RFC: INITIALIZE_DEFAULT / FINALIZE_DEFAULT => initialize! / finalize!

[simonbyrne]

Not sure what you think about this, but we want to be able to define callbacks that have predefined initializer/finalizers, e.g.

struct Diagnostics
  # some stuff
end
DiffEqBase.initialize!(d::Diagnostics, u, t, integrator) = # set up stuff
DiffEqBase.finalize!(d::Diagnostics, u, t, integrator) = # finalize stuff

DiscreteCallback(mycond, Diagnostics(details)) # don't need to pass explicit initializer / finalizer functions

We could do this now by defining additional methods for INITIALIZE_DEFAULT / FINALIZE_DEFAULT, but this seems a bit clearer.

If you're on board, I can add some docs.

[simonbyrne]

Okay, I realise this won't quite work as it is passed the DiscreteCallback, not the affect! argument.

I'll need to think a bit more about this.

[simonbyrne]

What I had in mind was something like this:
https://github.com/CliMA/TimeMachine.jl/pull/13/files#diff-f85085614ae2b81b449d2b6235530313731991388cf8d97b3614882bc8b036fd

[ChrisRackauckas]

Yeah I see what you're getting at. Usually for this kind of thing I'd make a callable type will all of the function dispatches and pass that type in all spots, but the init and finalize functions would clash so that's a little tricky.