class DoubleChameleonPointMass(object):
"""
class of the Chameleon model (See Suyu+2014) an elliptical truncated double isothermal profile
"""
param_names = [
'theta_E', 'ratio_chameleon', 'ratio_pointmass', 'w_c1', 'w_t1', 'e11',
'e21', 'w_c2', 'w_t2', 'e12', 'e22', 'center_x', 'center_y'
]
def __init__(self):
self.chameleon = DoubleChameleon()
self.pointMass = PointMass()
def function(self,
x,
y,
theta_E,
ratio_pointmass,
ratio_chameleon,
w_c1,
w_t1,
e11,
e21,
w_c2,
w_t2,
e12,
e22,
center_x=0,
center_y=0):
"""
:param x:
:param y:
:param theta_E:
:param ratio_pointmass:
:param ratio_chameleon:
:param w_c1:
:param w_t1:
:param e11:
:param e21:
:param w_c2:
:param w_t2:
:param e12:
:param e22:
:param center_x:
:param center_y:
:return:
"""
f_1 = self.pointMass.function(x, y,
theta_E / (1. + 1. / ratio_pointmass),
center_x, center_y)
f_2 = self.chameleon.function(x, y, theta_E / (1. + ratio_pointmass),
ratio_chameleon, w_c1, w_t1, e11, e21,
w_c2, w_t2, e12, e22, center_x, center_y)
return f_1 + f_2
def derivatives(self,
x,
y,
theta_E,
ratio_pointmass,
ratio_chameleon,
w_c1,
w_t1,
e11,
e21,
w_c2,
w_t2,
e12,
e22,
center_x=0,
center_y=0):
"""
:param x:
:param y:
:param theta_E:
:param ratio_pointmass:
:param ratio_chameleon:
:param w_c1:
:param w_t1:
:param e11:
:param e21:
:param w_c2:
:param w_t2:
:param e12:
:param e22:
:param center_x:
:param center_y:
:return:
"""
f_x1, f_y1 = self.pointMass.derivatives(
x, y, theta_E / (1. + 1. / ratio_pointmass), center_x, center_y)
f_x2, f_y2 = self.chameleon.derivatives(
x, y, theta_E / (1. + ratio_pointmass), ratio_chameleon, w_c1,
w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x, center_y)
return f_x1 + f_x2, f_y1 + f_y2
def hessian(self,
x,
y,
theta_E,
ratio_pointmass,
ratio_chameleon,
w_c1,
w_t1,
e11,
e21,
w_c2,
w_t2,
e12,
e22,
center_x=0,
center_y=0):
"""
:param x:
:param y:
:param theta_E:
:param ratio_pointmass:
:param ratio_chameleon:
:param w_c1:
:param w_t1:
:param e11:
:param e21:
:param w_c2:
:param w_t2:
:param e12:
:param e22:
:param center_x:
:param center_y:
:return:
"""
f_xx1, f_yy1, f_xy1 = self.pointMass.hessian(
x, y, theta_E / (1. + 1. / ratio_pointmass), center_x, center_y)
f_xx2, f_yy2, f_xy2 = self.chameleon.hessian(
x, y, theta_E / (1. + ratio_pointmass), ratio_chameleon, w_c1,
w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x, center_y)
return f_xx1 + f_xx2, f_yy1 + f_yy2, f_xy1 + f_xy2
class DoubleChameleonPointMass(LensProfileBase):
"""
class of the Chameleon model (See Suyu+2014) an elliptical truncated double isothermal profile
"""
param_names = ['alpha_1', 'ratio_chameleon', 'ratio_pointmass', 'w_c1', 'w_t1', 'e11', 'e21', 'w_c2', 'w_t2',
'e12', 'e22', 'center_x', 'center_y']
lower_limit_default = {'alpha_1': 0, 'ratio_chameleon': 0, 'ratio_pointmass': 0, 'w_c1': 0, 'w_t1': 0, 'e11': -0.8,
'e21': -0.8, 'w_c2': 0, 'w_t2': 0, 'e12': -0.8, 'e22': -0.8,
'center_x': -100, 'center_y': -100}
upper_limit_default = {'alpha_1': 100, 'ratio_chameleon': 100, 'ratio_pointmass': 100, 'w_c1': 100, 'w_t1': 100, 'e11': 0.8, 'e21': 0.8,
'w_c2': 100, 'w_t2': 100, 'e12': 0.8, 'e22': 0.8,
'center_x': 100, 'center_y': 100}
def __init__(self):
self.chameleon = DoubleChameleon()
self.pointMass = PointMass()
super(DoubleChameleonPointMass, self).__init__()
def function(self, x, y, alpha_1, ratio_pointmass, ratio_chameleon, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22,
center_x=0, center_y=0):
"""
#TODO chose better parameterization for combining point mass and Chameleon profiles
:param x: ra-coordinate
:param y: dec-coordinate
:param alpha_1: deflection angle at 1 (arcseconds) from the center
:param ratio_pointmass: ratio of point source Einstein radius to combined Chameleon deflection angle at r=1
:param ratio_chameleon: ratio in deflection angles at r=1 for the two Chameleon profiles
:param w_c1: Suyu+2014 for first profile
:param w_t1: Suyu+2014 for first profile
:param e11: ellipticity parameter for first profile
:param e21: ellipticity parameter for first profile
:param w_c2: Suyu+2014 for second profile
:param w_t2: Suyu+2014 for second profile
:param e12: ellipticity parameter for second profile
:param e22: ellipticity parameter for second profile
:param center_x: ra center
:param center_y: dec center
:return:
"""
f_1 = self.pointMass.function(x, y, alpha_1 / (1. + 1. / ratio_pointmass), center_x, center_y)
f_2 = self.chameleon.function(x, y, alpha_1 / (1. + ratio_pointmass), ratio_chameleon, w_c1, w_t1, e11, e21,
w_c2, w_t2, e12, e22, center_x, center_y)
return f_1 + f_2
def derivatives(self, x, y, alpha_1, ratio_pointmass, ratio_chameleon, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22,
center_x=0, center_y=0):
"""
:param x:
:param y:
:param alpha_1:
:param ratio_pointmass: ratio of point source Einstein radius to combined Chameleon deflection angle at r=1
:param ratio_chameleon: ratio in deflection angles at r=1 for the two Chameleon profiles
:param w_c1: Suyu+2014 for first profile
:param w_t1: Suyu+2014 for first profile
:param e11: ellipticity parameter for first profile
:param e21: ellipticity parameter for first profile
:param w_c2: Suyu+2014 for second profile
:param w_t2: Suyu+2014 for second profile
:param e12: ellipticity parameter for second profile
:param e22: ellipticity parameter for second profile
:param center_x: ra center
:param center_y: dec center
:return:
"""
f_x1, f_y1 = self.pointMass.derivatives(x, y, alpha_1 / (1. + 1. / ratio_pointmass), center_x, center_y)
f_x2, f_y2 = self.chameleon.derivatives(x, y, alpha_1 / (1. + ratio_pointmass), ratio_chameleon, w_c1, w_t1,
e11, e21, w_c2, w_t2, e12, e22, center_x, center_y)
return f_x1 + f_x2, f_y1 + f_y2
def hessian(self, x, y, alpha_1, ratio_pointmass, ratio_chameleon, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22,
center_x=0, center_y=0):
"""
:param x:
:param y:
:param alpha_1:
:param ratio_pointmass: ratio of point source Einstein radius to combined Chameleon deflection angle at r=1
:param ratio_chameleon: ratio in deflection angles at r=1 for the two Chameleon profiles
:param w_c1: Suyu+2014 for first profile
:param w_t1: Suyu+2014 for first profile
:param e11: ellipticity parameter for first profile
:param e21: ellipticity parameter for first profile
:param w_c2: Suyu+2014 for second profile
:param w_t2: Suyu+2014 for second profile
:param e12: ellipticity parameter for second profile
:param e22: ellipticity parameter for second profile
:param center_x: ra center
:param center_y: dec center
:return:
"""
f_xx1, f_xy1, f_yx1, f_yy1 = self.pointMass.hessian(x, y, alpha_1 / (1. + 1. / ratio_pointmass), center_x, center_y)
f_xx2, f_xy2, f_yx2, f_yy2 = self.chameleon.hessian(x, y, alpha_1 / (1. + ratio_pointmass), ratio_chameleon, w_c1, w_t1,
e11, e21, w_c2, w_t2, e12, e22, center_x, center_y)
return f_xx1 + f_xx2, f_xy1 + f_xy2, f_yx1 + f_yx2, f_yy1 + f_yy2
class TestSIS(object):
"""
tests the Gaussian methods
"""
def setup(self):
self.pointmass = PointMass()
def test_function(self):
x = np.array([0])
y = np.array([1])
theta_E = 1.
values = self.pointmass.function(x, y, theta_E)
assert values[0] == 0
x = np.array([0])
y = np.array([0])
values = self.pointmass.function(x, y, theta_E)
assert values[0] < 0
x = np.array([1, 3, 4])
y = np.array([0, 1, 1])
values = self.pointmass.function(x, y, theta_E)
assert values[0] == 0
assert values[1] == 1.151292546497023
assert values[2] == 1.4166066720281081
def test_derivatives(self):
x = np.array([1])
y = np.array([0])
theta_E = 1.
f_x, f_y = self.pointmass.derivatives(x, y, theta_E)
assert f_x[0] == 1
assert f_y[0] == 0
x = np.array([0])
y = np.array([0])
f_x, f_y = self.pointmass.derivatives(x, y, theta_E)
assert f_x[0] == 0
assert f_y[0] == 0
x = np.array([1, 3, 4])
y = np.array([0, 1, 1])
values = self.pointmass.derivatives(x, y, theta_E)
assert values[0][0] == 1
assert values[1][0] == 0
assert values[0][1] == 0.29999999999999999
assert values[1][1] == 0.099999999999999992
def test_hessian(self):
x = np.array([1])
y = np.array([0])
theta_E = 1.
f_xx, f_yy, f_xy = self.pointmass.hessian(x, y, theta_E)
assert f_xx[0] == -1
assert f_yy[0] == 1
assert f_xy[0] == -0
x = np.array([1, 3, 4])
y = np.array([0, 1, 1])
values = self.pointmass.hessian(x, y, theta_E)
assert values[0][0] == -1
assert values[1][0] == 1
assert values[2][0] == -0
assert values[0][1] == -0.080000000000000002
assert values[1][1] == 0.080000000000000002
assert values[2][1] == -0.059999999999999998