(Special) Orthogonal / Unitary / Euclidean groups

[kellertuer]

This PR aims to provide the special orthogonal group and the first concrete semidirect product: Special Euclidean, since the complex case is similar, this will also cover the special unitary case.

🛣️🗺️

• implement OrthogonalGroup
• Implement SpecialOrthogonalGroup
• Implement SpecialEuclideanGroup
• Implement UnitrayGroup
• Implement SpecialUnitaryGroup
• improve test coverage on the semidirect product groups.

[codecov]

Codecov Report

Attention: Patch coverage is 95.66396% with 16 lines in your changes missing coverage. Please review.

Project coverage is 98.53%. Comparing base (5246f30) to head (5b86c5f).

Files with missing lines	Patch %	Lines
src/utils.jl	78.04%	9 Missing ⚠️
src/interface.jl	70.83%	7 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #17      +/-   ##
==========================================
- Coverage   99.20%   98.53%   -0.67%     
==========================================
  Files          13       19       +6     
  Lines         756     1095     +339     
==========================================
+ Hits          750     1079     +329     
- Misses          6       16      +10     

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[kellertuer]

Status update 1: In theory SE(n) is defined, in practice I am not able to dispatch on the new const. Hence the constructor still falls back to calling the general show (of semidirect product) @mateuszbaran can you maybe take a look? After an hour of trying I am a bit out of ideas what is wrong with my constant SpecialEuclideanGroup definition.

[mateuszbaran]

I've fixed the issue with SpecialEuclideanGroup alias 🙂

[kellertuer]

Nice. I would not have noticed the tuple necessary during the rest of the year.

You changed one . to a map. Should I do that for the rest as well?

[kellertuer]

Oh and sorry for the capitalisation foo – Mac OS does not distinguish that on files when loading them … super annoying.

[mateuszbaran]

You changed one . to a map. Should I do that for the rest as well?

I generally prefer map over . when both are applicable because for the compiler it's much easier to optimize map.

Oh and sorry for the capitalisation foo – Mac OS does not distinguish that on files when loading them … super annoying.

No problem, that was an easy fix 🙂

[kellertuer]

The main work today was a bit of structure, since now one of my main worries already works – compose! – the remaining functions are hopefully just stuff to transfer from manifolds.jl the todo list is basically all commented our functions in the two new test files.

So I am confident that this should not be too complicated – and am quite happy with how semidirect turned out.

[kellertuer]

All dummies are there, now the rest is mainly getting all functions from the test suite implemented and tested.