Include alpha for determining scalartype of linear combination

Author: lkdvos

src/indexnotation/instantiators.jl

@@ -167,9 +167,9 @@ function instantiate_linearcombination(
     )
     out = Expr(:block)
     if alloc ∈ (NewTensor, TemporaryTensor)
-        if scaltype === nothing
-            scaltype = instantiate_scalartype(ex)
-        end
+        scaltype = @something(
+            scaltype, instantiate_scalartype(α === One() ? ex : Expr(:call, :*, α, ex))
+        )
         push!(
             out.args,
             instantiate(dst, β, ex.args[2], α, leftind, rightind, alloc, scaltype)

test/tensor.jl

@@ -581,4 +581,15 @@ end
         @test isblascontractable(pA, p)
         @test isblascontractable(conj(pA), p)
     end
+
+    @testset "Issue 220" begin
+        A = rand(2, 2)
+        B = rand(2, 2)
+        C = rand(2, 2)
+        D = rand(2, 2)
+        c = 1im
+        @tensor E[a; c] := c * (A[a b] * B[b c] + C[a b] * D[b c])
+        @test scalartype(E) == ComplexF64
+        @test E ≈ c * (A * B + C * D)
+    end
 end