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kdtree.py
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kdtree.py
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# vim: fileencoding=utf-8
import random
from rect import HyperRect
# Multidimensional Binary Search Trees Used for Associative Searching, Jon Louis Bentley
def kdtree(dimension):
return KDTree(dimension)
def static_kdtree(points):
return StaticKDTree(points)
def euclidean_dist(p1, p2):
assert len(p1) == len(p2)
return sum((a-b)**2 for a, b in zip(p1, p2)) ** 0.5
LOSON, HISON = 0, 1
class KDNode(object):
def __init__(self, point=None):
self.point = point
self.parent = None
self.children = [None, None]
@property
def loson(self):
return self.children[LOSON]
@loson.setter
def loson(self, value):
self.children[LOSON] = value
@property
def hison(self):
return self.children[HISON]
@hison.setter
def hison(self, value):
self.children[HISON] = value
def __len__(self):
return len(self.point)
def __repr__(self):
return '<KDNode at %r, loson:%r, hison:%r]>' % (self.point,
self.loson and self.loson.point or None, self.hison and self.hison.point or None)
class KDTree(object):
def __init__(self, dimensions):
self.dim = dimensions
self.root = None
self._rect = None
self._size = 0
def __len__(self):
return self._size
def __repr__(self):
return '<KDTree with root: %r>' % self.root
def _successor(self, node, point, _disc):
for i in range(_disc, self.dim) + range(0, _disc):
if point[i] < node.point[i]:
return LOSON
if point[i] > node.point[i]:
return HISON
raise Exception('the point is the same with node.point')
def _minimum(self, node, disc, _disc):
_node, _d = node, _disc
_disc_next = (_disc + 1) % self.dim
if _disc == disc:
child = node.loson
if child:
_node, _d = self._minimum(child, disc, _disc_next)
else:
if any(node.children):
_node, _d = min([self._minimum(child, disc, _disc_next) for child in node.children if child] + [(node, _disc)],
key=lambda node_disc: node_disc[0].point[disc])
return _node, _d
def _maximum(self, node, disc, _disc):
_node, _d = node, _disc
_disc_next = (_disc + 1) % self.dim
if _disc == disc:
child = node.hison
if child:
_node, _d = self._maximum(child, disc, _disc_next)
else:
if any(node.children):
_node, _d = max([self._maximum(child, disc, _disc_next) for child in node.children if child] + [(node, _disc)],
key=lambda node_disc: node_disc[0].point[disc])
return _node, _d
def insert(self, point):
''' insert a point into kdtree '''
new_node = KDNode(point)
node, _disc = self.root, 0
if not node:
self.root = new_node
self._rect = HyperRect.point(point)
else:
while True:
if node.point == point:
return node
son = self._successor(node, point, _disc)
child = node.children[son]
if not child:
break
node = child
_disc = (_disc + 1) % self.dim
node.children[son] = new_node
new_node.parent = node
self._rect.enlarge_to(point)
self._size += 1
return None
def _delete(self, node, _disc):
if not node.loson and not node.hison:
if node.parent:
son = LOSON if node.parent.loson is node else HISON
node.parent.children[son] = None
return None
disc = _disc
_disc = (_disc + 1) % self.dim
q, d = self._minimum(node.hison, disc, _disc) if node.hison else self._maximum(node.loson, disc, _disc)
node.point = q.point
qfather = q.parent
qson = LOSON if qfather.loson is q else HISON
qfather.children[qson] = self._delete(q, d)
return node
def delete(self, point):
''' delete a point from the kdtree '''
node, _disc = self.root, 0
while node:
if node.point == point:
break
node = node.children[self._successor(node, point, _disc)]
_disc = (_disc + 1) % self.dim
if node:
if node is self.root:
self.root = self._delete(node, _disc)
else:
self._delete(node, _disc)
self._size -= 1
if self._size == 1:
self._rect = HyperRect.point(point)
elif self._size == 0:
self._rect = None
return node
def _nn(self, node, point, _rect, dist, best, _disc):
if not node or _rect.min_dist(point) > dist:
return float('inf'), None
_disc_next = (_disc + 1) % self.dim
dist, best = min((euclidean_dist(node.point, point), node.point), (dist, best))
lower = _rect.get_lower(node.point, _disc)
upper = _rect.get_upper(node.point, _disc)
if point[_disc] < node.point[_disc]:
dist, best = min(self._nn(node.loson, point, lower, dist, best, _disc_next), (dist, best))
dist, best = min(self._nn(node.hison, point, upper, dist, best, _disc_next), (dist, best))
else:
dist, best = min(self._nn(node.hison, point, upper, dist, best, _disc_next), (dist, best))
dist, best = min(self._nn(node.loson, point, lower, dist, best, _disc_next), (dist, best))
return dist, best
def nn(self, point):
''' find the nearest neighbour of the point '''
return self._nn(self.root, point, self._rect, float('inf'), None, 0)[1]
def nn_with_dist(self, point):
''' find the nearest neighbour of the point, returned with the dist '''
return self._nn(self.root, point, self._rect, float('inf'), None, 0)
def _knn(self, node, point, _rect, dist, best, _disc):
if not node or _rect.min_dist(point) > dist:
return
_disc_next = (_disc + 1) % self.dim
d = euclidean_dist(node.point, point)
if d <= dist:
best.append((d, node.point))
lower = _rect.get_lower(node.point, _disc)
upper = _rect.get_upper(node.point, _disc)
self._knn(node.loson, point, lower, dist, best, _disc_next)
self._knn(node.hison, point, upper, dist, best, _disc_next)
def knn(self, point, dist):
''' find the k nearest neighbours(ordered) of the point '''
best = []
self._knn(self.root, point, self._rect, dist, best, 0)
return [x[1] for x in sorted(best)]
def knn_with_dist(self, point, dist):
''' find the k nearest neighbours(ordered) of the point,
returned with dists '''
best = []
self._knn(self.root, point, self._rect, dist, best, 0)
return sorted(best)
class StaticKDTree(KDTree):
def __init__(self, points):
if not points:
raise Exception('points must NOT be empty')
points = [p for p in points]
random.shuffle(points)
super(StaticKDTree, self).__init__(len(points[0]))
self._size = len(points)
self._rect = HyperRect.point(points[0])
for p in points:
self._rect.enlarge_to(p)
self.root = self._build(points, 0, 0, len(points)-1)
def _build(self, points, _disc, p, r):
if p > r:
return None
m = self._median(points, _disc, p, r)
n = KDNode(points[m])
_disc = (_disc + 1) % self.dim
l = self._build(points, _disc, p, m-1)
h = self._build(points, _disc, m+1, r)
if l:
n.loson = l
l.parent = n
if h:
n.hison = h
h.parent = n
return n
def _median(self, points, _disc, p, r):
return self._select(points, _disc, p, r, (r-p)/2+1)
def _select(self, points, _disc, p, r, i):
if p == r:
return p
q = self._partition(points, _disc, p, r)
k = q - p + 1
if i == k:
return q
elif i < k:
return self._select(points, _disc, p, q-1, i)
else:
return self._select(points, _disc, q+1, r, i-k)
def _partition(self, points, _disc, p, r):
x = points[r]
i = p - 1
for j in xrange(p, r):
if points[j][_disc] <= x[_disc]:
i += 1
temp = points[i]
points[i] = points[j]
points[j] = temp
i += 1
temp = points[i]
points[i] = points[r]
points[r] = temp
return i
def _not_supported(*a, **kw):
raise Exception('this method is not supported')
insert = delete = _not_supported
def insert_delete_test():
N = 1000000
r = functools.partial(random.randint, 1, N)
count = 0
while True:
if count % 10 == 0:
pass
#print 'test count: %d' % count
tree = KDTree(2)
points, ps = [], set()
for x in xrange(10000):
i = r()
if i not in ps:
points.append(Point(i, i))
ps.add(i)
for p in points:
tree.insert(p)
if len(tree) != len(points):
print 'ERROR: inserting error'
print 'points is %r' % points
break
nn = tree.nn_with_dist(Point(N/2, N/2))
print nn
print tree.knn(Point(N/2, N/2), nn[0]*2)
#random.shuffle(points)
for p in points:
tree.delete(p)
if len(tree) or tree.root:
print 'ERROR: deleting error'
print 'points is %r' % points
break
count += 1
def nn_test():
tree = KDTree(2)
tree.insert(Point(3, 3))
tree.insert(Point(1, 1))
tree.insert(Point(2, 2))
print tree.nn(Point(0.5, 0.5))
def knn_test():
tree = KDTree(2)
tree.insert(Point(3, 3))
tree.insert(Point(1, 1))
tree.insert(Point(2, 2))
print tree.knn(Point(0, 0), 4.5)
def static_test():
points = []
points.append(Point(3, 3))
points.append(Point(1, 1))
points.append(Point(2, 2))
tree = static_kdtree(points)
print tree
if __name__ == '__main__':
import random, functools
from point import Point
static_test()
#insert_delete_test()
#knn_test()