class TestGaussianKappaEllipse(object):
"""
test the Gaussian with Gaussian kappa
"""
def setup(self):
self.multi = MultiGaussianKappaEllipse()
self.single = GaussianEllipsePotential()
def test_function(self):
x, y = 1, 2
amp = 1
sigma = 1
e1, e2 = 0.1, -0.1
center_x, center_y = 1, 0
f_ = self.multi.function(x, y, amp=[amp], sigma=[sigma], e1=e1, e2=e2, center_x=center_x, center_y=center_y)
f_single = self.single.function(x, y, amp=amp, sigma=sigma, e1=e1, e2=e2, center_x=center_x, center_y=center_y)
npt.assert_almost_equal(f_, f_single, decimal=8)
def test_derivatives(self):
x, y = 1, 2
amp = 1
sigma = 1
e1, e2 = 0.1, -0.1
center_x, center_y = 1, 0
f_x, f_y = self.multi.derivatives(x, y, amp=[amp], sigma=[sigma], e1=e1, e2=e2, center_x=center_x, center_y=center_y)
f_x_s, f_y_s = self.single.derivatives(x, y, amp=amp, sigma=sigma, e1=e1, e2=e2, center_x=center_x, center_y=center_y)
npt.assert_almost_equal(f_x, f_x_s, decimal=8)
npt.assert_almost_equal(f_y, f_y_s, decimal=8)
def test_hessian(self):
x, y = 1, 2
amp = 1
sigma = 1
e1, e2 = 0.1, -0.1
center_x, center_y = 1, 0
f_xx, f_yy, f_xy = self.multi.hessian(x, y, amp=[amp], sigma=[sigma], e1=e1, e2=e2, center_x=center_x, center_y=center_y)
f_xx_s, f_yy_s, f_xy_s = self.single.hessian(x, y, amp=amp, sigma=sigma, e1=e1, e2=e2, center_x=center_x, center_y=center_y)
npt.assert_almost_equal(f_xx, f_xx_s, decimal=8)
npt.assert_almost_equal(f_yy, f_yy_s, decimal=8)
npt.assert_almost_equal(f_xy, f_xy_s, decimal=8)
def test_density_2d(self):
x, y = 1, 2
amp = 1
sigma = 1
e1, e2 = 0.1, -0.1
center_x, center_y = 1, 0
f_ = self.multi.density_2d(x, y, amp=[amp], sigma=[sigma], e1=e1, e2=e2, center_x=center_x, center_y=center_y)
f_single = self.single.density_2d(x, y, amp=amp, sigma=sigma, e1=e1, e2=e2, center_x=center_x, center_y=center_y)
npt.assert_almost_equal(f_, f_single, decimal=8)
def test_density(self):
r = 1
amp = 1
sigma = 1
e1, e2 = 0.1, -0.1
f_ = self.multi.density(r, amp=[amp], sigma=[sigma], e1=e1, e2=e2)
f_single = self.single.density(r, amp=amp, sigma=sigma, e1=e1, e2=e2)
npt.assert_almost_equal(f_, f_single, decimal=8)
class MultiGaussianKappaEllipse(object):
"""
"""
param_names = ['amp', 'sigma', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {
'amp': 0,
'sigma': 0,
'e1': -0.5,
'e2': -0.5,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'amp': 100,
'sigma': 100,
'e1': 0.5,
'e2': 0.5,
'center_x': 100,
'center_y': 100
}
def __init__(self):
self.gaussian_kappa = GaussianEllipsePotential()
def function(self,
x,
y,
amp,
sigma,
e1,
e2,
center_x=0,
center_y=0,
scale_factor=1):
"""
:param x:
:param y:
:param amp:
:param sigma:
:param center_x:
:param center_y:
:return:
"""
f_ = np.zeros_like(x, dtype=float)
for i in range(len(amp)):
f_ += self.gaussian_kappa.function(x,
y,
amp=scale_factor * amp[i],
sigma=sigma[i],
e1=e1,
e2=e2,
center_x=center_x,
center_y=center_y)
return f_
def derivatives(self,
x,
y,
amp,
sigma,
e1,
e2,
center_x=0,
center_y=0,
scale_factor=1):
"""
:param x:
:param y:
:param amp:
:param sigma:
:param center_x:
:param center_y:
:return:
"""
f_x, f_y = np.zeros_like(x, dtype=float), np.zeros_like(x, dtype=float)
for i in range(len(amp)):
f_x_i, f_y_i = self.gaussian_kappa.derivatives(x,
y,
amp=scale_factor *
amp[i],
sigma=sigma[i],
e1=e1,
e2=e2,
center_x=center_x,
center_y=center_y)
f_x += f_x_i
f_y += f_y_i
return f_x, f_y
def hessian(self,
x,
y,
amp,
sigma,
e1,
e2,
center_x=0,
center_y=0,
scale_factor=1):
"""
:param x:
:param y:
:param amp:
:param sigma:
:param center_x:
:param center_y:
:return:
"""
f_xx, f_yy, f_xy = np.zeros_like(x, dtype=float), np.zeros_like(
x, dtype=float), np.zeros_like(x, dtype=float)
for i in range(len(amp)):
f_xx_i, f_yy_i, f_xy_i = self.gaussian_kappa.hessian(
x,
y,
amp=scale_factor * amp[i],
sigma=sigma[i],
e1=e1,
e2=e2,
center_x=center_x,
center_y=center_y)
f_xx += f_xx_i
f_yy += f_yy_i
f_xy += f_xy_i
return f_xx, f_yy, f_xy
def density(self, r, amp, sigma, e1, e2, scale_factor=1):
"""
:param r:
:param amp:
:param sigma:
:return:
"""
d_ = np.zeros_like(r, dtype=float)
for i in range(len(amp)):
d_ += self.gaussian_kappa.density(r, scale_factor * amp[i],
sigma[i], e1, e2)
return d_
def density_2d(self,
x,
y,
amp,
sigma,
e1,
e2,
center_x=0,
center_y=0,
scale_factor=1):
"""
:param R:
:param am:
:param sigma_x:
:param sigma_y:
:return:
"""
d_3d = np.zeros_like(x, dtype=float)
for i in range(len(amp)):
d_3d += self.gaussian_kappa.density_2d(x, y, scale_factor * amp[i],
sigma[i], e1, e2, center_x,
center_y)
return d_3d
def mass_3d_lens(self, R, amp, sigma, e1, e2, scale_factor=1):
"""
:param R:
:param amp:
:param sigma:
:return:
"""
mass_3d = np.zeros_like(R, dtype=float)
for i in range(len(amp)):
mass_3d += self.gaussian_kappa.mass_3d_lens(
R, scale_factor * amp[i], sigma[i], e1, e2)
return mass_3d
class TestGaussianKappaPot(object):
"""
test the Gaussian with Gaussian kappa
"""
def setup(self):
self.gaussian_kappa = GaussianKappa()
self.ellipse = GaussianEllipsePotential()
def test_function(self):
x = 1
y = 1
e1, e2 = 0, 0
sigma = 1
amp = 1
f_ = self.ellipse.function(x, y, amp, sigma, e1, e2)
f_sphere = self.gaussian_kappa.function(x, y, amp=amp, sigma=sigma)
npt.assert_almost_equal(f_, f_sphere, decimal=8)
def test_derivatives(self):
x = 1
y = 1
e1, e2 = 0, 0
sigma = 1
amp = 1
f_x, f_y = self.ellipse.derivatives(x, y, amp, sigma, e1, e2)
f_x_sphere, f_y_sphere = self.gaussian_kappa.derivatives(x, y, amp=amp, sigma=sigma)
npt.assert_almost_equal(f_x, f_x_sphere, decimal=8)
npt.assert_almost_equal(f_y, f_y_sphere, decimal=8)
def test_hessian(self):
x = 1
y = 1
e1, e2 = 0, 0
sigma = 1
amp = 1
f_xx, f_xy, f_yx, f_yy = self.ellipse.hessian(x, y, amp, sigma, e1, e2)
f_xx_sphere, f_xy_sphere, f_yx_sphere, f_yy_sphere = self.gaussian_kappa.hessian(x, y, amp=amp, sigma=sigma)
npt.assert_almost_equal(f_xx, f_xx_sphere, decimal=5)
npt.assert_almost_equal(f_yy, f_yy_sphere, decimal=5)
npt.assert_almost_equal(f_xy, f_xy_sphere, decimal=5)
npt.assert_almost_equal(f_xy, f_yx, decimal=8)
def test_density_2d(self):
x = 1
y = 1
e1, e2 = 0, 0
sigma = 1
amp = 1
f_ = self.ellipse.density_2d(x, y, amp, sigma, e1, e2)
f_sphere = self.gaussian_kappa.density_2d(x, y, amp=amp, sigma=sigma)
npt.assert_almost_equal(f_, f_sphere, decimal=8)
def test_mass_2d(self):
r = 1
e1, e2 = 0, 0
sigma = 1
amp = 1
f_ = self.ellipse.mass_2d(r, amp, sigma, e1, e2)
f_sphere = self.gaussian_kappa.mass_2d(r, amp=amp, sigma=sigma)
npt.assert_almost_equal(f_, f_sphere, decimal=8)
def test_mass_2d_lens(self):
r = 1
e1, e2 = 0, 0
sigma = 1
amp = 1
f_ = self.ellipse.mass_2d_lens(r, amp, sigma, e1, e2)
f_sphere = self.gaussian_kappa.mass_2d_lens(r, amp=amp, sigma=sigma)
npt.assert_almost_equal(f_, f_sphere, decimal=8)