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