I am trying write a notebook to display some nonlinear optimization descent solvers. Using CairoMakie, I wanted to make a plot that looks something like this.
The arrows should have their tail at the current point in the descent solver and the head at the subsequent point. I have been able to plot a simple contour plot, but I was not sure how to
get these lines to work? Like would this be a a regular line plot or an arrow plot?
using CairoMakie
using LinearAlgebra
h(x) = x'*[2 0; 2 5]*x
xs = LinRange(-5, 5, 100)
ys = LinRange(-5, 5, 100)
zs = [h([x;y]) for x in xs, y in ys]
contour(zs, levels = -1:5:100)
This looks like the plot below.
So I just need a little nudge on how to get the following points with the arrows
into the plot. I did not include code for generating these points since it would make the MWE a little
more than minimal. But I can always add that in if people request it. I also made the function really simple but I have more complicated functions in reserve that will take multiple steps to reach the minimum.
(1, [10.2, 4.78])
(2, [0.0, 0.0])
Will something like this do the trick?
using GLMakie
# This is fake data for contour plot
N(x, y; μx=0, σx=1, μy=0, σy=1, ρ=0) = @. 1 / (2*π*σx*σy*sqrt(1-ρ^2)) * exp( -1/(2*(1-ρ^2)) * ( (x-μx)^2/σx^2 - 2*ρ*(x-μx)/σx*(y-μy)/σy + (y-μy)^2/σy^2 ) )
x = -2:0.05:2
y = -2:0.05:2
# This is fake data for points (arrow tails)
th = acos.(1 .- 2 .* rand(6))
ph = rand(6) .* 2 .* π
r = 2 .* exp.(collect(0:-0.2:-1.0) ./ 0.25)
xa = r .* sin.(th) .* cos.(ph)
ya = r .* sin.(th) .* sin.(ph)
# Arrow directions
u = xa[2:end] .- xa[1:end-1]
v = ya[2:end] .- ya[1:end-1]
fig = Figure(size=(800, 600))
ax = Axis(fig[1, 1])
contour!(ax, x, y, N(x, y'; ρ=0.5))
scatter!(ax, xa, ya; color=:black, markersize=4)
# Arrows are little shorter so head and tails do not overlap
arrows!(ax, xa[1:end-1], ya[1:end-1], u .* 0.95, v .* 0.95)
fig
For more detailed options for arrows see arrows | Makie
2 Likes
Oh yes, so it is a combination of contour, scatter, and arrows. Okay, I will study this a bit, but it looks like this will work. Excellent. Thanks so much for the example. I was not sure how to get that next step.
Maybe some arrows from MakieExtra?
