def closest(self, hpoint):
"""
Return point closest to HRect (from Moore's eqn. 6.6)
@param hpoint: HPoint
"""
p = HPoint(len(hpoint.coord))
for i, val in enumerate(hpoint.coord):
if val <= self.min.coord[i]:
p.coord[i] = self.min.coord[i]
elif val >= self.max.coord[i]:
p.coord[i] = self.max.coord[i]
else:
p.coord[i] = val
return p
def nearest_k(self, key, k, alpha):
"""
Find KD-tree nodes whose keys are k nearest neighbors to key. Uses
algorithm above. Neighbors are returned in ascending order of distance to
key.
@param key: [float] - key for KD-tree node
@param k: int - how many neighbors to find
@param alpha: float - alpha for approximate k-nn
"""
if k < 0 or k > self.m_count:
raise Exception(
"Number of neighbors (" + str(k) +
") cannot be negative or greater than number of nodes (" +
str(self.m_count) + ").")
if len(key) != self.m_K:
raise Exception("KDTree: wrong key size!")
nbrs = [None for _ in range(k)]
nnl = NearestNeighborList(k)
# initial call is with infinite hyper-rectangle and max distance
hrect = HRect.infinite_hrect(len(key))
max_dist_sqd = float("inf")
keypoint = HPoint(key)
KDNode.nnbr(self.m_root, keypoint, hrect, max_dist_sqd, 0, self.m_K,
nnl, alpha)
for i in range(k):
kdnode = nnl.remove_highest()
nbrs[k - i - 1] = kdnode.value
return nbrs
def search(self, key):
"""
Find KD-tree node whose key is identical to key. Uses algorithm
translated from 352.srch.c of Gonnet & Baeza-Yates.
@param key: [float] - key for KD-tree node
@return: Object - object at key, or None if not found
"""
if len(key) != self.m_K:
raise Exception("KDTree: wrong key size!")
kdnode = KDNode.srch(HPoint(key), self.m_root, self.m_K)
if kdnode is None:
return None
else:
return kdnode.value
def infinite_hrect(cls, dim):
"""
Create an infinite rectangle. Used in the initial conditions of KDTree.nearest()
"""
vmin = HPoint(dim)
vmax = HPoint(dim)
vmin.coord = [-float("inf") for _ in range(dim)]
vmax.coord = [float("inf") for _ in range(dim)]
return HRect(vmin, vmax)
def delete(self, key):
"""
Delete a node from a KD-tree. Instead of actually deleting node and
rebuilding tree, marks node as deleted. Hence, it is up to the caller to
rebuild the tree as needed for efficiency.
@param key: [float] - key for KD-tree node
"""
if len(key) != self.m_K:
raise Exception("KDTree: wrong key size!")
kdnode = KDNode.srch(HPoint(key), self.m_root, self.m_K)
if kdnode is None:
raise Exception("KDTree: key missing!")
else:
kdnode.deleted = True
self.m_count -= 1
def insert(self, key, value):
"""
Insert a node in a KD-tree. Uses algorithm translated from 352.ins.c of
Book{GonnetBaezaYates1991,
author = {G.H. Gonnet and R. Baeza-Yates},
title = {Handbook of Algorithms and Data Structures},
publisher = {Addison-Wesley},
year = {1991}
}
@param key: [float] - key for KD-tree node
@param value: Object - value at the key
"""
if len(key) != self.m_K:
raise Exception("KDTree: wrong key size!")
else:
self.m_root = KDNode.ins(HPoint(key), value, self.m_root, 0,
self.m_K)
self.m_count += 1
def nnbr(cls, kdnode, target, hrect, max_dist_sqd, level, K, nnl, alpha):
"""
Method Nearest Neighbor from Andrew Moore's thesis. Numbered
comments are direct quotes from there. Step "SDL" is added to
make the algorithm work correctly. NearestNeighborList solution
courtesy of Bjoern Heckel.
@param kdnode: KDNode
@param target: HPoint
@param hrect: HRect
@param max_dist_sqd: float
@param level: int
@param K: int
@param nnl: NearestNeighborList
@param alpha: float
"""
# 1. if kd is empty then set dist-sqd to infinity and exit.
if kdnode is None:
return
# 2. s := split field of kd
split = level % K
# 3. pivot := dom-elt field of kd
pivot = kdnode.key
pivot_to_target = HPoint.sqrdist(pivot, target)
# 4. Cut hr into to sub-hyperrectangles left-hr and right-hr.
# The cut plane is through pivot and perpendicular to the s
# dimension.
left_hrect = hrect # optimize by not cloning
right_hrect = hrect.clone()
left_hrect.max.coord[split] = pivot.coord[split]
right_hrect.min.coord[split] = pivot.coord[split]
# 5. target-in-left := target_s <= pivot_s
target_in_left = target.coord[split] < pivot.coord[split]
# 6. if target-in-left then
# 6.1. nearer-kd := left field of kd and nearer-hr := left-hr
# 6.2. further-kd := right field of kd and further-hr := right-hr
if target_in_left:
nearer_kdnode = kdnode.left
nearer_hrect = left_hrect
further_kdnode = kdnode.right
further_hrect = right_hrect
# 7. if not target-in-left then
# 7.1. nearer-kd := right field of kd and nearer-hr := right-hr
# 7.2. further-kd := left field of kd and further-hr := left-hr
else:
nearer_kdnode = kdnode.right
nearer_hrect = right_hrect
further_kdnode = kdnode.left
further_hrect = left_hrect
# 8. Recursively call Nearest Neighbor with parameters
# (nearer-kd, target, nearer-hr, max-dist-sqd), storing the
# results in nearest and dist-sqd
cls.nnbr(nearer_kdnode, target, nearer_hrect, max_dist_sqd, level + 1,
K, nnl, alpha)
# furthest node in acceptable set
if not nnl.is_capacity_reached():
dist_sqd = float("inf")
else:
# furthest distance in accepted set
dist_sqd = nnl.get_max_priority()
# 9. max-dist-sqd := minimum of max-dist-sqd and dist-sqd
if dist_sqd < max_dist_sqd:
max_dist_sqd = dist_sqd
# 10. A nearer point could only lie in further-kd if there were some
# part of further-hr within distance sqrt(max-dist-sqd) of
# target. If this is the case then
# CHAD: Scale this comparison by alpha?
closest = further_hrect.closest(target)
if HPoint.eucdist(closest, target) < math.sqrt(max_dist_sqd) / alpha:
# 10.1 if (pivot-target)^2 < dist-sqd then
if pivot_to_target < dist_sqd:
# 10.1.1 nearest := (pivot, range-elt field of kd)
# 10.1.2 dist-sqd = (pivot-target)^2
dist_sqd = pivot_to_target
# add to nnl
if not kdnode.deleted:
nnl.insert(kdnode, dist_sqd)
# 10.1.3 max-dist-sqd = dist-sqd
# max_dist_sqd = dist_sqd;
if nnl.is_capacity_reached():
max_dist_sqd = nnl.get_max_priority()
else:
max_dist_sqd = float("inf")
# 10.2 Recursively call Nearest Neighbor with parameters
# (further-kd, target, further-hr, max-dist_sqd),
# storing results in temp-nearest and temp-dist-sqd
cls.nnbr(further_kdnode, target, further_hrect, max_dist_sqd,
level + 1, K, nnl, alpha)
temp_dist_sqd = nnl.get_max_priority()
# 10.3 If tmp-dist-sqd < dist-sqd then
if temp_dist_sqd < dist_sqd:
# 10.3.1 nearest := temp_nearest and dist_sqd := temp_dist_sqd
dist_sqd = temp_dist_sqd
# SDL: otherwise, current point is nearest
elif pivot_to_target < max_dist_sqd:
#nearest = kdnode
dist_sqd = pivot_to_target
def nnbr(cls, kdnode, target, hrect, max_dist_sqd, level, K, nnl, alpha):
"""
Method Nearest Neighbor from Andrew Moore's thesis. Numbered
comments are direct quotes from there. Step "SDL" is added to
make the algorithm work correctly. NearestNeighborList solution
courtesy of Bjoern Heckel.
@param kdnode: KDNode
@param target: HPoint
@param hrect: HRect
@param max_dist_sqd: float
@param level: int
@param K: int
@param nnl: NearestNeighborList
@param alpha: float
"""
# 1. if kd is empty then set dist-sqd to infinity and exit.
if kdnode is None or kdnode.key is None or target is None:
return
# 2. s := split field of kd
split = level % K
# 3. pivot := dom-elt field of kd
pivot = kdnode.key;
pivot_to_target = HPoint.sqrdist(pivot, target);
# 4. Cut hr into to sub-hyperrectangles left-hr and right-hr.
# The cut plane is through pivot and perpendicular to the s
# dimension.
left_hrect = hrect # optimize by not cloning
right_hrect = hrect.clone()
left_hrect.max.coord[split] = pivot.coord[split]
right_hrect.min.coord[split] = pivot.coord[split]
# 5. target-in-left := target_s <= pivot_s
target_in_left = target.coord[split] < pivot.coord[split]
# 6. if target-in-left then
# 6.1. nearer-kd := left field of kd and nearer-hr := left-hr
# 6.2. further-kd := right field of kd and further-hr := right-hr
if target_in_left:
nearer_kdnode = kdnode.left
nearer_hrect = left_hrect
further_kdnode = kdnode.right
further_hrect = right_hrect
# 7. if not target-in-left then
# 7.1. nearer-kd := right field of kd and nearer-hr := right-hr
# 7.2. further-kd := left field of kd and further-hr := left-hr
else:
nearer_kdnode = kdnode.right;
nearer_hrect = right_hrect;
further_kdnode = kdnode.left;
further_hrect = left_hrect;
# 8. Recursively call Nearest Neighbor with parameters
# (nearer-kd, target, nearer-hr, max-dist-sqd), storing the
# results in nearest and dist-sqd
cls.nnbr(nearer_kdnode, target, nearer_hrect, max_dist_sqd, level + 1, K, nnl, alpha)
# furthest node in acceptable set
if not nnl.is_capacity_reached():
dist_sqd = float("inf")
else:
# furthest distance in accepted set
dist_sqd = nnl.get_max_priority()
# 9. max-dist-sqd := minimum of max-dist-sqd and dist-sqd
if dist_sqd < max_dist_sqd:
max_dist_sqd = dist_sqd
# 10. A nearer point could only lie in further-kd if there were some
# part of further-hr within distance sqrt(max-dist-sqd) of
# target. If this is the case then
# CHAD: Scale this comparison by alpha?
closest = further_hrect.closest(target)
if HPoint.eucdist(closest, target) < math.sqrt(max_dist_sqd) / alpha:
# 10.1 if (pivot-target)^2 < dist-sqd then
if pivot_to_target < dist_sqd:
# 10.1.1 nearest := (pivot, range-elt field of kd)
# 10.1.2 dist-sqd = (pivot-target)^2
dist_sqd = pivot_to_target
# add to nnl
if not kdnode.deleted:
nnl.insert(kdnode, dist_sqd)
# 10.1.3 max-dist-sqd = dist-sqd
# max_dist_sqd = dist_sqd;
if nnl.is_capacity_reached():
max_dist_sqd = nnl.get_max_priority()
else:
max_dist_sqd = float("inf")
# 10.2 Recursively call Nearest Neighbor with parameters
# (further-kd, target, further-hr, max-dist_sqd),
# storing results in temp-nearest and temp-dist-sqd
cls.nnbr(further_kdnode, target, further_hrect, max_dist_sqd, level + 1, K, nnl, alpha)
temp_dist_sqd = nnl.get_max_priority()
# 10.3 If tmp-dist-sqd < dist-sqd then
if temp_dist_sqd < dist_sqd:
# 10.3.1 nearest := temp_nearest and dist_sqd := temp_dist_sqd
dist_sqd = temp_dist_sqd
# SDL: otherwise, current point is nearest
elif pivot_to_target < max_dist_sqd:
#nearest = kdnode
dist_sqd = pivot_to_target