def test_total_flux(self):
deltapix = 0.1
x_grid, y_grid = util.make_grid(numPix=400, deltapix=deltapix)
r_eff = 1
I_eff = 1.
n_sersic = 2
flux_analytic = self.sersic.total_flux(amp=I_eff,
R_sersic=r_eff,
n_sersic=n_sersic,
e1=0,
e2=0)
flux_grid = self.sersic.function(x_grid,
y_grid,
R_sersic=r_eff,
n_sersic=n_sersic,
amp=I_eff)
flux_numeric = np.sum(flux_grid) * deltapix**2
npt.assert_almost_equal(flux_numeric / flux_analytic, 1, decimal=2)
# and here we check with ellipticity
e1, e2 = 0.1, 0
sersic_elliptic_major = SersicElliptic(smoothing=0.02,
sersic_major_axis=True)
flux_analytic_ell = sersic_elliptic_major.total_flux(amp=I_eff,
R_sersic=r_eff,
n_sersic=n_sersic,
e1=e1,
e2=e2)
flux_grid = sersic_elliptic_major.function(x_grid,
y_grid,
R_sersic=r_eff,
n_sersic=n_sersic,
amp=I_eff,
e1=e1,
e2=e2)
flux_numeric_ell = np.sum(flux_grid) * deltapix**2
npt.assert_almost_equal(flux_numeric_ell / flux_analytic_ell,
1,
decimal=2)
e1, e2 = 0.1, 0
sersic_elliptic_product = SersicElliptic(smoothing=0.02,
sersic_major_axis=False)
flux_analytic_ell = sersic_elliptic_product.total_flux(
amp=I_eff, R_sersic=r_eff, n_sersic=n_sersic, e1=e1, e2=e2)
flux_grid = sersic_elliptic_product.function(x_grid,
y_grid,
R_sersic=r_eff,
n_sersic=n_sersic,
amp=I_eff,
e1=e1,
e2=e2)
flux_numeric_ell = np.sum(flux_grid) * deltapix**2
npt.assert_almost_equal(flux_numeric_ell / flux_analytic_ell,
1,
decimal=2)
class TestSersicEllipseGaussDec(object):
"""
This class tests the methods for Gauss-decomposed elliptic Sersic
convergence.
"""
def setup(self):
self.sersic_gauss = SersicEllipseGaussDec()
self.sersic_light = SersicElliptic()
self.sersic_sphere = Sersic()
def test_function(self):
"""
Test the potential function of Gauss-decomposed elliptical Sersic by
asserting that the numerical derivative of the computed potential
matches with the analytical derivative values.
:return:
:rtype:
"""
k_eff = 1.
R_sersic = 1.
n_sersic = 1.
e1 = 0.2
e2 = 0.2
center_x = 0.
center_y = 0.
diff = 1.e-6
n = 5
xs = np.linspace(0.5 * R_sersic, 2. * R_sersic, n)
ys = np.linspace(0.5 * R_sersic, 2. * R_sersic, n)
for x, y in zip(xs, ys):
func = self.sersic_gauss.function(x, y, e1=e1, e2=e2,
center_x=center_x,
center_y=center_y,
n_sersic=n_sersic,
R_sersic=R_sersic,
k_eff=k_eff
)
func_dx = self.sersic_gauss.function(x+diff, y, e1=e1, e2=e2,
center_x=center_x,
center_y=center_y,
n_sersic=n_sersic,
R_sersic=R_sersic,
k_eff=k_eff
)
func_dy = self.sersic_gauss.function(x, y+diff, e1=e1, e2=e2,
center_x=center_x,
center_y=center_y,
n_sersic=n_sersic,
R_sersic=R_sersic,
k_eff=k_eff
)
f_x_num = (func_dx - func) / diff
f_y_num = (func_dy - func) / diff
f_x, f_y = self.sersic_gauss.derivatives(x, y, e1=e1, e2=e2,
center_x=center_x,
center_y=center_y,
n_sersic=n_sersic,
R_sersic=R_sersic,
k_eff=k_eff
)
npt.assert_almost_equal(f_x_num, f_x, decimal=4)
npt.assert_almost_equal(f_y_num, f_y, decimal=4)
def test_derivatives(self):
"""
Test the derivative function of Gauss-decomposed elliptical Sersic by
matching with the spherical case.
:return:
:rtype:
"""
k_eff = 1.
R_sersic = 1.
n_sersic = 1.
e1 = 5.e-5
e2 = 0.
center_x = 0.
center_y = 0.
n = 10
x = np.linspace(0.5*R_sersic, 2.*R_sersic, n)
y = np.linspace(0.5*R_sersic, 2.*R_sersic, n)
X, Y = np.meshgrid(x, y)
f_x_s, f_y_s = self.sersic_sphere.derivatives(X, Y, center_x=center_x,
center_y=center_y,
n_sersic=n_sersic,
R_sersic=R_sersic,
k_eff=k_eff
)
f_x, f_y = self.sersic_gauss.derivatives(X, Y, e1=e1, e2=e2,
center_x=center_x,
center_y=center_y,
n_sersic=n_sersic,
R_sersic=R_sersic,
k_eff=k_eff
)
npt.assert_allclose(f_x, f_x_s, rtol=1e-3, atol=0.)
npt.assert_allclose(f_y, f_y_s, rtol=1e-3, atol=0.)
npt.assert_almost_equal(f_x, f_x_s, decimal=3)
npt.assert_almost_equal(f_y, f_y_s, decimal=3)
def test_hessian(self):
"""
Test the Hessian function of Gauss-decomposed elliptical Sersic by
matching with the spherical case.
:return:
:rtype:
"""
k_eff = 1.
R_sersic = 1.
n_sersic = 1.
e1 = 5e-5
e2 = 0.
center_x = 0.
center_y = 0.
n = 10
x = np.linspace(0.5 * R_sersic, 2. * R_sersic, n)
y = np.linspace(0.5 * R_sersic, 2. * R_sersic, n)
X, Y = np.meshgrid(x, y)
f_xx_s, f_yy_s, f_xy_s = self.sersic_sphere.hessian(X, Y,
center_x=center_x,
center_y=center_y,
n_sersic=n_sersic,
R_sersic=R_sersic,
k_eff=k_eff)
f_xx, f_yy, f_xy = self.sersic_gauss.hessian(X, Y, e1=e1, e2=e2,
center_x=center_x,
center_y=center_y,
n_sersic=n_sersic,
R_sersic=R_sersic,
k_eff=k_eff)
npt.assert_almost_equal(f_xx_s, f_xx, decimal=3)
npt.assert_almost_equal(f_yy_s, f_yy, decimal=3)
npt.assert_almost_equal(f_xy_s, f_xy, decimal=3)
def test_density_2d(self):
"""
Test the density function of Gauss-decomposed elliptical Sersic by
checking with the spherical case.
:return:
:rtype:
"""
k_eff = 1.
R_sersic = 1.
n_sersic = 1.
e1 = 0.2
e2 = 0.2
center_x = 0.
center_y = 0.
n = 100
x = np.logspace(-1., 1., n)
y = np.logspace(-1., 1., n)
X, Y = np.meshgrid(x, y)
sersic_analytic = self.sersic_light.function(X, Y, e1=e1, e2=e2,
center_x=center_x,
center_y=center_y,
n_sersic=n_sersic,
R_sersic=R_sersic,
amp=k_eff)
sersic_gauss = self.sersic_gauss.density_2d(X, Y, e1=e1, e2=e2,
center_x=center_x,
center_y=center_y,
n_sersic=n_sersic,
R_sersic=R_sersic,
k_eff=k_eff)
assert np.all(
np.abs(sersic_analytic - sersic_gauss) / np.sqrt(sersic_analytic)
* 100. < 1.)
def test_gauss_decompose_sersic(self):
"""
Test that `gauss_decompose_sersic()` decomposes the Sersic profile within 1%
Poission noise at R_sersic.
:return:
:rtype:
"""
y = np.logspace(-1., 1., 100)
k_eff = 1.
R_sersic = 1.
n_sersic = 1.
amps, sigmas = self.sersic_gauss.gauss_decompose(n_sersic=n_sersic,
R_sersic=R_sersic, k_eff=k_eff)
sersic = self.sersic_gauss.get_kappa_1d(y, n_sersic=n_sersic,
R_sersic=R_sersic, k_eff=k_eff)
back_sersic = np.zeros_like(y)
for a, s in zip(amps, sigmas):
back_sersic += a * np.exp(-y ** 2 / 2. / s ** 2)
assert np.all(np.abs(sersic-back_sersic)/np.sqrt(sersic)*100. < 1.)
class TestSersic(object):
"""
tests the Gaussian methods
"""
def setup(self):
self.sersic = Sersic(smoothing=0.02)
self.sersic_elliptic = SersicElliptic(smoothing=0.02)
self.core_sersic = CoreSersic(smoothing=0.02)
def test_sersic(self):
x = np.array([1])
y = np.array([2])
I0_sersic = 1
R_sersic = 1
n_sersic = 1
center_x = 0
center_y = 0
values = self.sersic.function(x, y, I0_sersic, R_sersic, n_sersic,
center_x, center_y)
npt.assert_almost_equal(values[0], 0.12658651833626802, decimal=6)
x = np.array([0])
y = np.array([0])
values = self.sersic.function(x, y, I0_sersic, R_sersic, n_sersic,
center_x, center_y)
npt.assert_almost_equal(values[0], 5.1482559148107292, decimal=2)
x = np.array([2, 3, 4])
y = np.array([1, 1, 1])
values = self.sersic.function(x, y, I0_sersic, R_sersic, n_sersic,
center_x, center_y)
npt.assert_almost_equal(values[0], 0.12658651833626802, decimal=6)
npt.assert_almost_equal(values[1], 0.026902273598180083, decimal=6)
npt.assert_almost_equal(values[2], 0.0053957432862338055, decimal=6)
value = self.sersic.function(1000, 0, I0_sersic, R_sersic, n_sersic,
center_x, center_y)
npt.assert_almost_equal(value, 0, decimal=8)
def test_symmetry_r_sersic(self):
x = np.array([2, 3, 4])
y = np.array([1, 1, 1])
I0_sersic = 1
R_sersic1 = 1
R_sersic2 = 0.1
n_sersic = 1
center_x = 0
center_y = 0
values1 = self.sersic.function(x * R_sersic1, y * R_sersic1, I0_sersic,
R_sersic1, n_sersic, center_x, center_y)
values2 = self.sersic.function(x * R_sersic2, y * R_sersic2, I0_sersic,
R_sersic2, n_sersic, center_x, center_y)
npt.assert_almost_equal(values1[0], values2[0], decimal=6)
npt.assert_almost_equal(values1[1], values2[1], decimal=6)
npt.assert_almost_equal(values1[2], values2[2], decimal=6)
def test_sersic_center(self):
x = 0.01
y = 0.
I0_sersic = 1
R_sersic = 0.1
n_sersic = 4.
center_x = 0
center_y = 0
values = self.sersic.function(x, y, I0_sersic, R_sersic, n_sersic,
center_x, center_y)
npt.assert_almost_equal(values, 12.688073819377406, decimal=6)
def test_sersic_elliptic(self):
x = np.array([1])
y = np.array([2])
I0_sersic = 1
R_sersic = 1
n_sersic = 1
phi_G = 1
q = 0.9
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
center_x = 0
center_y = 0
values = self.sersic_elliptic.function(x, y, I0_sersic, R_sersic,
n_sersic, e1, e2, center_x,
center_y)
npt.assert_almost_equal(values[0], 0.12595366113005077, decimal=6)
x = np.array([0])
y = np.array([0])
values = self.sersic_elliptic.function(x, y, I0_sersic, R_sersic,
n_sersic, e1, e2, center_x,
center_y)
npt.assert_almost_equal(values[0], 5.1482553482055664, decimal=2)
x = np.array([2, 3, 4])
y = np.array([1, 1, 1])
values = self.sersic_elliptic.function(x, y, I0_sersic, R_sersic,
n_sersic, e1, e2, center_x,
center_y)
npt.assert_almost_equal(values[0], 0.11308277793465012, decimal=6)
npt.assert_almost_equal(values[1], 0.021188620675507107, decimal=6)
npt.assert_almost_equal(values[2], 0.0037276744362724477, decimal=6)
def test_core_sersic(self):
x = np.array([1])
y = np.array([2])
I0 = 1
Rb = 1
Re = 2
gamma = 3
n = 1
phi_G = 1
q = 0.9
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
center_x = 0
center_y = 0
values = self.core_sersic.function(x, y, I0, Rb, Re, n, gamma, e1, e2,
center_x, center_y)
npt.assert_almost_equal(values[0], 0.84489101, decimal=8)
x = np.array([0])
y = np.array([0])
values = self.core_sersic.function(x, y, I0, Rb, Re, n, gamma, e1, e2,
center_x, center_y)
npt.assert_almost_equal(values[0], 288406.09, decimal=0)
x = np.array([2, 3, 4])
y = np.array([1, 1, 1])
values = self.core_sersic.function(x, y, I0, Rb, Re, n, gamma, e1, e2,
center_x, center_y)
npt.assert_almost_equal(values[0], 0.79749529635325933, decimal=6)
npt.assert_almost_equal(values[1], 0.33653478121594838, decimal=6)
npt.assert_almost_equal(values[2], 0.14050402887681532, decimal=6)
def test_total_flux(self):
r_eff = 0.2
I_eff = 1.
n_sersic = 4
flux = self.sersic._total_flux(r_eff, I_eff, n_sersic)
npt.assert_almost_equal(flux, 0.9065917451904356, decimal=5)
class TestSersic(object):
"""
tests the Gaussian methods
"""
def setup(self):
self.sersic = Sersic(smoothing=0.02)
self.sersic_elliptic = SersicElliptic(smoothing=0.02)
self.core_sersic = CoreSersic(smoothing=0.02)
def test_sersic(self):
x = np.array([1])
y = np.array([2])
I0_sersic = 1
R_sersic = 1
n_sersic = 1
center_x = 0
center_y = 0
values = self.sersic.function(x, y, I0_sersic, R_sersic, n_sersic, center_x, center_y)
npt.assert_almost_equal(values[0], 0.12658651833626802, decimal=6)
x = np.array([0])
y = np.array([0])
values = self.sersic.function( x, y, I0_sersic, R_sersic, n_sersic, center_x, center_y)
npt.assert_almost_equal(values[0], 5.1482559148107292, decimal=2)
x = np.array([2,3,4])
y = np.array([1,1,1])
values = self.sersic.function( x, y, I0_sersic, R_sersic, n_sersic, center_x, center_y)
npt.assert_almost_equal(values[0], 0.12658651833626802, decimal=6)
npt.assert_almost_equal(values[1], 0.026902273598180083, decimal=6)
npt.assert_almost_equal(values[2], 0.0053957432862338055, decimal=6)
value = self.sersic.function(1000, 0, I0_sersic, R_sersic, n_sersic, center_x, center_y)
npt.assert_almost_equal(value, 0, decimal=8)
def test_symmetry_r_sersic(self):
x = np.array([2,3,4])
y = np.array([1,1,1])
I0_sersic = 1
R_sersic1 = 1
R_sersic2 = 0.1
n_sersic = 1
center_x = 0
center_y = 0
values1 = self.sersic.function(x*R_sersic1, y*R_sersic1, I0_sersic, R_sersic1, n_sersic, center_x, center_y)
values2 = self.sersic.function(x*R_sersic2, y*R_sersic2, I0_sersic, R_sersic2, n_sersic, center_x, center_y)
npt.assert_almost_equal(values1[0], values2[0], decimal=6)
npt.assert_almost_equal(values1[1], values2[1], decimal=6)
npt.assert_almost_equal(values1[2], values2[2], decimal=6)
def test_sersic_center(self):
x = 0.01
y = 0.
I0_sersic = 1
R_sersic = 0.1
n_sersic = 4.
center_x = 0
center_y = 0
values = self.sersic.function(x, y, I0_sersic, R_sersic, n_sersic, center_x, center_y)
npt.assert_almost_equal(values, 12.688073819377406, decimal=6)
def test_sersic_elliptic(self):
x = np.array([1])
y = np.array([2])
I0_sersic = 1
R_sersic = 1
n_sersic = 1
phi_G = 1
q = 0.9
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
center_x = 0
center_y = 0
values = self.sersic_elliptic.function(x, y, I0_sersic, R_sersic, n_sersic, e1, e2, center_x, center_y)
npt.assert_almost_equal(values[0], 0.12595366113005077, decimal=6)
x = np.array([0])
y = np.array([0])
values = self.sersic_elliptic.function(x, y, I0_sersic, R_sersic, n_sersic, e1, e2, center_x, center_y)
npt.assert_almost_equal(values[0], 5.1482553482055664, decimal=2)
x = np.array([2,3,4])
y = np.array([1,1,1])
values = self.sersic_elliptic.function(x, y, I0_sersic, R_sersic, n_sersic, e1, e2, center_x, center_y)
npt.assert_almost_equal(values[0], 0.11308277793465012, decimal=6)
npt.assert_almost_equal(values[1], 0.021188620675507107, decimal=6)
npt.assert_almost_equal(values[2], 0.0037276744362724477, decimal=6)
def test_core_sersic(self):
x = np.array([1])
y = np.array([2])
I0 = 1
Rb = 1
Re = 2
gamma = 3
n = 1
phi_G = 1
q = 0.9
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
center_x = 0
center_y = 0
values = self.core_sersic.function(x, y, I0, Rb, Re, n, gamma, e1, e2, center_x, center_y)
npt.assert_almost_equal(values[0], 0.10338957116342086, decimal=8)
x = np.array([0])
y = np.array([0])
values = self.core_sersic.function(x, y, I0, Rb, Re, n, gamma, e1, e2, center_x, center_y)
npt.assert_almost_equal(values[0], 187852.14004235074, decimal=0)
x = np.array([2,3,4])
y = np.array([1,1,1])
values = self.core_sersic.function(x, y, I0, Rb, Re, n, gamma, e1, e2, center_x, center_y)
npt.assert_almost_equal(values[0], 0.09255079955772508, decimal=6)
npt.assert_almost_equal(values[1], 0.01767817014938002, decimal=6)
npt.assert_almost_equal(values[2], 0.0032541063777438853, decimal=6)
def test_total_flux(self):
deltapix = 0.1
x_grid, y_grid = util.make_grid(numPix=400, deltapix=deltapix)
r_eff = 1
I_eff = 1.
n_sersic = 2
flux_analytic = self.sersic.total_flux(amp=I_eff, R_sersic=r_eff, n_sersic=n_sersic, e1=0, e2=0)
flux_grid = self.sersic.function(x_grid, y_grid, R_sersic=r_eff, n_sersic=n_sersic, amp=I_eff)
flux_numeric = np.sum(flux_grid) * deltapix**2
npt.assert_almost_equal(flux_numeric/flux_analytic, 1, decimal=2)
# and here we check with ellipticity
e1, e2 = 0.1, 0
flux_analytic_ell = self.sersic.total_flux(amp=I_eff, R_sersic=r_eff, n_sersic=n_sersic, e1=e1, e2=e2)
flux_grid = self.sersic_elliptic.function(x_grid, y_grid, R_sersic=r_eff, n_sersic=n_sersic, amp=I_eff, e1=e1, e2=e2)
flux_numeric_ell = np.sum(flux_grid) * deltapix ** 2
print(flux_analytic, flux_analytic_ell, flux_numeric_ell)
npt.assert_almost_equal(flux_numeric_ell / flux_analytic_ell, 1, decimal=2)