in reconstruct: average the sum, not sum the averages!

src/reconstruct.jl

@@ -12,9 +12,10 @@ function reconstruct(
     n = __outer_dim(wbdec)
     res = sum(zip(Ms, SymbolicWedderburn.direct_summands(wbdec))) do (M, ds)
         res = similar(M, n, n)
-        res = _reconstruct!(res, M, ds, __group_of(wbdec), wbdec.hom)
+        res = _reconstruct!(res, M, ds)
         return res
     end
+    res = average!(zero(res), res, __group_of(wbdec), wbdec.hom)
     return res
 end
 
@@ -22,16 +23,14 @@ function _reconstruct!(
     res::AbstractMatrix,
     M::AbstractMatrix,
     ds::SymbolicWedderburn.DirectSummand,
-    G,
-    hom,
 )
-    U = SymbolicWedderburn.image_basis(ds)
-    d = SymbolicWedderburn.degree(ds)
-    Θπ = (U' * M * U) .* d
-
     res .= zero(eltype(res))
-    Θπ = average!(res, Θπ, G, hom)
-    return Θπ
+    if !iszero(M)
+        U = SymbolicWedderburn.image_basis(ds)
+        d = SymbolicWedderburn.degree(ds)
+        res = (U' * M * U) .* d
+    end
+    return res
 end
 
 function __droptol!(M::AbstractMatrix, tol)
@@ -52,18 +51,18 @@ function average!(
         <:SymbolicWedderburn.ByPermutations,
     },
 )
+    res .= zero(eltype(res))
     @assert size(M) == size(res)
+    o = Groups.order(Int, G)
     for g in G
         p = SymbolicWedderburn.induce(hom, g)
         Threads.@threads for c in axes(res, 2)
-            # note: p is a permutation,
-            # so accesses below are guaranteed to be disjoint
             for r in axes(res, 1)
-                res[r^p, c^p] += M[r, c]
+                if !iszero(M[r, c])
+                    res[r^p, c^p] += M[r, c] / o
+                end
             end
         end
     end
-    o = Groups.order(Int, G)
-    res ./= o
     return res
 end