Support makie backends

[BambOoxX]

This is a first proposal to allow other Makie backends to be used with BifurcationKit.
The first main problem (solved in this draft) is that (un)stable branches are displayed with different line widths, which is incompatible with CairoMakie as is.
Another solution could be to have one plot per branch. But I'm not sure what is best.

Fixes #54 for CairoMakie at least.

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 64 lines in your changes missing coverage. Please review.

Project coverage is 88.49%. Comparing base (f1503bc) to head (fd53c55).
Report is 20 commits behind head on master.

Files with missing lines	Patch %	Lines
ext/MakieExt/plot.jl	0.00%	64 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #181      +/-   ##
==========================================
- Coverage   88.69%   88.49%   -0.21%     
==========================================
  Files          65       66       +1     
  Lines        9460     9515      +55     
==========================================
+ Hits         8391     8420      +29     
- Misses       1069     1095      +26     

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[rveltz]

My coding style is to have spaces around =

[BambOoxX]

Ah yes, sorry about that, I hit auto indent and forgot to check it. I just don't know yet in vscode how to change the formatting settings. Would you know ?

[rveltz]

not really

[rveltz]

My coding style is to have spaces around =

[rveltz]

Wow, thank you for this new PR!!

One issue I found is that the following does not work

function TMvf!(dz, z, p, t = 0)
    (;J, α, E0, τ, τD, τF, U0) = p
    E, x, u = z
    SS0 = J * u * x * E + E0
    SS1 = α * log(1 + exp(SS0 / α))
    dz[1] = (-E + SS1) / τ
    dz[2] = (1.0 - x) / τD - u * x * E
    dz[3] = (U0 - u) / τF +  U0 * (1 - u) * E
    dz
end

par_tm = (α = 1.5, τ = 0.013, J = 3.07, E0 = -2.0, τD = 0.200, U0 = 0.3, τF = 1.5, τS = 0.007)
z0 = [0.238616, 0.982747, 0.367876 ]
prob = BifurcationProblem(TMvf!, z0, par_tm, (@optic _.E0); record_from_solution = (x, p; k...) -> (E = x[1], x = x[2], u = x[3]),)

opts_br = ContinuationPar(p_min = -10.0, p_max = 1., dsmax = 0.1, n_inversion = 8, nev = 3)
br = continuation(prob, PALC(tangent = Bordered()), opts_br; plot = false, normC = norminf, bothside = true)

BK.plot(br, plotfold=false)
####################################################################################################
br_fold = BK.continuation(br, 2, (@optic _.α), ContinuationPar(br.contparams, p_min = 0.2, p_max = 5.), bothside = true)
BK.plot(br_fold)

[BambOoxX]

br_fold = BK.continuation(br, 2, (@optic _.α), ContinuationPar(br.contparams, p_min = 0.2, p_max = 5.), bothside = true)
BK.plot(br_fold)

This works on latest.

[rveltz]

Yep but this one is broken now :(

# test vector field for event detection
function Feve(X, p)
	p1, p2, k = p
	x, y = X
	out = similar(X)
	out[1] = p1 + x - y - x^k/k
	out[2] = p1 + y + x - 2y^k/k
	out
end

# parameters for the vector field
par = (p1 = -3., p2 = -3., k = 3)

# bifurcation problem
prob = BifurcationProblem(Feve, -2ones(2), par, (@optic _.p1);
	record_from_solution = (x, p; k...) -> x[1])

# parameters for the continuation
opts = ContinuationPar(max_steps = 150, p_min = -3., p_max = 4.0,
    # we disable bifurcation detection to focus
    # on the user passed events
    detect_bifurcation = 0, detect_fold = false,
    # parameters specific to event detection
    detect_event = 2)
# arguments for continuation
args = (prob, PALC(), opts)
kwargs = (plot = false, verbosity = 0,)
br = continuation(args...; kwargs...,)
BK.plot(br)


br = continuation(args...; kwargs...,
	event = SaveAtEvent((-2.,-1.); use_newton = true))

BK.plot(br)

[BambOoxX]

It should be okay now, it was because empty indices were not handled properly. Now any edge case should be okay. Although I can't test everything easily, sorry.

[rveltz]

Do you think it is good for merging?
I have tried deflated continuation, diagram and codim2, it seems to work well with CairoMakie

[BambOoxX]

At this point, I think it works. The only question is if there are other uses of line widths I did not meet during my tests. It's really the only problem I met with CairoMakie.
Also, I was thinking about a function capable of altering the backend set_plot_backend!(::AbstracPlotBackend) so that people could switch between Makie and Plots upon request.
Do you want me to add a commit with that before merging ?

[rveltz]

yes if you have a working solution, that would be awesome.
Thank you a lot for your work, it's really improved BK.

The Makie backend is slower than the Plots one during continuation. I think the Makie backend should rely on observables in that case but that's another issue.

[BambOoxX]

yes if you have a working solution, that would be awesome.

So actually, it doesn't exactly require set_plot_backend!, BK.plot will plot with Makie backends and Plots.plot with Plots backend, although it would be better to have BK.plot work for all backends.

Thank you a lot for your work, it's really improved BK.

Thanks, but compared to all the difficult math stuff, this is very easy ;).

The Makie backend is slower than the Plots one during continuation. I think the Makie backend should rely on observables in that case but that's another issue.

Yep I could work on that if you have examples that show the problem.

[rveltz]

Yep I could work on that if you have examples that show the problem.

Not really, when trying both backend on a simple example, I came to this subjective observation

[rveltz]

You might also be interested by https://github.com/gszep/BifurcationExplorer.jl