Power, Product, and semidirect product manifolds

[kellertuer]

⛳️

Work out the three meta Lie groups: power, product, semi-direct product

Note

The generalises are there, implementing all interface functions and tests for all three cases is still missing.

🛣️🗺️

• implement the product Lie group – maybe as own struct?
• check whether it is more reasonable for dispatch to indeed store a tuple of Lie groups in the Productmanifold. The outer operator should still be a tuple of operators or a properly typed product operation
• implement the power Lie group, here the op is the actual (element wise) op, since we can dispatcher manifold. Maybe still as own structure?
• also for power it might be better to store the Lie group inside for easier call to the subfiunctions – still the constructor should stay as the current ones are.
• Implement a default_|left|right]_action(G1, G2) which is used in the semidirect product generation short notation.
• implement functions for power manifold
• implement functions for product manifold
• find a general way to store a semi-direct product – maybe again as well based on two internally stored Lie groups.
• implement functions for semidirect product manifold
• 📈test coverage

[codecov]

Codecov Report

Attention: Patch coverage is 98.15951% with 6 lines in your changes missing coverage. Please review.

Project coverage is 99.12%. Comparing base (4233975) to head (c02a480).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/groups/semidirect_product_group.jl	81.81%	4 Missing ⚠️
src/interface.jl	84.61%	2 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##              main      #14      +/-   ##
===========================================
- Coverage   100.00%   99.12%   -0.88%     
===========================================
  Files            9       12       +3     
  Lines          397      683     +286     
===========================================
+ Hits           397      677     +280     
- Misses           0        6       +6     

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[kellertuer]

I turned runtests.jl into a bash script so that you can run test/runtest.jl now from command line as well. It runs even julia -O0 which on my machine reduces test time from 55 sec to 21 sec.

[kellertuer]

Status: The main part of designing these three is done.

The remainder is to implement all functions form the interface for these.

[kellertuer]

I think for all three the scheme and modelling is done. The only thing left is to implement (and test) all interface functions for these three generic cases.

[kellertuer]

@Affie since we discussed this in the last meeting: I now updated the transition page already.

Notably, the “new ways” to construct Lie groups – Given two Lie groups G and H are

• G^n for the power Lie group (or PowerLieGroup(G, args; kwargs...), where all arguments and keywords are the same as for PowerManifold) – also no need to twiddle around with the operation.
• G×H for the ProductLieGroup(G,H) – again no need to twiddle around with operations or building a product manifold before
• G⋉H for the semidirect one, at least as long as the action has a reasonable default default_left_action(G,H) is defined, otherwise LeftSemidirectProductLieGroup(G, H, a) for your action a is the thing to use.

I hope this is more unified and nicer now :)

For this PR I am mainly missing implementing a few product and semidirect product function defaults.

[kellertuer]

Tests are not yet fully running but all functions are in principle there for Power and Product Lie groups

the semidirect product is easier to finish on a next PR doing semidirect, SO(n) and SE(n), since then we have a concrete test case.

[kellertuer]

This PR should be finished now. There is one fallback on the interface not covered I think, but I do not know how to test it, maybe that fallback for inv and the identity is not necessary since for resolving an ambiguity it is implemented for every group separately anyways.

[kellertuer]

For the last 6 missing lines: the 4 in semidirect will be easy with a concrete example, the 2 in interface I am not sure how to it.
But this is the coverage I was aiming for and the next PR would do the first concrete semidirect one.

[mateuszbaran]

LGTM

[kellertuer]

Nice!