class TestEPLvsNIE(object):
"""
tests the Gaussian methods
"""
def setup(self):
from lenstronomy.LensModel.Profiles.epl import EPL
self.EPL = EPL()
from lenstronomy.LensModel.Profiles.nie import NIE
self.NIE = NIE()
def test_function(self):
phi_E = 1.
gamma = 2.
q = 0.999
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
x = np.array([1., 2])
y = np.array([2, 0])
values = self.EPL.function(x, y, phi_E, gamma, e1, e2)
values_nie = self.NIE.function(x, y, phi_E, e1, e2, 0.)
delta_f = values[0] - values[1]
delta_f_nie = values_nie[0] - values_nie[1]
npt.assert_almost_equal(delta_f, delta_f_nie, decimal=5)
q = 0.8
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
x = np.array([1., 2])
y = np.array([2, 0])
values = self.EPL.function(x, y, phi_E, gamma, e1, e2)
values_nie = self.NIE.function(x, y, phi_E, e1, e2, 0.)
delta_f = values[0] - values[1]
delta_f_nie = values_nie[0] - values_nie[1]
npt.assert_almost_equal(delta_f, delta_f_nie, decimal=5)
q = 0.4
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
x = np.array([1., 2])
y = np.array([2, 0])
values = self.EPL.function(x, y, phi_E, gamma, e1, e2)
values_nie = self.NIE.function(x, y, phi_E, e1, e2, 0.)
delta_f = values[0] - values[1]
delta_f_nie = values_nie[0] - values_nie[1]
npt.assert_almost_equal(delta_f, delta_f_nie, decimal=5)
def test_derivatives(self):
x = np.array([1])
y = np.array([2])
phi_E = 1.
gamma = 2.
q = 1.
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_x, f_y = self.EPL.derivatives(x, y, phi_E, gamma, e1, e2)
f_x_nie, f_y_nie = self.NIE.derivatives(x, y, phi_E, e1, e2, 0.)
npt.assert_almost_equal(f_x, f_x_nie, decimal=4)
npt.assert_almost_equal(f_y, f_y_nie, decimal=4)
q = 0.7
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_x, f_y = self.EPL.derivatives(x, y, phi_E, gamma, e1, e2)
f_x_nie, f_y_nie = self.NIE.derivatives(x, y, phi_E, e1, e2, 0.)
npt.assert_almost_equal(f_x, f_x_nie, decimal=4)
npt.assert_almost_equal(f_y, f_y_nie, decimal=4)
def test_hessian(self):
x = np.array([1.])
y = np.array([2.])
phi_E = 1.
gamma = 2.
q = 0.9
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_xx, f_xy, f_yx, f_yy = self.EPL.hessian(x, y, phi_E, gamma, e1, e2)
f_xx_nie, f_xy_nie, f_yx_nie, f_yy_nie = self.NIE.hessian(x, y, phi_E, e1, e2, 0.)
npt.assert_almost_equal(f_xx, f_xx_nie, decimal=4)
npt.assert_almost_equal(f_yy, f_yy_nie, decimal=4)
npt.assert_almost_equal(f_xy, f_xy_nie, decimal=4)
npt.assert_almost_equal(f_xy, f_yx, decimal=8)
def test_density_lens(self):
r = 1
kwargs = {'theta_E': 1, 'gamma': 2, 'e1': 0, 'e2': 0}
rho = self.EPL.density_lens(r, **kwargs)
from lenstronomy.LensModel.Profiles.spep import SPEP
spep = SPEP()
rho_spep = spep.density_lens(r, **kwargs)
npt.assert_almost_equal(rho, rho_spep, decimal=7)
def test_mass_3d_lens(self):
r = 1
kwargs = {'theta_E': 1, 'gamma': 2, 'e1': 0, 'e2': 0}
rho = self.EPL.mass_3d_lens(r, **kwargs)
from lenstronomy.LensModel.Profiles.spep import SPEP
spep = SPEP()
rho_spep = spep.mass_3d_lens(r, **kwargs)
npt.assert_almost_equal(rho, rho_spep, decimal=7)
def test_static(self):
x, y = 1., 1.
phi_G, q = 0.3, 0.8
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
kwargs_lens = {'theta_E': 1., 'gamma': 1.5, 'e1': e1, 'e2': e2}
f_ = self.EPL.function(x, y, **kwargs_lens)
self.EPL.set_static(**kwargs_lens)
f_static = self.EPL.function(x, y, **kwargs_lens)
npt.assert_almost_equal(f_, f_static, decimal=8)
self.EPL.set_dynamic()
kwargs_lens = {'theta_E': 2., 'gamma': 1.9, 'e1': e1, 'e2': e2}
f_dyn = self.EPL.function(x, y, **kwargs_lens)
assert f_dyn != f_static
def test_regularization(self):
phi_E = 1.
gamma = 2.
q = 1.
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
x = 0.
y = 0.
f_x, f_y = self.EPL.derivatives(x, y, phi_E, gamma, e1, e2)
npt.assert_almost_equal(f_x, 0.)
npt.assert_almost_equal(f_y, 0.)
x = 0.
y = 0.
f_xx, f_xy, f_yx, f_yy = self.EPL.hessian(x, y, phi_E, gamma, e1, e2)
assert f_xx > 10 ** 5
assert f_yy > 10 ** 5
#npt.assert_almost_equal(f_xx, 10**10)
#npt.assert_almost_equal(f_yy, 10**10)
npt.assert_almost_equal(f_xy, 0)
npt.assert_almost_equal(f_yx, 0)
class SIE(LensProfileBase):
"""
class for singular isothermal ellipsoid (SIS with ellipticity)
.. math::
\\kappa(x, y) = \\frac{1}{2} \\left(\\frac{\\theta_{E}}{\\sqrt{q x^2 + y^2/q}} \\right)
with :math:`\\theta_{E}` is the (circularized) Einstein radius,
:math:`q` is the minor/major axis ratio,
and :math:`x` and :math:`y` are defined in a coordinate sys- tem aligned with the major and minor axis of the lens.
In terms of eccentricities, this profile is defined as
.. math::
\\kappa(r) = \\frac{1}{2} \\left(\\frac{\\theta'_{E}}{r \\sqrt{1 − e*\\cos(2*\\phi)}} \\right)
with :math:`\\epsilon` is the ellipticity defined as
.. math::
\\epsilon = \\frac{1-q^2}{1+q^2}
And an Einstein radius :math:`\\theta'_{\\rm E}` related to the definition used is
.. math::
\\left(\\frac{\\theta'_{\\rm E}}{\\theta_{\\rm E}}\\right)^{2} = \\frac{2q}{1+q^2}.
"""
param_names = ['theta_E', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {
'theta_E': 0,
'e1': -0.5,
'e2': -0.5,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'theta_E': 100,
'e1': 0.5,
'e2': 0.5,
'center_x': 100,
'center_y': 100
}
def __init__(self, NIE=True):
"""
:param NIE: bool, if True, is using the NIE analytic model. Otherwise it uses PEMD with gamma=2 from fastell4py
"""
self._nie = NIE
if NIE:
from lenstronomy.LensModel.Profiles.nie import NIE
self.profile = NIE()
else:
from lenstronomy.LensModel.Profiles.epl import EPL
self.profile = EPL()
self._s_scale = 0.0000000001
self._gamma = 2
super(SIE, self).__init__()
def function(self, x, y, theta_E, e1, e2, center_x=0, center_y=0):
"""
:param x: x-coordinate (angular coordinates)
:param y: y-coordinate (angular coordinates)
:param theta_E: Einstein radius
:param e1: eccentricity
:param e2: eccentricity
:param center_x: centroid
:param center_y: centroid
:return:
"""
if self._nie:
return self.profile.function(x, y, theta_E, e1, e2, self._s_scale,
center_x, center_y)
else:
return self.profile.function(x, y, theta_E, self._gamma, e1, e2,
center_x, center_y)
def derivatives(self, x, y, theta_E, e1, e2, center_x=0, center_y=0):
"""
:param x: x-coordinate (angular coordinates)
:param y: y-coordinate (angular coordinates)
:param theta_E: Einstein radius
:param e1: eccentricity
:param e2: eccentricity
:param center_x: centroid
:param center_y: centroid
:return:
"""
if self._nie:
return self.profile.derivatives(x, y, theta_E, e1, e2,
self._s_scale, center_x, center_y)
else:
return self.profile.derivatives(x, y, theta_E, self._gamma, e1, e2,
center_x, center_y)
def hessian(self, x, y, theta_E, e1, e2, center_x=0, center_y=0):
"""
:param x: x-coordinate (angular coordinates)
:param y: y-coordinate (angular coordinates)
:param theta_E: Einstein radius
:param e1: eccentricity
:param e2: eccentricity
:param center_x: centroid
:param center_y: centroid
:return:
"""
if self._nie:
return self.profile.hessian(x, y, theta_E, e1, e2, self._s_scale,
center_x, center_y)
else:
return self.profile.hessian(x, y, theta_E, self._gamma, e1, e2,
center_x, center_y)
@staticmethod
def theta2rho(theta_E):
"""
converts projected density parameter (in units of deflection) into 3d density parameter
:param theta_E:
:return:
"""
fac1 = np.pi * 2
rho0 = theta_E / fac1
return rho0
@staticmethod
def mass_3d(r, rho0, e1=0, e2=0):
"""
mass enclosed a 3d sphere or radius r
:param r: radius in angular units
:param rho0: density at angle=1
:return: mass in angular units
"""
mass_3d = 4 * np.pi * rho0 * r
return mass_3d
def mass_3d_lens(self, r, theta_E, e1=0, e2=0):
"""
mass enclosed a 3d sphere or radius r given a lens parameterization with angular units
:param r: radius in angular units
:param theta_E: Einstein radius
:return: mass in angular units
"""
rho0 = self.theta2rho(theta_E)
return self.mass_3d(r, rho0)
def mass_2d(self, r, rho0, e1=0, e2=0):
"""
mass enclosed projected 2d sphere of radius r
:param r:
:param rho0:
:param e1:
:param e2:
:return:
"""
alpha = 2 * rho0 * np.pi**2
mass_2d = alpha * r
return mass_2d
def mass_2d_lens(self, r, theta_E, e1=0, e2=0):
"""
:param r:
:param theta_E:
:param e1:
:param e2:
:return:
"""
rho0 = self.theta2rho(theta_E)
return self.mass_2d(r, rho0)
def grav_pot(self, x, y, rho0, e1=0, e2=0, center_x=0, center_y=0):
"""
gravitational potential (modulo 4 pi G and rho0 in appropriate units)
:param x:
:param y:
:param rho0:
:param e1:
:param e2:
:param center_x:
:param center_y:
:return:
"""
x_ = x - center_x
y_ = y - center_y
r = np.sqrt(x_**2 + y_**2)
mass_3d = self.mass_3d(r, rho0)
pot = mass_3d / r
return pot
def density_lens(self, r, theta_E, 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.
:param r: radius in angles
:param theta_E: Einstein radius
:param e1: eccentricity component
:param e2: eccentricity component
:return: density
"""
rho0 = self.theta2rho(theta_E)
return self.density(r, rho0)
@staticmethod
def density(r, rho0, e1=0, e2=0):
"""
computes the density
:param r: radius in angles
:param rho0: density at angle=1
:return: density at r
"""
rho = rho0 / r**2
return rho
@staticmethod
def density_2d(x, y, rho0, e1=0, e2=0, center_x=0, center_y=0):
"""
projected density
:param x:
:param y:
:param rho0:
:param e1:
:param e2:
:param center_x:
:param center_y:
:return:
"""
x_ = x - center_x
y_ = y - center_y
r = np.sqrt(x_**2 + y_**2)
sigma = np.pi * rho0 / r
return sigma
class TestSIE(object):
"""
tests the Gaussian methods
"""
def setup(self):
from lenstronomy.LensModel.Profiles.sie import SIE
from lenstronomy.LensModel.Profiles.epl import EPL
from lenstronomy.LensModel.Profiles.nie import NIE
self.sie = SIE(NIE=False)
self.sie_nie = SIE(NIE=True)
self.epl = EPL()
self.nie = NIE()
def test_function(self):
x = np.array([1])
y = np.array([2])
theta_E = 1.
q = 0.9
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
values = self.sie.function(x, y, theta_E, e1, e2)
gamma = 2
values_spemd = self.epl.function(x, y, theta_E, gamma, e1, e2)
assert values == values_spemd
values_nie = self.sie_nie.function(x, y, theta_E, e1, e2)
s_scale = 0.0000001
values_spemd = self.nie.function(x, y, theta_E, e1, e2, s_scale)
npt.assert_almost_equal(values_nie, values_spemd, decimal=6)
def test_derivatives(self):
x = np.array([1])
y = np.array([2])
theta_E = 1.
q = 0.7
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
values = self.sie.derivatives(x, y, theta_E, e1, e2)
gamma = 2
values_spemd = self.epl.derivatives(x, y, theta_E, gamma, e1, e2)
assert values == values_spemd
values = self.sie_nie.derivatives(x, y, theta_E, e1, e2)
s_scale = 0.0000001
values_spemd = self.nie.derivatives(x, y, theta_E, e1, e2, s_scale)
npt.assert_almost_equal(values, values_spemd, decimal=6)
def test_hessian(self):
x = np.array([1])
y = np.array([2])
theta_E = 1.
q = 0.7
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
values = self.sie.hessian(x, y, theta_E, e1, e2)
gamma = 2
values_spemd = self.epl.hessian(x, y, theta_E, gamma, e1, e2)
assert values[0] == values_spemd[0]
values = self.sie_nie.hessian(x, y, theta_E, e1, e2)
s_scale = 0.0000001
values_spemd = self.nie.hessian(x, y, theta_E, e1, e2, s_scale)
npt.assert_almost_equal(values, values_spemd, decimal=5)
class TestEPL(object):
"""
tests the Gaussian methods
"""
def setup(self):
from lenstronomy.LensModel.Profiles.epl import EPL
self.EPL = EPL()
from lenstronomy.LensModel.Profiles.nie import NIE
self.NIE = NIE()
def test_function(self):
phi_E = 1.
t = 1.
q = 0.999
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
x = np.array([1., 2])
y = np.array([2, 0])
values = self.EPL.function(x, y, phi_E, e1, e2, t)
values_nie = self.NIE.function(x, y, phi_E, e1, e2, 0.)
delta_f = values[0] - values[1]
delta_f_nie = values_nie[0] - values_nie[1]
npt.assert_almost_equal(delta_f, delta_f_nie, decimal=5)
q = 0.8
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
x = np.array([1., 2])
y = np.array([2, 0])
values = self.EPL.function(x, y, phi_E, e1, e2, t)
values_nie = self.NIE.function(x, y, phi_E, e1, e2, 0.)
delta_f = values[0] - values[1]
delta_f_nie = values_nie[0] - values_nie[1]
npt.assert_almost_equal(delta_f, delta_f_nie, decimal=5)
q = 0.4
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
x = np.array([1., 2])
y = np.array([2, 0])
values = self.EPL.function(x, y, phi_E, e1, e2, t)
values_nie = self.NIE.function(x, y, phi_E, e1, e2, 0.)
delta_f = values[0] - values[1]
delta_f_nie = values_nie[0] - values_nie[1]
npt.assert_almost_equal(delta_f, delta_f_nie, decimal=5)
def test_derivatives(self):
x = np.array([1])
y = np.array([2])
phi_E = 1.
t = 1.
q = 1.
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_x, f_y = self.EPL.derivatives(x, y, phi_E, e1, e2, t)
f_x_nie, f_y_nie = self.NIE.derivatives(x, y, phi_E, e1, e2, 0.)
npt.assert_almost_equal(f_x, f_x_nie, decimal=4)
npt.assert_almost_equal(f_y, f_y_nie, decimal=4)
q = 0.7
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_x, f_y = self.EPL.derivatives(x, y, phi_E, e1, e2, t)
f_x_nie, f_y_nie = self.NIE.derivatives(x, y, phi_E, e1, e2, 0.)
npt.assert_almost_equal(f_x, f_x_nie, decimal=4)
npt.assert_almost_equal(f_y, f_y_nie, decimal=4)
def test_hessian(self):
x = np.array([1.])
y = np.array([2.])
phi_E = 1.
t = 1.
q = 0.9
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_xx, f_yy, f_xy = self.EPL.hessian(x, y, phi_E, e1, e2, t)
f_xx_nie, f_yy_nie, f_xy_nie = self.NIE.hessian(
x, y, phi_E, e1, e2, 0.)
npt.assert_almost_equal(f_xx, f_xx_nie, decimal=4)
npt.assert_almost_equal(f_yy, f_yy_nie, decimal=4)
npt.assert_almost_equal(f_xy, f_xy_nie, decimal=4)
def test_static(self):
x, y = 1., 1.
phi_G, q = 0.3, 0.8
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
kwargs_lens = {'theta_E': 1., 't': 1.5, 'e1': e1, 'e2': e2}
f_ = self.EPL.function(x, y, **kwargs_lens)
self.EPL.set_static(**kwargs_lens)
f_static = self.EPL.function(x, y, **kwargs_lens)
npt.assert_almost_equal(f_, f_static, decimal=8)
self.EPL.set_dynamic()
kwargs_lens = {'theta_E': 2., 't': 0.5, 'e1': e1, 'e2': e2}
f_dyn = self.EPL.function(x, y, **kwargs_lens)
assert f_dyn != f_static
class TestEPL_numba(object):
"""
tests the Gaussian methods
"""
def setup(self):
from lenstronomy.LensModel.Profiles.epl import EPL
self.EPL = EPL()
from lenstronomy.LensModel.Profiles.epl_numba import EPL_numba
self.EPL_numba = EPL_numba()
def test_function(self):
phi_E = 1.
gamma = 2.
q = 0.999
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
x = np.array([1., 2])
y = np.array([2, 0])
values = self.EPL.function(x, y, phi_E, gamma, e1, e2)
values_nb = self.EPL_numba.function(x, y, phi_E, gamma, e1, e2)
delta_f = values[0] - values[1]
delta_f_nb = values_nb[0] - values_nb[1]
npt.assert_almost_equal(delta_f, delta_f_nb, decimal=10)
q = 0.8
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
x = np.array([1., 2])
y = np.array([2, 0])
values = self.EPL.function(x, y, phi_E, gamma, e1, e2)
values_nb = self.EPL_numba.function(x, y, phi_E, gamma, e1, e2)
delta_f = values[0] - values[1]
delta_f_nb = values_nb[0] - values_nb[1]
npt.assert_almost_equal(delta_f, delta_f_nb, decimal=10)
q = 0.4
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
x = np.array([1., 2])
y = np.array([2, 0])
values = self.EPL.function(x, y, phi_E, gamma, e1, e2)
values_nb = self.EPL_numba.function(x, y, phi_E, gamma, e1, e2)
delta_f = values[0] - values[1]
delta_f_nb = values_nb[0] - values_nb[1]
npt.assert_almost_equal(delta_f, delta_f_nb, decimal=10)
def test_derivatives(self):
x = np.array([1])
y = np.array([2])
phi_E = 1.
gamma = 1.8
q = 1.
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_x, f_y = self.EPL.derivatives(x, y, phi_E, gamma, e1, e2)
f_x_nb, f_y_nb = self.EPL_numba.derivatives(x, y, phi_E, gamma, e1, e2)
npt.assert_almost_equal(f_x, f_x_nb, decimal=10)
npt.assert_almost_equal(f_y, f_y_nb, decimal=10)
q = 0.7
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_x, f_y = self.EPL.derivatives(x, y, phi_E, gamma, e1, e2)
f_x_nb, f_y_nb = self.EPL_numba.derivatives(x, y, phi_E, gamma, e1, e2)
npt.assert_almost_equal(f_x, f_x_nb, decimal=10)
npt.assert_almost_equal(f_y, f_y_nb, decimal=10)
def test_hessian(self):
x = np.array([1.])
y = np.array([2.])
phi_E = 1.
gamma = 2.2
q = 0.9
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_xx, f_xy, f_yx, f_yy = self.EPL.hessian(x, y, phi_E, gamma, e1, e2)
f_xx_nb, f_xy_nb, f_yx_nb, f_yy_nb = self.EPL_numba.hessian(
x, y, phi_E, gamma, e1, e2)
npt.assert_almost_equal(f_xx, f_xx_nb, decimal=10)
npt.assert_almost_equal(f_yy, f_yy_nb, decimal=10)
npt.assert_almost_equal(f_xy, f_xy_nb, decimal=10)
def test_regularization(self):
phi_E = 1.
gamma = 2.
q = 1.
phi_G = 1.
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
x = 0.
y = 0.
f_x, f_y = self.EPL_numba.derivatives(x, y, phi_E, gamma, e1, e2)
npt.assert_almost_equal(f_x, 0.)
npt.assert_almost_equal(f_y, 0.)
x = 0.
y = 0.
f_x, f_y = self.EPL.derivatives(x, y, phi_E, gamma, e1, e2)
npt.assert_almost_equal(f_x, 0.)
npt.assert_almost_equal(f_y, 0.)
x = 0.
y = 0.
f_x, f_y = self.EPL.derivatives(x, y, phi_E, gamma + 0.1, e1, e2)
npt.assert_almost_equal(f_x, 0.)
npt.assert_almost_equal(f_y, 0.)
x = 0.
y = 0.
f = self.EPL_numba.function(x, y, phi_E, gamma, e1, e2)
npt.assert_almost_equal(f, 0.)
x = 0.
y = 0.
f_xx, f_xy, f_yx, f_yy = self.EPL_numba.hessian(
x, y, phi_E, gamma, e1, e2)
npt.assert_almost_equal(f_xx, 1e10, decimal=10)
npt.assert_almost_equal(f_yy, 0, decimal=10)
npt.assert_almost_equal(
f_xy, 0, decimal=5) # floating point cancellation, so less precise
# Magnification:
npt.assert_almost_equal(1 / ((1 - f_xx) * (1 - f_yy) - f_xy**2),
0.,
decimal=10)
class SIE(LensProfileBase):
"""
class for singular isothermal ellipsoid (SIS with ellipticity)
"""
param_names = ['theta_E', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {
'theta_E': 0,
'e1': -0.5,
'e2': -0.5,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'theta_E': 100,
'e1': 0.5,
'e2': 0.5,
'center_x': 100,
'center_y': 100
}
def __init__(self, NIE=True):
"""
:param NIE: bool, if True, is using the NIE analytic model. Otherwise it uses PEMD with gamma=2 from fastell4py
"""
self._nie = NIE
if NIE:
from lenstronomy.LensModel.Profiles.nie import NIE
self.profile = NIE()
else:
from lenstronomy.LensModel.Profiles.epl import EPL
self.profile = EPL()
self._s_scale = 0.0000000001
self._gamma = 2
super(SIE, self).__init__()
def function(self, x, y, theta_E, e1, e2, center_x=0, center_y=0):
"""
:param x:
:param y:
:param theta_E:
:param q:
:param phi_G:
:param center_x:
:param center_y:
:return:
"""
if self._nie:
return self.profile.function(x, y, theta_E, e1, e2, self._s_scale,
center_x, center_y)
else:
return self.profile.function(x, y, theta_E, self._gamma, e1, e2,
center_x, center_y)
def derivatives(self, x, y, theta_E, e1, e2, center_x=0, center_y=0):
"""
:param x:
:param y:
:param theta_E:
:param q:
:param phi_G:
:param center_x:
:param center_y:
:return:
"""
if self._nie:
return self.profile.derivatives(x, y, theta_E, e1, e2,
self._s_scale, center_x, center_y)
else:
return self.profile.derivatives(x, y, theta_E, self._gamma, e1, e2,
center_x, center_y)
def hessian(self, x, y, theta_E, e1, e2, center_x=0, center_y=0):
"""
:param x:
:param y:
:param theta_E:
:param q:
:param phi_G:
:param center_x:
:param center_y:
:return:
"""
if self._nie:
return self.profile.hessian(x, y, theta_E, e1, e2, self._s_scale,
center_x, center_y)
else:
return self.profile.hessian(x, y, theta_E, self._gamma, e1, e2,
center_x, center_y)
@staticmethod
def theta2rho(theta_E):
"""
converts projected density parameter (in units of deflection) into 3d density parameter
:param theta_E:
:return:
"""
fac1 = np.pi * 2
rho0 = theta_E / fac1
return rho0
@staticmethod
def mass_3d(r, rho0, e1=0, e2=0):
"""
mass enclosed a 3d sphere or radius r
:param r: radius in angular units
:param rho0: density at angle=1
:return: mass in angular units
"""
mass_3d = 4 * np.pi * rho0 * r
return mass_3d
def mass_3d_lens(self, r, theta_E, e1=0, e2=0):
"""
mass enclosed a 3d sphere or radius r given a lens parameterization with angular units
:param r: radius in angular units
:param theta_E: Einstein radius
:return: mass in angular units
"""
rho0 = self.theta2rho(theta_E)
return self.mass_3d(r, rho0)
def mass_2d(self, r, rho0, e1=0, e2=0):
"""
mass enclosed projected 2d sphere of radius r
:param r:
:param rho0:
:param a:
:param s:
:return:
"""
alpha = np.pi * np.pi * 2 * rho0
mass_2d = alpha * r
return mass_2d
def mass_2d_lens(self, r, theta_E, e1=0, e2=0):
"""
:param r:
:param theta_E:
:return:
"""
rho0 = self.theta2rho(theta_E)
return self.mass_2d(r, rho0)
def grav_pot(self, x, y, rho0, e1=0, e2=0, center_x=0, center_y=0):
"""
gravitational potential (modulo 4 pi G and rho0 in appropriate units)
:param x:
:param y:
:param rho0:
:param a:
:param s:
:param center_x:
:param center_y:
:return:
"""
x_ = x - center_x
y_ = y - center_y
r = np.sqrt(x_**2 + y_**2)
mass_3d = self.mass_3d(r, rho0)
pot = mass_3d / r
return pot
def density_lens(self, r, theta_E, 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.
:param r: radius in angles
:param theta_E: Einstein radius
:param e1: eccentricity component
:param e2: eccentricity component
:return: density
"""
rho0 = self.theta2rho(theta_E)
return self.density(r, rho0)
@staticmethod
def density(r, rho0, e1=0, e2=0):
"""
computes the density
:param r: radius in angles
:param rho0: density at angle=1
:return: density at r
"""
rho = rho0 / r**2
return rho
@staticmethod
def density_2d(x, y, rho0, e1=0, e2=0, center_x=0, center_y=0):
"""
projected density
:param x:
:param y:
:param rho0:
:param center_x:
:param center_y:
:return:
"""
x_ = x - center_x
y_ = y - center_y
r = np.sqrt(x_**2 + y_**2)
sigma = np.pi * rho0 / r
return sigma