class Chameleon(LensProfileBase):
"""
class of the Chameleon model (See Suyu+2014) an elliptical truncated double isothermal profile
"""
param_names = ['alpha_1', 'w_c', 'w_t', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {'alpha_1': 0, 'w_c': 0, 'w_t': 0, 'e1': -0.8, 'e2': -0.8, 'center_x': -100, 'center_y': -100}
upper_limit_default = {'alpha_1': 100, 'w_c': 100, 'w_t': 100, 'e1': 0.8, 'e2': 0.8, 'center_x': 100, 'center_y': 100}
def __init__(self, static=False):
self._nie_1 = NIE()
self._nie_2 = NIE()
super(Chameleon, self).__init__()
self._static = static
def function(self, x, y, alpha_1, w_c, w_t, e1, e2, center_x=0, center_y=0):
"""
:param x: ra-coordinate
:param y: dec-coordinate
:param alpha_1: deflection angle at 1 (arcseconds) from the center
:param w_c: see Suyu+2014
:param w_t: see Suyu+2014
:param e1: ellipticity parameter
:param e2: ellipticity parameter
:param center_x: ra center
:param center_y: dec center
:return: lensing potential
"""
theta_E_conv, w_c, w_t, s_scale_1, s_scale_2 = self.param_convert(alpha_1, w_c, w_t, e1, e2)
f_1 = self._nie_1.function(x, y, theta_E_conv, e1, e2, s_scale_1, center_x, center_y)
f_2 = self._nie_2.function(x, y, theta_E_conv, e1, e2, s_scale_2, center_x, center_y)
f_ = f_1 - f_2
return f_
def derivatives(self, x, y, alpha_1, w_c, w_t, e1, e2, center_x=0, center_y=0):
"""
:param x: ra-coordinate
:param y: dec-coordinate
:param alpha_1: deflection angle at 1 (arcseconds) from the center
:param w_c: see Suyu+2014
:param w_t: see Suyu+2014
:param e1: ellipticity parameter
:param e2: ellipticity parameter
:param center_x: ra center
:param center_y: dec center
:return: deflection angles (RA, DEC)
"""
theta_E_conv, w_c, w_t, s_scale_1, s_scale_2 = self.param_convert(alpha_1, w_c, w_t, e1, e2)
f_x_1, f_y_1 = self._nie_1.derivatives(x, y, theta_E_conv, e1, e2, s_scale_1, center_x, center_y)
f_x_2, f_y_2 = self._nie_2.derivatives(x, y, theta_E_conv, e1, e2, s_scale_2, center_x, center_y)
f_x = f_x_1 - f_x_2
f_y = f_y_1 - f_y_2
return f_x, f_y
def hessian(self, x, y, alpha_1, w_c, w_t, e1, e2, center_x=0, center_y=0):
"""
:param x: ra-coordinate
:param y: dec-coordinate
:param alpha_1: deflection angle at 1 (arcseconds) from the center
:param w_c: see Suyu+2014
:param w_t: see Suyu+2014
:param e1: ellipticity parameter
:param e2: ellipticity parameter
:param center_x: ra center
:param center_y: dec center
:return: second derivatives of the lensing potential (Hessian: f_xx, f_xy, f_yx, f_yy)
"""
theta_E_conv, w_c, w_t, s_scale_1, s_scale_2 = self.param_convert(alpha_1, w_c, w_t, e1, e2)
f_xx_1, f_xy_1, f_yx_1, f_yy_1 = self._nie_1.hessian(x, y, theta_E_conv, e1, e2, s_scale_1, center_x, center_y)
f_xx_2, f_xy_2, f_yx_2, f_yy_2 = self._nie_2.hessian(x, y, theta_E_conv, e1, e2, s_scale_2, center_x, center_y)
f_xx = f_xx_1 - f_xx_2
f_yy = f_yy_1 - f_yy_2
f_xy = f_xy_1 - f_xy_2
f_yx = f_yx_1 - f_yx_2
return f_xx, f_xy, f_yx, f_yy
def param_convert(self, alpha_1, w_c, w_t, e1, e2):
"""
convert the parameter alpha_1 (deflection angle one arcsecond from the center) into the
"Einstein radius" scale parameter of the two NIE profiles
:param alpha_1: deflection angle at 1 (arcseconds) from the center
:param w_c: see Suyu+2014
:param w_t: see Suyu+2014
:param e1: eccentricity modulus
:param ee: eccentricity modulus
:return:
"""
if self._static is True:
return self._theta_convert_static, self._w_c_static, self._w_t_stactic, self._s_scale_1_static, self._s_scale_2_static
return self._param_convert(alpha_1, w_c, w_t, e1, e2)
def _param_convert(self, alpha_1, w_c, w_t, e1, e2):
if not w_t >= w_c:
return 0, w_t, w_c, 1, 1
s_scale_1 = w_c
s_scale_2 = w_t
f_x_1, f_y_1 = self._nie_1.derivatives(1, 0, theta_E=1, e1=0, e2=0, s_scale=s_scale_1)
f_x_2, f_y_2 = self._nie_2.derivatives(1, 0, theta_E=1, e1=0, e2=0, s_scale=s_scale_2)
f_x = f_x_1 - f_x_2
theta_E_convert = alpha_1 / f_x
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
s_scale_1 = np.sqrt(4 * w_c ** 2 / (1. + q) ** 2)
s_scale_2 = np.sqrt(4 * w_t ** 2 / (1. + q) ** 2)
return theta_E_convert, w_c, w_t, s_scale_1, s_scale_2
def set_static(self, alpha_1, w_c, w_t, e1, e2, center_x=0, center_y=0):
"""
:param logM:
:param concentration:
:param center_x:
:param center_y:
:return:
"""
self._static = True
self._theta_convert_static, self._w_c_static, self._w_t_stactic, self._s_scale_1_static, self._s_scale_2_static = self._param_convert(alpha_1, w_c, w_t, e1, e2)
self._nie_1.set_static(self._theta_convert_static, e1, e2, self._s_scale_1_static, center_x, center_y)
self._nie_2.set_static(self._theta_convert_static, e1, e2, self._s_scale_2_static, center_x, center_y)
def set_dynamic(self):
"""
:return:
"""
self._static = False
if hasattr(self, '_theta_convert_static'):
del self._theta_convert_static
if hasattr(self, '_w_c_static'):
del self._w_c_static
if hasattr(self, '_w_t_stactic'):
del self._w_t_stactic
if hasattr(self, '_s_scale_1_static'):
del self._s_scale_1_static
if hasattr(self, '_s_scale_2_static'):
del self._s_scale_2_static
self._nie_1.set_dynamic()
self._nie_2.set_dynamic()
class TestNIE(object):
"""
tests the Gaussian methods
"""
def setup(self):
self.nie = NIE()
self.spemd = SPEMD(suppress_fastell=True)
self.sis = SIS()
def test_function(self):
y = np.array([1., 2])
x = np.array([0., 0.])
theta_E = 1.
q = 0.9999
s = 0.00001
phi_G = 0
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
values = self.nie.function(x, y, theta_E, e1, e2, s_scale=s)
delta_pot = values[1] - values[0]
values_spemd = self.sis.function(x, y, theta_E)
delta_pot_spemd = values_spemd[1] - values_spemd[0]
npt.assert_almost_equal(delta_pot, delta_pot_spemd, decimal=4)
if bool_test is True:
q = 0.99
s = 0.000001
phi_G = 0
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
values = self.nie.function(x, y, theta_E, e1, e2, s_scale=s)
delta_pot = values[1] - values[0]
gamma = 2.
values_spemd = self.spemd.function(x, y, theta_E, gamma, e1, e2, s_scale=s)
delta_pot_spemd = values_spemd[1] - values_spemd[0]
npt.assert_almost_equal(delta_pot, delta_pot_spemd, decimal=2)
def test_derivatives(self):
x = np.array([1])
y = np.array([2])
theta_E = 1.
q = 0.99999
phi_G = 0
s = 0.0000001
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_x, f_y = self.nie.derivatives(x, y, theta_E, e1, e2, s_scale=s)
f_x_spemd, f_y_spemd = self.sis.derivatives(x, y, theta_E)
npt.assert_almost_equal(f_x, f_x_spemd, decimal=4)
npt.assert_almost_equal(f_y, f_y_spemd, decimal=4)
if bool_test is True:
q = 0.99
s = 0.000001
phi_G = 0
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_x, f_y = self.nie.derivatives(x, y, theta_E, e1, e2, s_scale=s)
gamma = 2.
f_x_spemd, f_y_spemd = self.spemd.derivatives(x, y, theta_E, gamma, e1, e2, s_scale=s)
print(f_x/f_x_spemd, 'ratio deflections')
print(1+(1-q)/2)
npt.assert_almost_equal(f_x, f_x_spemd, decimal=2)
npt.assert_almost_equal(f_y, f_y_spemd, decimal=2)
def test_hessian(self):
x = np.array([1])
y = np.array([2])
theta_E = 1.
q = 0.999999
phi_G = 0
s = 0.0000001
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_xx, f_yy, f_xy = self.nie.hessian(x, y, theta_E, e1, e2, s_scale=s)
f_xx_spemd, f_yy_spemd, f_xy_spemd = self.sis.hessian(x, y, theta_E)
npt.assert_almost_equal(f_xx, f_xx_spemd, decimal=4)
npt.assert_almost_equal(f_yy, f_yy_spemd, decimal=4)
npt.assert_almost_equal(f_xy, f_xy_spemd, decimal=4)
def test_convergence2surface_brightness(self):
from lenstronomy.LightModel.Profiles.nie import NIE as NIE_Light
nie_light = NIE_Light()
kwargs = {'e1': 0.3, 'e2': -0.05, 's_scale': 0.5}
x, y = util.make_grid(numPix=10, deltapix=0.1)
f_xx, f_yy, f_xy = self.nie.hessian(x, y, theta_E=1, **kwargs)
kappa = 1/2. * (f_xx + f_yy)
flux = nie_light.function(x, y, amp=1, **kwargs)
npt.assert_almost_equal(kappa/np.sum(kappa), flux/np.sum(flux), decimal=5)
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., 's_scale': .1, 'e1': e1, 'e2': e2}
f_ = self.nie.function(x, y, **kwargs_lens)
self.nie.set_static(**kwargs_lens)
f_static = self.nie.function(x, y, **kwargs_lens)
npt.assert_almost_equal(f_, f_static, decimal=8)
self.nie.set_dynamic()
kwargs_lens = {'theta_E': 2., 's_scale': .1, 'e1': e1, 'e2': e2}
f_dyn = self.nie.function(x, y, **kwargs_lens)
assert f_dyn != f_static
class TestNIE(object):
"""
tests the Gaussian methods
"""
def setup(self):
from lenstronomy.LensModel.Profiles.nie import NIE
from lenstronomy.LensModel.Profiles.spemd_smooth import SPEMD_SMOOTH
from lenstronomy.LensModel.Profiles.sis import SIS
self.nie = NIE()
self.spemd = SPEMD_SMOOTH()
self.sis = SIS()
def test_function(self):
y = np.array([1., 2])
x = np.array([0., 0.])
theta_E = 1.
q = 0.9999
s = 0.00001
phi_G = 0
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
values = self.nie.function(x, y, theta_E, e1, e2, s_scale=s)
delta_pot = values[1] - values[0]
values_spemd = self.sis.function(x, y, theta_E)
delta_pot_spemd = values_spemd[1] - values_spemd[0]
npt.assert_almost_equal(delta_pot, delta_pot_spemd, decimal=4)
if bool_test is True:
q = 0.99
s = 0.000001
phi_G = 0
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
values = self.nie.function(x, y, theta_E, e1, e2, s_scale=s)
delta_pot = values[1] - values[0]
gamma = 2.
values_spemd = self.spemd.function(x, y, theta_E, gamma, e1, e2, s_scale=s)
delta_pot_spemd = values_spemd[1] - values_spemd[0]
npt.assert_almost_equal(delta_pot, delta_pot_spemd, decimal=2)
def test_derivatives(self):
x = np.array([1])
y = np.array([2])
theta_E = 1.
q = 0.99999
phi_G = 0
s = 0.0000001
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_x, f_y = self.nie.derivatives(x, y, theta_E, e1, e2, s_scale=s)
f_x_spemd, f_y_spemd = self.sis.derivatives(x, y, theta_E)
npt.assert_almost_equal(f_x, f_x_spemd, decimal=4)
npt.assert_almost_equal(f_y, f_y_spemd, decimal=4)
if bool_test is True:
q = 0.99
s = 0.000001
phi_G = 0
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_x, f_y = self.nie.derivatives(x, y, theta_E, e1, e2, s_scale=s)
gamma = 2.
f_x_spemd, f_y_spemd = self.spemd.derivatives(x, y, theta_E, gamma, e1, e2, s_scale=s)
print(f_x/f_x_spemd, 'ratio deflections')
print(1+(1-q)/2)
npt.assert_almost_equal(f_x, f_x_spemd, decimal=2)
npt.assert_almost_equal(f_y, f_y_spemd, decimal=2)
def test_hessian(self):
x = np.array([1])
y = np.array([2])
theta_E = 1.
q = 0.999999
phi_G = 0
s = 0.0000001
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
f_xx, f_yy, f_xy = self.nie.hessian(x, y, theta_E, e1, e2, s_scale=s)
f_xx_spemd, f_yy_spemd, f_xy_spemd = self.sis.hessian(x, y, theta_E)
npt.assert_almost_equal(f_xx, f_xx_spemd, decimal=4)
npt.assert_almost_equal(f_yy, f_yy_spemd, decimal=4)
npt.assert_almost_equal(f_xy, f_xy_spemd, 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., 's_scale': .1, 'e1': e1, 'e2': e2}
f_ = self.nie.function(x, y, **kwargs_lens)
self.nie.set_static(**kwargs_lens)
f_static = self.nie.function(x, y, **kwargs_lens)
npt.assert_almost_equal(f_, f_static, decimal=8)
self.nie.set_dynamic()
kwargs_lens = {'theta_E': 2., 's_scale': .1, 'e1': e1, 'e2': e2}
f_dyn = self.nie.function(x, y, **kwargs_lens)
assert f_dyn != f_static
