From 9a157d682b1778a12358da57fed65e09587c9be9 Mon Sep 17 00:00:00 2001
From: Mateusz Baran <mateuszbaran89@gmail.com>
Date: Fri, 17 Jan 2025 12:07:13 +0100
Subject: [PATCH] initial sketch of rand with types

---
 src/groups/special_euclidean_group.jl |  6 +++++
 src/interface.jl                      | 35 ++++++++++++++++++++++++---
 2 files changed, 38 insertions(+), 3 deletions(-)

diff --git a/src/groups/special_euclidean_group.jl b/src/groups/special_euclidean_group.jl
index dc0265c9..4666d38d 100644
--- a/src/groups/special_euclidean_group.jl
+++ b/src/groups/special_euclidean_group.jl
@@ -102,6 +102,12 @@ struct SpecialEuclideanMatrixPoint{T} <: AbstractLieGroupPoint
     value::T
 end
 
+function ManifoldsBase.allocate_on(
+    M::SpecialEuclideanGroup, ::Type{SpecialEuclideanMatrixPoint}
+)
+    return SpecialEuclideanMatrixPoint(Matrix(undef, representation_size(M)...))
+end
+
 """
     SpecialEuclideanMatrixTVector <: AbstractLieGroupPoint
 
diff --git a/src/interface.jl b/src/interface.jl
index f415b0f7..8c3c6fde 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -904,8 +904,31 @@ Random.rand(::LieGroup; kwargs...)
 
 # New in LIeGroups – maybe move to ManifoldsBase at some point
 @doc "$(_doc_rand)"
-function Random.rand(G::LieGroup, T::Type; vector_at=nothing, kwargs...)
-    # TODO conitnue here and allocate the right thing.
+Random.rand(G::LieGroup, T::Type; vector_at=nothing, kwargs...)
+
+function Random.rand(M::AbstractManifold, T::Type, d::Integer; kwargs...)
+    return [rand(M, T; kwargs...) for _ in 1:d]
+end
+function Random.rand(rng::AbstractRNG, M::AbstractManifold, T::Type, d::Integer; kwargs...)
+    return [rand(rng, M, T; kwargs...) for _ in 1:d]
+end
+function Random.rand(M::AbstractManifold, T; vector_at=nothing, kwargs...)
+    if vector_at === nothing
+        pX = allocate_on(M, T)
+    else
+        pX = allocate_on(M, TangentSpaceType(), T)
+    end
+    rand!(M, pX; vector_at=vector_at, kwargs...)
+    return pX
+end
+function Random.rand(rng::AbstractRNG, M::AbstractManifold, T; vector_at=nothing, kwargs...)
+    if vector_at === nothing
+        pX = allocate_on(M, T)
+    else
+        pX = allocate_on(M, TangentSpaceType(), T)
+    end
+    rand!(rng, M, pX; vector_at=vector_at, kwargs...)
+    return pX
 end
 
 @doc "$(_doc_rand)"
@@ -997,6 +1020,12 @@ end
 
 #
 # Allocation hints - mainly pass-through, especially for power manifolds
+
+ManifoldsBase.allocate_on(G::LieGroup, T::Type) = ManifoldsBase.allocate_on(G.manifold, T)
+function ManifoldsBase.allocate_on(M::LieGroup, T::Type{<:AbstractArray})
+    return ManifoldsBase.allocate_on(M.manifold, T)
+end
+
 function ManifoldsBase.allocate_result(
     G::LieGroup,
     f::Union{typeof(compose),typeof(inv),typeof(conjugate),typeof(exp)},
@@ -1032,7 +1061,7 @@ macro default_lie_group_fallbacks(TG, TP, TV, pfield::Symbol, vfield::Symbol)
             return LieGroups.adjoint(M, g.$pfield, X.$vfield)
         end
 
-        function LieGroups.adjoint!(M::$TM, Y::$TV, g::$TP, X::$TV)
+        function LieGroups.adjoint!(M::$TG, Y::$TV, g::$TP, X::$TV)
             LieGroups.adjoint!(M, Y.$vfield, g.$pfield, X.$vfield)
             return Y
         end