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This commit also adds a script to calculate the CSDA range for electrons from a
table of the stopping power as a function of energy. We need this script since
the NIST ESTAR website will only output the stopping power above a certain
energy threshold (1 GeV for electrons).
See https://physics.nist.gov/PhysRefData/Star/Text/ESTAR.html.
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integral
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This commit speeds up the fast likelihood calculation by only computing the
time PDF for a single photon. Since the majority of the time in the fast
likelihood calculation is spent computing the time PDF this should speed things
up by quite a bit. I suspect this won't have a big effect on the likelihood
value, but I should do some more testing.
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This function is only used when the expected number of photons reaching a PMT
is *very* small. In this case, we still need to estimate the PMT hit time PDF
for indirect light which is modelled as a flat distribution starting at the
time where the PMT is most likely to be hit from direct light. Since we compute
the most likely time for a PMT to be hit from direct light by computing the
integral of the expected charge times the time and then dividing by the total
charge, when the total charge is very small this can introduce large errors.
Note that this code already existed but it was computed in the likelihood
function. This commit just moves it to its own function to make things look
nicer.
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This commit speeds up the likelihood function by about ~20% by using the
precomputed track positions, directions, times, etc. instead of interpolating
them on the fly.
It also switches to computing the number of points to integrate along the track
by dividing the track length by a specified distance, currently set to 1 cm.
This should hopefully speed things up for lower energies and result in more
stable fits at high energies.
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particle id
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This commit speeds up the likelihood calculation by returning zero early if the
angle between the PMT and the track is far from the Cerenkov angle.
Specifically we check to see that the angle is 5 "standard deviations" away.
Where the standard deviation is taken to be the RMS width of the angular
distribution.
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To characterize the angular distribution of photons from an electromagnetic
shower I came up with the following functional form:
f(cos_theta) ~ exp(-abs(cos_theta-mu)^alpha/beta)
and fit this to data simulated using RAT-PAC at several different energies. I
then fit the alpha and beta coefficients as a function of energy to the
functional form:
alpha = c0 + c1/log(c2*T0 + c3)
beta = c0 + c1/log(c2*T0 + c3).
where T0 is the initial energy of the electron in MeV and c0, c1, c2, and c3
are parameters which I fit.
The longitudinal distribution of the photons generated from an electromagnetic
shower is described by a gamma distribution:
f(x) = x**(a-1)*exp(-x/b)/(Gamma(a)*b**a).
This parameterization comes from the PDG "Passage of particles through matter"
section 32.5. I also fit the data from my RAT-PAC simulation, but currently I
am not using it, and instead using a simpler form to calculate the coefficients
from the PDG (although I estimated the b parameter from the RAT-PAC data).
I also sped up the calculation of the solid angle by making a lookup table
since it was taking a significant fraction of the time to compute the
likelihood function.
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things up
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sqrt(1-pow(cos_theta,2))
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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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This commit fixes a bug which was double counting the pmt response when
computing the direct charge and incorrectly multiplying the reflected charge by
the pmt response. I think this was just a typo left in when I added the
reflected charge.
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This commit updates path_init() to check that beta > 0 before dividing by it to
compute the time. Previously when fitting electrons it would occasionally
divide by zero which would cause the inf to propagate all the way through the
likelihood function.
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Occasionally when fitting electrons the kinetic energy at the last step would
be high enough that the electron never crossed the BETA_MIN threshold which
would cause the gsl routine to throw an error.
This commit updates particle_init() to set the kinetic energy at the last
step to zero to make sure that we can bisect the point along the track where
the speed drops to BETA_MIN.
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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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path coefficients
Previously I was adding the log likelihood of the path coefficients instead of
the *negative* log likelihood! When fitting electrons this would sometimes
cause the fit to become unstable and continue increasing the path coefficients
without bound since the gain in the likelihood caused by increasing the
coefficients was more than the loss caused by a worse fit to the PMT data.
Doh!
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