def trajectory_distances_and_speeds(
num_trajectories, object_ids, xs, ys, timestamps
):
"""
Compute the distance traveled and speed of sets of trajectories
Parameters
----------
num_trajectories
number of trajectories (unique object ids)
object_ids
column of object (e.g., vehicle) ids
xs
column of x-coordinates (in kilometers)
ys
column of y-coordinates (in kilometers)
timestamps
column of timestamps in any resolution
Returns
-------
result : cudf.DataFrame
meters : cudf.Series
trajectory distance (in kilometers)
speed : cudf.Series
trajectory speed (in meters/second)
Examples
--------
Compute the distances and speeds of derived trajectories
>>> objects, traj_offsets = cuspatial.derive_trajectories(...)
>>> dists_and_speeds = cuspatial.trajectory_distances_and_speeds(
len(traj_offsets)
objects['object_id'],
objects['x'],
objects['y'],
objects['timestamp']
)
>>> print(dists_and_speeds)
distance speed
trajectory_id
0 1000.0 100000.000000
1 1000.0 111111.109375
"""
object_ids = as_column(object_ids, dtype=np.int32)
xs, ys = normalize_point_columns(as_column(xs), as_column(ys))
timestamps = normalize_timestamp_column(as_column(timestamps))
df = DataFrame._from_table(
cpp_trajectory_distances_and_speeds(
num_trajectories, object_ids, xs, ys, timestamps
)
)
df.index.name = "trajectory_id"
return df
def trajectory_bounding_boxes(num_trajectories, object_ids, xs, ys):
""" Compute the bounding boxes of sets of trajectories.
Parameters
----------
num_trajectories
number of trajectories (unique object ids)
object_ids
column of object (e.g., vehicle) ids
xs
column of x-coordinates (in kilometers)
ys
column of y-coordinates (in kilometers)
Returns
-------
result : cudf.DataFrame
minimum bounding boxes (in kilometers) for each trajectory
x_min : cudf.Series
the minimum x-coordinate of each bounding box
y_min : cudf.Series
the minimum y-coordinate of each bounding box
x_max : cudf.Series
the maximum x-coordinate of each bounding box
y_max : cudf.Series
the maximum y-coordinate of each bounding box
Examples
--------
Compute the minimum bounding boxes of derived trajectories
>>> objects, traj_offsets = trajectory.derive_trajectories(
[0, 0, 1, 1], # object_id
[0, 1, 2, 3], # x
[0, 0, 1, 1], # y
[0, 10, 0, 10] # timestamp
)
>>> traj_bounding_boxes = cuspatial.trajectory_bounding_boxes(
len(traj_offsets),
objects['object_id'],
objects['x'],
objects['y']
)
>>> print(traj_bounding_boxes)
x_min y_min x_max y_max
0 0.0 0.0 2.0 2.0
1 1.0 1.0 3.0 3.0
"""
object_ids = as_column(object_ids, dtype=np.int32)
xs, ys = normalize_point_columns(as_column(xs), as_column(ys))
return DataFrame._from_table(
cpp_trajectory_bounding_boxes(num_trajectories, object_ids, xs, ys)
)
def derive_trajectories(object_ids, xs, ys, timestamps):
"""
Derive trajectories from object ids, points, and timestamps.
Parameters
----------
object_ids
column of object (e.g., vehicle) ids
xs
column of x-coordinates (in kilometers)
ys
column of y-coordinates (in kilometers)
timestamps
column of timestamps in any resolution
Returns
-------
result : tuple (objects, traj_offsets)
objects : cudf.DataFrame
object_ids, xs, ys, and timestamps sorted by
``(object_id, timestamp)``, used by ``trajectory_bounding_boxes``
and ``trajectory_distances_and_speeds``
traj_offsets : cudf.Series
offsets of discovered trajectories
Examples
--------
Compute sorted objects and discovered trajectories
>>> objects, traj_offsets = cuspatial.derive_trajectories(
[0, 1, 2, 3], # object_id
[0, 0, 1, 1], # x
[0, 0, 1, 1], # y
[0, 10, 0, 10] # timestamp
)
>>> print(traj_offsets)
0 0
1 2
>>> print(objects)
object_id x y timestamp
0 0 1 0 0
1 0 0 0 10
2 1 3 1 0
3 1 2 1 10
"""
object_ids = as_column(object_ids, dtype=np.int32)
xs, ys = normalize_point_columns(as_column(xs), as_column(ys))
timestamps = normalize_timestamp_column(as_column(timestamps))
objects, traj_offsets = cpp_derive_trajectories(
object_ids, xs, ys, timestamps
)
return DataFrame._from_table(objects), Series(data=traj_offsets)
def quadtree_on_points(xs, ys, x_min, x_max, y_min, y_max, scale, max_depth,
min_size):
""" Construct a quadtree from a set of points for a given area-of-interest
bounding box.
Parameters
----------
xs
Column of x-coordinates for each point
ys
Column of y-coordinates for each point
x_min
The lower-left x-coordinate of the area of interest bounding box
x_max
The upper-right x-coordinate of the area of interest bounding box
y_min
The lower-left y-coordinate of the area of interest bounding box
y_max
The upper-right y-coordinate of the area of interest bounding box
scale
Scale to apply to each point's distance from ``(x_min, y_min)``
max_depth
Maximum quadtree depth
min_size
Minimum number of points for a non-leaf quadtree node
Returns
-------
result : tuple (cudf.Series, cudf.DataFrame)
keys_to_points : cudf.Series(dtype=np.int32)
A column of sorted keys to original point indices
quadtree : cudf.DataFrame
A complete quadtree for the set of input points
key : cudf.Series(dtype=np.int32)
An int32 column of quadrant keys
level : cudf.Series(dtype=np.int8)
An int8 column of quadtree levels
is_quad : cudf.Series(dtype=np.bool_)
A boolean column indicating whether the node is a quad or leaf
length : cudf.Series(dtype=np.int32)
If this is a non-leaf quadrant (i.e. ``is_quad`` is ``True``),
this column's value is the number of children in the non-leaf
quadrant.
Otherwise this column's value is the number of points
contained in the leaf quadrant.
offset : cudf.Series(dtype=np.int32)
If this is a non-leaf quadrant (i.e. ``is_quad`` is ``True``),
this column's value is the position of the non-leaf quadrant's
first child.
Otherwise this column's value is the position of the leaf
quadrant's first point.
Notes
-----
* Swaps ``min_x`` and ``max_x`` if ``min_x > max_x``
* Swaps ``min_y`` and ``max_y`` if ``min_y > max_y``
Examples
--------
An example of selecting the ``min_size`` and ``scale`` based on input::
>>> np.random.seed(0)
>>> points = cudf.DataFrame({
"x": cudf.Series(np.random.normal(size=120)) * 500,
"y": cudf.Series(np.random.normal(size=120)) * 500,
})
>>> max_depth = 3
>>> min_size = 50
>>> min_x, min_y, max_x, max_y = (points["x"].min(),
points["y"].min(),
points["x"].max(),
points["y"].max())
>>> scale = max(max_x - min_x, max_y - min_y) // (1 << max_depth)
>>> print(
"min_size: " + str(min_size) + "\\n"
"num_points: " + str(len(points)) + "\\n"
"min_x: " + str(min_x) + "\\n"
"max_x: " + str(max_x) + "\\n"
"min_y: " + str(min_y) + "\\n"
"max_y: " + str(max_y) + "\\n"
"scale: " + str(scale) + "\\n"
)
min_size: 50
num_points: 120
min_x: -1577.4949079170394
max_x: 1435.877311993804
min_y: -1412.7015761122134
max_y: 1492.572387431971
scale: 301.0
>>> key_to_point, quadtree = cuspatial.quadtree_on_points(
points["x"],
points["y"],
min_x,
max_x,
min_y,
max_y,
scale, max_depth, min_size
)
>>> print(quadtree)
key level is_quad length offset
0 0 0 False 15 0
1 1 0 False 27 15
2 2 0 False 12 42
3 3 0 True 4 8
4 4 0 False 5 106
5 6 0 False 6 111
6 9 0 False 2 117
7 12 0 False 1 119
8 12 1 False 22 54
9 13 1 False 18 76
10 14 1 False 9 94
11 15 1 False 3 103
>>> print(key_to_point)
0 63
1 20
2 33
3 66
4 19
...
115 113
116 3
117 78
118 98
119 24
Length: 120, dtype: int32
"""
xs, ys = normalize_point_columns(as_column(xs), as_column(ys))
x_min, x_max, y_min, y_max = (
min(x_min, x_max),
max(x_min, x_max),
min(y_min, y_max),
max(y_min, y_max),
)
min_scale = max(x_max - x_min, y_max - y_min) / ((1 << max_depth) + 2)
if scale < min_scale:
warnings.warn("scale {} is less than required minimum ".format(scale) +
"scale {}. Clamping to minimum scale".format(min_scale))
key_to_point, quadtree = cpp_quadtree_on_points(
xs,
ys,
x_min,
x_max,
y_min,
y_max,
max(scale, min_scale),
max_depth,
min_size,
)
return Series(key_to_point), DataFrame._from_table(quadtree)
