Introduce the general linear group and the multiplication group operation.

[kellertuer]

🛣️🗺️

• GeneralLinearGroup
  • check_point, check_vector, distance, embed, norm (inherited from InvertibleMatrices)
  • get_coordinates, get_vector in the LieAlgebraOrthonormalBasis
  • exp, exp!, log,log! (will be inherited from matrix group operation
• AbstractMultiplicationGroupOperation
  • MatrixMultiplicationGroupOperation
  • exp, exp!
  • log, log!
  • *, /, \
  • compose
  • inv
  • diff_inv (formerly inv_diff)
  • diff_conjugate
  • diff_right_compose and diff_left_compose (formerly translate_diff)
  • identity_element, identity_element!
  • lie_bracket, lie_bracket!
• Resolve Transitioning from Manifolds.jl #7 by using a table how to transfer function calls
• document removal / replacement of inverse_translate_diff
• vee
• hat
• get_vector
• get_coordinates
• rand and rand!
• test coverage.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Please upload report for BASE (main@c695564). Learn more about missing BASE report.

Additional details and impacted files

@@           Coverage Diff            @@
##             main       #12   +/-   ##
========================================
  Coverage        ?   100.00%           
========================================
  Files           ?         9           
  Lines           ?       397           
  Branches        ?         0           
========================================
  Hits            ?       397           
  Misses          ?         0           
  Partials        ?         0           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[kellertuer]

there is now only text coverage missing, so I already mark this as “Ready-to-Review”.

For testing the test suite has to be extended slightly, but besides that this PR is feature-complete.

[mateuszbaran]

Good work 👍 . One idea to discuss: should GeneralLinearGroup have embed and project for tangent vectors that left-multiply (or left-divide) by point? GeneralUnitaryMatrices in Manifolds.jl has that.

[kellertuer]

Sounds reasonable. Do we want to stick to calling that “embed/project”? For me that is more of a change of a representer. We have the same X we just represent it once in the Lie algebra, once in the tangent space at g.

And in practice it is also just a call to the correct diff_compose, diff_inv combination, but sure, something nice to have which is easier to use.

So I am very much for introducing that here, but maybe we can have some better fitting names? Especially project does not fit so well for a change of a representer.

[kellertuer]

Now this is really finished.
With both addition and multiplication, the simpler Lie groups could now all be transferred.

[mateuszbaran]

A few comments

[mateuszbaran]

One more thing we might want to fix:

G = GeneralLinearGroup(3)
@test_throws ManifoldDomainError is_point(G, randn(ComplexF64, 3, 3); error=:error)

This used to work in Manifolds.jl but doesn't throw an error here.

[kellertuer]

That might ne more something for Invertible matrices?

[mateuszbaran]

I'm not really sure what goes wrong at the moment.

[mateuszbaran]

LGTM 👍