def setup(self):
cosmo = Cosmology()
mlow = 10**6
mhigh = 10**10
zlens = 0.5
zsource = 1.5
cone_opening_angle = 6.
m_pivot = 10**8
mass_function_model = 'sheth99'
use_lookup_table = True
geometry_type = 'DOUBLE_CONE'
self.lmf_lookup_ShethTormen = LensingMassFunction(
cosmo, zlens, zsource, mlow, mhigh, cone_opening_angle, m_pivot,
mass_function_model, use_lookup_table, geometry_type)
use_lookup_table = False
self.lmf_no_lookup_ShethTormen = LensingMassFunction(
cosmo, zlens, zsource, mlow, mhigh, cone_opening_angle, m_pivot,
mass_function_model, use_lookup_table, geometry_type)
self._m = np.logspace(6., 10, 50)
self.cosmo = cosmo
self.cone_opening_angle = cone_opening_angle
def build_LOS_mass_function(self, args):
if self.halo_mass_function is None:
if 'log_mlow_los' not in args.keys():
logLOS_mlow = realization_default.log_mlow
else:
logLOS_mlow = args['log_mlow_los']
if 'log_mhigh_los' not in args.keys():
logLOS_mhigh = realization_default.log_mhigh
else:
logLOS_mhigh = args['log_mhigh_los']
if 'mass_function_model' not in self._halo_mass_function_args.keys(
):
self._halo_mass_function_args.update({
'mass_function_model':
cosmo_default.default_mass_function
})
self.halo_mass_function = LensingMassFunction(
self.cosmology,
self.zlens,
self.zsource,
10**logLOS_mlow,
10**logLOS_mhigh,
cone_opening_angle=args['cone_opening_angle'],
**self._halo_mass_function_args)
return self.halo_mass_function
def setup(self):
zlens, zsource = 0.5, 2.
zmin = 0.01
zmax = 1.98
log_mlow = 6.
log_mhigh = 9.
host_m200 = 10**13
LOS_normalization = 1.
draw_poisson = False
log_mass_sheet_min = 7.
log_mass_sheet_max = 10.
kappa_scale = 1.
delta_power_law_index = -0.17
delta_power_law_index_coupling = 0.5
cone_opening_angle = 6.
m_pivot = 10**8
sigma_sub = 0.1
power_law_index = -1.9
subhalo_spatial_distribution = 'HOST_NFW'
kwargs_suppression = {'c_scale': 10.5, 'c_power': -0.2}
suppression_model = 'polynomial'
kwargs_cdm = {
'zmin': zmin,
'zmax': zmax,
'log_mc': None,
'log_mlow': log_mlow,
'sigma_sub': sigma_sub,
'kwargs_suppression': kwargs_suppression,
'suppression_model': suppression_model,
'a_wdm': None,
'b_wdm': None,
'c_wdm': None,
'c_scatter_dex': 0.2,
'log_mhigh': log_mhigh,
'host_m200': host_m200,
'LOS_normalization': LOS_normalization,
'draw_poisson': draw_poisson,
'subhalo_spatial_distribution': subhalo_spatial_distribution,
'log_mass_sheet_min': log_mass_sheet_min,
'log_mass_sheet_max': log_mass_sheet_max,
'kappa_scale': kappa_scale,
'power_law_index': power_law_index,
'delta_power_law_index': delta_power_law_index,
'delta_power_law_index_coupling': delta_power_law_index_coupling,
'm_pivot': m_pivot,
'cone_opening_angle': cone_opening_angle,
'subhalo_mass_sheet_scale': 1.,
'subhalo_convergence_correction_profile': 'NFW',
'r_tidal': '0.5Rs',
'mass_function_LOS_type': 'POWER_LAW'
}
kwargs_wdm = deepcopy(kwargs_cdm)
log_mc = 7.3
a_wdm = 0.8
b_wdm = 1.1
c_wdm = -1.2
kwargs_wdm['log_mc'] = log_mc
kwargs_wdm['a_wdm'] = a_wdm
kwargs_wdm['b_wdm'] = b_wdm
kwargs_wdm['c_wdm'] = c_wdm
kwargs_wdm['kwargs_suppression'] = kwargs_suppression
kwargs_wdm['suppression_model'] = suppression_model
kwargs_no_sheet = deepcopy(kwargs_cdm)
kwargs_no_sheet['mass_function_LOS_type'] = 'DELTA'
kwargs_no_sheet['mass_fraction'] = 0.1
kwargs_no_sheet['logM'] = 6.
lens_plane_redshifts = np.append(np.arange(0.01, 0.5, 0.02),
np.arange(0.5, 1.5, 0.02))
delta_zs = []
for i in range(0, len(lens_plane_redshifts) - 1):
delta_zs.append(lens_plane_redshifts[i + 1] -
lens_plane_redshifts[i])
delta_zs.append(1.5 - lens_plane_redshifts[-1])
cosmo = Cosmology()
self.lens_plane_redshifts = lens_plane_redshifts
self.delta_zs = delta_zs
self.halo_mass_function = LensingMassFunction(
cosmo,
0.5,
1.5,
kwargs_cdm['log_mlow'],
kwargs_cdm['log_mhigh'],
6.,
m_pivot=kwargs_cdm['m_pivot'],
geometry_type='DOUBLE_CONE')
self.geometry = Geometry(cosmo, 0.5, 1.5, 6., 'DOUBLE_CONE')
self.lens_cosmo = LensCosmo(zlens, zsource, cosmo)
self.kwargs_cdm = kwargs_cdm
self.kwargs_wdm = kwargs_wdm
self.kwargs_no_sheet = kwargs_no_sheet
def setup(self):
zlens, zsource = 0.5, 2.
zmin = 0.01
zmax = 1.98
log_mlow = 6.
log_mhigh = 9.
host_m200 = 10**13
LOS_normalization = 1.
draw_poisson = False
log_mass_sheet_min = 7.
log_mass_sheet_max = 10.
kappa_scale = 1.
delta_power_law_index = -0.1
delta_power_law_index_coupling = 0.5
cone_opening_angle = 6.
m_pivot = 10**8
sigma_sub = 0.1
power_law_index = -1.9
subhalo_spatial_distribution = 'HOST_NFW'
kwargs_cdm = {
'zmin': zmin,
'zmax': zmax,
'log_mc': None,
'log_mlow': log_mlow,
'sigma_sub': sigma_sub,
'c_scale': None,
'c_power': None,
'a_wdm': None,
'b_wdm': None,
'c_wdm': None,
'c_scatter_dex': 0.2,
'log_mhigh': log_mhigh,
'mdef_los': 'TNFW',
'host_m200': host_m200,
'LOS_normalization': LOS_normalization,
'draw_poisson': draw_poisson,
'subhalo_spatial_distribution': subhalo_spatial_distribution,
'log_mass_sheet_min': log_mass_sheet_min,
'log_mass_sheet_max': log_mass_sheet_max,
'kappa_scale': kappa_scale,
'power_law_index': power_law_index,
'delta_power_law_index': delta_power_law_index,
'delta_power_law_index_coupling': delta_power_law_index_coupling,
'm_pivot': m_pivot,
'cone_opening_angle': cone_opening_angle,
'subhalo_mass_sheet_scale': 1.,
'subhalo_convergence_correction_profile': 'NFW',
'r_tidal': '0.5Rs'
}
pyhalo = pyHalo(zlens, zsource)
self.realization_cdm = pyhalo.render(['TWO_HALO'], kwargs_cdm)[0]
lens_plane_redshifts, delta_zs = pyhalo.lens_plane_redshifts(
kwargs_cdm)
cosmo = Cosmology()
self.lens_plane_redshifts = lens_plane_redshifts
self.delta_zs = delta_zs
self.halo_mass_function = LensingMassFunction(
cosmo,
zlens,
zsource,
kwargs_cdm['log_mlow'],
kwargs_cdm['log_mhigh'],
kwargs_cdm['cone_opening_angle'],
m_pivot=kwargs_cdm['m_pivot'],
geometry_type='DOUBLE_CONE')
self.geometry = Geometry(cosmo, zlens, zsource,
kwargs_cdm['cone_opening_angle'],
'DOUBLE_CONE')
self.lens_cosmo = LensCosmo(zlens, zsource, cosmo)
self.kwargs_cdm = kwargs_cdm
self.rendering_class = TwoHaloContribution(
kwargs_cdm, self.halo_mass_function, self.geometry,
self.lens_cosmo, self.lens_plane_redshifts, self.delta_zs)
class TestLOS(object):
def setup(self):
zlens, zsource = 0.5, 2.
zmin = 0.01
zmax = 1.98
log_mlow = 6.
log_mhigh = 9.
host_m200 = 10**13
LOS_normalization = 1.
draw_poisson = False
log_mass_sheet_min = 7.
log_mass_sheet_max = 10.
kappa_scale = 1.
delta_power_law_index = -0.1
delta_power_law_index_coupling = 0.5
cone_opening_angle = 6.
m_pivot = 10**8
sigma_sub = 0.1
power_law_index = -1.9
subhalo_spatial_distribution = 'HOST_NFW'
kwargs_cdm = {
'zmin': zmin,
'zmax': zmax,
'log_mc': None,
'log_mlow': log_mlow,
'sigma_sub': sigma_sub,
'c_scale': None,
'c_power': None,
'a_wdm': None,
'b_wdm': None,
'c_wdm': None,
'c_scatter_dex': 0.2,
'log_mhigh': log_mhigh,
'mdef_los': 'TNFW',
'host_m200': host_m200,
'LOS_normalization': LOS_normalization,
'draw_poisson': draw_poisson,
'subhalo_spatial_distribution': subhalo_spatial_distribution,
'log_mass_sheet_min': log_mass_sheet_min,
'log_mass_sheet_max': log_mass_sheet_max,
'kappa_scale': kappa_scale,
'power_law_index': power_law_index,
'delta_power_law_index': delta_power_law_index,
'delta_power_law_index_coupling': delta_power_law_index_coupling,
'm_pivot': m_pivot,
'cone_opening_angle': cone_opening_angle,
'subhalo_mass_sheet_scale': 1.,
'subhalo_convergence_correction_profile': 'NFW',
'r_tidal': '0.5Rs'
}
pyhalo = pyHalo(zlens, zsource)
self.realization_cdm = pyhalo.render(['TWO_HALO'], kwargs_cdm)[0]
lens_plane_redshifts, delta_zs = pyhalo.lens_plane_redshifts(
kwargs_cdm)
cosmo = Cosmology()
self.lens_plane_redshifts = lens_plane_redshifts
self.delta_zs = delta_zs
self.halo_mass_function = LensingMassFunction(
cosmo,
zlens,
zsource,
kwargs_cdm['log_mlow'],
kwargs_cdm['log_mhigh'],
kwargs_cdm['cone_opening_angle'],
m_pivot=kwargs_cdm['m_pivot'],
geometry_type='DOUBLE_CONE')
self.geometry = Geometry(cosmo, zlens, zsource,
kwargs_cdm['cone_opening_angle'],
'DOUBLE_CONE')
self.lens_cosmo = LensCosmo(zlens, zsource, cosmo)
self.kwargs_cdm = kwargs_cdm
self.rendering_class = TwoHaloContribution(
kwargs_cdm, self.halo_mass_function, self.geometry,
self.lens_cosmo, self.lens_plane_redshifts, self.delta_zs)
def test_norm_slope(self):
delta_z = self.delta_zs[1]
norm, slope = self.rendering_class._norm_slope(self.lens_cosmo.z_lens,
delta_z)
slope_theory = self.halo_mass_function.plaw_index_z(
self.lens_cosmo.z_lens) + self.kwargs_cdm['delta_power_law_index']
npt.assert_almost_equal(slope, slope_theory)
norm_theory_background = self.halo_mass_function.norm_at_z_density(
self.lens_cosmo.z_lens, slope, self.kwargs_cdm['m_pivot'])
norm_theory_background *= self.geometry.volume_element_comoving(
self.lens_cosmo.z_lens, delta_z)
rmax = self.lens_cosmo.cosmo.D_C_transverse(self.lens_cosmo.z_lens + delta_z) - \
self.lens_cosmo.cosmo.D_C_transverse(self.lens_cosmo.z_lens)
boost = self.halo_mass_function.two_halo_boost(
self.kwargs_cdm['host_m200'], self.lens_cosmo.z_lens, rmax=rmax)
norm_theory = (boost - 1) * norm_theory_background
npt.assert_almost_equal(norm_theory, norm)
def test_rendering(self):
m = self.rendering_class.render_masses_at_z(self.lens_cosmo.z_lens,
0.02)
npt.assert_equal(True, len(m) > 0)
npt.assert_raises(Exception, self.rendering_class.render_masses_at_z,
0.9, 0.02)
x, y = self.rendering_class.render_positions_at_z(
self.lens_cosmo.z_lens, 10000)
rmax = np.max(np.hypot(x, y))
rmax_theory = 0.5 * self.kwargs_cdm[
'cone_opening_angle'] * self.geometry.rendering_scale(
self.lens_cosmo.z_lens)
npt.assert_array_less(rmax, rmax_theory)
x, y = self.rendering_class.render_positions_at_z(
self.lens_cosmo.z_lens, 0)
npt.assert_equal(True, len(x) == 0)
m, x, y, r3, redshifts, flag = self.rendering_class.render()
npt.assert_equal(len(m), len(x))
npt.assert_equal(len(y), len(r3))
n = 0
for z in np.unique(redshifts):
n += np.sum(redshifts == z)
npt.assert_equal(True, n == len(m))
npt.assert_equal(True, len(self.realization_cdm.halos) == len(m))
def test_convergence_correction(self):
kwargs_out, profile_names_out, redshifts = self.rendering_class.convergence_sheet_correction(
)
npt.assert_equal(0, len(kwargs_out))
npt.assert_equal(0, len(profile_names_out))
npt.assert_equal(0, len(redshifts))
def test_keys_convergence_sheets(self):
keywords_out = self.rendering_class.keys_convergence_sheets()
npt.assert_equal(len(keywords_out), 0)
def test_keys_rendering(self):
keywords_out = self.rendering_class.keyword_parse_render(
self.kwargs_cdm)
required_keys = [
'log_mlow', 'log_mhigh', 'host_m200', 'LOS_normalization',
'draw_poisson', 'delta_power_law_index', 'm_pivot', 'log_mc',
'a_wdm', 'b_wdm', 'c_wdm'
]
for x in required_keys:
npt.assert_equal(x in keywords_out.keys(), True)
kw_cdm = deepcopy(self.kwargs_cdm)
kw_cdm['log_mc'] = None
keywords_out = self.rendering_class.keyword_parse_render(kw_cdm)
npt.assert_equal(keywords_out['a_wdm'] is None, True)
npt.assert_equal(keywords_out['b_wdm'] is None, True)
npt.assert_equal(keywords_out['c_wdm'] is None, True)
def setup(self):
zlens, zsource = 0.5, 2.
zmin = 0.01
zmax = 1.98
log_mlow = 6.
log_mhigh = 9.
host_m200 = 10**13
LOS_normalization = 100.
draw_poisson = False
log_mass_sheet_min = 7.
log_mass_sheet_max = 10.
kappa_scale = 1.
delta_power_law_index = -0.17
delta_power_law_index_coupling = 0.7
cone_opening_angle = 6.
m_pivot = 10**8
sigma_sub = 0.6
power_law_index = -1.8
subhalo_spatial_distribution = 'HOST_NFW'
kwargs_cdm = {
'zmin': zmin,
'zmax': zmax,
'log_mc': None,
'log_mlow': log_mlow,
'sigma_sub': sigma_sub,
'c_scale': None,
'c_power': None,
'a_wdm': None,
'b_wdm': None,
'c_wdm': None,
'c_scatter_dex': 0.2,
'log_mhigh': log_mhigh,
'host_m200': host_m200,
'LOS_normalization': LOS_normalization,
'draw_poisson': draw_poisson,
'subhalo_spatial_distribution': subhalo_spatial_distribution,
'log_mass_sheet_min': log_mass_sheet_min,
'log_mass_sheet_max': log_mass_sheet_max,
'kappa_scale': kappa_scale,
'power_law_index': power_law_index,
'delta_power_law_index': delta_power_law_index,
'delta_power_law_index_coupling': delta_power_law_index_coupling,
'm_pivot': m_pivot,
'cone_opening_angle': cone_opening_angle,
'subhalo_mass_sheet_scale': 1.,
'subhalo_convergence_correction_profile': 'NFW',
'r_tidal': '0.5Rs',
'mdef_subs': 'TNFW',
'mdef_los': 'TNFW'
}
kwargs_wdm = deepcopy(kwargs_cdm)
log_mc = 7.1
a_wdm = 1.
b_wdm = 0.8
c_wdm = -1.3
kwargs_wdm['log_mc'] = log_mc
kwargs_wdm['a_wdm'] = a_wdm
kwargs_wdm['b_wdm'] = b_wdm
kwargs_wdm['c_wdm'] = c_wdm
kwargs_wdm['c_scale'] = 60.
kwargs_wdm['c_power'] = -0.17
pyhalo = pyHalo(zlens, zsource)
lens_plane_redshifts, delta_zs = pyhalo.lens_plane_redshifts(
kwargs_cdm)
cosmo = Cosmology()
self.lens_plane_redshifts = lens_plane_redshifts
self.delta_zs = delta_zs
self.halo_mass_function = LensingMassFunction(
cosmo,
zlens,
zsource,
kwargs_cdm['log_mlow'],
kwargs_cdm['log_mhigh'],
kwargs_cdm['cone_opening_angle'],
m_pivot=kwargs_cdm['m_pivot'],
geometry_type='DOUBLE_CONE',
use_lookup_table=True)
self.geometry = Geometry(cosmo, zlens, zsource,
kwargs_cdm['cone_opening_angle'],
'DOUBLE_CONE')
self.lens_cosmo = LensCosmo(zlens, zsource, cosmo)
self.kwargs_cdm = kwargs_cdm
self.kwargs_wdm = kwargs_wdm
pyhalo = pyHalo(zlens, zsource)
model_list_field = ['LINE_OF_SIGHT']
model_list_sub = ['SUBHALOS']
self.realization_cdm = pyhalo.render(model_list_sub + model_list_field,
kwargs_cdm)[0]
self.realization_cdm_field = pyhalo.render(model_list_field,
kwargs_cdm)[0]
self.realization_wdm_field = pyhalo.render(model_list_field,
kwargs_wdm)[0]
self.realization_wdm_subhalos = pyhalo.render(model_list_sub,
kwargs_wdm)[0]
class TestRenderedPopulations(object):
def setup(self):
zlens, zsource = 0.5, 2.
zmin = 0.01
zmax = 1.98
log_mlow = 6.
log_mhigh = 9.
host_m200 = 10**13
LOS_normalization = 100.
draw_poisson = False
log_mass_sheet_min = 7.
log_mass_sheet_max = 10.
kappa_scale = 1.
delta_power_law_index = -0.17
delta_power_law_index_coupling = 0.7
cone_opening_angle = 6.
m_pivot = 10**8
sigma_sub = 0.6
power_law_index = -1.8
subhalo_spatial_distribution = 'HOST_NFW'
kwargs_cdm = {
'zmin': zmin,
'zmax': zmax,
'log_mc': None,
'log_mlow': log_mlow,
'sigma_sub': sigma_sub,
'c_scale': None,
'c_power': None,
'a_wdm': None,
'b_wdm': None,
'c_wdm': None,
'c_scatter_dex': 0.2,
'log_mhigh': log_mhigh,
'host_m200': host_m200,
'LOS_normalization': LOS_normalization,
'draw_poisson': draw_poisson,
'subhalo_spatial_distribution': subhalo_spatial_distribution,
'log_mass_sheet_min': log_mass_sheet_min,
'log_mass_sheet_max': log_mass_sheet_max,
'kappa_scale': kappa_scale,
'power_law_index': power_law_index,
'delta_power_law_index': delta_power_law_index,
'delta_power_law_index_coupling': delta_power_law_index_coupling,
'm_pivot': m_pivot,
'cone_opening_angle': cone_opening_angle,
'subhalo_mass_sheet_scale': 1.,
'subhalo_convergence_correction_profile': 'NFW',
'r_tidal': '0.5Rs',
'mdef_subs': 'TNFW',
'mdef_los': 'TNFW'
}
kwargs_wdm = deepcopy(kwargs_cdm)
log_mc = 7.1
a_wdm = 1.
b_wdm = 0.8
c_wdm = -1.3
kwargs_wdm['log_mc'] = log_mc
kwargs_wdm['a_wdm'] = a_wdm
kwargs_wdm['b_wdm'] = b_wdm
kwargs_wdm['c_wdm'] = c_wdm
kwargs_wdm['c_scale'] = 60.
kwargs_wdm['c_power'] = -0.17
pyhalo = pyHalo(zlens, zsource)
lens_plane_redshifts, delta_zs = pyhalo.lens_plane_redshifts(
kwargs_cdm)
cosmo = Cosmology()
self.lens_plane_redshifts = lens_plane_redshifts
self.delta_zs = delta_zs
self.halo_mass_function = LensingMassFunction(
cosmo,
zlens,
zsource,
kwargs_cdm['log_mlow'],
kwargs_cdm['log_mhigh'],
kwargs_cdm['cone_opening_angle'],
m_pivot=kwargs_cdm['m_pivot'],
geometry_type='DOUBLE_CONE',
use_lookup_table=True)
self.geometry = Geometry(cosmo, zlens, zsource,
kwargs_cdm['cone_opening_angle'],
'DOUBLE_CONE')
self.lens_cosmo = LensCosmo(zlens, zsource, cosmo)
self.kwargs_cdm = kwargs_cdm
self.kwargs_wdm = kwargs_wdm
pyhalo = pyHalo(zlens, zsource)
model_list_field = ['LINE_OF_SIGHT']
model_list_sub = ['SUBHALOS']
self.realization_cdm = pyhalo.render(model_list_sub + model_list_field,
kwargs_cdm)[0]
self.realization_cdm_field = pyhalo.render(model_list_field,
kwargs_cdm)[0]
self.realization_wdm_field = pyhalo.render(model_list_field,
kwargs_wdm)[0]
self.realization_wdm_subhalos = pyhalo.render(model_list_sub,
kwargs_wdm)[0]
def test_mass_rendered_subhalos(self):
plaw_index = self.kwargs_cdm['power_law_index'] + \
self.kwargs_cdm['delta_power_law_index'] * self.kwargs_cdm['delta_power_law_index_coupling']
norm = normalization_sigmasub(self.kwargs_cdm['sigma_sub'],
self.kwargs_cdm['host_m200'],
self.lens_cosmo.z_lens,
self.geometry.kpc_per_arcsec_zlens,
self.kwargs_cdm['cone_opening_angle'],
plaw_index, self.kwargs_cdm['m_pivot'])
mtheory = integrate_power_law_analytic(
norm, 10**self.kwargs_cdm['log_mlow'],
10**self.kwargs_cdm['log_mhigh'], 1., plaw_index)
m_subs = 0.
for halo in self.realization_cdm.halos:
if halo.is_subhalo:
m_subs += halo.mass
ratio = mtheory / m_subs
npt.assert_array_less(1 - ratio, 0.05)
plaw_index = self.kwargs_wdm['power_law_index'] + \
self.kwargs_wdm['delta_power_law_index'] * self.kwargs_wdm['delta_power_law_index_coupling']
norm = normalization_sigmasub(self.kwargs_wdm['sigma_sub'],
self.kwargs_wdm['host_m200'],
self.lens_cosmo.z_lens,
self.geometry.kpc_per_arcsec_zlens,
self.kwargs_cdm['cone_opening_angle'],
plaw_index, self.kwargs_wdm['m_pivot'])
mtheory = integrate_power_law_quad(
norm, 10**self.kwargs_wdm['log_mlow'],
10**self.kwargs_wdm['log_mhigh'], self.kwargs_wdm['log_mc'], 1.,
plaw_index, self.kwargs_wdm['a_wdm'], self.kwargs_wdm['b_wdm'],
self.kwargs_wdm['c_wdm'])
m_subs = 0.
for halo in self.realization_wdm_subhalos.halos:
if halo.is_subhalo:
m_subs += halo.mass
ratio = mtheory / m_subs
npt.assert_array_less(1 - ratio, 0.1)
def test_mass_rendered_line_of_sight(self):
m_theory = 0
m_rendered = 0
for z, dz in zip(self.lens_plane_redshifts, self.delta_zs):
m_rendered += self.realization_cdm_field.mass_at_z_exact(z)
slope = self.halo_mass_function.plaw_index_z(
z) + self.kwargs_cdm['delta_power_law_index']
norm = self.kwargs_cdm['LOS_normalization'] * \
self.halo_mass_function.norm_at_z_density(z, slope, self.kwargs_cdm['m_pivot']) * \
self.geometry.volume_element_comoving(z, dz)
m_theory += integrate_power_law_analytic(
norm, 10**self.kwargs_cdm['log_mlow'],
10**self.kwargs_cdm['log_mhigh'], 1, slope)
ratio = m_theory / m_rendered
npt.assert_array_less(1 - ratio, 0.05)
m_theory = 0
m_rendered = 0
for z, dz in zip(self.lens_plane_redshifts, self.delta_zs):
m_rendered += self.realization_wdm_field.mass_at_z_exact(z)
slope = self.halo_mass_function.plaw_index_z(
z) + self.kwargs_wdm['delta_power_law_index']
norm = self.kwargs_cdm['LOS_normalization'] * \
self.halo_mass_function.norm_at_z_density(z, slope, self.kwargs_wdm['m_pivot']) * \
self.geometry.volume_element_comoving(z, dz)
m_theory += integrate_power_law_quad(
norm, 10**self.kwargs_wdm['log_mlow'],
10**self.kwargs_wdm['log_mhigh'], self.kwargs_wdm['log_mc'], 1,
slope, self.kwargs_wdm['a_wdm'], self.kwargs_wdm['b_wdm'],
self.kwargs_wdm['c_wdm'])
ratio = m_theory / m_rendered
npt.assert_array_less(1 - ratio, 0.05)
def test_wdm_mass_function(self):
mass_bins = np.linspace(6, 9, 20)
halo_masses_wdm = [
halo.mass for halo in self.realization_wdm_field.halos
]
log_halo_mass = np.log10(halo_masses_wdm)
h_wdm, logM = np.histogram(log_halo_mass, bins=mass_bins)
logmstep = (logM[1] - logM[0]) / 2
logM = logM[0:-1] + logmstep
mass_bins = np.linspace(6, 9, 20)
halo_masses_cdm = [
halo.mass for halo in self.realization_cdm_field.halos
]
log_halo_mass = np.log10(halo_masses_cdm)
h_cdm, _ = np.histogram(log_halo_mass, bins=mass_bins)
suppression_factor = WDM_suppression(
10**logM,
10**self.kwargs_wdm['log_mc'],
self.kwargs_wdm['a_wdm'],
self.kwargs_wdm['b_wdm'],
self.kwargs_wdm['c_wdm'],
)
for i in range(0, 10):
ratio = h_wdm[i] / h_cdm[i]
npt.assert_almost_equal(ratio, suppression_factor[i], 1)
def test_cdm_mass_function(self):
mass_bins = np.linspace(6, 9., 20)
halo_masses_sub = []
halo_masses_field = []
for halo in self.realization_cdm.halos:
if halo.is_subhalo:
halo_masses_sub.append(halo.mass)
else:
halo_masses_field.append(halo.mass)
log_halo_mass_sub = np.log10(halo_masses_sub)
log_halo_mass_field = np.log10(halo_masses_field)
h_sub, logM_sub = np.histogram(log_halo_mass_sub, bins=mass_bins)
h_field, logM_field = np.histogram(log_halo_mass_field, bins=mass_bins)
logN_sub = np.log10(h_sub)
logN_field = np.log10(h_field)
slope_theory = -0.9 + self.kwargs_cdm['delta_power_law_index']
slope = np.polyfit(logM_field[0:-1], logN_field, 1)[0]
npt.assert_array_less(abs(1 - slope / slope_theory), 0.05, 2)
slope_theory = (1+self.kwargs_cdm['power_law_index']) + self.kwargs_cdm['delta_power_law_index'] * \
self.kwargs_cdm['delta_power_law_index_coupling']
slope = np.polyfit(logM_sub[0:-1], logN_sub, 1)[0]
npt.assert_array_less(abs(1 - slope / slope_theory), 0.05, 2)
def setup(self):
zlens, zsource = 0.4, 2.
masses = [10**9.04, 10**8.2, 10**7.345, 10**7, 10**6.05, 10**7, 10**7]
x = [0.5, 0.1, -0.9, -1.4, 1.2, 0., -1.]
y = [0., 0.9, -1.4, -1., -0.4, 1., 0.9]
redshifts = [0.1, 0.2, 0.3, zlens, zlens, 0.94, 0.94]
subflags = [False, False, False, True, True, False, False]
r3d = [100] * len(masses)
mdefs_TNFW = ['TNFW'] * len(masses)
#
self.x = x
self.y = y
self.masses = masses
self.redshifts = redshifts
self.subflags = subflags
self.r3d = r3d
self.mdefs = mdefs_TNFW
masses2 = [10**6.34, 10**9.2, 10**8.36]
x2 = [1.5, 0.15, -1.9]
y2 = [0.2, 0.3, -0.44]
redshifts2 = [zlens, 0.4, 1.9]
subflags2 = [True, False, False]
r3d2 = [100] * len(masses2)
profile_args_TNFW = {
'mc_model': 'diemer19',
'c_scatter': False,
'c_scatter_dex': 0.1
}
cosmo = Cosmology()
halo_mass_function = LensingMassFunction(cosmo,
zlens,
zsource,
10**6,
10**9,
6.,
m_pivot=10**8)
self.halo_mass_function = halo_mass_function
kwargs_cdm = {
'zmin': 0.01,
'zmax': 1.98,
'log_mc': None,
'log_mlow': 6.,
'log_mhigh': 9.,
'host_m200': 10**13,
'LOS_normalization': 2000.,
'LOS_normalization_mass_sheet': 1.,
'draw_poisson': False,
'log_mass_sheet_min': 7.,
'log_mass_sheet_max': 10.,
'kappa_scale': 1.,
'delta_power_law_index': 0.,
'a_wdm': None,
'b_wdm': None,
'c_wdm': None,
'm_pivot': 10**8,
'cone_opening_angle': 6.,
'mass_function_LOS_type': 'POWER_LAW'
}
kwargs_cdm_2 = {
'zmin': 0.01,
'zmax': 1.98,
'log_mc': None,
'log_mlow': 6.,
'log_mhigh': 9.,
'host_m200': 10**13,
'LOS_normalization': 2000.,
'LOS_normalization_mass_sheet': 1.,
'draw_poisson': False,
'log_mass_sheet_min': 7.,
'log_mass_sheet_max': 10.,
'kappa_scale': 1.,
'delta_power_law_index': 0.,
'a_wdm': None,
'b_wdm': None,
'c_wdm': None,
'm_pivot': 10**8,
'cone_opening_angle': 6.,
'subtract_exact_mass_sheets': True,
'mass_function_LOS_type': 'POWER_LAW'
}
kwargs_cdm.update(profile_args_TNFW)
self.kwargs_cdm = kwargs_cdm
self.kwargs_cdm_2 = kwargs_cdm_2
lens_plane_redshifts = np.append(np.arange(0.01, 0.5, 0.02),
np.arange(0.5, 1.5, 0.02))
delta_zs = []
for i in range(0, len(lens_plane_redshifts) - 1):
delta_zs.append(lens_plane_redshifts[i + 1] -
lens_plane_redshifts[i])
delta_zs.append(1.5 - lens_plane_redshifts[-1])
geometry = Geometry(cosmo, 0.5, 1.5, 6., 'DOUBLE_CONE')
lens_cosmo = LensCosmo(zlens, zsource, cosmo)
self.lens_cosmo = lens_cosmo
halo_population = HaloPopulation(['LINE_OF_SIGHT'], self.kwargs_cdm,
lens_cosmo, geometry,
halo_mass_function,
lens_plane_redshifts, delta_zs)
self.rendering_classes = halo_population.rendering_classes
mdef = ['NFW'] * len(masses)
self.realization_cdm = Realization(
masses,
x,
y,
r3d,
mdef,
redshifts,
subflags,
lens_cosmo,
halos=None,
kwargs_realization=self.kwargs_cdm_2,
mass_sheet_correction=True,
rendering_classes=self.rendering_classes,
geometry=geometry)
mdef = ['PT_MASS'] * len(masses)
self.realization_cdm2 = Realization(
masses2,
x2,
y2,
r3d2,
mdef,
redshifts2,
subflags2,
lens_cosmo,
halos=None,
kwargs_realization=self.kwargs_cdm,
mass_sheet_correction=True,
rendering_classes=self.rendering_classes,
geometry=geometry)
mdef = ['PJAFFE'] * len(masses)
self.realization_cdm3 = Realization(
masses2,
x2,
y2,
r3d2,
mdef,
redshifts2,
subflags2,
lens_cosmo,
halos=None,
kwargs_realization=self.kwargs_cdm,
mass_sheet_correction=True,
rendering_classes=self.rendering_classes,
geometry=geometry)
self.halos_cdm = self.realization_cdm.halos
halo_tags = []
for halo in self.realization_cdm.halos:
halo_tags.append(halo.unique_tag)
self.halo_tags = halo_tags
halo_tags = []
for halo in self.realization_cdm2.halos:
halo_tags.append(halo.unique_tag)
self.halo_tags2 = halo_tags
self.real_1_data = [x, y, masses, redshifts, subflags, redshifts]
self.real_2_data = [x2, y2, masses2, redshifts2, subflags2, redshifts2]
class TestLOS(object):
def setup(self):
zlens, zsource = 0.5, 2.
zmin = 0.01
zmax = 1.98
log_mlow = 6.
log_mhigh = 9.
host_m200 = 10**13
LOS_normalization = 1.
draw_poisson = False
log_mass_sheet_min = 7.
log_mass_sheet_max = 10.
kappa_scale = 1.
delta_power_law_index = -0.1
delta_power_law_index_coupling = 0.5
cone_opening_angle = 6.
m_pivot = 10**8
sigma_sub = 0.1
power_law_index = -1.9
subhalo_spatial_distribution = 'HOST_NFW'
kwargs_cdm = {
'zmin': zmin,
'zmax': zmax,
'log_mc': None,
'log_mlow': log_mlow,
'sigma_sub': sigma_sub,
'c_scale': None,
'c_power': None,
'a_wdm': None,
'b_wdm': None,
'c_wdm': None,
'c_scatter_dex': 0.2,
'log_mhigh': log_mhigh,
'mdef_los': 'TNFW',
'host_m200': host_m200,
'LOS_normalization': LOS_normalization,
'draw_poisson': draw_poisson,
'subhalo_spatial_distribution': subhalo_spatial_distribution,
'log_mass_sheet_min': log_mass_sheet_min,
'log_mass_sheet_max': log_mass_sheet_max,
'kappa_scale': kappa_scale,
'power_law_index': power_law_index,
'delta_power_law_index': delta_power_law_index,
'delta_power_law_index_coupling': delta_power_law_index_coupling,
'm_pivot': m_pivot,
'cone_opening_angle': cone_opening_angle,
'subhalo_mass_sheet_scale': 1.,
'subhalo_convergence_correction_profile': 'NFW',
'r_tidal': '0.5Rs'
}
pyhalo = pyHalo(zlens, zsource)
self.realization_cdm = pyhalo.render(['LINE_OF_SIGHT'], kwargs_cdm)[0]
lens_plane_redshifts, delta_zs = pyhalo.lens_plane_redshifts(
kwargs_cdm)
cosmo = Cosmology()
self.lens_plane_redshifts = lens_plane_redshifts
self.delta_zs = delta_zs
self.halo_mass_function = LensingMassFunction(
cosmo,
zlens,
zsource,
kwargs_cdm['log_mlow'],
kwargs_cdm['log_mhigh'],
kwargs_cdm['cone_opening_angle'],
m_pivot=kwargs_cdm['m_pivot'],
geometry_type='DOUBLE_CONE')
self.geometry = Geometry(cosmo, zlens, zsource,
kwargs_cdm['cone_opening_angle'],
'DOUBLE_CONE')
self.lens_cosmo = LensCosmo(zlens, zsource, cosmo)
self.kwargs_cdm = kwargs_cdm
self.rendering_class = LineOfSight(kwargs_cdm, self.halo_mass_function,
self.geometry, self.lens_cosmo,
self.lens_plane_redshifts,
self.delta_zs)
self.logdelta_mass = 5.
kwargs_delta = {
'zmin': zmin,
'zmax': zmax,
'log_mc': None,
'log_mlow': log_mlow,
'sigma_sub': sigma_sub,
'c_scale': None,
'c_power': None,
'a_wdm': None,
'b_wdm': None,
'c_wdm': None,
'c_scatter_dex': 0.2,
'log_mhigh': log_mhigh,
'mdef_los': 'TNFW',
'host_m200': host_m200,
'LOS_normalization': LOS_normalization,
'draw_poisson': draw_poisson,
'subhalo_spatial_distribution': subhalo_spatial_distribution,
'log_mass_sheet_min': log_mass_sheet_min,
'log_mass_sheet_max': log_mass_sheet_max,
'kappa_scale': kappa_scale,
'power_law_index': power_law_index,
'delta_power_law_index': delta_power_law_index,
'delta_power_law_index_coupling': delta_power_law_index_coupling,
'm_pivot': m_pivot,
'logM': self.logdelta_mass,
'mass_fraction': 0.1,
'cone_opening_angle': cone_opening_angle,
'subhalo_mass_sheet_scale': 1.,
'subhalo_convergence_correction_profile': 'NFW',
'r_tidal': '0.5Rs',
'mass_function_LOS_type': 'DELTA'
}
self.rendering_class_delta = LineOfSight(
kwargs_delta, self.halo_mass_function, self.geometry,
self.lens_cosmo, self.lens_plane_redshifts, self.delta_zs)
def test_norm_slope(self):
test_index = [10, 20]
for i in test_index:
z = self.lens_plane_redshifts[i]
dz = self.delta_zs[i]
norm, slope = self.rendering_class._normalization_slope(z, dz)
slope_theory = self.halo_mass_function.plaw_index_z(
z) + self.kwargs_cdm['delta_power_law_index']
norm_theory = self.halo_mass_function.norm_at_z_density(
z, slope_theory, self.kwargs_cdm['m_pivot'])
dv = self.geometry.volume_element_comoving(z, dz)
norm_theory *= self.kwargs_cdm['LOS_normalization'] * dv
npt.assert_almost_equal(slope, slope_theory)
npt.assert_almost_equal(norm_theory, norm)
def test_rendering(self):
m = self.rendering_class.render_masses_at_z(0.7, 0.02)
npt.assert_equal(True, len(m) > 0)
x, y = self.rendering_class.render_positions_at_z(0.9, 10000)
rmax = np.max(np.hypot(x, y))
rmax_theory = 0.5 * self.kwargs_cdm[
'cone_opening_angle'] * self.geometry.rendering_scale(0.9)
npt.assert_array_less(rmax, rmax_theory)
x, y = self.rendering_class.render_positions_at_z(0.2, 0)
npt.assert_equal(True, len(x) == 0)
m, x, y, r3, redshifts, flag = self.rendering_class.render()
npt.assert_equal(len(m), len(x))
npt.assert_equal(len(y), len(r3))
n = 0
for z in np.unique(redshifts):
n += np.sum(redshifts == z)
npt.assert_equal(True, n == len(m))
npt.assert_equal(True, len(self.realization_cdm.halos) == len(m))
def test_convergence_correction(self):
idx = 20
z = self.lens_plane_redshifts[idx]
dz = self.delta_zs[idx]
log_mass_sheet_min = 8.
# factor of two because the kappa sheets are added at every other lens plane
norm, slope = self.rendering_class._normalization_slope(z, 2 * dz)
mtheory = integrate_power_law_analytic(
norm, 10**self.kwargs_cdm['log_mass_sheet_min'],
10**self.kwargs_cdm['log_mass_sheet_max'], 1., slope)
mtheory_2 = integrate_power_law_analytic(
norm, 10**log_mass_sheet_min,
10**self.kwargs_cdm['log_mass_sheet_max'], 1., slope)
area = self.geometry.angle_to_physical_area(
0.5 * self.kwargs_cdm['cone_opening_angle'], z)
kappa_theory = mtheory / self.lens_cosmo.sigma_crit_mass(z, area)
kappa_theory_2 = mtheory_2 / self.lens_cosmo.sigma_crit_mass(z, area)
kwargs_out, profile_names_out, redshifts = self.rendering_class.convergence_sheet_correction(
)
kwargs_out_2, profile_names_out_2, redshifts_2 = self.rendering_class.\
convergence_sheet_correction({'log_mass_sheet_min': log_mass_sheet_min})
idx = np.where(redshifts == z)[0][0]
kw = kwargs_out[idx]
kw2 = kwargs_out_2[idx]
name = profile_names_out[idx]
npt.assert_equal(True, name == 'CONVERGENCE')
kappa_generated = -kw['kappa']
kappa_generated_2 = -kw2['kappa']
npt.assert_almost_equal(kappa_theory, kappa_generated)
npt.assert_almost_equal(kappa_theory_2, kappa_generated_2)
npt.assert_equal(True, kw['kappa'] < 0.)
def test_keys_convergence_sheets(self):
keywords_out = self.rendering_class.keys_convergence_sheets(
self.kwargs_cdm)
required_keys = [
'log_mass_sheet_min', 'log_mass_sheet_max', 'kappa_scale', 'zmin',
'zmax', 'delta_power_law_index'
]
for x in required_keys:
npt.assert_equal(x in keywords_out.keys(), True)
def test_keys_rendering(self):
keywords_out = self.rendering_class.keyword_parse_render(
self.kwargs_cdm)
required_keys = [
'zmin', 'zmax', 'log_mc', 'log_mlow', 'log_mhigh', 'host_m200',
'LOS_normalization', 'draw_poisson', 'log_mass_sheet_min',
'log_mass_sheet_max', 'kappa_scale', 'a_wdm', 'b_wdm', 'c_wdm',
'delta_power_law_index', 'm_pivot'
]
for x in required_keys:
npt.assert_equal(x in keywords_out.keys(), True)
kw_cdm = deepcopy(self.kwargs_cdm)
kw_cdm['log_mc'] = None
keywords_out = self.rendering_class.keyword_parse_render(kw_cdm)
npt.assert_equal(keywords_out['a_wdm'] is None, True)
npt.assert_equal(keywords_out['b_wdm'] is None, True)
npt.assert_equal(keywords_out['c_wdm'] is None, True)
def test_delta_function_rendering(self):
m = self.rendering_class_delta.render_masses_at_z(0.5, 0.01)
for mi in m:
npt.assert_equal(np.log10(mi), self.logdelta_mass)
class TestLensingMassFunction(object):
def setup(self):
cosmo = Cosmology()
mlow = 10**6
mhigh = 10**10
zlens = 0.5
zsource = 1.5
cone_opening_angle = 6.
m_pivot = 10**8
mass_function_model = 'sheth99'
use_lookup_table = True
geometry_type = 'DOUBLE_CONE'
self.lmf_lookup_ShethTormen = LensingMassFunction(
cosmo, zlens, zsource, mlow, mhigh, cone_opening_angle, m_pivot,
mass_function_model, use_lookup_table, geometry_type)
use_lookup_table = False
self.lmf_no_lookup_ShethTormen = LensingMassFunction(
cosmo, zlens, zsource, mlow, mhigh, cone_opening_angle, m_pivot,
mass_function_model, use_lookup_table, geometry_type)
self._m = np.logspace(6., 10, 50)
self.cosmo = cosmo
self.cone_opening_angle = cone_opening_angle
def test_lookup(self):
dndm_1 = self.lmf_lookup_ShethTormen.dN_dMdV_comoving(self._m, 0.5)
dndm_2 = self.lmf_no_lookup_ShethTormen.dN_dMdV_comoving(self._m, 0.5)
npt.assert_almost_equal(dndm_1, dndm_2)
def test_normalization(self):
z = 0.5
plaw_index = self.lmf_lookup_ShethTormen.plaw_index_z(z)
rho_dv = self.lmf_lookup_ShethTormen.norm_at_z_density(
z, plaw_index, 10**8)
dz = 0.01
rho = self.lmf_no_lookup_ShethTormen.norm_at_z(z, plaw_index, dz,
10**8)
radius_arcsec = self.cone_opening_angle * 0.5
A = self.lmf_lookup_ShethTormen.geometry.angle_to_comoving_area(
radius_arcsec, z)
dr = self.cosmo.D_C_transverse(z + dz) - self.cosmo.D_C_transverse(z)
dv = A * dr
rho_2 = dv * rho_dv
npt.assert_almost_equal(rho_2 / rho, 1.0, 2)
def test_power_law_index(self):
plaw_index = self.lmf_lookup_ShethTormen.plaw_index_z(0.5)
npt.assert_almost_equal(plaw_index, -1.91)
plaw_index = self.lmf_no_lookup_ShethTormen.plaw_index_z(0.5)
npt.assert_almost_equal(np.round(plaw_index, 2), -1.91)
def test_two_halo_boost(self):
z = 0.5
m_halo = 10**13
def _integrand(x):
return self.lmf_no_lookup_ShethTormen.twohaloterm(x, m_halo, z)
dz = 0.01
dr = self.cosmo.D_C_transverse(z + dz) - self.cosmo.D_C_transverse(z)
integral_over_two_halo_term = quad(_integrand, 0.5, dr)[0]
length = dr - 0.5
average_value = integral_over_two_halo_term / length
# factor of two for symmetry in front/behind lens
boost_factor = 1 + 2 * average_value
boost_factor_no_lookup = self.lmf_no_lookup_ShethTormen.two_halo_boost(
m_halo, z, 0.5, dr)
boost_factor_lookup = self.lmf_lookup_ShethTormen.two_halo_boost(
m_halo, z, 0.5, dr)
npt.assert_almost_equal(boost_factor, boost_factor_no_lookup)
npt.assert_almost_equal(boost_factor, boost_factor_lookup)
def test_component_density(self):
f = 1.
rho = self.lmf_no_lookup_ShethTormen.component_density(f)
rho_dm = self.cosmo.astropy.Odm(
0.) * self.cosmo.astropy.critical_density(0.).value
rho_dm *= self.cosmo.density_to_MsunperMpc
npt.assert_almost_equal(rho, rho_dm, 4)
def test_mass_function_fit(self):
m = np.logspace(6, 10, 50)
m_pivot = 10**8
z = 0.2
norm_mpivot_8, index = self.lmf_no_lookup_ShethTormen._mass_function_params(
m, z)
norm_theory = self.lmf_no_lookup_ShethTormen.norm_at_z_density(
z, index, 10**8)
norm = norm_mpivot_8 / (m_pivot**index)
npt.assert_almost_equal(norm / norm_theory, 1., 3)
z = 1.2
norm_mpivot_8, index = self.lmf_no_lookup_ShethTormen._mass_function_params(
m, z)
norm_theory = self.lmf_no_lookup_ShethTormen.norm_at_z_density(
z, index, 10**8)
norm = norm_mpivot_8 / (m_pivot**index)
npt.assert_almost_equal(norm / norm_theory, 1., 3)
def test_mass_fraction_in_halos(self):
z = 0.5
mlow = 10**6
mhigh = 10**9
frac1 = self.lmf_no_lookup_ShethTormen.mass_fraction_in_halos(
z, mlow, mhigh, mlow_global=10**-4)
frac2 = self.lmf_no_lookup_ShethTormen.mass_fraction_in_halos(
z, 10**-4, mhigh, mlow_global=10**-4)
frac3 = self.lmf_no_lookup_ShethTormen.mass_fraction_in_halos(
z, 0.99999 * mhigh, mhigh)
npt.assert_almost_equal(frac2, 1)
npt.assert_almost_equal(frac1, 0.43799, 3)
npt.assert_almost_equal(frac3, 0., 3)
def test_norm(self):
h = self.cosmo.h
z = 0.5
mass_function = self.lmf_no_lookup_ShethTormen.dN_dMdV_comoving
m = np.logspace(6, 10, 10)
# units Mpc ^ -3 M ^ -1
mfunc = mass_function(m, z)
# to units (Mpc/h) ^ =3 M ^ -1
mfunc *= h**-3
# to units (Mpc/h) ^ -3 (M/h) ^ -1
mfunc *= h**-1
coefs = np.polyfit(np.log10(m), np.log10(mfunc), 1)
# coefs = (-1.907, 8.732)
m_h = m * h
# units (Mpc/h) ^ -3 ln(M/h)^-1
dndlogm = massFunction(m_h, z, q_out='dndlnM', model='sheth99')
# units (Mpc/h) ^ -3 M ^ -1
dndm = dndlogm / m
# units (Mpc/h) ^ -3 (M/h) ^ -1
dndm *= h**-1
coefs_theory = np.polyfit(np.log10(m), np.log10(dndm), 1)
# coefs_theory = (-1.907, 8.732)
npt.assert_almost_equal(coefs_theory, coefs)
def test_samples(self):
h = self.cosmo.h
z = 0.5
volume_element = 100000.
nbins = 15
m = np.logspace(6, 8.7, nbins)
m_h = m * h
dndlnmdv = massFunction(m_h, z, q_out='dndlnM', model='sheth99')
dndm_theory = dndlnmdv * h**3 / m
coefs_theory = np.polyfit(np.log10(m), np.log10(dndm_theory), 1)
norm_theory = coefs_theory[1]
plaw_index_theory = coefs_theory[0]
norm = volume_element * self.lmf_no_lookup_ShethTormen.norm_at_z_density(
z, plaw_index_theory, 10**8)
mfunc = GeneralPowerLaw(6, 8.7, plaw_index_theory, False, norm, None,
None, None, None)
mdraw = mfunc.draw()
dndm_model = []
mstep = 0.08
msteps = 10**np.arange(6, 8.7 + mstep, mstep)
for i in range(0, len(msteps) - 1):
cond1 = mdraw >= msteps[i]
cond2 = mdraw < msteps[i + 1]
n = np.sum(np.logical_and(cond1, cond2))
delta_m = msteps[i + 1] - msteps[i]
new = n / delta_m
dndm_model.append(new)
coefs_model = np.polyfit(np.log10(msteps[0:-1]), np.log10(dndm_model),
1)
norm_model = coefs_model[1]
npt.assert_almost_equal(
10**(norm_model - norm_theory) / volume_element, 1, 1)