(phǂlSSKrSSKJrJr /SQrS SjrS Sjr"SS5r"S S \5r S S jr g)N)cKDTree cKDTreeNode)minkowski_distance_pminkowski_distancedistance_matrix RectangleKDTreecZ[R"U5n[R"U5n[R"[R"URUR5S5nUR U5nUR U5nU[R :Xa+[R "[R"X- 5SS9$US:Xa+[R"[R"X- 5SS9$[R"[R"X- 5U-SS9$)aCompute the pth power of the L**p distance between two arrays. For efficiency, this function computes the L**p distance but does not extract the pth root. If `p` is 1 or infinity, this is equal to the actual L**p distance. The last dimensions of `x` and `y` must be the same length. Any other dimensions must be compatible for broadcasting. Parameters ---------- x : (..., K) array_like Input array. y : (..., K) array_like Input array. p : float, 1 <= p <= infinity Which Minkowski p-norm to use. Returns ------- dist : ndarray pth power of the distance between the input arrays. Examples -------- >>> from scipy.spatial import minkowski_distance_p >>> minkowski_distance_p([[0, 0], [0, 0]], [[1, 1], [0, 1]]) array([2., 1.]) float64)axisr) npasarray promote_typesdtypeastypeinfamaxabssum)xypcommon_datatypes H/var/www/html/venv/lib/python3.13/site-packages/scipy/spatial/_kdtree.pyrr s> 1 A 1 A &&r'7'7'I'02O !A !ABFF{wwrvvac{,, avvbffQSk++vvbffQSk1n2..c[R"U5n[R"U5nU[R:XdUS:Xa [XU5$[XU5SU- -$)a9Compute the L**p distance between two arrays. The last dimensions of `x` and `y` must be the same length. Any other dimensions must be compatible for broadcasting. Parameters ---------- x : (..., K) array_like Input array. y : (..., K) array_like Input array. p : float, 1 <= p <= infinity Which Minkowski p-norm to use. Returns ------- dist : ndarray Distance between the input arrays. Examples -------- >>> from scipy.spatial import minkowski_distance >>> minkowski_distance([[0, 0], [0, 0]], [[1, 1], [0, 1]]) array([ 1.41421356, 1. ]) rg?)rrrr)rrrs rrr?sR6 1 A 1 ABFF{a1f#A!,,#A!,r!t44rcX\rSrSrSrSrSrSrSrS Sjr S Sjr S S jr S S jr S r g )r bzDHyperrectangle class. Represents a Cartesian product of intervals. c[R"X5R[5Ul[R "X5R[5UlURRuUlg)zConstruct a hyperrectangle.N) rmaximumrfloatmaxesminimumminsshapem)selfr$r&s r__init__Rectangle.__init__gsKZZ+2259 JJu*11%8 **""rc\S[[URUR55S3$)Nz )listzipr&r$r)s r__repr__Rectangle.__repr__ms&T#dii"<=>a@@rc\[R"URUR- 5$)z Total volume.)rprodr$r&r0s rvolumeRectangle.volumepswwtzz$))+,,rc[R"UR5nX#U'[URU5n[R"UR5nX#U'[X0R5nXE4$)aYProduce 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 : float Position along axis `d` to split at. )rcopyr$r r&)r)dsplitmidlessgreaters rr:Rectangle.splitts\ggdjj!AC(ggdii AC,}rc [S[R"S[R"URU- XR- 55U5$)z Return the minimum distance between input and points in the hyperrectangle. Parameters ---------- x : array_like Input. p : float, optional Input. rrrr"r&r$r)rrs rmin_distance_pointRectangle.min_distance_points=" rzz!RZZ ! Qzz\BC   rcx[S[R"URU- XR- 5U5$)z Return the maximum distance between input and points in the hyperrectangle. Parameters ---------- x : array_like Input array. p : float, optional Input. rrrr"r$r&rAs rmax_distance_pointRectangle.max_distance_points,"!RZZ 1 a k%JANNrc [S[R"S[R"URUR- URUR- 55U5$)z Compute the minimum distance between points in the two hyperrectangles. Parameters ---------- other : hyperrectangle Input. p : float Input. rr@r)otherrs rmin_distance_rectangle Rectangle.min_distance_rectanglesO" JJq"**TYYu{{%:%*ZZ %:< =   rc[S[R"URUR- URUR- 5U5$)z Compute the maximum distance between points in the two hyperrectangles. Parameters ---------- other : hyperrectangle Input. p : float, optional Input. rrErIs rmax_distance_rectangle Rectangle.max_distance_rectangles?" rzz$**UZZ/TYY1FGL Lr)r(r$r&N)@)__name__ __module__ __qualname____firstlineno____doc__r*r1r5r:rBrFrKrN__static_attributes__rrr r bs2# A-. $ O & Lrr c^\rSrSrSr"SS5r"SS\5r"SS\5r\U4S j5r SU4S jjr S S S \ RS 4U4Sjjr SU4SjjrSU4SjjrSU4SjjrSU4SjjrSU4SjjrSrU=r$)r a 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 : array_like, shape (n,m) The n data points of dimension m to be indexed. This array is not copied unless this is necessary to produce a contiguous array of doubles, and so modifying this data will result in bogus results. The data are also copied if the kd-tree is built with copy_data=True. leafsize : positive int, optional The number of points at which the algorithm switches over to brute-force. Default: 10. compact_nodes : bool, optional If True, the kd-tree is built to shrink the hyperrectangles to the actual data range. This usually gives a more compact tree that is robust against degenerated input data and gives faster queries at the expense of longer build time. Default: True. copy_data : bool, optional If True the data is always copied to protect the kd-tree against data corruption. Default: False. balanced_tree : bool, optional If True, the median is used to split the hyperrectangles instead of the midpoint. This usually gives a more compact tree and faster queries at the expense of longer build time. Default: True. boxsize : array_like or scalar, optional Apply a m-d toroidal topology to the KDTree.. The topology is generated by :math:`x_i + n_i L_i` where :math:`n_i` are integers and :math:`L_i` is the boxsize along i-th dimension. The input data shall be wrapped into :math:`[0, L_i)`. A ValueError is raised if any of the data is outside of this bound. 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. Attributes ---------- data : ndarray, shape (n,m) The n data points of dimension m to be indexed. This array is not copied unless this is necessary to produce a contiguous array of doubles. The data are also copied if the kd-tree is built with ``copy_data=True``. leafsize : positive int The number of points at which the algorithm switches over to brute-force. m : int The dimension of a single data-point. n : int The number of data points. maxes : ndarray, shape (m,) The maximum value in each dimension of the n data points. mins : ndarray, shape (m,) The minimum value in each dimension of the n data points. size : int The number of nodes in the tree. cP\rSrSr\S Sj5rS SjrSrSrSr Sr S r S r g) KDTree.nodeiNcUc[RU5$URS:Xa[RU5$[R U5$)zDCreate either an inner or leaf node, wrapping a cKDTreeNode instancer )r node split_dimleafnode innernode) ckdtree_nodes r_createKDTree.node._create sG#{{<00''2-|44'' 55rc*Uc [5nXlgN)r_node)r)ras rr*KDTree.node.__init__*s#*} %Jrc0[U5[U5:$reidr)rJs r__lt__KDTree.node.__lt__/d8bi' 'rc0[U5[U5:$rerirks r__gt__KDTree.node.__gt__2rnrc0[U5[U5:*$rerirks r__le__KDTree.node.__le__5d8r%y( (rc0[U5[U5:$rerirks r__ge__KDTree.node.__ge__8rurc0[U5[U5:H$rerirks r__eq__KDTree.node.__eq__;rur)rfre) rQrRrSrT staticmethodrbr*rlrprsrwrzrVrWrrr]r[s2  6  6 &  ( ( ) ) )rr]c4\rSrSr\S5r\S5rSrg)KDTree.leafnodei>c.URR$re)rfindicesr0s ridxKDTree.leafnode.idx?s::%% %rc.URR$rerfchildrenr0s rrKDTree.leafnode.childrenC::&& &rrWN)rQrRrSrTpropertyrrrVrWrrr_r~>s(  &  &  '  'rr_cX^\rSrSrU4Sjr\S5r\S5r\S5rSr U=r $)KDTree.innernodeiGc >[U[5(de[TU] U5 [R R UR5Ul[R R UR5Ul gre) isinstancersuperr*r r]rblesserr<r=)r) ckdtreenode __class__s rr*KDTree.innernode.__init__Hs[k;77 77 G [ ) ++K,>,>?DI!;;..{/B/BCDLrc.URR$re)rfr^r0s rr^KDTree.innernode.split_dimNs::'' 'rc.URR$re)rfr:r0s rr:KDTree.innernode.splitRs::## #rc.URR$rerr0s rrKDTree.innernode.childrenVrr)r=r<) rQrRrSrTr*rr^r:rrV __classcell__rs@rr`rGsE D  (  (  $  $  '  'rr`c>[US5(d,[RR[TU]5UlUR $)N_tree)hasattrr r]rbrtreer)r)rs rr KDTree.treeZs4tW%%,,UW\:DJzzrc>[R"U5nURRS:Xa [ S5e[ TU]XX4XV5 g)Nc&KDTree does not work with complex data)rrrkind TypeErrorrr*)r)dataleafsize compact_nodes copy_data balanced_treeboxsizers rr*KDTree.__init__asCzz$ ::??c !DE E & 1rrrc>[R"U5nURRS:Xa [ S5eUc [ S5e[ T U]XX4XV5upx[U[5(a[R"U5nXx4$)a" Query the kd-tree for nearest neighbors. Parameters ---------- x : array_like, last dimension self.m An array of points to query. k : int or Sequence[int], optional Either the number of nearest neighbors to return, or a list of the k-th nearest neighbors to return, starting from 1. eps : nonnegative float, optional 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, optional Which Minkowski p-norm to use. 1 is the sum-of-absolute-values distance ("Manhattan" distance). 2 is the usual Euclidean distance. infinity is the maximum-coordinate-difference distance. A large, finite p may cause a ValueError if overflow can occur. distance_upper_bound : nonnegative float, optional 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. workers : int, optional Number of workers to use for parallel processing. If -1 is given all CPU threads are used. Default: 1. .. versionadded:: 1.6.0 Returns ------- d : float or array of floats The distances to the nearest neighbors. If ``x`` has shape ``tuple+(self.m,)``, then ``d`` has shape ``tuple+(k,)``. When k == 1, the last dimension of the output is squeezed. Missing neighbors are indicated with infinite distances. Hits are sorted by distance (nearest first). .. versionchanged:: 1.9.0 Previously if ``k=None``, then `d` was an object array of shape ``tuple``, containing lists of distances. This behavior has been removed, use `query_ball_point` instead. i : integer or array of integers The index of each neighbor in ``self.data``. ``i`` is the same shape as d. Missing neighbors are indicated with ``self.n``. Examples -------- >>> import numpy as np >>> from scipy.spatial import KDTree >>> x, y = np.mgrid[0:5, 2:8] >>> tree = KDTree(np.c_[x.ravel(), y.ravel()]) To query the nearest neighbours and return squeezed result, use >>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=1) >>> print(dd, ii, sep='\n') [2. 0.2236068] [ 0 13] To query the nearest neighbours and return unsqueezed result, use >>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=[1]) >>> print(dd, ii, sep='\n') [[2. ] [0.2236068]] [[ 0] [13]] To query the second nearest neighbours and return unsqueezed result, use >>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=[2]) >>> print(dd, ii, sep='\n') [[2.23606798] [0.80622577]] [[ 6] [19]] To query the first and second nearest neighbours, use >>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=2) >>> print(dd, ii, sep='\n') [[2. 2.23606798] [0.2236068 0.80622577]] [[ 0 6] [13 19]] or, be more specific >>> dd, ii = tree.query([[0, 0], [2.2, 2.9]], k=[1, 2]) >>> print(dd, ii, sep='\n') [[2. 2.23606798] [0.2236068 0.80622577]] [[ 0 6] [13 19]] rrz.k must be an integer or a sequence of integers) rrrrr ValueErrorrqueryrintintp) r)rkepsrdistance_upper_boundworkersr9irs rr KDTree.queryksvR JJqM 77<<3 DE E 9MN Nw}Q3+?I a   At rc >[R"U5nURRS:Xa [ S5e[ TU]XX4XVU5$)aFind 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 : array_like, float The radius of points to return, must broadcast to the length of x. p : float, optional Which Minkowski p-norm to use. Should be in the range [1, inf]. A finite large p may cause a ValueError if overflow can occur. 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)``. workers : int, optional Number of jobs to schedule for parallel processing. If -1 is given all processors are used. Default: 1. .. versionadded:: 1.6.0 return_sorted : bool, optional Sorts returned indices if True and does not sort them if False. If None, does not sort single point queries, but does sort multi-point queries which was the behavior before this option was added. .. versionadded:: 1.6.0 return_length : bool, optional Return the number of points inside the radius instead of a list of the indices. .. versionadded:: 1.6.0 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 -------- >>> import numpy as np >>> from scipy import spatial >>> x, y = np.mgrid[0:5, 0:5] >>> points = np.c_[x.ravel(), y.ravel()] >>> tree = spatial.KDTree(points) >>> sorted(tree.query_ball_point([2, 0], 1)) [5, 10, 11, 15] Query multiple points and plot the results: >>> import matplotlib.pyplot as plt >>> points = np.asarray(points) >>> plt.plot(points[:,0], points[:,1], '.') >>> for results in tree.query_ball_point(([2, 0], [3, 3]), 1): ... nearby_points = points[results] ... plt.plot(nearby_points[:,0], nearby_points[:,1], 'o') >>> plt.margins(0.1, 0.1) >>> plt.show() rr)rrrrrrquery_ball_point) r)rrrrr return_sorted return_lengthrs rrKDTree.query_ball_pointsLN JJqM 77<<3 DE Ew' !'-A Arc$>[TU]XX45$)a  Find all pairs of points between `self` and `other` 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``. Examples -------- You can search all pairs of points between two kd-trees within a distance: >>> import matplotlib.pyplot as plt >>> import numpy as np >>> from scipy.spatial import KDTree >>> rng = np.random.default_rng() >>> points1 = rng.random((15, 2)) >>> points2 = rng.random((15, 2)) >>> plt.figure(figsize=(6, 6)) >>> plt.plot(points1[:, 0], points1[:, 1], "xk", markersize=14) >>> plt.plot(points2[:, 0], points2[:, 1], "og", markersize=14) >>> kd_tree1 = KDTree(points1) >>> kd_tree2 = KDTree(points2) >>> indexes = kd_tree1.query_ball_tree(kd_tree2, r=0.2) >>> for i in range(len(indexes)): ... for j in indexes[i]: ... plt.plot([points1[i, 0], points2[j, 0]], ... [points1[i, 1], points2[j, 1]], "-r") >>> plt.show() )rquery_ball_tree)r)rJrrrrs rrKDTree.query_ball_tree-sbw&u88rc$>[TU]XX45$)aFind all pairs of points in `self` whose distance is at most r. 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. output_type : string, optional Choose the output container, 'set' or 'ndarray'. Default: 'set' .. versionadded:: 1.6.0 Returns ------- results : set or ndarray Set of pairs ``(i,j)``, with ``i < j``, for which the corresponding positions are close. If output_type is 'ndarray', an ndarry is returned instead of a set. Examples -------- You can search all pairs of points in a kd-tree within a distance: >>> import matplotlib.pyplot as plt >>> import numpy as np >>> from scipy.spatial import KDTree >>> rng = np.random.default_rng() >>> points = rng.random((20, 2)) >>> plt.figure(figsize=(6, 6)) >>> plt.plot(points[:, 0], points[:, 1], "xk", markersize=14) >>> kd_tree = KDTree(points) >>> pairs = kd_tree.query_pairs(r=0.2) >>> for (i, j) in pairs: ... plt.plot([points[i, 0], points[j, 0]], ... [points[i, 1], points[j, 1]], "-r") >>> plt.show() )r query_pairs)r)rrr output_typers rrKDTree.query_pairs`s\w"1::rc&>[TU]XX4U5$)aCount 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``. Data points on ``self`` and ``other`` are optionally weighted by the ``weights`` argument. (See below) This is adapted from the "two-point correlation" algorithm described by Gray and Moore [1]_. See notes for further discussion. Parameters ---------- other : KDTree The other tree to draw points from, can be the same tree as self. r : float or one-dimensional array of floats The radius to produce a count for. Multiple radii are searched with a single tree traversal. If the count is non-cumulative(``cumulative=False``), ``r`` defines the edges of the bins, and must be non-decreasing. p : float, optional 1<=p<=infinity. Which Minkowski p-norm to use. Default 2.0. A finite large p may cause a ValueError if overflow can occur. weights : tuple, array_like, or None, optional If None, the pair-counting is unweighted. If given as a tuple, weights[0] is the weights of points in ``self``, and weights[1] is the weights of points in ``other``; either can be None to indicate the points are unweighted. If given as an array_like, weights is the weights of points in ``self`` and ``other``. For this to make sense, ``self`` and ``other`` must be the same tree. If ``self`` and ``other`` are two different trees, a ``ValueError`` is raised. Default: None .. versionadded:: 1.6.0 cumulative : bool, optional Whether the returned counts are cumulative. When cumulative is set to ``False`` the algorithm is optimized to work with a large number of bins (>10) specified by ``r``. When ``cumulative`` is set to True, the algorithm is optimized to work with a small number of ``r``. Default: True .. versionadded:: 1.6.0 Returns ------- result : scalar or 1-D array The number of pairs. For unweighted counts, the result is integer. For weighted counts, the result is float. If cumulative is False, ``result[i]`` contains the counts with ``(-inf if i == 0 else r[i-1]) < R <= r[i]`` Notes ----- Pair-counting is the basic operation used to calculate the two point correlation functions from a data set composed of position of objects. Two point correlation function measures the clustering of objects and is widely used in cosmology to quantify the large scale structure in our Universe, but it may be useful for data analysis in other fields where self-similar assembly of objects also occur. The Landy-Szalay estimator for the two point correlation function of ``D`` measures the clustering signal in ``D``. [2]_ For example, given the position of two sets of objects, - objects ``D`` (data) contains the clustering signal, and - objects ``R`` (random) that contains no signal, .. math:: \xi(r) = \frac{ - 2 f + f^2}{f^2}, where the brackets represents counting pairs between two data sets in a finite bin around ``r`` (distance), corresponding to setting `cumulative=False`, and ``f = float(len(D)) / float(len(R))`` is the ratio between number of objects from data and random. The algorithm implemented here is loosely based on the dual-tree algorithm described in [1]_. We switch between two different pair-cumulation scheme depending on the setting of ``cumulative``. The computing time of the method we use when for ``cumulative == False`` does not scale with the total number of bins. The algorithm for ``cumulative == True`` scales linearly with the number of bins, though it is slightly faster when only 1 or 2 bins are used. [5]_. As an extension to the naive pair-counting, weighted pair-counting counts the product of weights instead of number of pairs. Weighted pair-counting is used to estimate marked correlation functions ([3]_, section 2.2), or to properly calculate the average of data per distance bin (e.g. [4]_, section 2.1 on redshift). .. [1] Gray and Moore, "N-body problems in statistical learning", Mining the sky, 2000, https://arxiv.org/abs/astro-ph/0012333 .. [2] Landy and Szalay, "Bias and variance of angular correlation functions", The Astrophysical Journal, 1993, http://adsabs.harvard.edu/abs/1993ApJ...412...64L .. [3] Sheth, Connolly and Skibba, "Marked correlations in galaxy formation models", Arxiv e-print, 2005, https://arxiv.org/abs/astro-ph/0511773 .. [4] Hawkins, et al., "The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe", Monthly Notices of the Royal Astronomical Society, 2002, http://adsabs.harvard.edu/abs/2003MNRAS.346...78H .. [5] https://github.com/scipy/scipy/pull/5647#issuecomment-168474926 Examples -------- You can count neighbors number between two kd-trees within a distance: >>> import numpy as np >>> from scipy.spatial import KDTree >>> rng = np.random.default_rng() >>> points1 = rng.random((5, 2)) >>> points2 = rng.random((5, 2)) >>> kd_tree1 = KDTree(points1) >>> kd_tree2 = KDTree(points2) >>> kd_tree1.count_neighbors(kd_tree2, 0.2) 1 This number is same as the total pair number calculated by `query_ball_tree`: >>> indexes = kd_tree1.query_ball_tree(kd_tree2, r=0.2) >>> sum([len(i) for i in indexes]) 1 )rcount_neighbors)r)rJrrweights cumulativers rrKDTree.count_neighborssdw&uZHHrc$>[TU]XX45$)aCompute a sparse distance matrix. Computes a distance matrix between two KDTrees, leaving as zero any distance greater than max_distance. Parameters ---------- other : KDTree max_distance : positive float p : float, 1<=p<=infinity Which Minkowski p-norm to use. A finite large p may cause a ValueError if overflow can occur. output_type : string, optional Which container to use for output data. Options: 'dok_matrix', 'coo_matrix', 'dict', or 'ndarray'. Default: 'dok_matrix'. .. versionadded:: 1.6.0 Returns ------- result : dok_matrix, coo_matrix, dict or ndarray Sparse matrix representing the results in "dictionary of keys" format. If a dict is returned the keys are (i,j) tuples of indices. If output_type is 'ndarray' a record array with fields 'i', 'j', and 'v' is returned, Examples -------- You can compute a sparse distance matrix between two kd-trees: >>> import numpy as np >>> from scipy.spatial import KDTree >>> rng = np.random.default_rng() >>> points1 = rng.random((5, 2)) >>> points2 = rng.random((5, 2)) >>> kd_tree1 = KDTree(points1) >>> kd_tree2 = KDTree(points2) >>> sdm = kd_tree1.sparse_distance_matrix(kd_tree2, 0.3) >>> sdm.toarray() array([[0. , 0. , 0.12295571, 0. , 0. ], [0. , 0. , 0. , 0. , 0. ], [0.28942611, 0. , 0. , 0.2333084 , 0. ], [0. , 0. , 0. , 0. , 0. ], [0.24617575, 0.29571802, 0.26836782, 0. , 0. ]]) You can check distances above the `max_distance` are zeros: >>> from scipy.spatial import distance_matrix >>> distance_matrix(points1, points2) array([[0.56906522, 0.39923701, 0.12295571, 0.8658745 , 0.79428925], [0.37327919, 0.7225693 , 0.87665969, 0.32580855, 0.75679479], [0.28942611, 0.30088013, 0.6395831 , 0.2333084 , 0.33630734], [0.31994999, 0.72658602, 0.71124834, 0.55396483, 0.90785663], [0.24617575, 0.29571802, 0.26836782, 0.57714465, 0.6473269 ]]) )rsparse_distance_matrix)r)rJ max_distancerrrs rrKDTree.sparse_distance_matrix$szw- 1 1r)r) TFTN)rPrrNF)rPr)rPrset)rPNT)rP dok_matrix)rQrRrSrTrUr]r_r`rrr*rrrrrrrrrVrrs@rr r sN`))>'4''D'& IN-11a12661sj;<;@KAZ19f.;`RIj:F>1>1rr c2[R"U5nURupE[R"U5nURupgXW:wa[SUSUS35eXF-U-U::a=[ USS2[R SS24U[R SS2SS24U5$[R "XF4[S9nXF:a([U5Hn [ X X5XSS24'M U$[U5Hn [ XU U5USS2U 4'M U$)aCompute the distance matrix. Returns the matrix of all pair-wise distances. Parameters ---------- x : (M, K) array_like Matrix of M vectors in K dimensions. y : (N, K) array_like Matrix of N vectors in K dimensions. p : float, 1 <= p <= infinity Which Minkowski p-norm to use. threshold : positive int If ``M * N * K`` > `threshold`, algorithm uses a Python loop instead of large temporary arrays. Returns ------- result : (M, N) ndarray Matrix containing the distance from every vector in `x` to every vector in `y`. Examples -------- >>> from scipy.spatial import distance_matrix >>> distance_matrix([[0,0],[0,1]], [[1,0],[1,1]]) array([[ 1. , 1.41421356], [ 1.41421356, 1. ]]) z x contains z$-dimensional vectors but y contains z-dimensional vectorsN)r) rrr'rrnewaxisemptyr#range) rrr thresholdr(rnkkresultrjs rrres@ 1 A 77DA 1 A GGEAw;qc)M4356 6 s1u !!AbjjN"3Abjj1n4EaHH1%e, 51X0a:s   1X0Q4:qs  r)r)ri@B) numpyr_ckdtreerr__all__rrr r rrWrrrsC* " 1/h 5FiLiLXT 1WT 1n3r