Fix recursive_mean to work without Statistics dependency

The move of Statistics.jl to a weak dependency caused recursive_mean to fail
because it used Statistics.mean internally. This fix:

- Removes the generic fallback `recursive_mean(x...) = mean(x...)` from utils.jl
- Adds explicit implementations for scalars and arrays of numbers that compute
  the mean without requiring Statistics
- Rewrites recursive_mean(A::ArrayPartition) to avoid using Statistics.mean

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

Author: ChrisRackauckas

src/array_partition.jl

@@ -291,7 +291,17 @@ function recursivecopy!(A::ArrayPartition, B::ArrayPartition)
 end
 recursivecopy(A::ArrayPartition) = ArrayPartition(copy.(A.x))
 
-recursive_mean(A::ArrayPartition) = mean((recursive_mean(x) for x in A.x))
+function recursive_mean(A::ArrayPartition)
+    n = npartitions(A)
+    if n == 0
+        return zero(eltype(A))
+    end
+    total = recursive_mean(A.x[1])
+    for i in 2:n
+        total += recursive_mean(A.x[i])
+    end
+    return total / n
+end
 
 # note: consider only first partition for recursive one and eltype
 recursive_one(A::ArrayPartition) = recursive_one(first(A.x))

src/utils.jl

@@ -291,7 +291,6 @@ end
 recursive_unitless_eltype(a::Type{T}) where {T <: Number} = typeof(one(eltype(a)))
 recursive_unitless_eltype(::Type{<:Enum{T}}) where {T} = T
 
-recursive_mean(x...) = mean(x...)
 function recursive_mean(vecvec::Vector{T}) where {T <: AbstractArray}
     out = zero(vecvec[1])
     for i in eachindex(vecvec)
@@ -300,6 +299,15 @@ function recursive_mean(vecvec::Vector{T}) where {T <: AbstractArray}
     out / length(vecvec)
 end
 
+# Fallback for scalars and general cases without Statistics
+function recursive_mean(x::AbstractArray{T}) where {T <: Number}
+    sum(x) / length(x)
+end
+
+function recursive_mean(x::Number)
+    x
+end
+
 # From Iterators.jl. Moved here since Iterators.jl is not precompile safe anymore.
 
 # Concatenate the output of n iterators