suzanne.soy/FreeCAD
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

PathHelix: Drop requirement of scipy.spatial

Browse Source 
It was deemed that scipy is too heavy a requirement for FreeCAD just for
this little feature. Fortunately it was possible to extract the k-d tree
module from scipy with just minor modifications - it is quite
self-contained.

Now, only numpy is required.
This commit is contained in:
Lorenz Hüdepohl 2017-01-06 13:20:18 +01:00
parent cd3c1d574e
commit 1edc151c5d
3 changed files with 950 additions and 2 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

1
src/Mod/Path/CMakeLists.txt
View File

@ -53,6 +53,7 @@ SET(PathScripts_SRCS
PathScripts/PathStock.py
PathScripts/PathStop.py
PathScripts/PathHelix.py
PathScripts/kdtree.py
PathScripts/PathSurface.py
PathScripts/PathToolLenOffset.py
PathScripts/PathToolLibraryManager.py

8
src/Mod/Path/PathScripts/PathHelix.py
View File

@ -198,7 +198,11 @@ def helix_cut(center, r_out, r_in, dr, zmax, zmin, dz, safe_z, tool_diameter, vf
return out
def features_by_centers(base, features):
import scipy.spatial
try:
from scipy.spatial import KDTree
except ImportError:
from PathScripts.kdtree import KDTree
features = sorted(features,
key = lambda feature : getattr(base.Shape, feature).Surface.Radius,
reverse = True)
@ -206,7 +210,7 @@ def features_by_centers(base, features):
coordinates = [(cylinder.Surface.Center.x, cylinder.Surface.Center.y) for cylinder in
[getattr(base.Shape, feature) for feature in features]]
tree = scipy.spatial.KDTree(coordinates)
tree = KDTree(coordinates)
seen = {}
by_centers = {}

943
src/Mod/Path/PathScripts/kdtree.py Normal file
View File

@ -0,0 +1,943 @@
# Copyright Anne M. Archibald 2008
# Released under the scipy license
#
# Copyright (c) 2001, 2002 Enthought, Inc.
# All rights reserved.
#
# Copyright (c) 2003-2016 SciPy Developers.
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# a. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
# b. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
# c. Neither the name of Enthought nor the names of the SciPy Developers
# may be used to endorse or promote products derived from this software
# without specific prior written permission.
#
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR CONTRIBUTORS
# BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
# OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
# THE POSSIBILITY OF SUCH DAMAGE.
from __future__ import division, print_function, absolute_import
import sys
import numpy as np
from heapq import heappush, heappop
__all__ = ['minkowski_distance_p', 'minkowski_distance',
'distance_matrix',
'Rectangle', 'KDTree']
def minkowski_distance_p(x, y, p=2):
"""
Compute the p-th power of the L**p distance between two arrays.
For efficiency, this function computes the L**p distance but does
not extract the pth root. If `p` is 1 or infinity, this is equal to
the actual L**p distance.
Parameters
----------
x : (M, K) array_like
Input array.
y : (N, K) array_like
Input array.
p : float, 1 <= p <= infinity
Which Minkowski p-norm to use.
Examples
--------
>>> minkowski_distance_p([[0,0],[0,0]], [[1,1],[0,1]])
array([2, 1])
"""
x = np.asarray(x)
y = np.asarray(y)
if p == np.inf:
return np.amax(np.abs(y-x), axis=-1)
elif p == 1:
return np.sum(np.abs(y-x), axis=-1)
else:
return np.sum(np.abs(y-x)**p, axis=-1)
def minkowski_distance(x, y, p=2):
"""
Compute the L**p distance between two arrays.
Parameters
----------
x : (M, K) array_like
Input array.
y : (N, K) array_like
Input array.
p : float, 1 <= p <= infinity
Which Minkowski p-norm to use.
Examples
--------
>>> minkowski_distance([[0,0],[0,0]], [[1,1],[0,1]])
array([ 1.41421356, 1. ])
"""
x = np.asarray(x)
y = np.asarray(y)
if p == np.inf or p == 1:
return minkowski_distance_p(x, y, p)
else:
return minkowski_distance_p(x, y, p)**(1./p)
class Rectangle(object):
"""Hyperrectangle class.
Represents a Cartesian product of intervals.
"""
def __init__(self, maxes, mins):
"""Construct a hyperrectangle."""
self.maxes = np.maximum(maxes,mins).astype(np.float)
self.mins = np.minimum(maxes,mins).astype(np.float)
self.m, = self.maxes.shape
def __repr__(self):
return "<Rectangle %s>" % list(zip(self.mins, self.maxes))
def volume(self):
"""Total volume."""
return np.prod(self.maxes-self.mins)
def split(self, d, split):
"""
Produce two hyperrectangles by splitting.
In general, if you need to compute maximum and minimum
distances to the children, it can be done more efficiently
by updating the maximum and minimum distances to the parent.
Parameters
----------
d : int
Axis to split hyperrectangle along.
split :
Input.
"""
mid = np.copy(self.maxes)
mid[d] = split
less = Rectangle(self.mins, mid)
mid = np.copy(self.mins)
mid[d] = split
greater = Rectangle(mid, self.maxes)
return less, greater
def min_distance_point(self, x, p=2.):
"""
Return the minimum distance between input and points in the hyperrectangle.
Parameters
----------
x : array_like
Input.
p : float, optional
Input.
"""
return minkowski_distance(0, np.maximum(0,np.maximum(self.mins-x,x-self.maxes)),p)
def max_distance_point(self, x, p=2.):
"""
Return the maximum distance between input and points in the hyperrectangle.
Parameters
----------
x : array_like
Input array.
p : float, optional
Input.
"""
return minkowski_distance(0, np.maximum(self.maxes-x,x-self.mins),p)
def min_distance_rectangle(self, other, p=2.):
"""
Compute the minimum distance between points in the two hyperrectangles.
Parameters
----------
other : hyperrectangle
Input.
p : float
Input.
"""
return minkowski_distance(0, np.maximum(0,np.maximum(self.mins-other.maxes,other.mins-self.maxes)),p)
def max_distance_rectangle(self, other, p=2.):
"""
Compute the maximum distance between points in the two hyperrectangles.
Parameters
----------
other : hyperrectangle
Input.
p : float, optional
Input.
"""
return minkowski_distance(0, np.maximum(self.maxes-other.mins,other.maxes-self.mins),p)
class KDTree(object):
"""
kd-tree for quick nearest-neighbor lookup
This class provides an index into a set of k-dimensional points which
can be used to rapidly look up the nearest neighbors of any point.
Parameters
----------
data : (N,K) array_like
The data points to be indexed. This array is not copied, and
so modifying this data will result in bogus results.
leafsize : int, optional
The number of points at which the algorithm switches over to
brute-force. Has to be positive.
Raises
------
RuntimeError
The maximum recursion limit can be exceeded for large data
sets. If this happens, either increase the value for the `leafsize`
parameter or increase the recursion limit by::
>>> import sys
>>> sys.setrecursionlimit(10000)
Notes
-----
The algorithm used is described in Maneewongvatana and Mount 1999.
The general idea is that the kd-tree is a binary tree, each of whose
nodes represents an axis-aligned hyperrectangle. Each node specifies
an axis and splits the set of points based on whether their coordinate
along that axis is greater than or less than a particular value.
During construction, the axis and splitting point are chosen by the
"sliding midpoint" rule, which ensures that the cells do not all
become long and thin.
The tree can be queried for the r closest neighbors of any given point
(optionally returning only those within some maximum distance of the
point). It can also be queried, with a substantial gain in efficiency,
for the r approximate closest neighbors.
For large dimensions (20 is already large) do not expect this to run
significantly faster than brute force. High-dimensional nearest-neighbor
queries are a substantial open problem in computer science.
The tree also supports all-neighbors queries, both with arrays of points
and with other kd-trees. These do use a reasonably efficient algorithm,
but the kd-tree is not necessarily the best data structure for this
sort of calculation.
"""
def __init__(self, data, leafsize=10):
self.data = np.asarray(data)
self.n, self.m = np.shape(self.data)
self.leafsize = int(leafsize)
if self.leafsize < 1:
raise ValueError("leafsize must be at least 1")
self.maxes = np.amax(self.data,axis=0)
self.mins = np.amin(self.data,axis=0)
self.tree = self.__build(np.arange(self.n), self.maxes, self.mins)
class node(object):
if sys.version_info[0] >= 3:
def __lt__(self, other):
return id(self) < id(other)
def __gt__(self, other):
return id(self) > id(other)
def __le__(self, other):
return id(self) <= id(other)
def __ge__(self, other):
return id(self) >= id(other)
def __eq__(self, other):
return id(self) == id(other)
class leafnode(node):
def __init__(self, idx):
self.idx = idx
self.children = len(idx)
class innernode(node):
def __init__(self, split_dim, split, less, greater):
self.split_dim = split_dim
self.split = split
self.less = less
self.greater = greater
self.children = less.children+greater.children
def __build(self, idx, maxes, mins):
if len(idx) <= self.leafsize:
return KDTree.leafnode(idx)
else:
data = self.data[idx]
# maxes = np.amax(data,axis=0)
# mins = np.amin(data,axis=0)
d = np.argmax(maxes-mins)
maxval = maxes[d]
minval = mins[d]
if maxval == minval:
# all points are identical; warn user?
return KDTree.leafnode(idx)
data = data[:,d]
# sliding midpoint rule; see Maneewongvatana and Mount 1999
# for arguments that this is a good idea.
split = (maxval+minval)/2
less_idx = np.nonzero(data <= split)[0]
greater_idx = np.nonzero(data > split)[0]
if len(less_idx) == 0:
split = np.amin(data)
less_idx = np.nonzero(data <= split)[0]
greater_idx = np.nonzero(data > split)[0]
if len(greater_idx) == 0:
split = np.amax(data)
less_idx = np.nonzero(data < split)[0]
greater_idx = np.nonzero(data >= split)[0]
if len(less_idx) == 0:
# _still_ zero? all must have the same value
if not np.all(data == data[0]):
raise ValueError("Troublesome data array: %s" % data)
split = data[0]
less_idx = np.arange(len(data)-1)
greater_idx = np.array([len(data)-1])
lessmaxes = np.copy(maxes)
lessmaxes[d] = split
greatermins = np.copy(mins)
greatermins[d] = split
return KDTree.innernode(d, split,
self.__build(idx[less_idx],lessmaxes,mins),
self.__build(idx[greater_idx],maxes,greatermins))
def __query(self, x, k=1, eps=0, p=2, distance_upper_bound=np.inf):
side_distances = np.maximum(0,np.maximum(x-self.maxes,self.mins-x))
if p != np.inf:
side_distances **= p
min_distance = np.sum(side_distances)
else:
min_distance = np.amax(side_distances)
# priority queue for chasing nodes
# entries are:
# minimum distance between the cell and the target
# distances between the nearest side of the cell and the target
# the head node of the cell
q = [(min_distance,
tuple(side_distances),
self.tree)]
# priority queue for the nearest neighbors
# furthest known neighbor first
# entries are (-distance**p, i)
neighbors = []
if eps == 0:
epsfac = 1
elif p == np.inf:
epsfac = 1/(1+eps)
else:
epsfac = 1/(1+eps)**p
if p != np.inf and distance_upper_bound != np.inf:
distance_upper_bound = distance_upper_bound**p
while q:
min_distance, side_distances, node = heappop(q)
if isinstance(node, KDTree.leafnode):
# brute-force
data = self.data[node.idx]
ds = minkowski_distance_p(data,x[np.newaxis,:],p)
for i in range(len(ds)):
if ds[i] < distance_upper_bound:
if len(neighbors) == k:
heappop(neighbors)
heappush(neighbors, (-ds[i], node.idx[i]))
if len(neighbors) == k:
distance_upper_bound = -neighbors[0][0]
else:
# we don't push cells that are too far onto the queue at all,
# but since the distance_upper_bound decreases, we might get
# here even if the cell's too far
if min_distance > distance_upper_bound*epsfac:
# since this is the nearest cell, we're done, bail out
break
# compute minimum distances to the children and push them on
if x[node.split_dim] < node.split:
near, far = node.less, node.greater
else:
near, far = node.greater, node.less
# near child is at the same distance as the current node
heappush(q,(min_distance, side_distances, near))
# far child is further by an amount depending only
# on the split value
sd = list(side_distances)
if p == np.inf:
min_distance = max(min_distance, abs(node.split-x[node.split_dim]))
elif p == 1:
sd[node.split_dim] = np.abs(node.split-x[node.split_dim])
min_distance = min_distance - side_distances[node.split_dim] + sd[node.split_dim]
else:
sd[node.split_dim] = np.abs(node.split-x[node.split_dim])**p
min_distance = min_distance - side_distances[node.split_dim] + sd[node.split_dim]
# far child might be too far, if so, don't bother pushing it
if min_distance <= distance_upper_bound*epsfac:
heappush(q,(min_distance, tuple(sd), far))
if p == np.inf:
return sorted([(-d,i) for (d,i) in neighbors])
else:
return sorted([((-d)**(1./p),i) for (d,i) in neighbors])
def query(self, x, k=1, eps=0, p=2, distance_upper_bound=np.inf):
"""
Query the kd-tree for nearest neighbors
Parameters
----------
x : array_like, last dimension self.m
An array of points to query.
k : integer
The number of nearest neighbors to return.
eps : nonnegative float
Return approximate nearest neighbors; the kth returned value
is guaranteed to be no further than (1+eps) times the
distance to the real kth nearest neighbor.
p : float, 1<=p<=infinity
Which Minkowski p-norm to use.
1 is the sum-of-absolute-values "Manhattan" distance
2 is the usual Euclidean distance
infinity is the maximum-coordinate-difference distance
distance_upper_bound : nonnegative float
Return only neighbors within this distance. This is used to prune
tree searches, so if you are doing a series of nearest-neighbor
queries, it may help to supply the distance to the nearest neighbor
of the most recent point.
Returns
-------
d : array of floats
The distances to the nearest neighbors.
If x has shape tuple+(self.m,), then d has shape tuple if
k is one, or tuple+(k,) if k is larger than one. Missing
neighbors are indicated with infinite distances. If k is None,
then d is an object array of shape tuple, containing lists
of distances. In either case the hits are sorted by distance
(nearest first).
i : array of integers
The locations of the neighbors in self.data. i is the same
shape as d.
Examples
--------
>>> from PathScripts import kdtree
>>> x, y = np.mgrid[0:5, 2:8]
>>> tree = kdtree.KDTree(zip(x.ravel(), y.ravel()))
>>> tree.data
array([[0, 2],
[0, 3],
[0, 4],
[0, 5],
[0, 6],
[0, 7],
[1, 2],
[1, 3],
[1, 4],
[1, 5],
[1, 6],
[1, 7],
[2, 2],
[2, 3],
[2, 4],
[2, 5],
[2, 6],
[2, 7],
[3, 2],
[3, 3],
[3, 4],
[3, 5],
[3, 6],
[3, 7],
[4, 2],
[4, 3],
[4, 4],
[4, 5],
[4, 6],
[4, 7]])
>>> pts = np.array([[0, 0], [2.1, 2.9]])
>>> tree.query(pts)
(array([ 2. , 0.14142136]), array([ 0, 13]))
"""
x = np.asarray(x)
if np.shape(x)[-1] != self.m:
raise ValueError("x must consist of vectors of length %d but has shape %s" % (self.m, np.shape(x)))
if p < 1:
raise ValueError("Only p-norms with 1<=p<=infinity permitted")
retshape = np.shape(x)[:-1]
if retshape != ():
if k is None:
dd = np.empty(retshape,dtype=np.object)
ii = np.empty(retshape,dtype=np.object)
elif k > 1:
dd = np.empty(retshape+(k,),dtype=np.float)
dd.fill(np.inf)
ii = np.empty(retshape+(k,),dtype=np.int)
ii.fill(self.n)
elif k == 1:
dd = np.empty(retshape,dtype=np.float)
dd.fill(np.inf)
ii = np.empty(retshape,dtype=np.int)
ii.fill(self.n)
else:
raise ValueError("Requested %s nearest neighbors; acceptable numbers are integers greater than or equal to one, or None")
for c in np.ndindex(retshape):
hits = self.__query(x[c], k=k, eps=eps, p=p, distance_upper_bound=distance_upper_bound)
if k is None:
dd[c] = [d for (d,i) in hits]
ii[c] = [i for (d,i) in hits]
elif k > 1:
for j in range(len(hits)):
dd[c+(j,)], ii[c+(j,)] = hits[j]
elif k == 1:
if len(hits) > 0:
dd[c], ii[c] = hits[0]
else:
dd[c] = np.inf
ii[c] = self.n
return dd, ii
else:
hits = self.__query(x, k=k, eps=eps, p=p, distance_upper_bound=distance_upper_bound)
if k is None:
return [d for (d,i) in hits], [i for (d,i) in hits]
elif k == 1:
if len(hits) > 0:
return hits[0]
else:
return np.inf, self.n
elif k > 1:
dd = np.empty(k,dtype=np.float)
dd.fill(np.inf)
ii = np.empty(k,dtype=np.int)
ii.fill(self.n)
for j in range(len(hits)):
dd[j], ii[j] = hits[j]
return dd, ii
else:
raise ValueError("Requested %s nearest neighbors; acceptable numbers are integers greater than or equal to one, or None")
def __query_ball_point(self, x, r, p=2., eps=0):
R = Rectangle(self.maxes, self.mins)
def traverse_checking(node, rect):
if rect.min_distance_point(x, p) > r / (1. + eps):
return []
elif rect.max_distance_point(x, p) < r * (1. + eps):
return traverse_no_checking(node)
elif isinstance(node, KDTree.leafnode):
d = self.data[node.idx]
return node.idx[minkowski_distance(d, x, p) <= r].tolist()
else:
less, greater = rect.split(node.split_dim, node.split)
return traverse_checking(node.less, less) + \
traverse_checking(node.greater, greater)
def traverse_no_checking(node):
if isinstance(node, KDTree.leafnode):
return node.idx.tolist()
else:
return traverse_no_checking(node.less) + \
traverse_no_checking(node.greater)
return traverse_checking(self.tree, R)
def query_ball_point(self, x, r, p=2., eps=0):
"""Find all points within distance r of point(s) x.
Parameters
----------
x : array_like, shape tuple + (self.m,)
The point or points to search for neighbors of.
r : positive float
The radius of points to return.
p : float, optional
Which Minkowski p-norm to use. Should be in the range [1, inf].
eps : nonnegative float, optional
Approximate search. Branches of the tree are not explored if their
nearest points are further than ``r / (1 + eps)``, and branches are
added in bulk if their furthest points are nearer than
``r * (1 + eps)``.
Returns
-------
results : list or array of lists
If `x` is a single point, returns a list of the indices of the
neighbors of `x`. If `x` is an array of points, returns an object
array of shape tuple containing lists of neighbors.
Notes
-----
If you have many points whose neighbors you want to find, you may save
substantial amounts of time by putting them in a KDTree and using
query_ball_tree.
Examples
--------
>>> from PathScripts import kdtree
>>> x, y = np.mgrid[0:4, 0:4]
>>> points = zip(x.ravel(), y.ravel())
>>> tree = kdtree.KDTree(points)
>>> tree.query_ball_point([2, 0], 1)
[4, 8, 9, 12]
"""
x = np.asarray(x)
if x.shape[-1] != self.m:
raise ValueError("Searching for a %d-dimensional point in a "
"%d-dimensional KDTree" % (x.shape[-1], self.m))
if len(x.shape) == 1:
return self.__query_ball_point(x, r, p, eps)
else:
retshape = x.shape[:-1]
result = np.empty(retshape, dtype=np.object)
for c in np.ndindex(retshape):
result[c] = self.__query_ball_point(x[c], r, p=p, eps=eps)
return result
def query_ball_tree(self, other, r, p=2., eps=0):
"""Find all pairs of points whose distance is at most r
Parameters
----------
other : KDTree instance
The tree containing points to search against.
r : float
The maximum distance, has to be positive.
p : float, optional
Which Minkowski norm to use. `p` has to meet the condition
``1 <= p <= infinity``.
eps : float, optional
Approximate search. Branches of the tree are not explored
if their nearest points are further than ``r/(1+eps)``, and
branches are added in bulk if their furthest points are nearer
than ``r * (1+eps)``. `eps` has to be non-negative.
Returns
-------
results : list of lists
For each element ``self.data[i]`` of this tree, ``results[i]`` is a
list of the indices of its neighbors in ``other.data``.
"""
results = [[] for i in range(self.n)]
def traverse_checking(node1, rect1, node2, rect2):
if rect1.min_distance_rectangle(rect2, p) > r/(1.+eps):
return
elif rect1.max_distance_rectangle(rect2, p) < r*(1.+eps):
traverse_no_checking(node1, node2)
elif isinstance(node1, KDTree.leafnode):
if isinstance(node2, KDTree.leafnode):
d = other.data[node2.idx]
for i in node1.idx:
results[i] += node2.idx[minkowski_distance(d,self.data[i],p) <= r].tolist()
else:
less, greater = rect2.split(node2.split_dim, node2.split)
traverse_checking(node1,rect1,node2.less,less)
traverse_checking(node1,rect1,node2.greater,greater)
elif isinstance(node2, KDTree.leafnode):
less, greater = rect1.split(node1.split_dim, node1.split)
traverse_checking(node1.less,less,node2,rect2)
traverse_checking(node1.greater,greater,node2,rect2)
else:
less1, greater1 = rect1.split(node1.split_dim, node1.split)
less2, greater2 = rect2.split(node2.split_dim, node2.split)
traverse_checking(node1.less,less1,node2.less,less2)
traverse_checking(node1.less,less1,node2.greater,greater2)
traverse_checking(node1.greater,greater1,node2.less,less2)
traverse_checking(node1.greater,greater1,node2.greater,greater2)
def traverse_no_checking(node1, node2):
if isinstance(node1, KDTree.leafnode):
if isinstance(node2, KDTree.leafnode):
for i in node1.idx:
results[i] += node2.idx.tolist()
else:
traverse_no_checking(node1, node2.less)
traverse_no_checking(node1, node2.greater)
else:
traverse_no_checking(node1.less, node2)
traverse_no_checking(node1.greater, node2)
traverse_checking(self.tree, Rectangle(self.maxes, self.mins),
other.tree, Rectangle(other.maxes, other.mins))
return results
def query_pairs(self, r, p=2., eps=0):
"""
Find all pairs of points within a distance.
Parameters
----------
r : positive float
The maximum distance.
p : float, optional
Which Minkowski norm to use. `p` has to meet the condition
``1 <= p <= infinity``.
eps : float, optional
Approximate search. Branches of the tree are not explored
if their nearest points are further than ``r/(1+eps)``, and
branches are added in bulk if their furthest points are nearer
than ``r * (1+eps)``. `eps` has to be non-negative.
Returns
-------
results : set
Set of pairs ``(i,j)``, with ``i < j``, for which the corresponding
positions are close.
"""
results = set()
def traverse_checking(node1, rect1, node2, rect2):
if rect1.min_distance_rectangle(rect2, p) > r/(1.+eps):
return
elif rect1.max_distance_rectangle(rect2, p) < r*(1.+eps):
traverse_no_checking(node1, node2)
elif isinstance(node1, KDTree.leafnode):
if isinstance(node2, KDTree.leafnode):
# Special care to avoid duplicate pairs
if id(node1) == id(node2):
d = self.data[node2.idx]
for i in node1.idx:
for j in node2.idx[minkowski_distance(d,self.data[i],p) <= r]:
if i < j:
results.add((i,j))
else:
d = self.data[node2.idx]
for i in node1.idx:
for j in node2.idx[minkowski_distance(d,self.data[i],p) <= r]:
if i < j:
results.add((i,j))
elif j < i:
results.add((j,i))
else:
less, greater = rect2.split(node2.split_dim, node2.split)
traverse_checking(node1,rect1,node2.less,less)
traverse_checking(node1,rect1,node2.greater,greater)
elif isinstance(node2, KDTree.leafnode):
less, greater = rect1.split(node1.split_dim, node1.split)
traverse_checking(node1.less,less,node2,rect2)
traverse_checking(node1.greater,greater,node2,rect2)
else:
less1, greater1 = rect1.split(node1.split_dim, node1.split)
less2, greater2 = rect2.split(node2.split_dim, node2.split)
traverse_checking(node1.less,less1,node2.less,less2)
traverse_checking(node1.less,less1,node2.greater,greater2)
# Avoid traversing (node1.less, node2.greater) and
# (node1.greater, node2.less) (it's the same node pair twice
# over, which is the source of the complication in the
# original KDTree.query_pairs)
if id(node1) != id(node2):
traverse_checking(node1.greater,greater1,node2.less,less2)
traverse_checking(node1.greater,greater1,node2.greater,greater2)
def traverse_no_checking(node1, node2):
if isinstance(node1, KDTree.leafnode):
if isinstance(node2, KDTree.leafnode):
# Special care to avoid duplicate pairs
if id(node1) == id(node2):
for i in node1.idx:
for j in node2.idx:
if i < j:
results.add((i,j))
else:
for i in node1.idx:
for j in node2.idx:
if i < j:
results.add((i,j))
elif j < i:
results.add((j,i))
else:
traverse_no_checking(node1, node2.less)
traverse_no_checking(node1, node2.greater)
else:
# Avoid traversing (node1.less, node2.greater) and
# (node1.greater, node2.less) (it's the same node pair twice
# over, which is the source of the complication in the
# original KDTree.query_pairs)
if id(node1) == id(node2):
traverse_no_checking(node1.less, node2.less)
traverse_no_checking(node1.less, node2.greater)
traverse_no_checking(node1.greater, node2.greater)
else:
traverse_no_checking(node1.less, node2)
traverse_no_checking(node1.greater, node2)
traverse_checking(self.tree, Rectangle(self.maxes, self.mins),
self.tree, Rectangle(self.maxes, self.mins))
return results
def count_neighbors(self, other, r, p=2.):
"""
Count how many nearby pairs can be formed.
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``.
This is the "two-point correlation" described in Gray and Moore 2000,
"N-body problems in statistical learning", and the code here is based
on their algorithm.
Parameters
----------
other : KDTree instance
The other tree to draw points from.
r : float or one-dimensional array of floats
The radius to produce a count for. Multiple radii are searched with
a single tree traversal.
p : float, 1<=p<=infinity
Which Minkowski p-norm to use
Returns
-------
result : int or 1-D array of ints
The number of pairs. Note that this is internally stored in a numpy
int, and so may overflow if very large (2e9).
"""
def traverse(node1, rect1, node2, rect2, idx):
min_r = rect1.min_distance_rectangle(rect2,p)
max_r = rect1.max_distance_rectangle(rect2,p)
c_greater = r[idx] > max_r
result[idx[c_greater]] += node1.children*node2.children
idx = idx[(min_r <= r[idx]) & (r[idx] <= max_r)]
if len(idx) == 0:
return
if isinstance(node1,KDTree.leafnode):
if isinstance(node2,KDTree.leafnode):
ds = minkowski_distance(self.data[node1.idx][:,np.newaxis,:],
other.data[node2.idx][np.newaxis,:,:],
p).ravel()
ds.sort()
result[idx] += np.searchsorted(ds,r[idx],side='right')
else:
less, greater = rect2.split(node2.split_dim, node2.split)
traverse(node1, rect1, node2.less, less, idx)
traverse(node1, rect1, node2.greater, greater, idx)
else:
if isinstance(node2,KDTree.leafnode):
less, greater = rect1.split(node1.split_dim, node1.split)
traverse(node1.less, less, node2, rect2, idx)
traverse(node1.greater, greater, node2, rect2, idx)
else:
less1, greater1 = rect1.split(node1.split_dim, node1.split)
less2, greater2 = rect2.split(node2.split_dim, node2.split)
traverse(node1.less,less1,node2.less,less2,idx)
traverse(node1.less,less1,node2.greater,greater2,idx)
traverse(node1.greater,greater1,node2.less,less2,idx)
traverse(node1.greater,greater1,node2.greater,greater2,idx)
R1 = Rectangle(self.maxes, self.mins)
R2 = Rectangle(other.maxes, other.mins)
if np.shape(r) == ():
r = np.array([r])
result = np.zeros(1,dtype=int)
traverse(self.tree, R1, other.tree, R2, np.arange(1))
return result[0]
elif len(np.shape(r)) == 1:
r = np.asarray(r)
n, = r.shape
result = np.zeros(n,dtype=int)
traverse(self.tree, R1, other.tree, R2, np.arange(n))
return result
else:
raise ValueError("r must be either a single value or a one-dimensional array of values")
def distance_matrix(x,y,p=2,threshold=1000000):
"""
Compute the distance matrix.
Returns the matrix of all pair-wise distances.
Parameters
----------
x : (M, K) array_like
TODO: description needed
y : (N, K) array_like
TODO: description needed
p : float, 1 <= p <= infinity
Which Minkowski p-norm to use.
threshold : positive int
If ``M * N * K`` > `threshold`, algorithm uses a Python loop instead
of large temporary arrays.
Returns
-------
result : (M, N) ndarray
Distance matrix.
Examples
--------
>>> distance_matrix([[0,0],[0,1]], [[1,0],[1,1]])
array([[ 1. , 1.41421356],
[ 1.41421356, 1. ]])
"""
x = np.asarray(x)
m, k = x.shape
y = np.asarray(y)
n, kk = y.shape
if k != kk:
raise ValueError("x contains %d-dimensional vectors but y contains %d-dimensional vectors" % (k, kk))
if m*n*k <= threshold:
return minkowski_distance(x[:,np.newaxis,:],y[np.newaxis,:,:],p)
else:
result = np.empty((m,n),dtype=np.float) # FIXME: figure out the best dtype
if m < n:
for i in range(m):
result[i,:] = minkowski_distance(x[i],y,p)
else:
for j in range(n):
result[:,j] = minkowski_distance(x,y[j],p)
return result