def test_rotate_gauss(self):
# test 1
time = 20 # random day
nmax = 4
kmax = 2
s = timer()
base_1, base_2, base_3 = c.basevectors_gsm(time)
matrix = c.rotate_gauss(nmax, kmax, base_1, base_2, base_3)
e = timer()
# load matfile
test = load_matfile(MATFILE_PATH, 'test_rotate_gauss')
matrix_mat = test['m_all'].transpose() # transposed in Matlab code
runtime = test['runtime']
print(" Time for matrix computation (Python): ", e - s)
print(" Time for matrix computation (Matlab): {:}".format(
runtime[0, 0]))
# absolute tolerance to account for close-to-zero matrix entries
self.assertIsNone(np.testing.assert_allclose(
matrix, matrix_mat, atol=1e-8))
# test 2
# rotate around y-axis to have dipole axis aligned with x-axis
base_1 = np.array([0, 0, -1])
base_2 = np.array([0, 1, 0])
base_3 = np.array([1, 0, 0])
nmax = 1 # only dipole terms
kmax = 1
matrix = c.rotate_gauss(nmax, kmax, base_1, base_2, base_3)
desired = np.array([[0, -1, 0], [1, 0, 0], [0, 0, 1]])
self.assertIsNone(np.testing.assert_allclose(
matrix, desired, atol=1e-10))
# test 3
time = np.arange(9).reshape((3, 3)) # random day
nmax = 4
kmax = 2
base_1, base_2, base_3 = c.basevectors_gsm(time)
matrix = c.rotate_gauss(nmax, kmax, base_1, base_2, base_3)
self.assertEqual(matrix.shape, (3, 3, 24, 8))
def test_matrix_geo_to_base(self):
theta_geo = np.linspace(1, 179, 10)
phi_geo = np.linspace(-179, 179, 10)
time = np.linspace(-300, 10000, 10)
for reference in ['sm', 'gsm', 'mag']:
print(f' Testing {reference.upper()}')
if reference == 'mag':
base_1, base_2, base_3 = c.basevectors_mag()
elif reference == 'sm':
base_1, base_2, base_3 = c.basevectors_sm(time)
elif reference == 'gsm':
base_1, base_2, base_3 = c.basevectors_gsm(time)
theta_ref, phi_ref, R = c.matrix_geo_to_base(
theta_geo, phi_geo, base_1, base_2, base_3, inverse=False)
theta_geo2, phi_geo2, R2 = c.matrix_geo_to_base(
theta_ref, phi_ref, base_1, base_2, base_3, inverse=True)
self.assertIsNone(
np.testing.assert_allclose(theta_geo, theta_geo2))
self.assertIsNone(
np.testing.assert_allclose(phi_geo, phi_geo2))
R_full = np.matmul(R, R2)
R_full2 = np.zeros((theta_geo.size, 3, 3))
for n in range(3):
R_full2[..., n, n] = 1.
self.assertIsNone(
np.testing.assert_allclose(R_full, R_full2, atol=1e-7))
def test_rotate_gsm_vector(self):
time = 20
nmax = 1
kmax = 1
radius = R_REF
theta_geo = 90/6
phi_geo = 90/8
g_gsm = np.array([1, 2, -1])
base_1, base_2, base_3 = c.basevectors_gsm(time)
matrix = c.rotate_gauss(nmax, kmax, base_1, base_2, base_3)
g_geo = np.matmul(matrix, g_gsm)
B_geo_1 = m.synth_values(g_geo, radius, theta_geo, phi_geo)
B_geo_1 = np.array(B_geo_1)
theta_gsm, phi_gsm, R = c.matrix_geo_to_base(theta_geo, phi_geo,
base_1, base_2, base_3)
B_gsm = m.synth_values(g_gsm, radius, theta_gsm, phi_gsm)
B_gsm = np.array(B_gsm)
B_geo_2 = np.matmul(R.transpose(), B_gsm)
self.assertIsNone(np.testing.assert_allclose(
B_geo_1, B_geo_2, rtol=1e-5))
def test_synth_rotate_gauss(self):
"""
Tests the accuracy of the Fourier representation of tranformation
matrices by comparing them with directly computed matrices (they are
considered correct).
"""
for reference in ['gsm', 'sm']:
print(f' Testing {reference.upper()} frame of reference.')
# load spectrum to synthesize matrices in time-domain
filepath = c.basicConfig[f'file.{reference.upper()}_spectrum']
try:
data = np.load(filepath)
except FileNotFoundError as e:
raise ValueError(
'Reference file "frequency_spectrum_{reference}.npz"'
' not found in "chaosmagpy/lib/".'
' Correct reference?') from e
frequency = data['frequency'] # oscillations per day
spectrum = data['spectrum']
print(" Testing 50 times within 1996 and 2024.")
for time in np.linspace(-4 * 365.25, 24 * 365.25, 50):
matrix_time = c.synth_rotate_gauss(time,
frequency,
spectrum,
scaled=data['scaled'])
nmax = int(np.sqrt(spectrum.shape[1] + 1) - 1)
kmax = int(np.sqrt(spectrum.shape[2] + 1) - 1)
if reference == 'gsm':
base_1, base_2, base_3 = c.basevectors_gsm(time)
elif reference == 'sm':
base_1, base_2, base_3 = c.basevectors_sm(time)
matrix = c.rotate_gauss(nmax, kmax, base_1, base_2, base_3)
stat = np.amax(np.abs(matrix - np.squeeze(matrix_time)))
print(' Computed year {:4.2f}, '
'max. abs. error = {:.3e}'.format(
time / 365.25 + 2000, stat),
end='')
if stat > 0.001:
print(' ' + min(int(stat / 0.001), 10) * '*')
else:
print('')
self.assertIsNone(
np.testing.assert_allclose(matrix,
np.squeeze(matrix_time),
rtol=1e-1,
atol=1e-1))
def test_geo_to_base(self):
time = np.linspace(1, 100, 10)
theta_geo = np.linspace(1, 179, 10)
phi_geo = np.linspace(-180, 179, 10)
# TEST GSM COORDINATES
# GSM test: load matfile
test = load_matfile(MATFILE_PATH, 'test_geo_to_gsm')
# reduce 2-D matrix to 1-D vectors
theta_gsm_mat = np.ravel(test['theta_gsm'])
phi_gsm_mat = np.ravel(test['phi_gsm'])
gsm_1, gsm_2, gsm_3 = c.basevectors_gsm(time)
theta_gsm, phi_gsm = c.geo_to_base(
theta_geo, phi_geo, gsm_1, gsm_2, gsm_3)
self.assertIsNone(np.testing.assert_allclose(theta_gsm, theta_gsm_mat))
self.assertIsNone(np.testing.assert_allclose(phi_gsm, phi_gsm_mat))
# test the inverse option: GEO -> GSM -> GEO
theta_geo2, phi_geo2 = c.geo_to_base(
theta_gsm, phi_gsm, gsm_1, gsm_2, gsm_3, inverse=True)
self.assertIsNone(np.testing.assert_allclose(theta_geo, theta_geo2))
self.assertIsNone(np.testing.assert_allclose(
phi_geo, c.center_azimuth(phi_geo2)))
# test the inverse option: GSM -> GEO -> GSM
theta_gsm2, phi_gsm2 = c.geo_to_base(
theta_geo2, phi_geo2, gsm_1, gsm_2, gsm_3)
self.assertIsNone(np.testing.assert_allclose(theta_gsm, theta_gsm2))
self.assertIsNone(np.testing.assert_allclose(
c.center_azimuth(phi_gsm), c.center_azimuth(phi_gsm2)))
# TEST SM COORDINATES
# SM test: load matfile
test = load_matfile(MATFILE_PATH, 'test_geo_to_sm')
# reduce 2-D matrix to 1-D vectors
theta_sm_mat = np.ravel(test['theta_sm'])
phi_sm_mat = np.ravel(test['phi_sm'])
sm_1, sm_2, sm_3 = c.basevectors_sm(time)
theta_sm, phi_sm = c.geo_to_base(
theta_geo, phi_geo, sm_1, sm_2, sm_3)
self.assertIsNone(np.testing.assert_allclose(theta_sm, theta_sm_mat))
self.assertIsNone(np.testing.assert_allclose(phi_sm, phi_sm_mat))
# test the inverse option: GEO -> SM -> GEO
theta_geo2, phi_geo2 = c.geo_to_base(
theta_sm, phi_sm, sm_1, sm_2, sm_3, inverse=True)
self.assertIsNone(np.testing.assert_allclose(theta_geo, theta_geo2))
self.assertIsNone(np.testing.assert_allclose(phi_geo, phi_geo2))
# test the inverse option: SM -> GEO -> SM
theta_sm2, phi_sm2 = c.geo_to_base(
theta_geo2, phi_geo2, sm_1, sm_2, sm_3)
self.assertIsNone(np.testing.assert_allclose(theta_sm, theta_sm2))
self.assertIsNone(np.testing.assert_allclose(phi_sm, phi_sm2))