Numpy array context rebased

[inducer]

This does a fair bit of stuff. The main components are a numpy array context and an in-depth rework of dataclass arraycontainer broadcasting. There is also a tweak to array container serialization ("Container serialization: iterable -> sequence, plus type aliases") that makes the serialized container a sequence and introduces a type alias for it. I've flagged some things that I'm less sure about in a self-review below.

The whole thing is probably best read commit-by-commit to avoid mixing changes that belong to different topic areas.

Closes #93
Closes #235
Closes #95

TODO

• Are np.minimum, np.maximum missing?

[inducer]

Hi all, please take a look, particularly with an eye towards how much you like the direction this is going. It should not break compatibility right now, but it contains some things that will need changing once we remove what's being deprecated now.

[inducer]

Also, sorry about the breakage from my last-minute changes, I'll fix that right away.

[alexfikl]

Went through the easy parts of this and left a bunch of nitpicks. Will have to look at the arithmetic changes a bit more carefully some other time though.

From the tests, the Bcast syntax seems a bit clunky with all the wrapping. Maybe we can introduce some helper functions?

result = broadcast(operator.op, container1, container2, level_or_actx=1)

? Will ponder a bit 😁

[alexfikl]

Was just googling around and found a jax pytree version of container math:
https://github.com/google/tree-math
It seems to just allow broadcasting scalars at the leaf level, so it's a lot smaller in scope.

[alexfikl]

Following a meeting with @inducer on Friday, he suggested I write down any random thoughts here, so that we can discuss. So here goes before I forget again!

My question was mostly related to what broadcasting we actually need to do? The broadcasting implementation here seems to be very general and very flexible (and quite explicit as well).

Having experience with the pytential part of the stack (as opposed to grudge), these operations seem to be required:

1. Just direct adding of two DOFArrays (no broadcasting here), e.g. x + y.
   • This should just work no questions asked.
2. Broadcast DOFArray with a scalar (of some sort? device or host), e.g. x + 1.
   • Can work with a rec_[multi]map_array_container, but having the overload work is nicer.
3. Broadcast a numpy object array (of scalars or of DOFArray) with a DOFArray, e.g. velocity - mean.
   • This should also work with a [multi]map_array_container, but having the overload work is nicer. Object arrays already broadcast constants, so that will just work.

i.e. all those could be handled (maybe a bit verbosely) without any broadcasting support in arraycontext.with_container_arithmetic. Broadcasting a scalar seems like a common enough case to implement here though.

What fancier broadcasting would we need to support? I guess mirgecom has the most advanced needs here.

[inducer]

Alright, Bcast is gone from this, now in #280 should we need it.

[alexfikl]

Without the new broadcasting interface it's mostly straightforward changes, so this looks good to me!

Went through the arithmetic changes as well, but they seem to mostly be handling the wealth of options and I couldn't spot anything fishy there.