Trajectory#
Functions for identifying and grouping trajectories from point data.
- cuspatial.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
- resulttuple (objects, traj_offsets)
- objectscudf.DataFrame
object_ids, xs, ys, and timestamps sorted by
(object_id, timestamp)
, used bytrajectory_bounding_boxes
andtrajectory_distances_and_speeds
- traj_offsetscudf.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
- cuspatial.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
- resultcudf.DataFrame
- meterscudf.Series
trajectory distance (in kilometers)
- speedcudf.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
- cuspatial.directed_hausdorff_distance(xs, ys, space_offsets)#
Compute the directed Hausdorff distances between all pairs of spaces.
- Parameters
- xs
column of x-coordinates
- ys
column of y-coordinates
- space_offsets
beginning index of each space, plus the last space’s end offset.
- Returns
- resultcudf.DataFrame
The pairwise directed distance matrix with one row and one column per input space; the value at row i, column j represents the hausdorff distance from space i to space j.
Examples
The directed Hausdorff distance from one space to another is the greatest of all the distances between any point in the first space to the closest point in the second.
Consider a pair of lines on a grid:
: x -----xyy--- : :
x_{0} = (0, 0), x_{1} = (0, 1)
y_{0} = (1, 0), y_{1} = (2, 0)
x_{0} is the closest point in
x
toy
. The distance from x_{0} to the farthest point iny
is 2.y_{0} is the closest point in
y
tox
. The distance from y_{0} to the farthest point inx
is 1.414.Compute the directed hausdorff distances between a set of spaces
>>> result = cuspatial.directed_hausdorff_distance( [0, 1, 0, 0], # xs [0, 0, 1, 2], # ys [0, 2, 4], # space_offsets ) >>> print(result) 0 1 0 0.0 1.414214 1 2.0 0.000000
- cuspatial.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
- resultcudf.DataFrame
minimum bounding boxes (in kilometers) for each trajectory
- x_mincudf.Series
the minimum x-coordinate of each bounding box
- y_mincudf.Series
the minimum y-coordinate of each bounding box
- x_maxcudf.Series
the maximum x-coordinate of each bounding box
- y_maxcudf.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
- class cuspatial.CubicSpline(t, y, ids=None, size=None, prefixes=None)#
Fits each column of the input Series y to a hermetic cubic spline.
cuspatial.CubicSpline
supports two usage patterns: The first is identical to scipy.interpolate.CubicSpline:curve = cuspatial.CubicSpline(t, y) new_points = curve(np.linspace(t.min, t.max, 50))
This allows API parity with scipy. This isn’t recommended, as scipy host based interpolation performance is likely to exceed GPU performance for a single curve.
However, cuSpatial massively outperforms scipy when many splines are fit simultaneously. Data must be arranged in a SoA format, and the exclusive prefix_sum of the separate curves must also be passed to the function.:
NUM_SPLINES = 100000 SPLINE_LENGTH = 101 t = cudf.Series( np.hstack((np.arange(SPLINE_LENGTH),) * NUM_SPLINES) ).astype('float32') y = cudf.Series( np.random.random(SPLINE_LENGTH*NUM_SPLINES) ).astype('float32') prefix_sum = cudf.Series( cp.arange(NUM_SPLINES + 1)*SPLINE_LENGTH ).astype('int32') curve = cuspatial.CubicSpline(t, y, prefixes=prefix_sum) new_samples = cudf.Series( np.hstack((np.linspace( 0, (SPLINE_LENGTH - 1), (SPLINE_LENGTH - 1) * 2 + 1 ),) * NUM_SPLINES) ).astype('float32') curve_ids = cudf.Series(np.repeat( np.arange(0, NUM_SPLINES), SPLINE_LENGTH * 2 - 1 ), dtype="int32") new_points = curve(new_samples, curve_ids)
Methods
__call__
(coordinates[, groups])Interpolates new input values coordinates using the .c DataFrame or map of DataFrames.
- CubicSpline.__init__(t, y, ids=None, size=None, prefixes=None)#
Computes various error preconditions on the input data, then uses CUDA to compute cubic splines for each set of input coordinates on the GPU in parallel.
- Parameters
- tcudf.Series
time sample values. Must be monotonically increasing.
- ycudf.Series
columns to have curves fit to according to x
- ids (Optional)cudf.Series
ids of each spline
- size (Optional)cudf.Series
fixed size of each spline
- prefixes (Optional)cudf.Series
alternative to size, allows splines of varying length. Not yet fully supported.
- Returns
- CubicSplinecallable o
o.c
contains the coefficients that can be used to compute new points along the spline fitting the originalt
data.o(n)
interpolates the spline coordinates along new input valuesn
.
- CubicSpline.__call__(coordinates, groups=None)#
Interpolates new input values coordinates using the .c DataFrame or map of DataFrames.