Source code for lenstronomy.LensModel.Profiles.spep

__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) # 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=0, e2=0): """ computes the spherical power-law mass enclosed (with SPP routiune) :param r: :param theta_E: :param gamma: :param q: :param phi_G: :return: """ return self.spp.mass_3d_lens(r, theta_E, gamma)
[docs] def density_lens(self, r, theta_E, gamma, e1=0, e2=0): """ :param r: :param theta_E: :param gamma: :param e1: :param e2: :return: """ 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