I want to plot a vector field in Julia. I could not find an example here.
Here there are some examples using plotly
, however, they do not work for me. I would like to plot the vector field by plotlyjs
or plotly
.
Here is an example code in Julia:
using Plots
pyplot()
x = collect(linspace(0,10,100));
X = repmat(x,1,length(x));
Y = repmat(x',length(x),1);
U = cos.(X.*Y);
V = sin.(X.*Y);
streamplot(X,Y,U,V)
Here is the Matlab example:
[x,y] = meshgrid(0:0.2:2,0:0.2:2);
u = cos(x).*y;
v = sin(x).*y;
figure
quiver(x,y,u,v)
We can also plot vector fields in three dimensions, i.e., for functions F:R3→R3. The principle is exactly the same; we plot vectors of length proportional to F(x,y,z) with tail anchored at the point (x,y,z).
add("StatsPlots") using StatsPlots # Required for the DataFrame user recipe # Now let's create the DataFrame using DataFrames df = DataFrame(a = 1:10, b = 10 * rand(10), c = 10 * rand(10)) # Plot the DataFrame by declaring the points by the column names @df df plot(:a, [:b :c]) # x = :a, y = [:b :c].
The short answer: use quiver
from Plots.jl.
quiver(x, y, quiver=(u, v))
In the following, I'll attempt to fully recreate the example you showed in Matlab.
First, we'll import Plots
and enable the plotly
backend.
using Plots
plotly()
We need to define a function similar to Matlab's meshgrid
. Since Plots will operate on our arrays of points regardless of their dimensionality, I chose to simply use repeat
and use the "flattened" outputs.
meshgrid(x, y) = (repeat(x, outer=length(y)), repeat(y, inner=length(x)))
Now, we can create x
, y
, u
, and v
using the same logic as the Matlab code. For the sake of brevity, we can use the @.
macro to vectorize all calls in the given expression.
x, y = meshgrid(0:0.2:2, 0:0.2:2)
u = @. cos(x) * y
v = @. sin(x) * y
From here, we can simply use the quiver
function from Plots, passing u
and v
as a 2-tuple to the keyword argument quiver
.
quiver(x, y, quiver=(u, v))
The result is close to the Matlab output, but it seems that Plots.jl scales the arrows to be longer than they are in Matlab. This is easily fixable, though; we can simply broadcast-multiply u
and v
by a scale constant.
scale = 0.2
u = @. scale * cos(x) * y
v = @. scale * sin(x) * y
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