def test_profile_normalization(self):
"""
Test that the mass enclosed within r200 of the composite profile is correct
and check that the ULDM core density is correct.
"""
profile_args = {'log10_m_uldm': -21, 'uldm_plaw': 1/3, 'scale_nfw':True}
mass = 1e10
zl = 0.5
zs = 1.5
single_halo = SingleHalo(mass, 0.5, 0.5, 'ULDM', zl, zl, zs, None, True, profile_args, None)
_, _, kwargs_lens, _ = single_halo.lensing_quantities(add_mass_sheet_correction=False)
Rs_angle, _ = single_halo.halos[0].lens_cosmo.nfw_physical2angle(mass, single_halo.halos[0].c, zl)
sigma_crit = single_halo.halos[0].lens_cosmo.sigmacrit
r200 = single_halo.halos[0].c * Rs_angle
cnfw_kwargs, uldm_kwargs = kwargs_lens
M_nfw = CNFW().mass_3d_lens(r200, cnfw_kwargs['Rs'], cnfw_kwargs['alpha_Rs']*sigma_crit, cnfw_kwargs['r_core'])
M_uldm = Uldm().mass_3d_lens(r200, uldm_kwargs['kappa_0']*sigma_crit, uldm_kwargs['theta_c'])
npt.assert_almost_equal((M_uldm+M_nfw)/mass,1,decimal=2) # less than 1% error
_,theta_c,kappa_0 = single_halo.halos[0].profile_args
rho0 = Uldm().density_lens(0,uldm_kwargs['kappa_0'],
uldm_kwargs['theta_c'])
rhos = CNFW().density_lens(0,cnfw_kwargs['Rs'],
cnfw_kwargs['alpha_Rs'],
cnfw_kwargs['r_core'])
rho_goal = Uldm().density_lens(0,kappa_0,theta_c)
npt.assert_array_less(np.array([1-(rho0+rhos)/rho_goal]),np.array([0.03])) # less than 3% error
def _rescaled_cnfw_params(self, cnfw_params, uldm_params):
"""
:param cnfw_params: cored NFW halo lensing params
:param uldm_params: ULDM halo lensing params
:return: rescaled cored NFW params to fill up the remainder of the mass budget such that
the composite profile has the inputted virial mass.
"""
r200 = self._c * cnfw_params['Rs']
rho0 = Uldm().density_lens(0, uldm_params['kappa_0'],
uldm_params['theta_c'])
rhos = CNFW().density_lens(0, cnfw_params['Rs'],
cnfw_params['alpha_Rs'],
cnfw_params['r_core'])
args = (r200, self.mass, cnfw_params['Rs'], cnfw_params['alpha_Rs'],
uldm_params['kappa_0'], uldm_params['theta_c'], rho0, rhos)
initial_guess = np.array([0.9, 1.1])
bounds = ((0.5, 10), (0.5, 1.5))
method = 'Nelder-Mead'
beta, q = minimize(self._function_to_minimize,
initial_guess,
args,
method=method,
bounds=bounds,
tol=0.1)['x']
if beta < 0:
raise ValueError(
'Negative CNFW core radius, tweak your parameters.')
elif q < 0:
raise ValueError(
'Negative ULDM profile mass, tweak your parameters.')
else:
pass
cnfw_params['r_core'] /= beta
uldm_params['kappa_0'] /= q
M_nfw = CNFW().mass_3d_lens(
r200, cnfw_params['Rs'],
cnfw_params['alpha_Rs'] * self._lens_cosmo.sigmacrit,
cnfw_params['r_core'])
M_uldm = Uldm().mass_3d_lens(
r200, uldm_params['kappa_0'] * self._lens_cosmo.sigmacrit,
uldm_params['theta_c'])
if (self._args['scale_nfw']):
# When scale_nfw is True rescale alpha_Rs to improve mass accuracy
scale = self.mass / (M_nfw + M_uldm)
cnfw_params['alpha_Rs'] *= scale
return [cnfw_params, uldm_params]
def _constraint_mass(self, beta, q, r, m_target, rs, alpha_rs, kappa_0,
theta_c):
"""
:param beta: CNFW core radius ('r_core') rescaling parameter
:param q: ULDM core density ('kappa_0') rescaling parameter
:param r: r200 of CNFW profile
:param m_target: halo virial mass
:param rs: CNFW scale radius
:param alpha_rs: CNFW deflection angle at rs, in absence of core
:param kappa_0: ULDM core density
:param theta_c: ULDM core radius
:return: Evaluated mass constraint equation for CNFW component profile
"""
r_core = beta * rs
sigma_crit = self.lens_cosmo.sigmacrit
args_nfw = (r, rs, alpha_rs * sigma_crit, r_core)
args_uldm = (r, kappa_0 * sigma_crit, theta_c)
m_nfw = CNFW().mass_3d_lens(*args_nfw) / m_target
m_uldm = q * Uldm().mass_3d_lens(*args_uldm) / m_target
penalty = np.absolute(m_nfw + m_uldm - 1)
if np.isnan(penalty):
return 1e+12
# penalize if not equal to zero
return penalty
def setup(self):
prof = CNFW()
self.func = prof._F
self.rs = 60
self.rmax2d = 40
self.rvir = 350
self.rcore = 10.
self.nfw = NFW3DCoreRejectionSampling(self.rs, self.rmax2d, self.rvir,
self.rcore)
def __init__(self, rendering_radius, Rs, r_core_host, r200):
"""
:param rendering_radius: the maximum projected 2D radius where halos are rendered [arcsec]
:param Rs: the scale radius of the host dark matter halo [kpc]
:param r_core_host: the core radius of the host dark matter halo [kpc]
:param r200: the virial radius of the host dark matter halo [kpc]
"""
self._cnfw_profile = CNFW()
self.rmax2d_kpc = rendering_radius
self._rs_kpc = Rs
self._xmin = 1e-4
self.xmax_2d = rendering_radius / Rs
self.xtidal = r_core_host / Rs
self.zmax_units_rs = r200 / Rs
self._xmin = rendering_radius / 30 / self._rs_kpc
self._norm = self._cnfw_profile._F(self._xmin, self.xtidal)
def _import_class(lens_type, custom_class, z_lens=None, z_source=None):
"""
:param lens_type: string, lens model type
:param custom_class: custom class
:param z_lens: lens redshift # currently only used in NFW_MC model as this is redshift dependent
:param z_source: source redshift # currently only used in NFW_MC model as this is redshift dependent
:return: class instance of the lens model type
"""
if lens_type == 'SHIFT':
from lenstronomy.LensModel.Profiles.alpha_shift import Shift
return Shift()
elif lens_type == 'SHEAR':
from lenstronomy.LensModel.Profiles.shear import Shear
return Shear()
elif lens_type == 'SHEAR_GAMMA_PSI':
from lenstronomy.LensModel.Profiles.shear import ShearGammaPsi
return ShearGammaPsi()
elif lens_type == 'CONVERGENCE':
from lenstronomy.LensModel.Profiles.convergence import Convergence
return Convergence()
elif lens_type == 'FLEXION':
from lenstronomy.LensModel.Profiles.flexion import Flexion
return Flexion()
elif lens_type == 'FLEXIONFG':
from lenstronomy.LensModel.Profiles.flexionfg import Flexionfg
return Flexionfg()
elif lens_type == 'POINT_MASS':
from lenstronomy.LensModel.Profiles.point_mass import PointMass
return PointMass()
elif lens_type == 'SIS':
from lenstronomy.LensModel.Profiles.sis import SIS
return SIS()
elif lens_type == 'SIS_TRUNCATED':
from lenstronomy.LensModel.Profiles.sis_truncate import SIS_truncate
return SIS_truncate()
elif lens_type == 'SIE':
from lenstronomy.LensModel.Profiles.sie import SIE
return SIE()
elif lens_type == 'SPP':
from lenstronomy.LensModel.Profiles.spp import SPP
return SPP()
elif lens_type == 'NIE':
from lenstronomy.LensModel.Profiles.nie import NIE
return NIE()
elif lens_type == 'NIE_SIMPLE':
from lenstronomy.LensModel.Profiles.nie import NIEMajorAxis
return NIEMajorAxis()
elif lens_type == 'CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import Chameleon
return Chameleon()
elif lens_type == 'DOUBLE_CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import DoubleChameleon
return DoubleChameleon()
elif lens_type == 'TRIPLE_CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import TripleChameleon
return TripleChameleon()
elif lens_type == 'SPEP':
from lenstronomy.LensModel.Profiles.spep import SPEP
return SPEP()
elif lens_type == 'SPEMD':
from lenstronomy.LensModel.Profiles.spemd import SPEMD
return SPEMD()
elif lens_type == 'SPEMD_SMOOTH':
from lenstronomy.LensModel.Profiles.spemd_smooth import SPEMD_SMOOTH
return SPEMD_SMOOTH()
elif lens_type == 'NFW':
from lenstronomy.LensModel.Profiles.nfw import NFW
return NFW()
elif lens_type == 'NFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.nfw_ellipse import NFW_ELLIPSE
return NFW_ELLIPSE()
elif lens_type == 'NFW_ELLIPSE_GAUSS_DEC':
from lenstronomy.LensModel.Profiles.gauss_decomposition import NFWEllipseGaussDec
return NFWEllipseGaussDec()
elif lens_type == 'TNFW':
from lenstronomy.LensModel.Profiles.tnfw import TNFW
return TNFW()
elif lens_type == 'CNFW':
from lenstronomy.LensModel.Profiles.cnfw import CNFW
return CNFW()
elif lens_type == 'CNFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.cnfw_ellipse import CNFW_ELLIPSE
return CNFW_ELLIPSE()
elif lens_type == 'CTNFW_GAUSS_DEC':
from lenstronomy.LensModel.Profiles.gauss_decomposition import CTNFWGaussDec
return CTNFWGaussDec()
elif lens_type == 'NFW_MC':
from lenstronomy.LensModel.Profiles.nfw_mass_concentration import NFWMC
return NFWMC(z_lens=z_lens, z_source=z_source)
elif lens_type == 'SERSIC':
from lenstronomy.LensModel.Profiles.sersic import Sersic
return Sersic()
elif lens_type == 'SERSIC_ELLIPSE_POTENTIAL':
from lenstronomy.LensModel.Profiles.sersic_ellipse_potential import SersicEllipse
return SersicEllipse()
elif lens_type == 'SERSIC_ELLIPSE_KAPPA':
from lenstronomy.LensModel.Profiles.sersic_ellipse_kappa import SersicEllipseKappa
return SersicEllipseKappa()
elif lens_type == 'SERSIC_ELLIPSE_GAUSS_DEC':
from lenstronomy.LensModel.Profiles.gauss_decomposition \
import SersicEllipseGaussDec
return SersicEllipseGaussDec()
elif lens_type == 'PJAFFE':
from lenstronomy.LensModel.Profiles.p_jaffe import PJaffe
return PJaffe()
elif lens_type == 'PJAFFE_ELLIPSE':
from lenstronomy.LensModel.Profiles.p_jaffe_ellipse import PJaffe_Ellipse
return PJaffe_Ellipse()
elif lens_type == 'HERNQUIST':
from lenstronomy.LensModel.Profiles.hernquist import Hernquist
return Hernquist()
elif lens_type == 'HERNQUIST_ELLIPSE':
from lenstronomy.LensModel.Profiles.hernquist_ellipse import Hernquist_Ellipse
return Hernquist_Ellipse()
elif lens_type == 'GAUSSIAN':
from lenstronomy.LensModel.Profiles.gaussian_potential import Gaussian
return Gaussian()
elif lens_type == 'GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.gaussian_kappa import GaussianKappa
return GaussianKappa()
elif lens_type == 'GAUSSIAN_ELLIPSE_KAPPA':
from lenstronomy.LensModel.Profiles.gaussian_ellipse_kappa import GaussianEllipseKappa
return GaussianEllipseKappa()
elif lens_type == 'GAUSSIAN_ELLIPSE_POTENTIAL':
from lenstronomy.LensModel.Profiles.gaussian_ellipse_potential import GaussianEllipsePotential
return GaussianEllipsePotential()
elif lens_type == 'MULTI_GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappa
return MultiGaussianKappa()
elif lens_type == 'MULTI_GAUSSIAN_KAPPA_ELLIPSE':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappaEllipse
return MultiGaussianKappaEllipse()
elif lens_type == 'INTERPOL':
from lenstronomy.LensModel.Profiles.interpol import Interpol
return Interpol()
elif lens_type == 'INTERPOL_SCALED':
from lenstronomy.LensModel.Profiles.interpol import InterpolScaled
return InterpolScaled()
elif lens_type == 'SHAPELETS_POLAR':
from lenstronomy.LensModel.Profiles.shapelet_pot_polar import PolarShapelets
return PolarShapelets()
elif lens_type == 'SHAPELETS_CART':
from lenstronomy.LensModel.Profiles.shapelet_pot_cartesian import CartShapelets
return CartShapelets()
elif lens_type == 'DIPOLE':
from lenstronomy.LensModel.Profiles.dipole import Dipole
return Dipole()
elif lens_type == 'CURVED_ARC':
from lenstronomy.LensModel.Profiles.curved_arc import CurvedArc
return CurvedArc()
elif lens_type == 'ARC_PERT':
from lenstronomy.LensModel.Profiles.arc_perturbations import ArcPerturbations
return ArcPerturbations()
elif lens_type == 'coreBURKERT':
from lenstronomy.LensModel.Profiles.coreBurkert import CoreBurkert
return CoreBurkert()
elif lens_type == 'CORED_DENSITY':
from lenstronomy.LensModel.Profiles.cored_density import CoredDensity
return CoredDensity()
elif lens_type == 'CORED_DENSITY_2':
from lenstronomy.LensModel.Profiles.cored_density_2 import CoredDensity2
return CoredDensity2()
elif lens_type == 'CORED_DENSITY_MST':
from lenstronomy.LensModel.Profiles.cored_density_mst import CoredDensityMST
return CoredDensityMST(profile_type='CORED_DENSITY')
elif lens_type == 'CORED_DENSITY_2_MST':
from lenstronomy.LensModel.Profiles.cored_density_mst import CoredDensityMST
return CoredDensityMST(profile_type='CORED_DENSITY_2')
elif lens_type == 'NumericalAlpha':
from lenstronomy.LensModel.Profiles.numerical_deflections import NumericalAlpha
return NumericalAlpha(custom_class)
else:
raise ValueError('%s is not a valid lens model' % lens_type)
def setup(self):
self.nfw = CNFW()
self.nfw_e = CNFW_ELLIPSE()
class TestCNFWELLIPSE(object):
"""
tests the Gaussian methods
"""
def setup(self):
self.nfw = CNFW()
self.nfw_e = CNFW_ELLIPSE()
def test_function(self):
x = np.array([1])
y = np.array([2])
Rs = 1.
alpha_Rs = 1.
q = 1.
phi_G = 0
r_core = 0.5
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
values = self.nfw.function(x, y, Rs, alpha_Rs, r_core=r_core)
values_e = self.nfw_e.function(x, y, Rs, alpha_Rs, r_core, e1, e2)
npt.assert_almost_equal(values[0], values_e[0], decimal=5)
x = np.array([0])
y = np.array([0])
q = .8
phi_G = 0
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
values = self.nfw_e.function(x, y, Rs, alpha_Rs, r_core, e1, e2)
npt.assert_almost_equal(values[0], 0, decimal=4)
x = np.array([2, 3, 4])
y = np.array([1, 1, 1])
values = self.nfw_e.function(x, y, Rs, alpha_Rs, r_core, e1, e2)
npt.assert_almost_equal(values[0], 1.8550220596738973, decimal=5)
npt.assert_almost_equal(values[1], 2.7684470762303537, decimal=5)
npt.assert_almost_equal(values[2], 3.7076606717487586, decimal=5)
def test_derivatives(self):
x = np.array([1])
y = np.array([2])
Rs = 1.
alpha_Rs = 1.
q = 1.
phi_G = 0
r_core = 0.5
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_x, f_y = self.nfw.derivatives(x, y, Rs, alpha_Rs, r_core)
f_x_e, f_y_e = self.nfw_e.derivatives(x, y, Rs, alpha_Rs, r_core, e1,
e2)
npt.assert_almost_equal(f_x[0], f_x_e[0], decimal=5)
npt.assert_almost_equal(f_y[0], f_y_e[0], decimal=5)
x = np.array([0])
y = np.array([0])
alpha_Rs = 0
f_x, f_y = self.nfw_e.derivatives(x, y, Rs, alpha_Rs, r_core, e1, e2)
npt.assert_almost_equal(f_x[0], 0, decimal=5)
npt.assert_almost_equal(f_y[0], 0, decimal=5)
x = np.array([1, 3, 4])
y = np.array([2, 1, 1])
alpha_Rs = 1.
q = .8
phi_G = 0
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
values = self.nfw_e.derivatives(x, y, Rs, alpha_Rs, r_core, e1, e2)
npt.assert_almost_equal(values[0][0], 0.3867896894988756, decimal=5)
npt.assert_almost_equal(values[1][0], 1.1603690684966268, decimal=5)
npt.assert_almost_equal(values[0][1], 0.9371571936062841, decimal=5)
npt.assert_almost_equal(values[1][1], 0.46857859680314207, decimal=5)
def test_hessian(self):
x = np.array([1])
y = np.array([2])
Rs = 1.
alpha_Rs = 1.
q = 1.
phi_G = 0
r_core = 0.5
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_xx, f_xy, f_yx, f_yy = self.nfw.hessian(x, y, Rs, alpha_Rs, r_core)
f_xx_e, f_xy_e, f_yx_e, f_yy_e = self.nfw_e.hessian(
x, y, Rs, alpha_Rs, r_core, e1, e2)
npt.assert_almost_equal(f_xx[0], f_xx_e[0], decimal=5)
npt.assert_almost_equal(f_yy[0], f_yy_e[0], decimal=5)
npt.assert_almost_equal(f_xy[0], f_xy_e[0], decimal=5)
npt.assert_almost_equal(f_yx[0], f_yx_e[0], decimal=5)
x = np.array([1, 3, 4])
y = np.array([2, 1, 1])
q = .8
phi_G = 0
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
values = self.nfw_e.hessian(x, y, Rs, alpha_Rs, r_core, e1, e2)
npt.assert_almost_equal(values[0][0], 0.3306510620859626, decimal=5)
npt.assert_almost_equal(values[3][0], 0.07493437759187316, decimal=5)
npt.assert_almost_equal(values[1][0], -0.1684167189042185, decimal=5)
npt.assert_almost_equal(values[0][1], 0.020280774837289073, decimal=5)
npt.assert_almost_equal(values[3][1], 0.3955523575349673, decimal=5)
npt.assert_almost_equal(values[1][1], -0.14605247788956888, decimal=5)
def test_mass_3d(self):
Rs = 10.
rho0 = 1.
r_core = 7.
R = np.linspace(0.1 * Rs, 4 * Rs, 1000)
alpha_Rs = self.nfw._rho2alpha(rho0, Rs, r_core)
m3d = self.nfw.mass_3d(R, Rs, rho0, r_core)
m3d_lens = self.nfw_e.mass_3d_lens(R, Rs, alpha_Rs, r_core)
npt.assert_almost_equal(m3d, m3d_lens, decimal=8)
def _import_class(self, lens_type, i, custom_class):
if lens_type == 'SHIFT':
from lenstronomy.LensModel.Profiles.alpha_shift import Shift
return Shift()
elif lens_type == 'SHEAR':
from lenstronomy.LensModel.Profiles.shear import Shear
return Shear()
elif lens_type == 'CONVERGENCE':
from lenstronomy.LensModel.Profiles.convergence import Convergence
return Convergence()
elif lens_type == 'FLEXION':
from lenstronomy.LensModel.Profiles.flexion import Flexion
return Flexion()
elif lens_type == 'POINT_MASS':
from lenstronomy.LensModel.Profiles.point_mass import PointMass
return PointMass()
elif lens_type == 'SIS':
from lenstronomy.LensModel.Profiles.sis import SIS
return SIS()
elif lens_type == 'SIS_TRUNCATED':
from lenstronomy.LensModel.Profiles.sis_truncate import SIS_truncate
return SIS_truncate()
elif lens_type == 'SIE':
from lenstronomy.LensModel.Profiles.sie import SIE
return SIE()
elif lens_type == 'SPP':
from lenstronomy.LensModel.Profiles.spp import SPP
return SPP()
elif lens_type == 'NIE':
from lenstronomy.LensModel.Profiles.nie import NIE
return NIE()
elif lens_type == 'NIE_SIMPLE':
from lenstronomy.LensModel.Profiles.nie import NIE_simple
return NIE_simple()
elif lens_type == 'CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import Chameleon
return Chameleon()
elif lens_type == 'DOUBLE_CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import DoubleChameleon
return DoubleChameleon()
elif lens_type == 'SPEP':
from lenstronomy.LensModel.Profiles.spep import SPEP
return SPEP()
elif lens_type == 'SPEMD':
from lenstronomy.LensModel.Profiles.spemd import SPEMD
return SPEMD()
elif lens_type == 'SPEMD_SMOOTH':
from lenstronomy.LensModel.Profiles.spemd_smooth import SPEMD_SMOOTH
return SPEMD_SMOOTH()
elif lens_type == 'NFW':
from lenstronomy.LensModel.Profiles.nfw import NFW
return NFW()
elif lens_type == 'NFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.nfw_ellipse import NFW_ELLIPSE
return NFW_ELLIPSE()
elif lens_type == 'TNFW':
from lenstronomy.LensModel.Profiles.tnfw import TNFW
return TNFW()
elif lens_type == 'CNFW':
from lenstronomy.LensModel.Profiles.cnfw import CNFW
return CNFW()
elif lens_type == 'SERSIC':
from lenstronomy.LensModel.Profiles.sersic import Sersic
return Sersic()
elif lens_type == 'SERSIC_ELLIPSE':
from lenstronomy.LensModel.Profiles.sersic_ellipse import SersicEllipse
return SersicEllipse()
elif lens_type == 'PJAFFE':
from lenstronomy.LensModel.Profiles.p_jaffe import PJaffe
return PJaffe()
elif lens_type == 'PJAFFE_ELLIPSE':
from lenstronomy.LensModel.Profiles.p_jaffe_ellipse import PJaffe_Ellipse
return PJaffe_Ellipse()
elif lens_type == 'HERNQUIST':
from lenstronomy.LensModel.Profiles.hernquist import Hernquist
return Hernquist()
elif lens_type == 'HERNQUIST_ELLIPSE':
from lenstronomy.LensModel.Profiles.hernquist_ellipse import Hernquist_Ellipse
return Hernquist_Ellipse()
elif lens_type == 'GAUSSIAN':
from lenstronomy.LensModel.Profiles.gaussian_potential import Gaussian
return Gaussian()
elif lens_type == 'GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.gaussian_kappa import GaussianKappa
return GaussianKappa()
elif lens_type == 'GAUSSIAN_KAPPA_ELLIPSE':
from lenstronomy.LensModel.Profiles.gaussian_kappa_ellipse import GaussianKappaEllipse
return GaussianKappaEllipse()
elif lens_type == 'MULTI_GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappa
return MultiGaussianKappa()
elif lens_type == 'MULTI_GAUSSIAN_KAPPA_ELLIPSE':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappaEllipse
return MultiGaussianKappaEllipse()
elif lens_type == 'INTERPOL':
from lenstronomy.LensModel.Profiles.interpol import Interpol
return Interpol(grid=False, min_grid_number=100)
elif lens_type == 'INTERPOL_SCALED':
from lenstronomy.LensModel.Profiles.interpol import InterpolScaled
return InterpolScaled()
elif lens_type == 'SHAPELETS_POLAR':
from lenstronomy.LensModel.Profiles.shapelet_pot_polar import PolarShapelets
return PolarShapelets()
elif lens_type == 'SHAPELETS_CART':
from lenstronomy.LensModel.Profiles.shapelet_pot_cartesian import CartShapelets
return CartShapelets()
elif lens_type == 'DIPOLE':
from lenstronomy.LensModel.Profiles.dipole import Dipole
return Dipole()
elif lens_type == 'FOREGROUND_SHEAR':
from lenstronomy.LensModel.Profiles.shear import Shear
self._foreground_shear = True
self._foreground_shear_idex = i
return Shear()
elif lens_type == 'coreBURKERT':
from lenstronomy.LensModel.Profiles.coreBurkert import coreBurkert
return coreBurkert()
elif lens_type == 'NumericalAlpha':
from lenstronomy.LensModel.Profiles.numerical_deflections import NumericalAlpha
return NumericalAlpha(custom_class[i])
else:
raise ValueError('%s is not a valid lens model' % lens_type)
def __init__(self):
self.cnfw = CNFW()
self._diff = 0.0000000001
super(CNFW_ELLIPSE, self).__init__()
class CNFW_ELLIPSE(LensProfileBase):
"""
this class contains functions concerning the NFW profile
relation are: R_200 = c * Rs
"""
param_names = [
'Rs', 'alpha_Rs', 'r_core', 'e1', 'e2', 'center_x', 'center_y'
]
lower_limit_default = {
'Rs': 0,
'alpha_Rs': 0,
'r_core': 0,
'e1': -0.5,
'e2': -0.5,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'Rs': 100,
'alpha_Rs': 10,
'r_core': 100,
'e1': 0.5,
'e2': 0.5,
'center_x': 100,
'center_y': 100
}
def __init__(self):
self.cnfw = CNFW()
self._diff = 0.0000000001
super(CNFW_ELLIPSE, self).__init__()
def function(self,
x,
y,
Rs,
alpha_Rs,
r_core,
e1,
e2,
center_x=0,
center_y=0):
"""
returns double integral of NFW profile
"""
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
x_shift = x - center_x
y_shift = y - center_y
cos_phi = np.cos(phi_G)
sin_phi = np.sin(phi_G)
e = min(abs(1. - q), 0.99)
xt1 = (cos_phi * x_shift + sin_phi * y_shift) * np.sqrt(1 - e)
xt2 = (-sin_phi * x_shift + cos_phi * y_shift) * np.sqrt(1 + e)
R_ = np.sqrt(xt1**2 + xt2**2)
f_ = self.cnfw.function(R_,
0,
Rs,
alpha_Rs,
r_core,
center_x=0,
center_y=0)
return f_
def derivatives(self,
x,
y,
Rs,
alpha_Rs,
r_core,
e1,
e2,
center_x=0,
center_y=0):
"""
returns df/dx and df/dy of the function (integral of NFW)
"""
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
x_shift = x - center_x
y_shift = y - center_y
cos_phi = np.cos(phi_G)
sin_phi = np.sin(phi_G)
e = min(abs(1. - q), 0.99)
xt1 = (cos_phi * x_shift + sin_phi * y_shift) * np.sqrt(1 - e)
xt2 = (-sin_phi * x_shift + cos_phi * y_shift) * np.sqrt(1 + e)
f_x_prim, f_y_prim = self.cnfw.derivatives(xt1,
xt2,
Rs,
alpha_Rs,
r_core,
center_x=0,
center_y=0)
f_x_prim *= np.sqrt(1 - e)
f_y_prim *= np.sqrt(1 + e)
f_x = cos_phi * f_x_prim - sin_phi * f_y_prim
f_y = sin_phi * f_x_prim + cos_phi * f_y_prim
return f_x, f_y
def hessian(self,
x,
y,
Rs,
alpha_Rs,
r_core,
e1,
e2,
center_x=0,
center_y=0):
"""
returns Hessian matrix of function d^2f/dx^2, d^f/dy^2, d^2/dxdy
"""
diff = 0.0000001
alpha_ra_dx, alpha_dec_dx = self.derivatives(x + diff, y, Rs, alpha_Rs,
r_core, e1, e2, center_x,
center_y)
alpha_ra_dy, alpha_dec_dy = self.derivatives(x, y + diff, Rs, alpha_Rs,
r_core, e1, e2, center_x,
center_y)
alpha_ra_dx_, alpha_dec_dx_ = self.derivatives(x - diff, y, Rs,
alpha_Rs, r_core, e1,
e2, center_x, center_y)
alpha_ra_dy_, alpha_dec_dy_ = self.derivatives(x, y - diff, Rs,
alpha_Rs, r_core, e1,
e2, center_x, center_y)
dalpha_rara = (alpha_ra_dx - alpha_ra_dx_) / diff / 2
dalpha_radec = (alpha_ra_dy - alpha_ra_dy_) / diff / 2
dalpha_decra = (alpha_dec_dx - alpha_dec_dx_) / diff / 2
dalpha_decdec = (alpha_dec_dy - alpha_dec_dy_) / diff / 2
f_xx = dalpha_rara
f_yy = dalpha_decdec
f_xy = dalpha_radec
f_yx = dalpha_decra
return f_xx, f_yy, f_xy
def mass_3d_lens(self, R, Rs, alpha_Rs, r_core, e1=0, e2=0):
"""
mass enclosed a 3d sphere or radius r given a lens parameterization with angular units
:return:
"""
return self.cnfw.mass_3d_lens(R, Rs, alpha_Rs, r_core)
def density_lens(self, R, Rs, alpha_Rs, r_core, e1=0, e2=0):
"""
computes the density at 3d radius r given lens model parameterization.
The integral in the LOS projection of this quantity results in the convergence quantity.
"""
return self.cnfw.density_lens(R, Rs, alpha_Rs, r_core)
class ProjectedNFW(object):
"""
This class approximates sampling from a full 3D NFW profile by
sampling the projected mass of a cored NFW profile in 2D, and then sampling
the z coordinate from a cored isothermal profile. This is MUCH faster than sampling from the
3D NFW profile, and is accurate to within a few percent.
"""
def __init__(self, rendering_radius, Rs, r_core_host, r200):
"""
:param rendering_radius: the maximum projected 2D radius where halos are rendered [arcsec]
:param Rs: the scale radius of the host dark matter halo [kpc]
:param r_core_host: the core radius of the host dark matter halo [kpc]
:param r200: the virial radius of the host dark matter halo [kpc]
"""
self._cnfw_profile = CNFW()
self.rmax2d_kpc = rendering_radius
self._rs_kpc = Rs
self._xmin = 1e-4
self.xmax_2d = rendering_radius / Rs
self.xtidal = r_core_host / Rs
self.zmax_units_rs = r200 / Rs
self._xmin = rendering_radius / 30 / self._rs_kpc
self._norm = self._cnfw_profile._F(self._xmin, self.xtidal)
@classmethod
def from_keywords_master(self, keywords_master, lens_cosmo, geometry):
keywords = self.keywords(keywords_master, lens_cosmo, geometry)
rendering_radius, Rs, r_core_host, r200 = keywords['rendering_radius'], \
keywords['Rs'], \
keywords['r_core'], \
keywords['host_r200']
return ProjectedNFW(rendering_radius, Rs, r_core_host, r200)
@staticmethod
def keywords(keywords_master, lenscosmo, geometry):
args_spatial = {}
kpc_per_arcsec_zlens = geometry.kpc_per_arcsec_zlens
zlens = lenscosmo.z_lens
# EVERYTHING EXPRESSED IN KPC
args_spatial['rendering_radius'] = 0.5 * keywords_master[
'cone_opening_angle'] * kpc_per_arcsec_zlens
if 'log_m_host' in keywords_master.keys():
keywords_master['host_m200'] = 10**keywords_master['log_m_host']
if 'host_m200' in keywords_master.keys():
# EVERYTHING EXPRESSED IN KPC
if 'host_c' not in keywords_master.keys():
keywords_master['host_c'] = lenscosmo.NFW_concentration(
keywords_master['host_m200'],
zlens,
model='diemer19',
mdef='200c',
logmhm=keywords_master['log_mc'],
scatter=True,
scatter_amplitude=keywords_master['c_scatter_dex'],
suppression_model=keywords_master['suppression_model'],
kwargs_suppresion=keywords_master['kwargs_suppression'])
if 'host_Rs' not in keywords_master.keys():
host_Rs = lenscosmo.NFW_params_physical(
keywords_master['host_m200'], keywords_master['host_c'],
zlens)[1]
host_r200 = host_Rs * keywords_master['host_c']
else:
host_Rs = keywords_master['host_Rs']
host_r200 = keywords_master['host_Rs'] * keywords_master[
'host_c']
args_spatial['Rs'] = host_Rs
args_spatial['rmax3d'] = host_r200
args_spatial['host_r200'] = host_Rs * keywords_master['host_c']
else:
raise Exception(
'Must specify the host halo mass when rendering subhalos')
if 'r_tidal' in keywords_master.keys():
if isinstance(keywords_master['r_tidal'], str):
if keywords_master['r_tidal'] == 'Rs':
args_spatial['r_core'] = args_spatial['Rs']
else:
if keywords_master['r_tidal'][-2:] != 'Rs':
raise ValueError(
'if specifying the tidal core radius as number*Rs, the last two '
'letters in the string must be "Rs".')
scale = float(keywords_master['r_tidal'][:-2])
args_spatial['r_core'] = scale * args_spatial['Rs']
else:
args_spatial['r_core'] = keywords_master['r_tidal']
return args_spatial
def cdf(self, u):
arg = u * np.arctan(self.zmax_units_rs / self.xtidal)
return self.xtidal * np.tan(arg)
def _projected_pdf(self, r2d_kpc):
x = r2d_kpc / self._rs_kpc
if isinstance(x, float) or isinstance(x, int):
x = max(x, self._xmin)
else:
x[np.where(x < self._xmin)] = self._xmin
p = self._cnfw_profile._F(x, self.xtidal) / self._norm
return p
def draw(self, N, rescale=1.0, center_x=0., center_y=0.):
if N == 0:
return [], [], [], []
n = 0
while True:
_x_kpc, _y_kpc, _r2d, _r3d = self._draw_uniform(
N, rescale, center_x, center_y)
prob = self._projected_pdf(_r2d)
u = np.random.uniform(size=len(prob))
keep = np.where(u < prob)[0]
if n == 0:
x_kpc = _x_kpc[keep]
y_kpc = _y_kpc[keep]
r3d = _r3d[keep]
else:
x_kpc = np.append(x_kpc, _x_kpc[keep])
y_kpc = np.append(y_kpc, _y_kpc[keep])
r3d = np.append(r3d, _r3d[keep])
n += len(keep)
if n >= N:
break
return x_kpc[0:N], y_kpc[0:N], r3d[0:N]
def _draw_uniform(self, N, rescale=1.0, center_x=0., center_y=0.):
if N == 0:
return [], [], [], []
angle = np.random.uniform(0, 2 * np.pi, int(N))
rmax = self.xmax_2d * rescale
r = np.random.uniform(0, rmax**2, int(N))
x_arcsec = r**.5 * np.cos(angle)
y_arcsec = r**.5 * np.sin(angle)
x_arcsec += center_x
y_arcsec += center_y
x_kpc, y_kpc = x_arcsec * self._rs_kpc, y_arcsec * self._rs_kpc
u = np.random.uniform(self._xmin, 0.999999, len(x_kpc))
z_units_rs = self.cdf(u)
z_kpc = z_units_rs * self._rs_kpc
return np.array(x_kpc), np.array(y_kpc), np.hypot(
x_kpc, y_kpc), np.sqrt(x_kpc**2 + y_kpc**2 + z_kpc**2)
def _import_class(lens_type,
custom_class,
kwargs_interp,
z_lens=None,
z_source=None):
"""
:param lens_type: string, lens model type
:param custom_class: custom class
:param z_lens: lens redshift # currently only used in NFW_MC model as this is redshift dependent
:param z_source: source redshift # currently only used in NFW_MC model as this is redshift dependent
:param kwargs_interp: interpolation keyword arguments specifying the numerics.
See description in the Interpolate() class. Only applicable for 'INTERPOL' and 'INTERPOL_SCALED' models.
:return: class instance of the lens model type
"""
if lens_type == 'SHIFT':
from lenstronomy.LensModel.Profiles.constant_shift import Shift
return Shift()
elif lens_type == 'NIE_POTENTIAL':
from lenstronomy.LensModel.Profiles.nie_potential import NIE_POTENTIAL
return NIE_POTENTIAL()
elif lens_type == 'CONST_MAG':
from lenstronomy.LensModel.Profiles.const_mag import ConstMag
return ConstMag()
elif lens_type == 'SHEAR':
from lenstronomy.LensModel.Profiles.shear import Shear
return Shear()
elif lens_type == 'SHEAR_GAMMA_PSI':
from lenstronomy.LensModel.Profiles.shear import ShearGammaPsi
return ShearGammaPsi()
elif lens_type == 'SHEAR_REDUCED':
from lenstronomy.LensModel.Profiles.shear import ShearReduced
return ShearReduced()
elif lens_type == 'CONVERGENCE':
from lenstronomy.LensModel.Profiles.convergence import Convergence
return Convergence()
elif lens_type == 'HESSIAN':
from lenstronomy.LensModel.Profiles.hessian import Hessian
return Hessian()
elif lens_type == 'FLEXION':
from lenstronomy.LensModel.Profiles.flexion import Flexion
return Flexion()
elif lens_type == 'FLEXIONFG':
from lenstronomy.LensModel.Profiles.flexionfg import Flexionfg
return Flexionfg()
elif lens_type == 'POINT_MASS':
from lenstronomy.LensModel.Profiles.point_mass import PointMass
return PointMass()
elif lens_type == 'SIS':
from lenstronomy.LensModel.Profiles.sis import SIS
return SIS()
elif lens_type == 'SIS_TRUNCATED':
from lenstronomy.LensModel.Profiles.sis_truncate import SIS_truncate
return SIS_truncate()
elif lens_type == 'SIE':
from lenstronomy.LensModel.Profiles.sie import SIE
return SIE()
elif lens_type == 'SPP':
from lenstronomy.LensModel.Profiles.spp import SPP
return SPP()
elif lens_type == 'NIE':
from lenstronomy.LensModel.Profiles.nie import NIE
return NIE()
elif lens_type == 'NIE_SIMPLE':
from lenstronomy.LensModel.Profiles.nie import NIEMajorAxis
return NIEMajorAxis()
elif lens_type == 'CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import Chameleon
return Chameleon()
elif lens_type == 'DOUBLE_CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import DoubleChameleon
return DoubleChameleon()
elif lens_type == 'TRIPLE_CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import TripleChameleon
return TripleChameleon()
elif lens_type == 'SPEP':
from lenstronomy.LensModel.Profiles.spep import SPEP
return SPEP()
elif lens_type == 'PEMD':
from lenstronomy.LensModel.Profiles.pemd import PEMD
return PEMD()
elif lens_type == 'SPEMD':
from lenstronomy.LensModel.Profiles.spemd import SPEMD
return SPEMD()
elif lens_type == 'EPL':
from lenstronomy.LensModel.Profiles.epl import EPL
return EPL()
elif lens_type == 'EPL_NUMBA':
from lenstronomy.LensModel.Profiles.epl_numba import EPL_numba
return EPL_numba()
elif lens_type == 'SPL_CORE':
from lenstronomy.LensModel.Profiles.splcore import SPLCORE
return SPLCORE()
elif lens_type == 'NFW':
from lenstronomy.LensModel.Profiles.nfw import NFW
return NFW()
elif lens_type == 'NFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.nfw_ellipse import NFW_ELLIPSE
return NFW_ELLIPSE()
elif lens_type == 'NFW_ELLIPSE_GAUSS_DEC':
from lenstronomy.LensModel.Profiles.gauss_decomposition import NFWEllipseGaussDec
return NFWEllipseGaussDec()
elif lens_type == 'NFW_ELLIPSE_CSE':
from lenstronomy.LensModel.Profiles.nfw_ellipse_cse import NFW_ELLIPSE_CSE
return NFW_ELLIPSE_CSE()
elif lens_type == 'TNFW':
from lenstronomy.LensModel.Profiles.tnfw import TNFW
return TNFW()
elif lens_type == 'TNFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.tnfw_ellipse import TNFW_ELLIPSE
return TNFW_ELLIPSE()
elif lens_type == 'CNFW':
from lenstronomy.LensModel.Profiles.cnfw import CNFW
return CNFW()
elif lens_type == 'CNFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.cnfw_ellipse import CNFW_ELLIPSE
return CNFW_ELLIPSE()
elif lens_type == 'CTNFW_GAUSS_DEC':
from lenstronomy.LensModel.Profiles.gauss_decomposition import CTNFWGaussDec
return CTNFWGaussDec()
elif lens_type == 'NFW_MC':
from lenstronomy.LensModel.Profiles.nfw_mass_concentration import NFWMC
return NFWMC(z_lens=z_lens, z_source=z_source)
elif lens_type == 'SERSIC':
from lenstronomy.LensModel.Profiles.sersic import Sersic
return Sersic()
elif lens_type == 'SERSIC_ELLIPSE_POTENTIAL':
from lenstronomy.LensModel.Profiles.sersic_ellipse_potential import SersicEllipse
return SersicEllipse()
elif lens_type == 'SERSIC_ELLIPSE_KAPPA':
from lenstronomy.LensModel.Profiles.sersic_ellipse_kappa import SersicEllipseKappa
return SersicEllipseKappa()
elif lens_type == 'SERSIC_ELLIPSE_GAUSS_DEC':
from lenstronomy.LensModel.Profiles.gauss_decomposition import SersicEllipseGaussDec
return SersicEllipseGaussDec()
elif lens_type == 'PJAFFE':
from lenstronomy.LensModel.Profiles.p_jaffe import PJaffe
return PJaffe()
elif lens_type == 'PJAFFE_ELLIPSE':
from lenstronomy.LensModel.Profiles.p_jaffe_ellipse import PJaffe_Ellipse
return PJaffe_Ellipse()
elif lens_type == 'HERNQUIST':
from lenstronomy.LensModel.Profiles.hernquist import Hernquist
return Hernquist()
elif lens_type == 'HERNQUIST_ELLIPSE':
from lenstronomy.LensModel.Profiles.hernquist_ellipse import Hernquist_Ellipse
return Hernquist_Ellipse()
elif lens_type == 'HERNQUIST_ELLIPSE_CSE':
from lenstronomy.LensModel.Profiles.hernquist_ellipse_cse import HernquistEllipseCSE
return HernquistEllipseCSE()
elif lens_type == 'GAUSSIAN':
from lenstronomy.LensModel.Profiles.gaussian_potential import Gaussian
return Gaussian()
elif lens_type == 'GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.gaussian_kappa import GaussianKappa
return GaussianKappa()
elif lens_type == 'GAUSSIAN_ELLIPSE_KAPPA':
from lenstronomy.LensModel.Profiles.gaussian_ellipse_kappa import GaussianEllipseKappa
return GaussianEllipseKappa()
elif lens_type == 'GAUSSIAN_ELLIPSE_POTENTIAL':
from lenstronomy.LensModel.Profiles.gaussian_ellipse_potential import GaussianEllipsePotential
return GaussianEllipsePotential()
elif lens_type == 'MULTI_GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappa
return MultiGaussianKappa()
elif lens_type == 'MULTI_GAUSSIAN_KAPPA_ELLIPSE':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappaEllipse
return MultiGaussianKappaEllipse()
elif lens_type == 'INTERPOL':
from lenstronomy.LensModel.Profiles.interpol import Interpol
return Interpol(**kwargs_interp)
elif lens_type == 'INTERPOL_SCALED':
from lenstronomy.LensModel.Profiles.interpol import InterpolScaled
return InterpolScaled(**kwargs_interp)
elif lens_type == 'SHAPELETS_POLAR':
from lenstronomy.LensModel.Profiles.shapelet_pot_polar import PolarShapelets
return PolarShapelets()
elif lens_type == 'SHAPELETS_CART':
from lenstronomy.LensModel.Profiles.shapelet_pot_cartesian import CartShapelets
return CartShapelets()
elif lens_type == 'DIPOLE':
from lenstronomy.LensModel.Profiles.dipole import Dipole
return Dipole()
elif lens_type == 'CURVED_ARC_CONST':
from lenstronomy.LensModel.Profiles.curved_arc_const import CurvedArcConst
return CurvedArcConst()
elif lens_type == 'CURVED_ARC_CONST_MST':
from lenstronomy.LensModel.Profiles.curved_arc_const import CurvedArcConstMST
return CurvedArcConstMST()
elif lens_type == 'CURVED_ARC_SPP':
from lenstronomy.LensModel.Profiles.curved_arc_spp import CurvedArcSPP
return CurvedArcSPP()
elif lens_type == 'CURVED_ARC_SIS_MST':
from lenstronomy.LensModel.Profiles.curved_arc_sis_mst import CurvedArcSISMST
return CurvedArcSISMST()
elif lens_type == 'CURVED_ARC_SPT':
from lenstronomy.LensModel.Profiles.curved_arc_spt import CurvedArcSPT
return CurvedArcSPT()
elif lens_type == 'CURVED_ARC_TAN_DIFF':
from lenstronomy.LensModel.Profiles.curved_arc_tan_diff import CurvedArcTanDiff
return CurvedArcTanDiff()
elif lens_type == 'ARC_PERT':
from lenstronomy.LensModel.Profiles.arc_perturbations import ArcPerturbations
return ArcPerturbations()
elif lens_type == 'coreBURKERT':
from lenstronomy.LensModel.Profiles.coreBurkert import CoreBurkert
return CoreBurkert()
elif lens_type == 'CORED_DENSITY':
from lenstronomy.LensModel.Profiles.cored_density import CoredDensity
return CoredDensity()
elif lens_type == 'CORED_DENSITY_2':
from lenstronomy.LensModel.Profiles.cored_density_2 import CoredDensity2
return CoredDensity2()
elif lens_type == 'CORED_DENSITY_EXP':
from lenstronomy.LensModel.Profiles.cored_density_exp import CoredDensityExp
return CoredDensityExp()
elif lens_type == 'CORED_DENSITY_MST':
from lenstronomy.LensModel.Profiles.cored_density_mst import CoredDensityMST
return CoredDensityMST(profile_type='CORED_DENSITY')
elif lens_type == 'CORED_DENSITY_2_MST':
from lenstronomy.LensModel.Profiles.cored_density_mst import CoredDensityMST
return CoredDensityMST(profile_type='CORED_DENSITY_2')
elif lens_type == 'CORED_DENSITY_EXP_MST':
from lenstronomy.LensModel.Profiles.cored_density_mst import CoredDensityMST
return CoredDensityMST(profile_type='CORED_DENSITY_EXP')
elif lens_type == 'NumericalAlpha':
from lenstronomy.LensModel.Profiles.numerical_deflections import NumericalAlpha
return NumericalAlpha(custom_class)
elif lens_type == 'MULTIPOLE':
from lenstronomy.LensModel.Profiles.multipole import Multipole
return Multipole()
elif lens_type == 'CSE':
from lenstronomy.LensModel.Profiles.cored_steep_ellipsoid import CSE
return CSE()
elif lens_type == 'ElliSLICE':
from lenstronomy.LensModel.Profiles.elliptical_density_slice import ElliSLICE
return ElliSLICE()
elif lens_type == 'ULDM':
from lenstronomy.LensModel.Profiles.uldm import Uldm
return Uldm()
elif lens_type == 'CORED_DENSITY_ULDM_MST':
from lenstronomy.LensModel.Profiles.cored_density_mst import CoredDensityMST
return CoredDensityMST(profile_type='CORED_DENSITY_ULDM')
else:
raise ValueError(
'%s is not a valid lens model. Supported are: %s.' %
(lens_type, _SUPPORTED_MODELS))
def setup(self):
self.cn = CNFW()
self.n = NFW()
class Testcnfw(object):
"""
tests the Gaussian methods
"""
def setup(self):
self.cn = CNFW()
self.n = NFW()
def test_pot(self):
pot1 = self.cn.function(2, 0, 1, 1, 0.5)
pot2 = self.n.function(2, 0, 1, 1)
npt.assert_almost_equal(pot1, pot2)
def _kappa_integrand(self, x, y, Rs, m0, r_core):
return 2 * np.pi * x * self.cn.density_2d(x, y, Rs, m0, r_core)
def test_derivatives(self):
Rs = 10.
rho0 = 1.
r_core = 7.
R = np.linspace(0.1 * Rs, 4 * Rs, 1000)
alpha = self.cn.cnfwAlpha(R, Rs, rho0, r_core, R, 0)[0]
alpha_theory = self.cn.mass_2d(R, Rs, rho0, r_core) / np.pi / R
theta_Rs = self.cn._rho2alpha(rho0, Rs, r_core)
alpha_derivatives = self.cn.derivatives(R, 0, Rs, theta_Rs, r_core)[0]
npt.assert_almost_equal(alpha / alpha_theory, 1)
npt.assert_almost_equal(alpha / alpha_derivatives, 1)
def test_mproj(self):
Rs = 10.
r_core = 0.7 * Rs
Rmax = np.linspace(0.6 * Rs, 1.1 * Rs, 1000)
dr = Rmax[1] - Rmax[0]
m0 = 1
m2d = self.cn.mass_2d(Rmax, Rs, m0, r_core)
integrand = np.gradient(m2d, dr)
kappa_integrand = self._kappa_integrand(Rmax, 0, Rs, m0, r_core)
mean_diff = np.absolute(kappa_integrand - integrand) * len(Rmax)**-1
npt.assert_almost_equal(mean_diff, 0, decimal=3)
def test_GF(self):
x_array = np.array([0.5, 0.8, 1.2])
b = 0.7
Garray = self.cn._G(x_array, b)
Farray = self.cn._F(x_array, b)
for i in range(0, len(x_array)):
npt.assert_almost_equal(Farray[i], self.cn._F(x_array[i], b))
npt.assert_almost_equal(Garray[i], self.cn._G(x_array[i], b))
def test_gamma(self):
Rs = 10.
rho0 = 1.
r_core = 0.7 * Rs
R = np.array([0.5 * Rs, 0.8 * Rs, 1.1 * Rs])
g1_array, g2_array = self.cn.cnfwGamma(R, Rs, rho0, r_core, R,
0.6 * Rs)
for i in range(0, len(R)):
g1, g2 = self.cn.cnfwGamma(R[i], Rs, rho0, r_core, R[i], 0.6 * Rs)
npt.assert_almost_equal(g1_array[i], g1)
npt.assert_almost_equal(g2_array[i], g2)
def test_rho_angle_transform(self):
Rs = float(10)
rho0 = float(1)
r_core = float(7)
theta_Rs = self.cn._rho2alpha(rho0, Rs, r_core)
theta_rs_2 = self.cn.cnfwAlpha(Rs, Rs, rho0, r_core, Rs, 0)[0]
npt.assert_almost_equal(theta_Rs * theta_rs_2**-1, 1)
rho0_2 = self.cn._alpha2rho0(theta_Rs, Rs, r_core)
npt.assert_almost_equal(rho0, rho0_2)
class Testcnfw(object):
"""
tests the Gaussian methods
"""
def setup(self):
self.cn = CNFW()
self.n = NFW()
def test_pot(self):
# this test requires that the CNFW profile with a very small core results in the potential of the NFW profile
pot1 = self.cn.function(x=2, y=0, Rs=1, alpha_Rs=1, r_core=0.001)
pot2 = self.n.function(x=2, y=0, Rs=1, alpha_Rs=1)
npt.assert_almost_equal(pot1 / pot2, 1, decimal=3)
def _kappa_integrand(self, x, y, Rs, m0, r_core):
return 2 * np.pi * x * self.cn.density_2d(x, y, Rs, m0, r_core)
def test_derivatives(self):
Rs = 10.
rho0 = 1.
r_core = 7.
R = np.linspace(0.1 * Rs, 4 * Rs, 1000)
alpha_Rs = self.cn._rho2alpha(rho0, Rs, r_core)
alpha = self.cn.alpha_r(R, Rs, rho0, r_core)
alpha_theory = self.cn.mass_2d(R, Rs, rho0, r_core) / np.pi / R
alpha_derivatives = self.cn.derivatives(R, 0, Rs, alpha_Rs, r_core)[0]
npt.assert_almost_equal(alpha_derivatives / alpha_theory, 1)
npt.assert_almost_equal(alpha / alpha_theory, 1)
npt.assert_almost_equal(alpha / alpha_derivatives, 1)
def test_mass_3d(self):
Rs = 10.
rho0 = 1.
r_core = 7.
R = np.linspace(0.1 * Rs, 4 * Rs, 1000)
alpha_Rs = self.cn._rho2alpha(rho0, Rs, r_core)
m3d = self.cn.mass_3d(R, Rs, rho0, r_core)
m3d_lens = self.cn.mass_3d_lens(R, Rs, alpha_Rs, r_core)
npt.assert_almost_equal(m3d, m3d_lens, decimal=8)
def test_mproj(self):
Rs = 10.
r_core = 0.7 * Rs
Rmax = np.linspace(0.6 * Rs, 1.1 * Rs, 1000)
dr = Rmax[1] - Rmax[0]
m0 = 1
m2d = self.cn.mass_2d(Rmax, Rs, m0, r_core)
integrand = np.gradient(m2d, dr)
kappa_integrand = self._kappa_integrand(Rmax, 0, Rs, m0, r_core)
mean_diff = np.absolute(kappa_integrand - integrand) * len(Rmax)**-1
npt.assert_almost_equal(mean_diff, 0, decimal=3)
def test_GF(self):
x_array = np.array([0.5, 0.8, 1.2])
b = 0.7
Garray = self.cn._G(x_array, b)
Farray = self.cn._F(x_array, b)
for i in range(0, len(x_array)):
npt.assert_almost_equal(Farray[i], self.cn._F(x_array[i], b))
npt.assert_almost_equal(Garray[i], self.cn._G(x_array[i], b))
def test_gamma(self):
Rs = 10.
rho0 = 1.
r_core = 0.7 * Rs
R = np.array([0.5 * Rs, 0.8 * Rs, 1.1 * Rs])
g1_array, g2_array = self.cn.cnfwGamma(R, Rs, rho0, r_core, R,
0.6 * Rs)
for i in range(0, len(R)):
g1, g2 = self.cn.cnfwGamma(R[i], Rs, rho0, r_core, R[i], 0.6 * Rs)
npt.assert_almost_equal(g1_array[i], g1)
npt.assert_almost_equal(g2_array[i], g2)