count_neighbors(self, other, r, p=2.0, weights=None, cumulative=True)
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 . See notes for further discussion.
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
.
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,
where the brackets represents counting pairs between two data sets in a finite bin around r
(distance), corresponding to setting :None:None:`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 . 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. .
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 (, section 2.2), or to properly calculate the average of data per distance bin (e.g. , section 2.1 on redshift).
<Unimplemented 'footnote' '.. [1] Gray and Moore,\n "N-body problems in statistical learning",\n Mining the sky, 2000,\n https://arxiv.org/abs/astro-ph/0012333'>
<Unimplemented 'footnote' '.. [2] Landy and Szalay,\n "Bias and variance of angular correlation functions",\n The Astrophysical Journal, 1993,\n http://adsabs.harvard.edu/abs/1993ApJ...412...64L'>
<Unimplemented 'footnote' '.. [3] Sheth, Connolly and Skibba,\n "Marked correlations in galaxy formation models",\n Arxiv e-print, 2005,\n https://arxiv.org/abs/astro-ph/0511773'>
<Unimplemented 'footnote' '.. [4] Hawkins, et al.,\n "The 2dF Galaxy Redshift Survey: correlation functions,\n peculiar velocities and the matter density of the Universe",\n Monthly Notices of the Royal Astronomical Society, 2002,\n http://adsabs.harvard.edu/abs/2003MNRAS.346...78H'>
<Unimplemented 'footnote' '.. [5] https://github.com/scipy/scipy/pull/5647#issuecomment-168474926'>
The other tree to draw points from, can be the same tree as self.
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.
1<=p<=infinity. Which Minkowski p-norm to use. Default 2.0. A finite large p may cause a ValueError if overflow can occur.
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
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
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]
Count how many nearby pairs can be formed.
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)See :
... sum([len(i) for i in indexes]) 1
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.spatial._kdtree.KDTree.count_neighbors
scipy.linalg._basic.solveh_banded
scipy.interpolate._rbfinterp.RBFInterpolator
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them