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The indices refer to the position in the data set used to construct the kd-tree. lesser : cKDTreeNode or None Subnode with the 'lesser' data points. This attribute is None for leafnodes. greater : cKDTreeNode or None Subnode with the 'greater' data points. This attribute is None for leafnodes. scipy.spatial._ckdtree.ordered_pairsscipy.spatial._ckdtree.coo_entriestakes no arguments%.200s() %s (%zd given)takes exactly one argumentBad call flags for CyFunctiontakes no keyword arguments%.200s() %sUnknown exception_cython_3_1_6an integer is required__pyx_capi____loader__loader__file__origin__package__parent__path__submodule_search_locationsneeds an argumentkeywords must be strings__pyx_fatalerrorexactly__cinit__Missing type objectunparsable format string'complex double''signed char''unsigned char''short''unsigned short''int''unsigned int''long''unsigned long''long long''unsigned long long''double''complex long double''bool''char''complex float''float'a structPython objecta pointera string'long double'buffer dtypeBuffer not C contiguous.othercannot import name %S__reduce_cython____setstate_cython__scipy/spatial/_ckdtree.pyx__init__setdok_matrixtupleExpected %s, got %.200s__pyx_unpickle_cKDTreeNode_thread_funcddiixxkkat mostat leastquery_pairssparse_distance_matrixname '%U' is not definedcoo_matrix__getstate__(n)_build_weightsqueryassignmentquery_ball_pointndarraycount_neighborsbuiltinscython_runtime__builtins__does not matchnumpyflatiterbroadcastgenericnumberunsignedintegerinexactcomplexfloatingflexiblecharacterufuncscipy._cyutilitymemoryview_allocate_bufferarray_cwrappermemoryview_cwrappermemview_sliceslice_memviewslicepybuffer_indexint (__Pyx_memviewslice *)transpose_memslicememoryview_fromsliceget_slice_from_memviewslice_copymemoryview_copymemoryview_copy_from_sliceget_best_orderslice_get_sizefill_contig_strides_arraycopy_data_to_temp_err_extents_err_dimint (PyObject *, PyObject *)_errint (void)_err_no_memorymemoryview_copy_contentsbroadcast_leadingrefcount_copyingrefcount_objects_in_slice_slice_assign_scalarformat_from_typeinfonumpy._core._multiarray_umathnumpy.core._multiarray_umath_ARRAY_API_ARRAY_API is NULL pointernumpy.import_arrayinit scipy.spatial._ckdtreequery_ball_treevlenvout__setstate____reduce____module____dictoffset____vectorcalloffset____weaklistoffset__func_doc__doc__func_name__name____qualname__func_dict__dict__func_globals__globals__func_closure__closure__func_code__code__func_defaults__defaults____kwdefaults____annotations___is_coroutineleafsizedatamaxesminsindicesboxsizedata_pointslevelsplit_dimchildrenstart_idxend_idxsplitlessergreater__array_interface__intp_tconst float64_tchar .Pu .$$D$$4D$$ ".:Tn z#:TnMvvMvvvvvMMvvMvvnnMvvvvvvvvvvvvvvvvWvWWvvvvvv<44<44444 44 444444444444444444<<D41W 44 444<4<h``h`````````````````````````hh8`P `````h`h?1$V7+ǕOONNNNNTUUUUxUTغƺ~lrH@0n\J8&PPDdffzfhfVfDf{jXF4 sparse_distance_matrix(self, other, max_distance, p=2.) Compute a sparse distance matrix Computes a distance matrix between two cKDTrees, leaving as zero any distance greater than max_distance. Parameters ---------- other : cKDTree 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'. 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 cKDTree >>> rng = np.random.default_rng() >>> points1 = rng.random((5, 2)) >>> points2 = rng.random((5, 2)) >>> kd_tree1 = cKDTree(points1) >>> kd_tree2 = cKDTree(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 ]]) count_neighbors(self, other, r, p=2., weights=None, cumulative=True) 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``. 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 : cKDTree instance 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 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 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, :arxiv:`astro-ph/0012333` .. [2] Landy and Szalay, "Bias and variance of angular correlation functions", The Astrophysical Journal, 1993, :doi:`10.1086/172900` .. [3] Sheth, Connolly and Skibba, "Marked correlations in galaxy formation models", 2005, :arxiv:`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, :doi:`10.1046/j.1365-2966.2003.07063.x` .. [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 cKDTree >>> rng = np.random.default_rng() >>> points1 = rng.random((5, 2)) >>> points2 = rng.random((5, 2)) >>> kd_tree1 = cKDTree(points1) >>> kd_tree2 = cKDTree(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 _build_weights(weights) Compute weights of nodes from weights of data points. This will sum up the total weight per node. This function is used internally. Parameters ---------- weights : array_like weights of data points; must be the same length as the data points. currently only scalar weights are supported. Therefore the weights array must be 1 dimensional. Returns ------- node_weights : array_like total weight for each KD-Tree node. query_pairs(self, r, p=2., eps=0, output_type='set') Find 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``. A finite large p may cause a ValueError if overflow can occur. 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' 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 cKDTree >>> 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 = cKDTree(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() query_ball_tree(self, other, r, p=2., eps=0) Find all pairs of points between `self` and `other` whose distance is at most r Parameters ---------- other : cKDTree 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``. A finite large p may cause a ValueError if overflow can occur. 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 cKDTree >>> 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 = cKDTree(points1) >>> kd_tree2 = cKDTree(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() query_ball_point(self, x, r, p=2., eps=0, workers=1, return_sorted=None, return_length=False) 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 : array_like, float The radius of points to return, shall 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. .. versionchanged:: 1.9.0 The "n_jobs" argument was renamed "workers". The old name "n_jobs" was deprecated in SciPy 1.6.0 and was removed in SciPy 1.9.0. 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:: 1.2.0 return_length: bool, optional Return the number of points inside the radius instead of a list of the indices. .. versionadded:: 1.3.0 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 cKDTree and using query_ball_tree. Examples -------- >>> import numpy as np >>> from scipy import spatial >>> x, y = np.mgrid[0:4, 0:4] >>> points = np.c_[x.ravel(), y.ravel()] >>> tree = spatial.cKDTree(points) >>> tree.query_ball_point([2, 0], 1) [4, 8, 9, 12] 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() query(self, x, k=1, eps=0, p=2, distance_upper_bound=np.inf, workers=1) Query the kd-tree for nearest neighbors Parameters ---------- x : array_like, last dimension self.m An array of points to query. k : list of integer or integer The list of k-th nearest neighbors to return. If k is an integer it is treated as a list of [1, ... k] (range(1, k+1)). Note that the counting starts from 1. eps : non-negative float Return approximate nearest neighbors; the k-th returned value is guaranteed to be no further than (1+eps) times the distance to the real k-th 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 A finite large p may cause a ValueError if overflow can occur. 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. workers : int, optional Number of workers to use for parallel processing. If -1 is given all CPU threads are used. Default: 1. .. versionchanged:: 1.9.0 The "n_jobs" argument was renamed "workers". The old name "n_jobs" was deprecated in SciPy 1.6.0 and was removed in SciPy 1.9.0. Returns ------- d : 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. i : ndarray of ints The index of each neighbor in ``self.data``. If ``x`` has shape ``tuple+(self.m,)``, then ``i`` has shape ``tuple+(k,)``. When k == 1, the last dimension of the output is squeezed. Missing neighbors are indicated with ``self.n``. Notes ----- If the KD-Tree is periodic, the position ``x`` is wrapped into the box. When the input k is a list, a query for arange(max(k)) is performed, but only columns that store the requested values of k are preserved. This is implemented in a manner that reduces memory usage. Examples -------- >>> import numpy as np >>> from scipy.spatial import cKDTree >>> x, y = np.mgrid[0:5, 2:8] >>> tree = cKDTree(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]] x must consist of vectors of length {} but has shape {}r must be non-decreasing for non-cumulative counting.numpy._core.umath failed to importnumpy._core.multiarray failed to importno default __reduce__ due to non-trivial __cinit__data must be finite, check for nan or inf valuescKDTree.sparse_distance_matrix (line 1461)cKDTree.query_ball_tree (line 997)cKDTree.query_ball_point (line 846)cKDTree.count_neighbors (line 1202)Two different trees are used. Specify weights for both in a tuple.Some input data are greater than the size of the periodic box.Only p-norms with 1<=p<=infinity permittedNumber of weights differ from the number of data pointsNote that Cython is deliberately stricter than PEP-484 and rejects subclasses of builtin types. If you need to pass subclasses then set the 'annotation_typing' directive to False.Incompatible checksums (0x%x vs (0x9704686, 0x690161e, 0xbefc888) = (_data, _indices, children, end_idx, greater, lesser, level, split, split_dim, start_idx))Cannot determine the number of cpus using os.cpu_count(), cannot use -1 for the number of workersAt1 t7$fDF$d& G4zZtCTTU _31 \V3a81G4xxuLQ A Ja fA KqAt1e A^3a 5c V1AqA LDQ Bb Ta nHA fARq +1 Q11AU*E%q! 2XQa 2V1G2TrA LDQ Bb Ta 1 U!1BarBarBar"F! 1 1A/C1B!j r!31CvRq T $O1IQ Jawe1 U(!3e1 2Rq *AQ 4r!6Q *AQ 5c 1 2Yaq rA! '#Rr2V1F#Q (rr3at61 $BfBb1Db !6#V2Q Rt1A  A^3a(!4y3aq(!4y3aq 1 E%q E%q qQa1AwaA./+,B 4s#U! *AQ k  "!HEN#Q >> import numpy as np >>> from scipy.spatial import cKDTree >>> rng = np.random.default_rng() >>> points1 = rng.random((5, 2)) >>> points2 = rng.random((5, 2)) >>> kd_tree1 = cKDTree(points1) >>> kd_tree2 = cKDTree(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 ]]) r must be either a single value or a one-dimensional array of values query(self, x, k=1, eps=0, p=2, distance_upper_bound=np.inf, workers=1) Query the kd-tree for nearest neighbors Parameters ---------- x : array_like, last dimension self.m An array of points to query. k : list of integer or integer The list of k-th nearest neighbors to return. If k is an integer it is treated as a list of [1, ... k] (range(1, k+1)). Note that the counting starts from 1. eps : non-negative float Return approximate nearest neighbors; the k-th returned value is guaranteed to be no further than (1+eps) times the distance to the real k-th 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 A finite large p may cause a ValueError if overflow can occur. 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. workers : int, optional Number of workers to use for parallel processing. If -1 is given all CPU threads are used. Default: 1. .. versionchanged:: 1.9.0 The "n_jobs" argument was renamed "workers". The old name "n_jobs" was deprecated in SciPy 1.6.0 and was removed in SciPy 1.9.0. Returns ------- d : 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. i : ndarray of ints The index of each neighbor in ``self.data``. If ``x`` has shape ``tuple+(self.m,)``, then ``i`` has shape ``tuple+(k,)``. When k == 1, the last dimension of the output is squeezed. Missing neighbors are indicated with ``self.n``. Notes ----- If the KD-Tree is periodic, the position ``x`` is wrapped into the box. When the input k is a list, a query for arange(max(k)) is performed, but only columns that store the requested values of k are preserved. This is implemented in a manner that reduces memory usage. Examples -------- >>> import numpy as np >>> from scipy.spatial import cKDTree >>> x, y = np.mgrid[0:5, 2:8] >>> tree = cKDTree(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]] query_pairs(self, r, p=2., eps=0, output_type='set') Find 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``. A finite large p may cause a ValueError if overflow can occur. 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' 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 cKDTree >>> 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 = cKDTree(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() query_ball_point(self, x, r, p=2., eps=0, workers=1, return_sorted=None, return_length=False) 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 : array_like, float The radius of points to return, shall 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. .. versionchanged:: 1.9.0 The "n_jobs" argument was renamed "workers". The old name "n_jobs" was deprecated in SciPy 1.6.0 and was removed in SciPy 1.9.0. 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:: 1.2.0 return_length: bool, optional Return the number of points inside the radius instead of a list of the indices. .. versionadded:: 1.3.0 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 cKDTree and using query_ball_tree. Examples -------- >>> import numpy as np >>> from scipy import spatial >>> x, y = np.mgrid[0:4, 0:4] >>> points = np.c_[x.ravel(), y.ravel()] >>> tree = spatial.cKDTree(points) >>> tree.query_ball_point([2, 0], 1) [4, 8, 9, 12] 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() query_ball_point.._thread_funcordered_pairs.__setstate_cython__data must be of shape (n, m), where there are n points of dimension mTrees passed to sparse_distance_matrix have different dimensionalityTrees passed to query_ball_tree have different dimensionalityTrees passed to count_neighbors have different dimensionalityT[Kt:TSWW``ddllppxx|}IIMMN G1F,avWA!qt7'cZwe3dR[[bbggjjnnvv}}~q,D 7!,D 1Negative input data are outside of the periodic box.$ARqa!"AV1*!2QfA!"AQ'aQgU"F!4vU#QA6 t6U!rqfBa -QivRq 3as$a *AQa|1Aa~Qa  $he1q'x' must be finite, check for nan or inf values query_ball_tree(self, other, r, p=2., eps=0) Find all pairs of points between `self` and `other` whose distance is at most r Parameters ---------- other : cKDTree 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``. A finite large p may cause a ValueError if overflow can occur. 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 cKDTree >>> 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 = cKDTree(points1) >>> kd_tree2 = cKDTree(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() count_neighbors(self, other, r, p=2., weights=None, cumulative=True) 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``. 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 : cKDTree instance 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 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 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, :arxiv:`astro-ph/0012333` .. [2] Landy and Szalay, "Bias and variance of angular correlation functions", The Astrophysical Journal, 1993, :doi:`10.1086/172900` .. [3] Sheth, Connolly and Skibba, "Marked correlations in galaxy formation models", 2005, :arxiv:`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, :doi:`10.1046/j.1365-2966.2003.07063.x` .. [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 cKDTree >>> rng = np.random.default_rng() >>> points1 = rng.random((5, 2)) >>> points2 = rng.random((5, 2)) >>> kd_tree1 = cKDTree(points1) >>> kd_tree2 = cKDTree(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 cKDTree.sparse_distance_matrix b 4rra 4r !'s%uBgU%q!'q U!5!1re1BfAMarab!1e1Be1EaqqSAV2U!A Qt4uA LDQ Eaq 4rTQ Aqordered_pairs.__reduce_cython__coo_entries.__setstate_cython__cKDTree.query_pairs (line 1090)cKDTreeNode.__setstate_cython__A%4Af -q  qHCs%wa ._thread_funccKDTree.__setstate_cython__Invalid number of workers __pyx_unpickle_cKDTreeNodecKDTree.query_ball_pointcKDTree.query_ball_treecKDTree.count_neighborscKDTree.__reduce_cython__sparse_distance_matrixscipy.spatial._ckdtreecoo_entries.dok_matrixcoo_entries.coo_matrixcKDTree.query (line 663)cKDTree._build_weightsordered_pairs.ndarraydistance_upper_boundA$hauG;aqwavWAQ'.ccoo_entries.ndarraycKDTree.query_pairsNotImplementedErrorInvalid output typecline_in_tracebackcKDTree.__setstate__cKDTree.__getstate__asyncio.coroutinesordered_pairs.setascontiguousarrayscipy._lib._utilquery_ball_pointcoo_entries.dict__setstate_cython__query_ball_tree__pyx_PickleErrorcount_neighborsreturn_inverseproper_weights, must be -1 or > 0copy_if_neededAttributeErrorreturn_sortedreturn_length__reduce_cython__other_weightsordered_pairscompact_nodes__class_getitem__cKDTree.query_build_weightsbalanced_treeuse_setstateself_weightsscipy.sparsereturn_index__pyx_checksumnum_of_nodesnode_weightsmax_distance_is_coroutine_initializing_thread_funcsort_outputquery_pairsoutput_typenum_workerscoo_entriescKDTreeNodePickleErrorImportError__pyx_vtable____pyx_resultint_resultdok_matrixcumulativecoo_matrixValueErrorthreadingres_dtype__reduce_ex____pyx_staten_queriesisenabledcpu_countcopy_dataTypeError__setstate____set_name__retshaperesults2res_dict__qualname____pyx_typeoperatorleafsizeitemsizeisscalarisfiniteiresults__getstate__fresultsadd_noteAt;ar6workersweightsversionuintptrtypestrstridesresultsreshaperes_arrnearestndarrayinverseindicesfloat64_dtypedisablecKDTreeboxsizeasarrayupdateuniquetargetsparsesingleresult__reduce__real_rr_ndimpickleobjectmytree__module__kwargsformatenable_dictdictdaemonarangeThreadzerosx_arrvvresuint8todokstatestartshapescipyranger_arrqueryotherordernumpyndminindexiiretemptydtypedescrddretcselfarray__all__alignw2npw1npvoutvlenviewuindtree__test__stop__spec__sizeselfrlenpvxxpvrrpairndim__name____main__kmaxjoinintp__func____dict__datacopyaxisargsaminamaxNonew2pw2nw1pw1nvxxvrrtmpstrsetrespxxprrppwpoppnwpkkpirpiipfrpdd__new__maxepscurcumanyallxxw2w1prosnpkkiigcdd)&?. xvsrpnmkji +QCvector::_M_default_append@@! ??________________vector::_M_realloc_insertcannot create std::vector larger than max_size()rect1 and rect2 have different dimensionsEncountering floating point overflow. 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