implement a general inv_diff

JuliaManifolds · Nov 13, 2023 · 63e0b6c · 63e0b6c
1 parent 1301240
commit 63e0b6c
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Showing 5 changed files with 3 additions and 69 deletions.
diff --git a/src/groups/addition_operation.jl b/src/groups/addition_operation.jl
@@ -74,14 +74,7 @@ end
 
 Compute the value of differential of additive matrix inversion ``p ↦ -p`` at ``X``, i.e. ``-X``.
 """
-function inv_diff(::AdditionGroupTrait, G::AbstractDecoratorManifold, p, X)
-    return -X
-end
-function inv_diff!(::AdditionGroupTrait, G::AbstractDecoratorManifold, Y, p, X)
-    Y .= X
-    Y .*= -1
-    return Y
-end
+inv_diff(::AdditionGroupTrait, G::AbstractDecoratorManifold, p, X)
 
 function is_identity(::AdditionGroupTrait, G::AbstractDecoratorManifold, q; kwargs...)
     return isapprox(G, q, zero(q); kwargs...)

diff --git a/src/groups/group.jl b/src/groups/group.jl
@@ -560,6 +560,8 @@ end
 
 @trait_function inv_diff!(G::AbstractDecoratorManifold, Y, p, X)
 
+inv_diff!(::TraitList{<:IsGroupManifold}, G::AbstractDecoratorManifold, Y, p, X) = -adjoint_action!(G, Y, p, X)
+
 function Base.copyto!(
     ::TraitList{IsGroupManifold{O}},
     ::AbstractDecoratorManifold,

diff --git a/src/groups/multiplication_operation.jl b/src/groups/multiplication_operation.jl
@@ -162,34 +162,6 @@ function inv!(
     return q
 end
 
-"""
-    inv_diff(::MultiplicationGroupTrait, G::AbstractDecoratorManifold, p, X)
-
-Compute the value of differential of matrix inversion ``p ↦ p^{-1}`` at ``X``.
-When tangent vectors are represented in Lie algebra in a left-invariant way, the formula
-reads ``-pXp^{-1}``. For matrix groups with ambient space tangent vectors, the formula would
-read ``-p^{-1}Xp^{-1}``. See the section about matrix inverse in [Giles:2008](@cite).
-"""
-function inv_diff(::MultiplicationGroupTrait, G::AbstractDecoratorManifold, p, X)
-    return -(p * X * inv(G, p))
-end
-function inv_diff(
-    ::MultiplicationGroupTrait,
-    G::AbstractDecoratorManifold,
-    p::AbstractArray{<:Number,0},
-    X::AbstractArray{<:Number,0},
-)
-    p_inv = inv(p[])
-    return -(p[] * X * p_inv)
-end
-
-function inv_diff!(::MultiplicationGroupTrait, G::AbstractDecoratorManifold, Y, p, X)
-    p_inv = inv(p)
-    Z = X * p_inv
-    mul!(Y, p, Z)
-    Y .*= -1
-    return Y
-end
 
 compose(::MultiplicationGroupTrait, G::AbstractDecoratorManifold, p, q) = p * q
 

diff --git a/src/groups/power_group.jl b/src/groups/power_group.jl
@@ -151,28 +151,6 @@ function inv!(
     return q
 end
 
-function inv_diff!(G::PowerGroup, Y, p, X)
-    GM = G.manifold
-    rep_size = representation_size(GM.manifold)
-    for i in get_iterator(GM)
-        inv_diff!(
-            GM.manifold,
-            _write(GM, rep_size, Y, i),
-            _read(GM, rep_size, p, i),
-            _read(GM, rep_size, X, i),
-        )
-    end
-    return Y
-end
-function inv_diff!(G::PowerGroupNestedReplacing, Y, p, X)
-    GM = G.manifold
-    N = GM.manifold
-    rep_size = representation_size(N)
-    for i in get_iterator(GM)
-        Y[i...] = inv_diff(N, _read(GM, rep_size, p, i), _read(GM, rep_size, X, i))
-    end
-    return Y
-end
 
 # lower level methods are added instead of top level ones to not have to deal
 # with `Identity` disambiguation

diff --git a/src/groups/product_group.jl b/src/groups/product_group.jl
@@ -114,17 +114,6 @@ function inv!(G::ProductGroup, q, p)
 end
 inv!(::ProductGroup, q::Identity{ProductOperation}, ::Identity{ProductOperation}) = q
 
-function inv_diff!(G::ProductGroup, Y, p, X)
-    M = G.manifold
-    map(
-        inv_diff!,
-        M.manifolds,
-        submanifold_components(G, Y),
-        submanifold_components(G, p),
-        submanifold_components(G, X),
-    )
-    return Y
-end
 
 _compose(G::ProductGroup, p, q) = _compose(G.manifold, p, q)
 function _compose(M::ProductManifold, p::ArrayPartition, q::ArrayPartition)