def __init__(self, suppress_fastell=False):
"""
:param suppress_fastell: bool, if True, does not raise if fastell4py is not installed
"""
self._s_scale = 0.0000001 # smoothing scale as used to numerically compute a power-law profile
self.spp = SPP()
self.spemd_smooth = SPEMD(suppress_fastell=suppress_fastell)
super(PEMD, self).__init__()
class SPEMD(object):
"""
class for smooth power law ellipse mass density profile
"""
param_names = ['theta_E', 'gamma', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {'theta_E': 0, 'gamma': 0, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100}
upper_limit_default = {'theta_E': 100, 'gamma': 100, 'e1': 0.5, 'e2': 0.5, 'center_x': 100, 'center_y': 100}
def __init__(self):
self.s2 = 0.00000001
self.spp = SPP()
self.spemd_smooth = SPEMD_SMOOTH()
def function(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
return self.spemd_smooth.function(x, y, theta_E, gamma, e1, e2, self.s2, center_x, center_y)
def derivatives(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
return self.spemd_smooth.derivatives(x, y, theta_E, gamma, e1, e2, self.s2, center_x, center_y)
def hessian(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
return self.spemd_smooth.hessian(x, y, theta_E, gamma, e1, e2, self.s2, center_x, center_y)
def mass_3d_lens(self, r, theta_E, gamma, e1, e2):
"""
computes the spherical power-law mass enclosed (with SPP routiune)
:param r:
:param theta_E:
:param gamma:
:param q:
:param phi_G:
:return:
"""
return self.spp.mass_3d_lens(r, theta_E, gamma)
def __init__(self,
kwargs_cosmo,
interpol_grid_num=100,
log_integration=False,
max_integrate=100,
min_integrate=0.001):
"""
:param kwargs_cosmo: keyword argument with angular diameter distances
"""
self._interp_grid_num = interpol_grid_num
self._log_int = log_integration
self._max_integrate = max_integrate # maximal integration (and interpolation) in units of arcsecs
self._min_integrate = min_integrate # min integration (and interpolation) in units of arcsecs
self._max_interpolate = max_integrate # we chose to set the interpolation range to the integration range
self._min_interpolate = min_integrate # we chose to set the interpolation range to the integration range
self._cosmo = Cosmo(**kwargs_cosmo)
self._spp = SPP()
Anisotropy.__init__(self, anisotropy_type='OM')
def test_function(self):
"""
:return:
"""
profile = PowerLaw()
spp = SPP()
sis = SIS()
x = np.linspace(0.1, 10, 10)
kwargs_light = {'amp': 1., 'gamma': 2, 'e1': 0, 'e2': 0}
kwargs_spp = {'theta_E': 1., 'gamma': 2}
kwargs_sis = {'theta_E': 1.}
flux = profile.function(x=x, y=1., **kwargs_light)
f_xx, f_xy, f_yx, f_yy = spp.hessian(x=x, y=1., **kwargs_spp)
kappa_spp = 1 / 2. * (f_xx + f_yy)
f_xx, f_xy, f_yx, f_yy = sis.hessian(x=x, y=1., **kwargs_sis)
kappa_sis = 1 / 2. * (f_xx + f_yy)
npt.assert_almost_equal(kappa_sis, kappa_spp, decimal=5)
npt.assert_almost_equal(flux / flux[0],
kappa_sis / kappa_sis[0],
decimal=5)
class SPEMD(object):
"""
class for smooth power law ellipse mass density profile
"""
def __init__(self):
self.s2 = 0.00000001
self.spp = SPP()
self.spemd_smooth = SPEMD_SMOOTH()
def function(self, x, y, theta_E, gamma, q, phi_G, center_x=0, center_y=0):
return self.spemd_smooth.function(x, y, theta_E, gamma, q, phi_G, self.s2, center_x, center_y)
def derivatives(self, x, y, theta_E, gamma, q, phi_G, center_x=0, center_y=0):
return self.spemd_smooth.derivatives(x, y, theta_E, gamma, q, phi_G, self.s2, center_x, center_y)
def hessian(self, x, y, theta_E, gamma, q, phi_G, center_x=0, center_y=0):
return self.spemd_smooth.hessian(x, y, theta_E, gamma, q, phi_G, self.s2, center_x, center_y)
def mass_3d_lens(self, r, theta_E, gamma, q, phi_G):
"""
computes the spherical power-law mass enclosed (with SPP routiune)
:param r:
:param theta_E:
:param gamma:
:param q:
:param phi_G:
:return:
"""
return self.spp.mass_3d_lens(r, theta_E, gamma)
def convert_params(self, theta_E, gamma, q):
"""
:param theta_E: Einstein radius
:param gamma: power law slope
:param q: axis ratio
:return: prefactor to SPEMP profile for FASTELL
"""
return self.spemd_smooth.convert_params(theta_E, gamma, q)
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.lens = SPP()
def setup(self):
self.SPEP = SPEP()
self.SPP = SPP()
self.SIS = SIS()
class TestSPEP(object):
"""
tests the Gaussian methods
"""
def setup(self):
self.SPEP = SPEP()
self.SPP = SPP()
self.SIS = SIS()
def test_function(self):
x = np.array([1])
y = np.array([2])
phi_E = 1.
gamma = 1.9
q = 1
phi_G = 0.
E = phi_E / (((3 - gamma) / 2.)**(1. / (1 - gamma)) * np.sqrt(q))
values_spep = self.SPEP.function(x, y, E, gamma, q, phi_G)
values_spp = self.SPP.function(x, y, E, gamma)
assert values_spep[0] == values_spp[0]
x = np.array([0])
y = np.array([0])
values_spep = self.SPEP.function(x, y, E, gamma, q, phi_G)
values_spp = self.SPP.function(x, y, E, gamma)
assert values_spep[0] == values_spp[0]
x = np.array([2, 3, 4])
y = np.array([1, 1, 1])
values_spep = self.SPEP.function(x, y, E, gamma, q, phi_G)
values_spp = self.SPP.function(x, y, E, gamma)
assert values_spep[0] == values_spp[0]
assert values_spep[1] == values_spp[1]
assert values_spep[2] == values_spp[2]
def test_derivatives(self):
x = np.array([1])
y = np.array([2])
phi_E = 1.
gamma = 1.9
q = 1
phi_G = 0.
E = phi_E / (((3 - gamma) / 2.)**(1. / (1 - gamma)) * np.sqrt(q))
f_x_spep, f_y_spep = self.SPEP.derivatives(x, y, E, gamma, q, phi_G)
f_x_spp, f_y_spp = self.SPP.derivatives(x, y, E, gamma)
assert f_x_spep[0] == f_x_spp[0]
assert f_y_spep[0] == f_y_spp[0]
x = np.array([0])
y = np.array([0])
f_x_spep, f_y_spep = self.SPEP.derivatives(x, y, E, gamma, q, phi_G)
f_x_spp, f_y_spp = self.SPP.derivatives(x, y, E, gamma)
assert f_x_spep[0] == f_x_spp[0]
assert f_y_spep[0] == f_y_spp[0]
x = np.array([1, 3, 4])
y = np.array([2, 1, 1])
f_x_spep, f_y_spep = self.SPEP.derivatives(x, y, E, gamma, q, phi_G)
f_x_spp, f_y_spp = self.SPP.derivatives(x, y, E, gamma)
assert f_x_spep[0] == f_x_spp[0]
assert f_y_spep[0] == f_y_spp[0]
assert f_x_spep[1] == f_x_spp[1]
assert f_y_spep[1] == f_y_spp[1]
assert f_x_spep[2] == f_x_spp[2]
assert f_y_spep[2] == f_y_spp[2]
def test_hessian(self):
x = np.array([1])
y = np.array([2])
phi_E = 1.
gamma = 1.9
q = 1.
phi_G = 0.
E = phi_E / (((3 - gamma) / 2.)**(1. / (1 - gamma)) * np.sqrt(q))
f_xx, f_yy, f_xy = self.SPEP.hessian(x, y, E, gamma, q, phi_G)
f_xx_spep, f_yy_spep, f_xy_spep = self.SPEP.hessian(
x, y, E, gamma, q, phi_G)
f_xx_spp, f_yy_spp, f_xy_spp = self.SPP.hessian(x, y, E, gamma)
assert f_xx_spep[0] == f_xx_spp[0]
assert f_yy_spep[0] == f_yy_spp[0]
assert f_xy_spep[0] == f_xy_spp[0]
x = np.array([1, 3, 4])
y = np.array([2, 1, 1])
f_xx_spep, f_yy_spep, f_xy_spep = self.SPEP.hessian(
x, y, E, gamma, q, phi_G)
f_xx_spp, f_yy_spp, f_xy_spp = self.SPP.hessian(x, y, E, gamma)
assert f_xx_spep[0] == f_xx_spp[0]
assert f_yy_spep[0] == f_yy_spp[0]
assert f_xy_spep[0] == f_xy_spp[0]
assert f_xx_spep[1] == f_xx_spp[1]
assert f_yy_spep[1] == f_yy_spp[1]
assert f_xy_spep[1] == f_xy_spp[1]
assert f_xx_spep[2] == f_xx_spp[2]
assert f_yy_spep[2] == f_yy_spp[2]
assert f_xy_spep[2] == f_xy_spp[2]
def test_compare_sis(self):
x = np.array([1])
y = np.array([2])
theta_E = 1.
gamma = 2.
f_sis = self.SIS.function(x, y, theta_E)
f_spp = self.SPP.function(x, y, theta_E, gamma)
f_x_sis, f_y_sis = self.SIS.derivatives(x, y, theta_E)
f_x_spp, f_y_spp = self.SPP.derivatives(x, y, theta_E, gamma)
f_xx_sis, f_yy_sis, f_xy_sis = self.SIS.hessian(x, y, theta_E)
f_xx_spp, f_yy_spp, f_xy_spp = self.SPP.hessian(x, y, theta_E, gamma)
npt.assert_almost_equal(f_sis[0], f_spp[0], decimal=7)
npt.assert_almost_equal(f_x_sis[0], f_x_spp[0], decimal=7)
npt.assert_almost_equal(f_y_sis[0], f_y_spp[0], decimal=7)
npt.assert_almost_equal(f_xx_sis[0], f_xx_spp[0], decimal=7)
npt.assert_almost_equal(f_yy_sis[0], f_yy_spp[0], decimal=7)
npt.assert_almost_equal(f_xy_sis[0], f_xy_spp[0], decimal=7)
def test_unit_conversion(self):
theta_E = 2.
gamma = 2.2
rho0 = self.SPP.theta2rho(theta_E, gamma)
theta_E_out = self.SPP.rho2theta(rho0, gamma)
assert theta_E == theta_E_out
def test_mass_2d_lens(self):
r = 1
theta_E = 1
gamma = 2
m_2d = self.SPP.mass_2d_lens(r, theta_E, gamma)
npt.assert_almost_equal(m_2d, 3.1415926535897931, decimal=8)
def test_grav_pot(self):
x, y = 1, 0
rho0 = 1
gamma = 2
grav_pot = self.SPP.grav_pot(x, y, rho0, gamma, center_x=0, center_y=0)
npt.assert_almost_equal(grav_pot, 12.566370614359172, decimal=8)
def __init__(self):
self.epl_major_axis = EPLMajorAxis()
self.spp = SPP()
super(EPL, self).__init__()
def __init__(self):
self._spp = SPP()
super(CurvedArcSPP, self).__init__()
class TestCurvedArc(object):
"""
tests the source model routines
"""
def setup(self):
self.model = CurvedArc()
self.spp = SPP()
def test_function(self):
output = self.model.function(1, 1, tangential_stretch=2, radial_stretch=1, r_curvature=2, direction=0, center_x=0, center_y=0)
theta_E, gamma, center_x_spp, center_y_spp = self.model._input2spp_parameterization(tangential_stretch=2, radial_stretch=1, r_curvature=2, direction=0,
center_x=0, center_y=0)
out_spp = self.spp.function(1, 1, theta_E, gamma, center_x_spp, center_y_spp) - self.spp.function(0, 0, theta_E, gamma, center_x_spp, center_y_spp)
npt.assert_almost_equal(output, out_spp, decimal=8)
def test_derivatives(self):
tangential_stretch = 5
radial_stretch = 1
r_curvature = 10
direction = 0.3
center_x = 0
center_y = 0
x, y = 1, 1
theta_E, gamma, center_x_spp, center_y_spp = self.model._input2spp_parameterization(tangential_stretch,
radial_stretch, r_curvature,
direction, center_x, center_y)
f_x, f_y = self.spp.derivatives(x, y, theta_E, gamma, center_x_spp, center_y_spp)
f_x0, f_y0 = self.spp.derivatives(center_x, center_y, theta_E, gamma, center_x_spp, center_y_spp)
f_x_new, f_y_new = self.model.derivatives(x, y, tangential_stretch, radial_stretch, r_curvature, direction, center_x, center_y)
npt.assert_almost_equal(f_x_new, f_x - f_x0, decimal=8)
npt.assert_almost_equal(f_y_new, f_y - f_y0, decimal=8)
def test_hessian(self):
lens = LensModel(lens_model_list=['CURVED_ARC'])
center_x, center_y = 0, 0
tangential_stretch = 10
radial_stretch = 1
kwargs_lens = [
{'tangential_stretch': tangential_stretch, 'radial_stretch': radial_stretch, 'r_curvature': 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, 'r_curvature': 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, 'r_curvature': 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, 'r_curvature': 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, 'r_curvature': 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 AnalyticKinematics(Anisotropy):
"""
class to compute eqn 20 in Suyu+2010 with a Monte-Carlo from rendering from the
light profile distribution and displacing them with a Gaussian seeing convolution.
This class assumes spherical symmetry in light and mass distribution and
- a Hernquist light profile (parameterised by the half-light radius)
- a power-law mass profile (parameterized by the Einstein radius and logarithmic slop)
The analytic equations for the kinematics in this approximation are presented e.g. in Suyu et al. 2010 and
the spectral rendering approach to compute the seeing convolved slit measurement is presented in Birrer et al. 2016.
The stellar anisotropy is parameterised based on Osipkov 1979; Merritt 1985.
All units are meant to be in angular arc seconds. The physical units are fold in through the angular diameter
distances
"""
def __init__(self,
kwargs_cosmo,
interpol_grid_num=100,
log_integration=False,
max_integrate=100,
min_integrate=0.001):
"""
:param kwargs_cosmo: keyword argument with angular diameter distances
"""
self._interp_grid_num = interpol_grid_num
self._log_int = log_integration
self._max_integrate = max_integrate # maximal integration (and interpolation) in units of arcsecs
self._min_integrate = min_integrate # min integration (and interpolation) in units of arcsecs
self._max_interpolate = max_integrate # we chose to set the interpolation range to the integration range
self._min_interpolate = min_integrate # we chose to set the interpolation range to the integration range
self._cosmo = Cosmo(**kwargs_cosmo)
self._spp = SPP()
Anisotropy.__init__(self, anisotropy_type='OM')
def _rho0_r0_gamma(self, theta_E, gamma):
# equation (14) in Suyu+ 2010
return -1 * math.gamma(gamma/2) / (np.sqrt(np.pi)*math.gamma((gamma-3)/2.)) * theta_E ** gamma / \
self._cosmo.arcsec2phys_lens(theta_E) * self._cosmo.epsilon_crit * const.M_sun / const.Mpc ** 3
@staticmethod
def draw_light(kwargs_light):
"""
:param kwargs_light: keyword argument (list) of the light model
:return: 3d radius (if possible), 2d projected radius, x-projected coordinate, y-projected coordinate
"""
if 'a' not in kwargs_light:
kwargs_light['a'] = 0.551 * kwargs_light['r_eff']
a = kwargs_light['a']
r = vel_util.draw_hernquist(a)
R, x, y = vel_util.project2d_random(r)
return r, R, x, y
def _sigma_s2(self, r, R, r_ani, a, gamma, rho0_r0_gamma):
"""
projected velocity dispersion
:param r: 3d radius of the light tracer particle
:param R: 2d projected radius of the light tracer particle
:param r_ani: anisotropy radius
:param a: scale of the Hernquist light profile
:param gamma: power-law slope of the mass profile
:param rho0_r0_gamma: combination of Einstein radius and power-law slope as equation (14) in Suyu+ 2010
:return: projected velocity dispersion
"""
beta = self.beta_r(r, **{'r_ani': r_ani})
return (1 - beta * R**2 / r**2) * self._sigma_r2_interp(
r, a, gamma, rho0_r0_gamma, r_ani)
def sigma_s2(self, r, R, kwargs_mass, kwargs_light, kwargs_anisotropy):
"""
returns unweighted los velocity dispersion for a specified projected radius, with weight 1
:param r: 3d radius (not needed for this calculation)
:param R: 2d projected radius (in angular units of arcsec)
:param kwargs_mass: mass model parameters (following lenstronomy lens model conventions)
:param kwargs_light: deflector light parameters (following lenstronomy light model conventions)
:param kwargs_anisotropy: anisotropy parameters, may vary according to anisotropy type chosen.
We refer to the Anisotropy() class for details on the parameters.
:return: line-of-sight projected velocity dispersion at projected radius R from 3d radius r
"""
a, gamma, rho0_r0_gamma, r_ani = self._read_out_params(
kwargs_mass, kwargs_light, kwargs_anisotropy)
return self._sigma_s2(r, R, r_ani, a, gamma, rho0_r0_gamma), 1
def sigma_r2(self, r, kwargs_mass, kwargs_light, kwargs_anisotropy):
"""
equation (19) in Suyu+ 2010
:param r: 3d radius
:param kwargs_mass: mass profile keyword arguments
:param kwargs_light: light profile keyword arguments
:param kwargs_anisotropy: anisotropy keyword arguments
:return: velocity dispersion in [m/s]
"""
a, gamma, rho0_r0_gamma, r_ani = self._read_out_params(
kwargs_mass, kwargs_light, kwargs_anisotropy)
return self._sigma_r2(r, a, gamma, rho0_r0_gamma, r_ani)
def _read_out_params(self, kwargs_mass, kwargs_light, kwargs_anisotropy):
"""
reads the relevant parameters out of the keyword arguments and transforms them to the conventions used in this
class
:param kwargs_mass: mass profile keyword arguments
:param kwargs_light: light profile keyword arguments
:param kwargs_anisotropy: anisotropy keyword arguments
:return: a (Rs of Hernquist profile), gamma, rho0_r0_gamma, r_ani
"""
if 'a' not in kwargs_light:
kwargs_light['a'] = 0.551 * kwargs_light['r_eff']
if 'rho0_r0_gamma' not in kwargs_mass:
kwargs_mass['rho0_r0_gamma'] = self._rho0_r0_gamma(
kwargs_mass['theta_E'], kwargs_mass['gamma'])
a = kwargs_light['a']
gamma = kwargs_mass['gamma']
rho0_r0_gamma = kwargs_mass['rho0_r0_gamma']
r_ani = kwargs_anisotropy['r_ani']
return a, gamma, rho0_r0_gamma, r_ani
def _sigma_r2(self, r, a, gamma, rho0_r0_gamma, r_ani):
"""
equation (19) in Suyu+ 2010
"""
# first term
prefac1 = 4 * np.pi * const.G * a**(-gamma) * rho0_r0_gamma / (3 -
gamma)
prefac2 = r * (r + a)**3 / (r**2 + r_ani**2)
# TODO check whether interpolation functions can speed this up
hyp1 = vel_util.hyp_2F1(a=2 + gamma,
b=gamma,
c=3 + gamma,
z=1. / (1 + r / a))
hyp2 = vel_util.hyp_2F1(a=3, b=gamma, c=1 + gamma, z=-a / r)
fac = r_ani**2 / a**2 * hyp1 / (
(2 + gamma) * (r / a + 1)**(2 + gamma)) + hyp2 / (gamma *
(r / a)**gamma)
return prefac1 * prefac2 * fac * (const.arcsec * self._cosmo.dd *
const.Mpc)**2
def _sigma_r2_interp(self, r, a, gamma, rho0_r0_gamma, r_ani):
"""
:param r:
:param a:
:param gamma:
:param rho0_r0_gamma:
:param r_ani:
:return:
"""
if not hasattr(self, '_interp_sigma_r2'):
min_log = np.log10(self._min_integrate)
max_log = np.log10(self._max_integrate)
r_array = np.logspace(min_log, max_log, self._interp_grid_num)
I_R_sigma2_array = []
for r_i in r_array:
I_R_sigma2_array.append(
self._sigma_r2(r_i, a, gamma, rho0_r0_gamma, r_ani))
self._interp_sigma_r2 = interp1d(np.log(r_array),
np.array(I_R_sigma2_array),
fill_value="extrapolate")
return self._interp_sigma_r2(np.log(r))
def grav_potential(self, r, kwargs_mass):
"""
Gravitational potential in SI units
:param r: radius (arc seconds)
:param kwargs_mass:
:return: gravitational potential
"""
theta_E = kwargs_mass['theta_E']
gamma = kwargs_mass['gamma']
mass_dimless = self._spp.mass_3d_lens(r, theta_E, gamma)
mass_dim = mass_dimless * const.arcsec ** 2 * self._cosmo.dd * self._cosmo.ds / self._cosmo.dds * const.Mpc * \
const.c ** 2 / (4 * np.pi * const.G)
grav_pot = -const.G * mass_dim / (r * const.arcsec * self._cosmo.dd *
const.Mpc)
return grav_pot
def delete_cache(self):
"""
deletes temporary cache tight to a specific model
:return:
"""
if hasattr(self, '_interp_sigma_r2'):
del self._interp_sigma_r2
class CurvedArc(object):
"""
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.
"""
def __init__(self):
self._spp = SPP()
def _input2spp_parameterization(self, tangential_stretch, radial_stretch,
r_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 r_curvature: curvature radius
:param direction: float, angle in radian
:param center_x: center of source in image plane
:param center_y: center of source in image plane
:return: parameters in terms of a spherical power-law profile resulting in the same observables
"""
center_x_spp = center_x - r_curvature * np.cos(direction)
center_y_spp = center_y - r_curvature * np.sin(direction)
theta_E, gamma = self._stretch2profile(tangential_stretch,
radial_stretch, r_curvature)
return theta_E, gamma, center_x_spp, center_y_spp
@staticmethod
def _stretch2profile(tangential_stretch, radial_stretch, r_curvature):
"""
:param tangential_stretch: float, stretch of intrinsic source in tangential direction
:param radial_stretch: float, stretch of intrinsic source in radial direction
:param r_curvature: radius of SPP where to have the specific tangential and radial stretch values
:return: theta_E, gamma of SPP profile
"""
gamma = (1. / radial_stretch - 1) / (1 - 1. / tangential_stretch) + 2
theta_E = abs(1 - 1. / tangential_stretch)**(1. /
(gamma - 1)) * r_curvature
return theta_E, gamma
def function(self, x, y, tangential_stretch, radial_stretch, r_curvature,
direction, center_x, center_y):
"""
ATTENTION: there may not be a global lensing potential!
:param x:
:param y:
:param tangential_stretch:
:param radial_stretch:
:param r_curvature:
:param direction:
:param center_x:
:param center_y:
:return:
"""
theta_E, gamma, center_x_spp, center_y_spp = self._input2spp_parameterization(
tangential_stretch, radial_stretch, r_curvature, direction,
center_x, center_y)
return self._spp.function(x, y, theta_E, gamma, center_x_spp,
center_y_spp) - self._spp.function(
center_x, center_y, theta_E, gamma,
center_x_spp, center_y_spp)
def derivatives(self, x, y, tangential_stretch, radial_stretch,
r_curvature, direction, center_x, center_y):
"""
:param x:
:param y:
:param tangential_stretch:
:param radial_stretch:
:param r_curvature:
:param direction:
:param center_x:
:param center_y:
:return:
"""
theta_E, gamma, center_x_spp, center_y_spp = self._input2spp_parameterization(
tangential_stretch, radial_stretch, r_curvature, direction,
center_x, center_y)
f_x, f_y = self._spp.derivatives(x, y, theta_E, gamma, center_x_spp,
center_y_spp)
f_x0, f_y0 = self._spp.derivatives(center_x, center_y, theta_E, gamma,
center_x_spp, center_y_spp)
return f_x - f_x0, f_y - f_y0
def hessian(self, x, y, tangential_stretch, radial_stretch, r_curvature,
direction, center_x, center_y):
"""
:param x:
:param y:
:param tangential_stretch:
:param radial_stretch:
:param r_curvature:
:param direction:
:param center_x:
:param center_y:
:return:
"""
theta_E, gamma, center_x_spp, center_y_spp = self._input2spp_parameterization(
tangential_stretch, radial_stretch, r_curvature, direction,
center_x, center_y)
return self._spp.hessian(x, y, theta_E, gamma, center_x_spp,
center_y_spp)
def __init__(self):
self.s2 = 0.00000001
self.spp = SPP()
self.spemd_smooth = SPEMD_SMOOTH()
class PEMD(LensProfileBase):
"""
class for power law ellipse mass density profile.
This class effectively calls the class SPEMD_SMOOTH with a fixed and very small central smoothing scale
to perform the numerical integral using the FASTELL code by Renan Barkana.
The Einstein ring parameter converts to the definition used by GRAVLENS as follow:
(theta_E / theta_E_gravlens) = sqrt[ (1+q^2) / (2 q) ]
"""
param_names = ['theta_E', 'gamma', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {
'theta_E': 0,
'gamma': 1.5,
'e1': -0.5,
'e2': -0.5,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'theta_E': 100,
'gamma': 2.5,
'e1': 0.5,
'e2': 0.5,
'center_x': 100,
'center_y': 100
}
def __init__(self, suppress_fastell=False):
"""
:param suppress_fastell: bool, if True, does not raise if fastell4py is not installed
"""
self._s_scale = 0.0001 # smoothing scale as used to numerically compute a power-law profile
self.spp = SPP()
self.spemd_smooth = SPEMD(suppress_fastell=suppress_fastell)
super(PEMD, self).__init__()
def function(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
"""
:param x: x-coordinate (angle)
:param y: y-coordinate (angle)
:param theta_E: Einstein radius (angle), pay attention to specific definition!
:param gamma: logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: x-position of lens center
:param center_y: y-position of lens center
:return: lensing potential
"""
return self.spemd_smooth.function(x, y, theta_E, gamma, e1, e2,
self._s_scale, center_x, center_y)
def derivatives(self,
x,
y,
theta_E,
gamma,
e1,
e2,
center_x=0,
center_y=0):
"""
:param x: x-coordinate (angle)
:param y: y-coordinate (angle)
:param theta_E: Einstein radius (angle), pay attention to specific definition!
:param gamma: logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: x-position of lens center
:param center_y: y-position of lens center
:return: deflection angles alpha_x, alpha_y
"""
return self.spemd_smooth.derivatives(x, y, theta_E, gamma, e1, e2,
self._s_scale, center_x, center_y)
def hessian(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
"""
:param x: x-coordinate (angle)
:param y: y-coordinate (angle)
:param theta_E: Einstein radius (angle), pay attention to specific definition!
:param gamma: logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: x-position of lens center
:param center_y: y-position of lens center
:return: Hessian components f_xx, f_yy, f_xy
"""
return self.spemd_smooth.hessian(x, y, theta_E, gamma, e1, e2,
self._s_scale, center_x, center_y)
def mass_3d_lens(self, r, theta_E, gamma, e1=None, e2=None):
"""
computes the spherical power-law mass enclosed (with SPP routine)
:param r: radius within the mass is computed
:param theta_E: Einstein radius
:param gamma: power-law slope
:param e1: eccentricity component (not used)
:param e2: eccentricity component (not used)
:return: mass enclosed a 3D radius r
"""
return self.spp.mass_3d_lens(r, theta_E, gamma)
def density_lens(self, r, theta_E, gamma, e1=None, e2=None):
"""
computes the density at 3d radius r given lens model parameterization.
The integral in the LOS projection of this quantity results in the convergence quantity.
:param r: radius within the mass is computed
:param theta_E: Einstein radius
:param gamma: power-law slope
:param e1: eccentricity component (not used)
:param e2: eccentricity component (not used)
:return: mass enclosed a 3D radius r
"""
return self.spp.density_lens(r, theta_E, gamma)
def __init__(self):
self.s2 = 0.00000001 # smoothing scale as used to numerically compute a power-law profile
self.spp = SPP()
self.spemd_smooth = SPEMD_SMOOTH()
super(SPEMD, self).__init__()
def __init__(self):
from lenstronomy.LensModel.Profiles.spp import SPP
self.spp = SPP()
class SPEP(object):
"""
class for Softened power-law elliptical potential (SPEP)
"""
def __init__(self):
from lenstronomy.LensModel.Profiles.spp import SPP
self.spp = SPP()
def function(self, x, y, theta_E, gamma, q, phi_G, center_x=0, center_y=0):
"""
:param x: set of x-coordinates
:type x: array of size (n)
:param theta_E: Einstein radius of lense
:type theta_E: float.
:param gamma: power law slope of mass profifle
:type gamma: <2 float
:param q: Axis ratio
:type q: 0<q<1
:param phi_G: position angel of SES
:type q: 0<phi_G<pi/2
:returns: function
:raises: AttributeError, KeyError
"""
gamma, q = self._param_bounds(gamma, q)
theta_E *= q
x_shift = x - center_x
y_shift = y - center_y
E = theta_E / (((3 - gamma) / 2.)**(1. / (1 - gamma)) * np.sqrt(q))
#E = phi_E
eta = -gamma + 3
xt1 = np.cos(phi_G) * x_shift + np.sin(phi_G) * y_shift
xt2 = -np.sin(phi_G) * x_shift + np.cos(phi_G) * y_shift
p2 = xt1**2 + xt2**2 / q**2
s2 = 0. # softening
return 2 * E**2 / eta**2 * ((p2 + s2) / E**2)**(eta / 2)
def derivatives(self,
x,
y,
theta_E,
gamma,
q,
phi_G,
center_x=0,
center_y=0):
# # @hope.jit
# def xy_prime(dx, dy, eta, a, E, xt1, xt2, q):
# fac = 1./eta*(a/(E*E))**(eta/2-1)*2
# dx[:] = fac*xt1
# dy[:] = fac*xt2/(q*q)
gamma, q = self._param_bounds(gamma, q)
phi_E_new = theta_E * q
x_shift = x - center_x
y_shift = y - center_y
E = phi_E_new / (((3 - gamma) / 2.)**(1. / (1 - gamma)) * np.sqrt(q))
# E = phi_E
eta = float(-gamma + 3)
cos_phi = np.cos(phi_G)
sin_phi = np.sin(phi_G)
xt1 = cos_phi * x_shift + sin_phi * y_shift
xt2 = -sin_phi * x_shift + cos_phi * y_shift
xt2difq2 = xt2 / (q * q)
P2 = xt1 * xt1 + xt2 * xt2difq2
if isinstance(P2, int) or isinstance(P2, float):
a = max(0.000001, P2)
else:
a = np.empty_like(P2)
p2 = P2[P2 > 0] #in the SIS regime
a[P2 == 0] = 0.000001
a[P2 > 0] = p2
fac = 1. / eta * (a / (E * E))**(eta / 2 - 1) * 2
f_x_prim = fac * xt1
f_y_prim = fac * xt2difq2
f_x = cos_phi * f_x_prim - sin_phi * f_y_prim
f_y = sin_phi * f_x_prim + cos_phi * f_y_prim
return f_x, f_y
def hessian(self, x, y, theta_E, gamma, q, phi_G, center_x=0, center_y=0):
gamma, q = self._param_bounds(gamma, q)
phi_E_new = theta_E * q
x_shift = x - center_x
y_shift = y - center_y
E = phi_E_new / (((3 - gamma) / 2.)**(1. / (1 - gamma)) * np.sqrt(q))
# E = phi_E
eta = float(-gamma + 3)
xt1 = np.cos(phi_G) * x_shift + np.sin(phi_G) * y_shift
xt2 = -np.sin(phi_G) * x_shift + np.cos(phi_G) * y_shift
P2 = xt1**2 + xt2**2 / q**2
if isinstance(P2, int) or isinstance(P2, float):
a = max(0.000001, P2)
else:
a = np.empty_like(P2)
p2 = P2[P2 > 0] #in the SIS regime
a[P2 == 0] = 0.000001
a[P2 > 0] = p2
s2 = 0. # softening
kappa = 1. / eta * (a / E**2)**(eta / 2 - 1) * (
(eta - 2) * (xt1**2 + xt2**2 / q**4) / a + (1 + 1 / q**2))
gamma1_value = 1. / eta * (a / E**2)**(
eta / 2 - 1) * (1 - 1 / q**2 + (eta / 2 - 1) *
(2 * xt1**2 - 2 * xt2**2 / q**4) / a)
gamma2_value = 4 * xt1 * xt2 / q**2 * (1. / 2 - 1 / eta) * (
a / E**2)**(eta / 2 - 2) / E**2
gamma1 = np.cos(2 * phi_G) * gamma1_value - np.sin(
2 * phi_G) * gamma2_value
gamma2 = +np.sin(2 * phi_G) * gamma1_value + np.cos(
2 * phi_G) * gamma2_value
f_xx = kappa + gamma1
f_yy = kappa - gamma1
f_xy = gamma2
return f_xx, f_yy, f_xy
def mass_3d_lens(self, r, theta_E, gamma, q, phi_G):
"""
computes the spherical power-law mass enclosed (with SPP routiune)
:param r:
:param theta_E:
:param gamma:
:param q:
:param phi_G:
:return:
"""
return self.spp.mass_3d_lens(r, theta_E, gamma)
def _param_bounds(self, gamma, q):
"""
bounds parameters
:param gamma:
:param q:
:return:
"""
if gamma < 1.4:
gamma = 1.4
if gamma > 2.9:
gamma = 2.9
if q < 0.3:
q = 0.3
return float(gamma), q
def __init__(self):
self._spp = SPP()
class PEMD(LensProfileBase):
"""
class for power law ellipse mass density profile.
This class effectively calls the class SPEMD_SMOOTH with a fixed and very small central smoothing scale
to perform the numerical integral using the FASTELL code by Renan Barkana.
.. math::
\\kappa(x, y) = \\frac{3-\\gamma}{2} \\left(\\frac{\\theta_{E}}{\\sqrt{q x^2 + y^2/q}} \\right)^{\\gamma-1}
with :math:`\\theta_{E}` is the (circularized) Einstein radius,
:math:`\\gamma` is the negative power-law slope of the 3D mass distributions,
:math:`q` is the minor/major axis ratio,
and :math:`x` and :math:`y` are defined in a coordinate system aligned with the major and minor axis of the lens.
In terms of eccentricities, this profile is defined as
.. math::
\\kappa(r) = \\frac{3-\\gamma}{2} \\left(\\frac{\\theta'_{E}}{r \\sqrt{1 − e*\\cos(2*\\phi)}} \\right)^{\\gamma-1}
with :math:`\\epsilon` is the ellipticity defined as
.. math::
\\epsilon = \\frac{1-q^2}{1+q^2}
And an Einstein radius :math:`\\theta'_{\\rm E}` related to the definition used is
.. math::
\\left(\\frac{\\theta'_{\\rm E}}{\\theta_{\\rm E}}\\right)^{2} = \\frac{2q}{1+q^2}.
"""
param_names = ['theta_E', 'gamma', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {
'theta_E': 0,
'gamma': 1.5,
'e1': -0.5,
'e2': -0.5,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'theta_E': 100,
'gamma': 2.5,
'e1': 0.5,
'e2': 0.5,
'center_x': 100,
'center_y': 100
}
def __init__(self, suppress_fastell=False):
"""
:param suppress_fastell: bool, if True, does not raise if fastell4py is not installed
"""
self._s_scale = 0.0000001 # smoothing scale as used to numerically compute a power-law profile
self.spp = SPP()
self.spemd_smooth = SPEMD(suppress_fastell=suppress_fastell)
super(PEMD, self).__init__()
def function(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
"""
:param x: x-coordinate (angle)
:param y: y-coordinate (angle)
:param theta_E: Einstein radius (angle), pay attention to specific definition!
:param gamma: logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: x-position of lens center
:param center_y: y-position of lens center
:return: lensing potential
"""
return self.spemd_smooth.function(x, y, theta_E, gamma, e1, e2,
self._s_scale, center_x, center_y)
def derivatives(self,
x,
y,
theta_E,
gamma,
e1,
e2,
center_x=0,
center_y=0):
"""
:param x: x-coordinate (angle)
:param y: y-coordinate (angle)
:param theta_E: Einstein radius (angle), pay attention to specific definition!
:param gamma: logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: x-position of lens center
:param center_y: y-position of lens center
:return: deflection angles alpha_x, alpha_y
"""
return self.spemd_smooth.derivatives(x, y, theta_E, gamma, e1, e2,
self._s_scale, center_x, center_y)
def hessian(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
"""
:param x: x-coordinate (angle)
:param y: y-coordinate (angle)
:param theta_E: Einstein radius (angle), pay attention to specific definition!
:param gamma: logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: x-position of lens center
:param center_y: y-position of lens center
:return: Hessian components f_xx, f_xy, f_yx, f_yy
"""
return self.spemd_smooth.hessian(x, y, theta_E, gamma, e1, e2,
self._s_scale, center_x, center_y)
def mass_3d_lens(self, r, theta_E, gamma, e1=None, e2=None):
"""
computes the spherical power-law mass enclosed (with SPP routine)
:param r: radius within the mass is computed
:param theta_E: Einstein radius
:param gamma: power-law slope
:param e1: eccentricity component (not used)
:param e2: eccentricity component (not used)
:return: mass enclosed a 3D radius r
"""
return self.spp.mass_3d_lens(r, theta_E, gamma)
def density_lens(self, r, theta_E, gamma, e1=None, e2=None):
"""
computes the density at 3d radius r given lens model parameterization.
The integral in the LOS projection of this quantity results in the convergence quantity.
:param r: radius within the mass is computed
:param theta_E: Einstein radius
:param gamma: power-law slope
:param e1: eccentricity component (not used)
:param e2: eccentricity component (not used)
:return: mass enclosed a 3D radius r
"""
return self.spp.density_lens(r, theta_E, gamma)
class SPEP(LensProfileBase):
"""
class for Softened power-law elliptical potential (SPEP)
"""
param_names = ['theta_E', 'gamma', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {
'theta_E': 0,
'gamma': 0,
'e1': -0.5,
'e2': -0.5,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'theta_E': 100,
'gamma': 100,
'e1': 0.5,
'e2': 0.5,
'center_x': 100,
'center_y': 100
}
def __init__(self):
self.spp = SPP()
super(SPEP, self).__init__()
def function(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
"""
:param x: set of x-coordinates
:type x: array of size (n)
:param theta_E: Einstein radius of lense
:type theta_E: float.
:param gamma: power law slope of mass profifle
:type gamma: <2 float
:param e1: eccentricity
:type e1: -1<e1<1
:param e2: eccentricity
:type e2: -1<e1<1
:returns: function
:raises: AttributeError, KeyError
"""
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
gamma, q = self._param_bounds(gamma, q)
theta_E *= q
x_shift = x - center_x
y_shift = y - center_y
E = theta_E / (((3 - gamma) / 2.)**(1. / (1 - gamma)) * np.sqrt(q))
#E = phi_E
eta = -gamma + 3
xt1 = np.cos(phi_G) * x_shift + np.sin(phi_G) * y_shift
xt2 = -np.sin(phi_G) * x_shift + np.cos(phi_G) * y_shift
p2 = xt1**2 + xt2**2 / q**2
s2 = 0. # softening
return 2 * E**2 / eta**2 * ((p2 + s2) / E**2)**(eta / 2)
def derivatives(self,
x,
y,
theta_E,
gamma,
e1,
e2,
center_x=0,
center_y=0):
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
gamma, q = self._param_bounds(gamma, q)
phi_E_new = theta_E * q
x_shift = x - center_x
y_shift = y - center_y
E = phi_E_new / (((3 - gamma) / 2.)**(1. / (1 - gamma)) * np.sqrt(q))
# E = phi_E
eta = float(-gamma + 3)
cos_phi = np.cos(phi_G)
sin_phi = np.sin(phi_G)
xt1 = cos_phi * x_shift + sin_phi * y_shift
xt2 = -sin_phi * x_shift + cos_phi * y_shift
xt2difq2 = xt2 / (q * q)
P2 = xt1 * xt1 + xt2 * xt2difq2
if isinstance(P2, int) or isinstance(P2, float):
a = max(0.000001, P2)
else:
a = np.empty_like(P2)
p2 = P2[P2 > 0] #in the SIS regime
a[P2 == 0] = 0.000001
a[P2 > 0] = p2
fac = 1. / eta * (a / (E * E))**(eta / 2 - 1) * 2
f_x_prim = fac * xt1
f_y_prim = fac * xt2difq2
f_x = cos_phi * f_x_prim - sin_phi * f_y_prim
f_y = sin_phi * f_x_prim + cos_phi * f_y_prim
return f_x, f_y
def hessian(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
gamma, q = self._param_bounds(gamma, q)
phi_E_new = theta_E * q
#x_shift = x - center_x
#y_shift = y - center_y
# shift
x_ = x - center_x
y_ = y - center_y
# rotate
x__, y__ = util.rotate(x_, y_, phi_G)
E = phi_E_new / (((3 - gamma) / 2.)**(1. / (1 - gamma)) * np.sqrt(q))
if E <= 0:
return np.zeros_like(x), np.zeros_like(x), np.zeros_like(
x), np.zeros_like(x)
# E = phi_E
eta = float(-gamma + 3)
#xt1 = np.cos(phi_G)*x_shift+np.sin(phi_G)*y_shift
#xt2 = -np.sin(phi_G)*x_shift+np.cos(phi_G)*y_shift
xt1, xt2 = x__, y__
P2 = xt1**2 + xt2**2 / q**2
if isinstance(P2, int) or isinstance(P2, float):
a = max(0.000001, P2)
else:
a = np.empty_like(P2)
p2 = P2[P2 > 0] #in the SIS regime
a[P2 == 0] = 0.000001
a[P2 > 0] = p2
s2 = 0. # softening
kappa = 1. / eta * (a / E**2)**(eta / 2 - 1) * (
(eta - 2) * (xt1**2 + xt2**2 / q**4) / a + (1 + 1 / q**2))
gamma1_value = 1. / eta * (a / E**2)**(
eta / 2 - 1) * (1 - 1 / q**2 + (eta / 2 - 1) *
(2 * xt1**2 - 2 * xt2**2 / q**4) / a)
gamma2_value = 4 * xt1 * xt2 / q**2 * (1. / 2 - 1 / eta) * (
a / E**2)**(eta / 2 - 2) / E**2
gamma1 = np.cos(2 * phi_G) * gamma1_value - np.sin(
2 * phi_G) * gamma2_value
gamma2 = +np.sin(2 * phi_G) * gamma1_value + np.cos(
2 * phi_G) * gamma2_value
f_xx = kappa + gamma1
f_yy = kappa - gamma1
f_xy = gamma2
return f_xx, f_xy, f_xy, f_yy
def mass_3d_lens(self, r, theta_E, gamma, e1=None, e2=None):
"""
computes the spherical power-law mass enclosed (with SPP routine)
:param r: radius within the mass is computed
:param theta_E: Einstein radius
:param gamma: power-law slope
:param e1: eccentricity component (not used)
:param e2: eccentricity component (not used)
:return: mass enclosed a 3D radius r
"""
return self.spp.mass_3d_lens(r, theta_E, gamma)
def density_lens(self, r, theta_E, gamma, e1=None, e2=None):
"""
computes the density at 3d radius r given lens model parameterization.
The integral in the LOS projection of this quantity results in the convergence quantity.
:param r: radius within the mass is computed
:param theta_E: Einstein radius
:param gamma: power-law slope
:param e1: eccentricity component (not used)
:param e2: eccentricity component (not used)
:return: mass enclosed a 3D radius r
"""
return self.spp.density_lens(r, theta_E, gamma)
@staticmethod
def _param_bounds(gamma, q):
"""
bounds parameters
:param gamma:
:param q:
:return:
"""
if gamma < 1.4:
gamma = 1.4
if gamma > 2.9:
gamma = 2.9
if q < 0.01:
q = 0.01
return float(gamma), q
def setup(self):
self.model = CurvedArc()
self.spp = SPP()
def __init__(self, lens_model_list, **kwargs):
"""
:param lens_model_list: list of strings with lens model names
:param foreground_shear: bool, when True, models a foreground non-linear shear distortion
"""
self.func_list = []
self._foreground_shear = False
for i, lens_type in enumerate(lens_model_list):
if lens_type == 'SHEAR':
from lenstronomy.LensModel.Profiles.external_shear import ExternalShear
self.func_list.append(ExternalShear())
elif lens_type == 'CONVERGENCE':
from lenstronomy.LensModel.Profiles.mass_sheet import MassSheet
self.func_list.append(MassSheet())
elif lens_type == 'FLEXION':
from lenstronomy.LensModel.Profiles.flexion import Flexion
self.func_list.append(Flexion())
elif lens_type == 'POINT_MASS':
from lenstronomy.LensModel.Profiles.point_mass import PointMass
self.func_list.append(PointMass())
elif lens_type == 'SIS':
from lenstronomy.LensModel.Profiles.sis import SIS
self.func_list.append(SIS())
elif lens_type == 'SIS_TRUNCATED':
from lenstronomy.LensModel.Profiles.sis_truncate import SIS_truncate
self.func_list.append(SIS_truncate())
elif lens_type == 'SIE':
from lenstronomy.LensModel.Profiles.sie import SIE
self.func_list.append(SIE())
elif lens_type == 'SPP':
from lenstronomy.LensModel.Profiles.spp import SPP
self.func_list.append(SPP())
elif lens_type == 'NIE':
from lenstronomy.LensModel.Profiles.nie import NIE
self.func_list.append(NIE())
elif lens_type == 'NIE_SIMPLE':
from lenstronomy.LensModel.Profiles.nie import NIE_simple
self.func_list.append(NIE_simple())
elif lens_type == 'CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import Chameleon
self.func_list.append(Chameleon())
elif lens_type == 'DOUBLE_CHAMELEON':
from lenstronomy.LensModel.Profiles.chameleon import DoubleChameleon
self.func_list.append(DoubleChameleon())
elif lens_type == 'SPEP':
from lenstronomy.LensModel.Profiles.spep import SPEP
self.func_list.append(SPEP())
elif lens_type == 'SPEMD':
from lenstronomy.LensModel.Profiles.spemd import SPEMD
self.func_list.append(SPEMD())
elif lens_type == 'SPEMD_SMOOTH':
from lenstronomy.LensModel.Profiles.spemd_smooth import SPEMD_SMOOTH
self.func_list.append(SPEMD_SMOOTH())
elif lens_type == 'NFW':
from lenstronomy.LensModel.Profiles.nfw import NFW
self.func_list.append(NFW(**kwargs))
elif lens_type == 'NFW_ELLIPSE':
from lenstronomy.LensModel.Profiles.nfw_ellipse import NFW_ELLIPSE
self.func_list.append(
NFW_ELLIPSE(interpol=False,
num_interp_X=1000,
max_interp_X=100))
elif lens_type == 'TNFW':
from lenstronomy.LensModel.Profiles.tnfw import TNFW
self.func_list.append(TNFW())
elif lens_type == 'SERSIC':
from lenstronomy.LensModel.Profiles.sersic import Sersic
self.func_list.append(Sersic())
elif lens_type == 'SERSIC_ELLIPSE':
from lenstronomy.LensModel.Profiles.sersic_ellipse import SersicEllipse
self.func_list.append(SersicEllipse())
elif lens_type == 'PJAFFE':
from lenstronomy.LensModel.Profiles.p_jaffe import PJaffe
self.func_list.append(PJaffe())
elif lens_type == 'PJAFFE_ELLIPSE':
from lenstronomy.LensModel.Profiles.p_jaffe_ellipse import PJaffe_Ellipse
self.func_list.append(PJaffe_Ellipse())
elif lens_type == 'HERNQUIST':
from lenstronomy.LensModel.Profiles.hernquist import Hernquist
self.func_list.append(Hernquist())
elif lens_type == 'HERNQUIST_ELLIPSE':
from lenstronomy.LensModel.Profiles.hernquist_ellipse import Hernquist_Ellipse
self.func_list.append(Hernquist_Ellipse())
elif lens_type == 'GAUSSIAN':
from lenstronomy.LensModel.Profiles.gaussian_potential import Gaussian
self.func_list.append(Gaussian())
elif lens_type == 'GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.gaussian_kappa import GaussianKappa
self.func_list.append(GaussianKappa())
elif lens_type == 'GAUSSIAN_KAPPA_ELLIPSE':
from lenstronomy.LensModel.Profiles.gaussian_kappa_ellipse import GaussianKappaEllipse
self.func_list.append(GaussianKappaEllipse())
elif lens_type == 'MULTI_GAUSSIAN_KAPPA':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappa
self.func_list.append(MultiGaussianKappa())
elif lens_type == 'MULTI_GAUSSIAN_KAPPA_ELLIPSE':
from lenstronomy.LensModel.Profiles.multi_gaussian_kappa import MultiGaussianKappaEllipse
self.func_list.append(MultiGaussianKappaEllipse())
elif lens_type == 'INTERPOL':
from lenstronomy.LensModel.Profiles.interpol import Interpol_func
self.func_list.append(
Interpol_func(grid=False, min_grid_number=100))
elif lens_type == 'INTERPOL_SCALED':
from lenstronomy.LensModel.Profiles.interpol import Interpol_func_scaled
self.func_list.append(
Interpol_func_scaled(grid=False, min_grid_number=100))
elif lens_type == 'SHAPELETS_POLAR':
from lenstronomy.LensModel.Profiles.shapelet_pot_polar import PolarShapelets
self.func_list.append(PolarShapelets())
elif lens_type == 'SHAPELETS_CART':
from lenstronomy.LensModel.Profiles.shapelet_pot_cartesian import CartShapelets
self.func_list.append(CartShapelets())
elif lens_type == 'DIPOLE':
from lenstronomy.LensModel.Profiles.dipole import Dipole
self.func_list.append(Dipole())
elif lens_type == 'FOREGROUND_SHEAR':
from lenstronomy.LensModel.Profiles.external_shear import ExternalShear
self.func_list.append(ExternalShear())
self._foreground_shear = True
self._foreground_shear_idex = i
else:
raise ValueError('%s is not a valid lens model' % lens_type)
self._model_list = lens_model_list
class CurvedArcSPP(LensProfileBase):
"""
lens model that describes a section of a highly magnified deflector region.
The parameterization is chosen to describe local observables efficient.
Observables are:
- curvature radius (basically bending relative to the center of the profile)
- radial stretch (plus sign) thickness of arc with parity (more generalized than the power-law slope)
- tangential stretch (plus sign). Infinity means at critical curve
- direction of curvature
- position of arc
Requirements:
- Should work with other perturbative models without breaking its meaning (say when adding additional shear terms)
- Must best reflect the observables in lensing
- minimal covariances between the parameters, intuitive parameterization.
"""
param_names = [
'tangential_stretch', 'radial_stretch', 'curvature', 'direction',
'center_x', 'center_y'
]
lower_limit_default = {
'tangential_stretch': -100,
'radial_stretch': -5,
'curvature': 0.000001,
'direction': -np.pi,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'tangential_stretch': 100,
'radial_stretch': 5,
'curvature': 100,
'direction': np.pi,
'center_x': 100,
'center_y': 100
}
def __init__(self):
self._spp = SPP()
super(CurvedArcSPP, self).__init__()
@staticmethod
def stretch2spp(tangential_stretch, radial_stretch, curvature, direction,
center_x, center_y):
"""
:param tangential_stretch: float, stretch of intrinsic source in tangential direction
:param radial_stretch: float, stretch of intrinsic source in radial direction
:param curvature: 1/curvature radius
:param direction: float, angle in radian
:param center_x: center of source in image plane
:param center_y: center of source in image plane
:return: parameters in terms of a spherical power-law profile resulting in the same observables
"""
center_x_spp, center_y_spp = center_deflector(curvature, direction,
center_x, center_y)
r_curvature = 1. / curvature
gamma = (1. / radial_stretch - 1) / (1 - 1. / tangential_stretch) + 2
theta_E = abs(1 - 1. / tangential_stretch)**(1. /
(gamma - 1)) * r_curvature
return theta_E, gamma, center_x_spp, center_y_spp
@staticmethod
def spp2stretch(theta_E, gamma, center_x_spp, center_y_spp, center_x,
center_y):
"""
turn Singular power-law lens model into stretch parameterization at position (center_x, center_y)
This is the inverse function of stretch2spp()
:param theta_E: Einstein radius of SPP model
:param gamma: power-law slope
:param center_x_spp: center of SPP model
:param center_y_spp: center of SPP model
:param center_x: center of curved model definition
:param center_y: center of curved model definition
:return: tangential_stretch, radial_stretch, curvature, direction
"""
r_curvature = np.sqrt((center_x_spp - center_x)**2 +
(center_y_spp - center_y)**2)
direction = np.arctan2(center_y - center_y_spp,
center_x - center_x_spp)
tangential_stretch = 1 / (1 - (theta_E / r_curvature)**(gamma - 1))
radial_stretch = 1 / (1 + (gamma - 2) *
(theta_E / r_curvature)**(gamma - 1))
curvature = 1. / r_curvature
return tangential_stretch, radial_stretch, curvature, direction
def function(self, x, y, tangential_stretch, radial_stretch, curvature,
direction, center_x, center_y):
"""
ATTENTION: there may not be a global lensing potential!
:param x:
:param y:
:param tangential_stretch: float, stretch of intrinsic source in tangential direction
:param radial_stretch: float, stretch of intrinsic source in radial direction
:param curvature: 1/curvature radius
:param direction: float, angle in radian
:param center_x: center of source in image plane
:param center_y: center of source in image plane
:return:
"""
theta_E, gamma, center_x_spp, center_y_spp = self.stretch2spp(
tangential_stretch, radial_stretch, curvature, direction, center_x,
center_y)
f_ = self._spp.function(x, y, theta_E, gamma, center_x_spp,
center_y_spp)
alpha_x, alpha_y = self._spp.derivatives(center_x, center_y, theta_E,
gamma, center_x_spp,
center_y_spp)
f_0 = alpha_x * (x - center_x) + alpha_y * (y - center_y)
return f_ - f_0
def derivatives(self, x, y, tangential_stretch, radial_stretch, curvature,
direction, center_x, center_y):
"""
:param x:
:param y:
:param tangential_stretch: float, stretch of intrinsic source in tangential direction
:param radial_stretch: float, stretch of intrinsic source in radial direction
:param curvature: 1/curvature radius
:param direction: float, angle in radian
:param center_x: center of source in image plane
:param center_y: center of source in image plane
:return:
"""
theta_E, gamma, center_x_spp, center_y_spp = self.stretch2spp(
tangential_stretch, radial_stretch, curvature, direction, center_x,
center_y)
f_x, f_y = self._spp.derivatives(x, y, theta_E, gamma, center_x_spp,
center_y_spp)
f_x0, f_y0 = self._spp.derivatives(center_x, center_y, theta_E, gamma,
center_x_spp, center_y_spp)
return f_x - f_x0, f_y - f_y0
def hessian(self, x, y, tangential_stretch, radial_stretch, curvature,
direction, center_x, center_y):
"""
:param x:
:param y:
:param tangential_stretch: float, stretch of intrinsic source in tangential direction
:param radial_stretch: float, stretch of intrinsic source in radial direction
:param curvature: 1/curvature radius
:param direction: float, angle in radian
:param center_x: center of source in image plane
:param center_y: center of source in image plane
:return:
"""
theta_E, gamma, center_x_spp, center_y_spp = self.stretch2spp(
tangential_stretch, radial_stretch, curvature, direction, center_x,
center_y)
return self._spp.hessian(x, y, theta_E, gamma, center_x_spp,
center_y_spp)
class EPL(LensProfileBase):
""""
Elliptical Power Law mass profile
.. math::
\\kappa(x, y) = \\frac{3-\\gamma}{2} \\left(\\frac{\\theta_{E}}{\\sqrt{q x^2 + y^2/q}} \\right)^{\\gamma-1}
with :math:`\\theta_{E}` is the (circularized) Einstein radius,
:math:`\\gamma` is the negative power-law slope of the 3D mass distributions,
:math:`q` is the minor/major axis ratio,
and :math:`x` and :math:`y` are defined in a coordinate sys- tem aligned with the major and minor axis of the lens.
In terms of eccentricities, this profile is defined as
.. math::
\\kappa(r) = \\frac{3-\\gamma}{2} \\left(\\frac{\\theta'_{E}}{r \\sqrt{1 − e*\\cos(2*\\phi)}} \\right)^{\\gamma-1}
with :math:`\\epsilon` is the ellipticity defined as
.. math::
\\epsilon = \\frac{1-q^2}{1+q^2}
And an Einstein radius :math:`\\theta'_{\\rm E}` related to the definition used is
.. math::
\\left(\\frac{\\theta'_{\\rm E}}{\\theta_{\\rm E}}\\right)^{2} = \\frac{2q}{1+q^2}.
The mathematical form of the calculation is presented by Tessore & Metcalf (2015), https://arxiv.org/abs/1507.01819.
The current implementation is using hyperbolic functions. The paper presents an iterative calculation scheme,
converging in few iterations to high precision and accuracy.
A (faster) implementation of the same model using numba is accessible as 'EPL_NUMBA' with the iterative calculation
scheme.
"""
param_names = ['theta_E', 'gamma', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {
'theta_E': 0,
'gamma': 1.5,
'e1': -0.5,
'e2': -0.5,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'theta_E': 100,
'gamma': 2.5,
'e1': 0.5,
'e2': 0.5,
'center_x': 100,
'center_y': 100
}
def __init__(self):
self.epl_major_axis = EPLMajorAxis()
self.spp = SPP()
super(EPL, self).__init__()
def param_conv(self, theta_E, gamma, e1, e2):
"""
converts parameters as defined in this class to the parameters used in the EPLMajorAxis() class
:param theta_E: Einstein radius as defined in the profile class
:param gamma: negative power-law slope
:param e1: eccentricity modulus
:param e2: eccentricity modulus
:return: b, t, q, phi_G
"""
if self._static is True:
return self._b_static, self._t_static, self._q_static, self._phi_G_static
return self._param_conv(theta_E, gamma, e1, e2)
@staticmethod
def _param_conv(theta_E, gamma, e1, e2):
"""
convert parameters from :math:`R = \\sqrt{q x^2 + y^2/q}` to
:math:`R = \\sqrt{q^2 x^2 + y^2}`
:param gamma: power law slope
:param theta_E: Einstein radius
:param e1: eccentricity component
:param e2: eccentricity component
:return: critical radius b, slope t, axis ratio q, orientation angle phi_G
"""
t = gamma - 1
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
b = theta_E * np.sqrt(q)
return b, t, q, phi_G
def set_static(self, theta_E, gamma, e1, e2, center_x=0, center_y=0):
"""
:param theta_E: Einstein radius
:param gamma: power law slope
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: profile center
:param center_y: profile center
:return: self variables set
"""
self._static = True
self._b_static, self._t_static, self._q_static, self._phi_G_static = self._param_conv(
theta_E, gamma, e1, e2)
def set_dynamic(self):
"""
:return:
"""
self._static = False
if hasattr(self, '_b_static'):
del self._b_static
if hasattr(self, '_t_static'):
del self._t_static
if hasattr(self, '_phi_G_static'):
del self._phi_G_static
if hasattr(self, '_q_static'):
del self._q_static
def function(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
"""
:param x: x-coordinate in image plane
:param y: y-coordinate in image plane
:param theta_E: Einstein radius
:param gamma: power law slope
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: profile center
:param center_y: profile center
:return: lensing potential
"""
b, t, q, phi_G = self.param_conv(theta_E, gamma, e1, e2)
# shift
x_ = x - center_x
y_ = y - center_y
# rotate
x__, y__ = util.rotate(x_, y_, phi_G)
# evaluate
f_ = self.epl_major_axis.function(x__, y__, b, t, q)
# rotate back
return f_
def derivatives(self,
x,
y,
theta_E,
gamma,
e1,
e2,
center_x=0,
center_y=0):
"""
:param x: x-coordinate in image plane
:param y: y-coordinate in image plane
:param theta_E: Einstein radius
:param gamma: power law slope
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: profile center
:param center_y: profile center
:return: alpha_x, alpha_y
"""
b, t, q, phi_G = self.param_conv(theta_E, gamma, e1, e2)
# shift
x_ = x - center_x
y_ = y - center_y
# rotate
x__, y__ = util.rotate(x_, y_, phi_G)
# evaluate
f__x, f__y = self.epl_major_axis.derivatives(x__, y__, b, t, q)
# rotate back
f_x, f_y = util.rotate(f__x, f__y, -phi_G)
return f_x, f_y
def hessian(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
"""
:param x: x-coordinate in image plane
:param y: y-coordinate in image plane
:param theta_E: Einstein radius
:param gamma: power law slope
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: profile center
:param center_y: profile center
:return: f_xx, f_xy, f_yx, f_yy
"""
b, t, q, phi_G = self.param_conv(theta_E, gamma, e1, e2)
# shift
x_ = x - center_x
y_ = y - center_y
# rotate
x__, y__ = util.rotate(x_, y_, phi_G)
# evaluate
f__xx, f__xy, f__yx, f__yy = self.epl_major_axis.hessian(
x__, y__, b, t, q)
# rotate back
kappa = 1. / 2 * (f__xx + f__yy)
gamma1__ = 1. / 2 * (f__xx - f__yy)
gamma2__ = f__xy
gamma1 = np.cos(2 * phi_G) * gamma1__ - np.sin(2 * phi_G) * gamma2__
gamma2 = +np.sin(2 * phi_G) * gamma1__ + np.cos(2 * phi_G) * gamma2__
f_xx = kappa + gamma1
f_yy = kappa - gamma1
f_xy = gamma2
return f_xx, f_xy, f_xy, f_yy
def mass_3d_lens(self, r, theta_E, gamma, e1=None, e2=None):
"""
computes the spherical power-law mass enclosed (with SPP routine)
:param r: radius within the mass is computed
:param theta_E: Einstein radius
:param gamma: power-law slope
:param e1: eccentricity component (not used)
:param e2: eccentricity component (not used)
:return: mass enclosed a 3D radius r
"""
return self.spp.mass_3d_lens(r, theta_E, gamma)
def density_lens(self, r, theta_E, gamma, e1=None, e2=None):
"""
computes the density at 3d radius r given lens model parameterization.
The integral in the LOS projection of this quantity results in the convergence quantity.
:param r: radius within the mass is computed
:param theta_E: Einstein radius
:param gamma: power-law slope
:param e1: eccentricity component (not used)
:param e2: eccentricity component (not used)
:return: mass enclosed a 3D radius r
"""
return self.spp.density_lens(r, theta_E, gamma)
def __init__(self):
self.spp = SPP()
super(SPEP, 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 TestCurvedArc(object):
"""
tests the source model routines
"""
def setup(self):
self.model = CurvedArc()
self.spp = SPP()
def test_spp2stretch(self):
center_x, center_y = 1, 1
theta_E = 1
gamma = 1.9
center_x_spp, center_y_spp = 0., 0
tangential_stretch, radial_stretch, curvature, direction = self.model.spp2stretch(
theta_E, gamma, center_x_spp, center_y_spp, center_x, center_y)
theta_E_new, gamma_new, center_x_spp_new, center_y_spp_new = self.model.stretch2spp(
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(gamma_new, gamma, decimal=8)
center_x, center_y = -1, 1
tangential_stretch, radial_stretch, curvature, direction = self.model.spp2stretch(
theta_E, gamma, center_x_spp, center_y_spp, center_x, center_y)
theta_E_new, gamma_new, center_x_spp_new, center_y_spp_new = self.model.stretch2spp(
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(gamma_new, gamma, decimal=8)
center_x, center_y = 0, 0.5
tangential_stretch, radial_stretch, curvature, direction = self.model.spp2stretch(
theta_E, gamma, center_x_spp, center_y_spp, center_x, center_y)
theta_E_new, gamma_new, center_x_spp_new, center_y_spp_new = self.model.stretch2spp(
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(gamma_new, gamma, decimal=8)
center_x, center_y = 0, -1.5
tangential_stretch, radial_stretch, r_curvature, direction = self.model.spp2stretch(
theta_E, gamma, center_x_spp, center_y_spp, center_x, center_y)
print(tangential_stretch, radial_stretch, r_curvature, direction)
theta_E_new, gamma_new, center_x_spp_new, center_y_spp_new = self.model.stretch2spp(
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(gamma_new, gamma, decimal=8)
def test_function(self):
center_x, center_y = 0., 0.
x, y = 1, 1
output = self.model.function(x,
y,
tangential_stretch=2,
radial_stretch=1,
curvature=1. / 2,
direction=0,
center_x=0,
center_y=0)
theta_E, gamma, center_x_spp, center_y_spp = self.model.stretch2spp(
tangential_stretch=2,
radial_stretch=1,
curvature=1. / 2,
direction=0,
center_x=0,
center_y=0)
out_spp = self.spp.function(1, 1, theta_E, gamma, center_x_spp,
center_y_spp)
alpha_x, alpha_y = self.spp.derivatives(center_x, center_y, theta_E,
gamma, center_x_spp,
center_y_spp)
f_0 = alpha_x * (x - center_x) + alpha_y * (y - center_y)
npt.assert_almost_equal(output, out_spp - f_0, 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, gamma, center_x_spp, center_y_spp = self.model.stretch2spp(
tangential_stretch, radial_stretch, curvature, direction, center_x,
center_y)
f_x, f_y = self.spp.derivatives(x, y, theta_E, gamma, center_x_spp,
center_y_spp)
f_x0, f_y0 = self.spp.derivatives(center_x, center_y, theta_E, gamma,
center_x_spp, center_y_spp)
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 - f_x0, decimal=8)
npt.assert_almost_equal(f_y_new, f_y - f_y0, decimal=8)
def test_hessian(self):
lens = LensModel(lens_model_list=['CURVED_ARC'])
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 = 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 = -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)