Add point capability to _produce_type to improve GPU compatibility

[mateuszbaran]

This is a draft of the enhancement discussed in #574 .

cc @zazabap

[mateuszbaran]

Does this test:

Manopt.jl/test/plans/test_stopping_criteria.jl

Line 25 in 99bb001

s = GradientDescentState(Euclidean(); p = 1.0)

intentionally verify that the solver works with an immutable p? I can make it work, though it would make the code a bit uglier.

[kellertuer]

intentionally verify that the solver works with an immutable p?

Yes, that test is intentionally, since Euclidean(1) would be vectors of length 1, but Euclidean() is our convention for reals/immutable. Internally we could Ref that – think we even do that already.

[kellertuer]

I think this is now a bit inconsistent. For the DistanceOverGradient you did a breaking change and moved the p from a keyword to a positional. Here you did not do that, but introduce a new constructor with p that moves that to a keyword.

I think until now, if needed, the p was a keyword (with rand(M) as default which has the same problem with a point type by the way). To be nonbreaking, maybe keeping that would be nice?

[mateuszbaran]

I understood the docs of DistanceOverGradient where they claim that p is the "initial point, used to track distance" as "p is the starting point of optimization". Is this just supposed to be an arbitrary point? If so, maybe it would be good to clarify it in the docstring. That's why I thought it's a bugfix rather than a breaking change.

[kellertuer]

A small comment

[mateuszbaran]

Yes, that test is intentionally, since Euclidean(1) would be vectors of length 1, but Euclidean() is our convention for reals/immutable. Internally we could Ref that – think we even do that already.

OK, then I think a new method in ManifoldsBase would be the cleanest solution.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 100.00%. Comparing base (88c7db6) to head (19c3287).

Additional details and impacted files

@@            Coverage Diff            @@
##            master      #577   +/-   ##
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  Coverage   100.00%   100.00%           
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  Files           91        91           
  Lines         9975     10013   +38     
=========================================
+ Hits          9975     10013   +38     

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