def test_divergence_free_magnetic_directions():
"Make sure the divergence free magnetic field angles are correct"
# Place the SEC at the equator
sec_r = R_EARTH + 100
sec_latlonr = np.array([[0., 0., sec_r]])
# Going around in a circle from the point
obs_latlonr = np.array([[5., 0., R_EARTH], [0., 5., R_EARTH],
[-5, 0., R_EARTH], [0., -5., R_EARTH]])
B = np.squeeze(pysecs.T_df(obs_latlonr, sec_latlonr))
angles = np.arctan2(B[:, 0], B[:, 1])
# southward, westward, northward, eastward
expected_angles = np.deg2rad([-90, 180., 90., 0.])
assert_allclose(angles, expected_angles, rtol=1e-10, atol=1e-10)
def test_divergence_free_magnetic_magnitudes_obs_under():
"Make sure the divergence free magnetic amplitudes are correct."
# Place the SEC at the North Pole
sec_r = R_EARTH + 100
sec_latlonr = np.array([[0., 0., sec_r]])
# Going out in an angle from the SEC (in longitude)
angles = np.linspace(0.1, 180)
obs_r = R_EARTH
obs_latlonr = np.zeros(angles.shape + (3, ))
obs_latlonr[:, 1] = angles
obs_latlonr[:, 2] = obs_r
B = np.squeeze(pysecs.T_df(obs_latlonr, sec_latlonr))
# All x components should be zero (angles goes around the equator and all
# quantities should be parallel to that)
assert_allclose(np.zeros(angles.shape), B[:, 0], atol=1e-16)
# Actual magnitude
mu0 = 4 * np.pi * 1e-7
# simplify calculations by storing this ratio
x = obs_r / sec_r
sin_theta = np.sin(np.deg2rad(angles))
cos_theta = np.cos(np.deg2rad(angles))
factor = 1. / np.sqrt(1 - 2 * x * cos_theta + x**2)
# Amm & Viljanen: Equation 9
Br = mu0 / (4 * np.pi * obs_r) * (factor - 1)
# Bz in opposite direction of Br
assert_allclose(-Br, B[:, 2])
# Amm & Viljanen: Equation 10
Btheta = -mu0 / (4 * np.pi * obs_r) * (factor *
(x - cos_theta) + cos_theta)
Btheta = np.divide(Btheta,
sin_theta,
out=np.zeros_like(sin_theta),
where=sin_theta != 0)
assert_allclose(Btheta, B[:, 1])