Source code for lenstronomy.LensModel.Profiles.nie_potential

__author__ = 'gipagano'

import numpy as np
import lenstronomy.Util.util as util
import lenstronomy.Util.param_util as param_util
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase

__all__ = ['NIE_POTENTIAL', 'NIEPotentialMajorAxis']


[docs]class NIE_POTENTIAL(LensProfileBase): """ this class implements the elliptical potential of Eq. (67) of `LECTURES ON GRAVITATIONAL LENSING <https://arxiv.org/pdf/astro-ph/9606001.pdf>`_ and Eq. (1) of `Blandford & Kochanek 1987 <http://adsabs.harvard.edu/full/1987ApJ...321..658B>`_, mapped to Eq. (8) of `Barnaka1998 <https://iopscience.iop.org/article/10.1086/305950/fulltext/37798.text.html>`_ to find the ellipticity bounds """ param_names = ['center_x', 'center_y', 'theta_E', 'theta_c', 'e1', 'e2'] lower_limit_default = {'center_x': -100, 'center_y': -100, 'theta_E': 0, 'theta_c': 0, 'e1': 0, 'e2': 0} upper_limit_default = {'center_x': 100, 'center_y': 100, 'theta_E': 10, 'theta_c': 10, 'e1': 0.2, 'e2': 0.2} def __init__(self): self.nie_potential_major_axis = NIEPotentialMajorAxis() super(NIE_POTENTIAL, self).__init__()
[docs] def param_conv(self, theta_E, theta_c, e1, e2): if self._static is True: return self._thetaE_transf_static, self._thetac_static, self._eps_static, self._phi_G_static return self._param_conv(theta_E, theta_c, e1, e2)
def _param_conv(self, theta_E, theta_c, e1, e2): """ convert the spherical averaged Einstein radius to an elliptical (major axis) Einstein radius and the individual eccentricities to the modulus of the eccentricity :param theta_E: Einstein radius :param theta_c: core radius :param e1: eccentricity component :param e2: eccentricity component :return: transformed Einstein radius, core radius, ellipticity modulus, orientation angle phi_G """ eps = np.sqrt(e1**2+e2**2) phi_G, q = param_util.ellipticity2phi_q(e1, e2) theta_E_conv = self._theta_q_convert(theta_E, q) theta_c_conv = self._theta_q_convert(theta_c, q) return theta_E_conv, theta_c_conv, eps, phi_G
[docs] def set_static(self, theta_E, theta_c, e1, e2, center_x=0, center_y=0): """ :param x: x-coordinate in image plane :param y: y-coordinate in image plane :param theta_E: Einstein radius :param theta_c: core radius :param e1: eccentricity component :param e2: eccentricity component :param center_x: profile center :param center_y: profile center :return: self variables set """ self._static = True self._thetaE_transf_static, self._thetac_static, self._eps_static, self._phi_G_static = self._param_conv(theta_E, theta_c, e1, e2)
[docs] def set_dynamic(self): """ :return: """ self._static = False if hasattr(self, '_thetaE_transf_static'): del self._thetaE_transf_static if hasattr(self, '_thetac_static'): del self._thetac_static if hasattr(self, '_eps_static'): del self._eps_static if hasattr(self, '_phi_G_static'): del self._phi_G_static
[docs] def function(self, x, y, theta_E, theta_c, e1, e2, center_x=0, center_y=0): """ :param x: x-coord (in angles) :param y: y-coord (in angles) :param theta_E: Einstein radius (in angles) :param theta_c: core radius (in angles) :param e1: eccentricity component, x direction(dimensionless) :param e2: eccentricity component, y direction (dimensionless) :return: lensing potential """ theta_E_conv, theta_c_conv, eps, phi_G = self.param_conv(theta_E, theta_c, e1, e2) # shift x_ = x - center_x y_ = y - center_y # rotate x__, y__ = util.rotate(x_, y_, phi_G) # evaluate f_ = self.nie_potential_major_axis.function(x__, y__, theta_E_conv, theta_c_conv, eps) # rotate back return f_
[docs] def derivatives(self, x, y, theta_E, theta_c, e1, e2, center_x=0, center_y=0): """ :param x: x-coord (in angles) :param y: y-coord (in angles) :param theta_E: Einstein radius (in angles) :param theta_c: core radius (in angles) :param e1: eccentricity component, x direction(dimensionless) :param e2: eccentricity component, y direction (dimensionless) :return: deflection angle (in angles) """ theta_E_conv, theta_c_conv, eps, phi_G = self.param_conv(theta_E, theta_c, e1, e2) # shift x_ = x - center_x y_ = y - center_y # rotate x__, y__ = util.rotate(x_, y_, phi_G) # evaluate f__x, f__y = self.nie_potential_major_axis.derivatives(x__, y__, theta_E_conv, theta_c_conv, eps) # rotate back f_x, f_y = util.rotate(f__x, f__y, -phi_G) return f_x, f_y
[docs] def hessian(self, x, y, theta_E, theta_c, e1, e2, center_x=0, center_y=0): """ :param x: x-coord (in angles) :param y: y-coord (in angles) :param theta_E: Einstein radius (in angles) :param theta_c: core radius (in angles) :param e1: eccentricity component, x direction(dimensionless) :param e2: eccentricity component, y direction (dimensionless) :return: hessian matrix (in angles) """ theta_E_conv, theta_c_conv, eps, phi_G = self.param_conv(theta_E, theta_c, e1, e2) # shift x_ = x - center_x y_ = y - center_y # rotate x__, y__ = util.rotate(x_, y_, phi_G) # evaluate f__xx, f__xy, _, f__yy = self.nie_potential_major_axis.hessian(x__, y__, theta_E_conv, theta_c_conv, eps) # rotate back kappa = 1./2 * (f__xx + f__yy) gamma1__ = 1./2 * (f__xx - f__yy) gamma2__ = f__xy gamma1 = np.cos(2 * phi_G) * gamma1__ - np.sin(2 * phi_G) * gamma2__ gamma2 = +np.sin(2 * phi_G) * gamma1__ + np.cos(2 * phi_G) * gamma2__ f_xx = kappa + gamma1 f_yy = kappa - gamma1 f_xy = gamma2 return f_xx, f_xy, f_xy, f_yy
def _theta_q_convert(self, theta_E, q): """ converts a spherical averaged Einstein radius/core radius to an elliptical (major axis) Einstein radius. This then follows the convention of the SPEMD profile in lenstronomy. (theta_E / theta_E_gravlens) = sqrt[ (1+q^2) / (2 q) ] :param theta_E: Einstein radius in lenstronomy conventions :param q: axis ratio minor/major :return: theta_E in convention of kappa= b *(q2(s2 + x2) + y2􏰉)−1/2 """ theta_E_new = theta_E / (np.sqrt((1.+q**2) / (2. * q))) #/ (1+(1-q)/2.) return theta_E_new
[docs]class NIEPotentialMajorAxis(LensProfileBase): """ this class implements the elliptical potential of Eq. (67) of `LECTURES ON GRAVITATIONAL LENSING <https://arxiv.org/pdf/astro-ph/9606001.pdf>`_ and Eq. (1) of `Blandford & Kochanek 1987 <http://adsabs.harvard.edu/full/1987ApJ...321..658B>`_, mapped to Eq. (8) of `Barnaka1998 <https://iopscience.iop.org/article/10.1086/305950/fulltext/37798.text.html>`_ to find the ellipticity bounds """ param_names = ['theta_E', 'theta_c', 'eps', 'center_x', 'center_y'] def __init__(self, diff=0.0000000001): self._diff = diff super(NIEPotentialMajorAxis, self).__init__()
[docs] def function(self, x, y, theta_E, theta_c, eps): f_ = theta_E*np.sqrt(theta_c**2+(1-eps)*x**2+(1+eps)*y**2) return f_
[docs] def derivatives(self, x, y, theta_E, theta_c, eps): """ returns df/dx and df/dy of the function """ factor = np.sqrt(theta_c**2+(1-eps)*x**2+(1+eps)*y**2) f_x = (theta_E/factor)*(1-eps)*x f_y = (theta_E/factor)*(1+eps)*y return f_x, f_y
[docs] def hessian(self, x, y, theta_E, theta_c, eps): """ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2 """ factor = np.sqrt(theta_c**2+(1-eps)*x**2+(1+eps)*y**2) f_xx = (1-eps)*(theta_E/factor) -(theta_E/factor**3)*(1-eps)**2*x**2 f_yy = (1+eps)*(theta_E/factor) -(theta_E/factor**3)*(1+eps)**2*y**2 f_xy = -(theta_E/factor**3)*(1-eps**2)*x*y return f_xx, f_xy, f_xy, f_yy