Mercurial > repos > shellac > guppy_basecaller

annotate env/lib/python3.7/site-packages/networkx/linalg/attrmatrix.py @ 2:6af9afd405e9 draft

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"planemo upload commit 0a63dd5f4d38a1f6944587f52a8cd79874177fc1"
author shellac
date Thu, 14 May 2020 14:56:58 -0400
parents 26e78fe6e8c4
children
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1 """
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2 Functions for constructing matrix-like objects from graph attributes.
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3 """
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4
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5 __all__ = ['attr_matrix', 'attr_sparse_matrix']
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6
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7 import networkx as nx
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8
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9
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10 def _node_value(G, node_attr):
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11 """Returns a function that returns a value from G.nodes[u].
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12
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13 We return a function expecting a node as its sole argument. Then, in the
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14 simplest scenario, the returned function will return G.nodes[u][node_attr].
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15 However, we also handle the case when `node_attr` is None or when it is a
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16 function itself.
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17
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18 Parameters
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19 ----------
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20 G : graph
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21 A NetworkX graph
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22
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23 node_attr : {None, str, callable}
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24 Specification of how the value of the node attribute should be obtained
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25 from the node attribute dictionary.
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26
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27 Returns
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28 -------
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29 value : function
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30 A function expecting a node as its sole argument. The function will
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31 returns a value from G.nodes[u] that depends on `edge_attr`.
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32
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33 """
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34 if node_attr is None:
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35 def value(u): return u
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36 elif not hasattr(node_attr, '__call__'):
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37 # assume it is a key for the node attribute dictionary
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38 def value(u): return G.nodes[u][node_attr]
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39 else:
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40 # Advanced: Allow users to specify something else.
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41 #
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42 # For example,
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43 # node_attr = lambda u: G.nodes[u].get('size', .5) * 3
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44 #
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45 value = node_attr
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46
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47 return value
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48
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49
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50 def _edge_value(G, edge_attr):
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51 """Returns a function that returns a value from G[u][v].
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52
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53 Suppose there exists an edge between u and v. Then we return a function
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54 expecting u and v as arguments. For Graph and DiGraph, G[u][v] is
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55 the edge attribute dictionary, and the function (essentially) returns
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56 G[u][v][edge_attr]. However, we also handle cases when `edge_attr` is None
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57 and when it is a function itself. For MultiGraph and MultiDiGraph, G[u][v]
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58 is a dictionary of all edges between u and v. In this case, the returned
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59 function sums the value of `edge_attr` for every edge between u and v.
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60
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61 Parameters
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62 ----------
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63 G : graph
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64 A NetworkX graph
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65
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66 edge_attr : {None, str, callable}
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67 Specification of how the value of the edge attribute should be obtained
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68 from the edge attribute dictionary, G[u][v]. For multigraphs, G[u][v]
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69 is a dictionary of all the edges between u and v. This allows for
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70 special treatment of multiedges.
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71
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72 Returns
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73 -------
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74 value : function
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75 A function expecting two nodes as parameters. The nodes should
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76 represent the from- and to- node of an edge. The function will
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77 return a value from G[u][v] that depends on `edge_attr`.
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78
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79 """
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80
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81 if edge_attr is None:
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82 # topological count of edges
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83
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84 if G.is_multigraph():
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85 def value(u, v): return len(G[u][v])
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86 else:
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87 def value(u, v): return 1
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88
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89 elif not hasattr(edge_attr, '__call__'):
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90 # assume it is a key for the edge attribute dictionary
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91
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92 if edge_attr == 'weight':
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93 # provide a default value
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94 if G.is_multigraph():
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95 def value(u, v): return sum([d.get(edge_attr, 1) for d in G[u][v].values()])
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96 else:
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97 def value(u, v): return G[u][v].get(edge_attr, 1)
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98 else:
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99 # otherwise, the edge attribute MUST exist for each edge
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100 if G.is_multigraph():
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101 def value(u, v): return sum([d[edge_attr] for d in G[u][v].values()])
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102 else:
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103 def value(u, v): return G[u][v][edge_attr]
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104
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105 else:
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106 # Advanced: Allow users to specify something else.
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107 #
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108 # Alternative default value:
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109 # edge_attr = lambda u,v: G[u][v].get('thickness', .5)
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110 #
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111 # Function on an attribute:
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112 # edge_attr = lambda u,v: abs(G[u][v]['weight'])
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113 #
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114 # Handle Multi(Di)Graphs differently:
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115 # edge_attr = lambda u,v: numpy.prod([d['size'] for d in G[u][v].values()])
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116 #
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117 # Ignore multiple edges
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118 # edge_attr = lambda u,v: 1 if len(G[u][v]) else 0
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119 #
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120 value = edge_attr
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121
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122 return value
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123
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124
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125 def attr_matrix(G, edge_attr=None, node_attr=None, normalized=False,
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126 rc_order=None, dtype=None, order=None):
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127 """Returns a NumPy matrix using attributes from G.
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128
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129 If only `G` is passed in, then the adjacency matrix is constructed.
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130
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131 Let A be a discrete set of values for the node attribute `node_attr`. Then
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132 the elements of A represent the rows and columns of the constructed matrix.
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133 Now, iterate through every edge e=(u,v) in `G` and consider the value
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134 of the edge attribute `edge_attr`. If ua and va are the values of the
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135 node attribute `node_attr` for u and v, respectively, then the value of
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136 the edge attribute is added to the matrix element at (ua, va).
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137
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138 Parameters
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139 ----------
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140 G : graph
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141 The NetworkX graph used to construct the NumPy matrix.
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142
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143 edge_attr : str, optional
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144 Each element of the matrix represents a running total of the
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145 specified edge attribute for edges whose node attributes correspond
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146 to the rows/cols of the matirx. The attribute must be present for
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147 all edges in the graph. If no attribute is specified, then we
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148 just count the number of edges whose node attributes correspond
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149 to the matrix element.
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150
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151 node_attr : str, optional
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152 Each row and column in the matrix represents a particular value
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153 of the node attribute. The attribute must be present for all nodes
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154 in the graph. Note, the values of this attribute should be reliably
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155 hashable. So, float values are not recommended. If no attribute is
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156 specified, then the rows and columns will be the nodes of the graph.
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157
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158 normalized : bool, optional
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159 If True, then each row is normalized by the summation of its values.
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160
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161 rc_order : list, optional
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162 A list of the node attribute values. This list specifies the ordering
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163 of rows and columns of the array. If no ordering is provided, then
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164 the ordering will be random (and also, a return value).
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165
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166 Other Parameters
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167 ----------------
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168 dtype : NumPy data-type, optional
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169 A valid NumPy dtype used to initialize the array. Keep in mind certain
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170 dtypes can yield unexpected results if the array is to be normalized.
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171 The parameter is passed to numpy.zeros(). If unspecified, the NumPy
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172 default is used.
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173
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174 order : {'C', 'F'}, optional
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175 Whether to store multidimensional data in C- or Fortran-contiguous
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176 (row- or column-wise) order in memory. This parameter is passed to
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177 numpy.zeros(). If unspecified, the NumPy default is used.
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178
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179 Returns
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180 -------
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181 M : NumPy matrix
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182 The attribute matrix.
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183
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184 ordering : list
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185 If `rc_order` was specified, then only the matrix is returned.
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186 However, if `rc_order` was None, then the ordering used to construct
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187 the matrix is returned as well.
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188
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189 Examples
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190 --------
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191 Construct an adjacency matrix:
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192
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193 >>> G = nx.Graph()
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194 >>> G.add_edge(0, 1, thickness=1, weight=3)
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195 >>> G.add_edge(0, 2, thickness=2)
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196 >>> G.add_edge(1, 2, thickness=3)
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197 >>> nx.attr_matrix(G, rc_order=[0, 1, 2])
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198 matrix([[0., 1., 1.],
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199 [1., 0., 1.],
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200 [1., 1., 0.]])
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201
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202 Alternatively, we can obtain the matrix describing edge thickness.
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203
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204 >>> nx.attr_matrix(G, edge_attr='thickness', rc_order=[0, 1, 2])
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205 matrix([[0., 1., 2.],
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206 [1., 0., 3.],
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207 [2., 3., 0.]])
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208
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209 We can also color the nodes and ask for the probability distribution over
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210 all edges (u,v) describing:
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211
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212 Pr(v has color Y | u has color X)
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213
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214 >>> G.nodes[0]['color'] = 'red'
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215 >>> G.nodes[1]['color'] = 'red'
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216 >>> G.nodes[2]['color'] = 'blue'
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217 >>> rc = ['red', 'blue']
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218 >>> nx.attr_matrix(G, node_attr='color', normalized=True, rc_order=rc)
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219 matrix([[0.33333333, 0.66666667],
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220 [1. , 0. ]])
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221
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222 For example, the above tells us that for all edges (u,v):
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223
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224 Pr( v is red | u is red) = 1/3
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225 Pr( v is blue | u is red) = 2/3
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226
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227 Pr( v is red | u is blue) = 1
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228 Pr( v is blue | u is blue) = 0
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229
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230 Finally, we can obtain the total weights listed by the node colors.
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231
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232 >>> nx.attr_matrix(G, edge_attr='weight', node_attr='color', rc_order=rc)
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233 matrix([[3., 2.],
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234 [2., 0.]])
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235
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236 Thus, the total weight over all edges (u,v) with u and v having colors:
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237
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238 (red, red) is 3 # the sole contribution is from edge (0,1)
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239 (red, blue) is 2 # contributions from edges (0,2) and (1,2)
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240 (blue, red) is 2 # same as (red, blue) since graph is undirected
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241 (blue, blue) is 0 # there are no edges with blue endpoints
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242
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243 """
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244 try:
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245 import numpy as np
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246 except ImportError:
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247 raise ImportError(
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248 "attr_matrix() requires numpy: http://scipy.org/ ")
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249
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250 edge_value = _edge_value(G, edge_attr)
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251 node_value = _node_value(G, node_attr)
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252
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253 if rc_order is None:
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254 ordering = list(set([node_value(n) for n in G]))
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255 else:
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256 ordering = rc_order
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257
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258 N = len(ordering)
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259 undirected = not G.is_directed()
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260 index = dict(zip(ordering, range(N)))
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261 M = np.zeros((N, N), dtype=dtype, order=order)
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262
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263 seen = set([])
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264 for u, nbrdict in G.adjacency():
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265 for v in nbrdict:
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266 # Obtain the node attribute values.
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267 i, j = index[node_value(u)], index[node_value(v)]
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268 if v not in seen:
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269 M[i, j] += edge_value(u, v)
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270 if undirected:
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271 M[j, i] = M[i, j]
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272
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273 if undirected:
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274 seen.add(u)
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275
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276 if normalized:
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277 M /= M.sum(axis=1).reshape((N, 1))
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278
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279 M = np.asmatrix(M)
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280
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281 if rc_order is None:
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282 return M, ordering
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283 else:
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284 return M
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285
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286
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287 def attr_sparse_matrix(G, edge_attr=None, node_attr=None,
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288 normalized=False, rc_order=None, dtype=None):
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289 """Returns a SciPy sparse matrix using attributes from G.
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290
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291 If only `G` is passed in, then the adjacency matrix is constructed.
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292
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293 Let A be a discrete set of values for the node attribute `node_attr`. Then
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294 the elements of A represent the rows and columns of the constructed matrix.
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295 Now, iterate through every edge e=(u,v) in `G` and consider the value
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296 of the edge attribute `edge_attr`. If ua and va are the values of the
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297 node attribute `node_attr` for u and v, respectively, then the value of
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298 the edge attribute is added to the matrix element at (ua, va).
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299
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300 Parameters
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301 ----------
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302 G : graph
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303 The NetworkX graph used to construct the NumPy matrix.
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304
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305 edge_attr : str, optional
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306 Each element of the matrix represents a running total of the
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307 specified edge attribute for edges whose node attributes correspond
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308 to the rows/cols of the matirx. The attribute must be present for
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309 all edges in the graph. If no attribute is specified, then we
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310 just count the number of edges whose node attributes correspond
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311 to the matrix element.
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312
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313 node_attr : str, optional
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314 Each row and column in the matrix represents a particular value
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315 of the node attribute. The attribute must be present for all nodes
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316 in the graph. Note, the values of this attribute should be reliably
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317 hashable. So, float values are not recommended. If no attribute is
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318 specified, then the rows and columns will be the nodes of the graph.
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319
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320 normalized : bool, optional
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321 If True, then each row is normalized by the summation of its values.
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322
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323 rc_order : list, optional
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324 A list of the node attribute values. This list specifies the ordering
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325 of rows and columns of the array. If no ordering is provided, then
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326 the ordering will be random (and also, a return value).
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327
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328 Other Parameters
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329 ----------------
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330 dtype : NumPy data-type, optional
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331 A valid NumPy dtype used to initialize the array. Keep in mind certain
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332 dtypes can yield unexpected results if the array is to be normalized.
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333 The parameter is passed to numpy.zeros(). If unspecified, the NumPy
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334 default is used.
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335
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336 Returns
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337 -------
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338 M : SciPy sparse matrix
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339 The attribute matrix.
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340
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341 ordering : list
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342 If `rc_order` was specified, then only the matrix is returned.
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343 However, if `rc_order` was None, then the ordering used to construct
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344 the matrix is returned as well.
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345
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346 Examples
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347 --------
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348 Construct an adjacency matrix:
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349
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350 >>> G = nx.Graph()
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351 >>> G.add_edge(0,1,thickness=1,weight=3)
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352 >>> G.add_edge(0,2,thickness=2)
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353 >>> G.add_edge(1,2,thickness=3)
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354 >>> M = nx.attr_sparse_matrix(G, rc_order=[0,1,2])
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355 >>> M.todense()
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356 matrix([[0., 1., 1.],
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357 [1., 0., 1.],
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358 [1., 1., 0.]])
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359
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360 Alternatively, we can obtain the matrix describing edge thickness.
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361
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362 >>> M = nx.attr_sparse_matrix(G, edge_attr='thickness', rc_order=[0,1,2])
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363 >>> M.todense()
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364 matrix([[0., 1., 2.],
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365 [1., 0., 3.],
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366 [2., 3., 0.]])
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367
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368 We can also color the nodes and ask for the probability distribution over
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369 all edges (u,v) describing:
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370
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371 Pr(v has color Y | u has color X)
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372
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373 >>> G.nodes[0]['color'] = 'red'
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374 >>> G.nodes[1]['color'] = 'red'
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375 >>> G.nodes[2]['color'] = 'blue'
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376 >>> rc = ['red', 'blue']
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377 >>> M = nx.attr_sparse_matrix(G, node_attr='color', \
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378 normalized=True, rc_order=rc)
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379 >>> M.todense()
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380 matrix([[0.33333333, 0.66666667],
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381 [1. , 0. ]])
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382
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383 For example, the above tells us that for all edges (u,v):
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384
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385 Pr( v is red | u is red) = 1/3
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386 Pr( v is blue | u is red) = 2/3
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387
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388 Pr( v is red | u is blue) = 1
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389 Pr( v is blue | u is blue) = 0
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390
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391 Finally, we can obtain the total weights listed by the node colors.
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392
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393 >>> M = nx.attr_sparse_matrix(G, edge_attr='weight',\
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394 node_attr='color', rc_order=rc)
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395 >>> M.todense()
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396 matrix([[3., 2.],
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397 [2., 0.]])
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398
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399 Thus, the total weight over all edges (u,v) with u and v having colors:
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400
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401 (red, red) is 3 # the sole contribution is from edge (0,1)
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402 (red, blue) is 2 # contributions from edges (0,2) and (1,2)
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403 (blue, red) is 2 # same as (red, blue) since graph is undirected
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404 (blue, blue) is 0 # there are no edges with blue endpoints
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405
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406 """
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407 try:
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408 import numpy as np
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409 from scipy import sparse
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410 except ImportError:
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411 raise ImportError(
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412 "attr_sparse_matrix() requires scipy: http://scipy.org/ ")
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413
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414 edge_value = _edge_value(G, edge_attr)
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415 node_value = _node_value(G, node_attr)
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416
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417 if rc_order is None:
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418 ordering = list(set([node_value(n) for n in G]))
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419 else:
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420 ordering = rc_order
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421
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422 N = len(ordering)
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423 undirected = not G.is_directed()
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424 index = dict(zip(ordering, range(N)))
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425 M = sparse.lil_matrix((N, N), dtype=dtype)
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426
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427 seen = set([])
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428 for u, nbrdict in G.adjacency():
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429 for v in nbrdict:
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430 # Obtain the node attribute values.
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431 i, j = index[node_value(u)], index[node_value(v)]
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432 if v not in seen:
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433 M[i, j] += edge_value(u, v)
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434 if undirected:
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435 M[j, i] = M[i, j]
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436
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437 if undirected:
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438 seen.add(u)
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439
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440 if normalized:
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441 norms = np.asarray(M.sum(axis=1)).ravel()
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442 for i, norm in enumerate(norms):
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443 M[i, :] /= norm
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444
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445 if rc_order is None:
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446 return M, ordering
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447 else:
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448 return M
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449
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450
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451 # fixture for pytest
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452 def setup_module(module):
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453 import pytest
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454 numpy = pytest.importorskip('numpy')
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455 scipy = pytest.importorskip('scipy')