Removing deprecated list of list in harmonic cache

[giacomomagni]

Explicit call of a function that has a list of list as input doesn't work with numba:

>>> import eko
>>> sx = eko.harmonics.compute_cache(3, 5,True)
>>> eko.anomalous_dimensions.as4.ggg.gamma_gg_nf0(3,sx)
/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/ir_utils.py:2152: NumbaPendingDeprecationWarning: 
Encountered the use of a type that is scheduled for deprecation: type 'reflected list' found for argument 'sx' of function 'gamma_gg_nf0'.

For more information visit https://numba.readthedocs.io/en/stable/reference/deprecation.html#deprecation-of-reflection-for-list-and-set-types

File "../eko/src/eko/anomalous_dimensions/as4/ggg.py", line 202:
@nb.njit(cache=True)
def gamma_gg_nf0(n, sx):
^

  warnings.warn(NumbaPendingDeprecationWarning(msg, loc=loc))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/dispatcher.py", line 487, in _compile_for_args
    raise e
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/dispatcher.py", line 420, in _compile_for_args
    return_val = self.compile(tuple(argtypes))
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/dispatcher.py", line 965, in compile
    cres = self._compiler.compile(args, return_type)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/dispatcher.py", line 125, in compile
    status, retval = self._compile_cached(args, return_type)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/dispatcher.py", line 139, in _compile_cached
    retval = self._compile_core(args, return_type)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/dispatcher.py", line 152, in _compile_core
    cres = compiler.compile_extra(self.targetdescr.typing_context,
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/compiler.py", line 693, in compile_extra
    return pipeline.compile_extra(func)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/compiler.py", line 429, in compile_extra
    return self._compile_bytecode()
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/compiler.py", line 497, in _compile_bytecode
    return self._compile_core()
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/compiler.py", line 476, in _compile_core
    raise e
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/compiler.py", line 463, in _compile_core
    pm.run(self.state)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/compiler_machinery.py", line 353, in run
    raise patched_exception
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/compiler_machinery.py", line 341, in run
    self._runPass(idx, pass_inst, state)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/compiler_lock.py", line 35, in _acquire_compile_lock
    return func(*args, **kwargs)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/compiler_machinery.py", line 296, in _runPass
    mutated |= check(pss.run_pass, internal_state)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/compiler_machinery.py", line 269, in check
    mangled = func(compiler_state)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/typed_passes.py", line 396, in run_pass
    lower.create_cpython_wrapper(flags.release_gil)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/lowering.py", line 305, in create_cpython_wrapper
    self.context.create_cpython_wrapper(self.library, self.fndesc,
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/cpu.py", line 183, in create_cpython_wrapper
    builder.build()
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/callwrapper.py", line 123, in build
    self.build_wrapper(api, builder, closure, args, kws)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/callwrapper.py", line 156, in build_wrapper
    val = cleanup_manager.add_arg(builder.load(obj), ty)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/callwrapper.py", line 59, in add_arg
    cleanup_arg()
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/callwrapper.py", line 41, in cleanup_arg
    self.api.reflect_native_value(ty, native.value, self.env_manager)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/pythonapi.py", line 1431, in reflect_native_value
    impl(typ, val, c)
  File "/project/theorie/gmagni/miniconda3/envs/n3lo_fit/lib/python3.10/site-packages/numba/core/boxing.py", line 755, in reflect_list
    raise TypeError(msg)
TypeError: Failed in nopython mode pipeline (step: native lowering)
cannot reflect element of reflected container: reflected list(reflected list(complex128)<iv=None>)<iv=None>

Possible solution is to promote the cache to be a regular numpy.ndarray adding some zeros. A bit cleaner but more complex would be to pass a dictionary.
Note that calling functions that don't need compute_cache as input works fine.

[alecandido]

We won't have an infinite number of perturbative orders (N3LO is likely to be the maximum, at least for 10-20 years).
And unless this cache is order of hundreds of megabytes (I'm pretty sure is not) we don't care even about a factor of 2 or some units on the size.

In this context, array are the cleanest thing we can use (everything else becomes dirtier because of numba).

[felixhekhorn]

Just to confirm, that after 20min matching did compile ...