import numpy as np
from lenstronomy.LensModel.Profiles.shear import ShearReduced
from lenstronomy.LensModel.Profiles.curved_arc_sis_mst import CurvedArcSISMST
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase
__all__ = ['CurvedArcSPT']
[docs]class CurvedArcSPT(LensProfileBase):
"""
Curved arc model based on SIS+MST with an additional non-linear shear distortions applied on the source coordinates
around the center.
This profile is effectively a Source Position Transform of a curved arc and a shear distortion.
"""
param_names = ['tangential_stretch', 'radial_stretch', 'curvature', 'direction', 'gamma1', 'gamma2', 'center_x',
'center_y']
lower_limit_default = {'tangential_stretch': -100, 'radial_stretch': -5, 'curvature': 0.000001, 'direction': -np.pi,
'gamma1': -0.5, 'gamma2': -0.5, 'center_x': -100, 'center_y': -100}
upper_limit_default = {'tangential_stretch': 100, 'radial_stretch': 5, 'curvature': 100, 'direction': np.pi,
'gamma1': 0.5, 'gamma2': 0.5, 'center_x': 100, 'center_y': 100}
def __init__(self):
self._curve = CurvedArcSISMST()
self._distort = ShearReduced()
super(CurvedArcSPT, self).__init__()
[docs] def function(self, x, y, tangential_stretch, radial_stretch, curvature, direction, gamma1, gamma2, 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 gamma1: non-linear reduced shear distortion in the source plane
:param gamma2: non-linear reduced shear distortion in the source plane
:param center_x: center of source in image plane
:param center_y: center of source in image plane
:return:
"""
raise NotImplemented('lensing potential for regularly curved arc is not implemented')
[docs] def derivatives(self, x, y, tangential_stretch, radial_stretch, curvature, direction, gamma1, gamma2, 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 gamma1: non-linear reduced shear distortion in the source plane
:param gamma2: non-linear reduced shear distortion in the source plane
:param center_x: center of source in image plane
:param center_y: center of source in image plane
:return:
"""
# computed regular curved arc deflection
f_x_c, f_y_c = self._curve.derivatives(x, y, tangential_stretch, radial_stretch, curvature, direction,
center_x, center_y)
# map to source plane coordinate system
beta_x, beta_y = x - f_x_c, y - f_y_c
# distort source plane coordinate system around (center_x, center_y)
f_x_b, f_y_b = self._distort.derivatives(beta_x, beta_y, gamma1, gamma2, ra_0=center_x, dec_0=center_y)
beta_x_, beta_y_ = beta_x - f_x_b, beta_y - f_y_b
# compute total deflection between initial coordinate and final source coordinate to match lens equation
# beta = theta - alpha
f_x, f_y = x - beta_x_, y - beta_y_
return f_x, f_y
[docs] def hessian(self, x, y, tangential_stretch, radial_stretch, curvature, direction, gamma1, gamma2, 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 gamma1: non-linear reduced shear distortion in the source plane
:param gamma2: non-linear reduced shear distortion in the source plane
:param center_x: center of source in image plane
:param center_y: center of source in image plane
:return:
"""
alpha_ra, alpha_dec = self.derivatives(x, y, tangential_stretch, radial_stretch, curvature, direction, gamma1,
gamma2, center_x, center_y)
diff = 0.0000001
alpha_ra_dx, alpha_dec_dx = self.derivatives(x + diff, y, tangential_stretch, radial_stretch, curvature,
direction, gamma1, gamma2, center_x, center_y)
alpha_ra_dy, alpha_dec_dy = self.derivatives(x, y + diff, tangential_stretch, radial_stretch, curvature,
direction, gamma1, gamma2, center_x, center_y)
f_xx = (alpha_ra_dx - alpha_ra) / diff
f_xy = (alpha_ra_dy - alpha_ra) / diff
f_yx = (alpha_dec_dx - alpha_dec) / diff
f_yy = (alpha_dec_dy - alpha_dec) / diff
return f_xx, f_xy, f_yx, f_yy