Fix complex matrix multiplication (#133)

* Added methods to currectly dispatch complex mul

* Added methods to dispatch correctly cpx matrix mul

Author: orkolorko

src/multiplication.jl

@@ -38,6 +38,29 @@ function set_multiplication_mode(multype)
     config[:multiplication] = multype
 end
 
+function *(A::AbstractMatrix{Complex{Interval{T}}}, B::AbstractMatrix) where T
+    return real(A)*B+im*imag(A)*B
+end
+
+function *(A::AbstractMatrix, B::AbstractMatrix{Complex{Interval{T}}}) where T
+    return A*real(B)+im*A*imag(B)
+end
+
+function *(A::AbstractMatrix{Complex{Interval{T}}}, B::AbstractMatrix{Complex{Interval{T}}}) where T
+    rA, iA = real(A), imag(A)
+    rB, iB = real(B), imag(B)
+    return rA*rB-iA*iB+im*(iA*rB+rA*iB)
+end
+
+function *(A::AbstractMatrix{Complex{T}}, B::AbstractMatrix{Interval{T}}) where {T}
+    return real(A)*B+im*imag(A)*B
+end
+
+function *(A::AbstractMatrix{Interval{T}}, B::AbstractMatrix{Complex{T}}) where {T}
+    return A*real(B)+im*A*imag(B)
+end
+
+
 function *(::MultiplicationType{:slow}, A, B)
     TS = promote_type(eltype(A), eltype(B))
     return mul!(similar(B, TS, (size(A,1), size(B,2))), A, B)

test/test_multiplication.jl

@@ -4,14 +4,22 @@
     @test get_multiplication_mode() == Dict(:multiplication => :fast)
 
     A = [2..4 -2..1; -1..2 2..4]
+    imA = im*A 
+    
     set_multiplication_mode(:slow)
     @test A * A == [0..18 -16..8; -8..16 0..18]
+    @test imA * imA == -1*[0..18 -16..8; -8..16 0..18]
 
     set_multiplication_mode(:rank1)
     @test A * A == [0..18 -16..8; -8..16 0..18]
+    @test imA * imA == -1*[0..18 -16..8; -8..16 0..18]
 
     set_multiplication_mode(:fast)
     @test A * A == [-2..19.5 -16..10; -10..16 -2..19.5]
     @test A * mid.(A) == [5..12.5 -8..2; -2..8 5..12.5]
     @test mid.(A) * A == [5..12.5 -8..2; -2..8 5..12.5]
+    
+    @test imA * imA == -1*[-2..19.5 -16..10; -10..16 -2..19.5]
+    @test mid.(A) * imA == im*[5..12.5 -8..2; -2..8 5..12.5]
+    @test imA * mid.(A) == im*[5..12.5 -8..2; -2..8 5..12.5]
 end