Restrict to real/complex

Author: jishnub

src/symmetric.jl

@@ -225,6 +225,7 @@ const RealHermSymComplexHerm{T<:Real,S} = Union{Hermitian{T,S}, Symmetric{T,S},
 const RealHermSymComplexSym{T<:Real,S} = Union{Hermitian{T,S}, Symmetric{T,S}, Symmetric{Complex{T},S}}
 const RealHermSymSymTriComplexHerm{T<:Real} = Union{RealHermSymComplexSym{T}, SymTridiagonal{T}}
 const SelfAdjoint = Union{SymTridiagonal{<:Real}, Symmetric{<:Real}, Hermitian}
+const SelfAdjointRealOrComplex = Union{SymTridiagonal{<:Real}, Symmetric{<:Real}, Hermitian{<:Union{Real,Complex}}}
 
 wrappertype(::Union{Symmetric, SymTridiagonal}) = Symmetric
 wrappertype(::Hermitian) = Hermitian
@@ -722,20 +723,20 @@ end
 
 mul(A::HermOrSym, B::HermOrSym) = A * copyto!(similar(parent(B)), B)
 
-# Multiplication of Hermitian and adjoint with an Adjoint destination
+# Multiplication of Hermitian and Adjoint with an Adjoint destination
 # may conjugate the terms to delegate the multiplication to the parents of the adjoints
-for (AdjTransT, SymHermT) in ((:AdjointAbsMat, :SelfAdjoint), (:(TransposeAbsMat{<:Union{Real,Complex}}), :RealHermSymComplexSym))
+# Only defined for commutative numbers
+for (AdjTransT, SymHermT) in (
+        (:(Adjoint{<:Union{Real,Complex}}), :SelfAdjointRealOrComplex),
+        (:(Transpose{<:Union{Real,Complex}}), :RealHermSymComplexSym))
+
     @eval begin
-        function mul!(C::$AdjTransT, A::$SymHermT, B::$AdjTransT, α::Number, β::Number)
-            _rmul_or_fill!(C, β)
-            isone(α) || rmul!(B, α)
-            mul!(wrapperop(C)(C), wrapperop(B)(B), A)
+        function mul!(C::$AdjTransT, A::$SymHermT, B::$AdjTransT, α::Union{Real,Complex}, β::Union{Real,Complex})
+            mul!(wrapperop(C)(C), wrapperop(B)(B), A, α, β)
             return C
         end
-        function mul!(C::$AdjTransT, A::$AdjTransT, B::$SymHermT, α::Number, β::Number)
-            _rmul_or_fill!(C, β)
-            isone(α) || rmul!(B, α)
-            mul!(wrapperop(C)(C), B, wrapperop(A)(A))
+        function mul!(C::$AdjTransT, A::$AdjTransT, B::$SymHermT, α::Union{Real,Complex}, β::Union{Real,Complex})
+            mul!(wrapperop(C)(C), B, wrapperop(A)(A), α, β)
             return C
         end
     end

test/symmetric.jl

@@ -888,6 +888,17 @@ end
         @test Bm * A ≈ Bm * Matrix(A)
         @test transpose(Bm) * A ≈ transpose(Bm) * Matrix(A)
         @test adjoint(Bm) * A ≈ adjoint(Bm) * Matrix(A)
+        C = similar(Bm, promote_type(T, S))
+        @test mul!(C, A, Bm) ≈ A * Bm
+        @test mul!(adjoint(C), A, adjoint(Bm)) ≈ A * adjoint(Bm)
+        @test mul!(transpose(C), A, transpose(Bm)) ≈ A * transpose(Bm)
+        rand!(C)
+        @test mul!(copy(C), A, Bm, 2, 3) ≈ A * Bm * 2 + C * 3
+        @test mul!(copy(C), Bm, A, 2, 3) ≈ Bm * A * 2 + C * 3
+        @test mul!(adjoint(copy(C)), A, adjoint(Bm), 2, 3) ≈ A * adjoint(Bm) * 2 + adjoint(C) * 3
+        @test mul!(adjoint(copy(C)), adjoint(Bm), A, 2, 3) ≈ adjoint(Bm) * A * 2 + adjoint(C) * 3
+        @test mul!(transpose(copy(C)), A, transpose(Bm), 2, 3) ≈ A * transpose(Bm) * 2 + transpose(C) * 3
+        @test mul!(transpose(copy(C)), transpose(Bm), A, 2, 3) ≈ transpose(Bm) * A * 2 + transpose(C) * 3
     end
     let A = adjoint(Hermitian(rand(S, n,n))), Bv = Vector(rand(T, n)), Bm = Matrix(rand(T, n,n))
         @test A * Bv ≈ Matrix(A) * Bv
@@ -897,6 +908,17 @@ end
         @test Bm * A ≈ Bm * Matrix(A)
         @test transpose(Bm) * A ≈ transpose(Bm) * Matrix(A)
         @test adjoint(Bm) * A ≈ adjoint(Bm) * Matrix(A)
+        C = similar(Bm, promote_type(T, S))
+        @test mul!(C, A, Bm) ≈ A * Bm
+        @test mul!(adjoint(C), A, adjoint(Bm)) ≈ A * adjoint(Bm)
+        @test mul!(transpose(C), A, transpose(Bm)) ≈ A * transpose(Bm)
+        rand!(C)
+        @test mul!(copy(C), A, Bm, 2, 3) ≈ A * Bm * 2 + C * 3
+        @test mul!(copy(C), Bm, A, 2, 3) ≈ Bm * A * 2 + C * 3
+        @test mul!(adjoint(copy(C)), A, adjoint(Bm), 2, 3) ≈ A * adjoint(Bm) * 2 + adjoint(C) * 3
+        @test mul!(adjoint(copy(C)), adjoint(Bm), A, 2, 3) ≈ adjoint(Bm) * A * 2 + adjoint(C) * 3
+        @test mul!(transpose(copy(C)), A, transpose(Bm), 2, 3) ≈ A * transpose(Bm) * 2 + transpose(C) * 3
+        @test mul!(transpose(copy(C)), transpose(Bm), A, 2, 3) ≈ transpose(Bm) * A * 2 + transpose(C) * 3
     end
     let Ahrs = transpose(Hermitian(Symmetric(rand(T, n, n)))),
         Acs = transpose(Symmetric(rand(S, n, n))),