VectorFieldPlots.jl

A simple package for plotting vector fields and phase portraits in Julia. The main utilities of this package are provided by the functions plot_vector_field and plot_phase_portrait, which take as inputs a list of x and y coordinates specifying the region to plot over, and a function f(x, y) that describes the vector field.

Installation

To download this package open up the Julia REPL, enter the package manager (type ] into the REPL) and type

add https://github.com/maxhcohen/VectorFieldPlots.jl.git

Example usage

The following code shows how to use this package to plot the vector field and phase portrait for the Van der Pol oscillator.

using Plots
using LaTeXStrings
using VectorFieldPlots

# Plot defaults so things look nice
default(grid=false, framestyle=:box, label="", fontfamily="Computer Modern")

# Parameters of Van der Pol oscillator
μ = 1.0

# Define vector field
f(x, y) = [y, μ*(1 - x^2)*y - x]

# Region to plot vector field over
xs = -5.0:0.5:5.0
ys = -5.0:0.5:5.0

# Coordinates for initial conditions of phase portraits and length of corresponding sim
xs_phase = -3.0:0.5:3.0
ys_phase = -3.0:0.5:3.0
T = 10.0

# Plot the vector field
fig = plot_vector_field(xs, ys, f, scale=0.35)
plot_phase_portrait!(xs_phase, ys_phase, f, T)
xlabel!(L"x")
ylabel!(L"y")
title!("Van der Pol oscillator")
xlims!(-5, 5)
display(fig)

The above code produces the following image:

By default, the length of each vector is normalized and then scaled according to the keyword argument scale so that the plot isn't cluttered. The magnitude of each vector is indicated by the colormap keyword argument which defaults to :viridis.

Example with PGFPlotsX.jl

It is also possible to use the internal functions from VectorFieldPlots.jl to quickly plot a vector field using PGFPlotsX.jl, which can then be easily included in a LaTeX document. The following code shows an example of this.

using PGFPlotsX
using LaTeXStrings
using LinearAlgebra
using VectorFieldPlots

# Define vector field
f(x, y) = [-y, x]

# Region to plot over
xs = -1.0:0.1:1.0
ys = -1.0:0.1:1.0
Xs, Ys = meshgrid(xs, ys)

# Compute vector field over meshgrid
scale = 0.075
normalize_arrows = true
dx, dy = mesh_vector_field(Xs, Ys, f, scale, normalize_arrows)

# Map magnitude to colors
c = norm.(f.(Xs, Ys))

# Make PGF Plot
fig = @pgf Axis(
    {   
        xlabel = L"x",
        ylabel = L"y",
        "colormap/viridis",
        colorbar,
    },
    Plot(
        {
            quiver = {u = "\\thisrow{u}", v = "\\thisrow{v}"},
            "-stealth",
            point_meta="\\thisrow{C}",
            "quiver/colored",
        },
        Table({meta="C"},
            x=Xs, y=Ys, u=dx, v=dy, C=c),
    ),
)

# Save to .tex document
pgfsave("vector_field.tex", fig)

This produces the following output