Source code for lenstronomy.LensModel.Profiles.curved_arc_spp

import numpy as np
from lenstronomy.LensModel.Profiles.spp import SPP
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase

__all__ = ['CurvedArcSPP', 'center_deflector']


[docs]class CurvedArcSPP(LensProfileBase): """ lens model that describes a section of a highly magnified deflector region. The parameterization is chosen to describe local observables efficient. Observables are: - curvature radius (basically bending relative to the center of the profile) - radial stretch (plus sign) thickness of arc with parity (more generalized than the power-law slope) - tangential stretch (plus sign). Infinity means at critical curve - direction of curvature - position of arc Requirements: - Should work with other perturbative models without breaking its meaning (say when adding additional shear terms) - Must best reflect the observables in lensing - minimal covariances between the parameters, intuitive parameterization. """ param_names = ['tangential_stretch', 'radial_stretch', 'curvature', 'direction', 'center_x', 'center_y'] lower_limit_default = {'tangential_stretch': -100, 'radial_stretch': -5, 'curvature': 0.000001, 'direction': -np.pi, 'center_x': -100, 'center_y': -100} upper_limit_default = {'tangential_stretch': 100, 'radial_stretch': 5, 'curvature': 100, 'direction': np.pi, 'center_x': 100, 'center_y': 100} def __init__(self): self._spp = SPP() super(CurvedArcSPP, self).__init__()
[docs] @staticmethod def stretch2spp(tangential_stretch, radial_stretch, curvature, direction, center_x, center_y): """ :param tangential_stretch: float, stretch of intrinsic source in tangential direction :param radial_stretch: float, stretch of intrinsic source in radial direction :param curvature: 1/curvature radius :param direction: float, angle in radian :param center_x: center of source in image plane :param center_y: center of source in image plane :return: parameters in terms of a spherical power-law profile resulting in the same observables """ center_x_spp, center_y_spp = center_deflector(curvature, direction, center_x, center_y) r_curvature = 1. / curvature gamma = (1./radial_stretch - 1) / (1 - 1./tangential_stretch) + 2 theta_E = abs(1 - 1./tangential_stretch)**(1./(gamma - 1)) * r_curvature return theta_E, gamma, center_x_spp, center_y_spp
[docs] @staticmethod def spp2stretch(theta_E, gamma, center_x_spp, center_y_spp, center_x, center_y): """ turn Singular power-law lens model into stretch parameterization at position (center_x, center_y) This is the inverse function of stretch2spp() :param theta_E: Einstein radius of SPP model :param gamma: power-law slope :param center_x_spp: center of SPP model :param center_y_spp: center of SPP model :param center_x: center of curved model definition :param center_y: center of curved model definition :return: tangential_stretch, radial_stretch, curvature, direction """ r_curvature = np.sqrt((center_x_spp - center_x)**2 + (center_y_spp - center_y)**2) direction = np.arctan2(center_y - center_y_spp, center_x - center_x_spp) tangential_stretch = 1 / (1 - (theta_E/r_curvature) ** (gamma - 1)) radial_stretch = 1 / (1 + (gamma - 2) * (theta_E/r_curvature) ** (gamma - 1)) curvature = 1./r_curvature return tangential_stretch, radial_stretch, curvature, direction
[docs] def function(self, x, y, tangential_stretch, radial_stretch, curvature, direction, center_x, center_y): """ ATTENTION: there may not be a global lensing potential! :param x: :param y: :param tangential_stretch: float, stretch of intrinsic source in tangential direction :param radial_stretch: float, stretch of intrinsic source in radial direction :param curvature: 1/curvature radius :param direction: float, angle in radian :param center_x: center of source in image plane :param center_y: center of source in image plane :return: """ theta_E, gamma, center_x_spp, center_y_spp = self.stretch2spp(tangential_stretch, radial_stretch, curvature, direction, center_x, center_y) f_ = self._spp.function(x, y, theta_E, gamma, center_x_spp, center_y_spp) alpha_x, alpha_y = self._spp.derivatives(center_x, center_y, theta_E, gamma, center_x_spp, center_y_spp) f_0 = alpha_x * (x - center_x) + alpha_y * (y - center_y) return f_ - f_0
[docs] def derivatives(self, x, y, tangential_stretch, radial_stretch, curvature, direction, center_x, center_y): """ :param x: :param y: :param tangential_stretch: float, stretch of intrinsic source in tangential direction :param radial_stretch: float, stretch of intrinsic source in radial direction :param curvature: 1/curvature radius :param direction: float, angle in radian :param center_x: center of source in image plane :param center_y: center of source in image plane :return: """ theta_E, gamma, center_x_spp, center_y_spp = self.stretch2spp(tangential_stretch, radial_stretch, curvature, direction, center_x, center_y) f_x, f_y = self._spp.derivatives(x, y, theta_E, gamma, center_x_spp, center_y_spp) f_x0, f_y0 = self._spp.derivatives(center_x, center_y, theta_E, gamma, center_x_spp, center_y_spp) return f_x - f_x0, f_y - f_y0
[docs] def hessian(self, x, y, tangential_stretch, radial_stretch, curvature, direction, center_x, center_y): """ :param x: :param y: :param tangential_stretch: float, stretch of intrinsic source in tangential direction :param radial_stretch: float, stretch of intrinsic source in radial direction :param curvature: 1/curvature radius :param direction: float, angle in radian :param center_x: center of source in image plane :param center_y: center of source in image plane :return: """ theta_E, gamma, center_x_spp, center_y_spp = self.stretch2spp(tangential_stretch, radial_stretch, curvature, direction, center_x, center_y) return self._spp.hessian(x, y, theta_E, gamma, center_x_spp, center_y_spp)
[docs]def center_deflector(curvature, direction, center_x, center_y): """ :param curvature: 1/curvature radius :param direction: float, angle in radian :param center_x: center of source in image plane :param center_y: center of source in image plane :return: center_spp_x, center_spp_y """ center_x_spp = center_x - np.cos(direction) / curvature center_y_spp = center_y - np.sin(direction) / curvature return center_x_spp, center_y_spp