Layout and control options

The recipe accepts keyword arguments that control the arrangement and how the control is displayed:

Keyword	Values	Effect
layout	:group / :split	one figure per quantity, or state/costate split
control	:components / :norm / :all	plot each control, its norm, or both
time	:default / :normalize	physical time, or rescaled to

Plots.plot(sol; layout=:split, control=:all)

Overlaying solutions

plot! adds a solution to an existing figure — handy for comparing two solves on the same axes:

plt = Plots.plot(sol)
Plots.plot!(plt, sol; time=:normalize)
plt

Because the recipe reads the typed solution (its time grids, interpolation kind, and dual structure) rather than raw arrays, the same call works for unified- and multiple-grid solutions alike — see Time grids.

Makie backend

A second backend renders the same figure with Makie.jl, at feature parity with the Plots backend (reference lines, step controls, overlay and forwarded attributes all supported). Load a Makie backend package (CairoMakie, GLMakie, …); the CTModelsMakie extension then provides Makie.plot(sol), returning a Makie.Figure:

Makie.plot(sol)

Makie.plot(sol; layout=:group, control=:all)

Makie.plot! overlays onto an existing figure, the same way Plots.plot! does:

f = Makie.plot(sol)
Makie.plot!(f, sol; time=:normalize)
f

The description and keyword arguments (layout, control, time, the *_style keywords, color, size) are identical to the Plots backend. When both Plots and a Makie package are loaded, plot must be qualified — Plots.plot(sol) renders with Plots, Makie.plot(sol) with Makie.

Style keywords beyond the neutral vocabulary (color, linewidth, linestyle, alpha, seriestype) are resolved per backend: the Plots backend forwards any attribute Plots recognises, while the Makie backend only forwards a fixed whitelist and drops the rest. See the Plotting Engine guide in the CTBase documentation ("User Attributes: Series vs Axis") for the exact rule.