compiler: Attach staggering metadata to IndexDerivative

[FabioLuporini]

I need this info for CIRE in PRO (so that we can be more surgical about "what derivatives to catch" during a CIRE round)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 83.82%. Comparing base (33c3b12) to head (e93685d).
⚠️ Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3024      +/-   ##
==========================================
+ Coverage   83.77%   83.82%   +0.04%     
==========================================
  Files         257      257              
  Lines       55007    55134     +127     
  Branches     4708     4719      +11     
==========================================
+ Hits        46083    46215     +132     
+ Misses       8109     8105       -4     
+ Partials      815      814       -1     

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pytest-gpu-aomp-amdgpuX	68.58% <63.63%> (+<0.01%)	⬆️
pytest-gpu-gcc-	78.46% <100.00%> (+0.05%)	⬆️
pytest-gpu-icx-	78.40% <100.00%> (+0.06%)	⬆️
pytest-gpu-nvc-nvidiaX	69.09% <63.63%> (-0.02%)	⬇️

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[EdCaunt]

Nitpick: excessively verbose docstring.

[EdCaunt]

This seems oddly convoluted? Can this really not be simplified at all?

[mloubout]

I don't understand the need or utility of this. THe staggering doesn't matter, x0 does and is already attached.

[FabioLuporini]

I don't understand the need or utility of this. THe staggering doesn't matter, x0 does and is already attached.

@mloubout how do I know if an IndexDerivative represents a staggered derivative, a centered derivative, or, fwiw, an interpolation ?

for the latter I guess I might look at the deriv_order and infer it if it's 0 ? (this is me speculating...)

what about staggered vs centered?

if I'm missing something, happy to close this;
if there's a neater way, happy to do it

I honestly cooked the simplest thing that came to mind

[mloubout]

how do I know if an IndexDerivative represents a staggered derivative, a centered derivative

Again, this has nothing to do with the staggering of the equation but with the difference betwenn x0 and expr.indices_ref. The staggering by itself does not matter, or we wouldn't need _eval_at, the only thing staggering does is define which grid an expr is defined. On top of it if the expr is e.g an Add, such as div(v) the staggering will only be the one of highest priority (so v_x) so not only the information isn't useful it wil not be correct since each term will have a different x0 at evaluation.

[FabioLuporini]

@mloubout I need a way to distinguish centered derivatives from staggered derivatives, because they tend to represent two similarly balanced sets of derivatives , in terms of total number, type and number of underlying objects they're applied to, and so on.

I could use the set of coefficients I guess, but not ideal

other ways?