def test_mge_kernel():
from lenstronomy.LightModel.Profiles.gaussian import MultiGaussian
mg = MultiGaussian()
fraction_list = [0.2, 0.7, 0.1]
sigmas_scaled = [5, 10, 15]
x, y = util.make_grid(numPix=101, deltapix=1)
kernel = mg.function(x, y, amp=fraction_list, sigma=sigmas_scaled)
kernel = util.array2image(kernel)
amps, sigmas, norm = kernel_util.mge_kernel(kernel, order=10)
print(amps, sigmas, norm)
kernel_new = mg.function(x, y, amp=amps, sigma=sigmas)
kernel_new = util.array2image(kernel_new)
#npt.assert_almost_equal(sigmas_scaled, sigmas)
#npt.assert_almost_equal(amps, fraction_list)
npt.assert_almost_equal(kernel_new, kernel, decimal=3)
def test_multi_gaussian_lens_light(self):
kwargs_profile = [{
'Rs': 0.16350224766074103,
'q': 0.4105628122365978,
'center_x': -0.019983826426838536,
'center_y': 0.90000011282957304,
'phi_G': 0.14944144075912402,
'sigma0': 1.3168943578511678
}, {
'Rs': 0.29187068596715743,
'q': 0.70799587973181288,
'center_x': 0.020568531548241405,
'center_y': 0.036038490364800925,
'Ra': 0.020000382843298824,
'phi_G': -0.37221683730659516,
'sigma0': 85.948773973262391
}]
kwargs_options = {
'lens_model_list': ['SPEP'],
'lens_model_internal_bool': [True],
'lens_light_model_internal_bool': [True, True],
'lens_light_model_list': ['HERNQUIST_ELLIPSE', 'PJAFFE_ELLIPSE']
}
lensAnalysis = LensAnalysis(kwargs_options)
amplitudes, sigma = lensAnalysis.multi_gaussian_lens_light(
kwargs_profile, n_comp=20)
mge = MultiGaussian()
flux = mge.function(1., 1, amp=amplitudes, sigma=sigma)
npt.assert_almost_equal(flux, 0.04531989512955493, decimal=8)
def pixel_kernel(self, num_pix):
"""
computes a pixelized kernel from the MGE parameters
:param num_pix: int, size of kernel (odd number per axis)
:return: pixel kernel centered
"""
from lenstronomy.LightModel.Profiles.gaussian import MultiGaussian
mg = MultiGaussian()
x, y = util.make_grid(numPix=num_pix, deltapix=self._pixel_scale)
kernel = mg.function(x, y, amp=self._fraction_list, sigma=self._sigmas_scaled)
kernel = util.array2image(kernel)
return kernel / np.sum(kernel)
def test_multi_gaussian_decomposition(self):
Rs = 1.
kwargs_light = [{'Rs': Rs, 'amp': 1., 'center_x': 0, 'center_y': 0}]
kwargs_options = {'light_model_list': ['HERNQUIST']}
lightModel = LightModel(**kwargs_options)
profile = LightProfileAnalysis(light_model=lightModel)
amplitudes, sigmas, center_x, center_y = profile.multi_gaussian_decomposition(kwargs_light, grid_spacing=0.01, grid_num=100, model_bool_list=None, n_comp=20,
center_x=None, center_y=None)
mge = MultiGaussian()
r_array = np.logspace(start=-2, stop=0.5, num=10)
print(r_array, 'test r_array')
flux = mge.function(r_array, 0, amp=amplitudes, sigma=sigmas, center_x=center_x, center_y=center_y)
flux_true = lightModel.surface_brightness(r_array, 0, kwargs_light)
npt.assert_almost_equal(flux / flux_true, 1, decimal=2)
# test off-center
Rs = 1.
offset = 1.
kwargs_light = [{'Rs': Rs, 'amp': 1., 'center_x': offset, 'center_y': 0}]
kwargs_options = {'light_model_list': ['HERNQUIST']}
lightModel = LightModel(**kwargs_options)
profile = LightProfileAnalysis(light_model=lightModel)
amplitudes, sigmas, center_x, center_y = profile.multi_gaussian_decomposition(kwargs_light, grid_spacing=0.01,
grid_num=100, model_bool_list=None,
n_comp=20,
center_x=None, center_y=None)
assert center_x == offset
assert center_y == 0
mge = MultiGaussian()
r_array = np.logspace(start=-2, stop=0.5, num=10)
print(r_array, 'test r_array')
flux = mge.function(r_array, 0, amp=amplitudes, sigma=sigmas, center_x=center_x, center_y=center_y)
flux_true = lightModel.surface_brightness(r_array, 0, kwargs_light)
npt.assert_almost_equal(flux / flux_true, 1, decimal=2)
"""
def test_multi_gaussian_lens_light(self):
kwargs_profile = [{
'Rs': 0.16350224766074103,
'e1': 0,
'e2': 0,
'center_x': 0,
'center_y': 0,
'amp': 1.3168943578511678
}, {
'Rs': 0.29187068596715743,
'e1': 0,
'e2': 0,
'center_x': 0,
'center_y': 0,
'Ra': 0.020000382843298824,
'amp': 85.948773973262391
}]
kwargs_options = {
'lens_model_list': ['SPEP'],
'lens_model_internal_bool': [True],
'lens_light_model_internal_bool': [True, True],
'lens_light_model_list': ['HERNQUIST_ELLIPSE', 'PJAFFE_ELLIPSE']
}
lensAnalysis = LensAnalysis(kwargs_options)
amplitudes, sigma, center_x, center_y = lensAnalysis.multi_gaussian_lens_light(
kwargs_profile, n_comp=20)
mge = MultiGaussian()
flux = mge.function(1.,
1,
amp=amplitudes,
sigma=sigma,
center_x=center_x,
center_y=center_y)
flux_true = lensAnalysis.LensLightModel.surface_brightness(
1, 1, kwargs_profile)
npt.assert_almost_equal(flux / flux_true, 1, decimal=2)
del kwargs_profile[0]['center_x']
del kwargs_profile[0]['center_y']
amplitudes_new, sigma, center_x, center_y = lensAnalysis.multi_gaussian_lens_light(
kwargs_profile, n_comp=20)
npt.assert_almost_equal(amplitudes_new, amplitudes, decimal=2)
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)
