Adjoint matrix and some jacobians

[mateuszbaran]

A generic implementation of adjoint matrix with optimized implementations for selected groups. I've adjusted optimized formulas to match our conventions so it's not exactly the same as in original papers for SE(2) and SE(3).

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 96.41%. Comparing base (d1d4166) to head (c94a12a).
Report is 1 commits behind head on master.

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+ Hits        11099    11175   +76     
- Misses        413      415    +2     

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[olivierverdier]

I think this is what I already implemented here (in a more general setting): https://olivierverdier.github.io/ManifoldGroupUtils.jl/stable/#ManifoldGroupUtils.matrix_from_lin_endomorphism-Tuple{Any,%20Any,%20ManifoldsBase.AbstractBasis}

[mateuszbaran]

That could be true but I'm not sure how to use your function to get the result that I want.

[olivierverdier]

If you have a vector $X$ in the Lie algebra, I think that it would be matrix_from_lin_endomorphism(G, Y -> lie_bracket(G, X, Y), DefaultOrthogonalBasis()).

[mateuszbaran]

I'm not sure it's the same adjoint. Anyway, here the primary need is to be able to overload the computation for selected manifolds with optimized code and doing that with matrix_from_lin_endomorphism would be tricky.

[kellertuer]

Here is a few small comments.