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benchmarks
detector_benchmarks
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0e836a1c
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0e836a1c
authored
5 months ago
by
Dmitry Kalinkin
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backwards_ecal: add energy resolution benchmark
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8f14f317
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benchmarks/backwards_ecal/backwards_ecal.org
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@@ -113,6 +113,122 @@ for energy in energies:
))
#+end_src
** Energy resolution
#+begin_src jupyter-python
fig, axs = plt.subplots(2, 4, sharex=True, sharey=True, figsize=(15, 6))
fig.suptitle(PLOT_TITLE)
axs = np.ravel(np.array(axs))
sigmas_rel_FWHM_cb = {}
fractions_below = {}
for ix, energy in enumerate(energies):
for use_clusters in [False, True]:
energy_value = float(energy.replace("GeV", "").replace("MeV", "e-3"))
if use_clusters:
clf_label = "leading cluster"
else:
clf_label = "sum all hits"
def clf(events):
if use_clusters:
return ak.drop_none(ak.max(events["EcalEndcapNClusters.energy"], axis=-1)) / energy_value
else:
return ak.sum(events["EcalEndcapNRecHits.energy"], axis=-1) / energy_value
e_pred = clf(e_eval[energy])
plt.sca(axs[ix])
counts, bins, patches = plt.hist(e_pred, weights=np.full_like(e_pred, 1.0 / ak.num(e_pred, axis=0)), bins=np.linspace(0.01, 1.01, 101), label=rf"$e^-$ {clf_label}", hatch=None if use_clusters else r"xxx", alpha=0.8 if use_clusters else 1.)
plt.title(f"{energy}")
e_over_p = (bins[1:] + bins[:-1]) / 2
import scipy.stats
def f(x, n, beta, m, loc, scale):
return n * scipy.stats.crystalball.pdf(x, beta, m, loc, scale)
p0 = (np.sum(counts[10:]), 2., 3., 0.95, 0.05)
try:
import scipy.optimize
par, pcov = scipy.optimize.curve_fit(f, e_over_p[5:], counts[5:], p0=p0, maxfev=10000)
except RuntimeError:
par = None
plt.plot(e_over_p, f(e_over_p, *par), label=rf"Crystal Ball fit", color="tab:green" if use_clusters else "green", lw=0.8)
def summarize_fit(par):
_, _, _, loc_cb, scale_cb = par
# Calculate FWHM
y_max = np.max(f(np.linspace(0., 1., 100), *par))
f_prime = lambda x: f(x, *par) - y_max / 2
x_plus, = scipy.optimize.root(f_prime, loc_cb + scale_cb).x
x_minus, = scipy.optimize.root(f_prime, loc_cb - scale_cb).x
color = "cyan" if use_clusters else "orange"
plt.axvline(x_minus, ls="--", lw=0.75, color=patches[0].get_facecolor(), label=r"$\mu - $FWHM")
plt.axvline(x_plus, ls=":", lw=0.75, color=patches[0].get_facecolor(), label=r"$\mu + $FWHM")
fwhm = (x_plus - x_minus) / loc_cb
sigma_rel_FWHM_cb = fwhm / 2 / np.sqrt(2 * np.log(2))
cutoff_x = loc_cb - fwhm
fraction_below = np.sum(counts[e_over_p < cutoff_x]) / ak.num(e_pred, axis=0)
return sigma_rel_FWHM_cb, fraction_below
sigma_rel_FWHM_cb, fraction_below = summarize_fit(par)
sigmas_rel_FWHM_cb.setdefault(clf_label, {})[energy] = sigma_rel_FWHM_cb
fractions_below.setdefault(clf_label, {})[energy] = fraction_below
plt.legend()
plt.xlabel("$E/p$", loc="right")
plt.ylabel("Event yield", loc="top")
fig.savefig(output_dir / f"resolution_plots.pdf", bbox_inches="tight")
plt.show()
plt.close(fig)
plt.figure()
energy_values = np.array([float(energy.replace("GeV", "").replace("MeV", "e-3")) for energy in energies])
for clf_label, sigma_rel_FWHM_cb in sigmas_rel_FWHM_cb.items():
sigma_over_e = np.array([sigma_rel_FWHM_cb[energy] for energy in energies]) * 100 # convert to %
def f(energy, stochastic, constant):
return np.sqrt((stochastic / np.sqrt(energy)) ** 2 + constant ** 2)
cond = energy_values >= 0.5
try:
import scipy.optimize
par, pcov = scipy.optimize.curve_fit(f, energy_values[cond], sigma_over_e[cond], maxfev=10000)
except RuntimeError:
par = None
stochastic, constant = par
plt.plot(
energy_values,
sigma_over_e,
marker=".",
label=f"{clf_label}"
)
plt.plot(
energy_values[cond],
f(energy_values[cond], *par),
color="black",
ls="--",
lw=0.5,
label=f"{clf_label}, ${np.ceil(stochastic * 10) / 10:.1f}\% / \sqrt{{E}} \oplus {np.ceil(constant * 10) / 10:.1f}\%$",
)
plt.plot(
energy_values,
np.sqrt((1 / energy_values) ** 2 + (1 / np.sqrt(energy_values)) ** 2 + 1 ** 2),
color="black", label=r"YR requirement $1\% / E \oplus 2.5\% / \sqrt{E} \oplus 1\%$",
)
plt.title(INPUT_PATH_FORMAT)
plt.legend()
plt.xlabel("Energy, GeV", loc="right")
plt.ylabel(r"$\sigma_{E} / E$ derived from FWHM, %", loc="top")
plt.savefig(output_dir / f"resolution.pdf", bbox_inches="tight")
plt.show()
#+end_src
** Pion rejection
#+begin_src jupyter-python
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