def test__convergence_values_correct(self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.4,
slope=1.6,
redshift_source=0.8,
redshift_lens=0.3)
kappa = power_law.convergence_from_radii(radii=np.array([0.5, 1, 1.5]))
assert kappa == pytest.approx(np.array([1.298, 0.857, 0.672]), 1e-3)
def test__critical_surface_mass_density_correct_value(self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.8,
slope=1.7,
redshift_source=0.8,
redshift_lens=0.3)
sigma_crit = power_law.critical_surface_density_of_lens
assert sigma_crit == pytest.approx(3076534993.9914, 1e-4)
def test__deflection_angle_values_correct(self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.4,
slope=1.6,
redshift_source=0.8,
redshift_lens=0.3)
alpha = power_law.deflections_from_radii(radii=np.array([0.5, 1, 1.5]))
assert alpha == pytest.approx(np.array([0.927, 1.224, 1.439]), 1e-3)
def test__density_values_correct(self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.4,
slope=1.6,
redshift_source=0.8,
redshift_lens=0.3)
sigma = power_law.density_from_radii(radii=np.array([0.5, 1, 1.5]))
assert sigma == pytest.approx(
np.array([9326310116, 3076534994, 1608110342]), 1e-3)
def test__slope_equal_to_power_law_input(self):
power_law = l1d.SphericalPowerLaw(
einstein_radius=1.8, slope=2, redshift_source=0.8, redshift_lens=0.3
)
radii = np.arange(0.2, 3, 0.002)
fit = l1d.PowerLawFit(profile=power_law, mask=None, radii=radii)
slope_lensing = fit.slope_via_lensing()
assert slope_lensing == pytest.approx(power_law.slope, 1e-4)
def test__convergence_at_einstein_radius_less_than_one(self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.8,
slope=2,
redshift_source=0.8,
redshift_lens=0.3)
radii = np.arange(0.2, 3, 0.002)
kappa_ein = power_law.convergence_at_einstein_radius_from_radii(
radii=radii)
assert kappa_ein < 1
def test__xi_two_equal_to_zero_for_sis(self):
power_law = l1d.SphericalPowerLaw(
einstein_radius=1.8, slope=2, redshift_source=0.8, redshift_lens=0.3
)
radii = np.arange(0.2, 3, 0.002)
fit = l1d.PowerLawFit(profile=power_law, mask=None, radii=radii)
xi_two = fit.xi_two()
assert xi_two == pytest.approx(0, 1e-3)
def test__surface_mass_density_values_correct(self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.4,
slope=1.6,
redshift_source=0.8,
redshift_lens=0.3)
sigma = power_law.surface_mass_density_from_radii(
radii=np.array([0.5, 1, 1.5]))
assert sigma == pytest.approx(
np.array([3994429111, 2635340405, 2066245712]), 1e-3)
def test__average_density_inside_einstein_radius_equal_to_sigma_crit(self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.8,
slope=1.7,
redshift_source=0.8,
redshift_lens=0.3)
sigma_crit = power_law.critical_surface_density_of_lens
integrand = (lambda r: 2 * np.pi * r * power_law.
surface_mass_density_from_radii(radii=r))
av_density = integrate.quad(integrand, 0,
power_law.einstein_radius)[0] / (
np.pi * power_law.einstein_radius**2)
assert av_density == pytest.approx(sigma_crit, 1e-3)
Hernquist = l1d.Hernquist(mass=3.4e11,
effective_radius=8.4,
redshift_lens=0.6,
redshift_source=1.2)
radii = np.arange(0.01, 10, 0.001)
einstein_radius = Hernquist.einstein_radius_in_kpc_from_radii(
radii=radii)
sigma_crit = Hernquist.critical_surface_density_of_lens
integrand = (lambda r: 2 * np.pi * r * Hernquist.
surface_mass_density_from_radii(radii=r))
av_density = integrate.quad(
integrand, 0, einstein_radius)[0] / (np.pi * einstein_radius**2)
assert av_density == pytest.approx(sigma_crit, 1e-3)
nfw = l1d.NFWHilbert(mass_at_200=2.5e13,
redshift_lens=0.6,
redshift_source=1.2)
radii = np.arange(0.01, 3, 0.001)
einstein_radius = nfw.einstein_radius_in_kpc_from_radii(radii=radii)
sigma_crit = nfw.critical_surface_density_of_lens
integrand = (lambda r: 2 * np.pi * r * nfw.
surface_mass_density_from_radii(radii=r))
av_density = integrate.quad(
integrand, 0, einstein_radius)[0] / (np.pi * einstein_radius**2)
assert av_density == pytest.approx(sigma_crit, 1e-3)
def test__tangential_eigenvalue_equal_to_from_alpha(self):
radii = np.arange(0.2, 3, 0.001)
power_law = l1d.SphericalPowerLaw(einstein_radius=1.8,
slope=1.8,
redshift_source=0.8,
redshift_lens=0.3)
eigenvalue = power_law.tangential_eigenvalue_from_radii(radii=radii)
alpha = power_law.deflections_from_radii(radii=radii)
eigenvalue_alpha = 1 - alpha / radii
mean_error = np.mean(eigenvalue_alpha - eigenvalue)
assert mean_error < 1e-4
nfw = l1d.NFWHilbert(mass_at_200=2.5e12,
redshift_lens=0.3,
redshift_source=0.8)
radii = np.arange(0.2, 3, 0.002)
eigenvalue = nfw.tangential_eigenvalue_from_radii(radii=radii)
alpha = nfw.deflections_from_radii(radii=radii)
eigenvalue_alpha = 1 - alpha / radii
mean_error = np.mean(eigenvalue_alpha - eigenvalue)
assert mean_error < 1e-4
Hernquist = l1d.Hernquist(mass=3.4e10,
effective_radius=1.8153,
redshift_lens=0.3,
redshift_source=0.8)
radii = np.arange(0.2, 3, 0.002)
eigenvalue = Hernquist.tangential_eigenvalue_from_radii(radii=radii)
alpha = Hernquist.deflections_from_radii(radii=radii)
eigenvalue_alpha = 1 - alpha / radii
mean_error = np.mean(eigenvalue_alpha - eigenvalue)
assert mean_error < 1e-4
def test__shear_isothermal_sphere_equals_analytic(self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.8,
slope=2,
redshift_source=0.8,
redshift_lens=0.3)
radii = np.arange(0.2, 3, 0.002)
shear_isothermal = power_law.shear_from_radii(radii=radii)
shear_isothermal_analytic = power_law.einstein_radius / (2 * radii)
mean_error = np.average(shear_isothermal - shear_isothermal_analytic)
assert mean_error < 1e-4
def test__shear_isothermal_sphere_equals_convergence(self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.8,
slope=2,
redshift_source=0.8,
redshift_lens=0.3)
radii = np.arange(0.2, 3, 0.002)
shear_isothermal = power_law.shear_from_radii(radii=radii)
kappa_isothermal = power_law.convergence_from_radii(radii=radii)
mean_error = np.average(shear_isothermal - kappa_isothermal)
assert mean_error < 1e-4
def test__convergence_from_deflections_and_analytic(self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.8,
slope=1.7,
redshift_source=0.8,
redshift_lens=0.3)
radii = np.arange(0.2, 3, 0.002)
kappa_analytic = power_law.convergence_from_radii(radii=radii)
kappa_from_deflections = convergence_via_deflections_from_profile_and_radii(
profile=power_law, radii=radii)
mean_error = np.average(kappa_analytic - kappa_from_deflections)
assert mean_error < 1e-4
def test__convergence_isothermal_equal_to_analytic_formula(self):
isothermal = l1d.SphericalPowerLaw(einstein_radius=1,
slope=2,
redshift_source=0.8,
redshift_lens=0.3)
radii = np.arange(0.2, 3, 0.002)
kappa_isothermal = isothermal.convergence_from_radii(radii=radii)
kappa_isothermal_analytic = np.divide(1 * isothermal.einstein_radius,
2 * radii)
assert kappa_isothermal == pytest.approx(kappa_isothermal_analytic,
1e-4)
def test__isoyhemral_tangential_eigenvalue_equal_to_zero_at_einstein_radius(
self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.8,
slope=2,
redshift_source=0.8,
redshift_lens=0.3)
radii = np.arange(0.2, 3, 0.002)
eigenvalue = power_law.tangential_eigenvalue_from_radii(radii=radii)
index = np.argmin(np.abs(np.array(radii) - power_law.einstein_radius))
assert eigenvalue[index] < 1e-4
def test__mean_power_law_convergence_within_einstein_radius_equal_to_one(
self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.8,
slope=2.3,
redshift_source=0.8,
redshift_lens=0.3)
integrand = lambda r: 2 * np.pi * r * power_law.convergence_from_radii(
radii=r)
av_kappa = integrate.quad(integrand, 0,
power_law.einstein_radius)[0] / (
np.pi * power_law.einstein_radius**2)
assert av_kappa == pytest.approx(1, 1e-3)
def test__convergence_equals_surface_mass_density_divided_by_sigma_crit(
self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.8,
slope=1.7,
redshift_source=0.8,
redshift_lens=0.3)
radii = np.arange(0.2, 3, 0.002)
kappa = power_law.convergence_from_radii(radii=radii)
sigma_crit = power_law.critical_surface_density_of_lens
rho = power_law.surface_mass_density_from_radii(radii=radii)
kappa_via_sigma = rho / sigma_crit
assert kappa == pytest.approx(kappa_via_sigma, 1e-3)
def test__mass_inside_einstein_radius_equal_to_einstein_mass(self):
power_law = l1d.SphericalPowerLaw(einstein_radius=1.8,
slope=1.7,
redshift_source=0.8,
redshift_lens=0.3)
radii = np.arange(0.2, 3, 0.002)
einstein_mass = power_law.einstein_mass_in_solar_masses_from_radii(
radii=radii)
mass_within_r_ein = power_law.two_dimensional_mass_enclosed_within_radii(
power_law.einstein_radius)
assert einstein_mass == pytest.approx(mass_within_r_ein, 1e-4)
Hernquist = l1d.Hernquist(mass=3.4e11,
effective_radius=8.4,
redshift_lens=0.6,
redshift_source=1.2)
radii = np.arange(0.2, 100, 0.001)
einstein_radius = Hernquist.einstein_radius_in_kpc_from_radii(
radii=radii)
einstein_mass = Hernquist.einstein_mass_in_solar_masses_from_radii(
radii=radii)
mass_within_r_ein = Hernquist.two_dimensional_mass_enclosed_within_radii(
einstein_radius)
assert einstein_mass == pytest.approx(mass_within_r_ein, 1e-3)
nfw = l1d.NFWHilbert(mass_at_200=2.5e13,
redshift_lens=0.6,
redshift_source=1.2)
radii = np.arange(0.01, 3, 0.001)
einstein_radius = nfw.einstein_radius_in_kpc_from_radii(radii=radii)
einstein_mass = nfw.einstein_mass_in_solar_masses_from_radii(
radii=radii)
mass_within_r_ein = nfw.two_dimensional_mass_enclosed_within_radii(
einstein_radius)
assert einstein_mass == pytest.approx(mass_within_r_ein, 1e-3)
def test__compare_to_autogalaxy__sigma_crit_equal_in_desired_units(self):
cosmo = cosmology.Planck15
power_law = l1d.SphericalPowerLaw(einstein_radius=1.4,
slope=1.6,
redshift_source=0.8,
redshift_lens=0.3)
sigma_crit = power_law.critical_surface_density_of_lens
autolens_sigma_crit = ag.util.cosmology.critical_surface_density_between_redshifts_from(
redshift_1=0.8,
redshift_0=0.3,
unit_length="kpc",
unit_mass="solMass",
cosmology=cosmo,
)
assert sigma_crit == pytest.approx(autolens_sigma_crit, 1e-4)
baryons = l1d.Hernquist(mass=10**11.4,
effective_radius=5.4,
redshift_lens=0.232,
redshift_source=1.3)
baryons_mass = l1d.Hernquist(mass=10**12.9,
effective_radius=1.1,
redshift_lens=0.3,
redshift_source=0.8)
DM = l1d.NFWHilbert(mass_at_200=2.31e13,
redshift_lens=0.3,
redshift_source=0.8)
isothermal = l1d.SphericalPowerLaw(einstein_radius=1.4,
slope=2.0,
redshift_lens=0.3,
redshift_source=0.8)
no_bh = l1d.SphericalPowerLaw(einstein_radius=1.4,
slope=3.0,
redshift_lens=0.3,
redshift_source=0.8)
DM_cored = l1d.generalisedNFW(mass_at_200=1.21e13,
beta=1.9,
redshift_lens=0.3,
redshift_source=0.8)
print(DM.scale_radius)
radii = np.arange(0.4, 100, 0.001)
baryons = l1d.Hernquist(mass=10**11.53,
effective_radius=8.4,
redshift_lens=0.232,
redshift_source=1.3)
baryons_mass = l1d.Hernquist(mass=10**11.53,
effective_radius=8.4,
redshift_lens=0.232,
redshift_source=1.3)
DM = l1d.NFWHilbert(mass_at_200=1.5e12,
redshift_lens=0.232,
redshift_source=1.3)
isothermal = l1d.SphericalPowerLaw(einstein_radius=1.5,
slope=2.0,
redshift_lens=0.132,
redshift_source=1.3)
DM_cored = l1d.generalisedNFW(mass_at_200=1.5e12,
beta=1.6,
redshift_lens=0.232,
redshift_source=1.3)
print(DM.scale_radius)
radii = np.arange(0.2, 200, 0.001)
true_profile = l1d.CombinedProfile(profiles=[baryons, DM])
true_profile_cored = l1d.CombinedProfile(profiles=[baryons_mass, DM_cored])
einstein_radius = true_profile.einstein_radius_in_kpc_from_radii(radii=radii)