def convert_to_dipole(coords, lat_ngp, lon_ngp,
coord_type_in=GEOCENTRIC_SPHERICAL):
""" Convert coordinates (by default geocentric spherical)
to dipole coordinates defined by the given latitude and longitude
of the geomagnetic pole.
The dipole coordinates are a simple rotated coordinate frame in which
the North pole (dipole latitude == 0) is aligned with the geomagnetic pole
and the prime meridian (dipole longitude == 0) is the meridian
passing trough the geomagnetic pole.
"""
rotation_matrix = get_dipole_rotation_matrix(lat_ngp, lon_ngp)
coords = convert(coords, coord_type_in, GEOCENTRIC_CARTESIAN)
coords = dot(coords, rotation_matrix)
coords = convert(coords, GEOCENTRIC_CARTESIAN, GEOCENTRIC_SPHERICAL)
return coords
def difflat_spherical_to_geodetic(latitude):
coords = zeros(latitude.shape + (3,))
coords[..., 0] = latitude
coords[..., 2] = 6371.2
return convert(
coords, GEOCENTRIC_SPHERICAL, GEODETIC_ABOVE_WGS84
)[..., 0] - latitude
def reference_sheval(cls, coords):
coords_spherical = convert(
coords, cls.source_coordinate_system, GEOCENTRIC_SPHERICAL
)
potential = empty(coords_spherical.shape[:-1])
gradient = empty(coords_spherical.shape)
iterator = nditer(
[
potential,
gradient[..., 0],
gradient[..., 1],
gradient[..., 2],
coords_spherical[..., 0],
coords_spherical[..., 1],
coords_spherical[..., 2],
],
op_flags=[
['writeonly'], ['writeonly'], ['writeonly'], ['writeonly'],
['readonly'], ['readonly'], ['readonly'],
],
)
for pot, grd_n, grd_e, grd_r, lat, lon, rad in iterator:
pot[...], grd_n[...], grd_e[...], grd_r[...] = (
cls._spherical_harmonics(lat, lon, rad)
)
gradient = cls._rotate_gradient(gradient, coords_spherical)
potential *= cls.scale_potential
for idx, scale in enumerate(cls.scale_gradient):
gradient[..., idx] *= scale
return potential, gradient
def convert_to_dipole(coords,
lat_ngp,
lon_ngp,
coord_type_in=GEOCENTRIC_SPHERICAL):
""" Convert coordinates (by default geocentric spherical)
to dipole coordinates defined by the given latitude and longitude
of the geomagnetic pole.
The dipole coordinates are a simple rotated coordinate frame in which
the North pole (dipole latitude == 0) is aligned with the geomagnetic pole
and the prime meridian (dipole longitude == 0) is the meridian
passing trough the geomagnetic pole.
"""
rotation_matrix = get_dipole_rotation_matrix(lat_ngp, lon_ngp)
coords = convert(coords, coord_type_in, GEOCENTRIC_CARTESIAN)
coords = dot(coords, rotation_matrix)
coords = convert(coords, GEOCENTRIC_CARTESIAN, GEOCENTRIC_SPHERICAL)
return coords
def test_eval_reference_values(self):
times, src_coords, expected_result = self.reference_values
coords = convert(src_coords, GEOCENTRIC_SPHERICAL, self.coord_type_in)
model_result = self.eval_model(times, coords)
try:
assert_allclose(model_result, expected_result)
except AssertionError:
print(tuple(float(f) for f in model_result))
raise
def test_eval_reference_values(self):
times, src_coords, expected_result = self.reference_values
coords = convert(src_coords, GEOCENTRIC_SPHERICAL, self.coord_type_in)
model_result = self.eval_model(times, coords)
try:
assert_allclose(model_result, expected_result)
except AssertionError:
print(tuple(float(f) for f in model_result))
raise
def _rotate_gradient(cls, vectors, coords):
if cls.target_coordinate_system == GEOCENTRIC_SPHERICAL:
return vectors
elif cls.target_coordinate_system == GEOCENTRIC_CARTESIAN:
latd = coords[..., 0]
lond = coords[..., 1]
return vrot_sph2cart(vectors, latd, lond)
elif cls.target_coordinate_system == GEODETIC_ABOVE_WGS84:
dlatd = convert(
coords, GEOCENTRIC_SPHERICAL, cls.target_coordinate_system
)[..., 0] - coords[..., 0]
return vrot_sph2geod(vectors, dlatd)
def test_eval_multi_time_invalid(self):
times = array([
time
for time in [nan, self.time_before, self.time, self.time_after]
if not isinf(time)
])
coords = convert(array([(0, 0, 6371.2) for _ in times]),
GEOCENTRIC_SPHERICAL, self.coord_type_in)
assert_allclose(
self.eval_model(times, coords),
self.eval_reference(times, coords),
)
def _rotate_gradient(cls, vectors, coords):
if cls.target_coordinate_system == GEOCENTRIC_SPHERICAL:
return vectors
elif cls.target_coordinate_system == GEOCENTRIC_CARTESIAN:
latd = coords[..., 0]
lond = coords[..., 1]
return vrot_sph2cart(vectors, latd, lond)
elif cls.target_coordinate_system == GEODETIC_ABOVE_WGS84:
dlatd = convert(coords, GEOCENTRIC_SPHERICAL,
cls.target_coordinate_system)[..., 0] - coords[...,
0]
return vrot_sph2geod(vectors, dlatd)
def _rotate_gradient(cls, vectors, coords_dipole, coords_in):
lat_dipole, lon_dipole = coords_dipole[..., 0], coords_dipole[..., 1]
if cls.target_coordinate_system == GEOCENTRIC_CARTESIAN:
lat_out, lon_out = None, None
else:
coords_out = convert(coords_in, cls.source_coordinate_system,
cls.target_coordinate_system)
lat_out, lon_out = coords_out[..., 0], coords_out[..., 1]
return vrot_from_dipole(vectors, cls.lat_ngp, cls.lon_ngp, lat_dipole,
lon_dipole, lat_out, lon_out,
cls.target_coordinate_system)
def test_eval_multi_time_invalid(self):
times = array([
time for time in [nan, self.time_before, self.time, self.time_after]
if not isinf(time)
])
coords = convert(
array([(0, 0, 6371.2) for _ in times]),
GEOCENTRIC_SPHERICAL, self.coord_type_in
)
assert_allclose(
self.eval_model(times, coords),
self.eval_reference(times, coords),
)
def _rotate_gradient(cls, vectors, coords_dipole, coords_in):
lat_dipole, lon_dipole = coords_dipole[..., 0], coords_dipole[..., 1]
if cls.target_coordinate_system == GEOCENTRIC_CARTESIAN:
lat_out, lon_out = None, None
else:
coords_out = convert(
coords_in, cls.source_coordinate_system,
cls.target_coordinate_system
)
lat_out, lon_out = coords_out[..., 0], coords_out[..., 1]
return vrot_from_dipole(
vectors, cls.lat_ngp, cls.lon_ngp, lat_dipole, lon_dipole,
lat_out, lon_out, cls.target_coordinate_system
)
def reference_vrot_from_dipole(cls, vectors, coords, latitude, longitude):
coords = asarray(coords)
rotation_matrix = get_dipole_rotation_matrix(latitude, longitude)
coords_dipole = convert_to_dipole(coords, latitude, longitude)
lat_dipole = coords_dipole[..., 0]
lon_dipole = coords_dipole[..., 1]
vectors = vrot_sph2cart(vectors, lat_dipole, lon_dipole)
vectors = dot(vectors, rotation_matrix.transpose())
if cls.target_coords_type != GEOCENTRIC_CARTESIAN:
coords_out = convert(
coords, GEOCENTRIC_SPHERICAL, cls.target_coords_type
)
lat_out = coords_out[..., 0]
lon_out = coords_out[..., 1]
vectors = vrot_cart2sph(vectors, lat_out, lon_out)
return vectors
def eval_vrot_from_dipole(cls, vectors, coords, latitude, longitude):
coords = asarray(coords)
coords_dipole = convert_to_dipole(coords, latitude, longitude)
lat_dipole = coords_dipole[..., 0]
lon_dipole = coords_dipole[..., 1]
if cls.target_coords_type != GEOCENTRIC_CARTESIAN:
coords_out = convert(
coords, GEOCENTRIC_SPHERICAL, cls.target_coords_type
)
lat_out = coords_out[..., 0]
lon_out = coords_out[..., 1]
else:
lat_out, lon_out = None, None
return vrot_from_dipole(
vectors, latitude, longitude, lat_dipole, lon_dipole,
lat_out, lon_out, cls.target_coords_type
)
def reference_sheval(cls, coords):
coords_spherical = convert(coords, cls.source_coordinate_system,
GEOCENTRIC_SPHERICAL)
potential = empty(coords_spherical.shape[:-1])
gradient = empty(coords_spherical.shape)
iterator = nditer(
[
potential,
gradient[..., 0],
gradient[..., 1],
gradient[..., 2],
coords_spherical[..., 0],
coords_spherical[..., 1],
coords_spherical[..., 2],
],
op_flags=[
['writeonly'],
['writeonly'],
['writeonly'],
['writeonly'],
['readonly'],
['readonly'],
['readonly'],
],
)
for pot, grd_n, grd_e, grd_r, lat, lon, rad in iterator:
pot[...], grd_n[...], grd_e[...], grd_r[...] = (
cls._spherical_harmonics(lat, lon, rad))
gradient = cls._rotate_gradient(gradient, coords_spherical)
potential *= cls.scale_potential
for idx, scale in enumerate(cls.scale_gradient):
gradient[..., idx] *= scale
return potential, gradient
def eval_convert_to_dipole(coords, latitude, longitude):
# to avoid pole longitude ambiguity compare Cartesian coordinates
return convert(
convert_to_dipole(coords, latitude, longitude),
GEOCENTRIC_SPHERICAL, GEOCENTRIC_CARTESIAN
)
def eval_convert(cls, coords):
return convert(coords, cls.source_coordinate_system,
cls.target_coordinate_system)
def reference_convert_to_dipole(coords, latitude, longitude):
rotation_matrix = get_dipole_rotation_matrix(latitude, longitude)
coords = convert(coords, GEOCENTRIC_SPHERICAL, GEOCENTRIC_CARTESIAN)
coords = dot(coords, rotation_matrix)
return coords
def coordinates(self):
return convert(array([
(lat, lon, 6371.2*uniform(1.0, 2.0)) for lat, lon
in product(self.range_lat, self.range_lon)
]), GEOCENTRIC_SPHERICAL, self.coord_type_in)
def coordinates(self):
return convert(array([
(lat, lon, 6371.2*uniform(1.0, 2.0)) for lat, lon
in product(self.range_lat, self.range_lon)
]), GEOCENTRIC_SPHERICAL, self.coord_type_in)
def difflat_geodetic_to_spherical(latitude):
coords = zeros(latitude.shape + (3,))
coords[..., 0] = latitude
return convert(
coords, GEODETIC_ABOVE_WGS84, GEOCENTRIC_SPHERICAL
)[..., 0] - latitude
def difflat_geodetic_to_spherical(latitude):
coords = zeros(latitude.shape + (3, ))
coords[..., 0] = latitude
return convert(coords, GEODETIC_ABOVE_WGS84,
GEOCENTRIC_SPHERICAL)[..., 0] - latitude
def difflat_spherical_to_geodetic(latitude):
coords = zeros(latitude.shape + (3, ))
coords[..., 0] = latitude
coords[..., 2] = 6371.2
return convert(coords, GEOCENTRIC_SPHERICAL,
GEODETIC_ABOVE_WGS84)[..., 0] - latitude
def eval_convert(cls, coords):
return convert(
coords, cls.source_coordinate_system, cls.target_coordinate_system
)
def coordinates(self):
return convert(
array([(lat, lon, 6371.2 * (1.0 + random()))
for lat, lon in product(range(-90, 91, 5),
range(-180, 181, 10))]),
GEOCENTRIC_SPHERICAL, GEOCENTRIC_CARTESIAN)
def coordinates(self):
return convert(array([
(lat, lon, 6371.2*(1.0 + random())) for lat, lon
in product(range(-90, 91, 5), range(-180, 181, 10))
]), GEOCENTRIC_SPHERICAL, GEOCENTRIC_CARTESIAN)