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I noticed when fitting electrons that the cquad integration routine was not
very stable, i.e. it would return different results for *very* small changes in
the fit parameters which would cause the fit to stall.
Since it's very important for the minimizer that the likelihood function not
jump around, I am switching to integrating over the path by just using a fixed
number of points and using the trapezoidal rule. This seems to be a lot more
stable, and as a bonus I was able to combine the three integrals (direct
charge, indirect charge, and time) so that we only have to do a single loop.
This should hopefully make the speed comparable since the cquad routine was
fairly effective at only using as many function evaluations as needed.
Another benefit to this approach is that if needed, it will be easier to port
to a GPU.
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Since we only have the range and dE/dx tables for light water for electrons and
protons it's not correct to use the heavy water density. Also, even though we
have both tables for muons, currently we only load the heavy water table, so we
hardcode the density to that of heavy water.
In the future, it would be nice to load both tables and use the correct one
depending on if we are fitting in the heavy or light water.
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To calculate the expected number of photons from reflected light we now
integrate over the track and use the PMT response table to calculate what
fraction of the light is reflected. Previously we were just using a constant
fraction of the total detected light which was faster since we only had to
integrate over the track once, but this should be more accurate.
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This commit updates the CHARGE_FRACTION value to now represent approximately
the fraction of light reflected from each PMT. It also updates the value to be
closer to the true value based on a couple of fits.
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Previously to avoid computing P(q,t|n)*P(n|mu) for large n when they were very
unlikely I was using a precomputed maximum n value based only on the expected
number of PE. However, this didn't take into account P(q|n).
This commit updates the likelihood function to dynamically decide when to quit
computing these probabilities when the probability for a given n divided by the
most likely probability is less than some threshold.
This threshold is currently set to 10**(-10) which means we quit calculating
these probabilities when the probability is 10 million times less likely than
the most probable value.
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This commit adds a fast function to calculate the expected number of PE at a
PMT without numerically integrating over the track. This calculation is *much*
faster than integrating over the track (~30 ms compared to several seconds) and
so we use it during the "quick" minimization phase of the fit to quickly find
the best position.
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This commit updates the likelihood fit to use the KL path expansion. Currently,
I'm just using one coefficient for the path in both x and y.
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The RMS scattering angle calculation comes from Equation 33.15 in the PDG
article on the passage of particles through matter. It's not entirely obvious
if this equation is correct for a long track. It seems like it should be
integrated along the track to add up the contributions at different energies,
but it's not obvious how to do that with the log term.
In any case, the way I was previously calculating it (by using the momentum and
velocity at each point along the track) was definitely wrong.
I will try this out and perhaps try to integrate it later.
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