scipy.spatial.cKDTree.query

cKDTree.query(self, x, k=1, eps=0, p=2, distance_upper_bound=np.inf, n_jobs=1)

Query the kd-tree for nearest neighbors

Parameters:

x : array_like, last dimension self.m

An array of points to query.

k : list of integer or integer

The list of k-th nearest neighbors to return. If k is an integer it is treated as a list of [1, … k] (range(1, k+1)). Note that the counting starts from 1.

eps : non-negative float

Return approximate nearest neighbors; the k-th returned value is guaranteed to be no further than (1+eps) times the distance to the real k-th nearest neighbor.

p : float, 1<=p<=infinity

Which Minkowski p-norm to use. 1 is the sum-of-absolute-values “Manhattan” distance 2 is the usual Euclidean distance infinity is the maximum-coordinate-difference distance

distance_upper_bound : nonnegative float

Return only neighbors within this distance. This is used to prune tree searches, so if you are doing a series of nearest-neighbor queries, it may help to supply the distance to the nearest neighbor of the most recent point.

n_jobs : int, optional

Number of jobs to schedule for parallel processing. If -1 is given all processors are used. Default: 1.

Returns:

d : array of floats

The distances to the nearest neighbors. If x has shape tuple+(self.m,), then d has shape tuple+(k,). When k == 1, the last dimension of the output is squeezed. Missing neighbors are indicated with infinite distances.

i : ndarray of ints

The locations of the neighbors in self.data. If x has shape tuple+(self.m,), then i has shape tuple+(k,). When k == 1, the last dimension of the output is squeezed. Missing neighbors are indicated with self.n.

Notes

If the KD-Tree is periodic, the position x is wrapped into the box.

When the input k is a list, a query for arange(max(k)) is performed, but only columns that store the requested values of k are preserved. This is implemented in a manner that reduces memory usage.

Examples

>>> import numpy as np
>>> from scipy.spatial import cKDTree
>>> x, y = np.mgrid[0:5, 2:8]
>>> tree = cKDTree(np.c_[x.ravel(), y.ravel()])

To query the nearest neighbours and return squeezed result, use

>>> dd, ii = tree.query([[0, 0], [2.1, 2.9]], k=1)
>>> print(dd, ii)
[2.         0.14142136] [ 0 13]

To query the nearest neighbours and return unsqueezed result, use

>>> dd, ii = tree.query([[0, 0], [2.1, 2.9]], k=[1])
>>> print(dd, ii)
[[2.        ]
 [0.14142136]] [[ 0]
 [13]]

To query the second nearest neighbours and return unsqueezed result, use

>>> dd, ii = tree.query([[0, 0], [2.1, 2.9]], k=[2])
>>> print(dd, ii)
[[2.23606798]
 [0.90553851]] [[ 6]
 [12]]

To query the first and second nearest neighbours, use

>>> dd, ii = tree.query([[0, 0], [2.1, 2.9]], k=2)
>>> print(dd, ii)
[[2.         2.23606798]
 [0.14142136 0.90553851]] [[ 0  6]
 [13 12]]

or, be more specific

>>> dd, ii = tree.query([[0, 0], [2.1, 2.9]], k=[1, 2])
>>> print(dd, ii)
[[2.         2.23606798]
 [0.14142136 0.90553851]] [[ 0  6]
 [13 12]]