BallTree for fast generalized Npoint problems
BallTree(X, leaf_size=40, metric=’minkowski’, **kwargs)
Parameters: 

X : arraylike, shape = [n_samples, n_features] 
n_samples is the number of points in the data set, and n_features is the dimension of the parameter space. Note: if X is a Ccontiguous array of doubles then data will not be copied. Otherwise, an internal copy will be made. 
leaf_size : positive integer (default = 40) 
Number of points at which to switch to bruteforce. Changing leaf_size will not affect the results of a query, but can significantly impact the speed of a query and the memory required to store the constructed tree. The amount of memory needed to store the tree scales as approximately n_samples / leaf_size. For a specified leaf_size , a leaf node is guaranteed to satisfy leaf_size <= n_points <= 2 * leaf_size , except in the case that n_samples < leaf_size . 
metric : string or DistanceMetric object 
the distance metric to use for the tree. Default=’minkowski’ with p=2 (that is, a euclidean metric). See the documentation of the DistanceMetric class for a list of available metrics. ball_tree.valid_metrics gives a list of the metrics which are valid for BallTree.  Additional keywords are passed to the distance metric class.

Attributes: 

data : memory view 
The training data 
Examples
Query for knearest neighbors
>>> import numpy as np
>>> np.random.seed(0)
>>> X = np.random.random((10, 3)) # 10 points in 3 dimensions
>>> tree = BallTree(X, leaf_size=2)
>>> dist, ind = tree.query(X[:1], k=3)
>>> print(ind) # indices of 3 closest neighbors
[0 3 1]
>>> print(dist) # distances to 3 closest neighbors
[ 0. 0.19662693 0.29473397]
Pickle and Unpickle a tree. Note that the state of the tree is saved in the pickle operation: the tree needs not be rebuilt upon unpickling.
>>> import numpy as np
>>> import pickle
>>> np.random.seed(0)
>>> X = np.random.random((10, 3)) # 10 points in 3 dimensions
>>> tree = BallTree(X, leaf_size=2)
>>> s = pickle.dumps(tree)
>>> tree_copy = pickle.loads(s)
>>> dist, ind = tree_copy.query(X[:1], k=3)
>>> print(ind) # indices of 3 closest neighbors
[0 3 1]
>>> print(dist) # distances to 3 closest neighbors
[ 0. 0.19662693 0.29473397]
Query for neighbors within a given radius
>>> import numpy as np
>>> np.random.seed(0)
>>> X = np.random.random((10, 3)) # 10 points in 3 dimensions
>>> tree = BallTree(X, leaf_size=2)
>>> print(tree.query_radius(X[:1], r=0.3, count_only=True))
3
>>> ind = tree.query_radius(X[:1], r=0.3)
>>> print(ind) # indices of neighbors within distance 0.3
[3 0 1]
Compute a gaussian kernel density estimate:
>>> import numpy as np
>>> np.random.seed(1)
>>> X = np.random.random((100, 3))
>>> tree = BallTree(X)
>>> tree.kernel_density(X[:3], h=0.1, kernel='gaussian')
array([ 6.94114649, 7.83281226, 7.2071716 ])
Compute a twopoint autocorrelation function
>>> import numpy as np
>>> np.random.seed(0)
>>> X = np.random.random((30, 3))
>>> r = np.linspace(0, 1, 5)
>>> tree = BallTree(X)
>>> tree.two_point_correlation(X, r)
array([ 30, 62, 278, 580, 820])
Methods
kernel_density (self, X, h[, kernel, atol, …])  Compute the kernel density estimate at points X with the given kernel, using the distance metric specified at tree creation. 
query (X[, k, return_distance, dualtree, …])  query the tree for the k nearest neighbors 
query_radius  query_radius(self, X, r, count_only = False): 
two_point_correlation  Compute the twopoint correlation function 
get_arrays  
get_n_calls  
get_tree_stats  
reset_n_calls  

__init__($self, /, *args, **kwargs)

Initialize self. See help(type(self)) for accurate signature.

kernel_density(self, X, h, kernel=’gaussian’, atol=0, rtol=1E8, breadth_first=True, return_log=False)

Compute the kernel density estimate at points X with the given kernel, using the distance metric specified at tree creation.
Parameters: 

X : arraylike, shape = [n_samples, n_features] 
An array of points to query. Last dimension should match dimension of training data. 
h : float 
the bandwidth of the kernel 
kernel : string 
specify the kernel to use. Options are  ‘gaussian’  ‘tophat’  ‘epanechnikov’  ‘exponential’  ‘linear’  ‘cosine’ Default is kernel = ‘gaussian’ 
atol, rtol : float (default = 0) 
Specify the desired relative and absolute tolerance of the result. If the true result is K_true, then the returned result K_ret satisfies abs(K_true  K_ret) < atol + rtol * K_ret The default is zero (i.e. machine precision) for both. 
breadth_first : boolean (default = False) 
if True, use a breadthfirst search. If False (default) use a depthfirst search. Breadthfirst is generally faster for compact kernels and/or high tolerances. 
return_log : boolean (default = False) 
return the logarithm of the result. This can be more accurate than returning the result itself for narrow kernels. 
Returns: 

density : ndarray 
The array of (log)density evaluations, shape = X.shape[:1] 

query(X, k=1, return_distance=True, dualtree=False, breadth_first=False)

query the tree for the k nearest neighbors
Parameters: 

X : arraylike, shape = [n_samples, n_features] 
An array of points to query 
k : integer (default = 1) 
The number of nearest neighbors to return 
return_distance : boolean (default = True) 
if True, return a tuple (d, i) of distances and indices if False, return array i 
dualtree : boolean (default = False) 
if True, use the dual tree formalism for the query: a tree is built for the query points, and the pair of trees is used to efficiently search this space. This can lead to better performance as the number of points grows large. 
breadth_first : boolean (default = False) 
if True, then query the nodes in a breadthfirst manner. Otherwise, query the nodes in a depthfirst manner. 
sort_results : boolean (default = True) 
if True, then distances and indices of each point are sorted on return, so that the first column contains the closest points. Otherwise, neighbors are returned in an arbitrary order. 
Returns: 

i : if return_distance == False 
(d,i) : if return_distance == True 
d : array of doubles  shape: x.shape[:1] + (k,) 
each entry gives the list of distances to the neighbors of the corresponding point 
i : array of integers  shape: x.shape[:1] + (k,) 
each entry gives the list of indices of neighbors of the corresponding point 

query_radius()

query_radius(self, X, r, count_only = False):
query the tree for neighbors within a radius r
Parameters: 

X : arraylike, shape = [n_samples, n_features] 
An array of points to query 
r : distance within which neighbors are returned 
r can be a single value, or an array of values of shape x.shape[:1] if different radii are desired for each point. 
return_distance : boolean (default = False) 
if True, return distances to neighbors of each point if False, return only neighbors Note that unlike the query() method, setting return_distance=True here adds to the computation time. Not all distances need to be calculated explicitly for return_distance=False. Results are not sorted by default: see sort_results keyword. 
count_only : boolean (default = False) 
if True, return only the count of points within distance r if False, return the indices of all points within distance r If return_distance==True, setting count_only=True will result in an error. 
sort_results : boolean (default = False) 
if True, the distances and indices will be sorted before being returned. If False, the results will not be sorted. If return_distance == False, setting sort_results = True will result in an error. 
Returns: 

count : if count_only == True 
ind : if count_only == False and return_distance == False 
(ind, dist) : if count_only == False and return_distance == True 
count : array of integers, shape = X.shape[:1] 
each entry gives the number of neighbors within a distance r of the corresponding point. 
ind : array of objects, shape = X.shape[:1] 
each element is a numpy integer array listing the indices of neighbors of the corresponding point. Note that unlike the results of a kneighbors query, the returned neighbors are not sorted by distance by default. 
dist : array of objects, shape = X.shape[:1] 
each element is a numpy double array listing the distances corresponding to indices in i. 

two_point_correlation()

Compute the twopoint correlation function
Parameters: 

X : arraylike, shape = [n_samples, n_features] 
An array of points to query. Last dimension should match dimension of training data. 
r : array_like 
A onedimensional array of distances 
dualtree : boolean (default = False) 
If true, use a dualtree algorithm. Otherwise, use a singletree algorithm. Dual tree algorithms can have better scaling for large N. 
Returns: 

counts : ndarray 
counts[i] contains the number of pairs of points with distance less than or equal to r[i] 