def test_broken_power_law_integral(self, p1, p2, gamma_b, integrator):
"""test the integration of the log parabola for different spectral
indexes and breaks and different integrating functions"""
bpwl = BrokenPowerLaw(
k_e_test,
p1,
p2,
gamma_b,
gamma_min_test,
gamma_max_test,
integrator=integrator,
)
numerical_integral = bpwl.integral(gamma_low=gamma_min_test,
gamma_up=gamma_max_test,
gamma_power=0)
analytical_integral = broken_power_law_integral(
k_e_test, p1, p2, gamma_b, gamma_min_test, gamma_max_test)
assert u.isclose(numerical_integral,
analytical_integral,
atol=0 * u.Unit("cm-3"),
rtol=1e-2)
def test_from_norm_at_gamma_1(self):
"""test the intialisation of the powerlaw from the normalisation at
gamma = 1"""
norm = 1e-13 * u.Unit("cm-3")
bpwl = BrokenPowerLaw.from_norm_at_gamma_1(
norm=norm,
p1=p1_test,
p2=p2_test,
gamma_b=gamma_b_test,
gamma_min=1,
gamma_max=gamma_max_test,
)
assert u.isclose(norm, bpwl(1), atol=0 * u.Unit("cm-3"), rtol=1e-2)
def test_from_normalised_energy_density(self):
"""test the intialisation of the powerlaw from the total particle
energy density"""
u_e = 3e-4 * u.Unit("erg cm-3")
bpwl = BrokenPowerLaw.from_normalised_energy_density(
u_e=u_e,
p1=p1_test,
p2=p2_test,
gamma_b=gamma_b_test,
gamma_min=gamma_min_test,
gamma_max=gamma_max_test,
)
# calculate u_e
u_e_calc = mec2 * bpwl.integral(
gamma_low=gamma_min_test, gamma_up=gamma_max_test, gamma_power=1)
assert u.isclose(u_e, u_e_calc, atol=0 * u.Unit("erg cm-3"), rtol=1e-2)
def test_from_normalised_density(self):
"""test the intialisation of the broken power law from the total particle
density"""
n_e_tot = 1e-5 * u.Unit("cm-3")
bpwl = BrokenPowerLaw.from_normalised_density(
n_e_tot=n_e_tot,
p1=p1_test,
p2=p2_test,
gamma_b=gamma_b_test,
gamma_min=gamma_min_test,
gamma_max=gamma_max_test,
)
# calculate n_e_tot
n_e_tot_calc = bpwl.integral(gamma_low=gamma_min_test,
gamma_up=gamma_max_test,
gamma_power=0)
assert u.isclose(n_e_tot,
n_e_tot_calc,
atol=0 * u.Unit("cm-3"),
rtol=1e-2)
from agnpy.utils.math import trapz_loglog
from agnpy.utils.conversion import mec2
import pytest
# variables with _test are global and meant to be used in all tests
# global PowerLaw
k_e_test = 1e-13 * u.Unit("cm-3")
p_test = 2.1
gamma_min_test = 10
gamma_max_test = 1e7
pwl_test = PowerLaw(k_e_test, p_test, gamma_min_test, gamma_max_test)
# global BrokenPowerLaw
p1_test = 2.1
p2_test = 3.1
gamma_b_test = 1e3
bpwl_test = BrokenPowerLaw(k_e_test, p1_test, p2_test, gamma_b_test,
gamma_min_test, gamma_max_test)
# global LogParabola
q_test = 0.2
gamma_0_test = 1e4
lp_test = LogParabola(k_e_test, p_test, q_test, gamma_0_test, gamma_min_test,
gamma_max_test)
# global PowerLaw exp Cutoff
gamma_c_test = 1e3
epwl_test = ExpCutoffPowerLaw(k_e_test, p_test, gamma_c_test, gamma_min_test,
gamma_max_test)
def power_law_integral(k_e, p, gamma_min, gamma_max):
"""analytical integral of the power law"""
if np.isclose(p, 1.0):
integral = np.log(gamma_max / gamma_min)