def test_curved_arc_estimate_tan_diff(self):
arc_tan_diff = CurvedArcTanDiff()
lens_model_list = ['SIE']
lens = LensModel(lens_model_list=lens_model_list)
arc = LensModel(lens_model_list=['CURVED_ARC_TAN_DIFF'])
theta_E = 4
# here we model an off-axis ellisoid relative to the x-axis
e1, e2 = 0., -0.1
x_0, y_0 = 5, 0
kwargs_lens = [{
'theta_E': theta_E,
'e1': e1,
'e2': e2,
'center_x': 0,
'center_y': 0
}]
ext = LensModelExtensions(lensModel=lens)
kwargs_arc = ext.curved_arc_estimate(x_0,
y_0,
kwargs_lens,
tan_diff=True,
smoothing_3rd=0.01)
theta_E_sie, e1_sie, e2_sie, kappa_ext, center_x_sis, center_y_sis = arc_tan_diff.stretch2sie_mst(
**kwargs_arc)
print(theta_E_sie, e1_sie, e2_sie, center_x_sis, center_y_sis)
npt.assert_almost_equal(e2_sie - e2, 0, decimal=1)
npt.assert_almost_equal(e1_sie, e1, decimal=3)
# here we model an off-axis ellisoid relative to the y-axis
e1, e2 = 0.1, 0.
x_0, y_0 = 0, 5
kwargs_lens = [{
'theta_E': theta_E,
'e1': e1,
'e2': e2,
'center_x': 0,
'center_y': 0
}]
ext = LensModelExtensions(lensModel=lens)
kwargs_arc = ext.curved_arc_estimate(x_0,
y_0,
kwargs_lens,
tan_diff=True,
smoothing_3rd=0.01)
theta_E_sie, e1_sie, e2_sie, kappa_ext, center_x_sis, center_y_sis = arc_tan_diff.stretch2sie_mst(
**kwargs_arc)
print(theta_E_sie, e1_sie, e2_sie, center_x_sis, center_y_sis)
npt.assert_almost_equal(e1_sie - e1, 0, decimal=1)
npt.assert_almost_equal(e2_sie, e2, decimal=3)
x, y = util.make_grid(numPix=100, deltapix=0.1)
kappa = lens.kappa(x, y, kwargs_lens)
kappa_arc = arc.kappa(x, y, [kwargs_arc])
def test_curved_arc_finite_area(self):
lens_model_list = ['SPP']
lens = LensModel(lens_model_list=lens_model_list)
arc = LensModel(lens_model_list=['CURVED_ARC_SPP'])
theta_E = 4
gamma = 2.
kwargs_lens = [{
'theta_E': theta_E,
'gamma': gamma,
'center_x': 0,
'center_y': 0
}]
ext = LensModelExtensions(lensModel=lens)
x_0, y_0 = 5, 0
kwargs_arc = ext.curved_arc_estimate(x_0, y_0, kwargs_lens)
dr = 0.001
kwargs_arc_finite = ext.curved_arc_finite_area(x_0, y_0, kwargs_lens,
dr)
npt.assert_almost_equal(kwargs_arc['direction'],
kwargs_arc_finite['direction'],
decimal=3)
npt.assert_almost_equal(kwargs_arc['radial_stretch'],
kwargs_arc_finite['radial_stretch'],
decimal=3)
npt.assert_almost_equal(kwargs_arc['tangential_stretch'],
kwargs_arc_finite['tangential_stretch'],
decimal=3)
npt.assert_almost_equal(kwargs_arc['curvature'],
kwargs_arc_finite['curvature'],
decimal=3)
def _test_curved_arc_recovery(self, kwargs_arc_init):
ext = LensModelExtensions(
LensModel(lens_model_list=['CURVED_ARC_TAN_DIFF']))
center_x, center_y = kwargs_arc_init['center_x'], kwargs_arc_init[
'center_y']
kwargs_arc = ext.curved_arc_estimate(center_x, center_y,
[kwargs_arc_init])
lambda_rad, lambda_tan, orientation_angle, dlambda_tan_dtan, dlambda_tan_drad, dlambda_rad_drad, dlambda_rad_dtan, dphi_tan_dtan, dphi_tan_drad, dphi_rad_drad, dphi_rad_dtan = ext.radial_tangential_differentials(
center_x, center_y, [kwargs_arc_init])
print(lambda_tan, dlambda_tan_dtan, kwargs_arc_init['dtan_dtan'])
npt.assert_almost_equal(kwargs_arc['tangential_stretch'] /
kwargs_arc_init['tangential_stretch'],
1,
decimal=3)
npt.assert_almost_equal(kwargs_arc['radial_stretch'],
kwargs_arc_init['radial_stretch'],
decimal=3)
npt.assert_almost_equal(kwargs_arc['curvature'],
kwargs_arc_init['curvature'],
decimal=2)
npt.assert_almost_equal(dphi_tan_dtan,
kwargs_arc_init['curvature'],
decimal=2)
npt.assert_almost_equal(kwargs_arc['direction'],
kwargs_arc_init['direction'],
decimal=3)
npt.assert_almost_equal(dlambda_tan_dtan / lambda_tan,
kwargs_arc_init['dtan_dtan'],
decimal=2)
def test_curved_arc_estimate(self):
lens_model_list = ['SPP']
lens = LensModel(lens_model_list=lens_model_list)
arc = LensModel(lens_model_list=['CURVED_ARC_SPP'])
theta_E = 4
gamma = 2.
kwargs_lens = [{
'theta_E': theta_E,
'gamma': gamma,
'center_x': 0,
'center_y': 0
}]
ext = LensModelExtensions(lensModel=lens)
x_0, y_0 = 5, 0
kwargs_arc = ext.curved_arc_estimate(x_0, y_0, kwargs_lens)
theta_E_arc, gamma_arc, center_x_spp_arc, center_y_spp_arc = CurvedArcSPP.stretch2spp(
**kwargs_arc)
npt.assert_almost_equal(theta_E_arc, theta_E, decimal=4)
npt.assert_almost_equal(gamma_arc, gamma, decimal=3)
npt.assert_almost_equal(center_x_spp_arc, 0, decimal=3)
npt.assert_almost_equal(center_y_spp_arc, 0, decimal=3)
x, y = util.make_grid(numPix=10, deltapix=1)
alpha_x, alpha_y = lens.alpha(x, y, kwargs_lens)
alpha0_x, alpha0_y = lens.alpha(x_0, y_0, kwargs_lens)
alpha_x_arc, alpha_y_arc = arc.alpha(x, y, [kwargs_arc])
npt.assert_almost_equal(alpha_x_arc, alpha_x - alpha0_x, decimal=3)
npt.assert_almost_equal(alpha_y_arc, alpha_y - alpha0_y, decimal=3)
x_0, y_0 = 0., 3
kwargs_arc = ext.curved_arc_estimate(x_0, y_0, kwargs_lens)
theta_E_arc, gamma_arc, center_x_spp_arc, center_y_spp_arc = CurvedArcSPP.stretch2spp(
**kwargs_arc)
print(kwargs_arc)
print(theta_E_arc, gamma_arc, center_x_spp_arc, center_y_spp_arc)
npt.assert_almost_equal(theta_E_arc, theta_E, decimal=4)
npt.assert_almost_equal(gamma_arc, gamma, decimal=3)
npt.assert_almost_equal(center_x_spp_arc, 0, decimal=3)
npt.assert_almost_equal(center_y_spp_arc, 0, decimal=3)
x_0, y_0 = -2, -3
kwargs_arc = ext.curved_arc_estimate(x_0, y_0, kwargs_lens)
theta_E_arc, gamma_arc, center_x_spp_arc, center_y_spp_arc = CurvedArcSPP.stretch2spp(
**kwargs_arc)
npt.assert_almost_equal(theta_E_arc, theta_E, decimal=4)
npt.assert_almost_equal(gamma_arc, gamma, decimal=3)
npt.assert_almost_equal(center_x_spp_arc, 0, decimal=3)
npt.assert_almost_equal(center_y_spp_arc, 0, decimal=3)
def test_arcs_at_image_position(self):
# lensing quantities
kwargs_spp = {
'theta_E': 1.26,
'gamma': 2.,
'e1': 0.1,
'e2': -0.1,
'center_x': 0.0,
'center_y': 0.0
} # parameters of the deflector lens model
# the lens model is a supperposition of an elliptical lens model with external shear
lens_model_list = ['SPEP'] #, 'SHEAR']
kwargs_lens = [kwargs_spp] #, kwargs_shear]
lens_model_class = LensModel(lens_model_list=lens_model_list)
lensEquationSolver = LensEquationSolver(lens_model_class)
source_x = 0.
source_y = 0.05
x_image, y_image = lensEquationSolver.findBrightImage(
source_x,
source_y,
kwargs_lens,
numImages=4,
min_distance=0.05,
search_window=5)
arc_model = LensModel(lens_model_list=['CURVED_ARC_SPP', 'SHIFT'])
for i in range(len(x_image)):
x0, y0 = x_image[i], y_image[i]
print(x0, y0, i)
ext = LensModelExtensions(lensModel=lens_model_class)
kwargs_arc_i = ext.curved_arc_estimate(x0, y0, kwargs_lens)
alpha_x, alpha_y = lens_model_class.alpha(x0, y0, kwargs_lens)
kwargs_arc = [
kwargs_arc_i, {
'alpha_x': alpha_x,
'alpha_y': alpha_y
}
]
print(kwargs_arc_i)
direction = kwargs_arc_i['direction']
print(np.cos(direction), np.sin(direction))
x, y = util.make_grid(numPix=5, deltapix=0.01)
x = x0
y = y0
gamma1_arc, gamma2_arc = arc_model.gamma(x, y, kwargs_arc)
gamma1, gamma2 = lens_model_class.gamma(x, y, kwargs_lens)
print(gamma1, gamma2)
npt.assert_almost_equal(gamma1_arc, gamma1, decimal=3)
npt.assert_almost_equal(gamma2_arc, gamma2, decimal=3)
theta_E_arc, gamma_arc, center_x_spp_arc, center_y_spp_arc = CurvedArcSPP.stretch2spp(
**kwargs_arc_i)
print(theta_E_arc, gamma_arc, center_x_spp_arc, center_y_spp_arc)
npt.assert_almost_equal(center_x_spp_arc, 0, decimal=3)
npt.assert_almost_equal(center_y_spp_arc, 0, decimal=3)
