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# Copyright Anne M. Archibald 2008
# Released under the scipy license
import numpy as np
from ._ckdtree import cKDTree, cKDTreeNode
__all__ = ['minkowski_distance_p', 'minkowski_distance',
'distance_matrix',
'Rectangle', 'KDTree']
def minkowski_distance_p(x, y, p=2):
"""Compute the pth power of the L**p distance between two arrays.
For efficiency, this function computes the L**p distance but does
not extract the pth root. If `p` is 1 or infinity, this is equal to
the actual L**p distance.
The last dimensions of `x` and `y` must be the same length. Any
other dimensions must be compatible for broadcasting.
Parameters
----------
x : (..., K) array_like
Input array.
y : (..., K) array_like
Input array.
p : float, 1 <= p <= infinity
Which Minkowski p-norm to use.
Returns
-------
dist : ndarray
pth power of the distance between the input arrays.
Examples
--------
>>> from scipy.spatial import minkowski_distance_p
>>> minkowski_distance_p([[0, 0], [0, 0]], [[1, 1], [0, 1]])
array([2, 1])
"""
x = np.asarray(x)
y = np.asarray(y)
# Find smallest common datatype with float64 (return type of this
# function) - addresses #10262.
# Don't just cast to float64 for complex input case.
common_datatype = np.promote_types(np.promote_types(x.dtype, y.dtype),
'float64')
# Make sure x and y are NumPy arrays of correct datatype.
x = x.astype(common_datatype)
y = y.astype(common_datatype)
if p == np.inf:
return np.amax(np.abs(y-x), axis=-1)
elif p == 1:
return np.sum(np.abs(y-x), axis=-1)
else:
return np.sum(np.abs(y-x)**p, axis=-1)
def minkowski_distance(x, y, p=2):
"""Compute the L**p distance between two arrays.
The last dimensions of `x` and `y` must be the same length. Any
other dimensions must be compatible for broadcasting.
Parameters
----------
x : (..., K) array_like
Input array.
y : (..., K) array_like
Input array.
p : float, 1 <= p <= infinity
Which Minkowski p-norm to use.
Returns
-------
dist : ndarray
Distance between the input arrays.
Examples
--------
>>> from scipy.spatial import minkowski_distance
>>> minkowski_distance([[0, 0], [0, 0]], [[1, 1], [0, 1]])
array([ 1.41421356, 1. ])
"""
x = np.asarray(x)
y = np.asarray(y)
if p == np.inf or p == 1:
return minkowski_distance_p(x, y, p)
else:
return minkowski_distance_p(x, y, p)**(1./p)
class Rectangle:
"""Hyperrectangle class.
Represents a Cartesian product of intervals.
"""
def __init__(self, maxes, mins):
"""Construct a hyperrectangle."""
self.maxes = np.maximum(maxes,mins).astype(float)
self.mins = np.minimum(maxes,mins).astype(float)
self.m, = self.maxes.shape
def __repr__(self):
return "<Rectangle %s>" % list(zip(self.mins, self.maxes))
def volume(self):
"""Total volume."""
return np.prod(self.maxes-self.mins)
def split(self, d, split):
"""Produce two hyperrectangles by splitting.
In general, if you need to compute maximum and minimum
distances to the children, it can be done more efficiently
by updating the maximum and minimum distances to the parent.
Parameters
----------
d : int
Axis to split hyperrectangle along.
split : float
Position along axis `d` to split at.
"""
mid = np.copy(self.maxes)
mid[d] = split
less = Rectangle(self.mins, mid)
mid = np.copy(self.mins)
mid[d] = split
greater = Rectangle(mid, self.maxes)
return less, greater
def min_distance_point(self, x, p=2.):
"""
Return the minimum distance between input and points in the
hyperrectangle.
Parameters
----------
x : array_like
Input.
p : float, optional
Input.
"""
return minkowski_distance(
0, np.maximum(0, np.maximum(self.mins-x, x-self.maxes)),
p
)
def max_distance_point(self, x, p=2.):
"""
Return the maximum distance between input and points in the hyperrectangle.
Parameters
----------
x : array_like
Input array.
p : float, optional
Input.
"""
return minkowski_distance(0, np.maximum(self.maxes-x, x-self.mins), p)
def min_distance_rectangle(self, other, p=2.):
"""
Compute the minimum distance between points in the two hyperrectangles.
Parameters
----------
other : hyperrectangle
Input.
p : float
Input.
"""
return minkowski_distance(
0,
np.maximum(0, np.maximum(self.mins-other.maxes,
other.mins-self.maxes)),
p
)
def max_distance_rectangle(self, other, p=2.):
"""
Compute the maximum distance between points in the two hyperrectangles.
Parameters
----------
other : hyperrectangle
Input.
p : float, optional
Input.
"""
return minkowski_distance(
0, np.maximum(self.maxes-other.mins, other.maxes-self.mins), p)
class KDTree(cKDTree):
"""kd-tree for quick nearest-neighbor lookup.
This class provides an index into a set of k-dimensional points
which can be used to rapidly look up the nearest neighbors of any
point.
Parameters
----------
data : array_like, shape (n,m)
The n data points of dimension m to be indexed. This array is
not copied unless this is necessary to produce a contiguous
array of doubles, and so modifying this data will result in
bogus results. The data are also copied if the kd-tree is built
with copy_data=True.
leafsize : positive int, optional
The number of points at which the algorithm switches over to
brute-force. Default: 10.
compact_nodes : bool, optional
If True, the kd-tree is built to shrink the hyperrectangles to
the actual data range. This usually gives a more compact tree that
is robust against degenerated input data and gives faster queries
at the expense of longer build time. Default: True.
copy_data : bool, optional
If True the data is always copied to protect the kd-tree against
data corruption. Default: False.
balanced_tree : bool, optional
If True, the median is used to split the hyperrectangles instead of
the midpoint. This usually gives a more compact tree and
faster queries at the expense of longer build time. Default: True.
boxsize : array_like or scalar, optional
Apply a m-d toroidal topology to the KDTree.. The topology is generated
by :math:`x_i + n_i L_i` where :math:`n_i` are integers and :math:`L_i`
is the boxsize along i-th dimension. The input data shall be wrapped
into :math:`[0, L_i)`. A ValueError is raised if any of the data is
outside of this bound.
Notes
-----
The algorithm used is described in Maneewongvatana and Mount 1999.
The general idea is that the kd-tree is a binary tree, each of whose
nodes represents an axis-aligned hyperrectangle. Each node specifies
an axis and splits the set of points based on whether their coordinate
along that axis is greater than or less than a particular value.
During construction, the axis and splitting point are chosen by the
"sliding midpoint" rule, which ensures that the cells do not all
become long and thin.
The tree can be queried for the r closest neighbors of any given point
(optionally returning only those within some maximum distance of the
point). It can also be queried, with a substantial gain in efficiency,
for the r approximate closest neighbors.
For large dimensions (20 is already large) do not expect this to run
significantly faster than brute force. High-dimensional nearest-neighbor
queries are a substantial open problem in computer science.
Attributes
----------
data : ndarray, shape (n,m)
The n data points of dimension m to be indexed. This array is
not copied unless this is necessary to produce a contiguous
array of doubles. The data are also copied if the kd-tree is built
with `copy_data=True`.
leafsize : positive int
The number of points at which the algorithm switches over to
brute-force.
m : int
The dimension of a single data-point.
n : int
The number of data points.
maxes : ndarray, shape (m,)
The maximum value in each dimension of the n data points.
mins : ndarray, shape (m,)
The minimum value in each dimension of the n data points.
size : int
The number of nodes in the tree.
"""
class node:
@staticmethod
def _create(ckdtree_node=None):
"""Create either an inner or leaf node, wrapping a cKDTreeNode instance"""
if ckdtree_node is None:
return KDTree.node(ckdtree_node)
elif ckdtree_node.split_dim == -1:
return KDTree.leafnode(ckdtree_node)
else:
return KDTree.innernode(ckdtree_node)
def __init__(self, ckdtree_node=None):
if ckdtree_node is None:
ckdtree_node = cKDTreeNode()
self._node = ckdtree_node
def __lt__(self, other):
return id(self) < id(other)
def __gt__(self, other):
return id(self) > id(other)
def __le__(self, other):
return id(self) <= id(other)
def __ge__(self, other):
return id(self) >= id(other)
def __eq__(self, other):
return id(self) == id(other)
class leafnode(node):
@property
def idx(self):
return self._node.indices
@property
def children(self):
return self._node.children
class innernode(node):
def __init__(self, ckdtreenode):
assert isinstance(ckdtreenode, cKDTreeNode)
super().__init__(ckdtreenode)
self.less = KDTree.node._create(ckdtreenode.lesser)
self.greater = KDTree.node._create(ckdtreenode.greater)
@property
def split_dim(self):
return self._node.split_dim
@property
def split(self):
return self._node.split
@property
def children(self):
return self._node.children
@property
def tree(self):
if not hasattr(self, "_tree"):
self._tree = KDTree.node._create(super().tree)
return self._tree
def __init__(self, data, leafsize=10, compact_nodes=True, copy_data=False,
balanced_tree=True, boxsize=None):
data = np.asarray(data)
if data.dtype.kind == 'c':
raise TypeError("KDTree does not work with complex data")
# Note KDTree has different default leafsize from cKDTree
super().__init__(data, leafsize, compact_nodes, copy_data,
balanced_tree, boxsize)
def query(
self, x, k=1, eps=0, p=2, distance_upper_bound=np.inf, workers=1):
r"""Query the kd-tree for nearest neighbors.
Parameters
----------
x : array_like, last dimension self.m
An array of points to query.
k : int or Sequence[int], optional
Either the number of nearest neighbors to return, or a list of the
k-th nearest neighbors to return, starting from 1.
eps : nonnegative float, optional
Return approximate nearest neighbors; the kth returned value
is guaranteed to be no further than (1+eps) times the
distance to the real kth nearest neighbor.
p : float, 1<=p<=infinity, optional
Which Minkowski p-norm to use.
1 is the sum-of-absolute-values distance ("Manhattan" distance).
2 is the usual Euclidean distance.
infinity is the maximum-coordinate-difference distance.
A large, finite p may cause a ValueError if overflow can occur.
distance_upper_bound : nonnegative float, optional
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.
workers : int, optional
Number of workers to use for parallel processing. If -1 is given
all CPU threads are used. Default: 1.
.. versionadded:: 1.6.0
Returns
-------
d : float or 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.
Hits are sorted by distance (nearest first).
.. versionchanged:: 1.9.0
Previously if ``k=None``, then `d` was an object array of
shape ``tuple``, containing lists of distances. This behavior
has been removed, use `query_ball_point` instead.
i : integer or array of integers
The index of each neighbor in ``self.data``.
``i`` is the same shape as d.
Missing neighbors are indicated with ``self.n``.
Examples
--------
>>> import numpy as np
>>> from scipy.spatial import KDTree
>>> x, y = np.mgrid[0:5, 2:8]
>>> tree = KDTree(np.c_[x.ravel(), y.ravel()])
To query the nearest neighbours and return squeezed result, use
>>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=1)
>>> print(dd, ii, sep='\n')
[2. 0.2236068]
[ 0 13]
To query the nearest neighbours and return unsqueezed result, use
>>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=[1])
>>> print(dd, ii, sep='\n')
[[2. ]
[0.2236068]]
[[ 0]
[13]]
To query the second nearest neighbours and return unsqueezed result,
use
>>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=[2])
>>> print(dd, ii, sep='\n')
[[2.23606798]
[0.80622577]]
[[ 6]
[19]]
To query the first and second nearest neighbours, use
>>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=2)
>>> print(dd, ii, sep='\n')
[[2. 2.23606798]
[0.2236068 0.80622577]]
[[ 0 6]
[13 19]]
or, be more specific
>>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=[1, 2])
>>> print(dd, ii, sep='\n')
[[2. 2.23606798]
[0.2236068 0.80622577]]
[[ 0 6]
[13 19]]
"""
x = np.asarray(x)
if x.dtype.kind == 'c':
raise TypeError("KDTree does not work with complex data")
if k is None:
raise ValueError("k must be an integer or a sequence of integers")
d, i = super().query(x, k, eps, p, distance_upper_bound, workers)
if isinstance(i, int):
i = np.intp(i)
return d, i
def query_ball_point(self, x, r, p=2., eps=0, workers=1,
return_sorted=None, return_length=False):
"""Find all points within distance r of point(s) x.
Parameters
----------
x : array_like, shape tuple + (self.m,)
The point or points to search for neighbors of.
r : array_like, float
The radius of points to return, must broadcast to the length of x.
p : float, optional
Which Minkowski p-norm to use. Should be in the range [1, inf].
A finite large p may cause a ValueError if overflow can occur.
eps : nonnegative float, optional
Approximate search. Branches of the tree are not explored if their
nearest points are further than ``r / (1 + eps)``, and branches are
added in bulk if their furthest points are nearer than
``r * (1 + eps)``.
workers : int, optional
Number of jobs to schedule for parallel processing. If -1 is given
all processors are used. Default: 1.
.. versionadded:: 1.6.0
return_sorted : bool, optional
Sorts returned indices if True and does not sort them if False. If
None, does not sort single point queries, but does sort
multi-point queries which was the behavior before this option
was added.
.. versionadded:: 1.6.0
return_length : bool, optional
Return the number of points inside the radius instead of a list
of the indices.
.. versionadded:: 1.6.0
Returns
-------
results : list or array of lists
If `x` is a single point, returns a list of the indices of the
neighbors of `x`. If `x` is an array of points, returns an object
array of shape tuple containing lists of neighbors.
Notes
-----
If you have many points whose neighbors you want to find, you may save
substantial amounts of time by putting them in a KDTree and using
query_ball_tree.
Examples
--------
>>> import numpy as np
>>> from scipy import spatial
>>> x, y = np.mgrid[0:5, 0:5]
>>> points = np.c_[x.ravel(), y.ravel()]
>>> tree = spatial.KDTree(points)
>>> sorted(tree.query_ball_point([2, 0], 1))
[5, 10, 11, 15]
Query multiple points and plot the results:
>>> import matplotlib.pyplot as plt
>>> points = np.asarray(points)
>>> plt.plot(points[:,0], points[:,1], '.')
>>> for results in tree.query_ball_point(([2, 0], [3, 3]), 1):
... nearby_points = points[results]
... plt.plot(nearby_points[:,0], nearby_points[:,1], 'o')
>>> plt.margins(0.1, 0.1)
>>> plt.show()
"""
x = np.asarray(x)
if x.dtype.kind == 'c':
raise TypeError("KDTree does not work with complex data")
return super().query_ball_point(
x, r, p, eps, workers, return_sorted, return_length)
def query_ball_tree(self, other, r, p=2., eps=0):
"""
Find all pairs of points between `self` and `other` whose distance is
at most r.
Parameters
----------
other : KDTree instance
The tree containing points to search against.
r : float
The maximum distance, has to be positive.
p : float, optional
Which Minkowski norm to use. `p` has to meet the condition
``1 <= p <= infinity``.
eps : float, optional
Approximate search. Branches of the tree are not explored
if their nearest points are further than ``r/(1+eps)``, and
branches are added in bulk if their furthest points are nearer
than ``r * (1+eps)``. `eps` has to be non-negative.
Returns
-------
results : list of lists
For each element ``self.data[i]`` of this tree, ``results[i]`` is a
list of the indices of its neighbors in ``other.data``.
Examples
--------
You can search all pairs of points between two kd-trees within a distance:
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> from scipy.spatial import KDTree
>>> rng = np.random.default_rng()
>>> points1 = rng.random((15, 2))
>>> points2 = rng.random((15, 2))
>>> plt.figure(figsize=(6, 6))
>>> plt.plot(points1[:, 0], points1[:, 1], "xk", markersize=14)
>>> plt.plot(points2[:, 0], points2[:, 1], "og", markersize=14)
>>> kd_tree1 = KDTree(points1)
>>> kd_tree2 = KDTree(points2)
>>> indexes = kd_tree1.query_ball_tree(kd_tree2, r=0.2)
>>> for i in range(len(indexes)):
... for j in indexes[i]:
... plt.plot([points1[i, 0], points2[j, 0]],
... [points1[i, 1], points2[j, 1]], "-r")
>>> plt.show()
"""
return super().query_ball_tree(other, r, p, eps)
def query_pairs(self, r, p=2., eps=0, output_type='set'):
"""Find all pairs of points in `self` whose distance is at most r.
Parameters
----------
r : positive float
The maximum distance.
p : float, optional
Which Minkowski norm to use. `p` has to meet the condition
``1 <= p <= infinity``.
eps : float, optional
Approximate search. Branches of the tree are not explored
if their nearest points are further than ``r/(1+eps)``, and
branches are added in bulk if their furthest points are nearer
than ``r * (1+eps)``. `eps` has to be non-negative.
output_type : string, optional
Choose the output container, 'set' or 'ndarray'. Default: 'set'
.. versionadded:: 1.6.0
Returns
-------
results : set or ndarray
Set of pairs ``(i,j)``, with ``i < j``, for which the corresponding
positions are close. If output_type is 'ndarray', an ndarry is
returned instead of a set.
Examples
--------
You can search all pairs of points in a kd-tree within a distance:
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> from scipy.spatial import KDTree
>>> rng = np.random.default_rng()
>>> points = rng.random((20, 2))
>>> plt.figure(figsize=(6, 6))
>>> plt.plot(points[:, 0], points[:, 1], "xk", markersize=14)
>>> kd_tree = KDTree(points)
>>> pairs = kd_tree.query_pairs(r=0.2)
>>> for (i, j) in pairs:
... plt.plot([points[i, 0], points[j, 0]],
... [points[i, 1], points[j, 1]], "-r")
>>> plt.show()
"""
return super().query_pairs(r, p, eps, output_type)
def count_neighbors(self, other, r, p=2., weights=None, cumulative=True):
"""Count how many nearby pairs can be formed.
Count the number of pairs ``(x1,x2)`` can be formed, with ``x1`` drawn
from ``self`` and ``x2`` drawn from ``other``, and where
``distance(x1, x2, p) <= r``.
Data points on ``self`` and ``other`` are optionally weighted by the
``weights`` argument. (See below)
This is adapted from the "two-point correlation" algorithm described by
Gray and Moore [1]_. See notes for further discussion.
Parameters
----------
other : KDTree
The other tree to draw points from, can be the same tree as self.
r : float or one-dimensional array of floats
The radius to produce a count for. Multiple radii are searched with
a single tree traversal.
If the count is non-cumulative(``cumulative=False``), ``r`` defines
the edges of the bins, and must be non-decreasing.
p : float, optional
1<=p<=infinity.
Which Minkowski p-norm to use.
Default 2.0.
A finite large p may cause a ValueError if overflow can occur.
weights : tuple, array_like, or None, optional
If None, the pair-counting is unweighted.
If given as a tuple, weights[0] is the weights of points in
``self``, and weights[1] is the weights of points in ``other``;
either can be None to indicate the points are unweighted.
If given as an array_like, weights is the weights of points in
``self`` and ``other``. For this to make sense, ``self`` and
``other`` must be the same tree. If ``self`` and ``other`` are two
different trees, a ``ValueError`` is raised.
Default: None
.. versionadded:: 1.6.0
cumulative : bool, optional
Whether the returned counts are cumulative. When cumulative is set
to ``False`` the algorithm is optimized to work with a large number
of bins (>10) specified by ``r``. When ``cumulative`` is set to
True, the algorithm is optimized to work with a small number of
``r``. Default: True
.. versionadded:: 1.6.0
Returns
-------
result : scalar or 1-D array
The number of pairs. For unweighted counts, the result is integer.
For weighted counts, the result is float.
If cumulative is False, ``result[i]`` contains the counts with
``(-inf if i == 0 else r[i-1]) < R <= r[i]``
Notes
-----
Pair-counting is the basic operation used to calculate the two point
correlation functions from a data set composed of position of objects.
Two point correlation function measures the clustering of objects and
is widely used in cosmology to quantify the large scale structure
in our Universe, but it may be useful for data analysis in other fields
where self-similar assembly of objects also occur.
The Landy-Szalay estimator for the two point correlation function of
``D`` measures the clustering signal in ``D``. [2]_
For example, given the position of two sets of objects,
- objects ``D`` (data) contains the clustering signal, and
- objects ``R`` (random) that contains no signal,
.. math::
\\xi(r) = \\frac{<D, D> - 2 f <D, R> + f^2<R, R>}{f^2<R, R>},
where the brackets represents counting pairs between two data sets
in a finite bin around ``r`` (distance), corresponding to setting
`cumulative=False`, and ``f = float(len(D)) / float(len(R))`` is the
ratio between number of objects from data and random.
The algorithm implemented here is loosely based on the dual-tree
algorithm described in [1]_. We switch between two different
pair-cumulation scheme depending on the setting of ``cumulative``.
The computing time of the method we use when for
``cumulative == False`` does not scale with the total number of bins.
The algorithm for ``cumulative == True`` scales linearly with the
number of bins, though it is slightly faster when only
1 or 2 bins are used. [5]_.
As an extension to the naive pair-counting,
weighted pair-counting counts the product of weights instead
of number of pairs.
Weighted pair-counting is used to estimate marked correlation functions
([3]_, section 2.2),
or to properly calculate the average of data per distance bin
(e.g. [4]_, section 2.1 on redshift).
.. [1] Gray and Moore,
"N-body problems in statistical learning",
Mining the sky, 2000,
https://arxiv.org/abs/astro-ph/0012333
.. [2] Landy and Szalay,
"Bias and variance of angular correlation functions",
The Astrophysical Journal, 1993,
http://adsabs.harvard.edu/abs/1993ApJ...412...64L
.. [3] Sheth, Connolly and Skibba,
"Marked correlations in galaxy formation models",
Arxiv e-print, 2005,
https://arxiv.org/abs/astro-ph/0511773
.. [4] Hawkins, et al.,
"The 2dF Galaxy Redshift Survey: correlation functions,
peculiar velocities and the matter density of the Universe",
Monthly Notices of the Royal Astronomical Society, 2002,
http://adsabs.harvard.edu/abs/2003MNRAS.346...78H
.. [5] https://github.com/scipy/scipy/pull/5647#issuecomment-168474926
Examples
--------
You can count neighbors number between two kd-trees within a distance:
>>> import numpy as np
>>> from scipy.spatial import KDTree
>>> rng = np.random.default_rng()
>>> points1 = rng.random((5, 2))
>>> points2 = rng.random((5, 2))
>>> kd_tree1 = KDTree(points1)
>>> kd_tree2 = KDTree(points2)
>>> kd_tree1.count_neighbors(kd_tree2, 0.2)
1
This number is same as the total pair number calculated by
`query_ball_tree`:
>>> indexes = kd_tree1.query_ball_tree(kd_tree2, r=0.2)
>>> sum([len(i) for i in indexes])
1
"""
return super().count_neighbors(other, r, p, weights, cumulative)
def sparse_distance_matrix(
self, other, max_distance, p=2., output_type='dok_matrix'):
"""Compute a sparse distance matrix.
Computes a distance matrix between two KDTrees, leaving as zero
any distance greater than max_distance.
Parameters
----------
other : KDTree
max_distance : positive float
p : float, 1<=p<=infinity
Which Minkowski p-norm to use.
A finite large p may cause a ValueError if overflow can occur.
output_type : string, optional
Which container to use for output data. Options: 'dok_matrix',
'coo_matrix', 'dict', or 'ndarray'. Default: 'dok_matrix'.
.. versionadded:: 1.6.0
Returns
-------
result : dok_matrix, coo_matrix, dict or ndarray
Sparse matrix representing the results in "dictionary of keys"
format. If a dict is returned the keys are (i,j) tuples of indices.
If output_type is 'ndarray' a record array with fields 'i', 'j',
and 'v' is returned,
Examples
--------
You can compute a sparse distance matrix between two kd-trees:
>>> import numpy as np
>>> from scipy.spatial import KDTree
>>> rng = np.random.default_rng()
>>> points1 = rng.random((5, 2))
>>> points2 = rng.random((5, 2))
>>> kd_tree1 = KDTree(points1)
>>> kd_tree2 = KDTree(points2)
>>> sdm = kd_tree1.sparse_distance_matrix(kd_tree2, 0.3)
>>> sdm.toarray()
array([[0. , 0. , 0.12295571, 0. , 0. ],
[0. , 0. , 0. , 0. , 0. ],
[0.28942611, 0. , 0. , 0.2333084 , 0. ],
[0. , 0. , 0. , 0. , 0. ],
[0.24617575, 0.29571802, 0.26836782, 0. , 0. ]])
You can check distances above the `max_distance` are zeros:
>>> from scipy.spatial import distance_matrix
>>> distance_matrix(points1, points2)
array([[0.56906522, 0.39923701, 0.12295571, 0.8658745 , 0.79428925],
[0.37327919, 0.7225693 , 0.87665969, 0.32580855, 0.75679479],
[0.28942611, 0.30088013, 0.6395831 , 0.2333084 , 0.33630734],
[0.31994999, 0.72658602, 0.71124834, 0.55396483, 0.90785663],
[0.24617575, 0.29571802, 0.26836782, 0.57714465, 0.6473269 ]])
"""
return super().sparse_distance_matrix(
other, max_distance, p, output_type)
def distance_matrix(x, y, p=2, threshold=1000000):
"""Compute the distance matrix.
Returns the matrix of all pair-wise distances.
Parameters
----------
x : (M, K) array_like
Matrix of M vectors in K dimensions.
y : (N, K) array_like
Matrix of N vectors in K dimensions.
p : float, 1 <= p <= infinity
Which Minkowski p-norm to use.
threshold : positive int
If ``M * N * K`` > `threshold`, algorithm uses a Python loop instead
of large temporary arrays.
Returns
-------
result : (M, N) ndarray
Matrix containing the distance from every vector in `x` to every vector
in `y`.
Examples
--------
>>> from scipy.spatial import distance_matrix
>>> distance_matrix([[0,0],[0,1]], [[1,0],[1,1]])
array([[ 1. , 1.41421356],
[ 1.41421356, 1. ]])
"""
x = np.asarray(x)
m, k = x.shape
y = np.asarray(y)
n, kk = y.shape
if k != kk:
raise ValueError(f"x contains {k}-dimensional vectors but y contains "
f"{kk}-dimensional vectors")
if m*n*k <= threshold:
return minkowski_distance(x[:,np.newaxis,:],y[np.newaxis,:,:],p)
else:
result = np.empty((m,n),dtype=float) # FIXME: figure out the best dtype
if m < n:
for i in range(m):
result[i,:] = minkowski_distance(x[i],y,p)
else:
for j in range(n):
result[:,j] = minkowski_distance(x,y[j],p)
return result