Fix docs build

[JonasKoziorek]

One of the algorithms stopped converging for examples in the docs. I changed the initial guesses and precision. This must have resulted from some changes in other libraries, probably NonlinearSolve.

[JonasKoziorek]

Strange, I pass the tests locally.

[Datseris]

Any way you can fix the tests? change tolerances or something? Docs wont build if tests fail.

Thanks for the PR!

[JonasKoziorek]

I will play around with parameters and see if it passes the tests.

[JonasKoziorek]

Any tips on how to debug why the tests run locally and not here?

[Datseris]

Can you tell me what is going wrong with the test? What is it supposed to be testing and what it finds instead?

[JonasKoziorek]

PeriodicOrbits.jl/test/algorithms/continuous_time/optimized_shooting.jl

Lines 29 to 30 in 11063cb

	res = periodic_orbits(ds, alg, igs)
	@test length(res) == 2

Given two initial guesses, the algorithm finds an orbit only for one of the guesses.
Maybe after the update of NonlinearSolve the SciML solver doesn't converge to the same result for the given initial guess. (11063cb#diff-72ed386c2a0cd1d23c0968297e70023ed98c22490d146dd89fc91f48369bad4dL18)

[Datseris]

Can you just check out the branch, run the initial conditions and see if you get the orbit you should, otherwise change the guess?

[Datseris]

Or, significantly increase the starting guess period for the second orbit.

[JonasKoziorek]

I just used two identical initial guesses. If I could simulate the CI environment somehow locally, I could perhaps debug why the CI fails but waiting 10 mins every time I make a change is tedious.

[Datseris]

But that's a poor choice no? We want to test that the algorithm can find at least two different periodic orbits, as it should. I thought that's what the test was trying to do (in the second half)

[Datseris]

Does it not work with a big change like 10 units of time?

[JonasKoziorek]

But that's a poor choice no? We want to test that the algorithm can find at least two different periodic orbits, as it should. I thought that's what the test was trying to do (in the second half)

Yes I know that it is a poor choice.
Just to be clear, for this algorithm the orbit is either found or not. So minimum 0 maximum 2 orbits. Ideally, I would like each initial guess to give me a different orbit.

[JonasKoziorek]

Does it not work with a big change like 10 units of time?

I can try, but why +10? Does Lorenz System have such orbits? The guess of time acts the same as a guess of spatial coordinates. If there is no orbit near with the spatial guess + temporal guess, the algorithm won't converge.

[Datseris]

I am confused: I thoguth you where searching for unstable periodic orbits in the chaotic lorenz system?

[JonasKoziorek]

I am confused: I thoguth you where searching for unstable periodic orbits in the chaotic lorenz system?

Yes, I know there should be infinitely many of them. But nevertheless, this algorithm doesn't work so well that it would converge to any guess I input. I think the guess has to be quite precise for the algorithm to converge.

[Datseris]

Okay, then let's simply remove the broken test and make a statement in the algorithm doc that the algorithm is not particularly accurate.