def test_predict_sec_above_below():
'''
Test SEC prediction at fixed locations relative to pole of SECS below ground
'''
# place SEC at north pole, 0 longitude, and 100 km altitude
lats = np.array([90, 90])
lons = np.array([0, 0])
rads = np.array([6378000. + 100000., 6378000. - 100000.])
secs_llr = np.array(list(zip(lats, lons, rads)))
# initialize secs object
sec_above_below = secs(secs_llr, amps=None, amps_var=None)
# initialize secsRegressor object
epsilon = 0.1
secsR = secsRegressor(sec_above_below, epsilon)
# predict magnetic disturbance at equator and at pole
latp = np.array([0, 90])
lonp = np.array([0, 0])
radp = np.array([6378000., 6378000.])
pred_llr = np.array(list(zip(latp, lonp, radp)))
# set SEC amplitude to 10,000 Amps, and make prediction
amps = np.array([1e4, -1e4])
pred = secsR.predict(pred_llr, amps)
# calculate exact solution using relationships found in Pulkinnen et al.'s
# 2003 Earth Planets Space article "Separation of the geomagnetic variation
# field on the ground into external and internal parts using the elementary
# current system method"
mu0 = 4 * np.pi * 1e-7 # N / A^2
Btheta90 = -(mu0 * amps[0]) / (4. * np.pi * radp[0] *
np.sin((90-latp[0]) * np.pi/180.)) * \
(((radp[0]/rads[0]) - np.cos((90-latp[0]) * np.pi/180.)) / \
np.sqrt(1 - (2. * radp[0] * np.cos((90-latp[0]) * np.pi/180.)) / \
rads[0] + (radp[0]/rads[0])**2) + \
np.cos((90-latp[0]) * np.pi/180.) )
Btheta90 += -(mu0 * amps[1]) / (4. * np.pi * radp[0] *
np.sin((90-latp[0]) * np.pi/180.)) * \
((radp[0] - rads[1] * np.cos((90-latp[0]) * np.pi/180.)) / \
np.sqrt(radp[0]**2 -
(2. * radp[0] * rads[1] * np.cos((90-latp[0]) * np.pi/180.)) + \
rads[1]**2) - 1.)
Brad0 = (mu0 * amps[0]) / (4. * np.pi * radp[1]) * \
(1. / (np.sqrt(1. - 2. * radp[1] * np.cos((90-latp[1]) * np.pi/180.) / \
rads[0] + (radp[1] / rads[0])**2) ) - 1. )
Brad0 += (mu0 * amps[1] * rads[1]) / (4. * np.pi * radp[1]**2) * \
(1. / (np.sqrt(1. - 2. * rads[1] * np.cos((90-latp[1]) * np.pi/180.) / \
radp[1] + (rads[1] / radp[1])**2) ) - 1. )
assert_approx_equal(pred[0, 0], Btheta90, significant=9)
assert_approx_equal(pred[1, 2], Brad0, significant=9)
def test_predict_sec_above_Bphis():
'''
Test SEC prediction at fixed locations relative to pole of SECS above ground;
this test actually checks the phi (longitudinal) vector component
'''
# place SEC at equator, 0 longitude, and 100 km altitude
lats = np.array([0])
lons = np.array([0])
rads = np.array([6378000. + 100000.])
secs_llr = np.array(list(zip(lats, lons, rads)))
# initialize secs object
sec_above = secs(secs_llr, amps=None, amps_var=None)
# initialize secsRegressor object
epsilon = 0.1
secsR = secsRegressor(sec_above, epsilon)
# predict magnetic disturbance at equator, but 90 degrees east and west
# of pole position; these are where the theta component caculated in the
# SEC frame will equal the negative of the phi component in geographic
# coordinates
latp = np.array([0, 0])
lonp = np.array([-90, 90])
radp = np.array([6378000., 6378000.])
pred_llr = np.array(list(zip(latp, lonp, radp)))
# set SEC amplitude to 10,000 Amps, and make prediction
amps = 1e4
pred = secsR.predict(pred_llr, amps)
# calculate exact solution using relationships found in Pulkinnen et al.'s
# 2003 Earth Planets Space article "Separation of the geomagnetic variation
# field on the ground into external and internal parts using the elementary
# current system method"
mu0 = 4 * np.pi * 1e-7 # N / A^2
Btheta90 = -(mu0 * amps) / (4. * np.pi * radp[0] *
np.sin((lonp[0] - lons[0]) * np.pi/180.)) * \
(((radp[0]/rads[0]) - np.cos((lonp[0] - lons[0]) * np.pi/180.)) / \
np.sqrt(1 - (2. * radp[0] * np.cos((lonp[0] - lons[0]) * np.pi/180.)) / \
rads[0] + (radp[0]/rads[0])**2) + \
np.cos((lonp[0] - lons[0]) * np.pi/180.) )
Bphi90minus = -Btheta90
Bphi90plus = Btheta90
assert_approx_equal(pred[0, 1], Bphi90minus, significant=9)
assert_approx_equal(pred[1, 1], Bphi90plus, significant=9)
def test_fit_sec_above_below():
'''
Fit uncorrupted B-field predictions generated by known SECs above and below
the pole
'''
# place SEC at north pole, 0 latitude, and 100 km altitude
lats = np.array([90, 90])
lons = np.array([0, 0])
rads = np.array([6378000. + 100000., 6378000. - 100000.])
secs_llr = np.array(list(zip(lats, lons, rads)))
# initialize secs object
sec_above_below = secs(secs_llr, amps=None, amps_var=None)
# initialize secsRegressor object
epsilon = 0.1
secsR = secsRegressor(sec_above_below, epsilon)
# predict magnetic disturbance at equator and at pole
latp = np.linspace(90, 0, 901)
lonp = np.zeros(latp.shape)
radp = np.zeros(latp.shape) + 6378000.
pred_llr = np.array(list(zip(latp, lonp, radp)))
# set SEC amplitude to 10,000 Amps, and make prediction
amps = np.array([1e4, -1e4])
pred = secsR.predict(pred_llr, amps)
# fit the 2 SECs assuming 1nT uncertainty on observations
secsR.fit(pred_llr, pred, np.ones(pred.shape) * 1e-9)
assert_approx_equal(secsR.secs_.amps[0], 10000., significant=9)
assert_approx_equal(secsR.secs_.amps[1], -10000., significant=9)
assert_approx_equal(np.sqrt(secsR.secs_.amps_var[0]),
286.46658513,
significant=9)
assert_approx_equal(np.sqrt(secsR.secs_.amps_var[1]),
299.97580929,
significant=9)
def test_regress_construct():
'''
Test construction of secs regressor
'''
# place SEC at north pole, 0 latitude, and 100 km altitude
lats = np.array([90])
lons = np.array([0])
rads = np.array([6378000 + 100000])
secs_llr = np.array(list(zip(lats, lons, rads)))
# initialize secs object
sec1 = secs(secs_llr, amps=None, amps_var=None)
# initialize secsRegressor object
epsilon = 0.1
secsR = secsRegressor(sec1, epsilon)
assert_equal(secsR.secs.n_secs, 1)
assert_equal(secsR.secs.latitude, 90)
assert_equal(secsR.secs.longitude, 0)
assert_equal(secsR.secs.radius, 6378000 + 100000)
assert_equal(secsR.epsilon, 0.1)
for good in np.isfinite(dist_Z.data)]])
# end 'for ob in stations:'
# necessary to remove these outside the loop due to implicit loop indexing
for bo in badObs:
iagaCodes.remove(bo)
# convert lists to numpy arrays with time varying along axis 0
obs_lat_lon_r = np.transpose(obs_lat_lon_r, (0, 1)) # time-invariant
obs_Btheta_Bphi_Br = np.transpose(obs_Btheta_Bphi_Br, (2, 0, 1))
obs_sigma_Btheta_Bphi_Br = np.transpose(obs_sigma_Btheta_Bphi_Br,
(2, 0, 1))
# initialize the secs object and secsRegressor
imp = secsRegressor(secs(secs_lat_lon_r), epsilon)
# Finally, generate a map for each time step
X = []
Y = []
Z = []
for tidx in np.arange(len(obs_Btheta_Bphi_Br)):
# these element-wise comparisons help avoid re-calculation of various
# imp attributes that would be much more computationally intensive
if np.array_equal(obs_Btheta_Bphi_Br[tidx], imp.obs_Btheta_Bphi_Br_):
obs_Bt_Bp_Br = imp.obs_Btheta_Bphi_Br_
else:
obs_Bt_Bp_Br = obs_Btheta_Bphi_Br[tidx]
if np.array_equal(obs_sigma_Btheta_Bphi_Br[tidx],
imp.obs_sigma_Btheta_Bphi_Br_):