ManifoldProjection and complex numbers

[paolo-mgi]

Question❓
Please bear with me I am not an experienced programmer and I might be doing something silly.

I am trying to integrate
p = 200.0
function psi(du,u,p,t)
du[1] = -im * p * u[1]
du[2] = -im * p * u[2]
end

function g(u,resid)
resid[1] = abs(sol.u[1]) - 1
resid[2] = abs(sol.u[2]) - 1
end

cb = ManifoldProjection(g)

sol = solve(prob,callback = cb)
and I get

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

Stacktrace:
[1] throw_cannot_dual(V::Type)
@ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/dual.jl:41
[2] ForwardDiff.Dual{ForwardDiff.Tag{DiffEqCallbacks.NonAutonomousFunction{typeof(g), false}, ComplexF64}, ComplexF64, 2}(value::ComplexF64, partials::ForwardDiff.Partials{2, ComplexF64})

After many web-searches it seems to me that this is an old problem since 2018. My question is motivated by the stochastic Schroedinger equation where one needs an efficient integrator capable of preserving the norm of a complex vector for ensemble simulations.
Many thanks!

[ChrisRackauckas]

This is a limitation of ForwardDiff. I think if you switch it to a differentiation method in the nonlinear solve that is not ForwardDiff it should work fine. Let me know if you have any troubles with that.