Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/sitepackages/networkx/algorithms/bipartite/matrix.py @ 0:4f3585e2f14b draft default tip
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author  shellac 

date  Mon, 22 Mar 2021 18:12:50 +0000 
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1 """ 
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2 ==================== 
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3 Biadjacency matrices 
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4 ==================== 
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5 """ 
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6 import itertools 
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7 from networkx.convert_matrix import _generate_weighted_edges 
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8 import networkx as nx 
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9 
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10 __all__ = ["biadjacency_matrix", "from_biadjacency_matrix"] 
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11 
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12 
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13 def biadjacency_matrix( 
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14 G, row_order, column_order=None, dtype=None, weight="weight", format="csr" 
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15 ): 
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16 r"""Returns the biadjacency matrix of the bipartite graph G. 
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17 
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18 Let `G = (U, V, E)` be a bipartite graph with node sets 
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19 `U = u_{1},...,u_{r}` and `V = v_{1},...,v_{s}`. The biadjacency 
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20 matrix [1]_ is the `r` x `s` matrix `B` in which `b_{i,j} = 1` 
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21 if, and only if, `(u_i, v_j) \in E`. If the parameter `weight` is 
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22 not `None` and matches the name of an edge attribute, its value is 
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23 used instead of 1. 
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24 
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25 Parameters 
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26  
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27 G : graph 
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28 A NetworkX graph 
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29 
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30 row_order : list of nodes 
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31 The rows of the matrix are ordered according to the list of nodes. 
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32 
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33 column_order : list, optional 
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34 The columns of the matrix are ordered according to the list of nodes. 
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35 If column_order is None, then the ordering of columns is arbitrary. 
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36 
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37 dtype : NumPy datatype, optional 
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38 A valid NumPy dtype used to initialize the array. If None, then the 
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39 NumPy default is used. 
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40 
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41 weight : string or None, optional (default='weight') 
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42 The edge data key used to provide each value in the matrix. 
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43 If None, then each edge has weight 1. 
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44 
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45 format : str in {'bsr', 'csr', 'csc', 'coo', 'lil', 'dia', 'dok'} 
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46 The type of the matrix to be returned (default 'csr'). For 
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47 some algorithms different implementations of sparse matrices 
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48 can perform better. See [2]_ for details. 
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49 
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50 Returns 
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51  
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52 M : SciPy sparse matrix 
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53 Biadjacency matrix representation of the bipartite graph G. 
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54 
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55 Notes 
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56  
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57 No attempt is made to check that the input graph is bipartite. 
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58 
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59 For directed bipartite graphs only successors are considered as neighbors. 
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60 To obtain an adjacency matrix with ones (or weight values) for both 
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61 predecessors and successors you have to generate two biadjacency matrices 
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62 where the rows of one of them are the columns of the other, and then add 
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63 one to the transpose of the other. 
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64 
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65 See Also 
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66  
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67 adjacency_matrix 
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68 from_biadjacency_matrix 
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69 
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70 References 
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71  
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72 .. [1] https://en.wikipedia.org/wiki/Adjacency_matrix#Adjacency_matrix_of_a_bipartite_graph 
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73 .. [2] Scipy Dev. References, "Sparse Matrices", 
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74 https://docs.scipy.org/doc/scipy/reference/sparse.html 
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75 """ 
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76 from scipy import sparse 
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77 
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78 nlen = len(row_order) 
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79 if nlen == 0: 
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80 raise nx.NetworkXError("row_order is empty list") 
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81 if len(row_order) != len(set(row_order)): 
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82 msg = "Ambiguous ordering: `row_order` contained duplicates." 
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83 raise nx.NetworkXError(msg) 
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84 if column_order is None: 
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85 column_order = list(set(G)  set(row_order)) 
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86 mlen = len(column_order) 
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87 if len(column_order) != len(set(column_order)): 
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88 msg = "Ambiguous ordering: `column_order` contained duplicates." 
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89 raise nx.NetworkXError(msg) 
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90 
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91 row_index = dict(zip(row_order, itertools.count())) 
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92 col_index = dict(zip(column_order, itertools.count())) 
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93 
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94 if G.number_of_edges() == 0: 
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95 row, col, data = [], [], [] 
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96 else: 
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97 row, col, data = zip( 
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98 *( 
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99 (row_index[u], col_index[v], d.get(weight, 1)) 
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100 for u, v, d in G.edges(row_order, data=True) 
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101 if u in row_index and v in col_index 
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102 ) 
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103 ) 
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104 M = sparse.coo_matrix((data, (row, col)), shape=(nlen, mlen), dtype=dtype) 
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105 try: 
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106 return M.asformat(format) 
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107 # From Scipy 1.1.0, asformat will throw a ValueError instead of an 
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108 # AttributeError if the format if not recognized. 
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109 except (AttributeError, ValueError) as e: 
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110 raise nx.NetworkXError(f"Unknown sparse matrix format: {format}") from e 
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111 
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112 
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113 def from_biadjacency_matrix(A, create_using=None, edge_attribute="weight"): 
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114 r"""Creates a new bipartite graph from a biadjacency matrix given as a 
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115 SciPy sparse matrix. 
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116 
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117 Parameters 
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118  
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119 A: scipy sparse matrix 
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120 A biadjacency matrix representation of a graph 
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121 
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122 create_using: NetworkX graph 
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123 Use specified graph for result. The default is Graph() 
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124 
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125 edge_attribute: string 
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126 Name of edge attribute to store matrix numeric value. The data will 
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127 have the same type as the matrix entry (int, float, (real,imag)). 
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128 
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129 Notes 
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130  
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131 The nodes are labeled with the attribute `bipartite` set to an integer 
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132 0 or 1 representing membership in part 0 or part 1 of the bipartite graph. 
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133 
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134 If `create_using` is an instance of :class:`networkx.MultiGraph` or 
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135 :class:`networkx.MultiDiGraph` and the entries of `A` are of 
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136 type :class:`int`, then this function returns a multigraph (of the same 
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137 type as `create_using`) with parallel edges. In this case, `edge_attribute` 
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138 will be ignored. 
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139 
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140 See Also 
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141  
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142 biadjacency_matrix 
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143 from_numpy_array 
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144 
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145 References 
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146  
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147 [1] https://en.wikipedia.org/wiki/Adjacency_matrix#Adjacency_matrix_of_a_bipartite_graph 
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148 """ 
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149 G = nx.empty_graph(0, create_using) 
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150 n, m = A.shape 
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151 # Make sure we get even the isolated nodes of the graph. 
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152 G.add_nodes_from(range(n), bipartite=0) 
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153 G.add_nodes_from(range(n, n + m), bipartite=1) 
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154 # Create an iterable over (u, v, w) triples and for each triple, add an 
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155 # edge from u to v with weight w. 
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156 triples = ((u, n + v, d) for (u, v, d) in _generate_weighted_edges(A)) 
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157 # If the entries in the adjacency matrix are integers and the graph is a 
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158 # multigraph, then create parallel edges, each with weight 1, for each 
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159 # entry in the adjacency matrix. Otherwise, create one edge for each 
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160 # positive entry in the adjacency matrix and set the weight of that edge to 
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161 # be the entry in the matrix. 
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162 if A.dtype.kind in ("i", "u") and G.is_multigraph(): 
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163 chain = itertools.chain.from_iterable 
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164 triples = chain(((u, v, 1) for d in range(w)) for (u, v, w) in triples) 
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165 G.add_weighted_edges_from(triples, weight=edge_attribute) 
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166 return G 