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#!python
#cython: boundscheck=False
#cython: wraparound=False
#cython: cdivision=True
# By Jake Vanderplas (2013) <jakevdp@cs.washington.edu>
# written for the scikit-learn project
# License: BSD
__all__ = ['KDTree']
DOC_DICT = {'BinaryTree': 'KDTree', 'binary_tree': 'kd_tree'}
VALID_METRICS = ['EuclideanDistance', 'ManhattanDistance',
'ChebyshevDistance', 'MinkowskiDistance']
include "binary_tree.pxi"
# Inherit KDTree from BinaryTree
cdef class KDTree(BinaryTree):
__doc__ = CLASS_DOC.format(**DOC_DICT)
pass
#----------------------------------------------------------------------
# The functions below specialized the Binary Tree as a KD Tree
#
# Note that these functions use the concept of "reduced distance".
# The reduced distance, defined for some metrics, is a quantity which
# is more efficient to compute than the distance, but preserves the
# relative rankings of the true distance. For example, the reduced
# distance for the Euclidean metric is the squared-euclidean distance.
# For some metrics, the reduced distance is simply the distance.
cdef int allocate_data(BinaryTree tree, ITYPE_t n_nodes,
ITYPE_t n_features) except -1:
"""Allocate arrays needed for the KD Tree"""
tree.node_bounds_arr = np.zeros((2, n_nodes, n_features), dtype=DTYPE)
tree.node_bounds = get_memview_DTYPE_3D(tree.node_bounds_arr)
return 0
cdef int init_node(BinaryTree tree, ITYPE_t i_node,
ITYPE_t idx_start, ITYPE_t idx_end) except -1:
"""Initialize the node for the dataset stored in tree.data"""
cdef ITYPE_t n_features = tree.data.shape[1]
cdef ITYPE_t i, j
cdef DTYPE_t rad = 0
cdef DTYPE_t* lower_bounds = &tree.node_bounds[0, i_node, 0]
cdef DTYPE_t* upper_bounds = &tree.node_bounds[1, i_node, 0]
cdef DTYPE_t* data = &tree.data[0, 0]
cdef ITYPE_t* idx_array = &tree.idx_array[0]
cdef DTYPE_t* data_row
# determine Node bounds
for j in range(n_features):
lower_bounds[j] = INF
upper_bounds[j] = -INF
# Compute the actual data range. At build time, this is slightly
# slower than using the previously-computed bounds of the parent node,
# but leads to more compact trees and thus faster queries.
for i in range(idx_start, idx_end):
data_row = data + idx_array[i] * n_features
for j in range(n_features):
lower_bounds[j] = fmin(lower_bounds[j], data_row[j])
upper_bounds[j] = fmax(upper_bounds[j], data_row[j])
for j in range(n_features):
if tree.dist_metric.p == INF:
rad = fmax(rad, 0.5 * (upper_bounds[j] - lower_bounds[j]))
else:
rad += pow(0.5 * abs(upper_bounds[j] - lower_bounds[j]),
tree.dist_metric.p)
tree.node_data[i_node].idx_start = idx_start
tree.node_data[i_node].idx_end = idx_end
# The radius will hold the size of the circumscribed hypersphere measured
# with the specified metric: in querying, this is used as a measure of the
# size of each node when deciding which nodes to split.
tree.node_data[i_node].radius = pow(rad, 1. / tree.dist_metric.p)
return 0
cdef DTYPE_t min_rdist(BinaryTree tree, ITYPE_t i_node,
DTYPE_t* pt) nogil except -1:
"""Compute the minimum reduced-distance between a point and a node"""
cdef ITYPE_t n_features = tree.data.shape[1]
cdef DTYPE_t d, d_lo, d_hi, rdist=0.0
cdef ITYPE_t j
if tree.dist_metric.p == INF:
for j in range(n_features):
d_lo = tree.node_bounds[0, i_node, j] - pt[j]
d_hi = pt[j] - tree.node_bounds[1, i_node, j]
d = (d_lo + fabs(d_lo)) + (d_hi + fabs(d_hi))
rdist = fmax(rdist, 0.5 * d)
else:
# here we'll use the fact that x + abs(x) = 2 * max(x, 0)
for j in range(n_features):
d_lo = tree.node_bounds[0, i_node, j] - pt[j]
d_hi = pt[j] - tree.node_bounds[1, i_node, j]
d = (d_lo + fabs(d_lo)) + (d_hi + fabs(d_hi))
rdist += pow(0.5 * d, tree.dist_metric.p)
return rdist
cdef DTYPE_t min_dist(BinaryTree tree, ITYPE_t i_node, DTYPE_t* pt) except -1:
"""Compute the minimum distance between a point and a node"""
if tree.dist_metric.p == INF:
return min_rdist(tree, i_node, pt)
else:
return pow(min_rdist(tree, i_node, pt), 1. / tree.dist_metric.p)
cdef DTYPE_t max_rdist(BinaryTree tree,
ITYPE_t i_node, DTYPE_t* pt) except -1:
"""Compute the maximum reduced-distance between a point and a node"""
cdef ITYPE_t n_features = tree.data.shape[1]
cdef DTYPE_t d, d_lo, d_hi, rdist=0.0
cdef ITYPE_t j
if tree.dist_metric.p == INF:
for j in range(n_features):
rdist = fmax(rdist, fabs(pt[j] - tree.node_bounds[0, i_node, j]))
rdist = fmax(rdist, fabs(pt[j] - tree.node_bounds[1, i_node, j]))
else:
for j in range(n_features):
d_lo = fabs(pt[j] - tree.node_bounds[0, i_node, j])
d_hi = fabs(pt[j] - tree.node_bounds[1, i_node, j])
rdist += pow(fmax(d_lo, d_hi), tree.dist_metric.p)
return rdist
cdef DTYPE_t max_dist(BinaryTree tree, ITYPE_t i_node, DTYPE_t* pt) except -1:
"""Compute the maximum distance between a point and a node"""
if tree.dist_metric.p == INF:
return max_rdist(tree, i_node, pt)
else:
return pow(max_rdist(tree, i_node, pt), 1. / tree.dist_metric.p)
cdef inline int min_max_dist(BinaryTree tree, ITYPE_t i_node, DTYPE_t* pt,
DTYPE_t* min_dist, DTYPE_t* max_dist) nogil except -1:
"""Compute the minimum and maximum distance between a point and a node"""
cdef ITYPE_t n_features = tree.data.shape[1]
cdef DTYPE_t d, d_lo, d_hi
cdef ITYPE_t j
min_dist[0] = 0.0
max_dist[0] = 0.0
if tree.dist_metric.p == INF:
for j in range(n_features):
d_lo = tree.node_bounds[0, i_node, j] - pt[j]
d_hi = pt[j] - tree.node_bounds[1, i_node, j]
d = (d_lo + fabs(d_lo)) + (d_hi + fabs(d_hi))
min_dist[0] = fmax(min_dist[0], 0.5 * d)
max_dist[0] = fmax(max_dist[0],
fabs(pt[j] - tree.node_bounds[0, i_node, j]))
max_dist[0] = fmax(max_dist[0],
fabs(pt[j] - tree.node_bounds[1, i_node, j]))
else:
# as above, use the fact that x + abs(x) = 2 * max(x, 0)
for j in range(n_features):
d_lo = tree.node_bounds[0, i_node, j] - pt[j]
d_hi = pt[j] - tree.node_bounds[1, i_node, j]
d = (d_lo + fabs(d_lo)) + (d_hi + fabs(d_hi))
min_dist[0] += pow(0.5 * d, tree.dist_metric.p)
max_dist[0] += pow(fmax(fabs(d_lo), fabs(d_hi)),
tree.dist_metric.p)
min_dist[0] = pow(min_dist[0], 1. / tree.dist_metric.p)
max_dist[0] = pow(max_dist[0], 1. / tree.dist_metric.p)
return 0
cdef inline DTYPE_t min_rdist_dual(BinaryTree tree1, ITYPE_t i_node1,
BinaryTree tree2, ITYPE_t i_node2) except -1:
"""Compute the minimum reduced distance between two nodes"""
cdef ITYPE_t n_features = tree1.data.shape[1]
cdef DTYPE_t d, d1, d2, rdist=0.0
cdef DTYPE_t zero = 0.0
cdef ITYPE_t j
if tree1.dist_metric.p == INF:
for j in range(n_features):
d1 = (tree1.node_bounds[0, i_node1, j]
- tree2.node_bounds[1, i_node2, j])
d2 = (tree2.node_bounds[0, i_node2, j]
- tree1.node_bounds[1, i_node1, j])
d = (d1 + fabs(d1)) + (d2 + fabs(d2))
rdist = fmax(rdist, 0.5 * d)
else:
# here we'll use the fact that x + abs(x) = 2 * max(x, 0)
for j in range(n_features):
d1 = (tree1.node_bounds[0, i_node1, j]
- tree2.node_bounds[1, i_node2, j])
d2 = (tree2.node_bounds[0, i_node2, j]
- tree1.node_bounds[1, i_node1, j])
d = (d1 + fabs(d1)) + (d2 + fabs(d2))
rdist += pow(0.5 * d, tree1.dist_metric.p)
return rdist
cdef inline DTYPE_t min_dist_dual(BinaryTree tree1, ITYPE_t i_node1,
BinaryTree tree2, ITYPE_t i_node2) except -1:
"""Compute the minimum distance between two nodes"""
return tree1.dist_metric._rdist_to_dist(min_rdist_dual(tree1, i_node1,
tree2, i_node2))
cdef inline DTYPE_t max_rdist_dual(BinaryTree tree1, ITYPE_t i_node1,
BinaryTree tree2, ITYPE_t i_node2) except -1:
"""Compute the maximum reduced distance between two nodes"""
cdef ITYPE_t n_features = tree1.data.shape[1]
cdef DTYPE_t d, d1, d2, rdist=0.0
cdef DTYPE_t zero = 0.0
cdef ITYPE_t j
if tree1.dist_metric.p == INF:
for j in range(n_features):
rdist = fmax(rdist, fabs(tree1.node_bounds[0, i_node1, j]
- tree2.node_bounds[1, i_node2, j]))
rdist = fmax(rdist, fabs(tree1.node_bounds[1, i_node1, j]
- tree2.node_bounds[0, i_node2, j]))
else:
for j in range(n_features):
d1 = fabs(tree1.node_bounds[0, i_node1, j]
- tree2.node_bounds[1, i_node2, j])
d2 = fabs(tree1.node_bounds[1, i_node1, j]
- tree2.node_bounds[0, i_node2, j])
rdist += pow(fmax(d1, d2), tree1.dist_metric.p)
return rdist
cdef inline DTYPE_t max_dist_dual(BinaryTree tree1, ITYPE_t i_node1,
BinaryTree tree2, ITYPE_t i_node2) except -1:
"""Compute the maximum distance between two nodes"""
return tree1.dist_metric._rdist_to_dist(max_rdist_dual(tree1, i_node1,
tree2, i_node2))
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