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@LLI`LLE1gE1LsLL\LVHL\LL!L\^HhaLHL8_fff.LLL 4\ LLLLE1 \L fDHL [L |x L^E1HDž8L[E1E1^Ax8Au0LLL J[ LLLLM@[]H= HH`LML y]L HL8_.L8aLLZLCDHLLrZLLLXLPfInAfInfl=wAA=wAH8x H fɿLLLHEHEM)E,\LLHLI AxAt _fLLLL sYL _LL@LHY0L_H'H=.7E1N(fK[H=HH]LM%p[E1bHHHHH5 H81.] E1bN{]LHH8E1bQHKfInLkfHnfl=wAE=wAEx LL)EHtHHHWH5HHDžHHfHHXHH_H\\HLE1d@YH=<HL5\LML YL H LLE1I߹dvHxsLLI߹d?HfHH$XHH H- E'M9+fDHY=wHHuHHHEHErIċx MtLtA$x A$ LE1eHE1UL^HDž8HZHLE1gqH8LALH7ZILLIڹgHDž 1IH{H=HSHWHH4 =wHGHH5tHHu HHËHF x H5HTHBHHHHt?1 }1H9})HcHATD9~މ9|A9@AQ1A9ff.UHAVIAUATASHH /KL`IM5FDL;9HHIE;butI=wHLL1HFIHD`(HHx AEx AEH [A\A]A^]@MEpIEpMMHA=wAIH(H=HDLLMLEHMKHMLEHLMHI;H(I}pMEpHtx Ax AHtx LM DL׉ΉMMHc9aLcIME;`9MHcLE)HwHM؍PHHHHHHHHLLILEЋM؃E`I 8=fDUH߉G fDLH [A\A]A^]Bad call flags for CyFunctionkeywords must be stringsbuiltinscython_runtime__builtins__scipy.sparse.csgraph._toolsdoes not matchnumpyflatiterbroadcastndarraygenericnumberunsignedintegerinexactcomplexfloatingflexiblecharacterufuncnumpy._core._multiarray_umathnumpy.core._multiarray_umath_ARRAY_API_ARRAY_API is NULL pointernumpy.import_arrayreconstruct_pathbuffer dtypeconstruct_dist_matrix__module__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_coroutine__dictoffset____vectorcalloffset____weaklistoffset____reduce__an integer is required%.200s() takes %.8s %zd positional argument%.1s (%zd given)scipy/sparse/csgraph/_tools.pyxscipy.sparse.csgraph._tools.csgraph_to_masked'%.200s' object does not support slice %.10sscipy.sparse.csgraph._tools.csgraph_from_maskedscipy.sparse.csgraph._tools.csgraph_masked_from_densescipy.sparse.csgraph._tools.csgraph_from_denseCannot convert %.200s to %.200sOut of bounds on buffer access (axis %d)scipy.sparse.csgraph._tools._populate_graphscipy.sparse.csgraph._tools.csgraph_to_denseUnexpected format string character: '%c'Buffer dtype mismatch, expected %s%s%s but got %sBuffer dtype mismatch, expected '%s' but got %s in '%s.%s'Shared Cython type %.200s is not a type objectShared Cython type %.200s has the wrong size, try recompilingscipy.sparse.csgraph._tools.__defaults__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 ')'__name__ must be set to a string object__qualname__ must be set to a string objectfunction's dictionary may not be deletedsetting function's dictionary to a non-dict__annotations__ must be set to a dict objectInterpreter change detected - this module can only be loaded into one interpreter per process.__defaults__ must be set to a tuple objectchanges to cyfunction.__defaults__ will not currently affect the values used in function calls__kwdefaults__ must be set to a dict objectchanges to cyfunction.__kwdefaults__ will not currently affect the values used in function calls%s() got multiple values for keyword argument '%U'%.200s() keywords must be strings%.200s.%.200s is not a type object%.200s.%.200s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObjectunbound method %.200S() needs an argument while calling a Python objectNULL result without error in PyObject_Callcalling %R should have returned an instance of BaseException, not %Rraise: exception class must be a subclass of BaseException../../../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.%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 type_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../../../../../../usr/lib/python3/dist-packages/numpy/__init__.cython-30.pxdinit scipy.sparse.csgraph._tools%s() got an unexpected keyword argument '%U'cannot fit '%.200s' into an index-sized integer'%.200s' object is not subscriptable'%.200s' object is unsliceablescipy.sparse.csgraph._tools.reconstruct_pathBuffer 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._tools._construct_dist_matrixscipy.sparse.csgraph._tools.construct_dist_matrix_cython_3_1_6._common_types_metatype_cython_3_1_6.cython_function_or_methodscipy.sparse.csgraph._tools.__pyx_defaults__int__ returned non-int (type %.200s). 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 int-ʌ$dԓ@?@ O "    G 2 * p@@p@@@@@@@h@@hhh@@@@@@@@@@@@@@@@pph@@@h@@@ph@p,,,,,,,,,,,,,,,,,,,,,,,,,,,M,:,,,,,,XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX;!$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$# !$#$#$#$#$#$#!$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#$#!$#~! !t^Hzeros_validationvalidate_graphtocsrtoarray__test__sumspmatrix__spec__shape__set_name__searchsortedsctreescipy/sparse/csgraph/_tools.pyxscipy.sparse.csgraph._toolsscipy.sparse._sputilsscipy.sparseresreconstruct_path (line 415) 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.]]) reconstruct_pathravelrange__qualname__pydata_sparse_fill_valuepydata_sparse_clspredecessorspoppindorderonesnumpy._core.umath failed to importnumpy._core.multiarray failed to importnumpynull_valuenpnnullndimnan_nullnan__name____module__minimummatrixmasked_valuesmasked_invalidmasked_arraymask__main__malilissparseisnanisinfisenabledis_pydata_spmatrix_is_coroutineint32_initializinginfinity_nullinfindptrindicesidx_gridgraph should have two dimensionsgraph should be a square arraygraph and predecessors must have the same shapegraphgc__func__from_scipy_sparseformatfloat64fill_valuefillenableemptydtypedist_matrixdisabledirecteddense_outputdata2datacumsumcsr_outputcsr_matrixcsr_arraycsrcsgraph_to_masked (line 341) 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_maskedcsgraph_to_dense (line 223) 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_to_densecsgraph should be a square matrixcsgraph_origcsgraph must be sparsecsgraph must be lil, csr, or csc formatcsgraph_masked_from_dense (line 83) 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_masked_from_densecsgraph_from_masked (line 18) 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) csgraph_from_maskedcsgraph_from_dense (line 172) 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_from_densecsgraphcsccopy_if_densecopyconstruct_dist_matrix (line 525) construct_dist_matrix(graph, predecessors, directed=True, null_value=np.inf) Construct distance matrix from a predecessor matrix .. versionadded:: 0.11.0 Parameters ---------- graph : array_like or sparse The N x N matrix representation of a directed or undirected graph. If dense, then non-edges are indicated by zeros or infinities. predecessors : array_like The N x N matrix of predecessors of each node (see Notes below). 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]. null_value : bool, optional value to use for distances between unconnected nodes. Default is np.inf Returns ------- dist_matrix : ndarray The N x N matrix of distances between nodes along the path specified by the predecessor matrix. If no path exists, the distance is zero. Notes ----- The predecessor matrix is of the form optionally returned by `shortest_path`. Row i of the predecessor matrix contains information on the shortest paths from point i: each entry predecessors[i, j] gives the index of the previous node in the path from point i to point j. If no path exists between point i and j, then predecessors[i, j] = -9999 It should be noted that `shortest_path` only returns distance matrix by default. With ``return_predecessors=True``, it returns a tuple with distance matrix as its first element and predecessors array as second element. Examples -------- >>> import numpy as np >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import construct_dist_matrix >>> 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, 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.]]) construct_dist_matrixcompressedcline_in_traceback__class_getitem____class__cboolasyncio.coroutinesastypeasarrayarrayargsortarange?ValueErrorType of predecessors array should be np.int32TypeErrorNImportErrorITYPEDTYPEC. construct_dist_matrix(graph, predecessors, directed=True, null_value=np.inf) Construct distance matrix from a predecessor matrix .. versionadded:: 0.11.0 Parameters ---------- graph : array_like or sparse The N x N matrix representation of a directed or undirected graph. If dense, then non-edges are indicated by zeros or infinities. predecessors : array_like The N x N matrix of predecessors of each node (see Notes below). 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]. null_value : bool, optional value to use for distances between unconnected nodes. Default is np.inf Returns ------- dist_matrix : ndarray The N x N matrix of distances between nodes along the path specified by the predecessor matrix. If no path exists, the distance is zero. Notes ----- The predecessor matrix is of the form optionally returned by `shortest_path`. Row i of the predecessor matrix contains information on the shortest paths from point i: each entry predecessors[i, j] gives the index of the previous node in the path from point i to point j. If no path exists between point i and j, then predecessors[i, j] = -9999 It should be noted that `shortest_path` only returns distance matrix by default. With ``return_predecessors=True``, it returns a tuple with distance matrix as its first element and predecessors array as second element. Examples -------- >>> import numpy as np >>> from scipy.sparse import csr_array >>> from scipy.sparse.csgraph import construct_dist_matrix >>> 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, 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 %'q\ Q N!7*F!&a)Q2XQa|7#Qiq|7#U!j"F!5a!7.%Q 1h,Ax Q1nAYj QvQa ]"Bd!bawgQa G`;G`0G `(G`G( F# F`F`F`F`F `F``F`PF `GF`AF`0F`?! > >`> `>`>``> E>`8> `(> `!>`> `> `>`= `=`=`=`= `=`X P @PXo0   `6X oooo0P@PPP`PpPPPPPPPPPQQ Q0Q@QPQ`QpQQQQQQQQQRR R0R@RPR`RpRRRRRRRRRSS S0S@SPS`SpSSSSSSSSSTT T0T@TPT`TpTTTTTTTTTUU U0U@UPU`UpUUUUUUUUUVV V0V@VPV`VpVVVVVVVV`$k$kE$kE$`da$`da$Bb$Tb$Tb$B%B%C%C'% C1% C:%`FdH%`FdU%Fed%U ct%0R$ %@%0%(%PCI4pnBn2pGpC3`G@ H@I@6@n^ip6`6M6c@ADD$`@vr$P  0`}  c > `w#  /usr/lib/debug/.dwz/x86_64-linux-gnu/python3-scipy.debug/\G,ճSW6_127d39b2a2c3a901908d2e1c4fe735a52793cb.debug1aټ.shstrtab.note.gnu.build-id.gnu.hash.dynsym.dynstr.gnu.version.gnu.version_r.rela.dyn.rela.plt.init.plt.got.plt.sec.text.fini.rodata.eh_frame_hdr.eh_frame.note.gnu.property.note.package.init_array.fini_array.data.rel.ro.dynamic.got.plt.data.bss.gnu_debugaltlink.gnu_debuglink $o$( 00h 0 8oEo0TX^B`6`6 hPPc P PnVVwWW]] @@   0 00  pPPXX`` rx``(  M!4 0