Add rrule ⊗

fixes #88

ext/TensorKitChainRulesCoreExt.jl

@@ -99,6 +99,36 @@ function ChainRulesCore.rrule(::typeof(*), a::Number, b::AbstractTensorMap)
     return a * b, times_pullback
 end
 
+function ChainRulesCore.rrule(::typeof(⊗), A::AbstractTensorMap, B::AbstractTensorMap)
+    C = A ⊗ B
+    projectA = ProjectTo(A)
+    projectB = ProjectTo(B)
+    function otimes_pullback(ΔC_)
+        ΔC = unthunk(ΔC_)
+        pΔC = ((codomainind(A)..., (domainind(A) .+ numout(B))...),
+               ((codomainind(B) .+ numout(A))...,
+                (domainind(B) .+ (numin(A) + numout(A)))...))
+        dA_ = @thunk begin
+            ipA = (codomainind(A), domainind(A))
+            pB = (allind(B), ())
+            dA = zerovector(A,
+                            TensorOperations.promote_contract(scalartype(ΔC),
+                                                              scalartype(B)))
+            dA = tensorcontract!(dA, ipA, ΔC, pΔC, :N, B, pB, :C)
+            return projectA(dA)
+        end
+        dB_ = @thunk begin
+            ipB = (codomainind(B), domainind(B))
+            pA = ((), allind(A))
+            dB = zerovector(B, TensorOperations.promote_contract(scalartype(ΔC), scalartype(A)))
+            dB = tensorcontract!(dB, ipB, A, pA, :C, ΔC, pΔC, :N)
+            return projectB(dB)
+        end
+        return NoTangent(), dA_, dB_
+    end
+    return C, otimes_pullback
+end
+
 function ChainRulesCore.rrule(::typeof(permute), tsrc::AbstractTensorMap, p::Index2Tuple;
                               copy::Bool=false)
     function permute_pullback(Δtdst)

test/ad.jl

@@ -127,6 +127,10 @@ Vlist = ((ℂ^2, (ℂ^3)', ℂ^3, ℂ^2, (ℂ^2)'),
         test_rrule(*, A, C)
 
         test_rrule(permute, A, ((1, 3, 2), (5, 4)))
+
+        D = TensorMap(randn, T, V[1] ⊗ V[2] ← V[3])
+        E = TensorMap(randn, T, V[4] ← V[5])
+        test_rrule(⊗, D, E)
     end
 
     @testset "Linear Algebra part II with scalartype $T" for T in (Float64, ComplexF64)