add 🐬 functionality

src/spaces/homspace.jl

@@ -147,6 +147,22 @@ function select(W::HomSpace{S}, (p₁, p₂)::Index2Tuple{N₁,N₂}) where {S,N
     return cod ← dom
 end
 
+"""
+    flip(W::HomSpace, I)
+
+Return a new `HomSpace` object by applying `flip` to each of the spaces in the domain and
+codomain of `W` for which the linear index `i` satisfies `i ∈ I`.
+"""
+function flip(W::HomSpace{S}, I) where {S}
+    cod′ = let cod = codomain(W)
+        ProductSpace{S}(ntuple(i -> i ∈ I ? flip(cod[i]) : cod[i], numout(W)))
+    end
+    dom′ = let dom = domain(W)
+        ProductSpace{S}(ntuple(i -> (i + numout(W)) ∈ I ? flip(dom[i]) : dom[i], numin(W)))
+    end
+    return cod′ ← dom′
+end
+
 """
     compose(W::HomSpace, V::HomSpace)
 

src/tensors/indexmanipulations.jl

@@ -1,5 +1,21 @@
 # Index manipulations
 #---------------------
+"""
+    flip(t::AbstractTensorMap, I) -> t′::AbstractTensorMap
+
+Return a new tensor that is isomorphic to `t` but where the arrows on the indices `i` that satisfy
+`i ∈ I` are flipped, i.e. `space(t′, i) = flip(space(t, i))`.
+"""
+function flip(t::AbstractTensorMap, I)
+    P = flip(space(t), I)
+    t2 = similar(t, P)
+    for (c, b) in blocks(t)
+        copy!(t2[c], b)
+    end
+    return t
+end
+flip(t::TensorMap, I) = TensorMap(t.data, flip(space(t), I))
+
 """
     permute!(tdst::AbstractTensorMap, tsrc::AbstractTensorMap, (p₁, p₂)::Index2Tuple)
         -> tdst

test/tensors.jl

@@ -326,6 +326,23 @@ for V in spacelist
                 @test HrA12array ≈ convert(Array, HrA12)
             end
         end
+        if BraidingStyle(I) isa Bosonic # TODO: add fermionic tests by including parity tensors
+            @timedtestset "Index flipping: test via contraction" begin
+                t1 = rand(ComplexF64, V1 ⊗ V2 ⊗ V3 ← V4)
+                t2 = rand(ComplexF64, V2' ⊗ V5 ← V4' ⊗ V1)
+                @tensor ta[a, b] := t1[x, y, a, z] * t2[y, b, z, x]
+                @tensor tb[a, b] := flip(t1, 1)[x, y, a, z] * flip(t2, 4)[y, b, z, x]
+                @test ta ≈ tb
+                @tensor tb[a, b] := flip(t1, (2, 4))[x, y, a, z] *
+                                    flip(t2, (1, 3))[y, b, z, x]
+                @test ta ≈ tb
+                @tensor tb[a, b] := flip(t1, (1, 2, 4))[x, y, a, z] *
+                                    flip(t2, (1, 3, 4))[y, b, z, x]
+                @tensor tb[a, b] := flip(t1, (1, 3))[x, y, a, z] *
+                                    flip(t2, (2, 4))[y, b, z, x]
+                @test flip(ta, (1, 2)) ≈ tb
+            end
+        end
         @timedtestset "Multiplication of isometries: test properties" begin
             W2 = V4 ⊗ V5
             W1 = W2 ⊗ (oneunit(V1) ⊕ oneunit(V1))