CompositeAlgorithm and switching compatibility

[ChrisRackauckas]

This library is almost compatible with the CompositeAlgorithm. The issue is just the return. The solution of the integrator.integrator is appropriately the CompositeSolution, but the integrator's solution is just an ODESolution. The former is required because it has the alg_choice field which makes the interpolant match the chosen algorithm.

[devmotion]

I updated the type of the returned solution and added some tests in https://github.com/JuliaDiffEq/DelayDiffEq.jl/tree/composite. However, something seems to be incorrect/broken as the following example of the first Robertson problem in #67 shows:

sol = solve(prob_dde_rober1, MethodOfSteps(AutoTsit5(Rosenbrock23())); initial_order = 1)

all(sol.alg_choice .== 1)

plot(sol)

[ChrisRackauckas]

If you check the solution, at the end the current algorithm should be 2, but all(sol.alg_choice .== 1) is true, so the interpolant is broken since it's using the wrong interpolation.

[ChrisRackauckas]

integrator_utils.jl on line 88 has:

      if typeof(integrator.alg) <: OrdinaryDiffEqCompositeAlgorithm
        copyat_or_push!(integrator.sol.alg_choice,integrator.saveiter,integrator.cache.current)
      end

I don't think we update cache.current in the other cache.

[ChrisRackauckas]

[ChrisRackauckas]

I merged master into your branch and fixed the current in the cache and now it's interpolating properly.

[ChrisRackauckas]

@YingboMa letting you know this is working

[ChrisRackauckas]

Is the branch missing anything or is it ready to merge? LGTM?

[devmotion]

No, I guess it's complete and ready to merge. Thanks for the fix!

[ChrisRackauckas]

Thank you too. Good team effort 👍