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Re-initialisation is not supported.scipy.sparse.csgraph._traversalcompile time Python version %d.%d of module '%.100s' %s runtime version %d.%dbase class '%.200s' is not a heap typeextension type '%.200s' has no __dict__ slot, but base type '%.200s' has: either add 'cdef dict __dict__' to the extension type or add '__slots__ = [...]' to the base typeint (struct __pyx_array_obj *)struct __pyx_array_obj *(PyObject *, Py_ssize_t, char *, char const *, char *)PyObject *(PyObject *, int, int, __Pyx_TypeInfo const *)struct __pyx_memoryview_obj *(struct __pyx_memoryview_obj *, PyObject *)int (__Pyx_memviewslice *, Py_ssize_t, Py_ssize_t, Py_ssize_t, int, int, int *, Py_ssize_t, Py_ssize_t, Py_ssize_t, int, int, int, int)char *(Py_buffer *, char *, Py_ssize_t, Py_ssize_t)PyObject *(__Pyx_memviewslice, int, PyObject *(*)(char *), int (*)(char *, PyObject *), int)__Pyx_memviewslice *(struct __pyx_memoryview_obj *, __Pyx_memviewslice *)void (struct __pyx_memoryview_obj *, __Pyx_memviewslice *)PyObject *(struct __pyx_memoryview_obj *)PyObject *(struct __pyx_memoryview_obj *, __Pyx_memviewslice *)char (__Pyx_memviewslice *, int)Py_ssize_t (__Pyx_memviewslice *, int)Py_ssize_t (Py_ssize_t *, Py_ssize_t *, Py_ssize_t, int, char)void *(__Pyx_memviewslice *, __Pyx_memviewslice *, char, int)int (int, Py_ssize_t, Py_ssize_t)int (PyObject *, PyObject *, int)int (__Pyx_memviewslice, __Pyx_memviewslice, int, int, int)void (__Pyx_memviewslice *, int, int)void (__Pyx_memviewslice *, int, int, int)void (char *, Py_ssize_t *, Py_ssize_t *, int, int)void (__Pyx_memviewslice *, int, size_t, void *, int)void (char *, Py_ssize_t *, Py_ssize_t *, int, size_t, void *)_ARRAY_API is not PyCapsule objectmodule compiled against ABI version 0x%x but this version of numpy is 0x%xmodule was compiled against NumPy C-API version 0x%x (NumPy 1.23) but the running NumPy has C-API version 0x%x. Check the section C-API incompatibility at the Troubleshooting ImportError section at https://numpy.org/devdocs/user/troubleshooting-importerror.html#c-api-incompatibility for indications on how to solve this problem.FATAL: module compiled as unknown endianFATAL: module compiled as little endian, but detected different endianness at runtime../../tmp/build-env-99e64tom/lib/python3.12/site-packages/numpy/__init__.cython-30.pxdinit scipy.sparse.csgraph._traversalscipy.sparse.csgraph._traversal._connected_components_directedBuffer acquisition failed on assignment; and then reacquiring the old buffer failed too!scipy.sparse.csgraph._traversal._connected_components_directed2'%.200s' object is unsliceablescipy.sparse.csgraph._traversal.breadth_first_ordertoo many values to unpack (expected %zd)need more than %zd value%.1s to unpackscipy.sparse.csgraph._traversal.breadth_first_treescipy.sparse.csgraph._traversal._breadth_first_undirectedscipy.sparse.csgraph._traversal._depth_first_directedscipy.sparse.csgraph._traversal._depth_first_directed2scipy.sparse.csgraph._traversal._depth_first_undirectedscipy.sparse.csgraph._traversal.connected_componentsscipy.sparse.csgraph._traversal._breadth_first_directedscipy.sparse.csgraph._traversal._breadth_first_directed2scipy.sparse.csgraph._traversal.depth_first_orderscipy.sparse.csgraph._traversal.depth_first_treeobject of type 'NoneType' has no len()only single character unicode strings can be converted to Py_UCS4, got length %zd'NoneType' object is not iterabledictionary changed size during iteration'NoneType' object is not subscriptable'NoneType' object has no attribute '%.30s'scipy.sparse.csgraph._traversal.__pyx_fused_cpdef_cython_3_1_6.fused_cython_function_cython_3_1_6.cython_function_or_method_cython_3_1_6._common_types_metatypescipy.sparse.csgraph._traversal.__pyx_defaults__pyx_fuse_1_1_connected_components_undirected__pyx_fuse_1_0_connected_components_undirected__pyx_fuse_0_1_connected_components_undirected__pyx_fuse_0_0_connected_components_undirected__pyx_fuse_1_connected_components_directed__pyx_fuse_0_connected_components_directed__pyx_fuse_1_1_depth_first_undirected__pyx_fuse_1_0_depth_first_undirected__pyx_fuse_0_1_depth_first_undirected__pyx_fuse_0_0_depth_first_undirected__pyx_fuse_1_depth_first_directed__pyx_fuse_0_depth_first_directed__pyx_fuse_1_1_breadth_first_undirected__pyx_fuse_1_0_breadth_first_undirected__pyx_fuse_0_1_breadth_first_undirected__pyx_fuse_0_0_breadth_first_undirected__pyx_fuse_1_breadth_first_directed__pyx_fuse_0_breadth_first_directedP P p PP `p P P, D    fr ~ P 8N Z =  =                                                                f         B N   Z                   r   v   *    d 6  d tl l tl l l l l l\l l \l l LLLl l l l l l l l l l l l l l l l ttl vl\l l \l l l tLl t      ;     |l \ \\\  |l \ \ v`````````F``F``````````````````F[````````````````````````O[O``````````````````.```O``````````````````uDcDQD?D-DD]]K]9]']]]5v#vvuuuَǎV0F040"00<)o]K6! xcN9$oZE0!7 7666666y6d6ZZZZuZ`ZKZ6Z!Z Z poooozhVD2 n\J8xq\]BHB3BB BAp[F1*zdtt~thtRt>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import depth_first_order >>> graph = [ ... [0, 1, 2, 0], ... [0, 0, 0, 1], ... [2, 0, 0, 3], ... [0, 0, 0, 0] ... ] >>> graph = csr_array(graph) >>> print(graph) Coords Values (0, 1) 1 (0, 2) 2 (1, 3) 1 (2, 0) 2 (2, 3) 3 >>> depth_first_order(graph,0) (array([0, 1, 3, 2], dtype=int32), array([-9999, 0, 0, 1], dtype=int32)) breadth_first_order(csgraph, i_start, directed=True, return_predecessors=True) Return a breadth-first ordering starting with specified node. Note that a breadth-first order is not unique, but the tree which it generates is unique. .. versionadded:: 0.11.0 Parameters ---------- csgraph : array_like or sparse array or matrix The N x N compressed sparse graph. The input csgraph will be converted to csr format for the calculation. i_start : int The index of starting node. directed : bool, optional If True (default), then operate on a directed graph: only move from point i to point j along paths csgraph[i, j]. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j along csgraph[i, j] or csgraph[j, i]. return_predecessors : bool, optional If True (default), then return the predecessor array (see below). Returns ------- node_array : ndarray, one dimension The breadth-first list of nodes, starting with specified node. The length of node_array is the number of nodes reachable from the specified node. predecessors : ndarray, one dimension Returned only if return_predecessors is True. The length-N list of predecessors of each node in a breadth-first tree. If node i is in the tree, then its parent is given by predecessors[i]. If node i is not in the tree (and for the parent node) then predecessors[i] = -9999. Notes ----- If multiple valid solutions are possible, output may vary with SciPy and Python version. Examples -------- >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import breadth_first_order >>> graph = [ ... [0, 1, 2, 0], ... [0, 0, 0, 1], ... [2, 0, 0, 3], ... [0, 0, 0, 0] ... ] >>> graph = csr_array(graph) >>> print(graph) Coords Values (0, 1) 1 (0, 2) 2 (1, 3) 1 (2, 0) 2 (2, 3) 3 >>> breadth_first_order(graph,0) (array([0, 1, 2, 3], dtype=int32), array([-9999, 0, 0, 1], dtype=int32)) depth_first_tree(csgraph, i_start, directed=True) Return a tree generated by a depth-first search. Note that a tree generated by a depth-first search is not unique: it depends on the order that the children of each node are searched. .. versionadded:: 0.11.0 Parameters ---------- csgraph : array_like or sparse array or matrix The N x N matrix representing the compressed sparse graph. The input csgraph will be converted to csr format for the calculation. i_start : int The index of starting node. directed : bool, optional If True (default), then operate on a directed graph: only move from point i to point j along paths csgraph[i, j]. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j along csgraph[i, j] or csgraph[j, i]. Returns ------- cstree : csr matrix The N x N directed compressed-sparse representation of the depth- first tree drawn from csgraph, starting at the specified node. Notes ----- If multiple valid solutions are possible, output may vary with SciPy and Python version. Examples -------- The following example shows the computation of a depth-first tree over a simple four-component graph, starting at node 0:: input graph depth first tree from (0) (0) (0) / \ \ 3 8 8 / \ \ (3)---5---(1) (3) (1) \ / \ / 6 2 6 2 \ / \ / (2) (2) In compressed sparse representation, the solution looks like this: >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import depth_first_tree >>> X = csr_array([[0, 8, 0, 3], ... [0, 0, 2, 5], ... [0, 0, 0, 6], ... [0, 0, 0, 0]]) >>> Tcsr = depth_first_tree(X, 0, directed=False) >>> Tcsr.toarray().astype(int) array([[0, 8, 0, 0], [0, 0, 2, 0], [0, 0, 0, 6], [0, 0, 0, 0]]) Note that the resulting graph is a Directed Acyclic Graph which spans the graph. Unlike a breadth-first tree, a depth-first tree of a given graph is not unique if the graph contains cycles. If the above solution had begun with the edge connecting nodes 0 and 3, the result would have been different. breadth_first_tree(csgraph, i_start, directed=True) Return the tree generated by a breadth-first search Note that a breadth-first tree from a specified node is unique. .. versionadded:: 0.11.0 Parameters ---------- csgraph : array_like or sparse array or matrix The N x N matrix representing the compressed sparse graph. The input csgraph will be converted to csr format for the calculation. i_start : int The index of starting node. directed : bool, optional If True (default), then operate on a directed graph: only move from point i to point j along paths csgraph[i, j]. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j along csgraph[i, j] or csgraph[j, i]. Returns ------- cstree : csr matrix The N x N directed compressed-sparse representation of the breadth- first tree drawn from csgraph, starting at the specified node. Notes ----- If multiple valid solutions are possible, output may vary with SciPy and Python version. Examples -------- The following example shows the computation of a depth-first tree over a simple four-component graph, starting at node 0:: input graph breadth first tree from (0) (0) (0) / \ / \ 3 8 3 8 / \ / \ (3)---5---(1) (3) (1) \ / / 6 2 2 \ / / (2) (2) In compressed sparse representation, the solution looks like this: >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import breadth_first_tree >>> X = csr_array([[0, 8, 0, 3], ... [0, 0, 2, 5], ... [0, 0, 0, 6], ... [0, 0, 0, 0]]) >>> Tcsr = breadth_first_tree(X, 0, directed=False) >>> Tcsr.toarray().astype(int) array([[0, 8, 0, 3], [0, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0]]) Note that the resulting graph is a Directed Acyclic Graph which spans the graph. A breadth-first tree from a given node is unique. connected_components(csgraph, directed=True, connection='weak', return_labels=True) Analyze the connected components of a sparse graph .. versionadded:: 0.11.0 Parameters ---------- csgraph : array_like or sparse array or matrix The N x N matrix representing the compressed sparse graph. The input csgraph will be converted to csr format for the calculation. directed : bool, optional If True (default), then operate on a directed graph: only move from point i to point j along paths csgraph[i, j]. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j along csgraph[i, j] or csgraph[j, i]. connection : str, optional ['weak'|'strong']. For directed graphs, the type of connection to use. Nodes i and j are strongly connected if a path exists both from i to j and from j to i. A directed graph is weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph. If directed == False, this keyword is not referenced. return_labels : bool, optional If True (default), then return the labels for each of the connected components. Returns ------- n_components: int The number of connected components. labels: ndarray The length-N array of labels of the connected components. References ---------- .. [1] D. J. Pearce, "An Improved Algorithm for Finding the Strongly Connected Components of a Directed Graph", Technical Report, 2005 Examples -------- >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import connected_components >>> graph = [ ... [0, 1, 1, 0, 0], ... [0, 0, 1, 0, 0], ... [0, 0, 0, 0, 0], ... [0, 0, 0, 0, 1], ... [0, 0, 0, 0, 0] ... ] >>> graph = csr_array(graph) >>> print(graph) Coords Values (0, 1) 1 (0, 2) 1 (1, 2) 1 (3, 4) 1 >>> n_components, labels = connected_components(csgraph=graph, directed=False, return_labels=True) >>> n_components 2 >>> labels array([0, 0, 0, 1, 1], dtype=int32) scipy/sparse/csgraph/_traversal.pyx_connected_components_undirected[ndarray,ndarray,ndarray,ndarray]scipy.sparse.csgraph._validationnumpy._core.umath failed to importnumpy._core.multiarray failed to importconnection must be 'weak' or 'strong'Note 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.Function call with ambiguous argument typesscipy.sparse.csgraph._traversal depth_first_tree(csgraph, i_start, directed=True) Return a tree generated by a depth-first search. Note that a tree generated by a depth-first search is not unique: it depends on the order that the children of each node are searched. .. versionadded:: 0.11.0 Parameters ---------- csgraph : array_like or sparse array or matrix The N x N matrix representing the compressed sparse graph. The input csgraph will be converted to csr format for the calculation. i_start : int The index of starting node. directed : bool, optional If True (default), then operate on a directed graph: only move from point i to point j along paths csgraph[i, j]. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j along csgraph[i, j] or csgraph[j, i]. Returns ------- cstree : csr matrix The N x N directed compressed-sparse representation of the depth- first tree drawn from csgraph, starting at the specified node. Notes ----- If multiple valid solutions are possible, output may vary with SciPy and Python version. Examples -------- The following example shows the computation of a depth-first tree over a simple four-component graph, starting at node 0:: input graph depth first tree from (0) (0) (0) / \ \ 3 8 8 / \ \ (3)---5---(1) (3) (1) \ / \ / 6 2 6 2 \ / \ / (2) (2) In compressed sparse representation, the solution looks like this: >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import depth_first_tree >>> X = csr_array([[0, 8, 0, 3], ... [0, 0, 2, 5], ... [0, 0, 0, 6], ... [0, 0, 0, 0]]) >>> Tcsr = depth_first_tree(X, 0, directed=False) >>> Tcsr.toarray().astype(int) array([[0, 8, 0, 0], [0, 0, 2, 0], [0, 0, 0, 6], [0, 0, 0, 0]]) Note that the resulting graph is a Directed Acyclic Graph which spans the graph. Unlike a breadth-first tree, a depth-first tree of a given graph is not unique if the graph contains cycles. If the above solution had begun with the edge connecting nodes 0 and 3, the result would have been different. depth_first_order(csgraph, i_start, directed=True, return_predecessors=True) Return a depth-first ordering starting with specified node. Note that a depth-first order is not unique. Furthermore, for graphs with cycles, the tree generated by a depth-first search is not unique either. .. versionadded:: 0.11.0 Parameters ---------- csgraph : array_like or sparse array or matrix The N x N compressed sparse graph. The input csgraph will be converted to csr format for the calculation. i_start : int The index of starting node. directed : bool, optional If True (default), then operate on a directed graph: only move from point i to point j along paths csgraph[i, j]. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j along csgraph[i, j] or csgraph[j, i]. return_predecessors : bool, optional If True (default), then return the predecessor array (see below). Returns ------- node_array : ndarray, one dimension The depth-first list of nodes, starting with specified node. The length of node_array is the number of nodes reachable from the specified node. predecessors : ndarray, one dimension Returned only if return_predecessors is True. The length-N list of predecessors of each node in a depth-first tree. If node i is in the tree, then its parent is given by predecessors[i]. If node i is not in the tree (and for the parent node) then predecessors[i] = -9999. Notes ----- If multiple valid solutions are possible, output may vary with SciPy and Python version. Examples -------- >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import depth_first_order >>> graph = [ ... [0, 1, 2, 0], ... [0, 0, 0, 1], ... [2, 0, 0, 3], ... [0, 0, 0, 0] ... ] >>> graph = csr_array(graph) >>> print(graph) Coords Values (0, 1) 1 (0, 2) 2 (1, 3) 1 (2, 0) 2 (2, 3) 3 >>> depth_first_order(graph,0) (array([0, 1, 3, 2], dtype=int32), array([-9999, 0, 0, 1], dtype=int32)) _depth_first_directed[ndarray,ndarray]_connected_components_undirected_connected_components_directed[ndarray,ndarray] connected_components(csgraph, directed=True, connection='weak', return_labels=True) Analyze the connected components of a sparse graph .. versionadded:: 0.11.0 Parameters ---------- csgraph : array_like or sparse array or matrix The N x N matrix representing the compressed sparse graph. The input csgraph will be converted to csr format for the calculation. directed : bool, optional If True (default), then operate on a directed graph: only move from point i to point j along paths csgraph[i, j]. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j along csgraph[i, j] or csgraph[j, i]. connection : str, optional ['weak'|'strong']. For directed graphs, the type of connection to use. Nodes i and j are strongly connected if a path exists both from i to j and from j to i. A directed graph is weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph. If directed == False, this keyword is not referenced. return_labels : bool, optional If True (default), then return the labels for each of the connected components. Returns ------- n_components: int The number of connected components. labels: ndarray The length-N array of labels of the connected components. References ---------- .. [1] D. J. Pearce, "An Improved Algorithm for Finding the Strongly Connected Components of a Directed Graph", Technical Report, 2005 Examples -------- >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import connected_components >>> graph = [ ... [0, 1, 1, 0, 0], ... [0, 0, 1, 0, 0], ... [0, 0, 0, 0, 0], ... [0, 0, 0, 0, 1], ... [0, 0, 0, 0, 0] ... ] >>> graph = csr_array(graph) >>> print(graph) Coords Values (0, 1) 1 (0, 2) 1 (1, 2) 1 (3, 4) 1 >>> n_components, labels = connected_components(csgraph=graph, directed=False, return_labels=True) >>> n_components 2 >>> labels array([0, 0, 0, 1, 1], dtype=int32) _breadth_first_undirected[ndarray,ndarray,ndarray,ndarray] breadth_first_tree(csgraph, i_start, directed=True) Return the tree generated by a breadth-first search Note that a breadth-first tree from a specified node is unique. .. versionadded:: 0.11.0 Parameters ---------- csgraph : array_like or sparse array or matrix The N x N matrix representing the compressed sparse graph. The input csgraph will be converted to csr format for the calculation. i_start : int The index of starting node. directed : bool, optional If True (default), then operate on a directed graph: only move from point i to point j along paths csgraph[i, j]. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j along csgraph[i, j] or csgraph[j, i]. Returns ------- cstree : csr matrix The N x N directed compressed-sparse representation of the breadth- first tree drawn from csgraph, starting at the specified node. Notes ----- If multiple valid solutions are possible, output may vary with SciPy and Python version. Examples -------- The following example shows the computation of a depth-first tree over a simple four-component graph, starting at node 0:: input graph breadth first tree from (0) (0) (0) / \ / \ 3 8 3 8 / \ / \ (3)---5---(1) (3) (1) \ / / 6 2 2 \ / / (2) (2) In compressed sparse representation, the solution looks like this: >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import breadth_first_tree >>> X = csr_array([[0, 8, 0, 3], ... [0, 0, 2, 5], ... [0, 0, 0, 6], ... [0, 0, 0, 0]]) >>> Tcsr = breadth_first_tree(X, 0, directed=False) >>> Tcsr.toarray().astype(int) array([[0, 8, 0, 3], [0, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0]]) Note that the resulting graph is a Directed Acyclic Graph which spans the graph. A breadth-first tree from a given node is unique. breadth_first_order(csgraph, i_start, directed=True, return_predecessors=True) Return a breadth-first ordering starting with specified node. Note that a breadth-first order is not unique, but the tree which it generates is unique. .. versionadded:: 0.11.0 Parameters ---------- csgraph : array_like or sparse array or matrix The N x N compressed sparse graph. The input csgraph will be converted to csr format for the calculation. i_start : int The index of starting node. directed : bool, optional If True (default), then operate on a directed graph: only move from point i to point j along paths csgraph[i, j]. If False, then find the shortest path on an undirected graph: the algorithm can progress from point i to j along csgraph[i, j] or csgraph[j, i]. return_predecessors : bool, optional If True (default), then return the predecessor array (see below). Returns ------- node_array : ndarray, one dimension The breadth-first list of nodes, starting with specified node. The length of node_array is the number of nodes reachable from the specified node. predecessors : ndarray, one dimension Returned only if return_predecessors is True. The length-N list of predecessors of each node in a breadth-first tree. If node i is in the tree, then its parent is given by predecessors[i]. If node i is not in the tree (and for the parent node) then predecessors[i] = -9999. Notes ----- If multiple valid solutions are possible, output may vary with SciPy and Python version. Examples -------- >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import breadth_first_order >>> graph = [ ... [0, 1, 2, 0], ... [0, 0, 0, 1], ... [2, 0, 0, 3], ... [0, 0, 0, 0] ... ] >>> graph = csr_array(graph) >>> print(graph) Coords Values (0, 1) 1 (0, 2) 2 (1, 3) 1 (2, 0) 2 (2, 3) 3 >>> breadth_first_order(graph,0) (array([0, 1, 2, 3], dtype=int32), array([-9999, 0, 0, 1], dtype=int32)) _depth_first_undirected[ndarray,ndarray,ndarray,ndarray]_breadth_first_directed[ndarray,ndarray] Routines for traversing graphs in compressed sparse format #=QNnAYj Qaq &F!#2V1CvQ U!1Qaq( 'z +1G2V1*!1+2*G1+4Jiq+6aqy)1y!"/Pzs((!jzs#Q1nAYa#7!*! 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