def test_potential():
ell = LevelEllipsoid('GRS80')
n_test = 100 # * 2
r_ = np.geomspace(ell.b, 1e8, num=n_test)
r_ = np.append(-r_[::-1], r_)
x, y, z = np.meshgrid(r_, r_, r_, indexing='ij')
sphlat, _, radius = transform.cartesian_to_spherical(x, y, z)
cond = radius < ell.polar_equation(sphlat)
x_ = np.ma.masked_where(cond, x).compressed()
y_ = np.ma.masked_where(cond, y).compressed()
z_ = np.ma.masked_where(cond, z).compressed()
sphlat, _, radius = transform.cartesian_to_spherical(x_, y_, z_)
rlat, _, u = transform.cartesian_to_ellipsoidal(x_, y_, z_, ell=ell)
gravity_potential_ell = ell.gravity_potential(rlat, u)
gravity_potential_sph = ell.gravity_potential_sph(sphlat, radius)
np.testing.assert_almost_equal(
gravity_potential_sph,
gravity_potential_ell, decimal=4)
gravitational_potential_ell = ell.gravitational_potential(rlat, u)
gravitational_potential_sph = ell.gravitational_potential_sph(
sphlat, radius)
np.testing.assert_almost_equal(
gravitational_potential_sph,
gravitational_potential_ell, decimal=4)
def test_surface_gravity_potential():
ell = LevelEllipsoid('GRS80')
# geodetic latitude
lat = np.arange(-90, 90, 0.1, dtype=float)
rlat, _, u = transform.geodetic_to_ellipsoidal(lat=lat,
lon=0.0, height=0.0, ell=ell)
gravity_potential_0 = ell.gravity_potential(rlat, u)
np.testing.assert_almost_equal(
ell.surface_potential,
gravity_potential_0, decimal=5)
geoclat, _, radius = transform.geodetic_to_spherical(lat=lat,
lon=0.0, height=0.0, ell=ell)
gravity_potential_sph_0 = ell.gravity_potential_sph(geoclat, radius)
np.testing.assert_almost_equal(
ell.surface_potential,
gravity_potential_sph_0, decimal=5)
np.testing.assert_almost_equal(
gravity_potential_sph_0,
gravity_potential_0, decimal=5)