def assert_lens_integrals(self, Model, kwargs):
"""
checks whether the integral in projection of the density_lens() function is the convergence
:param Model: lens model instance
:param kwargs: keyword arguments of lens model
:return:
"""
lensModel = Model()
int_profile = ProfileIntegrals(lensModel)
r = 2.
kappa_num = int_profile.density_2d(r, kwargs, lens_param=True)
f_xx, f_yy, f_xy = lensModel.hessian(r, 0, **kwargs)
kappa = 1./2 * (f_xx + f_yy)
npt.assert_almost_equal(kappa_num, kappa, decimal=2)
def assert_lens_integrals(self, Model, kwargs, pi_convention=True):
"""
checks whether the integral in projection of the density_lens() function is the convergence
:param Model: lens model instance
:param kwargs: keyword arguments of lens model
:return:
"""
lensModel = Model()
int_profile = ProfileIntegrals(lensModel)
r = 2.
kappa_num = int_profile.density_2d(r, kwargs, lens_param=True)
f_xx, f_xy, f_yx, f_yy = lensModel.hessian(r, 0, **kwargs)
kappa = 1. / 2 * (f_xx + f_yy)
npt.assert_almost_equal(kappa_num, kappa, decimal=2)
try:
del kwargs['center_x']
del kwargs['center_y']
except:
pass
bool_mass_2d_lens = False
try:
mass_2d = lensModel.mass_2d_lens(r, **kwargs)
bool_mass_2d_lens = True
except:
pass
if bool_mass_2d_lens:
alpha_x, alpha_y = lensModel.derivatives(r, 0, **kwargs)
alpha = np.sqrt(alpha_x**2 + alpha_y**2)
if pi_convention:
npt.assert_almost_equal(alpha, mass_2d / r / np.pi, decimal=5)
else:
npt.assert_almost_equal(alpha, mass_2d / r, decimal=5)
try:
mass_3d = lensModel.mass_3d_lens(r, **kwargs)
bool_mass_3d_lens = True
except:
bool_mass_3d_lens = False
if bool_mass_3d_lens:
mass_3d_num = int_profile.mass_enclosed_3d(r,
kwargs_profile=kwargs,
lens_param=True)
print(mass_3d, mass_3d_num, 'test num')
npt.assert_almost_equal(mass_3d / mass_3d_num, 1, decimal=2)
def assert_lens_integrals(self, Model, kwargs):
"""
checks whether the integral in projection of the density_lens() function is the convergence
:param Model: lens model instance
:param kwargs: keyword arguments of lens model
:return:
"""
lensModel = Model()
int_profile = ProfileIntegrals(lensModel)
r = 2.
kappa_num = int_profile.density_2d(r, kwargs, lens_param=True)
f_xx, f_yy, f_xy = lensModel.hessian(r, 0, **kwargs)
kappa = 1. / 2 * (f_xx + f_yy)
npt.assert_almost_equal(kappa_num, kappa, decimal=2)
if hasattr(lensModel, 'mass_2d_lens'):
mass_2d = lensModel.mass_2d_lens(r, **kwargs)
alpha_x, alpha_y = lensModel.derivatives(r, 0, **kwargs)
alpha = np.sqrt(alpha_x**2 + alpha_y**2)
npt.assert_almost_equal(alpha, mass_2d / r / np.pi, decimal=5)
class TestP_JAFFW(object):
"""
tests the Gaussian methods
"""
def setup(self):
self.profile = PJaffe()
def test_function(self):
x = np.array([1])
y = np.array([2])
sigma0 = 1.
Ra, Rs = 0.5, 0.8
values = self.profile.function(x, y, sigma0, Ra, Rs)
assert values[0] == 0.87301557036070054
x = np.array([0])
y = np.array([0])
sigma0 = 1.
Ra, Rs = 0.5, 0.8
values = self.profile.function(x, y, sigma0, Ra, Rs)
assert values[0] == 0.20267440905756931
x = np.array([2, 3, 4])
y = np.array([1, 1, 1])
values = self.profile.function(x, y, sigma0, Ra, Rs)
assert values[0] == 0.87301557036070054
assert values[1] == 1.0842781309377669
assert values[2] == 1.2588604178849985
def test_derivatives(self):
x = np.array([1])
y = np.array([2])
sigma0 = 1.
Ra, Rs = 0.5, 0.8
f_x, f_y = self.profile.derivatives(x, y, sigma0, Ra, Rs)
assert f_x[0] == 0.11542369603751264
assert f_y[0] == 0.23084739207502528
x = np.array([0])
y = np.array([0])
f_x, f_y = self.profile.derivatives(x, y, sigma0, Ra, Rs)
assert f_x[0] == 0
assert f_y[0] == 0
x = np.array([1, 3, 4])
y = np.array([2, 1, 1])
values = self.profile.derivatives(x, y, sigma0, Ra, Rs)
assert values[0][0] == 0.11542369603751264
assert values[1][0] == 0.23084739207502528
assert values[0][1] == 0.19172866612512479
assert values[1][1] == 0.063909555375041588
def test_hessian(self):
x = np.array([1])
y = np.array([2])
sigma0 = 1.
Ra, Rs = 0.5, 0.8
f_xx, f_yy, f_xy = self.profile.hessian(x, y, sigma0, Ra, Rs)
assert f_xx[0] == 0.077446121589827679
assert f_yy[0] == -0.036486601753227141
assert f_xy[0] == -0.075955148895369876
x = np.array([1, 3, 4])
y = np.array([2, 1, 1])
values = self.profile.hessian(x, y, sigma0, Ra, Rs)
assert values[0][0] == 0.077446121589827679
assert values[1][0] == -0.036486601753227141
assert values[2][0] == -0.075955148895369876
assert values[0][1] == -0.037260794616683197
assert values[1][1] == 0.052668405375961035
assert values[2][1] == -0.033723449997241584
def test_mass_tot(self):
rho0 = 1.
Ra, Rs = 0.5, 0.8
values = self.profile.mass_tot(rho0, Ra, Rs)
npt.assert_almost_equal(values, 2.429441083345073, decimal=10)
def test_mass_3d_lens(self):
mass = self.profile.mass_3d_lens(r=1, sigma0=1, Ra=0.5, Rs=0.8)
npt.assert_almost_equal(mass, 0.87077306005349242, decimal=8)
def test_grav_pot(self):
x = 1
y = 2
rho0 = 1.
Ra, Rs = 0.5, 0.8
grav_pot = self.profile.grav_pot(x,
y,
rho0,
Ra,
Rs,
center_x=0,
center_y=0)
npt.assert_almost_equal(grav_pot, 0.89106542283974155, decimal=10)
class TestP_JAFFW(object):
"""
tests the Gaussian methods
"""
def setup(self):
self.profile = PJaffe()
def test_function(self):
x = np.array([1])
y = np.array([2])
sigma0 = 1.
Ra, Rs = 0.5, 0.8
values = self.profile.function(x, y, sigma0, Ra, Rs)
npt.assert_almost_equal(values[0], 0.87301557036070054, decimal=8)
x = np.array([0])
y = np.array([0])
sigma0 = 1.
Ra, Rs = 0.5, 0.8
values = self.profile.function(x, y, sigma0, Ra, Rs)
npt.assert_almost_equal(values[0], 0.20267440905756931, decimal=8)
x = np.array([2, 3, 4])
y = np.array([1, 1, 1])
values = self.profile.function(x, y, sigma0, Ra, Rs)
npt.assert_almost_equal(values[0], 0.87301557036070054, decimal=8)
npt.assert_almost_equal(values[1], 1.0842781309377669, decimal=8)
npt.assert_almost_equal(values[2], 1.2588604178849985, decimal=8)
def test_derivatives(self):
x = np.array([1])
y = np.array([2])
sigma0 = 1.
Ra, Rs = 0.5, 0.8
f_x, f_y = self.profile.derivatives(x, y, sigma0, Ra, Rs)
npt.assert_almost_equal(f_x[0], 0.11542369603751264, decimal=8)
npt.assert_almost_equal(f_y[0], 0.23084739207502528, decimal=8)
x = np.array([0])
y = np.array([0])
f_x, f_y = self.profile.derivatives(x, y, sigma0, Ra, Rs)
assert f_x[0] == 0
assert f_y[0] == 0
x = np.array([1, 3, 4])
y = np.array([2, 1, 1])
values = self.profile.derivatives(x, y, sigma0, Ra, Rs)
npt.assert_almost_equal(values[0][0], 0.11542369603751264, decimal=8)
npt.assert_almost_equal(values[1][0], 0.23084739207502528, decimal=8)
npt.assert_almost_equal(values[0][1], 0.19172866612512479, decimal=8)
npt.assert_almost_equal(values[1][1], 0.063909555375041588, decimal=8)
def test_hessian(self):
x = np.array([1])
y = np.array([2])
sigma0 = 1.
Ra, Rs = 0.5, 0.8
f_xx, f_xy, f_yx, f_yy = self.profile.hessian(x, y, sigma0, Ra, Rs)
npt.assert_almost_equal(f_xx[0], 0.077446121589827679, decimal=8)
npt.assert_almost_equal(f_yy[0], -0.036486601753227141, decimal=8)
npt.assert_almost_equal(f_xy[0], -0.075955148895369876, decimal=8)
x = np.array([1, 3, 4])
y = np.array([2, 1, 1])
values = self.profile.hessian(x, y, sigma0, Ra, Rs)
npt.assert_almost_equal(values[0][0], 0.077446121589827679, decimal=8)
npt.assert_almost_equal(values[3][0], -0.036486601753227141, decimal=8)
npt.assert_almost_equal(values[1][0], values[2][0], decimal=8)
def test_mass_tot(self):
rho0 = 1.
Ra, Rs = 0.5, 0.8
values = self.profile.mass_tot(rho0, Ra, Rs)
npt.assert_almost_equal(values, 2.429441083345073, decimal=10)
def test_mass_3d_lens(self):
mass = self.profile.mass_3d_lens(r=1, sigma0=1, Ra=0.5, Rs=0.8)
npt.assert_almost_equal(mass, 0.87077306005349242, decimal=8)
def test_grav_pot(self):
x = 1
y = 2
rho0 = 1.
r = np.sqrt(x**2 + y**2)
Ra, Rs = 0.5, 0.8
grav_pot = self.profile.grav_pot(r, rho0, Ra, Rs)
npt.assert_almost_equal(grav_pot, 0.89106542283974155, decimal=10)