def miscentering(density_model):
return maszcal.lensing.Miscentering(
rho_func=density_model.rho_tot,
misc_distrib=maszcal.stats.MiscenteringDistributions.
rayleigh_dist,
miscentering_func=meso.Rho().miscenter,
)
def miscentering(density_model):
return maszcal.lensing.Miscentering(
rho_func=density_model.rho_tot,
misc_distrib=maszcal.stats.MiscenteringDistributions.
rayleigh_dist,
miscentering_func=meso.Rho(
num_offset_radii=40,
num_phis=10,
).miscenter,
)
def it_takes_a_density_function_and_creates_a_miscentered_version(miscentering):
rs = np.logspace(-2, 2, 30)
param_1 = np.ones(3)
param_2 = np.ones(2)
rho_params = (param_1, param_2)
miscenter_model = meso.Rho()
ul = miscenter_model.max_radius
ll = miscenter_model.min_radius
interval = ul - ll
misc_params = (np.array([1/interval, 1/interval]), np.array([0.5, 0.5]))
rho_cents = rho_with_analytic_result(rs, param_1, param_2)
rho_miscs = miscentering.rho(rs, misc_params, rho_params).squeeze()
analytical_answer = 1/3 * (ll**2 + ul**2 + ul*ll + 3*rs**2)
analytical_answer = analytical_answer[:, None, None] * param_1[None, :, None] * param_2[None, None, :]
analytical_answer = rho_cents/2 + analytical_answer/2
assert np.allclose(rho_miscs, analytical_answer, rtol=1e-3)
def it_matches_a_monte_carlo_miscentered_profile(radial_grid, density,
rng):
rho_func = scipy.interpolate.interp1d(radial_grid,
density,
kind='cubic')
rs = np.geomspace(0.01, 100, 100)
offsets = rng.rayleigh(scale=SCALE, size=NUM_MC)
phis = 2 * np.pi * rng.random(size=NUM_MC)
rho_arg = get_arg(rs, offsets, phis)
idx = np.argwhere(rho_arg < radial_grid.min())
rho_arg = np.delete(rho_arg, idx[:, 1:], axis=1)
plt.hist(
np.log(np.repeat(rs, NUM_MC)),
bins=48,
histtype='stepfilled',
color='black',
alpha=0.8,
label='radius',
)
plt.hist(
np.log(rho_arg).flatten(),
bins=48,
color=COLORS[0],
histtype='stepfilled',
alpha=0.8,
label='miscentered radius',
)
plt.xlabel(r'$\ln(r)$')
plt.ylabel('number')
plt.legend(loc='best')
plt.gcf().set_size_inches(6, 4)
plt.savefig(PLOT_DIR + 'radius_hist.svg', bbox_inches='tight')
plt.gcf().clear()
rhos = rho_func(rs)
rhos_mc = rho_func(rho_arg).mean(axis=(1))
meso_rhos_coarse = meso.Rho(
num_offset_radii=50,
num_phis=4,
).miscenter(rs, rho_func, prob_dist_func=rayleigh_dist)
meso_rhos_medium = meso.Rho(
num_offset_radii=100,
num_phis=12,
).miscenter(rs, rho_func, prob_dist_func=rayleigh_dist)
meso_rhos_fine = meso.Rho(
num_offset_radii=200,
num_phis=36,
).miscenter(rs, rho_func, prob_dist_func=rayleigh_dist)
plt.plot(rs, rhos, color='black', label='centered')
plt.plot(rs,
meso_rhos_coarse,
color=COLORS[1],
alpha=0.8,
linestyle=':',
label='coarse')
plt.plot(rs,
meso_rhos_medium,
color=COLORS[1],
alpha=0.8,
linestyle='--',
label='medium')
plt.plot(rs,
meso_rhos_fine,
color=COLORS[1],
alpha=0.8,
linestyle='-',
label='fine')
plt.plot(rs, rhos_mc, color=COLORS[0], alpha=0.8, label='Monte Carlo')
plt.xscale('log')
plt.yscale('log')
plt.xlabel(r'$r$ (Mpc)')
plt.ylabel(r'$\rho(r)$')
plt.legend(loc='best')
plt.gcf().set_size_inches(6, 4)
plt.savefig(PLOT_DIR + 'rho_comparison.svg', bbox_inches='tight')
plt.gcf().clear()
plt.plot(rs, rs**2 * rhos, color='black', label='centered')
plt.plot(rs,
rs**2 * meso_rhos_coarse,
color=COLORS[1],
alpha=0.8,
linestyle=':',
label='coarse')
plt.plot(rs,
rs**2 * meso_rhos_medium,
color=COLORS[1],
alpha=0.8,
linestyle='--',
label='medium')
plt.plot(rs,
rs**2 * meso_rhos_fine,
color=COLORS[1],
alpha=0.8,
linestyle='-',
label='fine')
plt.plot(rs,
rs**2 * rhos_mc,
color=COLORS[0],
alpha=0.8,
label='Monte Carlo')
plt.xscale('log')
plt.xlabel(r'$r$ (Mpc)')
plt.ylabel(r'$r^2 \rho(r)$')
plt.legend(loc='best')
plt.gcf().set_size_inches(6, 4)
plt.savefig(PLOT_DIR + 'rho_comparison_scaled.svg',
bbox_inches='tight')
plt.gcf().clear()
def miscentering():
return core.Miscentering(
rho_func=rho_with_analytic_result,
misc_distrib=prob_dist_func,
miscentering_func=meso.Rho().miscenter,
)
def miscenter_model():
return meso.Rho()
def miscenter_model():
return meso.Rho(
num_offset_radii=50,
num_phis=4,
)
