Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/sitepackages/networkx/drawing/layout.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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0
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1 """ 
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2 ****** 
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3 Layout 
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4 ****** 
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5 
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6 Node positioning algorithms for graph drawing. 
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7 
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8 For `random_layout()` the possible resulting shape 
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9 is a square of side [0, scale] (default: [0, 1]) 
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10 Changing `center` shifts the layout by that amount. 
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11 
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12 For the other layout routines, the extent is 
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13 [center  scale, center + scale] (default: [1, 1]). 
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14 
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15 Warning: Most layout routines have only been tested in 2dimensions. 
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16 
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17 """ 
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18 import networkx as nx 
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19 from networkx.utils import random_state 
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20 
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21 __all__ = [ 
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22 "bipartite_layout", 
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23 "circular_layout", 
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24 "kamada_kawai_layout", 
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25 "random_layout", 
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26 "rescale_layout", 
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27 "rescale_layout_dict", 
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28 "shell_layout", 
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29 "spring_layout", 
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30 "spectral_layout", 
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31 "planar_layout", 
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32 "fruchterman_reingold_layout", 
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33 "spiral_layout", 
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34 "multipartite_layout", 
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35 ] 
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36 
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37 
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38 def _process_params(G, center, dim): 
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39 # Some boilerplate code. 
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40 import numpy as np 
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41 
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42 if not isinstance(G, nx.Graph): 
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43 empty_graph = nx.Graph() 
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44 empty_graph.add_nodes_from(G) 
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45 G = empty_graph 
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46 
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47 if center is None: 
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48 center = np.zeros(dim) 
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49 else: 
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50 center = np.asarray(center) 
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51 
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52 if len(center) != dim: 
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53 msg = "length of center coordinates must match dimension of layout" 
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54 raise ValueError(msg) 
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55 
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56 return G, center 
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57 
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58 
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59 @random_state(3) 
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60 def random_layout(G, center=None, dim=2, seed=None): 
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61 """Position nodes uniformly at random in the unit square. 
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62 
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63 For every node, a position is generated by choosing each of dim 
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64 coordinates uniformly at random on the interval [0.0, 1.0). 
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65 
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66 NumPy (http://scipy.org) is required for this function. 
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67 
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68 Parameters 
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69  
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70 G : NetworkX graph or list of nodes 
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71 A position will be assigned to every node in G. 
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72 
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73 center : arraylike or None 
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74 Coordinate pair around which to center the layout. 
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75 
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76 dim : int 
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77 Dimension of layout. 
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78 
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79 seed : int, RandomState instance or None optional (default=None) 
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80 Set the random state for deterministic node layouts. 
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81 If int, `seed` is the seed used by the random number generator, 
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82 if numpy.random.RandomState instance, `seed` is the random 
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83 number generator, 
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84 if None, the random number generator is the RandomState instance used 
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85 by numpy.random. 
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86 
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87 Returns 
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88  
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89 pos : dict 
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90 A dictionary of positions keyed by node 
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91 
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92 Examples 
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93  
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94 >>> G = nx.lollipop_graph(4, 3) 
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95 >>> pos = nx.random_layout(G) 
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96 
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97 """ 
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98 import numpy as np 
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99 
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100 G, center = _process_params(G, center, dim) 
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101 pos = seed.rand(len(G), dim) + center 
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102 pos = pos.astype(np.float32) 
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103 pos = dict(zip(G, pos)) 
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104 
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105 return pos 
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106 
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107 
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108 def circular_layout(G, scale=1, center=None, dim=2): 
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109 # dim=2 only 
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110 """Position nodes on a circle. 
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111 
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112 Parameters 
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113  
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114 G : NetworkX graph or list of nodes 
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115 A position will be assigned to every node in G. 
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116 
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117 scale : number (default: 1) 
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118 Scale factor for positions. 
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119 
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120 center : arraylike or None 
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121 Coordinate pair around which to center the layout. 
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122 
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123 dim : int 
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124 Dimension of layout. 
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125 If dim>2, the remaining dimensions are set to zero 
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126 in the returned positions. 
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127 If dim<2, a ValueError is raised. 
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128 
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129 Returns 
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130  
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131 pos : dict 
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132 A dictionary of positions keyed by node 
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133 
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134 Raises 
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135  
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136 ValueError 
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137 If dim < 2 
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138 
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139 Examples 
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140  
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141 >>> G = nx.path_graph(4) 
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142 >>> pos = nx.circular_layout(G) 
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143 
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144 Notes 
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145  
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146 This algorithm currently only works in two dimensions and does not 
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147 try to minimize edge crossings. 
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148 
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149 """ 
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150 import numpy as np 
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151 
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152 if dim < 2: 
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153 raise ValueError("cannot handle dimensions < 2") 
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154 
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155 G, center = _process_params(G, center, dim) 
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156 
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157 paddims = max(0, (dim  2)) 
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158 
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159 if len(G) == 0: 
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160 pos = {} 
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161 elif len(G) == 1: 
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162 pos = {nx.utils.arbitrary_element(G): center} 
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163 else: 
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164 # Discard the extra angle since it matches 0 radians. 
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165 theta = np.linspace(0, 1, len(G) + 1)[:1] * 2 * np.pi 
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166 theta = theta.astype(np.float32) 
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167 pos = np.column_stack( 
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168 [np.cos(theta), np.sin(theta), np.zeros((len(G), paddims))] 
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169 ) 
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170 pos = rescale_layout(pos, scale=scale) + center 
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171 pos = dict(zip(G, pos)) 
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172 
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173 return pos 
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174 
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175 
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176 def shell_layout(G, nlist=None, rotate=None, scale=1, center=None, dim=2): 
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177 """Position nodes in concentric circles. 
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178 
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179 Parameters 
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180  
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181 G : NetworkX graph or list of nodes 
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182 A position will be assigned to every node in G. 
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183 
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184 nlist : list of lists 
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185 List of node lists for each shell. 
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186 
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187 rotate : angle in radians (default=pi/len(nlist)) 
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188 Angle by which to rotate the starting position of each shell 
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189 relative to the starting position of the previous shell. 
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190 To recreate behavior before v2.5 use rotate=0. 
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191 
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192 scale : number (default: 1) 
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193 Scale factor for positions. 
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194 
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195 center : arraylike or None 
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196 Coordinate pair around which to center the layout. 
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197 
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198 dim : int 
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199 Dimension of layout, currently only dim=2 is supported. 
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200 Other dimension values result in a ValueError. 
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201 
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202 Returns 
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203  
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204 pos : dict 
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205 A dictionary of positions keyed by node 
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206 
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207 Raises 
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208  
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209 ValueError 
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210 If dim != 2 
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211 
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212 Examples 
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213  
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214 >>> G = nx.path_graph(4) 
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215 >>> shells = [[0], [1, 2, 3]] 
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216 >>> pos = nx.shell_layout(G, shells) 
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217 
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218 Notes 
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219  
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220 This algorithm currently only works in two dimensions and does not 
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221 try to minimize edge crossings. 
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222 
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223 """ 
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224 import numpy as np 
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225 
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226 if dim != 2: 
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227 raise ValueError("can only handle 2 dimensions") 
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228 
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229 G, center = _process_params(G, center, dim) 
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230 
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231 if len(G) == 0: 
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232 return {} 
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233 if len(G) == 1: 
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234 return {nx.utils.arbitrary_element(G): center} 
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235 
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236 if nlist is None: 
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237 # draw the whole graph in one shell 
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238 nlist = [list(G)] 
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239 
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240 radius_bump = scale / len(nlist) 
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241 
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242 if len(nlist[0]) == 1: 
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243 # single node at center 
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244 radius = 0.0 
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245 else: 
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246 # else start at r=1 
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247 radius = radius_bump 
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248 
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249 if rotate is None: 
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250 rotate = np.pi / len(nlist) 
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251 first_theta = rotate 
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252 npos = {} 
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253 for nodes in nlist: 
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254 # Discard the last angle (endpoint=False) since 2*pi matches 0 radians 
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255 theta = ( 
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256 np.linspace(0, 2 * np.pi, len(nodes), endpoint=False, dtype=np.float32) 
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257 + first_theta 
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258 ) 
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259 pos = radius * np.column_stack([np.cos(theta), np.sin(theta)]) + center 
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260 npos.update(zip(nodes, pos)) 
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261 radius += radius_bump 
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262 first_theta += rotate 
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263 
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264 return npos 
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265 
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266 
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267 def bipartite_layout( 
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268 G, nodes, align="vertical", scale=1, center=None, aspect_ratio=4 / 3 
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269 ): 
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270 """Position nodes in two straight lines. 
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271 
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272 Parameters 
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273  
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274 G : NetworkX graph or list of nodes 
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275 A position will be assigned to every node in G. 
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276 
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277 nodes : list or container 
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278 Nodes in one node set of the bipartite graph. 
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279 This set will be placed on left or top. 
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280 
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281 align : string (default='vertical') 
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282 The alignment of nodes. Vertical or horizontal. 
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283 
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284 scale : number (default: 1) 
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285 Scale factor for positions. 
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286 
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287 center : arraylike or None 
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288 Coordinate pair around which to center the layout. 
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289 
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290 aspect_ratio : number (default=4/3): 
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291 The ratio of the width to the height of the layout. 
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292 
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293 Returns 
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294  
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295 pos : dict 
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296 A dictionary of positions keyed by node. 
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297 
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298 Examples 
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299  
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300 >>> G = nx.bipartite.gnmk_random_graph(3, 5, 10, seed=123) 
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301 >>> top = nx.bipartite.sets(G)[0] 
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302 >>> pos = nx.bipartite_layout(G, top) 
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303 
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304 Notes 
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305  
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306 This algorithm currently only works in two dimensions and does not 
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307 try to minimize edge crossings. 
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308 
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309 """ 
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310 
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311 import numpy as np 
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312 
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313 G, center = _process_params(G, center=center, dim=2) 
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314 if len(G) == 0: 
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315 return {} 
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316 
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317 height = 1 
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318 width = aspect_ratio * height 
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319 offset = (width / 2, height / 2) 
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320 
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321 top = set(nodes) 
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322 bottom = set(G)  top 
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323 nodes = list(top) + list(bottom) 
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324 
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325 if align == "vertical": 
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326 left_xs = np.repeat(0, len(top)) 
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327 right_xs = np.repeat(width, len(bottom)) 
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328 left_ys = np.linspace(0, height, len(top)) 
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329 right_ys = np.linspace(0, height, len(bottom)) 
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330 
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331 top_pos = np.column_stack([left_xs, left_ys])  offset 
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332 bottom_pos = np.column_stack([right_xs, right_ys])  offset 
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333 
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334 pos = np.concatenate([top_pos, bottom_pos]) 
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335 pos = rescale_layout(pos, scale=scale) + center 
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336 pos = dict(zip(nodes, pos)) 
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337 return pos 
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338 
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339 if align == "horizontal": 
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340 top_ys = np.repeat(height, len(top)) 
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341 bottom_ys = np.repeat(0, len(bottom)) 
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342 top_xs = np.linspace(0, width, len(top)) 
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343 bottom_xs = np.linspace(0, width, len(bottom)) 
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344 
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345 top_pos = np.column_stack([top_xs, top_ys])  offset 
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346 bottom_pos = np.column_stack([bottom_xs, bottom_ys])  offset 
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347 
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348 pos = np.concatenate([top_pos, bottom_pos]) 
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349 pos = rescale_layout(pos, scale=scale) + center 
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350 pos = dict(zip(nodes, pos)) 
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351 return pos 
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352 
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353 msg = "align must be either vertical or horizontal." 
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354 raise ValueError(msg) 
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355 
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356 
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357 @random_state(10) 
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358 def fruchterman_reingold_layout( 
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359 G, 
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360 k=None, 
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361 pos=None, 
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362 fixed=None, 
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363 iterations=50, 
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364 threshold=1e4, 
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365 weight="weight", 
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366 scale=1, 
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367 center=None, 
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368 dim=2, 
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369 seed=None, 
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370 ): 
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371 """Position nodes using FruchtermanReingold forcedirected algorithm. 
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372 
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373 The algorithm simulates a forcedirected representation of the network 
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374 treating edges as springs holding nodes close, while treating nodes 
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375 as repelling objects, sometimes called an antigravity force. 
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376 Simulation continues until the positions are close to an equilibrium. 
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377 
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378 There are some hardcoded values: minimal distance between 
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379 nodes (0.01) and "temperature" of 0.1 to ensure nodes don't fly away. 
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380 During the simulation, `k` helps determine the distance between nodes, 
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381 though `scale` and `center` determine the size and place after 
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382 rescaling occurs at the end of the simulation. 
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383 
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384 Fixing some nodes doesn't allow them to move in the simulation. 
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385 It also turns off the rescaling feature at the simulation's end. 
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386 In addition, setting `scale` to `None` turns off rescaling. 
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387 
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388 Parameters 
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389  
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390 G : NetworkX graph or list of nodes 
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391 A position will be assigned to every node in G. 
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392 
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393 k : float (default=None) 
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394 Optimal distance between nodes. If None the distance is set to 
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395 1/sqrt(n) where n is the number of nodes. Increase this value 
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396 to move nodes farther apart. 
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397 
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398 pos : dict or None optional (default=None) 
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399 Initial positions for nodes as a dictionary with node as keys 
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400 and values as a coordinate list or tuple. If None, then use 
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401 random initial positions. 
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402 
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403 fixed : list or None optional (default=None) 
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404 Nodes to keep fixed at initial position. 
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405 ValueError raised if `fixed` specified and `pos` not. 
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406 
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407 iterations : int optional (default=50) 
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408 Maximum number of iterations taken 
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409 
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410 threshold: float optional (default = 1e4) 
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411 Threshold for relative error in node position changes. 
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412 The iteration stops if the error is below this threshold. 
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413 
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414 weight : string or None optional (default='weight') 
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415 The edge attribute that holds the numerical value used for 
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416 the edge weight. If None, then all edge weights are 1. 
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417 
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418 scale : number or None (default: 1) 
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419 Scale factor for positions. Not used unless `fixed is None`. 
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420 If scale is None, no rescaling is performed. 
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421 
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422 center : arraylike or None 
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423 Coordinate pair around which to center the layout. 
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424 Not used unless `fixed is None`. 
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425 
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426 dim : int 
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427 Dimension of layout. 
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428 
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429 seed : int, RandomState instance or None optional (default=None) 
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430 Set the random state for deterministic node layouts. 
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431 If int, `seed` is the seed used by the random number generator, 
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432 if numpy.random.RandomState instance, `seed` is the random 
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433 number generator, 
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434 if None, the random number generator is the RandomState instance used 
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435 by numpy.random. 
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436 
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437 Returns 
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438  
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439 pos : dict 
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440 A dictionary of positions keyed by node 
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441 
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442 Examples 
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443  
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444 >>> G = nx.path_graph(4) 
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445 >>> pos = nx.spring_layout(G) 
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446 
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447 # The same using longer but equivalent function name 
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448 >>> pos = nx.fruchterman_reingold_layout(G) 
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449 """ 
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450 import numpy as np 
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451 
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452 G, center = _process_params(G, center, dim) 
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453 
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454 if fixed is not None: 
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455 if pos is None: 
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456 raise ValueError("nodes are fixed without positions given") 
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457 for node in fixed: 
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458 if node not in pos: 
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459 raise ValueError("nodes are fixed without positions given") 
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460 nfixed = {node: i for i, node in enumerate(G)} 
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461 fixed = np.asarray([nfixed[node] for node in fixed]) 
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462 
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463 if pos is not None: 
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464 # Determine size of existing domain to adjust initial positions 
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465 dom_size = max(coord for pos_tup in pos.values() for coord in pos_tup) 
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466 if dom_size == 0: 
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467 dom_size = 1 
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468 pos_arr = seed.rand(len(G), dim) * dom_size + center 
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469 
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470 for i, n in enumerate(G): 
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471 if n in pos: 
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472 pos_arr[i] = np.asarray(pos[n]) 
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473 else: 
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474 pos_arr = None 
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475 dom_size = 1 
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476 
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477 if len(G) == 0: 
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478 return {} 
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479 if len(G) == 1: 
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480 return {nx.utils.arbitrary_element(G.nodes()): center} 
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481 
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482 try: 
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483 # Sparse matrix 
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484 if len(G) < 500: # sparse solver for large graphs 
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485 raise ValueError 
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486 A = nx.to_scipy_sparse_matrix(G, weight=weight, dtype="f") 
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487 if k is None and fixed is not None: 
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488 # We must adjust k by domain size for layouts not near 1x1 
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489 nnodes, _ = A.shape 
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490 k = dom_size / np.sqrt(nnodes) 
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491 pos = _sparse_fruchterman_reingold( 
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492 A, k, pos_arr, fixed, iterations, threshold, dim, seed 
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493 ) 
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494 except ValueError: 
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495 A = nx.to_numpy_array(G, weight=weight) 
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496 if k is None and fixed is not None: 
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497 # We must adjust k by domain size for layouts not near 1x1 
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498 nnodes, _ = A.shape 
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499 k = dom_size / np.sqrt(nnodes) 
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500 pos = _fruchterman_reingold( 
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501 A, k, pos_arr, fixed, iterations, threshold, dim, seed 
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502 ) 
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503 if fixed is None and scale is not None: 
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504 pos = rescale_layout(pos, scale=scale) + center 
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505 pos = dict(zip(G, pos)) 
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506 return pos 
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507 
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508 
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509 spring_layout = fruchterman_reingold_layout 
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510 
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511 
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512 @random_state(7) 
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513 def _fruchterman_reingold( 
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514 A, k=None, pos=None, fixed=None, iterations=50, threshold=1e4, dim=2, seed=None 
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515 ): 
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516 # Position nodes in adjacency matrix A using FruchtermanReingold 
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517 # Entry point for NetworkX graph is fruchterman_reingold_layout() 
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518 import numpy as np 
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519 
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520 try: 
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521 nnodes, _ = A.shape 
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522 except AttributeError as e: 
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523 msg = "fruchterman_reingold() takes an adjacency matrix as input" 
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524 raise nx.NetworkXError(msg) from e 
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525 
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526 if pos is None: 
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527 # random initial positions 
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528 pos = np.asarray(seed.rand(nnodes, dim), dtype=A.dtype) 
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529 else: 
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530 # make sure positions are of same type as matrix 
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531 pos = pos.astype(A.dtype) 
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532 
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533 # optimal distance between nodes 
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534 if k is None: 
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535 k = np.sqrt(1.0 / nnodes) 
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536 # the initial "temperature" is about .1 of domain area (=1x1) 
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537 # this is the largest step allowed in the dynamics. 
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538 # We need to calculate this in case our fixed positions force our domain 
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539 # to be much bigger than 1x1 
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540 t = max(max(pos.T[0])  min(pos.T[0]), max(pos.T[1])  min(pos.T[1])) * 0.1 
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541 # simple cooling scheme. 
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542 # linearly step down by dt on each iteration so last iteration is size dt. 
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543 dt = t / float(iterations + 1) 
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544 delta = np.zeros((pos.shape[0], pos.shape[0], pos.shape[1]), dtype=A.dtype) 
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545 # the inscrutable (but fast) version 
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546 # this is still O(V^2) 
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547 # could use multilevel methods to speed this up significantly 
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548 for iteration in range(iterations): 
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549 # matrix of difference between points 
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550 delta = pos[:, np.newaxis, :]  pos[np.newaxis, :, :] 
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551 # distance between points 
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552 distance = np.linalg.norm(delta, axis=1) 
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553 # enforce minimum distance of 0.01 
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554 np.clip(distance, 0.01, None, out=distance) 
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555 # displacement "force" 
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556 displacement = np.einsum( 
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557 "ijk,ij>ik", delta, (k * k / distance ** 2  A * distance / k) 
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558 ) 
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559 # update positions 
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560 length = np.linalg.norm(displacement, axis=1) 
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561 length = np.where(length < 0.01, 0.1, length) 
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562 delta_pos = np.einsum("ij,i>ij", displacement, t / length) 
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563 if fixed is not None: 
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564 # don't change positions of fixed nodes 
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565 delta_pos[fixed] = 0.0 
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566 pos += delta_pos 
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567 # cool temperature 
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568 t = dt 
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569 err = np.linalg.norm(delta_pos) / nnodes 
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570 if err < threshold: 
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571 break 
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572 return pos 
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573 
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574 
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575 @random_state(7) 
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576 def _sparse_fruchterman_reingold( 
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577 A, k=None, pos=None, fixed=None, iterations=50, threshold=1e4, dim=2, seed=None 
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578 ): 
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579 # Position nodes in adjacency matrix A using FruchtermanReingold 
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580 # Entry point for NetworkX graph is fruchterman_reingold_layout() 
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581 # Sparse version 
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582 import numpy as np 
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583 
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584 try: 
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585 nnodes, _ = A.shape 
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586 except AttributeError as e: 
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587 msg = "fruchterman_reingold() takes an adjacency matrix as input" 
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588 raise nx.NetworkXError(msg) from e 
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589 try: 
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590 from scipy.sparse import coo_matrix 
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591 except ImportError as e: 
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592 msg = "_sparse_fruchterman_reingold() scipy numpy: http://scipy.org/ " 
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593 raise ImportError(msg) from e 
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594 # make sure we have a LIst of Lists representation 
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595 try: 
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596 A = A.tolil() 
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597 except AttributeError: 
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598 A = (coo_matrix(A)).tolil() 
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599 
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600 if pos is None: 
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601 # random initial positions 
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602 pos = np.asarray(seed.rand(nnodes, dim), dtype=A.dtype) 
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603 else: 
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604 # make sure positions are of same type as matrix 
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605 pos = pos.astype(A.dtype) 
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606 
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607 # no fixed nodes 
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608 if fixed is None: 
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609 fixed = [] 
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610 
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611 # optimal distance between nodes 
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612 if k is None: 
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613 k = np.sqrt(1.0 / nnodes) 
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614 # the initial "temperature" is about .1 of domain area (=1x1) 
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615 # this is the largest step allowed in the dynamics. 
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616 t = max(max(pos.T[0])  min(pos.T[0]), max(pos.T[1])  min(pos.T[1])) * 0.1 
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617 # simple cooling scheme. 
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618 # linearly step down by dt on each iteration so last iteration is size dt. 
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619 dt = t / float(iterations + 1) 
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620 
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621 displacement = np.zeros((dim, nnodes)) 
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622 for iteration in range(iterations): 
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623 displacement *= 0 
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624 # loop over rows 
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625 for i in range(A.shape[0]): 
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626 if i in fixed: 
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627 continue 
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628 # difference between this row's node position and all others 
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629 delta = (pos[i]  pos).T 
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630 # distance between points 
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631 distance = np.sqrt((delta ** 2).sum(axis=0)) 
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632 # enforce minimum distance of 0.01 
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633 distance = np.where(distance < 0.01, 0.01, distance) 
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634 # the adjacency matrix row 
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635 Ai = np.asarray(A.getrowview(i).toarray()) 
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636 # displacement "force" 
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637 displacement[:, i] += ( 
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638 delta * (k * k / distance ** 2  Ai * distance / k) 
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639 ).sum(axis=1) 
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640 # update positions 
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641 length = np.sqrt((displacement ** 2).sum(axis=0)) 
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642 length = np.where(length < 0.01, 0.1, length) 
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643 delta_pos = (displacement * t / length).T 
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644 pos += delta_pos 
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645 # cool temperature 
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646 t = dt 
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647 err = np.linalg.norm(delta_pos) / nnodes 
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648 if err < threshold: 
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649 break 
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650 return pos 
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651 
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652 
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653 def kamada_kawai_layout( 
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654 G, dist=None, pos=None, weight="weight", scale=1, center=None, dim=2 
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655 ): 
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656 """Position nodes using KamadaKawai pathlength costfunction. 
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657 
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658 Parameters 
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659  
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660 G : NetworkX graph or list of nodes 
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661 A position will be assigned to every node in G. 
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662 
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663 dist : dict (default=None) 
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664 A twolevel dictionary of optimal distances between nodes, 
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665 indexed by source and destination node. 
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666 If None, the distance is computed using shortest_path_length(). 
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667 
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668 pos : dict or None optional (default=None) 
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669 Initial positions for nodes as a dictionary with node as keys 
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670 and values as a coordinate list or tuple. If None, then use 
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671 circular_layout() for dim >= 2 and a linear layout for dim == 1. 
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672 
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673 weight : string or None optional (default='weight') 
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674 The edge attribute that holds the numerical value used for 
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675 the edge weight. If None, then all edge weights are 1. 
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676 
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677 scale : number (default: 1) 
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678 Scale factor for positions. 
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679 
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680 center : arraylike or None 
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681 Coordinate pair around which to center the layout. 
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682 
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683 dim : int 
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684 Dimension of layout. 
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685 
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686 Returns 
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687  
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688 pos : dict 
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689 A dictionary of positions keyed by node 
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690 
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691 Examples 
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692  
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693 >>> G = nx.path_graph(4) 
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694 >>> pos = nx.kamada_kawai_layout(G) 
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695 """ 
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696 import numpy as np 
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697 
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698 G, center = _process_params(G, center, dim) 
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699 nNodes = len(G) 
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700 if nNodes == 0: 
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701 return {} 
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702 
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703 if dist is None: 
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704 dist = dict(nx.shortest_path_length(G, weight=weight)) 
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705 dist_mtx = 1e6 * np.ones((nNodes, nNodes)) 
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706 for row, nr in enumerate(G): 
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707 if nr not in dist: 
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708 continue 
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709 rdist = dist[nr] 
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710 for col, nc in enumerate(G): 
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711 if nc not in rdist: 
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712 continue 
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713 dist_mtx[row][col] = rdist[nc] 
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714 
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715 if pos is None: 
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716 if dim >= 3: 
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717 pos = random_layout(G, dim=dim) 
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718 elif dim == 2: 
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719 pos = circular_layout(G, dim=dim) 
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720 else: 
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721 pos = {n: pt for n, pt in zip(G, np.linspace(0, 1, len(G)))} 
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722 pos_arr = np.array([pos[n] for n in G]) 
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723 
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724 pos = _kamada_kawai_solve(dist_mtx, pos_arr, dim) 
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725 
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726 pos = rescale_layout(pos, scale=scale) + center 
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727 return dict(zip(G, pos)) 
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728 
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729 
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730 def _kamada_kawai_solve(dist_mtx, pos_arr, dim): 
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731 # Anneal node locations based on the KamadaKawai costfunction, 
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732 # using the supplied matrix of preferred internode distances, 
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733 # and starting locations. 
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734 
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735 import numpy as np 
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736 from scipy.optimize import minimize 
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737 
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738 meanwt = 1e3 
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739 costargs = (np, 1 / (dist_mtx + np.eye(dist_mtx.shape[0]) * 1e3), meanwt, dim) 
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740 
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741 optresult = minimize( 
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742 _kamada_kawai_costfn, 
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743 pos_arr.ravel(), 
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744 method="LBFGSB", 
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745 args=costargs, 
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746 jac=True, 
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747 ) 
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748 
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749 return optresult.x.reshape((1, dim)) 
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750 
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751 
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752 def _kamada_kawai_costfn(pos_vec, np, invdist, meanweight, dim): 
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753 # Costfunction and gradient for KamadaKawai layout algorithm 
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754 nNodes = invdist.shape[0] 
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755 pos_arr = pos_vec.reshape((nNodes, dim)) 
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756 
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757 delta = pos_arr[:, np.newaxis, :]  pos_arr[np.newaxis, :, :] 
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758 nodesep = np.linalg.norm(delta, axis=1) 
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759 direction = np.einsum("ijk,ij>ijk", delta, 1 / (nodesep + np.eye(nNodes) * 1e3)) 
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760 
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761 offset = nodesep * invdist  1.0 
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762 offset[np.diag_indices(nNodes)] = 0 
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763 
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764 cost = 0.5 * np.sum(offset ** 2) 
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765 grad = np.einsum("ij,ij,ijk>ik", invdist, offset, direction)  np.einsum( 
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766 "ij,ij,ijk>jk", invdist, offset, direction 
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767 ) 
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768 
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769 # Additional parabolic term to encourage mean position to be near origin: 
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770 sumpos = np.sum(pos_arr, axis=0) 
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771 cost += 0.5 * meanweight * np.sum(sumpos ** 2) 
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772 grad += meanweight * sumpos 
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773 
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774 return (cost, grad.ravel()) 
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775 
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776 
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777 def spectral_layout(G, weight="weight", scale=1, center=None, dim=2): 
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778 """Position nodes using the eigenvectors of the graph Laplacian. 
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779 
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780 Using the unnormalized Laplacian, the layout shows possible clusters of 
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781 nodes which are an approximation of the ratio cut. If dim is the number of 
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782 dimensions then the positions are the entries of the dim eigenvectors 
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783 corresponding to the ascending eigenvalues starting from the second one. 
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784 
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785 Parameters 
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786  
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787 G : NetworkX graph or list of nodes 
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788 A position will be assigned to every node in G. 
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789 
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790 weight : string or None optional (default='weight') 
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791 The edge attribute that holds the numerical value used for 
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792 the edge weight. If None, then all edge weights are 1. 
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793 
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794 scale : number (default: 1) 
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795 Scale factor for positions. 
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796 
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797 center : arraylike or None 
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798 Coordinate pair around which to center the layout. 
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799 
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800 dim : int 
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801 Dimension of layout. 
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802 
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803 Returns 
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804  
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805 pos : dict 
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806 A dictionary of positions keyed by node 
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807 
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808 Examples 
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809  
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810 >>> G = nx.path_graph(4) 
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811 >>> pos = nx.spectral_layout(G) 
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812 
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813 Notes 
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814  
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815 Directed graphs will be considered as undirected graphs when 
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816 positioning the nodes. 
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817 
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818 For larger graphs (>500 nodes) this will use the SciPy sparse 
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819 eigenvalue solver (ARPACK). 
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820 """ 
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821 # handle some special cases that break the eigensolvers 
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822 import numpy as np 
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823 
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824 G, center = _process_params(G, center, dim) 
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825 
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826 if len(G) <= 2: 
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827 if len(G) == 0: 
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828 pos = np.array([]) 
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829 elif len(G) == 1: 
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830 pos = np.array([center]) 
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831 else: 
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832 pos = np.array([np.zeros(dim), np.array(center) * 2.0]) 
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833 return dict(zip(G, pos)) 
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834 try: 
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835 # Sparse matrix 
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836 if len(G) < 500: # dense solver is faster for small graphs 
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837 raise ValueError 
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838 A = nx.to_scipy_sparse_matrix(G, weight=weight, dtype="d") 
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839 # Symmetrize directed graphs 
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840 if G.is_directed(): 
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841 A = A + np.transpose(A) 
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842 pos = _sparse_spectral(A, dim) 
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843 except (ImportError, ValueError): 
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844 # Dense matrix 
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845 A = nx.to_numpy_array(G, weight=weight) 
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846 # Symmetrize directed graphs 
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847 if G.is_directed(): 
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848 A += A.T 
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849 pos = _spectral(A, dim) 
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850 
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851 pos = rescale_layout(pos, scale=scale) + center 
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852 pos = dict(zip(G, pos)) 
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853 return pos 
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854 
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855 
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856 def _spectral(A, dim=2): 
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857 # Input adjacency matrix A 
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858 # Uses dense eigenvalue solver from numpy 
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859 import numpy as np 
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860 
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861 try: 
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862 nnodes, _ = A.shape 
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863 except AttributeError as e: 
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864 msg = "spectral() takes an adjacency matrix as input" 
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865 raise nx.NetworkXError(msg) from e 
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866 
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867 # form Laplacian matrix where D is diagonal of degrees 
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868 D = np.identity(nnodes, dtype=A.dtype) * np.sum(A, axis=1) 
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869 L = D  A 
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870 
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871 eigenvalues, eigenvectors = np.linalg.eig(L) 
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872 # sort and keep smallest nonzero 
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873 index = np.argsort(eigenvalues)[1 : dim + 1] # 0 index is zero eigenvalue 
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874 return np.real(eigenvectors[:, index]) 
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875 
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876 
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877 def _sparse_spectral(A, dim=2): 
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878 # Input adjacency matrix A 
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879 # Uses sparse eigenvalue solver from scipy 
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880 # Could use multilevel methods here, see Koren "On spectral graph drawing" 
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881 import numpy as np 
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882 from scipy.sparse import spdiags 
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883 from scipy.sparse.linalg.eigen import eigsh 
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884 
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885 try: 
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886 nnodes, _ = A.shape 
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887 except AttributeError as e: 
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888 msg = "sparse_spectral() takes an adjacency matrix as input" 
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889 raise nx.NetworkXError(msg) from e 
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890 
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891 # form Laplacian matrix 
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892 data = np.asarray(A.sum(axis=1).T) 
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893 D = spdiags(data, 0, nnodes, nnodes) 
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894 L = D  A 
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895 
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896 k = dim + 1 
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897 # number of Lanczos vectors for ARPACK solver.What is the right scaling? 
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898 ncv = max(2 * k + 1, int(np.sqrt(nnodes))) 
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899 # return smallest k eigenvalues and eigenvectors 
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900 eigenvalues, eigenvectors = eigsh(L, k, which="SM", ncv=ncv) 
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901 index = np.argsort(eigenvalues)[1:k] # 0 index is zero eigenvalue 
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902 return np.real(eigenvectors[:, index]) 
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903 
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904 
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905 def planar_layout(G, scale=1, center=None, dim=2): 
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906 """Position nodes without edge intersections. 
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907 
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908 Parameters 
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909  
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910 G : NetworkX graph or list of nodes 
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911 A position will be assigned to every node in G. If G is of type 
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912 nx.PlanarEmbedding, the positions are selected accordingly. 
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913 
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914 scale : number (default: 1) 
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915 Scale factor for positions. 
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916 
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917 center : arraylike or None 
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918 Coordinate pair around which to center the layout. 
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919 
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920 dim : int 
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921 Dimension of layout. 
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922 
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923 Returns 
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924  
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925 pos : dict 
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926 A dictionary of positions keyed by node 
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927 
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928 Raises 
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929  
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930 NetworkXException 
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931 If G is not planar 
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932 
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933 Examples 
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934  
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935 >>> G = nx.path_graph(4) 
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936 >>> pos = nx.planar_layout(G) 
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937 """ 
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938 import numpy as np 
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939 
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940 if dim != 2: 
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941 raise ValueError("can only handle 2 dimensions") 
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942 
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943 G, center = _process_params(G, center, dim) 
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944 
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945 if len(G) == 0: 
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946 return {} 
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947 
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948 if isinstance(G, nx.PlanarEmbedding): 
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949 embedding = G 
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950 else: 
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951 is_planar, embedding = nx.check_planarity(G) 
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952 if not is_planar: 
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953 raise nx.NetworkXException("G is not planar.") 
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954 pos = nx.combinatorial_embedding_to_pos(embedding) 
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955 node_list = list(embedding) 
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956 pos = np.row_stack([pos[x] for x in node_list]) 
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957 pos = pos.astype(np.float64) 
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958 pos = rescale_layout(pos, scale=scale) + center 
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959 return dict(zip(node_list, pos)) 
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960 
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961 
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962 def spiral_layout(G, scale=1, center=None, dim=2, resolution=0.35, equidistant=False): 
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963 """Position nodes in a spiral layout. 
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964 
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965 Parameters 
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966  
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967 G : NetworkX graph or list of nodes 
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968 A position will be assigned to every node in G. 
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969 scale : number (default: 1) 
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970 Scale factor for positions. 
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971 center : arraylike or None 
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972 Coordinate pair around which to center the layout. 
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973 dim : int 
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974 Dimension of layout, currently only dim=2 is supported. 
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975 Other dimension values result in a ValueError. 
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976 resolution : float 
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977 The compactness of the spiral layout returned. 
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978 Lower values result in more compressed spiral layouts. 
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979 equidistant : bool 
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980 If True, nodes will be plotted equidistant from each other. 
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981 Returns 
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982  
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983 pos : dict 
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984 A dictionary of positions keyed by node 
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985 Raises 
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986  
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987 ValueError 
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988 If dim != 2 
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989 
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990 Examples 
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991  
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992 >>> G = nx.path_graph(4) 
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993 >>> pos = nx.spiral_layout(G) 
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994 
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995 Notes 
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996  
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997 This algorithm currently only works in two dimensions. 
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998 
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999 """ 
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1000 import numpy as np 
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1001 
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1002 if dim != 2: 
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1003 raise ValueError("can only handle 2 dimensions") 
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1004 
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1005 G, center = _process_params(G, center, dim) 
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1006 
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1007 if len(G) == 0: 
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1008 return {} 
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1009 if len(G) == 1: 
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1010 return {nx.utils.arbitrary_element(G): center} 
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1011 
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1012 pos = [] 
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1013 if equidistant: 
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1014 chord = 1 
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1015 step = 0.5 
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1016 theta = resolution 
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1017 for _ in range(len(G)): 
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1018 r = step * theta 
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1019 theta += chord / r 
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1020 pos.append([np.cos(theta) * r, np.sin(theta) * r]) 
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1021 
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1022 else: 
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1023 # set the starting angle and step 
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1024 step = 1 
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1025 angle = 0.0 
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1026 dist = 0.0 
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1027 # set the radius for the spiral to the number of nodes in the graph 
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1028 radius = len(G) 
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1029 
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1030 while dist * np.hypot(np.cos(angle), np.sin(angle)) < radius: 
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1031 pos.append([dist * np.cos(angle), dist * np.sin(angle)]) 
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1032 dist += step 
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1033 angle += resolution 
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1034 
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1035 pos = rescale_layout(np.array(pos), scale=scale) + center 
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1036 
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1037 pos = dict(zip(G, pos)) 
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1038 
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1039 return pos 
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1040 
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1041 
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1042 def multipartite_layout(G, subset_key="subset", align="vertical", scale=1, center=None): 
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1043 """Position nodes in layers of straight lines. 
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1044 
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1045 Parameters 
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1046  
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1047 G : NetworkX graph or list of nodes 
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1048 A position will be assigned to every node in G. 
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1049 
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1050 subset_key : string (default='subset') 
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1051 Key of node data to be used as layer subset. 
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1052 
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1053 align : string (default='vertical') 
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1054 The alignment of nodes. Vertical or horizontal. 
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1055 
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1056 scale : number (default: 1) 
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1057 Scale factor for positions. 
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1058 
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1059 center : arraylike or None 
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1060 Coordinate pair around which to center the layout. 
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1061 
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1062 Returns 
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1063  
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1064 pos : dict 
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1065 A dictionary of positions keyed by node. 
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1066 
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1067 Examples 
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1068  
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1069 >>> G = nx.complete_multipartite_graph(28, 16, 10) 
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1070 >>> pos = nx.multipartite_layout(G) 
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1071 
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1072 Notes 
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1073  
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1074 This algorithm currently only works in two dimensions and does not 
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1075 try to minimize edge crossings. 
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1076 
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1077 Network does not need to be a complete multipartite graph. As long as nodes 
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1078 have subset_key data, they will be placed in the corresponding layers. 
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1079 
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1080 """ 
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1081 import numpy as np 
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1082 
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1083 G, center = _process_params(G, center=center, dim=2) 
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1084 if len(G) == 0: 
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1085 return {} 
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1086 
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1087 layers = {} 
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1088 for v, data in G.nodes(data=True): 
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1089 try: 
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1090 layer = data[subset_key] 
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1091 except KeyError: 
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1092 msg = "all nodes must have subset_key (default='subset') as data" 
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1093 raise ValueError(msg) 
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1094 layers[layer] = [v] + layers.get(layer, []) 
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1095 
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1096 pos = None 
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1097 nodes = [] 
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1098 if align == "vertical": 
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1099 width = len(layers) 
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1100 for i, layer in layers.items(): 
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1101 height = len(layer) 
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1102 xs = np.repeat(i, height) 
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1103 ys = np.arange(0, height, dtype=float) 
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1104 offset = ((width  1) / 2, (height  1) / 2) 
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1105 layer_pos = np.column_stack([xs, ys])  offset 
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1106 if pos is None: 
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1107 pos = layer_pos 
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1108 else: 
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1109 pos = np.concatenate([pos, layer_pos]) 
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1110 nodes.extend(layer) 
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1111 pos = rescale_layout(pos, scale=scale) + center 
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1112 pos = dict(zip(nodes, pos)) 
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1113 return pos 
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1114 
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1115 if align == "horizontal": 
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1116 height = len(layers) 
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1117 for i, layer in layers.items(): 
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1118 width = len(layer) 
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1119 xs = np.arange(0, width, dtype=float) 
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1120 ys = np.repeat(i, width) 
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1121 offset = ((width  1) / 2, (height  1) / 2) 
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1122 layer_pos = np.column_stack([xs, ys])  offset 
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1123 if pos is None: 
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1124 pos = layer_pos 
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1125 else: 
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1126 pos = np.concatenate([pos, layer_pos]) 
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1127 nodes.extend(layer) 
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1128 pos = rescale_layout(pos, scale=scale) + center 
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1129 pos = dict(zip(nodes, pos)) 
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1130 return pos 
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1131 
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1132 msg = "align must be either vertical or horizontal." 
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1133 raise ValueError(msg) 
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1134 
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1135 
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1136 def rescale_layout(pos, scale=1): 
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1137 """Returns scaled position array to (scale, scale) in all axes. 
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1138 
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1139 The function acts on NumPy arrays which hold position information. 
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1140 Each position is one row of the array. The dimension of the space 
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1141 equals the number of columns. Each coordinate in one column. 
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1142 
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1143 To rescale, the mean (center) is subtracted from each axis separately. 
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1144 Then all values are scaled so that the largest magnitude value 
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1145 from all axes equals `scale` (thus, the aspect ratio is preserved). 
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1146 The resulting NumPy Array is returned (order of rows unchanged). 
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1147 
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1148 Parameters 
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1149  
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1150 pos : numpy array 
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1151 positions to be scaled. Each row is a position. 
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1152 
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1153 scale : number (default: 1) 
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1154 The size of the resulting extent in all directions. 
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1155 
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1156 Returns 
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1157  
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1158 pos : numpy array 
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1159 scaled positions. Each row is a position. 
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1160 
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1161 See Also 
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1162  
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1163 rescale_layout_dict 
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1164 """ 
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1165 # Find max length over all dimensions 
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1166 lim = 0 # max coordinate for all axes 
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1167 for i in range(pos.shape[1]): 
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1168 pos[:, i] = pos[:, i].mean() 
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1169 lim = max(abs(pos[:, i]).max(), lim) 
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1170 # rescale to (scale, scale) in all directions, preserves aspect 
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1171 if lim > 0: 
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1172 for i in range(pos.shape[1]): 
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1173 pos[:, i] *= scale / lim 
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1174 return pos 
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1175 
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1176 
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1177 def rescale_layout_dict(pos, scale=1): 
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1178 """Return a dictionary of scaled positions keyed by node 
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1179 
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1180 Parameters 
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1181  
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1182 pos : A dictionary of positions keyed by node 
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1183 
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1184 scale : number (default: 1) 
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1185 The size of the resulting extent in all directions. 
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1186 
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1187 Returns 
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1188  
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1189 pos : A dictionary of positions keyed by node 
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1190 
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1191 Examples 
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1192  
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1193 >>> pos = {0: (0, 0), 1: (1, 1), 2: (0.5, 0.5)} 
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1194 >>> nx.rescale_layout_dict(pos) 
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1195 {0: (1.0, 1.0), 1: (1.0, 1.0), 2: (0.0, 0.0)} 
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1196 
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1197 >>> pos = {0: (0, 0), 1: (1, 1), 2: (0.5, 0.5)} 
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1198 >>> nx.rescale_layout_dict(pos, scale=2) 
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1199 {0: (2.0, 2.0), 1: (2.0, 2.0), 2: (0.0, 0.0)} 
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1200 
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1201 See Also 
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1202  
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1203 rescale_layout 
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1204 """ 
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1205 import numpy as np 
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1206 
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1207 if not pos: # empty_graph 
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1208 return {} 
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset

1209 pos_v = np.array(list(pos.values())) 
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset

1210 pos_v = rescale_layout(pos_v, scale=scale) 
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset

1211 return {k: tuple(v) for k, v in zip(pos.keys(), pos_v)} 