We consider the complex plane (in a sense of expressing a complex number
Linearity:
Product rule：
Chain rule:
a = ComplexField(2+3im)
b = ComplexField(4+im)
c = ComplexField(1+2im)
println(a*b)
println(a*b')
f(x) = real(x)
gnu = numerical_Wiltingerderivative(f,a)
println("Numerical grad: ", gnu)
g = gradient(f,a)[1]
println("Autograd: ", g)
@test abs(gnu-g.z) < 1e-4
f2(x) = real(x*x'+x+x'+x*x*x')
gnu = numerical_Wiltingerderivative(f2,a)
println("Numerical grad: ", gnu)
g = gradient(f2,a)[1]
println("Autograd: ", g)
@test abs(gnu-g.z) < 1e-4