class TestGaussianKappa(object): """ test the Gaussian with Gaussian kappa """ def setup(self): self.gaussian_kappa = MultiGaussianKappa() self.gaussian = Gaussian() self.g_kappa = GaussianKappa() def test_derivatives(self): x = np.linspace(0, 5, 10) y = np.linspace(0, 5, 10) amp = [1. * 2 * np.pi] center_x = 0. center_y = 0. sigma = [1.] f_x, f_y = self.gaussian_kappa.derivatives(x, y, amp, sigma, center_x, center_y) npt.assert_almost_equal(f_x[2], 0.63813558702212059, decimal=8) npt.assert_almost_equal(f_y[2], 0.63813558702212059, decimal=8) def test_hessian(self): x = np.linspace(0, 5, 10) y = np.linspace(0, 5, 10) amp = [1. * 2 * np.pi] center_x = 0. center_y = 0. sigma = [1.] f_xx, f_yy, f_xy = self.gaussian_kappa.hessian(x, y, amp, sigma, center_x, center_y) kappa = 1. / 2 * (f_xx + f_yy) kappa_true = self.gaussian.function(x, y, amp[0], sigma[0], sigma[0], center_x, center_y) print(kappa_true) print(kappa) npt.assert_almost_equal(kappa[0], kappa_true[0], decimal=5) npt.assert_almost_equal(kappa[1], kappa_true[1], decimal=5) def test_density_2d(self): x = np.linspace(0, 5, 10) y = np.linspace(0, 5, 10) amp = [1. * 2 * np.pi] center_x = 0. center_y = 0. sigma = [1.] f_xx, f_yy, f_xy = self.gaussian_kappa.hessian(x, y, amp, sigma, center_x, center_y) kappa = 1. / 2 * (f_xx + f_yy) amp_3d = self.g_kappa._amp2d_to_3d(amp, sigma[0], sigma[0]) density_2d = self.gaussian_kappa.density_2d(x, y, amp_3d, sigma, center_x, center_y) npt.assert_almost_equal(kappa[1], density_2d[1], decimal=5) npt.assert_almost_equal(kappa[2], density_2d[2], decimal=5) def test_density(self): amp = [1. * 2 * np.pi] sigma = [1.] density = self.gaussian_kappa.density(1., amp, sigma) npt.assert_almost_equal(density, 0.6065306597126334, decimal=8)
def test_multi_gaussian_lens(self): kwargs_options = {'lens_model_list': ['SPEP']} e1, e2 = param_util.phi_q2_ellipticity(0, 0.9) kwargs_lens = [{ 'gamma': 1.8, 'theta_E': 0.6, 'e1': e1, 'e2': e2, 'center_x': 0.5, 'center_y': -0.1 }] lensAnalysis = LensAnalysis(kwargs_options) amplitudes, sigmas, center_x, center_y = lensAnalysis.multi_gaussian_lens( kwargs_lens, n_comp=20) model = MultiGaussianKappa() x = np.logspace(-2, 0.5, 10) + 0.5 y = np.zeros_like(x) - 0.1 f_xx, f_yy, fxy = model.hessian(x, y, amplitudes, sigmas, center_x=0.5, center_y=-0.1) kappa_mge = (f_xx + f_yy) / 2 kappa_true = lensAnalysis.LensModel.kappa(x, y, kwargs_lens) print(kappa_true / kappa_mge) for i in range(len(x)): npt.assert_almost_equal(kappa_mge[i] / kappa_true[i], 1, 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_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)