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annotate env/lib/python3.7/site-packages/networkx/linalg/spectrum.py @ 0:26e78fe6e8c4 draft

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"planemo upload commit c699937486c35866861690329de38ec1a5d9f783"
author shellac
date Sat, 02 May 2020 07:14:21 -0400
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1 """
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2 Eigenvalue spectrum of graphs.
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3 """
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4 # Copyright (C) 2004-2019 by
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5 # Aric Hagberg <hagberg@lanl.gov>
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6 # Dan Schult <dschult@colgate.edu>
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7 # Pieter Swart <swart@lanl.gov>
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8 # All rights reserved.
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9 # BSD license.
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10 import networkx as nx
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11 __author__ = "\n".join(['Aric Hagberg <aric.hagberg@gmail.com>',
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12 'Pieter Swart (swart@lanl.gov)',
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13 'Dan Schult(dschult@colgate.edu)',
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14 'Jean-Gabriel Young (jean.gabriel.young@gmail.com)'])
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15
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16 __all__ = ['laplacian_spectrum', 'adjacency_spectrum', 'modularity_spectrum',
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17 'normalized_laplacian_spectrum', 'bethe_hessian_spectrum']
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18
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19
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20 def laplacian_spectrum(G, weight='weight'):
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21 """Returns eigenvalues of the Laplacian of G
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22
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23 Parameters
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24 ----------
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25 G : graph
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26 A NetworkX graph
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27
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28 weight : string or None, optional (default='weight')
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29 The edge data key used to compute each value in the matrix.
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30 If None, then each edge has weight 1.
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31
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32 Returns
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33 -------
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34 evals : NumPy array
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35 Eigenvalues
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36
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37 Notes
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38 -----
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39 For MultiGraph/MultiDiGraph, the edges weights are summed.
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40 See to_numpy_matrix for other options.
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41
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42 See Also
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43 --------
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44 laplacian_matrix
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45 """
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46 from scipy.linalg import eigvalsh
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47 return eigvalsh(nx.laplacian_matrix(G, weight=weight).todense())
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48
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49
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50 def normalized_laplacian_spectrum(G, weight='weight'):
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51 """Return eigenvalues of the normalized Laplacian of G
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52
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53 Parameters
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54 ----------
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55 G : graph
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56 A NetworkX graph
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57
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58 weight : string or None, optional (default='weight')
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59 The edge data key used to compute each value in the matrix.
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60 If None, then each edge has weight 1.
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61
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62 Returns
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63 -------
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64 evals : NumPy array
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65 Eigenvalues
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66
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67 Notes
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68 -----
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69 For MultiGraph/MultiDiGraph, the edges weights are summed.
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70 See to_numpy_matrix for other options.
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71
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72 See Also
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73 --------
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74 normalized_laplacian_matrix
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75 """
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76 from scipy.linalg import eigvalsh
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77 return eigvalsh(nx.normalized_laplacian_matrix(G, weight=weight).todense())
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78
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79
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80 def adjacency_spectrum(G, weight='weight'):
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81 """Returns eigenvalues of the adjacency matrix of G.
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82
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83 Parameters
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84 ----------
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85 G : graph
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86 A NetworkX graph
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87
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88 weight : string or None, optional (default='weight')
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89 The edge data key used to compute each value in the matrix.
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90 If None, then each edge has weight 1.
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91
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92 Returns
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93 -------
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94 evals : NumPy array
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95 Eigenvalues
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96
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97 Notes
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98 -----
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99 For MultiGraph/MultiDiGraph, the edges weights are summed.
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100 See to_numpy_matrix for other options.
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101
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102 See Also
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103 --------
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104 adjacency_matrix
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105 """
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106 from scipy.linalg import eigvals
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107 return eigvals(nx.adjacency_matrix(G, weight=weight).todense())
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108
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109
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110 def modularity_spectrum(G):
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111 """Returns eigenvalues of the modularity matrix of G.
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112
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113 Parameters
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114 ----------
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115 G : Graph
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116 A NetworkX Graph or DiGraph
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117
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118 Returns
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119 -------
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120 evals : NumPy array
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121 Eigenvalues
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122
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123 See Also
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124 --------
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125 modularity_matrix
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126
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127 References
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128 ----------
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129 .. [1] M. E. J. Newman, "Modularity and community structure in networks",
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130 Proc. Natl. Acad. Sci. USA, vol. 103, pp. 8577-8582, 2006.
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131 """
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132 from scipy.linalg import eigvals
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133 if G.is_directed():
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134 return eigvals(nx.directed_modularity_matrix(G))
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135 else:
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136 return eigvals(nx.modularity_matrix(G))
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137
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138
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139 def bethe_hessian_spectrum(G, r=None):
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140 """Returns eigenvalues of the Bethe Hessian matrix of G.
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141
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142 Parameters
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143 ----------
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144 G : Graph
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145 A NetworkX Graph or DiGraph
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146
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147 r : float
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148 Regularizer parameter
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149
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150 Returns
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151 -------
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152 evals : NumPy array
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153 Eigenvalues
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154
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155 See Also
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156 --------
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157 bethe_hessian_matrix
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158
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159 References
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160 ----------
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161 .. [1] A. Saade, F. Krzakala and L. Zdeborová
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162 "Spectral clustering of graphs with the bethe hessian",
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163 Advances in Neural Information Processing Systems. 2014.
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164 """
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165 from scipy.linalg import eigvalsh
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166 return eigvalsh(nx.bethe_hessian_matrix(G, r).todense())
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167
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168
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169 # fixture for pytest
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170 def setup_module(module):
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171 import pytest
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172 scipy.linalg = pytest.importorskip('scipy.linalg')