Proof of concept for non-array point

[blegat]

This gives

julia> @variable(model, x in Hyperbolic(2), start = HyperboloidPoint([1, 2]))
HyperboloidPoint(VariableRef[_[5], _[6]])

What are the operations we could do on x that would result in a scalar objective function ?

[codecov]

Codecov Report

❌ Patch coverage is 27.27273% with 8 lines in your changes missing coverage. Please review.
✅ Project coverage is 99.65%. Comparing base (7ccb6f8) to head (d483e99).
⚠️ Report is 2 commits behind head on kellertuer/fix-313-a-jump-tutorial.

Files with missing lines	Patch %	Lines
ext/ManoptJuMPExt.jl	33.33%	6 Missing ⚠️
ext/ManoptJuMPManifoldsExt.jl	0.00%	2 Missing ⚠️

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##           kellertuer/fix-313-a-jump-tutorial     #491      +/-   ##
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[kellertuer]

I do not understand the question, sorry. Maybe call the cost function?

edit: Or doe you mean which functions are implemented specifically for this? All of them. Exp, log, (replace +-) retractions (approximate exp/log)....
But the prior PR therefore “unwrapped” the variables before going to the state/solver.

[kellertuer]

Can we maybe have a it of documentation here? The official docs mainly state “please ask a developer”. If that code is here in Manopt I am a developer and by now I tried for about half a year maybe to understand something – and I simply do not.

[kellertuer]

...your docs do not help https://jump.dev/JuMP.jl/stable/api/JuMP/#JuMP.add_variable – they state I should ask you, and neither are my code archeology skill that good nor have all my tries of that not lead to me understanding how this is supposed to work, nor what for example the string is.

[kellertuer]

This concept also can not work, since the point type is not “available” in Manopt. We can not just “rewrite” the existing parts.

The existing one is an extension

• Manopt & JuMP

But for specific manifold we need an extension to

• Manopt, Manifold & JuMP

The Other PR defines the Manifolds-type-wrapper in the first extension and tries a proof of concept in the second.
I am not yet sure how this idea could be fit into this general setting, nor have I understood how it is meant to work.

[blegat]

Yes I mean what would be a typical objective I can use in the tests.

But the prior PR therefore “unwrapped” the variables before going to the state/solver.

The solver still receives them unwrapped, we'll have to pass the point type as well. The only difference here is that they are wrapped at the JuMP level so the user will be able to use the operators you have define for HyperboloicPoint to build the objective function

[kellertuer]

Hm, I still do not follow. We do not do much magic with the cost (I think you do).

So I am not sure what “the operators” refers to some “build” of an objective function. We do not “build” anything here.

The user really only implements a cost(M,p) where M is a manifold and p is a point thereon. Maybe Manopt is much much simpler and much less what you think in this sense?

I am still not sure what need to be done here then. Nor do I understand the approach to an extend that I can adapt it for the PR.

But I understand that this is never meant to be merged but just a proof of concept (that I would have added as a comment in the other PR).

[blegat]

I just meant : if you give le an example of cost function, just the way you write it with Manopt, I can turn this proof of concept into a working state :)

[kellertuer]

function f(M::Hyperbolic, p::HyperboloidPoint) # though this is internally the same as arrays actually
    #compute something based on p.value, I am not creative enough right now... ;)
    return 7.0
end

gradients the same grad_f(M, p) ...but we also support in-place ones: grad_f!(M, X, p) that compute in-place of X. not sure jump can support that.

[kellertuer]

Since we now can both push to #454, we could close this and add it directly there?

[blegat]

Yes, I just merged it into it :)