Integrate with Manifolds.jl

[dehann]

This also affects ApproxManifoldProducts.jl directly.

• E(n), https://julianlsolvers.github.io/Manifolds.jl/latest/manifolds/euclidean.html
• S(1), https://julianlsolvers.github.io/Manifolds.jl/latest/manifolds/circle.html
• SO(n), https://julianlsolvers.github.io/Manifolds.jl/latest/manifolds/rotations.html
  • Quaternions, https://julianlsolvers.github.io/Manifolds.jl/latest/lib/numbers.html#Manifolds.QuaternionNumbers
• SE(n), https://julianlsolvers.github.io/Manifolds.jl/latest/manifolds/group.html#Special-Euclidean-group-1

Relevant to IncrementalInference discussion:

• Manifold optimization JuliaNLSolvers/Optim.jl#435

Docs

• https://julianlsolvers.github.io/Optim.jl/stable/#algo/manifolds/

---

Other references

• Consolidate/Standardize with GeometryBasics.jl #341 (GeometryBasics.jl)

[dehann]

Retroactively influences JuliaRobotics/DistributedFactorGraphs.jl#147

[dehann]

@Affie, if I understand your earlier comment right -- Optim.jl currently has support for Sphere or Euclidean and other Manifolds.jl but not SE(n) (Special Euclidean) yet?

[Affie]

Optim.jl currently has support for Sphere or Euclidean and other Manifolds.jl but not SE(n) (Special Euclidean) yet?

Optim.jl does not support Manifolds.jl yet as far as I can tell.

SE(n)

Thanks, I missed SE in Manifolds.jl, I didn't think to look in decorators.

[Affie]

JuliaManifolds/Manifolds.jl#35

[kellertuer]

Cool, that you already have this in your plans!

Some simple integration to Optim.jl will happen at some time, for example a gradient descent is quite straight forward.
(Biased side note): For more advanced algorithms doing Optimization on Manifold, see Manopt.jl, which will also switch to be based on Manifolds.jl as soon as there is a public release.

[dehann]

JuliaManifolds/Manopt.jl#24

[dehann]

https://discourse.julialang.org/t/understanding-macros-a-macro-to-decorate-a-type/12204

[dehann]

xref #341

[dehann]

xref, need to rebuild densities starting from JuliaRobotics/ApproxManifoldProducts.jl#41

[dehann]

v0.15.0 closes this issue (from RoME.jl perspective). Major future work remains deeper inside and will be tracked at JuliaRobotics/ApproxManifoldProducts.jl#41

[dehann]

PS, the local manifolds, SE2E2_Manifold and BearingRange_Manifold are not yet consolidated with the standard Manifolds.jl interface format. That work still remains to be done. The main delivery here is that all variables and surrounding code from RoME IIF AMP not expect and use <:Manifold.