complex number support

[GiggleLiu]

Related Issues

#157
#324
#364

This is a quick fix for some complex valued functions. Any thoughts?

NOTE: I copied some functions from Base, because they fixed the type to foating point numbers.

[YingboMa]

I am not sure if it makes sense to define these methods in ForwardDiff.jl, since they should all be generic callbacks that are independent of Dual, right?

[GiggleLiu]

@YingboMa
Although we get only 3 votes in #456 , but I need to differentiate complex number in one of my recent projects.
Do you think we should take the chance to polish and get this PR merged?

[ChrisRackauckas]

Is this not all covered by JuliaLang/julia#36030 ?

[ChrisRackauckas]

Looking at the two PRs, it seems like @YingboMa upstreamed it all to Base where it should go (correct me if I'm wrong and anything was left out). So complex AD is thus fixed on v1.6. However, the tests are still definitely useful from here. So I'd suggest the following:

• Move these overloads to an internal module. Document in the README using ForwardDiff.Complex for v1.4 as a compatibility workaround.
• Use this to in the tests

and everything is good to go. The other alternative would be to move these behind an @static if definition, but I would be weary of having such central dispatches modified by such a core package outside of the system image. If you want invalidations, this is how you get invalidations.

[ChrisRackauckas]

Handled by JuliaLang/julia#36030

[GiggleLiu]

Thanks! @ChrisRackauckas

[DEKOHG]

Hello,
I just installed the newest version of DifferentialEquations.jl . However, I still got an error with stiff solvers (eg. Rodas4P) for complex numbers calculation. I have tried on both julia 1.8.2 and julia 1.7.2 and my DifferentialEquations is v7.6.0

ERROR: ArgumentError: Cannot create a dual over scalar type ComplexF64. If the type behaves as a scalar, define ForwardDiff.can_dual(::Type{ComplexF64}) = true.

[petar-andrejic]

Handled by JuliaLang/julia#36030

Not entirely handled, complex valued functions of multiple real arguments don't work, e.g.

julia> ForwardDiff.gradient(x->exp(im * (x[1] + x[2])), [1.0,2.0])

ERROR: DimensionMismatch: gradient(f, x) expects that f(x) is a real number. Perhaps you meant jacobian(f, x)?

[davidschlegel]

Hello, I just installed the newest version of DifferentialEquations.jl . However, I still got an error with stiff solvers (eg. Rodas4P) for complex numbers calculation. I have tried on both julia 1.8.2 and julia 1.7.2 and my DifferentialEquations is v7.6.0

ERROR: ArgumentError: Cannot create a dual over scalar type ComplexF64. If the type behaves as a scalar, define ForwardDiff.can_dual(::Type{ComplexF64}) = true.

I also still get the same error. Is there a way to manually change the way forward differentiation is handled?

[ChrisRackauckas]

For DiffEq? You just set autodiff=false (Rodas5P(autodiff=false)) or pass a jac function into ODEFunction if you want full control of it.

[davidschlegel]

Sorry, it was not clear from my question. Of course, setting autodiff=false works but is not efficient.
Can I autodiff a complex ODE in DiffEq? Currently it does not work out-of-the-box, but perhaps one can manually pass a Jacobian that is calculated using ForwardDiff...

[ChrisRackauckas]

It uses ForwardDiff by default, and you can pass any Jacobian function you want via jac in the ODEFunction.

[davidschlegel]

Exactly, but right now, this throws an error, when trying to autodiff a complex ODE.

[ChrisRackauckas]

So then I don't get the question?

[davidschlegel]

Right now, afaik, ForwardDiff does not handle automatic differentiation for complex functions out-of-the-box. However, DiffEq relies on ForwardDiff when computing jacobians and more. Is there any solution to still use automatic differentiation (eg using a different package) for DiffEq?

[ChrisRackauckas]

Yes, just use jac in the ODEFunction.