def test_light_3d(self): gaussianEllipse = GaussianEllipse() gaussian = Gaussian() sigma = 1 r = 1. amp = 1. flux_spherical = gaussian.light_3d(r, amp, sigma) flux = gaussianEllipse.light_3d(r, amp, sigma) npt.assert_almost_equal(flux, flux_spherical, decimal=8) multiGaussian = MultiGaussian() multiGaussianEllipse = MultiGaussianEllipse() amp = [1, 2] sigma = [1., 2] flux_spherical = multiGaussian.light_3d(r, amp, sigma) flux = multiGaussianEllipse.light_3d(r, amp, sigma) npt.assert_almost_equal(flux, flux_spherical, decimal=8)
class TestMGE(object): """ tests the Gaussian methods """ def setup(self): self.sersic = Sersic() self.multiGaussian = MultiGaussian() def test_mge_1d_sersic(self): n_comp = 30 r_sersic = 1. n_sersic = 3.7 I0_sersic = 1. rs = np.logspace(-2., 1., 50) * r_sersic ss = self.sersic.function(rs, np.zeros_like(rs), amp=I0_sersic, n_sersic=n_sersic, R_sersic=r_sersic) amplitudes, sigmas, norm = mge.mge_1d(rs, ss, N=n_comp) ss_mge = self.multiGaussian.function(rs, np.zeros_like(rs), amp=amplitudes, sigma=sigmas) #print((ss - ss_mge)/ss) for i in range(10, len(ss) - 10): #print(rs[i]) npt.assert_almost_equal((ss_mge[i] - ss[i]) / ss[i], 0, decimal=1) amplitudes, sigmas, norm = mge.mge_1d(rs, np.zeros_like(rs), N=n_comp) assert amplitudes[0] == 0 amplitudes, sigmas, norm = mge.mge_1d(rs, np.zeros_like(rs), N=0) assert amplitudes[0] == 0 def test_mge_sersic_radius(self): n_comp = 30 r_sersic = .5 n_sersic = 3.7 I0_sersic = 1. rs = np.logspace(-2., 1., 50) * r_sersic ss = self.sersic.function(rs, np.zeros_like(rs), amp=I0_sersic, n_sersic=n_sersic, R_sersic=r_sersic) amplitudes, sigmas, norm = mge.mge_1d(rs, ss, N=n_comp) ss_mge = self.multiGaussian.function(rs, np.zeros_like(rs), amp=amplitudes, sigma=sigmas) print((ss - ss_mge) / (ss + ss_mge)) for i in range(10, len(ss) - 10): #print(rs[i]) npt.assert_almost_equal((ss_mge[i] - ss[i]) / (ss[i]), 0, decimal=1) def test_mge_sersic_n_sersic(self): n_comp = 20 r_sersic = 1.5 n_sersic = .5 I0_sersic = 1. rs = np.logspace(-2., 1., 50) * r_sersic ss = self.sersic.function(rs, np.zeros_like(rs), amp=I0_sersic, n_sersic=n_sersic, R_sersic=r_sersic) amplitudes, sigmas, norm = mge.mge_1d(rs, ss, N=n_comp) ss_mge = self.multiGaussian.function(rs, np.zeros_like(rs), amp=amplitudes, sigma=sigmas) for i in range(10, len(ss) - 10): npt.assert_almost_equal((ss_mge[i] - ss[i]) / (ss[i] + ss_mge[i]), 0, decimal=1) n_comp = 20 r_sersic = 1.5 n_sersic = 3.5 I0_sersic = 1. rs = np.logspace(-2., 1., 50) * r_sersic ss = self.sersic.function(rs, np.zeros_like(rs), amp=I0_sersic, n_sersic=n_sersic, R_sersic=r_sersic) amplitudes, sigmas, norm = mge.mge_1d(rs, ss, N=n_comp) ss_mge = self.multiGaussian.function(rs, np.zeros_like(rs), amp=amplitudes, sigma=sigmas) for i in range(10, len(ss) - 10): npt.assert_almost_equal((ss_mge[i] - ss[i]) / (ss[i] + ss_mge[i]), 0, decimal=1) def test_hernquist(self): hernquist = Hernquist() n_comp = 20 sigma0 = 1 r_eff = 1.5 rs = np.logspace(-2., 1., 50) * r_eff * 0.5 ss = hernquist.function(rs, np.zeros_like(rs), sigma0, Rs=r_eff) amplitudes, sigmas, norm = mge.mge_1d(rs, ss, N=n_comp) ss_mge = self.multiGaussian.function(rs, np.zeros_like(rs), amp=amplitudes, sigma=sigmas) for i in range(10, len(ss) - 10): npt.assert_almost_equal((ss_mge[i] - ss[i]) / (ss[i] + ss_mge[i]), 0, decimal=2) def test_hernquist_deprojection(self): hernquist = Hernquist() n_comp = 20 sigma0 = 1 r_eff = 1.5 rs = np.logspace(-2., 1., 50) * r_eff * 0.5 ss = hernquist.function(rs, np.zeros_like(rs), sigma0, Rs=r_eff) amplitudes, sigmas, norm = mge.mge_1d(rs, ss, N=n_comp) amplitudes_3d, sigmas_3d = mge.de_projection_3d(amplitudes, sigmas) ss_3d_mge = self.multiGaussian.function(rs, np.zeros_like(rs), amp=amplitudes_3d, sigma=sigmas_3d) ss_3d_mulit = self.multiGaussian.light_3d(rs, amp=amplitudes, sigma=sigmas) for i in range(10, len(ss_3d_mge)): npt.assert_almost_equal((ss_3d_mge[i] - ss_3d_mulit[i]) / (ss_3d_mulit[i] + ss_3d_mge[i]), 0, decimal=1) ss_3d = hernquist.light_3d(rs, sigma0, Rs=r_eff) for i in range(10, len(ss_3d) - 10): npt.assert_almost_equal( (ss_3d_mge[i] - ss_3d[i]) / (ss_3d[i] + ss_3d_mge[i]), 0, decimal=1) 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_example(self): n_comp = 10 rs = np.array([ 0.01589126, 0.01703967, 0.01827108, 0.01959148, 0.0210073, 0.02252544, 0.02415329, 0.02589879, 0.02777042, 0.02977731, 0.03192923, 0.03423667, 0.03671086, 0.03936385, 0.04220857, 0.04525886, 0.0485296, 0.0520367, 0.05579724, 0.05982956, 0.06415327, 0.06878945, 0.07376067, 0.07909115, 0.08480685, 0.09093561, 0.09750727, 0.10455385, 0.11210966, 0.12021152, 0.12889887, 0.13821403, 0.14820238, 0.15891255, 0.17039672, 0.18271082, 0.19591482, 0.21007304, 0.22525444, 0.24153295, 0.25898787, 0.2777042, 0.29777311, 0.31929235, 0.34236672, 0.36710861, 0.39363853, 0.42208569, 0.45258865, 0.48529597, 0.52036697, 0.55797244, 0.59829556, 0.64153272, 0.6878945, 0.73760673, 0.79091152, 0.8480685, 0.90935605, 0.97507269, 1.04553848, 1.12109664, 1.20211518, 1.28898871, 1.38214034, 1.48202378, 1.58912553, 1.70396721, 1.82710819, 1.95914822, 2.10073042, 2.25254437, 2.4153295, 2.58987865, 2.77704199, 2.9777311, 3.19292345, 3.42366716, 3.67108607, 3.93638527, 4.22085689, 4.5258865, 4.85295974, 5.20366966, 5.57972441, 5.98295559, 6.41532717, 6.87894505, 7.37606729, 7.90911519, 8.48068497, 9.09356051, 9.75072687, 10.45538481, 11.21096643, 12.02115183, 12.88988708, 13.82140341, 14.82023784, 15.89125526 ]) kappa = np.array([ 12.13776067, 11.60484966, 11.09533396, 10.60818686, 10.14242668, 9.69711473, 9.27135349, 8.86428482, 8.47508818, 8.10297905, 7.7472073, 7.40705574, 7.08183863, 6.77090034, 6.47361399, 6.18938022, 5.917626, 5.65780342, 5.40938864, 5.1718808, 4.94480104, 4.72769151, 4.52011448, 4.3216514, 4.13190214, 3.9504841, 3.77703149, 3.61119459, 3.45263901, 3.30104507, 3.1561071, 3.01753287, 2.88504297, 2.75837025, 2.63725931, 2.52146595, 2.41075668, 2.30490829, 2.20370736, 2.10694982, 2.01444058, 1.92599312, 1.84142909, 1.76057799, 1.6832768, 1.60936965, 1.53870751, 1.47114792, 1.40655465, 1.34479745, 1.28575181, 1.22929867, 1.17532421, 1.12371958, 1.07438074, 1.02720821, 0.98210687, 0.93898578, 0.897758, 0.85834039, 0.82065349, 0.78462129, 0.75017114, 0.71723359, 0.68574222, 0.65563353, 0.62684681, 0.59932403, 0.57300967, 0.5478507, 0.52379638, 0.5007982, 0.47880979, 0.45778683, 0.43768691, 0.41846951, 0.40009589, 0.38252899, 0.3657334, 0.34967525, 0.33432216, 0.31964317, 0.30560868, 0.29219041, 0.27936129, 0.26709545, 0.25536817, 0.24415579, 0.23343571, 0.22318631, 0.21338694, 0.20401782, 0.19506006, 0.18649562, 0.17830721, 0.17047832, 0.16299318, 0.15583668, 0.14899441, 0.14245255 ]) amplitudes, sigmas, norm = mge.mge_1d(rs, kappa, N=n_comp) 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_yy_nfw, f_xy_nfw = nfw.hessian(rs, 0, **kwargs_lens_nfw) f_xx_s, f_yy_s, f_xy_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_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_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)