class ToyMonteCarlo(object):
def main(self):
global weights, densities, weighted_densities
plt.figure()
cluster = clusters.SingleStation()
self.station = cluster.stations[0]
R = np.linspace(0, 100, 100)
densities = []
weights = []
for E in np.linspace(1e13, 1e17, 10000):
relative_flux = E ** -2.7
Ne = 10 ** (np.log10(E) - 15 + 4.8)
self.ldf = KascadeLdf(Ne)
min_dens = self.calculate_minimum_density_for_station_at_R(R)
weights.append(relative_flux)
densities.append(min_dens)
weights = np.array(weights)
densities = np.array(densities).T
weighted_densities = (np.sum(weights * densities, axis=1) /
np.sum(weights))
plt.plot(R, weighted_densities)
plt.yscale('log')
plt.ylabel("Min. density [m^{-2}]")
plt.xlabel("Core distance [m]")
plt.axvline(5.77)
plt.show()
def calculate_minimum_density_for_station_at_R(self, R):
densities = self.calculate_densities_for_station_at_R(R)
return np.min(densities, axis=0)
def calculate_densities_for_station_at_R(self, R):
densities = []
for detector in self.station.detectors:
densities.append(self.calculate_densities_for_detector_at_R(
detector, R))
return np.array(densities)
def calculate_densities_for_detector_at_R(self, detector, R):
x = 0
y = R
x0, y0 = detector.get_xy_coordinates()
r = np.sqrt((x - x0) ** 2 + (y - y0) ** 2)
return self.ldf.calculate_ldf_value(r)
class EnergySensitivity(object):
def __init__(self):
# Detectors
stations = [501, 503, 506]
self.cluster = ScienceParkCluster(stations=stations)
# Conditions
self.detection_probability = 0.5
self.min_detectors = 2
self.min_stations = 3
# Shower parameters
self.ldf = KascadeLdf()
self.grid_points = 2500
self.max_radius = 1000
self.min_energy = 1e12
self.max_energy = 1e21
self.start_energy = 1e17
self.bisections = 11
# Throw showers in a regular grid around center mass of the station
xc, yc, _ = self.cluster.calc_center_of_mass_coordinates()
self.xx = np.linspace(-self.max_radius + xc, self.max_radius + xc,
np.sqrt(self.grid_points))
self.yy = np.linspace(-self.max_radius + yc, self.max_radius + yc,
np.sqrt(self.grid_points))
def main(self):
# Cache detector positions
for station in self.cluster.stations:
for detector in station.detectors:
detector.xy_coordinates = detector.get_xy_coordinates()
# Results
self.results = self.get_min_energy_per_bin()
def show_restults(self):
self.plot_scintillators_in_cluster()
self.plot_energy_acceptance()
# self.draw_background_map()
def get_area_energy(self, energy):
n_bins = np.sum(self.results < energy)
bin_area = abs((self.xx[1] - self.xx[0]) * (self.yy[1] - self.yy[0]))
area = n_bins * bin_area
return area
def get_min_energy_per_bin(self):
worker_pool = Pool()
temp_multi_find_min_energy = partial(multi_find_min_energy, self)
results = worker_pool.map(temp_multi_find_min_energy,
product(self.xx, self.yy))
worker_pool.close()
worker_pool.join()
# results = [temp_multi_find_min_energy(xy) for xy in product(self.xx, self.yy)]
results = np.array(results).reshape((len(self.xx), len(self.yy))).T
return results
def find_min_energy(self, xc, yc):
# Use bisection to quickly get the final energy
energy = self.start_energy
lo = self.min_energy
hi = self.max_energy
for _ in range(self.bisections):
n_electrons = 10**(np.log10(energy) - 15 + 4.8)
station_densities = self.calculate_densities_for_cluster(
xc, yc, n_electrons)
p_cluster = self.detection_probability_for_cluster(
station_densities)
if p_cluster == self.detection_probability:
break
elif p_cluster < self.detection_probability:
lo = energy
else:
hi = energy
energy = 10**((np.log10(lo) + np.log10(hi)) / 2.0)
return energy
def detection_probability_for_cluster(self, station_densities):
"""Determine the probability of 'coincidence'
Calculate the probability of the requested coincidence using
statistics. Fist the probability of a good detection in each station
is determined. Then it looks for the probability that at least a given
number of stations detects the shower.
:param station_densities: list of densities at each detectors in
each of the stations.
:return: probability of a coicidence.
"""
if len(station_densities) < self.min_stations:
# To few stations
return 0
p_stations = [
self.detection_probability_for_station(detector_densities)
for detector_densities in station_densities
]
p0_stations = [1. - p for p in p_stations]
p_cluster = self.calculate_p(p_stations, p0_stations,
self.min_stations)
return p_cluster
def detection_probability_for_station(self, detector_densities):
"""Determine the probability of 'trigger'
Calculate the probability of the requested detection using Poisson
statistics. Each detector will be marked as hit when it has at least
one particle. At least `min_detectors` need to be hit to count towards
the probability of a good detection.
:param detector_densities: list of densities at each detectors in
the station.
:return: list of probabilities for each station.
"""
if len(detector_densities) < self.min_detectors:
# To few detectors
return 0
p0_detectors = [self.p0(density) for density in detector_densities]
p_detectors = [1. - p0 for p0 in p0_detectors]
p_station = self.calculate_p(p_detectors, p0_detectors,
self.min_detectors)
return p_station
def calculate_p(self, p, p0, min_n):
n_p = len(p)
p_total = 0
for n in range(min_n, n_p + 1):
for i in combinations(range(n_p), n):
p_combination = 1.
for j in range(n_p):
if j in i:
# Probability of trigger
p_combination *= p[j]
else:
# Probability of no trigger
p_combination *= p0[j]
p_total += p_combination
return p_total
def p(self, detector_density):
"""Chance of at least one particle in detector"""
return 1.0 - self.p0(detector_density)
def p0(self, detector_density):
"""Chance of detecting no particle in a detector"""
return np.exp(-detector_density / 2.)
def calculate_densities_for_cluster(self, x, y, n_electrons):
densities = [
self.calculate_densities_for_station(station, x, y, n_electrons)
for station in self.cluster.stations
]
return densities
def calculate_densities_for_station(self, station, x, y, n_electrons):
densities = [
self.calculate_densities_for_detector(detector, x, y, n_electrons)
for detector in station.detectors
]
return densities
def calculate_densities_for_detector(self, detector, x, y, n_electrons):
r = self.calculate_detector_core_distance(detector, x, y)
density = self.ldf.calculate_ldf_value(r, n_electrons)
return density
def calculate_detector_core_distance(self, detector, x, y):
x0, y0 = detector.xy_coordinates
r = np.sqrt((x - x0)**2 + (y - y0)**2)
return r
def plot_scintillators_in_cluster(self):
# Draw station locations on a map
for station in self.cluster.stations:
for detector in station.detectors:
detector_x, detector_y = detector.get_xy_coordinates()
plt.scatter(detector_x,
detector_y,
marker=',',
c='r',
edgecolor='none',
s=6)
station_x, station_y, station_a = station.get_xyalpha_coordinates()
plt.scatter(station_x,
station_y,
marker=',',
c='b',
edgecolor='none',
s=3)
def plot_energy_acceptance(self):
# Grid
min_energy = np.log10(self.min_energy)
max_energy = np.log10(self.max_energy)
levels = (max_energy - min_energy) * 3 + 1
label_levels = (max_energy - min_energy) + 1
contour = plt.contour(self.xx, self.yy, self.results,
np.logspace(min_energy, max_energy, levels))
plt.clabel(contour,
np.logspace(min_energy, max_energy, label_levels),
inline=1,
fontsize=8,
fmt='%.0e')
def draw_background_map(self):
self_path = os.path.dirname(__file__)
map_path = os.path.join(self_path,
"backgrounds/ScienceParkMap_1.092.png")
# Draw Science Park Map on 1:1 scale (1 meter = 1 pixel)
background = plt.imread(map_path)
# determine pixel:meter ratio for different OSM zoom levels at Science Park..
bg_scale = 1.092
bg_width = background.shape[1] * bg_scale
bg_height = background.shape[0] * bg_scale
plt.imshow(background,
aspect='equal',
alpha=0.5,
extent=[-bg_width, bg_width, -bg_height, bg_height])
