wrote Equal_sum_subsets iterator

src/pairwise.jl

@@ -17,7 +17,7 @@ function _pairwise!(::Val{:none}, f, dest::AbstractMatrix{V}, x, y,
     #cov(x) is faster than cov(x, x)
     (f == cov) && (f = ((x, y) -> x === y ? cov(x) : cov(x, y)))
 
-    Threads.@threads for subset in equal_sum_subsets(nc, Threads.nthreads())
+    Threads.@threads for subset in Equal_sum_subsets(nc, Threads.nthreads())
         for j in subset
             for i = (symmetric ? j : 1):nr
                 # For performance, diagonal is special-cased
@@ -96,7 +96,7 @@ function _pairwise!(::Val{:pairwise}, f, dest::AbstractMatrix{V}, x, y, symmetri
     nmtx = promoted_nmtype(x)[]
     nmty = promoted_nmtype(y)[]
 
-    Threads.@threads for subset in equal_sum_subsets(nc, Threads.nthreads())
+    Threads.@threads for subset in Equal_sum_subsets(nc, Threads.nthreads())
         scratch_fx = task_local_vector(:scratch_fx, nmtx, m)
         scratch_fy = task_local_vector(:scratch_fy, nmty, m)
         for j in subset
@@ -393,6 +393,8 @@ function handle_pairwise(x::AbstractVector, y::AbstractVector;
     return view(scratch_fx, lb:(j-1)), view(scratch_fy, lb:(j-1))
 end
 
+#TODO remove tsts for equal_sum_subsets, add tests for Equal_sum_subsets, rename to Equal_sum_vectors?
+
 #=Condition a) makes equal_sum_subsets useful for load-balancing the multi-threaded section
 of _pairwise! in the non-symmetric case, and condition b) for the symmetric case.=#
 """
@@ -440,4 +442,66 @@ function task_local_vector(key::Symbol, similarto::AbstractArray{V},
     length::Int)::Vector{V} where {V}
     haskey(task_local_storage(), key) || task_local_storage(key, similar(similarto, length))
     return task_local_storage(key)
+end
+
+#Alternative approach - use an iterator.
+
+"""
+    Equal_sum_subsets
+
+An iterator enabling the partition of the integers 1 to n into `num_subsets` vectors such
+that a) each subset has (approximately) the same number of elements; and b) the sum of the
+elements in each subset is nearly equal. If `n` is a multiple of `2 * num_subsets` both
+conditions hold exactly.
+
+## Example
+```julia-repl
+julia> for s in KendallTau.Equal_sum_subsets(30,5)
+println((s, sum(s)))
+end
+([30, 21, 20, 11, 10, 1], 93)
+([29, 22, 19, 12, 9, 2], 93)
+([28, 23, 18, 13, 8, 3], 93)
+([27, 24, 17, 14, 7, 4], 93)
+([26, 25, 16, 15, 6, 5], 93)
+```
+"""
+struct Equal_sum_subsets
+    n::Int64
+    num_subsets::Int64
+end
+
+Base.length(x::Equal_sum_subsets) = min(x.n, x.num_subsets)
+
+Base.firstindex(x::Equal_sum_subsets) = 1
+
+function Base.iterate(ess::Equal_sum_subsets, state::Int64=1)
+    state > length(ess) && return (nothing)
+    return (getindex(ess, state), state + 1)
+end
+
+function demo(n, num_subsets)
+    for s in Equal_sum_subsets(n, num_subsets)
+        println(s, sum(s))
+    end
+end
+
+function Base.getindex(ess::Equal_sum_subsets, i::Int64=1)
+    i > length(ess) && return (nothing)
+    n, nss = ess.n, ess.num_subsets
+    s = 2i - 1
+    b = 2nss - s
+    result = zeros(Int64, div(n, nss) + ((i <= rem(n, nss)) ? 1 : 0))
+    result[1] = n - i + 1
+    k = 1
+    while true
+        x = result[k] - (mod(k, 2) == 0 ? s : b)
+        if x > 0
+            k += 1
+            result[k] = x
+        else
+            break
+        end
+    end
+    return result
 end

src/rankcorr.jl

@@ -112,7 +112,7 @@ function _pairwise!(::Val{:pairwise}, f::typeof(corspearman),
     fl64 = Float64[]
     nmtx = promoted_nmtype(x)[]
     nmty = promoted_nmtype(y)[]
-    Threads.@threads for subset in equal_sum_subsets(nr, Threads.nthreads())
+    Threads.@threads for subset in Equal_sum_subsets(nr, Threads.nthreads())
 
         for i in subset
 
@@ -482,7 +482,7 @@ function corkendall_loop!(skipmissing::Symbol, f::typeof(corkendall), dest::Abst
 
     symmetric = x === y
 
-    Threads.@threads for subset in equal_sum_subsets(nr, Threads.nthreads())
+    Threads.@threads for subset in Equal_sum_subsets(nr, Threads.nthreads())
 
         for i in subset