Allow subsetting tunables after system creation

[AayushSabharwal]

Add a function change_tunables(sys, new_tunables) which takes a completed split = true system and makes new_tunables the tunables and moves the old tunables to constants. Useful for optimizing only specified parameters.

[DhairyaLGandhi]

This seems underspecified. What is this new_tunables object supposed to be? Is it a vector which is the size as expected by sys and do we trust its ordering? Is it labelled as in Pair/ NamedTuple? How is the subsetting intended to be used? Can it be a simple swap like:

function change_tunables(sys, new_tunables)
    p = MTK.get_p(sys, [])
    tunables, repack, _ = SS.canonicalize(SS.Tunable(), p)
    new_p_ = repack(new_tunables)
    new_p = SS.replace(SS.Constants(), new_p_, tunables)
    # update the default values in the sys somehow; equivalent to remake(sys, p = ...)
end

[ChrisRackauckas]

@SebastianM-C can you describe a bit more what's most helpful? It could either be new_tunables is just a vector of parameters that's the new tunables, or it's a Vector{Pair{BasicSymbolic,Bool}} which says x => true, y=>false for which ones to change.

[SebastianM-C]

I think the first variant is better, just specify the new tunables.

[AayushSabharwal]

MTK determines what variables are in which partition using the index_cache::IndexCache field in System. The tunables are determined using the tunable_idx field of IndexCache, which maps tunable parameters to their index in the tunables vector.

new_tunables should be a vector of parameters that is a subset of tunable_parameters(sys, parameters(sys)) (not satisfying this is an error). Entries corresponding to these parameters should stay in tunable_idx, and the rest of the parameters should be added to constant_idx. Some edge cases off the top of my head:

1. Array parameters are either entirely tunable or entirely non-tunable. new_tunables can only contain un-scalarized array parameters. Occurrence of scalarized parameters is an error.
2. Each mapping (tunable_idx/constant_idx, etc.) contains multiple versions of each parameter. For any parameter p, we have entries for p, default_toterm(p), renamespace(sys, p), renamespace(sys, default_toterm(p)). All 4 of these need to be removed from tunable_idx for each p not in new_tunables, and all 4 should be added to constant_idx. Refer to this snippet.

It might be helpful to pull out snippets of the IndexCache constructor into utility functions. It is messy, so let me know if you need me to hop on a call and help figure things out. While not relevant here, the discrete parameters piece took me a while to come up with and is annoyingly convoluted.