def test_03_energy(self):
n = 1000
log10e_min = 19.
log10e = auger.rand_energy_from_auger(n, log10e_min)
self.assertTrue(log10e.size == n)
self.assertTrue((log10e >= log10e_min).all() & (log10e <= 20.5).all())
self.assertTrue(len(log10e[log10e > log10e_min + 0.1]) < n)
def test_08_convert_spectrum(self):
log10e = np.linspace(17.5, 20.4, 10000)
spectrum15 = auger.spectrum(log10e, normalize2bin=10, year=15)
spectrum17 = auger.spectrum(log10e, normalize2bin=10, year=17)
self.assertTrue(
np.allclose(spectrum15, spectrum17, rtol=1e-16, atol=1e-17))
n = 10000
bins = np.linspace(17.5, 20.5, 31)
e_15 = np.histogram(auger.rand_energy_from_auger(n,
log10e_min=17.5,
log10e_max=None,
ebin=0.1,
year=15),
bins=bins)
e_17 = np.histogram(auger.rand_energy_from_auger(n,
log10e_min=17.5,
log10e_max=None,
ebin=0.1,
year=17),
bins=bins)
self.assertTrue(np.allclose(e_15[0], e_17[0], rtol=1.3, atol=100))
def test_07_lna_xmax_moments(self):
n = 100000
log10e = auger.rand_energy_from_auger(n, log10e_min=17.8)
masses = 2 * auger.rand_charge_from_auger(log10e)
l_ec, mln_a, vln_a = auger.ln_a_moments(log10e, masses)
# check if uhecrs get heavier
self.assertTrue((mln_a[0] < mln_a[-1]) & (vln_a[0] > vln_a[-1]))
m_xmax, v_xmax = auger.ln_a_moments2xmax_moments(l_ec, mln_a, vln_a)
std_xmax = np.sqrt(auger.var_xmax(l_ec, 0.8 * np.exp(mln_a)))
self.assertTrue((std_xmax < 100).all())
mln_a2, vln_a2 = auger.xmax_moments2ln_a_moments(l_ec, m_xmax, v_xmax)
self.assertTrue(np.allclose(mln_a, mln_a2))
self.assertTrue(np.allclose(vln_a, vln_a2))
def setup_roi(nside=256,
ncrs=2000,
roi_size=0.25,
energy_spectrum='uniform',
energy_ordering=False,
emin=19):
npix = hpt.nside2npix(nside)
roipix = 0
angles_pix_to_roi = hpt.angle(nside, roipix, np.arange(npix))
iso_map = np.zeros(npix)
iso_map[angles_pix_to_roi < roi_size] = 1
p = np.cumsum(iso_map)
pix = np.sort(p.searchsorted(np.random.rand(ncrs) * p[-1]))
if energy_spectrum == 'auger':
energies = auger.rand_energy_from_auger(ncrs, emin)
elif energy_spectrum == 'uniform':
energies = np.random.uniform(10, 20, ncrs)
if energy_ordering:
energies = np.sort(energies)[::-1]
return pix, energies
capsize=0,
label='Data 2017')
yl = r'$E^{3} \, J(E)$ [km$^{-2}$ yr$^{-1}$ sr$^{-1}$ eV$^{2}$]'
plt.ylabel(yl, fontsize=16)
plt.xlabel(r'$\log_{10}$($E$/eV)', fontsize=16)
# Analytic parametrization of AUGER energy spectrum
log10e = np.arange(17.5, 20.5, 0.02)
dN = auger.spectrum_analytic(log10e, year=19)
E3_dN = 10**(3 * log10e) * dN # multiply with E^3 for better visability
plt.plot(log10e, E3_dN, color='red', label='Parametrization 2017')
plt.savefig('energy_spectrum.png')
plt.clf()
# We sample energies which follow the above parametrized energy spectrum
n, emin = 1e7, 18.5 # n: number of drawn samples; emin: 10 EeV; lower energy cut
log10e_sample = auger.rand_energy_from_auger(n=int(n), log10e_min=emin)
log10e_bins = np.arange(18.5, 20.55, 0.05)
n, bins = np.histogram(log10e_sample, bins=log10e_bins)
E3_dN_sampled = 10**(
(3 - 1) *
(log10e_bins[:-1])) * n # -1 for correcting logarithmic bin width
plt.plot(log10e[50:], E3_dN[50:], color='red')
plt.plot(log10e_bins[:-1],
E3_dN_sampled * E3_dN[50] / E3_dN_sampled[0],
marker='s',
color='k',
ls='None')
plt.yscale('log')
plt.xlabel('log10(E[eV])', fontsize=16)
plt.ylabel('E$^3$ dN', fontsize=16)
import numpy as np
import matplotlib.pyplot as plt
from astrotools import auger, coord, skymap
print("Test: module coord.py")
# Creates an isotropic arrival map and convert galactic longitudes (lons) and
# galactic latitudes (lats) into cartesian vectors
ncrs = 3000 # number of cosmic rays
log10e_min = 18.5 # minimum energy in log10(E / eV)
lons = coord.rand_phi(ncrs) # isotropic in phi (~Uniform(-pi, pi))
lats = coord.rand_theta(ncrs) # isotropic in theta (Uniform in cos(theta))
vecs = coord.ang2vec(lons, lats)
log10e = auger.rand_energy_from_auger(n=ncrs, log10e_min=log10e_min)
# Plot an example map with sampled energies. If you specify the opath keyword in
# the skymap function, the plot will be automatically saved and closed
skymap.scatter(vecs, c=log10e, opath='isotropic_sky.png')
# Creates an arrival map with a source located at v_src=(1, 0, 0) and apply a
# fisher distribution around it with gaussian spread sigma=10 degree
v_src = np.array([1, 0, 0])
kappa = 1. / np.radians(10.)**2
vecs = coord.rand_fisher_vec(v_src, kappa=kappa, n=ncrs)
# if you dont specify the opath you can use (fig, ax) to plot more stuff
fig, ax = skymap.scatter(vecs, c=log10e)
plt.scatter(0, 0, s=100, c='red', marker='*') # plot source in the center
plt.savefig('fisher_single_source_10deg.png', bbox_inches='tight')
plt.close()
# We can also use the coord.rand_fisher_vec() function to apply an angular uncertainty
ncrs = 3000 # number of cosmic rays log10e_min = 18.5 # minimum energy in log10(E / eV) nside = 64 # resolution of the HEALPix map (default: 64) npix = hpt.nside2npix(nside) # Create a dipole distribution for a healpy map lon, lat = np.radians(45), np.radians(60) # Position of the maximum of the dipole (healpy and astrotools definition) vec_max = hpt.ang2vec(lat, lon) # Convert this to a vector amplitude = 0.5 # amplitude of dipole dipole = hpt.dipole_pdf(nside, amplitude, vec_max, pdf=False) skymap.heatmap(dipole, opath='dipole.png') # Draw random events from this distribution pixel = hpt.rand_pix_from_map(dipole, n=ncrs) # returns 3000 random pixel from this map vecs = hpt.rand_vec_in_pix(nside, pixel) # Random vectors within the drawn pixel skymap.scatter(vecs, c=auger.rand_energy_from_auger(ncrs, log10e_min), opath='dipole_events.png') # Create a healpy map that follows the exposure of an observatory at latitude # a0 = -35.25 (Pierre Auger Observatory) and maximum zenith angle of 60 degree exposure = hpt.exposure_pdf(nside, a0=-35.25, zmax=60) skymap.heatmap(exposure, opath='exposure.png') # Note, if you want to sample from the exposure healpy map random vectors you # have to be careful with the above method hpt.rand_vec_in_pix, # as the exposure healpy map reads out the exposure value in the pixel centers, # whereas hpt.rand_vec_in_pix might sample some directions where # the exposure already dropped to zero. If you want to sample only isoptropic # arrival directions it is instead recommended to use # coord.rand_exposure_vec(), or if you can not avoid healpy # pixelization use <code> hpt.rand_exposure_vec_in_pix </code>.
# If you just have a single cosmic ray set you want to use the ComicRaysBase. You can
# set arbitrary content in the container. Objects with shape (self.crs) will be
# stored in an internal array called 'shape_array', all other data in a
# dictionary called 'general_object_store'.
nside = 64
npix = hpt.nside2npix(nside)
ncrs = 5000
exposure = hpt.exposure_pdf(nside)
lon, lat = hpt.pix2ang(nside, hpt.rand_pix_from_map(exposure, n=ncrs))
crs = cosmic_rays.CosmicRaysBase(ncrs) # Initialize cosmic ray container
# you can set arbitrary content in the container. Objects with different shape
# than (ncrs) will be stored in an internal dictionary called 'general_object_store'
crs['lon'], crs['lat'] = lon, lat
crs['date'] = 'today'
crs['log10e'] = auger.rand_energy_from_auger(log10e_min=19, n=ncrs)
crs.set('vecs', coord.ang2vec(lon, lat)) # another possibility to set content
crs.keys() # will print the keys that are existing
# Save, load and plot cosmic ray base container
opath = 'cr_base_container.npz'
crs.save(opath)
crs_load = cosmic_rays.CosmicRaysBase(opath)
crs_load.plot_heatmap(opath='cr_base_healpy.png')
crs_load.plot_eventmap(opath='cr_base_eventmap.png')
# You can also quickly write all data in an usual ASCII file:
crs.save_readable('cr_base.txt')
# For a big simulation with a lot of sets (simulated skys), you should use the
########################################
# Module: auger.py
########################################
print("Test: module auger.py")
# Analytic parametrization of AUGER energy spectrum
log10e = np.arange(18., 20.5, 0.02)
dN = auger.spectrum_analytic(log10e)
E = 10**(log10e - 18)
E3_dN = E**3 * dN # multiply with E^3 for better visability
# We sample energies which follow the above energy spectrum
n, emin = 1e7, 18.5 # n: number of drawn samples; emin: 10 EeV; lower energy cut
norm = 4.85e16 * n # norm to account for solid angle area
log10e_sample = auger.rand_energy_from_auger(n=int(n), log10e_min=emin)
log10e_bins = np.arange(18.5, 20.55, 0.05)
n, bins = np.histogram(log10e_sample, bins=log10e_bins)
E3_dN_sampled = 10**(
(3 - 1) *
(log10e_bins[:-1] - 18)) * n # -1 for correcting logarithmic bin width
plt.plot(log10e, norm * E3_dN, color='red')
plt.plot(log10e_bins[:-1], E3_dN_sampled, marker='s', color='k', ls='None')
plt.yscale('log')
plt.xlabel('log10(E[eV])', fontsize=16)
plt.ylabel('E$^3$ dN', fontsize=16)
plt.savefig('energy_spectrum.png')
plt.clf()
########################################