def test_spemd(self):
from lenstronomy.LensModel.Profiles.spep import SPEP
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappa
spep = SPEP()
mge_kappa = MultiGaussianKappa()
n_comp = 8
theta_E = 1.41
kwargs = {'theta_E': theta_E, 'e1': 0, 'e2': 0, 'gamma': 1.61}
rs = np.logspace(-2., 1., 100) * theta_E
f_xx, f_yy, f_xy = spep.hessian(rs, 0, **kwargs)
kappa = 1 / 2. * (f_xx + f_yy)
amplitudes, sigmas, norm = mge.mge_1d(rs, kappa, N=n_comp)
kappa_mge = self.multiGaussian.function(rs,
np.zeros_like(rs),
amp=amplitudes,
sigma=sigmas)
f_xx_mge, f_yy_mge, f_xy_mge = mge_kappa.hessian(rs,
np.zeros_like(rs),
amp=amplitudes,
sigma=sigmas)
for i in range(0, 80):
npt.assert_almost_equal(kappa_mge[i],
1. / 2 * (f_xx_mge[i] + f_yy_mge[i]),
decimal=1)
npt.assert_almost_equal((kappa[i] - kappa_mge[i]) / kappa[i],
0,
decimal=1)
f_ = spep.function(theta_E, 0, **kwargs)
f_mge = mge_kappa.function(theta_E, 0, sigma=sigmas, amp=amplitudes)
npt.assert_almost_equal(f_mge / f_, 1, decimal=2)
def test_nfw_sersic(self):
kwargs_lens_nfw = {'alpha_Rs': 1.4129647849966354, 'Rs': 7.0991113634274736}
kwargs_lens_sersic = {'k_eff': 0.24100561407593576, 'n_sersic': 1.8058507329346063, 'R_sersic': 1.0371803141813705}
from lenstronomy.LensModel.Profiles.nfw import NFW
from lenstronomy.LensModel.Profiles.sersic import Sersic
nfw = NFW()
sersic = Sersic()
theta_E = 1.5
n_comp = 10
rs = np.logspace(-2., 1., 100) * theta_E
f_xx_nfw, f_xy_nfw, f_yx_nfw, f_yy_nfw = nfw.hessian(rs, 0, **kwargs_lens_nfw)
f_xx_s, f_xy_s, f_yx_s, f_yy_s = sersic.hessian(rs, 0, **kwargs_lens_sersic)
kappa = 1 / 2. * (f_xx_nfw + f_xx_s + f_yy_nfw + f_yy_s)
amplitudes, sigmas, norm = mge.mge_1d(rs, kappa, N=n_comp)
kappa_mge = self.multiGaussian.function(rs, np.zeros_like(rs), amp=amplitudes, sigma=sigmas)
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappa
mge_kappa = MultiGaussianKappa()
f_xx_mge, f_xy_mge, f_yx_mge, f_yy_mge = mge_kappa.hessian(rs, np.zeros_like(rs), amp=amplitudes, sigma=sigmas)
for i in range(0, 80):
npt.assert_almost_equal(kappa_mge[i], 1. / 2 * (f_xx_mge[i] + f_yy_mge[i]), decimal=1)
npt.assert_almost_equal((kappa[i] - kappa_mge[i]) / kappa[i], 0, decimal=1)
f_nfw = nfw.function(theta_E, 0, **kwargs_lens_nfw)
f_s = sersic.function(theta_E, 0, **kwargs_lens_sersic)
f_mge = mge_kappa.function(theta_E, 0, sigma=sigmas, amp=amplitudes)
npt.assert_almost_equal(f_mge / (f_nfw + f_s), 1, decimal=2)