def find_collocations(self, primary_data, secondary_data, max_interval,
max_distance, **kwargs):
timer = time.time()
# Find all spatial collocations by brute-force:
primary_points = geocentric2cart(typhon.constants.earth_radius,
primary_data["lat"],
primary_data["lon"])
secondary_points = geocentric2cart(typhon.constants.earth_radius,
secondary_data["lat"],
secondary_data["lon"])
distances = distance_matrix(np.column_stack(primary_points),
np.column_stack(secondary_points))
primary_indices, secondary_indices = np.nonzero(
distances < max_distance * 1000)
logging.debug(
"\tFound {} primary and {} secondary spatial collocations in "
"{:.2f}s.".format(primary_indices.size, secondary_indices.size,
time.time() - timer))
# Check the temporal condition:
if max_interval is not None:
intervals = \
np.abs(primary_data["time"][primary_indices]
- secondary_data["time"][secondary_indices])
passed_time_check = intervals < max_interval
primary_indices = primary_indices[passed_time_check]
secondary_indices = secondary_indices[passed_time_check]
return Array(primary_indices), Array(secondary_indices)
def test_geocentric2cart2geocentric(self):
"""Test conversion from geocentric to cartesian system and back."""
ref = (1, -13, 42)
cart = geodesy.geocentric2cart(*ref)
geo = geodesy.cart2geocentric(*cart)
assert np.allclose(ref, geo)
def test_geocentric2cart2geocentric(self):
"""Test conversion from geocentric to cartesian system and back."""
ref = (1, -13, 42)
cart = geodesy.geocentric2cart(*ref)
geo = geodesy.cart2geocentric(*cart)
assert np.allclose(ref, geo)
def test_geocentric2cart(self):
"""Test conversion from cartesian to geocentric system."""
geocentric = (np.array([1, 1, 1]), np.array([0, 0, 90]), np.array([0, 90, 0])) # r # lat # lon
reference = (np.array([1, 0, 0]), np.array([0, 1, 0]), np.array([0, 0, 1])) # x # y # z
conversion = geodesy.geocentric2cart(*geocentric)
assert np.allclose(conversion, reference)
def _to_metric(self, lat, lon):
if not (isinstance(lat, np.ndarray) or isinstance(lon, np.ndarray)):
raise ValueError("lat and lon must be numpy.ndarray objects (no "
"pandas.Series or xarray.DataArray)!")
if self.metric == "minkowski":
return np.column_stack(geocentric2cart(earth_radius, lat, lon))
elif self.metric == "haversine":
return np.radians(np.column_stack([lat, lon]))
else:
raise ValueError(f"Unknown metric '{self.metric}!'")
def test_geocentric2cart(self):
"""Test conversion from geocentric to cartesian system."""
geocentric = (np.array([1, 1, 1]), # r
np.array([0, 0, 90]), # lat
np.array([0, 90, 0]), # lon
)
reference = (np.array([1, 0, 0]), # x
np.array([0, 1, 0]), # y
np.array([0, 0, 1]), # z
)
conversion = geodesy.geocentric2cart(*geocentric)
assert np.allclose(conversion, reference)
def find_collocations(self, primary_data, secondary_data, max_interval,
max_distance, **kwargs):
if max_interval is not None:
max_interval = to_timedelta(max_interval)
if max_distance is None:
# Search for temporal collocations only
primary_time = \
primary_data["time"].astype("M8[s]").astype("int")
secondary_time = \
secondary_data["time"].astype("M8[s]").astype("int")
# The BallTree implementation only allows 2-dimensional data, hence
# we need to add an empty second dimension
# TODO: Change this
primary_points = np.column_stack(
[primary_time, np.zeros_like(primary_time)])
secondary_points = np.column_stack(
[secondary_time, np.zeros_like(secondary_time)])
max_radius = max_interval.total_seconds()
else:
# We try to find collocations by building one 3-d Ball tree
# (see https://en.wikipedia.org/wiki/K-d_tree) and searching for
# the nearest neighbours. Since a k-d tree cannot handle latitude /
# longitude data, we have to convert them to 3D-cartesian
# coordinates. This introduces an error of the distance calculation
# since it is now the distance in a 3D euclidean space and not the
# distance along the sphere any longer. When having two points with
# a distance of 5 degrees in longitude, the error is smaller than
# 177 meters.
cart_points = geocentric2cart(
6371000.0, # typhon.constants.earth_radius,
primary_data["lat"],
primary_data["lon"])
primary_points = np.column_stack(cart_points)
# We need to convert the secondary data as well:
cart_points = geocentric2cart(
6371000.0, # typhon.constants.earth_radius,
secondary_data["lat"],
secondary_data["lon"])
secondary_points = np.column_stack(cart_points)
# The parameter max_distance is in kilometers, so we have to
# convert it to meters.
max_radius = max_distance * 1000
# It is more efficient to build the tree with the largest data corpus:
tree_with_primary = primary_points.size > secondary_points.size
# Search for all collocations
if tree_with_primary:
tree = SklearnBallTree(primary_points, leaf_size=self.leaf_size)
results = tree.query_radius(secondary_points, r=max_radius)
# Build the list of the collocation pairs:
pairs = np.array(
[[primary_index, secondary_index]
for secondary_index, primary_indices in enumerate(results)
for primary_index in primary_indices]).T
else:
tree = SklearnBallTree(secondary_points, leaf_size=self.leaf_size)
results = tree.query_radius(primary_points, r=max_radius)
# Build the list of the collocation pairs:
pairs = np.array(
[[primary_index, secondary_index]
for primary_index, secondary_indices in enumerate(results)
for secondary_index in secondary_indices]).T
# No collocations were found.
if not pairs.any():
return pairs
# Check here for temporal collocations:
if max_distance is not None and max_interval is not None:
# Check whether the time differences between the spatial
# collocations are less than the temporal boundary:
passed_time_check = np.abs(primary_data["time"][pairs[0]] -
secondary_data["time"][pairs[1]]
) < np.timedelta64(max_interval)
# Just keep all indices which satisfy the temporal condition.
pairs = pairs[:, passed_time_check]
return pairs
