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The ability to return an instance of a strict subclass of int is deprecated, and may be removed in a future version of Python.__int__ returned non-int (type %.200s)value too large to convert to intInterpreter change detected - this module can only be loaded into one interpreter per process.unbound method %.200S() needs an argument__annotations__ must be set to a dict object__kwdefaults__ must be set to a dict objectchanges to cyfunction.__kwdefaults__ will not currently affect the values used in function calls__defaults__ must be set to a tuple objectchanges to cyfunction.__defaults__ will not currently affect the values used in function calls__qualname__ must be set to a string object__name__ must be set to a string object%.200s.%.200s is not a type object%.200s.%.200s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObjectUnexpected format string character: '%c' while calling a Python objectNULL result without error in PyObject_Callscipy/sparse/csgraph/_tools.pyxscipy.sparse.csgraph._tools.__defaults__Buffer dtype mismatch, expected %s%s%s but got %sBuffer dtype mismatch, expected '%s' but got %s in '%s.%s'Expected a dimension of size %zu, got %zuExpected %d dimensions, got %dPython does not define a standard format string size for long double ('g')..Buffer dtype mismatch; next field is at offset %zd but %zd expectedBig-endian buffer not supported on little-endian compilerBuffer acquisition: Expected '{' after 'T'Cannot handle repeated arrays in format stringDoes not understand character buffer dtype format string ('%c')Expected a dimension of size %zu, got %dExpected a comma in format string, got '%c'Expected %d dimension(s), got %dUnexpected end of format string, expected ')'Buffer has wrong number of dimensions (expected %d, got %d)Item size of buffer (%zd byte%s) does not match size of '%s' (%zd byte%s)../scipy/sparse/csgraph/parameters.pxiModule '_tools' has already been imported. Re-initialisation is not supported.compile time Python version %d.%d of module '%.100s' %s runtime version %d.%dFailed to import '%.20s.decompress' - cannot initialise module strings. String compression was configured with the C macro 'CYTHON_COMPRESS_STRINGS=%d'.base 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 type%.200s does not export expected C %.8s %.200sC %.8s %.200s.%.200s has wrong signature (expected %.500s, got %.500s)_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. 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[0, 1, 2, 0], ... [0, 0, 0, 1], ... [0, 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, 3) 3 >>> pred = np.array([[-9999, 0, 0, 2], ... [1, -9999, 0, 1], ... [2, 0, -9999, 2], ... [1, 3, 3, -9999]], dtype=np.int32) >>> construct_dist_matrix(graph=graph, predecessors=pred, directed=False) array([[0., 1., 2., 5.], [1., 0., 3., 1.], [2., 3., 0., 3.], [2., 1., 3., 0.]]) reconstruct_path(csgraph, predecessors, directed=True) Construct a tree from a graph and a predecessor list. .. versionadded:: 0.11.0 Parameters ---------- csgraph : array_like or sparse array or matrix The N x N matrix representing the directed or undirected graph from which the predecessors are drawn. predecessors : array_like, one dimension The length-N array of indices of predecessors for the tree. The index of the parent of node i is given by predecessors[i]. 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 operate 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 tree drawn from csgraph which is encoded by the predecessor list. Examples -------- >>> import numpy as np >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import reconstruct_path >>> graph = [ ... [0, 1, 2, 0], ... [0, 0, 0, 1], ... [0, 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, 3) 3 >>> pred = np.array([-9999, 0, 0, 1], dtype=np.int32) >>> cstree = reconstruct_path(csgraph=graph, predecessors=pred, directed=False) >>> cstree.todense() array([[0., 1., 2., 0.], [0., 0., 0., 1.], [0., 0., 0., 0.], [0., 0., 0., 0.]]) csgraph_to_masked(csgraph) Convert a sparse graph representation to a masked array representation .. versionadded:: 0.11.0 Parameters ---------- csgraph : csr_array, csc_array, or lil_array Sparse representation of a graph. Returns ------- graph : MaskedArray The masked dense representation of the sparse graph. Examples -------- >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import csgraph_to_masked >>> graph = csr_array( [ ... [0, 1, 2, 0], ... [0, 0, 0, 1], ... [0, 0, 0, 3], ... [0, 0, 0, 0] ... ]) >>> graph >>> csgraph_to_masked(graph) masked_array( data=[[ --, 1.0, 2.0, --], [ --, --, --, 1.0], [ --, --, --, 3.0], [ --, --, --, --]], mask=[[ True, False, False, True], [ True, True, True, False], [ True, True, True, False], [ True, True, True, True]], fill_value=1e+20) csgraph_to_dense(csgraph, null_value=0) Convert a sparse graph representation to a dense representation .. versionadded:: 0.11.0 Parameters ---------- csgraph : csr_array, csc_array, or lil_array Sparse representation of a graph. null_value : float, optional The value used to indicate null edges in the dense representation. Default is 0. Returns ------- graph : ndarray The dense representation of the sparse graph. Notes ----- For normal sparse graph representations, calling csgraph_to_dense with null_value=0 produces an equivalent result to using dense format conversions in the main sparse package. When the sparse representations have repeated values, however, the results will differ. The tools in scipy.sparse will add repeating values to obtain a final value. This function will select the minimum among repeating values to obtain a final value. For example, here we'll create a two-node directed sparse graph with multiple edges from node 0 to node 1, of weights 2 and 3. This illustrates the difference in behavior: >>> from scipy.sparse import csr_array, csgraph >>> import numpy as np >>> data = np.array([2, 3]) >>> indices = np.array([1, 1]) >>> indptr = np.array([0, 2, 2]) >>> M = csr_array((data, indices, indptr), shape=(2, 2)) >>> M.toarray() array([[0, 5], [0, 0]]) >>> csgraph.csgraph_to_dense(M) array([[0., 2.], [0., 0.]]) The reason for this difference is to allow a compressed sparse graph to represent multiple edges between any two nodes. As most sparse graph algorithms are concerned with the single lowest-cost edge between any two nodes, the default scipy.sparse behavior of summing multiple weights does not make sense in this context. The other reason for using this routine is to allow for graphs with zero-weight edges. Let's look at the example of a two-node directed graph, connected by an edge of weight zero: >>> from scipy.sparse import csr_array, csgraph >>> data = np.array([0.0]) >>> indices = np.array([1]) >>> indptr = np.array([0, 1, 1]) >>> M = csr_array((data, indices, indptr), shape=(2, 2)) >>> M.toarray() array([[0., 0.], [0., 0.]]) >>> csgraph.csgraph_to_dense(M, np.inf) array([[inf, 0.], [inf, inf]]) In the first case, the zero-weight edge gets lost in the dense representation. In the second case, we can choose a different null value and see the true form of the graph. Examples -------- >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import csgraph_to_dense >>> graph = csr_array( [ ... [0, 1, 2, 0], ... [0, 0, 0, 1], ... [0, 0, 0, 3], ... [0, 0, 0, 0] ... ]) >>> graph >>> csgraph_to_dense(graph) array([[0., 1., 2., 0.], [0., 0., 0., 1.], [0., 0., 0., 3.], [0., 0., 0., 0.]]) csgraph_from_dense(graph, null_value=0, nan_null=True, infinity_null=True) Construct a CSR-format sparse graph from a dense matrix. .. versionadded:: 0.11.0 Parameters ---------- graph : array_like Input graph. Shape should be (n_nodes, n_nodes). null_value : float or None (optional) Value that denotes non-edges in the graph. Default is zero. infinity_null : bool If True (default), then infinite entries (both positive and negative) are treated as null edges. nan_null : bool If True (default), then NaN entries are treated as non-edges Returns ------- csgraph : csr_array Compressed sparse representation of graph, Examples -------- >>> from scipy.sparse.csgraph import csgraph_from_dense >>> graph = [ ... [0, 1, 2, 0], ... [0, 0, 0, 1], ... [0, 0, 0, 3], ... [0, 0, 0, 0] ... ] >>> csgraph_from_dense(graph) csgraph_masked_from_dense(graph, null_value=0, nan_null=True, infinity_null=True, copy=True) Construct a masked array graph representation from a dense matrix. .. versionadded:: 0.11.0 Parameters ---------- graph : array_like Input graph. Shape should be (n_nodes, n_nodes). null_value : float or None (optional) Value that denotes non-edges in the graph. Default is zero. infinity_null : bool If True (default), then infinite entries (both positive and negative) are treated as null edges. nan_null : bool If True (default), then NaN entries are treated as non-edges Returns ------- csgraph : MaskedArray masked array representation of graph Examples -------- >>> from scipy.sparse.csgraph import csgraph_masked_from_dense >>> graph = [ ... [0, 1, 2, 0], ... [0, 0, 0, 1], ... [0, 0, 0, 3], ... [0, 0, 0, 0] ... ] >>> csgraph_masked_from_dense(graph) masked_array( data=[[--, 1, 2, --], [--, --, --, 1], [--, --, --, 3], [--, --, --, --]], mask=[[ True, False, False, True], [ True, True, True, False], [ True, True, True, False], [ True, True, True, True]], fill_value=0) csgraph_from_masked(graph) Construct a CSR-format graph from a masked array. .. versionadded:: 0.11.0 Parameters ---------- graph : MaskedArray Input graph. Shape should be (n_nodes, n_nodes). Returns ------- csgraph : csr_array Compressed sparse representation of graph, Examples -------- >>> import numpy as np >>> from scipy.sparse.csgraph import csgraph_from_masked >>> graph_masked = np.ma.masked_array(data =[ ... [0, 1, 2, 0], ... [0, 0, 0, 1], ... [0, 0, 0, 3], ... [0, 0, 0, 0] ... ], ... mask=[[ True, False, False, True], ... [ True, True, True, False], ... [ True, True, True, False], ... [ True, True, True, True]], ... fill_value = 0) >>> csgraph_from_masked(graph_masked) Tools and utilities for working with compressed sparse graphs @@?;TIPpP(d5@H! wPp@d xp  4"l ##% & `&$(H)D)|-@..@/l001p22, 2@ 3T p4l 4 5 8 @

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