Implement complex for dual arguments (#90)

* Implement complex wrappers

* Test complex implementations

* Increment version number

* Overload complex for types

Project.toml

@@ -1,6 +1,6 @@
 name = "DualNumbers"
 uuid = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"
-version = "0.6.6"
+version = "0.6.7"
 
 [deps]
 Calculus = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"

src/dual.jl

@@ -39,6 +39,13 @@ dual(x::ReComp, y::ReComp) = Dual(x, y)
 dual(x::ReComp) = Dual(x)
 dual(z::Dual) = z
 
+function Base.complex(x::Dual, y::Dual)
+    dual(complex(value(x), value(y)), complex(epsilon(x), epsilon(y)))
+end
+Base.complex(x::Real, y::Dual) = complex(dual(x), y)
+Base.complex(x::Dual, y::Real) = complex(x, dual(y))
+Base.complex(::Type{Dual{T}}) where {T} = Dual{complex(T)}
+
 const realpart = value
 const dualpart = epsilon
 

test/automatic_differentiation_test.jl

@@ -200,6 +200,14 @@ test(x, y) = x^2 + y
 @test epsilon(Dual(-2.0,1.0)^Dual(2.0,0.0)) == -4
 
 
+# test complex and dual mixing
+@test complex(dual(1, 2), dual(3, 4)) == dual(complex(1, 3), complex(2, 4))
+@test complex(1, dual(2, 3)) == dual(complex(1, 2), complex(0, 3))
+@test complex(dual(1, 2), 3) == dual(complex(1, 3), complex(2, 0))
+@test complex(dual(1, 2)) == dual(complex(1, 0), complex(2, 0))
+@test complex(Dual128) === DualComplex256
+@test complex(Dual64) === DualComplex128
+
 # test for flipsign
 flipsign(Dual(1.0,1.0),2.0) == Dual(1.0,1.0)
 flipsign(Dual(1.0,1.0),-2.0) == Dual(-1.0,-1.0)