JuliaManifolds/LieGroups.jl

New linear representation type

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#6 opened on Sep 18, 2024

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help wanted

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Description

Many group actions are actually linear representations, which allows to define apply_diff automatically. I would suggest the following:

  1. Create a new abstract type AbstractLinearRepresentation:
abstract type AbstractLinearRepresentation{AD <: ActionDirection} <: AbstractGroupAction{AD} end
  1. Define apply_diff for this class of group actions:
Manifolds.apply_diff(A::AbstractLinearRepresentation, g, ::Any, X) = apply(A, g, X)
  1. Make the existing linear group actions derive from AbstractLinearRepresentation For instance:
struct TranslationAction{TAD<:ActionDirection,TM<:AbstractManifold,TRn<:TranslationGroup} <:
       AbstractLinearRepresentation{TAD}
    manifold::TM
    Rn::TRn
end
  1. Clean up existing code Most of the existing implementations of apply_diff follow this pattern (because they are linear representation), for instance:
  • apply_diff(::TranslationAction,...)
  • apply_diff(::RotationActionOnVector,...)
  • apply_diff(::RotationTranslationOnVector,...)`

Contributor guide

Research direction
Review existing linear representation implementations (TranslationAction, RotationActionOnVector, RotationTranslationOnVector) and ensure they derive from AbstractLinearRepresentation. Verify that apply diff can be defined generically for AbstractLinearRepresentation as proposed.
Tech stack
julia
Domain
backend
Issue type
Feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
2
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Half day
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Clear
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Julia
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60