class TestGaussianKappa(object):
"""
test the Gaussian with Gaussian kappa
"""
def setup(self):
self.gaussian_kappa = MultiGaussian_kappa()
self.gaussian = Gaussian()
self.g_kappa = GaussianKappa()
def test_derivatives(self):
x = np.linspace(0, 5, 10)
y = np.linspace(0, 5, 10)
amp = [1. * 2 * np.pi]
center_x = 0.
center_y = 0.
sigma = [1.]
f_x, f_y = self.gaussian_kappa.derivatives(x, y, amp, sigma, center_x,
center_y)
npt.assert_almost_equal(f_x[2], 0.63813558702212059, decimal=8)
npt.assert_almost_equal(f_y[2], 0.63813558702212059, decimal=8)
def test_hessian(self):
x = np.linspace(0, 5, 10)
y = np.linspace(0, 5, 10)
amp = [1. * 2 * np.pi]
center_x = 0.
center_y = 0.
sigma = [1.]
f_xx, f_yy, f_xy = self.gaussian_kappa.hessian(x, y, amp, sigma,
center_x, center_y)
kappa = 1. / 2 * (f_xx + f_yy)
kappa_true = self.gaussian.function(x, y, amp[0], sigma[0], sigma[0],
center_x, center_y)
print(kappa_true)
print(kappa)
npt.assert_almost_equal(kappa[0], kappa_true[0], decimal=5)
npt.assert_almost_equal(kappa[1], kappa_true[1], decimal=5)
def test_density_2d(self):
x = np.linspace(0, 5, 10)
y = np.linspace(0, 5, 10)
amp = [1. * 2 * np.pi]
center_x = 0.
center_y = 0.
sigma = [1.]
f_xx, f_yy, f_xy = self.gaussian_kappa.hessian(x, y, amp, sigma,
center_x, center_y)
kappa = 1. / 2 * (f_xx + f_yy)
amp_3d = self.g_kappa._amp2d_to_3d(amp, sigma[0], sigma[0])
density_2d = self.gaussian_kappa.density_2d(x, y, amp_3d, sigma,
center_x, center_y)
npt.assert_almost_equal(kappa[1], density_2d[1], decimal=5)
npt.assert_almost_equal(kappa[2], density_2d[2], decimal=5)
def test_density(self):
amp = [1. * 2 * np.pi]
sigma = [1.]
density = self.gaussian_kappa.density(1., amp, sigma)
npt.assert_almost_equal(density, 0.6065306597126334, decimal=8)
class TestGaussianKappa(object):
"""
test the Gaussian with Gaussian kappa
"""
def setup(self):
self.gaussian_kappa = GaussianKappa()
self.gaussian = Gaussian()
def test_derivatives(self):
x = np.linspace(0, 5, 10)
y = np.linspace(0, 5, 10)
amp = 1. * 2 * np.pi
center_x = 0.
center_y = 0.
sigma_x = 1.
sigma_y = 1.
f_x, f_y = self.gaussian_kappa.derivatives(x, y, amp, sigma_x, sigma_y,
center_x, center_y)
npt.assert_almost_equal(f_x[2], 0.63813558702212059, decimal=8)
npt.assert_almost_equal(f_y[2], 0.63813558702212059, decimal=8)
def test_hessian(self):
x = np.linspace(0, 5, 10)
y = np.linspace(0, 5, 10)
amp = 1. * 2 * np.pi
center_x = 0.
center_y = 0.
sigma_x = 1.
sigma_y = 1.
f_xx, f_yy, f_xy = self.gaussian_kappa.hessian(x, y, amp, sigma_x,
sigma_y, center_x,
center_y)
kappa = 1. / 2 * (f_xx + f_yy)
kappa_true = self.gaussian.function(x, y, amp, sigma_x, sigma_y,
center_x, center_y)
print(kappa_true)
print(kappa)
npt.assert_almost_equal(kappa[0], kappa_true[0], decimal=5)
npt.assert_almost_equal(kappa[1], kappa_true[1], decimal=5)
def test_density_2d(self):
x = np.linspace(0, 5, 10)
y = np.linspace(0, 5, 10)
amp = 1. * 2 * np.pi
center_x = 0.
center_y = 0.
sigma_x = 1.
sigma_y = 1.
f_xx, f_yy, f_xy = self.gaussian_kappa.hessian(x, y, amp, sigma_x,
sigma_y, center_x,
center_y)
kappa = 1. / 2 * (f_xx + f_yy)
amp_3d = self.gaussian_kappa._amp2d_to_3d(amp, sigma_x, sigma_y)
density_2d = self.gaussian_kappa.density_2d(x, y, amp_3d, sigma_x,
sigma_y, center_x,
center_y)
npt.assert_almost_equal(kappa[1], density_2d[1], decimal=5)
npt.assert_almost_equal(kappa[2], density_2d[2], decimal=5)
def test_3d_2d_convention(self):
x = np.linspace(0, 5, 10)
y = np.linspace(0, 5, 10)
amp = 1. * 2 * np.pi
center_x = 0.
center_y = 0.
sigma_x = 1.
sigma_y = 1.
amp_3d = self.gaussian_kappa._amp2d_to_3d(amp, sigma_x, sigma_y)
density_2d_gauss = self.gaussian_kappa.density_2d(
x, y, amp_3d, sigma_x, sigma_y, center_x, center_y)
density_2d = self.gaussian.function(x, y, amp, sigma_x, sigma_y,
center_x, center_y)
npt.assert_almost_equal(density_2d_gauss[1], density_2d[1], decimal=5)
