Implement infectivity radius on Stiefel

[kellertuer]

cf. Zimmermann & Stoye https://arxiv.org/abs/2405.02268v1 .

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[mateuszbaran]

That was quick! The failure is caused by a new ambiguity:

injectivity_radius(M::AbstractDecoratorManifold, m::AbstractRetractionMethod) @ ManifoldsBase ~/.julia/packages/ManifoldsBase/pOL51/src/nested_trait.jl:305,
injectivity_radius(::Stiefel, p) @ Manifolds ~/work/Manifolds.jl/Manifolds.jl/src/manifolds/StiefelEuclideanMetric.jl:112

[kellertuer]

Oh we should maybe check ambiguities on the infectivity radius. – So how do we reduce this? Or do we increase the bound?

[mateuszbaran]

It's real, you can try calling injectivity_radius(Stiefel(5, 2), ExponentialRetraction()) and it would fail. You can probably just delete injectivity_radius(::Stiefel, p) = π though.

[kellertuer]

Then the special point tests fail. But if that is ok, we can do that (that is remove the point ones).

[mateuszbaran]

Then the special point tests fail. But if that is ok, we can do that (that is remove the point ones).

You can limit the type of p in injectivity_radius(::Stiefel, p) to those special point types.

[kellertuer]

or leave them out, we would specialise to arrays or such, and that might not be to useful (we otherwise do not do that I think).

[mateuszbaran]

I think the variant with p should work. You can also disambiguate by defining injectivity_radius(M::Stiefel, m::AbstractRetractionMethod). Or we shouldn't have made injectivity_radius so prone to ambiguities.

[kellertuer]

I omitted the p variants for now, but sure in the long run we should make the infectivity radius a bit less prone to ambiguities.