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Draft: Educated prescaling for RICH1 and RICH2 alignment optimization

Anatoly Solomin requested to merge richalign_EducatedPrescaling into master

Software alignment of the RICH1 and RICH2 optical systems by the use of data, suffers from extremely uneven -- between central and peripheral mirrors -- population with Cherenkov photons. The difference is about five orders of magnitude for the minbias events. That causes huge redundancy in the number of events needed to populate sufficiently the peripheral mirrors. To mitigate that, a highly depleted subset of events that populate central areas with Cherenkov photons at approximately the same density as the peripheral ones, needs to be preselected by the HLT1 lines.

Because reconstruction of photons at the HLT1 level is not feasible, due to the performance limitations, a certain "dictionary", in terms of the tracks' kinematics, rather than in terms of photon numbers, needs to be used in HLT1, to make the event selection decisions.

This MR is dedicated to making use of the arrays, prepared in advance, aka "dictionaries", of the spatial angular intervals for the tracks, in the corresponding RICH1 and RICH2 prescaling lines. The "key" here is the ordinal number of the particular angular interval, and the "value" is the magnitude of the element. The meaning of the magnitude of an element is its interval's "degree of demand" in (0, 1] range, to which a random number, generated for each track in the same range, is compared to.

The logic is to select the event if it has at least one track hitting at least one such angular interval, such that the decision on that track is positive. The latter happens when the random number, generated for that track, is less than the "degree of demand" of that interval. In other words, intervals, that are responsible for population of the "central" areas and are hit by the tracks very often, are in the slightest demand, and therefore, the corresponding events are selected very rarely. In contrast, intervals with degree of demand close to 1, are hit very rarely, but such events are always selected.

The degrees of demand are calibrated in advance, in such a way (omitting some subtle details), that a fairly even population of the mirrors is ensured, at a minimum number of events to be processed in the full HLT2 reconstruction of events, including reconstruction of the Cherenkov photons.

The mechanism is a principal extension of the so-called random prescaling, in that the decision is taken randomly, but based on a dictionary of the degrees of demand, Hence -- "educated" random prescaling. Specifically, the already existing deterministic quasi-random number generation algorithm is used (DeterministicScaler). The latter is modified for usage of the Odin-supplied event data, and its usage across the rest of the Allen code is updated accordingly.

Closes #166.

Edited by Anatoly Solomin

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