Plotting

AbstractVectorOfArray and AbstractDiffEqArray types include Plots.jl recipes so they can be visualised directly with plot(A).

VectorOfArray

A VectorOfArray plots as a matrix where each inner array is a column:

using RecursiveArrayTools, Plots
A = VectorOfArray([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
plot(A)   # 3 series (components) vs column index

DiffEqArray

A DiffEqArray plots as component time series against A.t:

u = [[sin(t), cos(t)] for t in 0:0.1:2pi]
t = collect(0:0.1:2pi)
A = DiffEqArray(u, t)
plot(A)   # plots sin and cos vs t

If the DiffEqArray carries a symbolic system (via variables and independent_variables keyword arguments), the axis labels and series names are set automatically from the symbol names.

Dense (Interpolated) Plotting

When a DiffEqArray has an interpolation object in its interp field and dense = true, calling plot(A) generates a smooth curve by evaluating the interpolation at many points rather than connecting only the saved time steps.

using SciMLBase: LinearInterpolation

u = [[1.0, 0.0], [0.0, 1.0], [-1.0, 0.0], [0.0, -1.0]]
t = [0.0, 1.0, 2.0, 3.0]
interp = LinearInterpolation(t, u)
A = DiffEqArray(u, t; interp = interp, dense = true)
plot(A)   # smooth interpolated curve with 1000+ points

Plot Recipe Keyword Arguments

The AbstractDiffEqArray recipe accepts the following keyword arguments, which can be passed directly to plot:

Example:

plot(A; denseplot = true, plotdensity = 5000, tspan = (0.0, 2.0))

Selecting Variables with idxs

The idxs keyword controls which variables appear in the plot. It supports several formats:

Single component

plot(A; idxs = 1)      # plot component 1 vs time
plot(A; idxs = 2)      # plot component 2 vs time

Multiple components

plot(A; idxs = [1, 3, 5])   # plot components 1, 3, 5 vs time

Phase-space plots (component vs component)

Use a tuple where index 0 represents the independent variable (time):

plot(A; idxs = (1, 2))      # component 1 vs component 2
plot(A; idxs = (0, 1))      # time vs component 1 (same as default)
plot(A; idxs = (1, 2, 3))   # 3D plot of components 1, 2, 3

Symbolic indexing

When the DiffEqArray carries a symbolic system, variables can be referenced by symbol:

A = DiffEqArray(u, t; variables = [:x, :y], independent_variables = [:t])
plot(A; idxs = :x)           # plot x vs time
plot(A; idxs = [:x, :y])     # plot both
plot(A; idxs = (:x, :y))     # phase plot of x vs y

Custom transformations

A function can be applied to the plotted values:

plot(A; idxs = (norm, 0, 1, 2))   # plot norm(u1, u2) vs time

The tuple format is (f, xvar, yvar) or (f, xvar, yvar, zvar) where f is applied element-wise.

Callable Interface

Any AbstractDiffEqArray with an interp field supports callable syntax for interpolation, independent of plotting:

A(0.5)                    # interpolate all components at t=0.5
A(0.5; idxs = 1)          # interpolate component 1 at t=0.5
A([0.1, 0.5, 0.9])       # interpolate at multiple times (returns DiffEqArray)
A(0.5, Val{1})            # first derivative at t=0.5
A(0.5; continuity = :right)  # right-continuity at discontinuities

The interpolation object must be callable as interp(t, idxs, deriv, p, continuity), matching the protocol used by SciMLBase's LinearInterpolation, HermiteInterpolation, and ConstantInterpolation.

When no interpolation is available (interp === nothing), calling A(t) throws an error.

ODE Solution Plotting

ODE solutions from DifferentialEquations.jl are subtypes of AbstractDiffEqArray and inherit all of the above functionality, plus additional features:

• Automatic dense plotting: denseplot defaults to true when the solver provides dense output.
• Analytic solution overlay: plot(sol; plot_analytic = true) overlays the exact solution if the problem defines one.
• Discrete variables: Time-varying parameters are plotted as step functions with dashed lines and markers.
• Symbolic indexing: Full symbolic indexing through ModelingToolkit is supported, including observed (derived) variables.

These advanced features are defined in SciMLBase and activate automatically when plotting solution objects.

Plot Helper API

DEFAULT_PLOT_FUNC(x, y)
DEFAULT_PLOT_FUNC(x, y, z)

plottable_indices(x)

plot_indices(A::AbstractArray)

getindepsym_defaultt(A)

interpret_vars(vars, A)

add_labels!(labels, x, dims, A, strs)

diffeq_to_arrays(A, denseplot, plotdensity, tspan, vars, tscale, plotat)

solplot_vecs_and_labels(dims, vars, plott, A)