open3d.ml.tf.models.KDTree

class open3d.ml.tf.models.KDTree(X, leaf_size=40, metric='minkowski', **kwargs)

KDTree for fast generalized N-point problems

Parameters

  • X (array-like of 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 C-contiguous array of doubles then data will not be copied. Otherwise, an internal copy will be made.

  • leaf_size (positive int, default=40) – Number of points at which to switch to brute-force. 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 (str 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. kd_tree.valid_metrics gives a list of the metrics which are valid for KDTree.

  • keywords are passed to the distance metric class. (Additional) –

  • Note (Callable functions in the metric parameter are NOT supported for KDTree) –

  • Ball Tree. Function call overhead will result in very poor performance. (and) –

data

The training data

Type

memory view

Examples

Query for k-nearest neighbors

>>> import numpy as np
>>> rng = np.random.RandomState(0)
>>> X = rng.random_sample((10, 3))  # 10 points in 3 dimensions
>>> tree = KDTree(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
>>> rng = np.random.RandomState(0)
>>> X = rng.random_sample((10, 3))  # 10 points in 3 dimensions
>>> tree = KDTree(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
>>> rng = np.random.RandomState(0)
>>> X = rng.random_sample((10, 3))  # 10 points in 3 dimensions
>>> tree = KDTree(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
>>> rng = np.random.RandomState(42)
>>> X = rng.random_sample((100, 3))
>>> tree = KDTree(X)                
>>> tree.kernel_density(X[:3], h=0.1, kernel='gaussian')
array([ 6.94114649,  7.83281226,  7.2071716 ])

Compute a two-point auto-correlation function

>>> import numpy as np
>>> rng = np.random.RandomState(0)
>>> X = rng.random_sample((30, 3))
>>> r = np.linspace(0, 1, 5)
>>> tree = KDTree(X)                
>>> tree.two_point_correlation(X, r)
array([ 30,  62, 278, 580, 820])
__init__(*args, **kwargs)

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

get_arrays(self)

Get data and node arrays.

Returns

arrays – Arrays for storing tree data, index, node data and node bounds.

Return type

tuple of array

get_n_calls(self)

Get number of calls.

Returns

n_calls – number of distance computation calls

Return type

int

get_tree_stats(self)

Get tree status.

Returns

tree_stats – (number of trims, number of leaves, number of splits)

Return type

tuple of int

kernel_density()
kernel_density(self, X, h, kernel=’gaussian’, atol=0, rtol=1E-8,

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 (array-like of 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 (str, default="gaussian") – specify the kernel to use. Options are - ‘gaussian’ - ‘tophat’ - ‘epanechnikov’ - ‘exponential’ - ‘linear’ - ‘cosine’ Default is kernel = ‘gaussian’

  • rtol (atol,) – 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 (bool, default=False) – If True, use a breadth-first search. If False (default) use a depth-first search. Breadth-first is generally faster for compact kernels and/or high tolerances.

  • return_log (bool, default=False) – Return the logarithm of the result. This can be more accurate than returning the result itself for narrow kernels.

Returns

density – The array of (log)-density evaluations

Return type

ndarray of shape X.shape[:-1]

query()
query(X, k=1, return_distance=True,

dualtree=False, breadth_first=False)

query the tree for the k nearest neighbors

Parameters

  • X (array-like of shape (n_samples, n_features)) – An array of points to query

  • k (int, default=1) – The number of nearest neighbors to return

  • return_distance (bool, default=True) – if True, return a tuple (d, i) of distances and indices if False, return array i

  • dualtree (bool, 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 (bool, default=False) – if True, then query the nodes in a breadth-first manner. Otherwise, query the nodes in a depth-first manner.

  • sort_results (bool, 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 (ndarray of shape X.shape[:-1] + k, dtype=double) – Each entry gives the list of distances to the neighbors of the corresponding point.

  • i (ndarray of shape X.shape[:-1] + k, dtype=int) – Each entry gives the list of indices of neighbors of the corresponding point.

query_radius()

query_radius(X, r, return_distance=False, count_only=False, sort_results=False)

query the tree for neighbors within a radius r

Parameters

  • X (array-like of 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 (bool, 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 (bool, 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 (bool, 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 (ndarray of shape X.shape[:-1], dtype=int) – Each entry gives the number of neighbors within a distance r of the corresponding point.

  • ind (ndarray of shape X.shape[:-1], dtype=object) – Each element is a numpy integer array listing the indices of neighbors of the corresponding point. Note that unlike the results of a k-neighbors query, the returned neighbors are not sorted by distance by default.

  • dist (ndarray of shape X.shape[:-1], dtype=object) – Each element is a numpy double array listing the distances corresponding to indices in i.

reset_n_calls(self)

Reset number of calls to 0.

two_point_correlation(X, r, dualtree=False)

Compute the two-point correlation function

Parameters

  • X (array-like of shape (n_samples, n_features)) – An array of points to query. Last dimension should match dimension of training data.

  • r (array-like) – A one-dimensional array of distances

  • dualtree (bool, default=False) – If True, use a dualtree algorithm. Otherwise, use a single-tree algorithm. Dual tree algorithms can have better scaling for large N.

Returns

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

Return type

ndarray

data
idx_array
node_bounds
node_data
sample_weight
sum_weight
valid_metrics = ['euclidean', 'l2', 'minkowski', 'p', 'manhattan', 'cityblock', 'l1', 'chebyshev', 'infinity']