def test__f_func_correct_values(self):
Hernquist = l1d.Hernquist(mass=3.4e10,
effective_radius=8.4,
redshift_lens=0.3,
redshift_source=0.8)
f = Hernquist.f_func(x=np.array([0.5, 1.5]))
assert f == pytest.approx(np.array([-0.520691993, 0.2477253115]))
def test_density_values_correct(self):
Hernquist = l1d.Hernquist(mass=3.4e10,
effective_radius=1.8153,
redshift_lens=0.3,
redshift_source=0.8)
rho = Hernquist.density_from_radii(radii=np.array([0.5, 1, 1.5]))
assert rho == pytest.approx(
np.array([3206677372, 676408508, 230880770]), 1e-3)
def test__effective_radius_from_combined_profile(self):
hernquist = l1d.Hernquist(effective_radius=1.0,
mass=100.0,
redshift_source=0.5,
redshift_lens=1.0)
combined = l1d.CombinedProfile(profiles=[hernquist])
assert combined.effective_radius == 1.0
def test__deflection_angle_values_correct(self):
Hernquist = l1d.Hernquist(mass=3.4e10,
effective_radius=1.8153,
redshift_lens=0.3,
redshift_source=0.8)
alpha = Hernquist.deflections_from_radii(radii=np.array([0.5, 1, 1.5]))
assert alpha == pytest.approx(np.array([1.2211165, 0, 1.045731397]),
1e-3)
def test__convergence_at_einstein_radius_less_than_one(self):
Hernquist = l1d.Hernquist(mass=3.4e10,
effective_radius=8.4,
redshift_lens=0.3,
redshift_source=0.8)
radii = np.arange(0.2, 3, 0.002)
kappa_ein = Hernquist.convergence_at_einstein_radius_from_radii(
radii=radii)
assert kappa_ein < 1
def test__hernquist__mass_within_half_mass_radius_equal_to_half_total_three_d_mass(
self):
Hernquist = l1d.Hernquist(mass=3.4e10,
effective_radius=8.4,
redshift_lens=0.3,
redshift_source=0.8)
mass_3d = Hernquist.three_dimensional_mass_enclosed_within_radii(
radii=Hernquist.half_mass_radius)
assert mass_3d == pytest.approx(Hernquist.mass * 0.5, 1e-3)
def test__surface_mass_density_values_correct(self):
Hernquist = l1d.Hernquist(mass=3.4e10,
effective_radius=1.8153,
redshift_lens=0.3,
redshift_source=0.8)
sigma = Hernquist.surface_mass_density_from_radii(
radii=np.array([0.5, 1, 1.5]))
assert sigma == pytest.approx(np.array([4053818282, 0, 682832509]),
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__convergence_equal_to_surface_mass_density_divided_by_sigma_crit(
self):
Hernquist = l1d.Hernquist(mass=3.4e10,
effective_radius=8.4,
redshift_lens=0.3,
redshift_source=0.8)
radii = np.arange(0.2, 3, 0.002)
rho = Hernquist.surface_mass_density_from_radii(radii=radii)
kappa = Hernquist.convergence_from_radii(radii=radii)
kappa_via_sigma = rho / Hernquist.critical_surface_density_of_lens
assert kappa == pytest.approx(kappa_via_sigma, 1e-4)
def test__convergence_values_correct(self):
Hernquist = l1d.Hernquist(mass=3.4e10,
effective_radius=1.8153,
redshift_lens=0.3,
redshift_source=0.8)
kappa = Hernquist.convergence_from_radii(radii=np.array([0.5, 1.5]))
kappa_s = Hernquist.kappa_s
assert kappa == pytest.approx(np.array([1.318168568, 0.2219485564]),
1e-3)
assert kappa_s == pytest.approx(1.758883964, 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__convergence_from_deflections_and_analytic(self):
Hernquist = l1d.Hernquist(mass=3.4e10,
effective_radius=8.4,
redshift_lens=0.3,
redshift_source=0.8)
radii = np.arange(0.2, 3, 0.002)
kappa_analytic = Hernquist.convergence_from_radii(radii=radii)
kappa_from_deflections = convergence_via_deflections_from_profile_and_radii(
profile=Hernquist, radii=radii)
mean_error = np.average(kappa_analytic - kappa_from_deflections)
assert mean_error < 1e-4
def test__convergence_at_einstein_radius_less_than_one(self):
dm = l1d.NFWHilbert(mass_at_200=2.5e12,
redshift_lens=0.3,
redshift_source=1.0)
baryons = l1d.Hernquist(mass=3.4e11,
effective_radius=3.2,
redshift_lens=0.3,
redshift_source=1.0)
combined = l1d.CombinedProfile(profiles=[dm, baryons])
radii = np.arange(0.2, 8, 0.002)
kappa_ein = combined.convergence_at_einstein_radius_from_radii(
radii=radii)
assert kappa_ein < 1
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__deflections_equals_sum_of_individual_profile_deflections(self):
dm = l1d.NFWHilbert(mass_at_200=2.5e14,
redshift_lens=0.3,
redshift_source=1.0)
baryons = l1d.Hernquist(mass=3.4e11,
effective_radius=8.4,
redshift_lens=0.6,
redshift_source=1.2)
combined = l1d.CombinedProfile(profiles=[dm, baryons])
radii = np.arange(0.2, 3, 0.002)
alpha_combined = combined.deflections_from_radii(radii=radii)
alpha_NFW = dm.deflections_from_radii(radii=radii)
alpha_pl = baryons.deflections_from_radii(radii=radii)
assert alpha_combined == pytest.approx(alpha_NFW + alpha_pl, 1e-4)
def test__mean_Hernquist_convergence_within_einstein_radius_equal_to_one(
self):
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)
integrand = lambda r: 2 * np.pi * r * Hernquist.convergence_from_radii(
radii=r)
einstein_radius = Hernquist.einstein_radius_in_kpc_from_radii(
radii=radii)
av_kappa = integrate.quad(
integrand, 0, einstein_radius)[0] / (np.pi * einstein_radius**2)
assert av_kappa == pytest.approx(1, 1e-3)
def test__surface_mass_density_equals_sum_of_individual_profiles(self):
dm = l1d.NFWHilbert(mass_at_200=2.5e14,
redshift_lens=0.3,
redshift_source=1.0)
baryons = l1d.Hernquist(mass=3.4e11,
effective_radius=8.4,
redshift_lens=0.6,
redshift_source=1.2)
combined = l1d.CombinedProfile(profiles=[dm, baryons])
radii = np.arange(0.2, 3, 0.002)
sigma_combined = combined.surface_mass_density_from_radii(radii=radii)
sigma_NFW = dm.surface_mass_density_from_radii(radii=radii)
sigma_pl = baryons.surface_mass_density_from_radii(radii=radii)
sigma_sum = sigma_NFW + sigma_pl
assert sigma_combined == pytest.approx(sigma_sum, 1e-4)
def test__convergence_equals_sum_of_individual_profile_convergence(self):
dm = l1d.NFWHilbert(mass_at_200=2.5e14,
redshift_lens=0.3,
redshift_source=1.0)
baryons = l1d.Hernquist(mass=3.4e11,
effective_radius=8.4,
redshift_lens=0.6,
redshift_source=1.2)
combined = l1d.CombinedProfile(profiles=[dm, baryons])
radii = np.arange(0.2, 3, 0.002)
kappa_combined = combined.convergence_from_radii(radii=radii)
kappa_NFW = dm.convergence_from_radii(radii=radii)
kappa_pl = baryons.convergence_from_radii(radii=radii)
kappa_sum = kappa_NFW + kappa_pl
assert kappa_combined == pytest.approx(kappa_sum, 1e-4)
def test__convergence_from_deflections_and_analytic(self):
dm = l1d.NFWHilbert(mass_at_200=2.5e14,
redshift_lens=0.3,
redshift_source=1.0)
baryons = l1d.Hernquist(mass=3.4e11,
effective_radius=8.4,
redshift_lens=0.6,
redshift_source=1.2)
combined = l1d.CombinedProfile(profiles=[dm, baryons])
radii = np.arange(0.2, 8, 0.002)
kappa_analytic = combined.convergence_from_radii(radii=radii)
kappa_from_deflections = convergence_via_deflections_from_profile_and_radii(
profile=combined, radii=radii)
mean_error = np.average(kappa_analytic - kappa_from_deflections)
assert mean_error < 1e-4
def test__three_d_mass_from_dynamics_slope_and_normalization_equals_analytic(self):
dm = l1d.NFWHilbert(
mass_at_200=2.5e12, redshift_lens=0.3, redshift_source=1.0
)
baryons = l1d.Hernquist(
mass=3.4e11, effective_radius=3.2, redshift_lens=0.3, redshift_source=1.0
)
combined = l1d.CombinedProfile(profiles=[dm, baryons])
radii = np.arange(0.2, 8, 0.002)
fit = l1d.PowerLawFit(profile=combined, mask=None, radii=radii)
rho_0, slope = fit.slope_and_normalisation_via_dynamics()
reff = combined.effective_radius
mdyn = combined.three_dimensional_mass_enclosed_within_effective_radius
mdyn_from_dyn = mass_dynamical(rho0=rho_0, g=slope, Reff=reff * u.kpc)
assert mdyn == pytest.approx(mdyn_from_dyn, 1e-3)
def test__einstein_mass_from_dynamics_slope_and_normalization_equals_analytic(self):
dm = l1d.NFWHilbert(
mass_at_200=2.5e12, redshift_lens=0.3, redshift_source=1.0
)
baryons = l1d.Hernquist(
mass=3.4e11, effective_radius=3.2, redshift_lens=0.3, redshift_source=1.0
)
combined = l1d.CombinedProfile(profiles=[dm, baryons])
radii = np.arange(0.2, 8, 0.002)
fit = l1d.PowerLawFit(profile=combined, mask=None, radii=radii)
rho_0, slope = fit.slope_and_normalisation_via_dynamics()
rein = combined.einstein_radius_in_kpc_from_radii(radii=radii)
mein = combined.einstein_mass_in_solar_masses_from_radii(radii=radii)
mein_from_dyn = mass_einstein(rho0=rho_0, g=slope, Rein=rein * u.kpc)
assert mein == pytest.approx(mein_from_dyn, 1e-3)
def test__mean_combined_convergence_within_einstein_radius_equal_to_one(
self):
nfw = l1d.NFWHilbert(mass_at_200=2.5e13,
redshift_lens=0.5,
redshift_source=1.0)
Hernquist = l1d.Hernquist(mass=2e11,
effective_radius=5,
redshift_lens=0.5,
redshift_source=1.0)
combined = l1d.CombinedProfile([nfw, Hernquist])
radii = np.arange(0.1, 8, 0.001)
einstein_radius = combined.einstein_radius_in_kpc_from_radii(
radii=radii)
integrand = lambda r: 2 * np.pi * r * combined.convergence_from_radii(
radii=r)
av_kappa = integrate.quad(
integrand, 0, einstein_radius)[0] / (np.pi * einstein_radius**2)
assert av_kappa == pytest.approx(1, 1e-3)
import matplotlib.pyplot as plt
import numpy as np
import lens1d as l1d
from astropy import cosmology
cosmo = cosmology.Planck15
fig_path = "/Users/dgmt59/Documents/Plots/1D/"
radii = np.arange(0.01, 50, 0.001)
hernquist = l1d.Hernquist(mass=10**11.21,
effective_radius=5.68,
redshift_lens=0.351,
redshift_source=1.071)
total = l1d.CombinedProfile.from_hernquist_and_dark_matter_fraction_within_effective_radius(
hernquist=hernquist, dark_matter_fraction=0.4)
kappa_total = total.convergence_from_radii(radii=radii)
fig1 = plt.figure(1)
plt.loglog(radii, kappa_total, label="total")
plt.legend()
plt.show()
import matplotlib.pyplot as plt
import os
import numpy as np
import pandas as pd
import lens1d as l1d
fig_path = "/Users/dgmt59/Documents/Plots/one_d_slacs/"
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)
"slacs1143-0144",
"slacs1250+0523",
# 'slacs1432+6317',
"slacs2238-0754",
"slacs2341+0000",
])
lens_name_check = np.array(["slacs0912+0029"])
for lens in lens_name:
f = open(f"{lens}_mass_test_1d", "w")
for mass in masses:
baryons = l1d.Hernquist(
mass=10**mass,
effective_radius=slacs["R_eff"][lens],
redshift_lens=slacs["z_lens"][lens],
redshift_source=slacs["z_source"][lens],
)
DM = l1d.NFWHilbert(
mass_at_200=slacs["M200"][lens],
redshift_lens=slacs["z_lens"][lens],
redshift_source=slacs["z_source"][lens],
)
true_profile = l1d.CombinedProfile(profiles=[baryons, DM])
mask_einstein_radius = true_profile.mask_einstein_radius_from_radii(
width=5, radii=radii)
fit_mask = l1d.PowerLawFit(profile=true_profile,
radii=radii,
import matplotlib.pyplot as plt
import os
import numpy as np
import pandas as pd
import lens1d as l1d
fig_path = "/Users/dgmt59/Documents/Plots/one_d_slacs/"
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)
"slacs1143-0144",
"slacs1250+0523",
# 'slacs1432+6317',
"slacs2238-0754",
"slacs2341+0000",
])
radii = np.arange(0.01, 100, 0.001)
f = open("slacs_like_test_f_dm", "w")
for i in range(len(lens_name)):
baryons = l1d.Hernquist(
mass=10**(slacs["log[M*/M]_chab"][lens_name[i]]),
effective_radius=slacs["R_eff"][lens_name[i]],
redshift_lens=slacs["z_lens"][lens_name[i]],
redshift_source=slacs["z_source"][lens_name[i]],
)
true_profile = l1d.CombinedProfile.from_hernquist_and_dark_matter_fraction_within_effective_radius(
hernquist=baryons,
dark_matter_fraction=slacs["f_dm_chab"][lens_name[i]])
mask_einstein_radius = true_profile.mask_einstein_radius_from_radii(
width=5, radii=radii)
fit_mask = l1d.PowerLawFit(profile=true_profile,
radii=radii,
mask=mask_einstein_radius)
fit_no_mask = l1d.PowerLawFit(profile=true_profile, radii=radii, mask=None)
