Pointing systematics HWP class

[yusuke-takase]

As I presented today's telecon, I have implemented the pointing systematics due to wedged transmissive HWP (or precessing reflective HWP) which causes a rotational disturbance to the pointings around the expected pointing direction.
The HWP angle redefinition that happened recently (#340) is also covered.

Current version of pointing-sys API has Simulation and List[DetectorInfo] as arguments like:

pntsys = lbs.PointingSys(sim, dets_list)

However it was not useful for MPI distribution, so in this PR, the Observation is added in arguments as:

pntsys = lbs.PointingSys(sim, obs, dets_list)

By this changing, we can multiply any systematic quaternions to any chunk of time given by MPI.

And several methods that do quaternion multiplications were bit messy and redundant, so everything is unified to this method:

lbs.left_multiply_syst_quats(
    result: RotQuaternion,
    syst_quats: RotQuaternion,
    detector: DetectorInfo,
    start_time,
    sampling_rate_hz
)

---

Maybe following thing should not discussed here though let me point it out.

An issue that I met in a preparation of e2e-pipeline for the pointing systematics is #189 .
Because this HWP-pointing systematics is happened in 19Hz intrinsically, so we forced to compute the spin2ecliptic_quats in 19Hz as well to perform the RotQuaternion multiplication without stacking.

It requires a lot of memory because when we call the Simulation.set_scanning_strategy(), all MPI processes compute quaternions start to end of simulation.
It can be avoided by:

(obs,) = sim.create_observations(
    detectors=dets,
    n_blocks_det=1,
    n_blocks_time=size,
    split_list_over_processes=False
)
scanning_strategy = lbs.SpinningScanningStrategy.from_imo(
    url= f"/releases/{imo_version}/satellite/scanning_parameters/",
    imo=imo,
)
sim.spin2ecliptic_quats = scanning_strategy.generate_spin2ecl_quaternions(
    start_time=obs.start_time,
    time_span_s=obs.n_samples/obs.sampling_rate_hz,
    delta_time_s=delta_time_s,
)

although if it is solved in clever way, it's definitely useful.

[ziotom78]

Yeah, that is a long-standing TODO, but the idea I got at the time was to split the computation across the MPI processes and then gather all the quaternions in each process so that all the quaternions are available everywhere. This is, of course, not going to work in this specific case.

Your trick is probably the best way to do this. Perhaps we could add a paragraph or two about this in the documentation?

[yusuke-takase]

Hi @ziotom78,
Thank you for responding it! I understood the idea, it just contributes the calculation time reduction, not for memory allocation. Okay, I keep my way and I'm happy to write its documentation.

After #342 is merged, shall I write all of pointing systematics API usages, and this MPI tips? (Because I'm busy due to my PhD thesis writing, it takes a time bit...)

[yusuke-takase]

Hi @ziotom78 ,

I wrote documentation of pointing systematics. I think it is ready to be merged into master if you are convinced.