__author__ = 'sibirrer'
import numpy as np
import lenstronomy.Util.param_util as param_util
from lenstronomy.Util import util
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase
from lenstronomy.LensModel.Profiles.spp import SPP
__all__ = ['SPEP']
[docs]class SPEP(LensProfileBase):
"""
class for Softened power-law elliptical potential (SPEP)
"""
param_names = ['theta_E', 'gamma', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {'theta_E': 0, 'gamma': 0, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100}
upper_limit_default = {'theta_E': 100, 'gamma': 100, 'e1': 0.5, 'e2': 0.5, 'center_x': 100, 'center_y': 100}
def __init__(self):
self.spp = SPP()
super(SPEP, self).__init__()
[docs] def function(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
"""
:param x: set of x-coordinates
:type x: array of size (n)
:param theta_E: Einstein radius of lense
:type theta_E: float.
:param gamma: power law slope of mass profifle
:type gamma: <2 float
:param q: Axis ratio
:type q: 0<q<1
:param phi_G: position angel of SES
:type q: 0<phi_G<pi/2
:returns: function
:raises: AttributeError, KeyError
"""
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
gamma, q = self._param_bounds(gamma, q)
theta_E *= q
x_shift = x - center_x
y_shift = y - center_y
E = theta_E / (((3 - gamma) / 2.) ** (1. / (1 - gamma)) * np.sqrt(q))
#E = phi_E
eta = -gamma+3
xt1 = np.cos(phi_G)*x_shift+np.sin(phi_G)*y_shift
xt2 = -np.sin(phi_G)*x_shift+np.cos(phi_G)*y_shift
p2 = xt1**2+xt2**2/q**2
s2 = 0. # softening
return 2 * E**2/eta**2 * ((p2 + s2)/E**2)**(eta/2)
[docs] def derivatives(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
gamma, q = self._param_bounds(gamma, q)
phi_E_new = theta_E * q
x_shift = x - center_x
y_shift = y - center_y
E = phi_E_new / (((3-gamma)/2.)**(1./(1-gamma))*np.sqrt(q))
# E = phi_E
eta = float(-gamma+3)
cos_phi = np.cos(phi_G)
sin_phi = np.sin(phi_G)
xt1=cos_phi*x_shift+sin_phi*y_shift
xt2=-sin_phi*x_shift+cos_phi*y_shift
xt2difq2 = xt2/(q*q)
P2=xt1*xt1+xt2*xt2difq2
if isinstance(P2, int) or isinstance(P2, float):
a = max(0.000001,P2)
else:
a=np.empty_like(P2)
p2 = P2[P2 > 0] #in the SIS regime
a[P2 == 0] = 0.000001
a[P2 > 0] = p2
fac = 1./eta*(a/(E*E))**(eta/2-1)*2
f_x_prim = fac*xt1
f_y_prim = fac*xt2difq2
f_x = cos_phi*f_x_prim-sin_phi*f_y_prim
f_y = sin_phi*f_x_prim+cos_phi*f_y_prim
return f_x, f_y
[docs] def hessian(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
gamma, q = self._param_bounds(gamma, q)
phi_E_new = theta_E * q
#x_shift = x - center_x
#y_shift = y - center_y
# shift
x_ = x - center_x
y_ = y - center_y
# rotate
x__, y__ = util.rotate(x_, y_, phi_G)
E = phi_E_new / (((3-gamma)/2.)**(1./(1-gamma))*np.sqrt(q))
if E <= 0:
return np.zeros_like(x), np.zeros_like(x), np.zeros_like(x), np.zeros_like(x)
# E = phi_E
eta = float(-gamma+3)
#xt1 = np.cos(phi_G)*x_shift+np.sin(phi_G)*y_shift
#xt2 = -np.sin(phi_G)*x_shift+np.cos(phi_G)*y_shift
xt1, xt2 = x__, y__
P2 = xt1**2+xt2**2/q**2
if isinstance(P2, int) or isinstance(P2, float):
a = max(0.000001, P2)
else:
a=np.empty_like(P2)
p2 = P2[P2>0] #in the SIS regime
a[P2==0] = 0.000001
a[P2>0] = p2
s2 = 0. # softening
kappa=1./eta*(a/E**2)**(eta/2-1)*((eta-2)*(xt1**2+xt2**2/q**4)/a+(1+1/q**2))
gamma1_value=1./eta*(a/E**2)**(eta/2-1)*(1-1/q**2+(eta/2-1)*(2*xt1**2-2*xt2**2/q**4)/a)
gamma2_value=4*xt1*xt2/q**2*(1./2-1/eta)*(a/E**2)**(eta/2-2)/E**2
gamma1 = np.cos(2*phi_G)*gamma1_value-np.sin(2*phi_G)*gamma2_value
gamma2 = +np.sin(2*phi_G)*gamma1_value+np.cos(2*phi_G)*gamma2_value
f_xx = kappa + gamma1
f_yy = kappa - gamma1
f_xy = gamma2
return f_xx, f_xy, f_xy, f_yy
[docs] def mass_3d_lens(self, r, theta_E, gamma, e1=None, e2=None):
"""
computes the spherical power-law mass enclosed (with SPP routine)
:param r: radius within the mass is computed
:param theta_E: Einstein radius
:param gamma: power-law slope
:param e1: eccentricity component (not used)
:param e2: eccentricity component (not used)
:return: mass enclosed a 3D radius r
"""
return self.spp.mass_3d_lens(r, theta_E, gamma)
[docs] def density_lens(self, r, theta_E, gamma, e1=None, e2=None):
"""
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 within the mass is computed
:param theta_E: Einstein radius
:param gamma: power-law slope
:param e1: eccentricity component (not used)
:param e2: eccentricity component (not used)
:return: mass enclosed a 3D radius r
"""
return self.spp.density_lens(r, theta_E, gamma)
def _param_bounds(self, gamma, q):
"""
bounds parameters
:param gamma:
:param q:
:return:
"""
if gamma < 1.4:
gamma = 1.4
if gamma > 2.9:
gamma = 2.9
if q < 0.01:
q = 0.01
return float(gamma), q