Support complex output in derivative (#583)

Author: antoine-levitt

src/derivative.jl

@@ -70,6 +70,7 @@ Set `check` to `Val{false}()` to disable tag checking. This can lead to perturba
 end
 
 derivative(f, x::AbstractArray) = throw(DimensionMismatch("derivative(f, x) expects that x is a real number. Perhaps you meant gradient(f, x)?"))
+derivative(f, x::Complex) = throw(DimensionMismatch("derivative(f, x) expects that x is a real number (does not support Wirtinger derivatives). Separate real and imaginary parts of the input."))
 
 #####################
 # result extraction #
@@ -78,9 +79,13 @@ derivative(f, x::AbstractArray) = throw(DimensionMismatch("derivative(f, x) expe
 # non-mutating #
 #--------------#
 
-@inline extract_derivative(::Type{T}, y::Dual) where {T}          = partials(T, y, 1)
 @inline extract_derivative(::Type{T}, y::Real) where {T}          = zero(y)
+@inline extract_derivative(::Type{T}, y::Complex) where {T}       = zero(y)
+@inline extract_derivative(::Type{T}, y::Dual) where {T}          = partials(T, y, 1)
 @inline extract_derivative(::Type{T}, y::AbstractArray) where {T} = map(d -> extract_derivative(T,d), y)
+@inline function extract_derivative(::Type{T}, y::Complex{TD}) where {T, TD <: Dual}
+    complex(partials(T, real(y), 1), partials(T, imag(y), 1))
+end
 
 # mutating #
 #----------#

test/DerivativeTest.jl

@@ -100,4 +100,8 @@ end
     @test_throws DimensionMismatch ForwardDiff.derivative(sum, fill(2pi, 3))
 end
 
+@testset "complex output" begin
+    @test ForwardDiff.derivative(x -> (1+im)*x, 0) == (1+im)
+end
+
 end # module