# Copyright 2004 by Thomas Hamelryck.
# All rights reserved.
# This code is part of the Biopython distribution and governed by its
# license. Please see the LICENSE file that should have been included
# as part of this package.
"""KD tree data structure for searching N-dimensional vectors.
The KD tree data structure can be used for all kinds of searches that
involve N-dimensional vectors, e.g. neighbor searches (find all points
within a radius of a given point) or finding all point pairs in a set
that are within a certain radius of each other. See "Computational Geometry:
Algorithms and Applications" (Mark de Berg, Marc van Kreveld, Mark Overmars,
Otfried Schwarzkopf). Author: Thomas Hamelryck.
"""
from __future__ import print_function
from numpy import sum, sqrt, array
from numpy import random
from Bio.KDTree import _CKDTree
__docformat__ = "restructuredtext en"
def _dist(p, q):
diff = p - q
return sqrt(sum(diff * diff))
def _neighbor_test(nr_points, dim, bucket_size, radius):
"""Test all fixed radius neighbor search.
Test all fixed radius neighbor search using the
KD tree C module.
Arguments:
- nr_points: number of points used in test
- dim: dimension of coords
- bucket_size: nr of points per tree node
- radius: radius of search (typically 0.05 or so)
Returns true if the test passes.
"""
# KD tree search
kdt = _CKDTree.KDTree(dim, bucket_size)
coords = random.random((nr_points, dim))
kdt.set_data(coords)
neighbors = kdt.neighbor_search(radius)
r = [neighbor.radius for neighbor in neighbors]
if r is None:
l1 = 0
else:
l1 = len(r)
# now do a slow search to compare results
neighbors = kdt.neighbor_simple_search(radius)
r = [neighbor.radius for neighbor in neighbors]
if r is None:
l2 = 0
else:
l2 = len(r)
if l1 == l2:
# print("Passed.")
return True
else:
print("Not passed: %i != %i." % (l1, l2))
return False
def _test(nr_points, dim, bucket_size, radius):
"""Test neighbor search.
Test neighbor search using the KD tree C module.
Arguments:
- nr_points: number of points used in test
- dim: dimension of coords
- bucket_size: nr of points per tree node
- radius: radius of search (typically 0.05 or so)
Returns true if the test passes.
"""
# kd tree search
kdt = _CKDTree.KDTree(dim, bucket_size)
coords = random.random((nr_points, dim))
center = coords[0]
kdt.set_data(coords)
kdt.search_center_radius(center, radius)
r = kdt.get_indices()
if r is None:
l1 = 0
else:
l1 = len(r)
l2 = 0
# now do a manual search to compare results
for i in range(0, nr_points):
p = coords[i]
if _dist(p, center) <= radius:
l2 = l2 + 1
if l1 == l2:
# print("Passed.")
return True
else:
print("Not passed: %i != %i." % (l1, l2))
return False
class KDTree(object):
"""KD tree implementation (C++, SWIG python wrapper)
The KD tree data structure can be used for all kinds of searches that
involve N-dimensional vectors, e.g. neighbor searches (find all points
within a radius of a given point) or finding all point pairs in a set
that are within a certain radius of each other.
Reference:
Computational Geometry: Algorithms and Applications
Second Edition
Mark de Berg, Marc van Kreveld, Mark Overmars, Otfried Schwarzkopf
published by Springer-Verlag
2nd rev. ed. 2000.
ISBN: 3-540-65620-0
The KD tree data structure is described in chapter 5, pg. 99.
The following article made clear to me that the nodes should
contain more than one point (this leads to dramatic speed
improvements for the "all fixed radius neighbor search", see
below):
JL Bentley, "Kd trees for semidynamic point sets," in Sixth Annual ACM
Symposium on Computational Geometry, vol. 91. San Francisco, 1990
This KD implementation also performs a "all fixed radius neighbor search",
i.e. it can find all point pairs in a set that are within a certain radius
of each other. As far as I know the algorithm has not been published.
"""
def __init__(self, dim, bucket_size=1):
self.dim = dim
self.kdt = _CKDTree.KDTree(dim, bucket_size)
self.built = 0
# Set data
def set_coords(self, coords):
"""Add the coordinates of the points.
Arguments:
- coords: two dimensional NumPy array. E.g. if the points
have dimensionality D and there are N points, the coords
array should be NxD dimensional.
"""
if coords.min() <= -1e6 or coords.max() >= 1e6:
raise Exception("Points should lie between -1e6 and 1e6")
if len(coords.shape) != 2 or coords.shape[1] != self.dim:
raise Exception("Expected a Nx%i NumPy array" % self.dim)
self.kdt.set_data(coords)
self.built = 1
# Fixed radius search for a point
def search(self, center, radius):
"""Search all points within radius of center.
Arguments:
- center: one dimensional NumPy array. E.g. if the points have
dimensionality D, the center array should be D dimensional.
- radius: float>0
"""
if not self.built:
raise Exception("No point set specified")
if center.shape != (self.dim,):
raise Exception("Expected a %i-dimensional NumPy array"
% self.dim)
self.kdt.search_center_radius(center, radius)
def get_radii(self):
"""Return radii.
Return the list of distances from center after
a neighbor search.
"""
a = self.kdt.get_radii()
if a is None:
return []
return a
def get_indices(self):
"""Return the list of indices.
Return the list of indices after a neighbor search.
The indices refer to the original coords NumPy array. The
coordinates with these indices were within radius of center.
For an index pair, the first index<second index.
"""
a = self.kdt.get_indices()
if a is None:
return []
return a
# Fixed radius search for all points
def all_search(self, radius):
"""All fixed neighbor search.
Search all point pairs that are within radius.
Arguments:
- radius: float (>0)
"""
if not self.built:
raise Exception("No point set specified")
self.neighbors = self.kdt.neighbor_search(radius)
def all_get_indices(self):
"""Return All Fixed Neighbor Search results.
Return a Nx2 dim NumPy array containing
the indices of the point pairs, where N
is the number of neighbor pairs.
"""
a = array([[neighbor.index1, neighbor.index2] for neighbor in self.neighbors])
return a
def all_get_radii(self):
"""Return All Fixed Neighbor Search results.
Return an N-dim array containing the distances
of all the point pairs, where N is the number
of neighbor pairs..
"""
return [neighbor.radius for neighbor in self.neighbors]
if __name__ == "__main__":
nr_points = 100000
dim = 3
bucket_size = 10
query_radius = 10
coords = 200 * random.random((nr_points, dim))
kdtree = KDTree(dim, bucket_size)
# enter coords
kdtree.set_coords(coords)
# Find all point pairs within radius
kdtree.all_search(query_radius)
# get indices & radii of points
# indices is a list of tuples. Each tuple contains the
# two indices of a point pair within query_radius of
# each other.
indices = kdtree.all_get_indices()
radii = kdtree.all_get_radii()
print("Found %i point pairs within radius %f." % (len(indices), query_radius))
# Do 10 individual queries
for i in range(0, 10):
# pick a random center
center = random.random(dim)
# search neighbors
kdtree.search(center, query_radius)
# get indices & radii of points
indices = kdtree.get_indices()
radii = kdtree.get_radii()
x, y, z = center
print("Found %i points in radius %f around center (%.2f, %.2f, %.2f)." % (len(indices), query_radius, x, y, z))