fill! for array power manifold

src/PowerManifold.jl

@@ -549,12 +549,19 @@ end
 Fill a point `P` on the [`AbstractPowerManifold`](@ref) `M`, setting every entry to `p`.
 
 !!! note
-    while usually the manifold is a first argument in all functions in `ManifoldsBase.jl`,
+    while usually the manifold is the first argument in all functions in `ManifoldsBase.jl`,
     we follow the signature of `fill!`, where the power manifold serves are the size information.
 """
+function fill!(P, p, M::PowerManifoldNestedReplacing)
+    for i in get_iterator(M)
+        P[i...] = p # can we do something that this is closer to fill/fill! and set the ref to p?
+    end
+    return P
+end
 function fill!(P, p, M::AbstractPowerManifold)
+    rep_size = representation_size(M.manifold)
     for i in get_iterator(M)
-        P[M, i] = p # can we do something that this is closer to fill/fill! and set the ref to p?
+        copyto!(M.manifold, _write(M, rep_size, P, i), p)
     end
     return P
 end

test/power.jl

@@ -1,7 +1,12 @@
 using Test
 using ManifoldsBase
 using ManifoldsBase:
-    AbstractNumbers, ℝ, ℂ, NestedReplacingPowerRepresentation, VectorSpaceType
+    AbstractNumbers,
+    DefaultManifold,
+    ℝ,
+    ℂ,
+    NestedReplacingPowerRepresentation,
+    VectorSpaceType
 using StaticArrays
 using LinearAlgebra
 using Random
@@ -24,6 +29,23 @@ end
 
 struct TestArrayRepresentation <: AbstractPowerRepresentation end
 
+const TestPowerManifoldMultidimensional =
+    AbstractPowerManifold{𝔽,<:AbstractManifold{𝔽},TestArrayRepresentation} where {𝔽}
+
+function ManifoldsBase.representation_size(M::TestPowerManifoldMultidimensional)
+    return (representation_size(M.manifold)..., ManifoldsBase.get_parameter(M.size)...)
+end
+
+@inline function ManifoldsBase._write(
+    ::TestPowerManifoldMultidimensional,
+    rep_size::Tuple,
+    x::AbstractArray,
+    i::Tuple,
+)
+    return view(x, ManifoldsBase.rep_size_to_colons(rep_size)..., i...)
+end
+
+
 @testset "Power Manifold" begin
 
     @testset "Power Manifold with a test representation" begin
@@ -400,5 +422,14 @@ struct TestArrayRepresentation <: AbstractPowerRepresentation end
         fill!(P2, p, N)
         @test P2[N, 1] == p
         @test P2[N, 2] == p
+
+        NAR = PowerManifold(M, TestArrayRepresentation(), 2)
+        P1 = fill(p, NAR)
+        @test P1 isa Matrix{Float64}
+        @test P1 == [1.0 1.0; 2.0 2.0; 3.0 3.0]
+
+        P2 = similar(P1)
+        fill!(P2, p, NAR)
+        @test P2 == [1.0 1.0; 2.0 2.0; 3.0 3.0]
     end
 end