def test_SensitivityPointSource_sensitivity_MC():
np.random.seed(314159)
alpha = 1.
n_sig = 20
n_bgr = 10
# one bin with the bin-centre at 1 TeV
energy_bin_edges = np.array([.1, 10]) * u.TeV
energies_sig = np.ones(n_sig)
energies_bgr = np.ones(n_bgr)
sens = SensitivityPointSource(reco_energies={
's': energies_sig * u.TeV,
'b': energies_bgr * u.TeV
})
# sens.event_weights = {'s': energies_sig, 'b': energies_bgr}
sensitivity = sens.get_sensitivity(
alpha=alpha,
signal_list=("s"),
mode="MC",
sensitivity_source_flux=crab_source_rate,
sensitivity_energy_bin_edges=energy_bin_edges,
min_n=0,
max_background_ratio=1)
# the ratio between sensitivity and reference flux (i.e. from the crab nebula) should
# be the scaling factor that needs to be applied to n_sig to produce a 5 sigma result
# in the lima formula
ratio = sensitivity["Sensitivity"][0] / (crab_source_rate(1 * u.TeV)).value
np.testing.assert_allclose(
[sigma_lima(ratio * n_sig + alpha * n_bgr, n_bgr, alpha)], [5],
atol=0.0066)
def test_SensitivityPointSource_sensitivity_MC():
np.random.seed(314159)
alpha = 1.
n_sig = 20
n_bgr = 10
# one bin with the bin-centre at 1 TeV
energy_bin_edges = np.array([.1, 10]) * u.TeV
energies_sig = np.ones(n_sig)
energies_bgr = np.ones(n_bgr)
sens = SensitivityPointSource(reco_energies={'s': energies_sig * u.TeV,
'b': energies_bgr * u.TeV})
# sens.event_weights = {'s': energies_sig, 'b': energies_bgr}
sensitivity = sens.get_sensitivity(alpha=alpha, signal_list=("s"), mode="MC",
sensitivity_source_flux=crab_source_rate,
sensitivity_energy_bin_edges=energy_bin_edges,
min_n=0, max_background_ratio=1)
# the ratio between sensitivity and reference flux (i.e. from the crab nebula) should
# be the scaling factor that needs to be applied to n_sig to produce a 5 sigma result
# in the lima formula
ratio = sensitivity["Sensitivity"][0] / (crab_source_rate(1 * u.TeV)).value
np.testing.assert_allclose(
[sigma_lima(ratio * n_sig + alpha * n_bgr, n_bgr, alpha)], [5], atol=0.0066)
def test_SensitivityPointSource_sensitivity_data():
alpha = 1.
n_on = 30
n_off = 10
# one bin with the bin-centre at 1 TeV
energy_bin_edges = np.array([.1, 10]) * u.TeV
energies_sig = np.ones(n_on)
energies_bgr = np.ones(n_off)
sens = SensitivityPointSource(reco_energies={
's': energies_sig * u.TeV,
'b': energies_bgr * u.TeV
})
sensitivity = sens.get_sensitivity(
alpha=alpha,
signal_list=("s"),
mode="data",
sensitivity_source_flux=crab_source_rate,
sensitivity_energy_bin_edges=energy_bin_edges,
min_n=0,
max_background_ratio=1)
# the ratio between sensitivity and reference flux (i.e. from the crab nebula) should
# be the scaling factor that needs to be applied to n_sig=n_on-n_off*alpha to produce
# a 5 sigma result in the lima formula
ratio = sensitivity["Sensitivity"][0] / (crab_source_rate(1 * u.TeV)).value
np.testing.assert_allclose([
sigma_lima(ratio *
(n_on - n_off * alpha) + n_off * alpha, n_off, alpha)
], [5])
def make_sensitivity_plots(SensCalc, sensitivities,
SensCalc_t, sensitivities_t):
bin_centres_g = (edges_gammas[1:] + edges_gammas[:-1]) / 2.
bin_centres_p = (edges_proton[1:] + edges_proton[:-1]) / 2.
bin_widths_g = np.diff(edges_gammas.value)
bin_widths_p = np.diff(edges_proton.value)
# the point-source sensitivity binned in energy
plt.figure()
# draw the crab flux as a reference
crab_bins = np.logspace(-2, 2.5, 17)
plt.loglog(crab_bins,
(crab_source_rate(crab_bins * u.TeV)
* (crab_bins * u.TeV)**2).to(sensitivity_unit).value,
color="red", ls="dashed", label="Crab Nebula")
plt.loglog(crab_bins,
(crab_source_rate(crab_bins * u.TeV)
* (crab_bins * u.TeV)**2).to(sensitivity_unit).value / 10,
color="red", ls="dashed", alpha=.66, label="Crab Nebula / 10")
plt.loglog(crab_bins,
(crab_source_rate(crab_bins * u.TeV)
* (crab_bins * u.TeV)**2).to(sensitivity_unit).value / 100,
color="red", ls="dashed", alpha=.33, label="Crab Nebula / 100")
# some semi-official line to compare
ref_loge, ref_sens = *(np.array([
(-1.8, 6.87978e-11), (-1.6, 1.87765e-11),
(-1.4, 7.00645e-12), (-1.2, 1.77677e-12), (-1.0, 8.19263e-13),
(-0.8, 4.84879e-13), (-0.6, 3.00256e-13), (-0.4, 2.07787e-13),
(-0.2, 1.4176e-13), (0.0, 1.06069e-13), (0.2, 8.58209e-14),
(0.4, 6.94294e-14), (0.6, 6.69301e-14), (0.8, 7.61169e-14),
(1.0, 7.13895e-14), (1.2, 9.49376e-14), (1.4, 1.25208e-13),
(1.6, 1.91209e-13), (1.8, 3.11611e-13), (2.0, 4.80354e-13)]).T),
plt.loglog(10**ref_loge,
((ref_sens) * (u.erg * u.cm**2 * u.s)**(-1)).to(flux_unit).value,
marker="s", color="black", ms=3, linewidth=1,
label="reference")
sens_low, sens_up = (
(sensitivities["Sensitivity"] -
sensitivities["Sensitivity_low"]).to(flux_unit) *
sensitivities["Energy"].to(u.erg)**2,
(sensitivities["Sensitivity_up"] -
sensitivities["Sensitivity"]).to(flux_unit) *
sensitivities["Energy"].to(u.erg)**2)
# plt.errorbar(
plt.loglog(
sensitivities["Energy"] / energy_unit,
(sensitivities["Sensitivity"].to(flux_unit) *
sensitivities["Energy"].to(u.erg)**2).to(sensitivity_unit).value,
# (sens_low.value, sens_up.value),
color="darkred",
marker="s",
label="wavelets")
# plt.loglog(
# sensitivities["Energy"] / energy_unit,
# (sensitivities["Sensitivity_base"].to(flux_unit) *
# sensitivities["Energy"].to(u.erg)**2).to(sensitivity_unit).value,
# color="darkgreen",
# marker="^",
# ls="",
# label="wavelets (no upscale)")
# tailcuts
sens_low_t, sens_up_t = (
(sensitivities_t["Sensitivity"] -
sensitivities_t["Sensitivity_low"]).to(flux_unit) *
sensitivities_t["Energy"].to(u.erg)**2,
(sensitivities_t["Sensitivity_up"] -
sensitivities_t["Sensitivity"]).to(flux_unit) *
sensitivities_t["Energy"].to(u.erg)**2)
# plt.errorbar(
plt.loglog(
sensitivities_t["Energy"] / energy_unit,
(sensitivities_t["Sensitivity"].to(flux_unit) *
sensitivities_t["Energy"].to(u.erg)**2).to(sensitivity_unit).value,
# (sens_low_t.value, sens_up_t.value),
color="darkorange",
marker="s", ls="--",
label="tailcuts")
# plt.loglog(
# sensitivities_t["Energy"].to(energy_unit),
# (sensitivities_t["Sensitivity_base"].to(flux_unit) *
# sensitivities_t["Energy"].to(u.erg)**2),
# color="darkblue",
# marker="v",
# ls="",
# label="tailcuts (no upscale)")
plt.legend(title="Obsetvation Time: {}".format(observation_time), loc=1)
plt.xlabel(r'$E_\mathrm{reco}$' + ' / {:latex}'.format(energy_unit))
plt.ylabel(r'$E^2 \Phi /$ {:latex}'.format(sensitivity_unit))
plt.gca().set_xscale("log")
plt.grid()
plt.xlim([1e-2, 2e2])
plt.ylim([5e-15, 5e-10])
if args.write:
save_fig(args.plots_dir + "sensitivity")
# plot the sensitivity ratios
try:
plt.figure()
plt.semilogx(sensitivities_t["Energy"].to(energy_unit)[1:-2].value,
(sensitivities_t["Sensitivity"].to(flux_unit) *
sensitivities_t["Energy"].to(u.erg)**2)[1:-2] /
(sensitivities["Sensitivity"].to(flux_unit) *
sensitivities["Energy"].to(u.erg)**2)[1:-2],
label=r"Sens$_\mathrm{tail}$ / Sens$_\mathrm{wave}$"
)
plt.legend()
# plt.semilogx(sensitivities_t["Energy"].to(energy_unit)[[0, -1]],
# [1, 1], ls="--", color="gray")
# plt.xlim(sensitivities_t["Energy"].to(energy_unit)[[0, -1]].value)
# plt.ylim([.25, 1.1])
plt.xlabel('E / {:latex}'.format(energy_unit))
plt.ylabel("ratio")
if args.write:
save_fig(args.plots_dir + "sensitivity_ratio")
except:
plt.close()
# plot a sky image of the events
# useless since too few MC background events left
if False:
fig2 = plt.figure()
plt.hexbin(
[(ph - 180) * np.sin(th * u.deg) for
ph, th in zip(chain(gammas['phi'], proton['phi']),
chain(gammas['theta'], proton['theta']))],
[a for a in chain(gammas['theta'], proton['theta'])],
gridsize=41, extent=[-2, 2, 18, 22],
C=[a for a in chain(weights['g'], weights['p'])],
bins='log'
)
plt.colorbar().set_label("log(Number of Events)")
plt.axes().set_aspect('equal')
plt.xlabel(r"$\sin(\vartheta) \cdot (\varphi-180) / ${:latex}"
.format(angle_unit))
plt.ylabel(r"$\vartheta$ / {:latex}".format(angle_unit))
if args.write:
save_fig("plots/skymap")
def make_sensitivity_plots(SensCalc, sensitivities,
SensCalc_t, sensitivities_t):
bin_centres_g = (edges_gammas[1:] + edges_gammas[:-1]) / 2.
bin_centres_p = (edges_proton[1:] + edges_proton[:-1]) / 2.
bin_widths_g = np.diff(edges_gammas.value)
bin_widths_p = np.diff(edges_proton.value)
# the point-source sensitivity binned in energy
plt.figure()
# draw the crab flux as a reference
crab_bins = np.logspace(-2, 2.5, 17)
plt.loglog(crab_bins,
(crab_source_rate(crab_bins * u.TeV)
* (crab_bins * u.TeV)**2).to(sensitivity_unit).value,
color="red", ls="dashed", label="Crab Nebula")
plt.loglog(crab_bins,
(crab_source_rate(crab_bins * u.TeV)
* (crab_bins * u.TeV)**2).to(sensitivity_unit).value / 10,
color="red", ls="dashed", alpha=.66, label="Crab Nebula / 10")
plt.loglog(crab_bins,
(crab_source_rate(crab_bins * u.TeV)
* (crab_bins * u.TeV)**2).to(sensitivity_unit).value / 100,
color="red", ls="dashed", alpha=.33, label="Crab Nebula / 100")
# some semi-official line to compare
ref_loge, ref_sens = *(np.array([
(-1.8, 6.87978e-11), (-1.6, 1.87765e-11),
(-1.4, 7.00645e-12), (-1.2, 1.77677e-12), (-1.0, 8.19263e-13),
(-0.8, 4.84879e-13), (-0.6, 3.00256e-13), (-0.4, 2.07787e-13),
(-0.2, 1.4176e-13), (0.0, 1.06069e-13), (0.2, 8.58209e-14),
(0.4, 6.94294e-14), (0.6, 6.69301e-14), (0.8, 7.61169e-14),
(1.0, 7.13895e-14), (1.2, 9.49376e-14), (1.4, 1.25208e-13),
(1.6, 1.91209e-13), (1.8, 3.11611e-13), (2.0, 4.80354e-13)]).T),
plt.loglog(10**ref_loge,
((ref_sens) * (u.erg * u.cm**2 * u.s)**(-1)).to(flux_unit).value,
marker="s", color="black", ms=3, linewidth=1,
label="reference")
sens_low, sens_up = (
(sensitivities["Sensitivity"] -
sensitivities["Sensitivity_low"]).to(flux_unit) *
sensitivities["Energy"].to(u.erg)**2,
(sensitivities["Sensitivity_up"] -
sensitivities["Sensitivity"]).to(flux_unit) *
sensitivities["Energy"].to(u.erg)**2)
# plt.errorbar(
plt.loglog(
sensitivities["Energy"] / energy_unit,
(sensitivities["Sensitivity"].to(flux_unit) *
sensitivities["Energy"].to(u.erg)**2).to(sensitivity_unit).value,
# (sens_low.value, sens_up.value),
color="darkred",
marker="s",
label="wavelets")
# plt.loglog(
# sensitivities["Energy"] / energy_unit,
# (sensitivities["Sensitivity_base"].to(flux_unit) *
# sensitivities["Energy"].to(u.erg)**2).to(sensitivity_unit).value,
# color="darkgreen",
# marker="^",
# ls="",
# label="wavelets (no upscale)")
# tailcuts
sens_low_t, sens_up_t = (
(sensitivities_t["Sensitivity"] -
sensitivities_t["Sensitivity_low"]).to(flux_unit) *
sensitivities_t["Energy"].to(u.erg)**2,
(sensitivities_t["Sensitivity_up"] -
sensitivities_t["Sensitivity"]).to(flux_unit) *
sensitivities_t["Energy"].to(u.erg)**2)
# plt.errorbar(
plt.loglog(
sensitivities_t["Energy"] / energy_unit,
(sensitivities_t["Sensitivity"].to(flux_unit) *
sensitivities_t["Energy"].to(u.erg)**2).to(sensitivity_unit).value,
# (sens_low_t.value, sens_up_t.value),
color="darkorange",
marker="s", ls="--",
label="tailcuts")
# plt.loglog(
# sensitivities_t["Energy"].to(energy_unit),
# (sensitivities_t["Sensitivity_base"].to(flux_unit) *
# sensitivities_t["Energy"].to(u.erg)**2),
# color="darkblue",
# marker="v",
# ls="",
# label="tailcuts (no upscale)")
plt.legend(title="Obsetvation Time: {}".format(observation_time), loc=1)
plt.xlabel(r'$E_\mathrm{reco}$' + ' / {:latex}'.format(energy_unit))
plt.ylabel(r'$E^2 \Phi /$ {:latex}'.format(sensitivity_unit))
plt.gca().set_xscale("log")
plt.grid()
plt.xlim([1e-2, 2e2])
plt.ylim([5e-15, 5e-10])
if args.write:
save_fig(args.plots_dir + "sensitivity")
# plot the sensitivity ratios
try:
plt.figure()
plt.semilogx(sensitivities_t["Energy"].to(energy_unit)[1:-2].value,
(sensitivities_t["Sensitivity"].to(flux_unit) *
sensitivities_t["Energy"].to(u.erg)**2)[1:-2] /
(sensitivities["Sensitivity"].to(flux_unit) *
sensitivities["Energy"].to(u.erg)**2)[1:-2],
label=r"Sens$_\mathrm{tail}$ / Sens$_\mathrm{wave}$"
)
plt.legend()
# plt.semilogx(sensitivities_t["Energy"].to(energy_unit)[[0, -1]],
# [1, 1], ls="--", color="gray")
# plt.xlim(sensitivities_t["Energy"].to(energy_unit)[[0, -1]].value)
# plt.ylim([.25, 1.1])
plt.xlabel('E / {:latex}'.format(energy_unit))
plt.ylabel("ratio")
if args.write:
save_fig(args.plots_dir + "sensitivity_ratio")
except:
plt.close()
# plot a sky image of the events
# useless since too few MC background events left
if False:
fig2 = plt.figure()
plt.hexbin(
[(ph - 180) * np.sin(th * u.deg) for
ph, th in zip(chain(gammas['phi'], proton['phi']),
chain(gammas['theta'], proton['theta']))],
[a for a in chain(gammas['theta'], proton['theta'])],
gridsize=41, extent=[-2, 2, 18, 22],
C=[a for a in chain(weights['g'], weights['p'])],
bins='log'
)
plt.colorbar().set_label("log(Number of Events)")
plt.axes().set_aspect('equal')
plt.xlabel(r"$\sin(\vartheta) \cdot (\varphi-180) / ${:latex}"
.format(angle_unit))
plt.ylabel(r"$\vartheta$ / {:latex}".format(angle_unit))
if args.write:
save_fig("plots/skymap")