def __init__(self, profile_type='CORED_DENSITY'):
if profile_type == 'CORED_DENSITY':
self._profile = CoredDensity()
elif profile_type == 'CORED_DENSITY_2':
self._profile = CoredDensity2()
else:
raise ValueError(
'profile_type %s not supported for CoredDensityMST instance.' %
profile_type)
self._convergence = Convergence()
super(CoredDensityMST, self).__init__()
def __init__(self, profile_type='CORED_DENSITY'):
if profile_type == 'CORED_DENSITY':
self._profile = CoredDensity()
elif profile_type == 'CORED_DENSITY_2':
self._profile = CoredDensity2()
elif profile_type == 'CORED_DENSITY_EXP':
self._profile = CoredDensityExp()
# Due to parameters name conventions/positioning, right now only the free soliton with
# the default value of slope = 8 is supported
elif profile_type == 'CORED_DENSITY_ULDM':
self._profile = Uldm()
else:
raise ValueError('profile_type %s not supported for CoredDensityMST instance.' % profile_type)
self._convergence = Convergence()
super(CoredDensityMST, self).__init__()
class TestConvergence(object):
"""
tests the Gaussian methods
"""
def setup(self):
self.profile = Convergence()
self.kwargs_lens = {'kappa_ext': 0.1}
def test_function(self):
x = np.array([1])
y = np.array([0])
values = self.profile.function(x, y, **self.kwargs_lens)
npt.assert_almost_equal(values[0],
self.kwargs_lens['kappa_ext'] / 2,
decimal=5)
x = np.array([0])
y = np.array([0])
values = self.profile.function(x, y, **self.kwargs_lens)
npt.assert_almost_equal(values[0], 0, decimal=5)
x = np.array([2, 3, 4])
y = np.array([1, 1, 1])
values = self.profile.function(x, y, **self.kwargs_lens)
npt.assert_almost_equal(values[0], 0.25, decimal=5)
npt.assert_almost_equal(values[1], 0.5, decimal=5)
def test_derivatives(self):
x = np.array([1])
y = np.array([2])
f_x, f_y = self.profile.derivatives(x, y, **self.kwargs_lens)
npt.assert_almost_equal(f_x[0], 0.1, decimal=5)
npt.assert_almost_equal(f_y[0], 0.2, decimal=5)
x = np.array([1, 3, 4])
y = np.array([2, 1, 1])
values = self.profile.derivatives(x, y, **self.kwargs_lens)
npt.assert_almost_equal(values[0][0], 0.1, decimal=5)
npt.assert_almost_equal(values[1][0], 0.2, decimal=5)
def test_hessian(self):
x = np.array([1])
y = np.array([2])
f_xx, f_xy, f_yx, f_yy = self.profile.hessian(x, y, **self.kwargs_lens)
npt.assert_almost_equal(f_xx, 0.1, decimal=5)
npt.assert_almost_equal(f_yy, 0.1, decimal=5)
npt.assert_almost_equal(f_xy, 0, decimal=5)
npt.assert_almost_equal(f_yx, 0, decimal=5)
x = np.array([1, 3, 4])
y = np.array([2, 1, 1])
values = self.profile.hessian(x, y, **self.kwargs_lens)
npt.assert_almost_equal(values[0], 0.1, decimal=5)
npt.assert_almost_equal(values[3], 0.1, decimal=5)
npt.assert_almost_equal(values[1], 0, decimal=5)
class TestCurvedArcSISMST(object):
"""
tests the source model routines
"""
def setup(self):
self.model = CurvedArcSISMST()
self.sis = SIS()
self.mst = Convergence()
def test_spp2stretch(self):
center_x, center_y = 1, 1
theta_E = 1
kappa = 0.1
center_x_spp, center_y_spp = 0., 0
tangential_stretch, radial_stretch, curvature, direction = self.model.sis_mst2stretch(theta_E, kappa, center_x_spp, center_y_spp, center_x, center_y)
theta_E_new, kappa_new, center_x_spp_new, center_y_spp_new = self.model.stretch2sis_mst(tangential_stretch, radial_stretch, curvature, direction, center_x, center_y)
npt.assert_almost_equal(center_x_spp_new, center_x_spp, decimal=8)
npt.assert_almost_equal(center_y_spp_new, center_y_spp, decimal=8)
npt.assert_almost_equal(theta_E_new, theta_E, decimal=8)
npt.assert_almost_equal(kappa_new, kappa, decimal=8)
center_x, center_y = -1, 1
tangential_stretch, radial_stretch, curvature, direction = self.model.sis_mst2stretch(theta_E, kappa,
center_x_spp, center_y_spp,
center_x, center_y)
theta_E_new, kappa_new, center_x_spp_new, center_y_spp_new = self.model.stretch2sis_mst(tangential_stretch,
radial_stretch, curvature,
direction, center_x,
center_y)
npt.assert_almost_equal(center_x_spp_new, center_x_spp, decimal=8)
npt.assert_almost_equal(center_y_spp_new, center_y_spp, decimal=8)
npt.assert_almost_equal(theta_E_new, theta_E, decimal=8)
npt.assert_almost_equal(kappa_new, kappa, decimal=8)
center_x, center_y = 0, 0.5
tangential_stretch, radial_stretch, curvature, direction = self.model.sis_mst2stretch(theta_E, kappa,
center_x_spp, center_y_spp,
center_x, center_y)
theta_E_new, kappa_new, center_x_spp_new, center_y_spp_new = self.model.stretch2sis_mst(tangential_stretch,
radial_stretch, curvature,
direction, center_x,
center_y)
npt.assert_almost_equal(center_x_spp_new, center_x_spp, decimal=8)
npt.assert_almost_equal(center_y_spp_new, center_y_spp, decimal=8)
npt.assert_almost_equal(theta_E_new, theta_E, decimal=8)
npt.assert_almost_equal(kappa_new, kappa, decimal=8)
center_x, center_y = 0, -1.5
tangential_stretch, radial_stretch, r_curvature, direction = self.model.sis_mst2stretch(theta_E, kappa,
center_x_spp, center_y_spp,
center_x, center_y)
print(tangential_stretch, radial_stretch, r_curvature, direction)
theta_E_new, kappa_new, center_x_spp_new, center_y_spp_new = self.model.stretch2sis_mst(tangential_stretch,
radial_stretch, r_curvature,
direction, center_x,
center_y)
npt.assert_almost_equal(center_x_spp_new, center_x_spp, decimal=8)
npt.assert_almost_equal(center_y_spp_new, center_y_spp, decimal=8)
npt.assert_almost_equal(theta_E_new, theta_E, decimal=8)
npt.assert_almost_equal(kappa_new, kappa, decimal=8)
def test_function(self):
center_x, center_y = 0., 0.
x, y = 1, 1
radial_stretch = 1
output = self.model.function(x, y, tangential_stretch=2, radial_stretch=radial_stretch, curvature=1./2, direction=0, center_x=center_x, center_y=center_y)
theta_E, kappa_ext, center_x_sis, center_y_sis = self.model.stretch2sis_mst(tangential_stretch=2, radial_stretch=radial_stretch, curvature=1./2, direction=0,
center_x=center_x, center_y=center_y)
f_sis_out = self.sis.function(1, 1, theta_E, center_x_sis, center_y_sis) # - self.sis.function(0, 0, theta_E, center_x_sis, center_y_sis)
alpha_x, alpha_y = self.sis.derivatives(center_x, center_y, theta_E, center_x_sis, center_y_sis)
f_sis_0_out = alpha_x * (x - center_x) + alpha_y * (y - center_y)
f_mst_out = self.mst.function(x, y, kappa_ext, ra_0=center_x, dec_0=center_y)
lambda_mst = 1. / radial_stretch
f_out = lambda_mst * (f_sis_out - f_sis_0_out) + f_mst_out
npt.assert_almost_equal(output, f_out, decimal=8)
def test_derivatives(self):
tangential_stretch = 5
radial_stretch = 1
curvature = 1./10
direction = 0.3
center_x = 0
center_y = 0
x, y = 1, 1
theta_E, kappa, center_x_spp, center_y_spp = self.model.stretch2sis_mst(tangential_stretch,
radial_stretch, curvature,
direction, center_x, center_y)
f_x_sis, f_y_sis = self.sis.derivatives(x, y, theta_E, center_x_spp, center_y_spp)
f_x_mst, f_y_mst = self.mst.derivatives(x, y, kappa, ra_0=center_x, dec_0=center_y)
f_x0, f_y0 = self.sis.derivatives(center_x, center_y, theta_E, center_x_spp, center_y_spp)
f_x_new, f_y_new = self.model.derivatives(x, y, tangential_stretch, radial_stretch, curvature, direction, center_x, center_y)
npt.assert_almost_equal(f_x_new, f_x_sis + f_x_mst - f_x0, decimal=8)
npt.assert_almost_equal(f_y_new, f_y_sis + f_y_mst - f_y0, decimal=8)
def test_hessian(self):
lens = LensModel(lens_model_list=['CURVED_ARC_SIS_MST'])
center_x, center_y = 0, 0
tangential_stretch = 10
radial_stretch = 1
kwargs_lens = [
{'tangential_stretch': tangential_stretch, 'radial_stretch': radial_stretch, 'curvature': 1./10.5, 'direction': 0.,
'center_x': center_x, 'center_y': center_y}]
mag = lens.magnification(center_x, center_y, kwargs=kwargs_lens)
npt.assert_almost_equal(mag, tangential_stretch * radial_stretch, decimal=8)
center_x, center_y = 2, 3
tangential_stretch = 10
radial_stretch = 1
kwargs_lens = [
{'tangential_stretch': tangential_stretch, 'radial_stretch': radial_stretch, 'curvature': 1./10.5, 'direction': 0.,
'center_x': center_x, 'center_y': center_y}]
mag = lens.magnification(center_x, center_y, kwargs=kwargs_lens)
npt.assert_almost_equal(mag, tangential_stretch * radial_stretch, decimal=8)
center_x, center_y = 0, 0
tangential_stretch = 5
radial_stretch = 1.2
kwargs_lens = [
{'tangential_stretch': tangential_stretch, 'radial_stretch': radial_stretch, 'curvature': 1. / 10.5,
'direction': 0.,
'center_x': center_x, 'center_y': center_y}]
mag = lens.magnification(center_x, center_y, kwargs=kwargs_lens)
npt.assert_almost_equal(mag, tangential_stretch * radial_stretch, decimal=8)
center_x, center_y = 0, 0
tangential_stretch = 3
radial_stretch = -1
kwargs_lens = [
{'tangential_stretch': tangential_stretch, 'radial_stretch': radial_stretch, 'curvature': 1./10.5,
'direction': 0.,
'center_x': center_x, 'center_y': center_y}]
mag = lens.magnification(center_x, center_y, kwargs=kwargs_lens)
print(tangential_stretch, radial_stretch, 'stretches')
npt.assert_almost_equal(mag, tangential_stretch * radial_stretch, decimal=8)
center_x, center_y = 0, 0
tangential_stretch = -3
radial_stretch = -1
kwargs_lens = [
{'tangential_stretch': tangential_stretch, 'radial_stretch': radial_stretch, 'curvature': 1./10.5,
'direction': 0.,
'center_x': center_x, 'center_y': center_y}]
mag = lens.magnification(center_x, center_y, kwargs=kwargs_lens)
npt.assert_almost_equal(mag, tangential_stretch * radial_stretch, decimal=8)
center_x, center_y = 0, 0
tangential_stretch = 10.4
radial_stretch = 0.6
kwargs_lens = [
{'tangential_stretch': tangential_stretch, 'radial_stretch': radial_stretch, 'curvature': 1./10.5,
'direction': 0.,
'center_x': center_x, 'center_y': center_y}]
mag = lens.magnification(center_x, center_y, kwargs=kwargs_lens)
npt.assert_almost_equal(mag, tangential_stretch * radial_stretch, decimal=8)
def test_curved_arc_recovery(self):
"""
test whether the curved arc parameters are satisfied in differential form
"""
ext = LensModelExtensions(LensModel(lens_model_list=['CURVED_ARC_SIS_MST']))
center_x, center_y = 1, 1. # test works except at (0,0) where the direction angle is not well defined
tangential_stretch = 10.
radial_stretch = 1.2
curvature, direction = 0.02, 0.5
kwargs_lens = {'tangential_stretch': tangential_stretch, 'radial_stretch': radial_stretch,
'curvature': curvature, 'direction': direction, 'center_x': center_x, 'center_y': center_y}
self._test_curved_arc_recovery(kwargs_lens)
def _test_curved_arc_recovery(self, kwargs_arc_init):
ext = LensModelExtensions(LensModel(lens_model_list=['CURVED_ARC_SIS_MST']))
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])
npt.assert_almost_equal(kwargs_arc['tangential_stretch'], kwargs_arc_init['tangential_stretch'], 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=3)
npt.assert_almost_equal(dphi_tan_dtan, kwargs_arc_init['curvature'], decimal=3)
npt.assert_almost_equal(kwargs_arc['direction'], kwargs_arc_init['direction'], decimal=3)
npt.assert_almost_equal(dlambda_tan_dtan, 0, decimal=3)
class CoredDensityMST(LensProfileBase):
"""
approximate mass-sheet transform of a density core. This routine takes the parameters of the density core and
subtracts a mass=sheet that approximates the cored profile in it's center to counter-act (in approximation) this
model. This allows for better sampling of the mass-sheet transformed quantities that do not have strong covariances.
Attention!!! The interpretation of the result is that the mass sheet as 'CONVERGENCE' that is present needs to be
subtracted in post-processing.
"""
param_names = ['lambda_approx', 'r_core', 'center_x', 'center_y']
lower_limit_default = {
'lambda_approx': -1,
'r_core': 0,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'lambda_approx': 10,
'r_core': 100,
'center_x': 100,
'center_y': 100
}
def __init__(self, profile_type='CORED_DENSITY'):
if profile_type == 'CORED_DENSITY':
self._profile = CoredDensity()
elif profile_type == 'CORED_DENSITY_2':
self._profile = CoredDensity2()
elif profile_type == 'CORED_DENSITY_EXP':
self._profile = CoredDensityExp()
else:
raise ValueError(
'profile_type %s not supported for CoredDensityMST instance.' %
profile_type)
self._convergence = Convergence()
super(CoredDensityMST, self).__init__()
def function(self, x, y, lambda_approx, r_core, center_x=0, center_y=0):
"""
lensing potential of approximate mass-sheet correction
:param x: x-coordinate
:param y: y-coordinate
:param lambda_approx: approximate mass sheet transform
:param r_core: core radius of the cored density profile
:param center_x: x-center of the profile
:param center_y: y-center of the profile
:return: lensing potential correction
"""
kappa_ext = 1 - lambda_approx
f_cored_density = self._profile.function(x, y, kappa_ext, r_core,
center_x, center_y)
f_ms = self._convergence.function(x, y, kappa_ext, center_x, center_y)
return f_cored_density - f_ms
def derivatives(self, x, y, lambda_approx, r_core, center_x=0, center_y=0):
"""
deflection angles of approximate mass-sheet correction
:param x: x-coordinate
:param y: y-coordinate
:param lambda_approx: approximate mass sheet transform
:param r_core: core radius of the cored density profile
:param center_x: x-center of the profile
:param center_y: y-center of the profile
:return: alpha_x, alpha_y
"""
kappa_ext = 1 - lambda_approx
f_x_cd, f_y_cd = self._profile.derivatives(x, y, kappa_ext, r_core,
center_x, center_y)
f_x_ms, f_y_ms = self._convergence.derivatives(x, y, kappa_ext,
center_x, center_y)
return f_x_cd - f_x_ms, f_y_cd - f_y_ms
def hessian(self, x, y, lambda_approx, r_core, center_x=0, center_y=0):
"""
Hessian terms of approximate mass-sheet correction
:param x: x-coordinate
:param y: y-coordinate
:param lambda_approx: approximate mass sheet transform
:param r_core: core radius of the cored density profile
:param center_x: x-center of the profile
:param center_y: y-center of the profile
:return: df/dxx, df/dyy, df/dxy
"""
kappa_ext = 1 - lambda_approx
f_xx_cd, f_yy_cd, f_xy_cd = self._profile.hessian(
x, y, kappa_ext, r_core, center_x, center_y)
f_xx_ms, f_yy_ms, f_xy_ms = self._convergence.hessian(
x, y, kappa_ext, center_x, center_y)
return f_xx_cd - f_xx_ms, f_yy_cd - f_yy_ms, f_xy_cd - f_xy_ms
class CurvedArcTanDiff(LensProfileBase):
"""
Curved arc model with an additional non-zero tangential stretch differential in tangential direction component
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', 'dtan_dtan',
'direction', 'center_x', 'center_y'
]
lower_limit_default = {
'tangential_stretch': -100,
'radial_stretch': -5,
'curvature': 0.000001,
'dtan_dtan': -10,
'direction': -np.pi,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'tangential_stretch': 100,
'radial_stretch': 5,
'curvature': 100,
'dtan_dtan': 10,
'direction': np.pi,
'center_x': 100,
'center_y': 100
}
def __init__(self):
self._sie = SIE(NIE=True)
self._mst = Convergence()
super(CurvedArcTanDiff, self).__init__()
@staticmethod
def stretch2sie_mst(tangential_stretch, radial_stretch, curvature,
dtan_dtan, 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 dtan_dtan: d(tangential_stretch) / d(tangential direction) / tangential stretch
: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 SIS + MST resulting in the same observables
"""
center_x_sis, center_y_sis = center_deflector(curvature, direction,
center_x, center_y)
r_curvature = 1. / curvature
lambda_mst = 1. / radial_stretch
kappa_ext = 1 - lambda_mst
theta_E = r_curvature * (1. - radial_stretch / tangential_stretch)
# analytic relation (see Birrer 2021)
dlambda_tan_dr = tangential_stretch / r_curvature * (
1 - tangential_stretch / radial_stretch)
# translate tangential eigenvalue gradient in lens ellipticity
dtan_dtan_ = dtan_dtan * tangential_stretch
epsilon = np.abs(dtan_dtan_ / dlambda_tan_dr)
# bound epsilon by (-1, 1)
epsilon = np.minimum(epsilon, 0.99999)
q = np.sqrt((1 - epsilon) / (1 + epsilon))
if dtan_dtan_ < 0:
phi = direction - np.pi / 4
else:
phi = direction + np.pi / 4
e1_sie, e2_sie = param_util.phi_q2_ellipticity(phi, q)
# ellipticity adopted Einstein radius to match local tangential and radial stretch
factor = np.sqrt(1 + q**2) / np.sqrt(2 * q)
theta_E_sie = theta_E * factor
return theta_E_sie, e1_sie, e2_sie, kappa_ext, center_x_sis, center_y_sis
def function(self, x, y, tangential_stretch, radial_stretch, curvature,
dtan_dtan, 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 dtan_dtan: d(tangential_stretch) / d(tangential direction) / tangential stretch
:param center_x: center of source in image plane
:param center_y: center of source in image plane
:return:
"""
lambda_mst = 1. / radial_stretch
theta_E_sie, e1_sie, e2_sie, kappa_ext, center_x_sis, center_y_sis = self.stretch2sie_mst(
tangential_stretch, radial_stretch, curvature, dtan_dtan,
direction, center_x, center_y)
f_sis = self._sie.function(
x, y, theta_E_sie, e1_sie, e2_sie, center_x_sis, center_y_sis
) # - self._sis.function(center_x, center_y, theta_E, center_x_sis, center_y_sis)
alpha_x, alpha_y = self._sie.derivatives(center_x, center_y,
theta_E_sie, e1_sie, e2_sie,
center_x_sis, center_y_sis)
f_sis_0 = alpha_x * (x - center_x) + alpha_y * (y - center_y)
f_mst = self._mst.function(x,
y,
kappa_ext,
ra_0=center_x,
dec_0=center_y)
return lambda_mst * (f_sis - f_sis_0) + f_mst
def derivatives(self, x, y, tangential_stretch, radial_stretch, curvature,
dtan_dtan, 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 dtan_dtan: d(tangential_stretch) / d(tangential direction) / tangential stretch
:param center_x: center of source in image plane
:param center_y: center of source in image plane
:return:
"""
lambda_mst = 1. / radial_stretch
theta_E_sie, e1_sie, e2_sie, kappa_ext, center_x_sis, center_y_sis = self.stretch2sie_mst(
tangential_stretch, radial_stretch, curvature, dtan_dtan,
direction, center_x, center_y)
f_x_sis, f_y_sis = self._sie.derivatives(x, y, theta_E_sie, e1_sie,
e2_sie, center_x_sis,
center_y_sis)
f_x0, f_y0 = self._sie.derivatives(center_x, center_y, theta_E_sie,
e1_sie, e2_sie, center_x_sis,
center_y_sis)
f_x_mst, f_y_mst = self._mst.derivatives(x,
y,
kappa_ext,
ra_0=center_x,
dec_0=center_y)
f_x = lambda_mst * (f_x_sis - f_x0) + f_x_mst
f_y = lambda_mst * (f_y_sis - f_y0) + f_y_mst
return f_x, f_y
def hessian(self, x, y, tangential_stretch, radial_stretch, curvature,
dtan_dtan, 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 dtan_dtan: d(tangential_stretch) / d(tangential direction) / tangential stretch
:param center_x: center of source in image plane
:param center_y: center of source in image plane
:return:
"""
lambda_mst = 1. / radial_stretch
theta_E_sie, e1_sie, e2_sie, kappa_ext, center_x_sis, center_y_sis = self.stretch2sie_mst(
tangential_stretch, radial_stretch, curvature, dtan_dtan,
direction, center_x, center_y)
f_xx_sis, f_xy_sis, f_yx_sis, f_yy_sis = self._sie.hessian(
x, y, theta_E_sie, e1_sie, e2_sie, center_x_sis, center_y_sis)
f_xx_mst, f_xy_mst, f_yx_mst, f_yy_mst = self._mst.hessian(
x, y, kappa_ext, ra_0=center_x, dec_0=center_y)
return lambda_mst * f_xx_sis + f_xx_mst, lambda_mst * f_xy_sis + f_xy_mst, lambda_mst * f_yx_sis + f_yx_mst, lambda_mst * f_yy_sis + f_yy_mst
def __init__(self):
self._sie = SIE(NIE=True)
self._mst = Convergence()
super(CurvedArcTanDiff, self).__init__()
def _import_class(self, lens_type, i, custom_class):
if lens_type == 'SHIFT':
from lenstronomy.LensModel.Profiles.alpha_shift import Shift
return Shift()
elif lens_type == 'SHEAR':
from lenstronomy.LensModel.Profiles.shear import Shear
return Shear()
elif lens_type == 'CONVERGENCE':
from lenstronomy.LensModel.Profiles.convergence import Convergence
return Convergence()
elif lens_type == 'FLEXION':
from lenstronomy.LensModel.Profiles.flexion import Flexion
return Flexion()
elif lens_type == 'POINT_MASS':
from lenstronomy.LensModel.Profiles.point_mass import PointMass
return PointMass()
elif lens_type == 'SIS':
from lenstronomy.LensModel.Profiles.sis import SIS
return SIS()
elif lens_type == 'SIS_TRUNCATED':
from lenstronomy.LensModel.Profiles.sis_truncate import SIS_truncate
return SIS_truncate()
elif lens_type == 'SIE':
from lenstronomy.LensModel.Profiles.sie import SIE
return SIE()
elif lens_type == 'SPP':
from lenstronomy.LensModel.Profiles.spp import SPP
return SPP()
elif lens_type == 'NIE':
from lenstronomy.LensModel.Profiles.nie import NIE
return NIE()
elif lens_type == 'NIE_SIMPLE':
from lenstronomy.LensModel.Profiles.nie import NIE_simple
return NIE_simple()
elif lens_type == 'CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import Chameleon
return Chameleon()
elif lens_type == 'DOUBLE_CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import DoubleChameleon
return DoubleChameleon()
elif lens_type == 'SPEP':
from lenstronomy.LensModel.Profiles.spep import SPEP
return SPEP()
elif lens_type == 'SPEMD':
from lenstronomy.LensModel.Profiles.spemd import SPEMD
return SPEMD()
elif lens_type == 'SPEMD_SMOOTH':
from lenstronomy.LensModel.Profiles.spemd_smooth import SPEMD_SMOOTH
return SPEMD_SMOOTH()
elif lens_type == 'NFW':
from lenstronomy.LensModel.Profiles.nfw import NFW
return NFW()
elif lens_type == 'NFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.nfw_ellipse import NFW_ELLIPSE
return NFW_ELLIPSE()
elif lens_type == 'TNFW':
from lenstronomy.LensModel.Profiles.tnfw import TNFW
return TNFW()
elif lens_type == 'CNFW':
from lenstronomy.LensModel.Profiles.cnfw import CNFW
return CNFW()
elif lens_type == 'SERSIC':
from lenstronomy.LensModel.Profiles.sersic import Sersic
return Sersic()
elif lens_type == 'SERSIC_ELLIPSE':
from lenstronomy.LensModel.Profiles.sersic_ellipse import SersicEllipse
return SersicEllipse()
elif lens_type == 'PJAFFE':
from lenstronomy.LensModel.Profiles.p_jaffe import PJaffe
return PJaffe()
elif lens_type == 'PJAFFE_ELLIPSE':
from lenstronomy.LensModel.Profiles.p_jaffe_ellipse import PJaffe_Ellipse
return PJaffe_Ellipse()
elif lens_type == 'HERNQUIST':
from lenstronomy.LensModel.Profiles.hernquist import Hernquist
return Hernquist()
elif lens_type == 'HERNQUIST_ELLIPSE':
from lenstronomy.LensModel.Profiles.hernquist_ellipse import Hernquist_Ellipse
return Hernquist_Ellipse()
elif lens_type == 'GAUSSIAN':
from lenstronomy.LensModel.Profiles.gaussian_potential import Gaussian
return Gaussian()
elif lens_type == 'GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.gaussian_kappa import GaussianKappa
return GaussianKappa()
elif lens_type == 'GAUSSIAN_KAPPA_ELLIPSE':
from lenstronomy.LensModel.Profiles.gaussian_kappa_ellipse import GaussianKappaEllipse
return GaussianKappaEllipse()
elif lens_type == 'MULTI_GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappa
return MultiGaussianKappa()
elif lens_type == 'MULTI_GAUSSIAN_KAPPA_ELLIPSE':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappaEllipse
return MultiGaussianKappaEllipse()
elif lens_type == 'INTERPOL':
from lenstronomy.LensModel.Profiles.interpol import Interpol
return Interpol(grid=False, min_grid_number=100)
elif lens_type == 'INTERPOL_SCALED':
from lenstronomy.LensModel.Profiles.interpol import InterpolScaled
return InterpolScaled()
elif lens_type == 'SHAPELETS_POLAR':
from lenstronomy.LensModel.Profiles.shapelet_pot_polar import PolarShapelets
return PolarShapelets()
elif lens_type == 'SHAPELETS_CART':
from lenstronomy.LensModel.Profiles.shapelet_pot_cartesian import CartShapelets
return CartShapelets()
elif lens_type == 'DIPOLE':
from lenstronomy.LensModel.Profiles.dipole import Dipole
return Dipole()
elif lens_type == 'FOREGROUND_SHEAR':
from lenstronomy.LensModel.Profiles.shear import Shear
self._foreground_shear = True
self._foreground_shear_idex = i
return Shear()
elif lens_type == 'coreBURKERT':
from lenstronomy.LensModel.Profiles.coreBurkert import coreBurkert
return coreBurkert()
elif lens_type == 'NumericalAlpha':
from lenstronomy.LensModel.Profiles.numerical_deflections import NumericalAlpha
return NumericalAlpha(custom_class[i])
else:
raise ValueError('%s is not a valid lens model' % lens_type)
def __init__(self):
self._shear = Shear()
self._convergence = Convergence()
super(ShearReduced, self).__init__()
class CurvedArcConstMST(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._mst = Convergence()
self._curve = CurvedArcConst()
super(CurvedArcConstMST, self).__init__()
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:
"""
raise NotImplemented(
'lensing potential for regularly curved arc is not implemented')
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:
"""
lambda_mst = 1. / radial_stretch
kappa_ext = 1 - lambda_mst
curve_stretch = tangential_stretch / radial_stretch
f_x_curve, f_y_curve = self._curve.derivatives(x, y, curve_stretch,
curvature, direction,
center_x, center_y)
f_x_mst, f_y_mst = self._mst.derivatives(x,
y,
kappa_ext,
ra_0=center_x,
dec_0=center_y)
f_x = lambda_mst * f_x_curve + f_x_mst
f_y = lambda_mst * f_y_curve + f_y_mst
return f_x, f_y
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:
"""
lambda_mst = 1. / radial_stretch
kappa_ext = 1 - lambda_mst
curve_stretch = tangential_stretch / radial_stretch
f_xx_c, f_xy_c, f_yx_c, f_yy_c = self._curve.hessian(
x, y, curve_stretch, curvature, direction, center_x, center_y)
f_xx_mst, f_xy_mst, f_yx_mst, f_yy_mst = self._mst.hessian(
x, y, kappa_ext, ra_0=center_x, dec_0=center_y)
f_xx = lambda_mst * f_xx_c + f_xx_mst
f_xy = lambda_mst * f_xy_c + f_xy_mst
f_yx = lambda_mst * f_yx_c + f_yx_mst
f_yy = lambda_mst * f_yy_c + f_yy_mst
return f_xx, f_xy, f_yx, f_yy
class TestCurvedArcSISMST(object):
"""
tests the source model routines
"""
def setup(self):
self.model = CurvedArcSISMST()
self.sis = SIS()
self.mst = Convergence()
def test_spp2stretch(self):
center_x, center_y = 1, 1
theta_E = 1
kappa = 0.1
center_x_spp, center_y_spp = 0., 0
tangential_stretch, radial_stretch, curvature, direction = self.model.sis_mst2stretch(
theta_E, kappa, center_x_spp, center_y_spp, center_x, center_y)
theta_E_new, kappa_new, center_x_spp_new, center_y_spp_new = self.model.stretch2sis_mst(
tangential_stretch, radial_stretch, curvature, direction, center_x,
center_y)
npt.assert_almost_equal(center_x_spp_new, center_x_spp, decimal=8)
npt.assert_almost_equal(center_y_spp_new, center_y_spp, decimal=8)
npt.assert_almost_equal(theta_E_new, theta_E, decimal=8)
npt.assert_almost_equal(kappa_new, kappa, decimal=8)
center_x, center_y = -1, 1
tangential_stretch, radial_stretch, curvature, direction = self.model.sis_mst2stretch(
theta_E, kappa, center_x_spp, center_y_spp, center_x, center_y)
theta_E_new, kappa_new, center_x_spp_new, center_y_spp_new = self.model.stretch2sis_mst(
tangential_stretch, radial_stretch, curvature, direction, center_x,
center_y)
npt.assert_almost_equal(center_x_spp_new, center_x_spp, decimal=8)
npt.assert_almost_equal(center_y_spp_new, center_y_spp, decimal=8)
npt.assert_almost_equal(theta_E_new, theta_E, decimal=8)
npt.assert_almost_equal(kappa_new, kappa, decimal=8)
center_x, center_y = 0, 0.5
tangential_stretch, radial_stretch, curvature, direction = self.model.sis_mst2stretch(
theta_E, kappa, center_x_spp, center_y_spp, center_x, center_y)
theta_E_new, kappa_new, center_x_spp_new, center_y_spp_new = self.model.stretch2sis_mst(
tangential_stretch, radial_stretch, curvature, direction, center_x,
center_y)
npt.assert_almost_equal(center_x_spp_new, center_x_spp, decimal=8)
npt.assert_almost_equal(center_y_spp_new, center_y_spp, decimal=8)
npt.assert_almost_equal(theta_E_new, theta_E, decimal=8)
npt.assert_almost_equal(kappa_new, kappa, decimal=8)
center_x, center_y = 0, -1.5
tangential_stretch, radial_stretch, r_curvature, direction = self.model.sis_mst2stretch(
theta_E, kappa, center_x_spp, center_y_spp, center_x, center_y)
print(tangential_stretch, radial_stretch, r_curvature, direction)
theta_E_new, kappa_new, center_x_spp_new, center_y_spp_new = self.model.stretch2sis_mst(
tangential_stretch, radial_stretch, r_curvature, direction,
center_x, center_y)
npt.assert_almost_equal(center_x_spp_new, center_x_spp, decimal=8)
npt.assert_almost_equal(center_y_spp_new, center_y_spp, decimal=8)
npt.assert_almost_equal(theta_E_new, theta_E, decimal=8)
npt.assert_almost_equal(kappa_new, kappa, decimal=8)
def test_function(self):
center_x, center_y = 0., 0.
x, y = 1, 1
radial_stretch = 1
output = self.model.function(x,
y,
tangential_stretch=2,
radial_stretch=radial_stretch,
curvature=1. / 2,
direction=0,
center_x=center_x,
center_y=center_y)
theta_E, kappa_ext, center_x_sis, center_y_sis = self.model.stretch2sis_mst(
tangential_stretch=2,
radial_stretch=radial_stretch,
curvature=1. / 2,
direction=0,
center_x=center_x,
center_y=center_y)
f_sis_out = self.sis.function(
1, 1, theta_E, center_x_sis, center_y_sis
) # - self.sis.function(0, 0, theta_E, center_x_sis, center_y_sis)
alpha_x, alpha_y = self.sis.derivatives(center_x, center_y, theta_E,
center_x_sis, center_y_sis)
f_sis_0_out = alpha_x * (x - center_x) + alpha_y * (y - center_y)
f_mst_out = self.mst.function(x,
y,
kappa_ext,
ra_0=center_x,
dec_0=center_y)
lambda_mst = 1. / radial_stretch
f_out = lambda_mst * (f_sis_out - f_sis_0_out) + f_mst_out
npt.assert_almost_equal(output, f_out, decimal=8)
def test_derivatives(self):
tangential_stretch = 5
radial_stretch = 1
curvature = 1. / 10
direction = 0.3
center_x = 0
center_y = 0
x, y = 1, 1
theta_E, kappa, center_x_spp, center_y_spp = self.model.stretch2sis_mst(
tangential_stretch, radial_stretch, curvature, direction, center_x,
center_y)
f_x_sis, f_y_sis = self.sis.derivatives(x, y, theta_E, center_x_spp,
center_y_spp)
f_x_mst, f_y_mst = self.mst.derivatives(x,
y,
kappa,
ra_0=center_x,
dec_0=center_y)
f_x0, f_y0 = self.sis.derivatives(center_x, center_y, theta_E,
center_x_spp, center_y_spp)
f_x_new, f_y_new = self.model.derivatives(x, y, tangential_stretch,
radial_stretch, curvature,
direction, center_x,
center_y)
npt.assert_almost_equal(f_x_new, f_x_sis + f_x_mst - f_x0, decimal=8)
npt.assert_almost_equal(f_y_new, f_y_sis + f_y_mst - f_y0, decimal=8)
def test_hessian(self):
lens = LensModel(lens_model_list=['CURVED_ARC_SIS_MST'])
center_x, center_y = 0, 0
tangential_stretch = 10
radial_stretch = 1
kwargs_lens = [{
'tangential_stretch': tangential_stretch,
'radial_stretch': radial_stretch,
'curvature': 1. / 10.5,
'direction': 0.,
'center_x': center_x,
'center_y': center_y
}]
mag = lens.magnification(center_x, center_y, kwargs=kwargs_lens)
npt.assert_almost_equal(mag,
tangential_stretch * radial_stretch,
decimal=8)
center_x, center_y = 2, 3
tangential_stretch = 10
radial_stretch = 1
kwargs_lens = [{
'tangential_stretch': tangential_stretch,
'radial_stretch': radial_stretch,
'curvature': 1. / 10.5,
'direction': 0.,
'center_x': center_x,
'center_y': center_y
}]
mag = lens.magnification(center_x, center_y, kwargs=kwargs_lens)
npt.assert_almost_equal(mag,
tangential_stretch * radial_stretch,
decimal=8)
center_x, center_y = 0, 0
tangential_stretch = 5
radial_stretch = 1.2
kwargs_lens = [{
'tangential_stretch': tangential_stretch,
'radial_stretch': radial_stretch,
'curvature': 1. / 10.5,
'direction': 0.,
'center_x': center_x,
'center_y': center_y
}]
mag = lens.magnification(center_x, center_y, kwargs=kwargs_lens)
npt.assert_almost_equal(mag,
tangential_stretch * radial_stretch,
decimal=8)
center_x, center_y = 0, 0
tangential_stretch = 3
radial_stretch = -1
kwargs_lens = [{
'tangential_stretch': tangential_stretch,
'radial_stretch': radial_stretch,
'curvature': 1. / 10.5,
'direction': 0.,
'center_x': center_x,
'center_y': center_y
}]
mag = lens.magnification(center_x, center_y, kwargs=kwargs_lens)
print(tangential_stretch, radial_stretch, 'stretches')
npt.assert_almost_equal(mag,
tangential_stretch * radial_stretch,
decimal=8)
center_x, center_y = 0, 0
tangential_stretch = -3
radial_stretch = -1
kwargs_lens = [{
'tangential_stretch': tangential_stretch,
'radial_stretch': radial_stretch,
'curvature': 1. / 10.5,
'direction': 0.,
'center_x': center_x,
'center_y': center_y
}]
mag = lens.magnification(center_x, center_y, kwargs=kwargs_lens)
npt.assert_almost_equal(mag,
tangential_stretch * radial_stretch,
decimal=8)
center_x, center_y = 0, 0
tangential_stretch = 10.4
radial_stretch = 0.6
kwargs_lens = [{
'tangential_stretch': tangential_stretch,
'radial_stretch': radial_stretch,
'curvature': 1. / 10.5,
'direction': 0.,
'center_x': center_x,
'center_y': center_y
}]
mag = lens.magnification(center_x, center_y, kwargs=kwargs_lens)
npt.assert_almost_equal(mag,
tangential_stretch * radial_stretch,
decimal=8)
class CurvedArcSISMST(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._sis = SIS()
self._mst = Convergence()
super(CurvedArcSISMST, self).__init__()
@staticmethod
def stretch2sis_mst(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 SIS + MST resulting in the same observables
"""
center_x_sis, center_y_sis = center_deflector(curvature, direction,
center_x, center_y)
r_curvature = 1. / curvature
lambda_mst = 1. / radial_stretch
kappa_ext = 1 - lambda_mst
theta_E = r_curvature * (1. - radial_stretch / tangential_stretch)
return theta_E, kappa_ext, center_x_sis, center_y_sis
@staticmethod
def sis_mst2stretch(theta_E, kappa_ext, center_x_sis, center_y_sis,
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 SIS profile
:param kappa_ext: external convergence (MST factor 1 - kappa_ext)
:param center_x_sis: center of SPP model
:param center_y_sis: 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
:return:
"""
r_curvature = np.sqrt((center_x_sis - center_x)**2 +
(center_y_sis - center_y)**2)
direction = np.arctan2(center_y - center_y_sis,
center_x - center_x_sis)
radial_stretch = 1. / (1 - kappa_ext)
tangential_stretch = 1 / (1 - (theta_E / r_curvature)) * radial_stretch
curvature = 1. / r_curvature
return tangential_stretch, radial_stretch, curvature, direction
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:
"""
lambda_mst = 1. / radial_stretch
theta_E, kappa_ext, center_x_sis, center_y_sis = self.stretch2sis_mst(
tangential_stretch, radial_stretch, curvature, direction, center_x,
center_y)
f_sis = self._sis.function(
x, y, theta_E, center_x_sis, center_y_sis
) # - self._sis.function(center_x, center_y, theta_E, center_x_sis, center_y_sis)
alpha_x, alpha_y = self._sis.derivatives(center_x, center_y, theta_E,
center_x_sis, center_y_sis)
f_sis_0 = alpha_x * (x - center_x) + alpha_y * (y - center_y)
f_mst = self._mst.function(x,
y,
kappa_ext,
ra_0=center_x,
dec_0=center_y)
return lambda_mst * (f_sis - f_sis_0) + f_mst
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:
"""
lambda_mst = 1. / radial_stretch
theta_E, kappa_ext, center_x_sis, center_y_sis = self.stretch2sis_mst(
tangential_stretch, radial_stretch, curvature, direction, center_x,
center_y)
f_x_sis, f_y_sis = self._sis.derivatives(x, y, theta_E, center_x_sis,
center_y_sis)
f_x0, f_y0 = self._sis.derivatives(center_x, center_y, theta_E,
center_x_sis, center_y_sis)
f_x_mst, f_y_mst = self._mst.derivatives(x,
y,
kappa_ext,
ra_0=center_x,
dec_0=center_y)
f_x = lambda_mst * (f_x_sis - f_x0) + f_x_mst
f_y = lambda_mst * (f_y_sis - f_y0) + f_y_mst
return f_x, f_y
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:
"""
lambda_mst = 1. / radial_stretch
theta_E, kappa_ext, center_x_sis, center_y_sis = self.stretch2sis_mst(
tangential_stretch, radial_stretch, curvature, direction, center_x,
center_y)
f_xx_sis, f_yy_sis, f_xy_sis = self._sis.hessian(
x, y, theta_E, center_x_sis, center_y_sis)
f_xx_mst, f_yy_mst, f_xy_mst = self._mst.hessian(x,
y,
kappa_ext,
ra_0=center_x,
dec_0=center_y)
return lambda_mst * f_xx_sis + f_xx_mst, lambda_mst * f_yy_sis + f_yy_mst, lambda_mst * f_xy_sis + f_xy_mst
def __init__(self):
self._sis = SIS()
self._mst = Convergence()
super(CurvedArcSISMST, self).__init__()
def setup(self):
self.model = CurvedArcTanDiff()
self.sie = SIE()
self.mst = Convergence()
def setup(self):
self.profile = Convergence()
self.kwargs_lens = {'kappa_ext': 0.1}
def setup(self):
self.model = CurvedArcSISMST()
self.sis = SIS()
self.mst = Convergence()
def __init__(self):
self._mst = Convergence()
self._curve = CurvedArcConst()
super(CurvedArcConstMST, self).__init__()
def _import_class(lens_type,
custom_class,
kwargs_interp,
z_lens=None,
z_source=None):
"""
:param lens_type: string, lens model type
:param custom_class: custom class
:param z_lens: lens redshift # currently only used in NFW_MC model as this is redshift dependent
:param z_source: source redshift # currently only used in NFW_MC model as this is redshift dependent
:param kwargs_interp: interpolation keyword arguments specifying the numerics.
See description in the Interpolate() class. Only applicable for 'INTERPOL' and 'INTERPOL_SCALED' models.
:return: class instance of the lens model type
"""
if lens_type == 'SHIFT':
from lenstronomy.LensModel.Profiles.constant_shift import Shift
return Shift()
elif lens_type == 'NIE_POTENTIAL':
from lenstronomy.LensModel.Profiles.nie_potential import NIE_POTENTIAL
return NIE_POTENTIAL()
elif lens_type == 'CONST_MAG':
from lenstronomy.LensModel.Profiles.const_mag import ConstMag
return ConstMag()
elif lens_type == 'SHEAR':
from lenstronomy.LensModel.Profiles.shear import Shear
return Shear()
elif lens_type == 'SHEAR_GAMMA_PSI':
from lenstronomy.LensModel.Profiles.shear import ShearGammaPsi
return ShearGammaPsi()
elif lens_type == 'SHEAR_REDUCED':
from lenstronomy.LensModel.Profiles.shear import ShearReduced
return ShearReduced()
elif lens_type == 'CONVERGENCE':
from lenstronomy.LensModel.Profiles.convergence import Convergence
return Convergence()
elif lens_type == 'HESSIAN':
from lenstronomy.LensModel.Profiles.hessian import Hessian
return Hessian()
elif lens_type == 'FLEXION':
from lenstronomy.LensModel.Profiles.flexion import Flexion
return Flexion()
elif lens_type == 'FLEXIONFG':
from lenstronomy.LensModel.Profiles.flexionfg import Flexionfg
return Flexionfg()
elif lens_type == 'POINT_MASS':
from lenstronomy.LensModel.Profiles.point_mass import PointMass
return PointMass()
elif lens_type == 'SIS':
from lenstronomy.LensModel.Profiles.sis import SIS
return SIS()
elif lens_type == 'SIS_TRUNCATED':
from lenstronomy.LensModel.Profiles.sis_truncate import SIS_truncate
return SIS_truncate()
elif lens_type == 'SIE':
from lenstronomy.LensModel.Profiles.sie import SIE
return SIE()
elif lens_type == 'SPP':
from lenstronomy.LensModel.Profiles.spp import SPP
return SPP()
elif lens_type == 'NIE':
from lenstronomy.LensModel.Profiles.nie import NIE
return NIE()
elif lens_type == 'NIE_SIMPLE':
from lenstronomy.LensModel.Profiles.nie import NIEMajorAxis
return NIEMajorAxis()
elif lens_type == 'CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import Chameleon
return Chameleon()
elif lens_type == 'DOUBLE_CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import DoubleChameleon
return DoubleChameleon()
elif lens_type == 'TRIPLE_CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import TripleChameleon
return TripleChameleon()
elif lens_type == 'SPEP':
from lenstronomy.LensModel.Profiles.spep import SPEP
return SPEP()
elif lens_type == 'PEMD':
from lenstronomy.LensModel.Profiles.pemd import PEMD
return PEMD()
elif lens_type == 'SPEMD':
from lenstronomy.LensModel.Profiles.spemd import SPEMD
return SPEMD()
elif lens_type == 'EPL':
from lenstronomy.LensModel.Profiles.epl import EPL
return EPL()
elif lens_type == 'EPL_NUMBA':
from lenstronomy.LensModel.Profiles.epl_numba import EPL_numba
return EPL_numba()
elif lens_type == 'SPL_CORE':
from lenstronomy.LensModel.Profiles.splcore import SPLCORE
return SPLCORE()
elif lens_type == 'NFW':
from lenstronomy.LensModel.Profiles.nfw import NFW
return NFW()
elif lens_type == 'NFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.nfw_ellipse import NFW_ELLIPSE
return NFW_ELLIPSE()
elif lens_type == 'NFW_ELLIPSE_GAUSS_DEC':
from lenstronomy.LensModel.Profiles.gauss_decomposition import NFWEllipseGaussDec
return NFWEllipseGaussDec()
elif lens_type == 'NFW_ELLIPSE_CSE':
from lenstronomy.LensModel.Profiles.nfw_ellipse_cse import NFW_ELLIPSE_CSE
return NFW_ELLIPSE_CSE()
elif lens_type == 'TNFW':
from lenstronomy.LensModel.Profiles.tnfw import TNFW
return TNFW()
elif lens_type == 'TNFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.tnfw_ellipse import TNFW_ELLIPSE
return TNFW_ELLIPSE()
elif lens_type == 'CNFW':
from lenstronomy.LensModel.Profiles.cnfw import CNFW
return CNFW()
elif lens_type == 'CNFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.cnfw_ellipse import CNFW_ELLIPSE
return CNFW_ELLIPSE()
elif lens_type == 'CTNFW_GAUSS_DEC':
from lenstronomy.LensModel.Profiles.gauss_decomposition import CTNFWGaussDec
return CTNFWGaussDec()
elif lens_type == 'NFW_MC':
from lenstronomy.LensModel.Profiles.nfw_mass_concentration import NFWMC
return NFWMC(z_lens=z_lens, z_source=z_source)
elif lens_type == 'SERSIC':
from lenstronomy.LensModel.Profiles.sersic import Sersic
return Sersic()
elif lens_type == 'SERSIC_ELLIPSE_POTENTIAL':
from lenstronomy.LensModel.Profiles.sersic_ellipse_potential import SersicEllipse
return SersicEllipse()
elif lens_type == 'SERSIC_ELLIPSE_KAPPA':
from lenstronomy.LensModel.Profiles.sersic_ellipse_kappa import SersicEllipseKappa
return SersicEllipseKappa()
elif lens_type == 'SERSIC_ELLIPSE_GAUSS_DEC':
from lenstronomy.LensModel.Profiles.gauss_decomposition import SersicEllipseGaussDec
return SersicEllipseGaussDec()
elif lens_type == 'PJAFFE':
from lenstronomy.LensModel.Profiles.p_jaffe import PJaffe
return PJaffe()
elif lens_type == 'PJAFFE_ELLIPSE':
from lenstronomy.LensModel.Profiles.p_jaffe_ellipse import PJaffe_Ellipse
return PJaffe_Ellipse()
elif lens_type == 'HERNQUIST':
from lenstronomy.LensModel.Profiles.hernquist import Hernquist
return Hernquist()
elif lens_type == 'HERNQUIST_ELLIPSE':
from lenstronomy.LensModel.Profiles.hernquist_ellipse import Hernquist_Ellipse
return Hernquist_Ellipse()
elif lens_type == 'HERNQUIST_ELLIPSE_CSE':
from lenstronomy.LensModel.Profiles.hernquist_ellipse_cse import HernquistEllipseCSE
return HernquistEllipseCSE()
elif lens_type == 'GAUSSIAN':
from lenstronomy.LensModel.Profiles.gaussian_potential import Gaussian
return Gaussian()
elif lens_type == 'GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.gaussian_kappa import GaussianKappa
return GaussianKappa()
elif lens_type == 'GAUSSIAN_ELLIPSE_KAPPA':
from lenstronomy.LensModel.Profiles.gaussian_ellipse_kappa import GaussianEllipseKappa
return GaussianEllipseKappa()
elif lens_type == 'GAUSSIAN_ELLIPSE_POTENTIAL':
from lenstronomy.LensModel.Profiles.gaussian_ellipse_potential import GaussianEllipsePotential
return GaussianEllipsePotential()
elif lens_type == 'MULTI_GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappa
return MultiGaussianKappa()
elif lens_type == 'MULTI_GAUSSIAN_KAPPA_ELLIPSE':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappaEllipse
return MultiGaussianKappaEllipse()
elif lens_type == 'INTERPOL':
from lenstronomy.LensModel.Profiles.interpol import Interpol
return Interpol(**kwargs_interp)
elif lens_type == 'INTERPOL_SCALED':
from lenstronomy.LensModel.Profiles.interpol import InterpolScaled
return InterpolScaled(**kwargs_interp)
elif lens_type == 'SHAPELETS_POLAR':
from lenstronomy.LensModel.Profiles.shapelet_pot_polar import PolarShapelets
return PolarShapelets()
elif lens_type == 'SHAPELETS_CART':
from lenstronomy.LensModel.Profiles.shapelet_pot_cartesian import CartShapelets
return CartShapelets()
elif lens_type == 'DIPOLE':
from lenstronomy.LensModel.Profiles.dipole import Dipole
return Dipole()
elif lens_type == 'CURVED_ARC_CONST':
from lenstronomy.LensModel.Profiles.curved_arc_const import CurvedArcConst
return CurvedArcConst()
elif lens_type == 'CURVED_ARC_CONST_MST':
from lenstronomy.LensModel.Profiles.curved_arc_const import CurvedArcConstMST
return CurvedArcConstMST()
elif lens_type == 'CURVED_ARC_SPP':
from lenstronomy.LensModel.Profiles.curved_arc_spp import CurvedArcSPP
return CurvedArcSPP()
elif lens_type == 'CURVED_ARC_SIS_MST':
from lenstronomy.LensModel.Profiles.curved_arc_sis_mst import CurvedArcSISMST
return CurvedArcSISMST()
elif lens_type == 'CURVED_ARC_SPT':
from lenstronomy.LensModel.Profiles.curved_arc_spt import CurvedArcSPT
return CurvedArcSPT()
elif lens_type == 'CURVED_ARC_TAN_DIFF':
from lenstronomy.LensModel.Profiles.curved_arc_tan_diff import CurvedArcTanDiff
return CurvedArcTanDiff()
elif lens_type == 'ARC_PERT':
from lenstronomy.LensModel.Profiles.arc_perturbations import ArcPerturbations
return ArcPerturbations()
elif lens_type == 'coreBURKERT':
from lenstronomy.LensModel.Profiles.coreBurkert import CoreBurkert
return CoreBurkert()
elif lens_type == 'CORED_DENSITY':
from lenstronomy.LensModel.Profiles.cored_density import CoredDensity
return CoredDensity()
elif lens_type == 'CORED_DENSITY_2':
from lenstronomy.LensModel.Profiles.cored_density_2 import CoredDensity2
return CoredDensity2()
elif lens_type == 'CORED_DENSITY_EXP':
from lenstronomy.LensModel.Profiles.cored_density_exp import CoredDensityExp
return CoredDensityExp()
elif lens_type == 'CORED_DENSITY_MST':
from lenstronomy.LensModel.Profiles.cored_density_mst import CoredDensityMST
return CoredDensityMST(profile_type='CORED_DENSITY')
elif lens_type == 'CORED_DENSITY_2_MST':
from lenstronomy.LensModel.Profiles.cored_density_mst import CoredDensityMST
return CoredDensityMST(profile_type='CORED_DENSITY_2')
elif lens_type == 'CORED_DENSITY_EXP_MST':
from lenstronomy.LensModel.Profiles.cored_density_mst import CoredDensityMST
return CoredDensityMST(profile_type='CORED_DENSITY_EXP')
elif lens_type == 'NumericalAlpha':
from lenstronomy.LensModel.Profiles.numerical_deflections import NumericalAlpha
return NumericalAlpha(custom_class)
elif lens_type == 'MULTIPOLE':
from lenstronomy.LensModel.Profiles.multipole import Multipole
return Multipole()
elif lens_type == 'CSE':
from lenstronomy.LensModel.Profiles.cored_steep_ellipsoid import CSE
return CSE()
elif lens_type == 'ElliSLICE':
from lenstronomy.LensModel.Profiles.elliptical_density_slice import ElliSLICE
return ElliSLICE()
elif lens_type == 'ULDM':
from lenstronomy.LensModel.Profiles.uldm import Uldm
return Uldm()
elif lens_type == 'CORED_DENSITY_ULDM_MST':
from lenstronomy.LensModel.Profiles.cored_density_mst import CoredDensityMST
return CoredDensityMST(profile_type='CORED_DENSITY_ULDM')
else:
raise ValueError(
'%s is not a valid lens model. Supported are: %s.' %
(lens_type, _SUPPORTED_MODELS))
def _import_class(lens_type, custom_class, z_lens=None, z_source=None):
"""
:param lens_type: string, lens model type
:param custom_class: custom class
:param z_lens: lens redshift # currently only used in NFW_MC model as this is redshift dependent
:param z_source: source redshift # currently only used in NFW_MC model as this is redshift dependent
:return: class instance of the lens model type
"""
if lens_type == 'SHIFT':
from lenstronomy.LensModel.Profiles.alpha_shift import Shift
return Shift()
elif lens_type == 'SHEAR':
from lenstronomy.LensModel.Profiles.shear import Shear
return Shear()
elif lens_type == 'SHEAR_GAMMA_PSI':
from lenstronomy.LensModel.Profiles.shear import ShearGammaPsi
return ShearGammaPsi()
elif lens_type == 'CONVERGENCE':
from lenstronomy.LensModel.Profiles.convergence import Convergence
return Convergence()
elif lens_type == 'FLEXION':
from lenstronomy.LensModel.Profiles.flexion import Flexion
return Flexion()
elif lens_type == 'FLEXIONFG':
from lenstronomy.LensModel.Profiles.flexionfg import Flexionfg
return Flexionfg()
elif lens_type == 'POINT_MASS':
from lenstronomy.LensModel.Profiles.point_mass import PointMass
return PointMass()
elif lens_type == 'SIS':
from lenstronomy.LensModel.Profiles.sis import SIS
return SIS()
elif lens_type == 'SIS_TRUNCATED':
from lenstronomy.LensModel.Profiles.sis_truncate import SIS_truncate
return SIS_truncate()
elif lens_type == 'SIE':
from lenstronomy.LensModel.Profiles.sie import SIE
return SIE()
elif lens_type == 'SPP':
from lenstronomy.LensModel.Profiles.spp import SPP
return SPP()
elif lens_type == 'NIE':
from lenstronomy.LensModel.Profiles.nie import NIE
return NIE()
elif lens_type == 'NIE_SIMPLE':
from lenstronomy.LensModel.Profiles.nie import NIEMajorAxis
return NIEMajorAxis()
elif lens_type == 'CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import Chameleon
return Chameleon()
elif lens_type == 'DOUBLE_CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import DoubleChameleon
return DoubleChameleon()
elif lens_type == 'TRIPLE_CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import TripleChameleon
return TripleChameleon()
elif lens_type == 'SPEP':
from lenstronomy.LensModel.Profiles.spep import SPEP
return SPEP()
elif lens_type == 'SPEMD':
from lenstronomy.LensModel.Profiles.spemd import SPEMD
return SPEMD()
elif lens_type == 'SPEMD_SMOOTH':
from lenstronomy.LensModel.Profiles.spemd_smooth import SPEMD_SMOOTH
return SPEMD_SMOOTH()
elif lens_type == 'NFW':
from lenstronomy.LensModel.Profiles.nfw import NFW
return NFW()
elif lens_type == 'NFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.nfw_ellipse import NFW_ELLIPSE
return NFW_ELLIPSE()
elif lens_type == 'NFW_ELLIPSE_GAUSS_DEC':
from lenstronomy.LensModel.Profiles.gauss_decomposition import NFWEllipseGaussDec
return NFWEllipseGaussDec()
elif lens_type == 'TNFW':
from lenstronomy.LensModel.Profiles.tnfw import TNFW
return TNFW()
elif lens_type == 'CNFW':
from lenstronomy.LensModel.Profiles.cnfw import CNFW
return CNFW()
elif lens_type == 'CNFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.cnfw_ellipse import CNFW_ELLIPSE
return CNFW_ELLIPSE()
elif lens_type == 'CTNFW_GAUSS_DEC':
from lenstronomy.LensModel.Profiles.gauss_decomposition import CTNFWGaussDec
return CTNFWGaussDec()
elif lens_type == 'NFW_MC':
from lenstronomy.LensModel.Profiles.nfw_mass_concentration import NFWMC
return NFWMC(z_lens=z_lens, z_source=z_source)
elif lens_type == 'SERSIC':
from lenstronomy.LensModel.Profiles.sersic import Sersic
return Sersic()
elif lens_type == 'SERSIC_ELLIPSE_POTENTIAL':
from lenstronomy.LensModel.Profiles.sersic_ellipse_potential import SersicEllipse
return SersicEllipse()
elif lens_type == 'SERSIC_ELLIPSE_KAPPA':
from lenstronomy.LensModel.Profiles.sersic_ellipse_kappa import SersicEllipseKappa
return SersicEllipseKappa()
elif lens_type == 'SERSIC_ELLIPSE_GAUSS_DEC':
from lenstronomy.LensModel.Profiles.gauss_decomposition \
import SersicEllipseGaussDec
return SersicEllipseGaussDec()
elif lens_type == 'PJAFFE':
from lenstronomy.LensModel.Profiles.p_jaffe import PJaffe
return PJaffe()
elif lens_type == 'PJAFFE_ELLIPSE':
from lenstronomy.LensModel.Profiles.p_jaffe_ellipse import PJaffe_Ellipse
return PJaffe_Ellipse()
elif lens_type == 'HERNQUIST':
from lenstronomy.LensModel.Profiles.hernquist import Hernquist
return Hernquist()
elif lens_type == 'HERNQUIST_ELLIPSE':
from lenstronomy.LensModel.Profiles.hernquist_ellipse import Hernquist_Ellipse
return Hernquist_Ellipse()
elif lens_type == 'GAUSSIAN':
from lenstronomy.LensModel.Profiles.gaussian_potential import Gaussian
return Gaussian()
elif lens_type == 'GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.gaussian_kappa import GaussianKappa
return GaussianKappa()
elif lens_type == 'GAUSSIAN_ELLIPSE_KAPPA':
from lenstronomy.LensModel.Profiles.gaussian_ellipse_kappa import GaussianEllipseKappa
return GaussianEllipseKappa()
elif lens_type == 'GAUSSIAN_ELLIPSE_POTENTIAL':
from lenstronomy.LensModel.Profiles.gaussian_ellipse_potential import GaussianEllipsePotential
return GaussianEllipsePotential()
elif lens_type == 'MULTI_GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappa
return MultiGaussianKappa()
elif lens_type == 'MULTI_GAUSSIAN_KAPPA_ELLIPSE':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappaEllipse
return MultiGaussianKappaEllipse()
elif lens_type == 'INTERPOL':
from lenstronomy.LensModel.Profiles.interpol import Interpol
return Interpol()
elif lens_type == 'INTERPOL_SCALED':
from lenstronomy.LensModel.Profiles.interpol import InterpolScaled
return InterpolScaled()
elif lens_type == 'SHAPELETS_POLAR':
from lenstronomy.LensModel.Profiles.shapelet_pot_polar import PolarShapelets
return PolarShapelets()
elif lens_type == 'SHAPELETS_CART':
from lenstronomy.LensModel.Profiles.shapelet_pot_cartesian import CartShapelets
return CartShapelets()
elif lens_type == 'DIPOLE':
from lenstronomy.LensModel.Profiles.dipole import Dipole
return Dipole()
elif lens_type == 'CURVED_ARC':
from lenstronomy.LensModel.Profiles.curved_arc import CurvedArc
return CurvedArc()
elif lens_type == 'ARC_PERT':
from lenstronomy.LensModel.Profiles.arc_perturbations import ArcPerturbations
return ArcPerturbations()
elif lens_type == 'coreBURKERT':
from lenstronomy.LensModel.Profiles.coreBurkert import CoreBurkert
return CoreBurkert()
elif lens_type == 'CORED_DENSITY':
from lenstronomy.LensModel.Profiles.cored_density import CoredDensity
return CoredDensity()
elif lens_type == 'CORED_DENSITY_2':
from lenstronomy.LensModel.Profiles.cored_density_2 import CoredDensity2
return CoredDensity2()
elif lens_type == 'CORED_DENSITY_MST':
from lenstronomy.LensModel.Profiles.cored_density_mst import CoredDensityMST
return CoredDensityMST(profile_type='CORED_DENSITY')
elif lens_type == 'CORED_DENSITY_2_MST':
from lenstronomy.LensModel.Profiles.cored_density_mst import CoredDensityMST
return CoredDensityMST(profile_type='CORED_DENSITY_2')
elif lens_type == 'NumericalAlpha':
from lenstronomy.LensModel.Profiles.numerical_deflections import NumericalAlpha
return NumericalAlpha(custom_class)
else:
raise ValueError('%s is not a valid lens model' % lens_type)
class ShearReduced(LensProfileBase):
"""
reduced shear distortions :math:`\\gamma' = \\gamma / (1-\\kappa)`.
This distortion keeps the magnification as unity and, thus, does not change the size of apparent objects.
To keep the magnification at unity, it requires
.. math::
(1-\\kappa)^2 - \\gamma_1^2 - \\gamma_2^ = 1
Thus, for given pair of reduced shear :math:`(\\gamma'_1, \\gamma'_2)`, an additional convergence term is calculated
and added to the lensing distortions.
"""
param_names = ['gamma1', 'gamma2', 'ra_0', 'dec_0']
lower_limit_default = {
'gamma1': -0.5,
'gamma2': -0.5,
'ra_0': -100,
'dec_0': -100
}
upper_limit_default = {
'gamma1': 0.5,
'gamma2': 0.5,
'ra_0': 100,
'dec_0': 100
}
def __init__(self):
self._shear = Shear()
self._convergence = Convergence()
super(ShearReduced, self).__init__()
@staticmethod
def _kappa_reduced(gamma1, gamma2):
"""
compute convergence such that magnification is unity
:param gamma1: reduced shear
:param gamma2: reduced shear
:return: kappa
"""
kappa = 1 - 1. / np.sqrt(1 - gamma1**2 - gamma2**2)
gamma1_ = (1 - kappa) * gamma1
gamma2_ = (1 - kappa) * gamma2
return kappa, gamma1_, gamma2_
def function(self, x, y, gamma1, gamma2, ra_0=0, dec_0=0):
"""
:param x: x-coordinate (angle)
:param y: y0-coordinate (angle)
:param gamma1: shear component
:param gamma2: shear component
:param ra_0: x/ra position where shear deflection is 0
:param dec_0: y/dec position where shear deflection is 0
:return: lensing potential
"""
kappa, gamma1_, gamma2_ = self._kappa_reduced(gamma1, gamma2)
f_shear = self._shear.function(x, y, gamma1_, gamma2_, ra_0, dec_0)
f_kappa = self._convergence.function(x, y, kappa, ra_0, dec_0)
return f_shear + f_kappa
def derivatives(self, x, y, gamma1, gamma2, ra_0=0, dec_0=0):
"""
:param x: x-coordinate (angle)
:param y: y0-coordinate (angle)
:param gamma1: shear component
:param gamma2: shear component
:param ra_0: x/ra position where shear deflection is 0
:param dec_0: y/dec position where shear deflection is 0
:return: deflection angles
"""
kappa, gamma1_, gamma2_ = self._kappa_reduced(gamma1, gamma2)
f_x_shear, f_y_shear = self._shear.derivatives(x, y, gamma1_, gamma2_,
ra_0, dec_0)
f_x_kappa, f_y_kappa = self._convergence.derivatives(
x, y, kappa, ra_0, dec_0)
return f_x_shear + f_x_kappa, f_y_shear + f_y_kappa
def hessian(self, x, y, gamma1, gamma2, ra_0=0, dec_0=0):
"""
:param x: x-coordinate (angle)
:param y: y0-coordinate (angle)
:param gamma1: shear component
:param gamma2: shear component
:param ra_0: x/ra position where shear deflection is 0
:param dec_0: y/dec position where shear deflection is 0
:return: f_xx, f_xy, f_yx, f_yy
"""
kappa, gamma1_, gamma2_ = self._kappa_reduced(gamma1, gamma2)
f_xx_g, f_xy_g, f_yx_g, f_yy_g = self._shear.hessian(
x, y, gamma1_, gamma2_, ra_0, dec_0)
f_xx_k, f_xy_k, f_yx_k, f_yy_k = self._convergence.hessian(
x, y, kappa, ra_0, dec_0)
f_xx = f_xx_g + f_xx_k
f_yy = f_yy_g + f_yy_k
f_xy = f_xy_g + f_xy_k
return f_xx, f_xy, f_xy, f_yy