Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/shortest_paths/tests/test_weighted.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 import pytest |
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2 |
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3 import networkx as nx |
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4 from networkx.utils import pairwise |
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5 |
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6 |
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7 def validate_path(G, s, t, soln_len, path, weight="weight"): |
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8 assert path[0] == s |
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9 assert path[-1] == t |
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10 |
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11 if callable(weight): |
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12 weight_f = weight |
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13 else: |
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14 if G.is_multigraph(): |
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15 |
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16 def weight_f(u, v, d): |
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17 return min(e.get(weight, 1) for e in d.values()) |
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18 |
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19 else: |
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20 |
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21 def weight_f(u, v, d): |
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22 return d.get(weight, 1) |
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23 |
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24 computed = sum(weight_f(u, v, G[u][v]) for u, v in pairwise(path)) |
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25 assert soln_len == computed |
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26 |
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27 |
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28 def validate_length_path(G, s, t, soln_len, length, path, weight="weight"): |
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29 assert soln_len == length |
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30 validate_path(G, s, t, length, path, weight=weight) |
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31 |
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32 |
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33 class WeightedTestBase: |
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34 """Base class for test classes that test functions for computing |
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35 shortest paths in weighted graphs. |
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36 |
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37 """ |
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38 |
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39 def setup(self): |
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40 """Creates some graphs for use in the unit tests.""" |
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41 cnlti = nx.convert_node_labels_to_integers |
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42 self.grid = cnlti(nx.grid_2d_graph(4, 4), first_label=1, ordering="sorted") |
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43 self.cycle = nx.cycle_graph(7) |
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44 self.directed_cycle = nx.cycle_graph(7, create_using=nx.DiGraph()) |
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45 self.XG = nx.DiGraph() |
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46 self.XG.add_weighted_edges_from( |
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47 [ |
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48 ("s", "u", 10), |
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49 ("s", "x", 5), |
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50 ("u", "v", 1), |
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51 ("u", "x", 2), |
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52 ("v", "y", 1), |
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53 ("x", "u", 3), |
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54 ("x", "v", 5), |
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55 ("x", "y", 2), |
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56 ("y", "s", 7), |
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57 ("y", "v", 6), |
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58 ] |
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59 ) |
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60 self.MXG = nx.MultiDiGraph(self.XG) |
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61 self.MXG.add_edge("s", "u", weight=15) |
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62 self.XG2 = nx.DiGraph() |
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63 self.XG2.add_weighted_edges_from( |
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64 [ |
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65 [1, 4, 1], |
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66 [4, 5, 1], |
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67 [5, 6, 1], |
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68 [6, 3, 1], |
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69 [1, 3, 50], |
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70 [1, 2, 100], |
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71 [2, 3, 100], |
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72 ] |
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73 ) |
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74 |
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75 self.XG3 = nx.Graph() |
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76 self.XG3.add_weighted_edges_from( |
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77 [[0, 1, 2], [1, 2, 12], [2, 3, 1], [3, 4, 5], [4, 5, 1], [5, 0, 10]] |
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78 ) |
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79 |
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80 self.XG4 = nx.Graph() |
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81 self.XG4.add_weighted_edges_from( |
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82 [ |
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83 [0, 1, 2], |
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84 [1, 2, 2], |
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85 [2, 3, 1], |
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86 [3, 4, 1], |
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87 [4, 5, 1], |
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88 [5, 6, 1], |
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89 [6, 7, 1], |
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90 [7, 0, 1], |
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91 ] |
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92 ) |
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93 self.MXG4 = nx.MultiGraph(self.XG4) |
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94 self.MXG4.add_edge(0, 1, weight=3) |
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95 self.G = nx.DiGraph() # no weights |
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96 self.G.add_edges_from( |
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97 [ |
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98 ("s", "u"), |
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99 ("s", "x"), |
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100 ("u", "v"), |
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101 ("u", "x"), |
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102 ("v", "y"), |
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103 ("x", "u"), |
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104 ("x", "v"), |
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105 ("x", "y"), |
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106 ("y", "s"), |
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107 ("y", "v"), |
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109 ) |
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110 |
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111 |
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112 class TestWeightedPath(WeightedTestBase): |
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113 def test_dijkstra(self): |
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114 (D, P) = nx.single_source_dijkstra(self.XG, "s") |
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115 validate_path(self.XG, "s", "v", 9, P["v"]) |
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116 assert D["v"] == 9 |
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117 |
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118 validate_path( |
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119 self.XG, "s", "v", 9, nx.single_source_dijkstra_path(self.XG, "s")["v"] |
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120 ) |
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121 assert dict(nx.single_source_dijkstra_path_length(self.XG, "s"))["v"] == 9 |
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122 |
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123 validate_path( |
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124 self.XG, "s", "v", 9, nx.single_source_dijkstra(self.XG, "s")[1]["v"] |
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125 ) |
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126 validate_path( |
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127 self.MXG, "s", "v", 9, nx.single_source_dijkstra_path(self.MXG, "s")["v"] |
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128 ) |
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129 |
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130 GG = self.XG.to_undirected() |
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131 # make sure we get lower weight |
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132 # to_undirected might choose either edge with weight 2 or weight 3 |
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133 GG["u"]["x"]["weight"] = 2 |
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134 (D, P) = nx.single_source_dijkstra(GG, "s") |
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135 validate_path(GG, "s", "v", 8, P["v"]) |
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136 assert D["v"] == 8 # uses lower weight of 2 on u<->x edge |
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137 validate_path(GG, "s", "v", 8, nx.dijkstra_path(GG, "s", "v")) |
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138 assert nx.dijkstra_path_length(GG, "s", "v") == 8 |
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139 |
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140 validate_path(self.XG2, 1, 3, 4, nx.dijkstra_path(self.XG2, 1, 3)) |
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141 validate_path(self.XG3, 0, 3, 15, nx.dijkstra_path(self.XG3, 0, 3)) |
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142 assert nx.dijkstra_path_length(self.XG3, 0, 3) == 15 |
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143 validate_path(self.XG4, 0, 2, 4, nx.dijkstra_path(self.XG4, 0, 2)) |
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144 assert nx.dijkstra_path_length(self.XG4, 0, 2) == 4 |
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145 validate_path(self.MXG4, 0, 2, 4, nx.dijkstra_path(self.MXG4, 0, 2)) |
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146 validate_path( |
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147 self.G, "s", "v", 2, nx.single_source_dijkstra(self.G, "s", "v")[1] |
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148 ) |
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149 validate_path( |
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150 self.G, "s", "v", 2, nx.single_source_dijkstra(self.G, "s")[1]["v"] |
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151 ) |
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152 |
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153 validate_path(self.G, "s", "v", 2, nx.dijkstra_path(self.G, "s", "v")) |
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154 assert nx.dijkstra_path_length(self.G, "s", "v") == 2 |
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155 |
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156 # NetworkXError: node s not reachable from moon |
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157 pytest.raises(nx.NetworkXNoPath, nx.dijkstra_path, self.G, "s", "moon") |
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158 pytest.raises(nx.NetworkXNoPath, nx.dijkstra_path_length, self.G, "s", "moon") |
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159 |
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160 validate_path(self.cycle, 0, 3, 3, nx.dijkstra_path(self.cycle, 0, 3)) |
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161 validate_path(self.cycle, 0, 4, 3, nx.dijkstra_path(self.cycle, 0, 4)) |
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162 |
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163 assert nx.single_source_dijkstra(self.cycle, 0, 0) == (0, [0]) |
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164 |
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165 def test_bidirectional_dijkstra(self): |
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166 validate_length_path( |
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167 self.XG, "s", "v", 9, *nx.bidirectional_dijkstra(self.XG, "s", "v") |
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168 ) |
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169 validate_length_path( |
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170 self.G, "s", "v", 2, *nx.bidirectional_dijkstra(self.G, "s", "v") |
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171 ) |
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172 validate_length_path( |
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173 self.cycle, 0, 3, 3, *nx.bidirectional_dijkstra(self.cycle, 0, 3) |
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174 ) |
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175 validate_length_path( |
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176 self.cycle, 0, 4, 3, *nx.bidirectional_dijkstra(self.cycle, 0, 4) |
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177 ) |
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178 validate_length_path( |
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179 self.XG3, 0, 3, 15, *nx.bidirectional_dijkstra(self.XG3, 0, 3) |
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180 ) |
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181 validate_length_path( |
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182 self.XG4, 0, 2, 4, *nx.bidirectional_dijkstra(self.XG4, 0, 2) |
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183 ) |
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184 |
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185 # need more tests here |
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186 P = nx.single_source_dijkstra_path(self.XG, "s")["v"] |
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187 validate_path( |
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188 self.XG, |
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189 "s", |
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190 "v", |
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191 sum(self.XG[u][v]["weight"] for u, v in zip(P[:-1], P[1:])), |
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192 nx.dijkstra_path(self.XG, "s", "v"), |
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193 ) |
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194 |
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195 # check absent source |
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196 G = nx.path_graph(2) |
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197 pytest.raises(nx.NodeNotFound, nx.bidirectional_dijkstra, G, 3, 0) |
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198 |
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199 def test_weight_functions(self): |
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200 def heuristic(*z): |
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201 return hash(z) |
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202 |
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203 def getpath(pred, v, s): |
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204 return [v] if v == s else getpath(pred, pred[v], s) + [v] |
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205 |
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206 def goldberg_radzik(g, s, t, weight="weight"): |
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207 pred, dist = nx.goldberg_radzik(g, s, weight=weight) |
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208 dist = dist[t] |
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209 return dist, getpath(pred, t, s) |
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210 |
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211 def astar(g, s, t, weight="weight"): |
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212 path = nx.astar_path(g, s, t, heuristic, weight=weight) |
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213 dist = nx.astar_path_length(g, s, t, heuristic, weight=weight) |
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214 return dist, path |
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215 |
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216 def vlp(G, s, t, l, F, w): |
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217 res = F(G, s, t, weight=w) |
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218 validate_length_path(G, s, t, l, *res, weight=w) |
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219 |
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220 G = self.cycle |
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221 s = 6 |
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222 t = 4 |
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223 path = [6] + list(range(t + 1)) |
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224 |
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225 def weight(u, v, _): |
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226 return 1 + v ** 2 |
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227 |
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228 length = sum(weight(u, v, None) for u, v in pairwise(path)) |
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229 vlp(G, s, t, length, nx.bidirectional_dijkstra, weight) |
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230 vlp(G, s, t, length, nx.single_source_dijkstra, weight) |
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231 vlp(G, s, t, length, nx.single_source_bellman_ford, weight) |
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232 vlp(G, s, t, length, goldberg_radzik, weight) |
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233 vlp(G, s, t, length, astar, weight) |
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234 |
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235 def weight(u, v, _): |
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236 return 2 ** (u * v) |
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237 |
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238 length = sum(weight(u, v, None) for u, v in pairwise(path)) |
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239 vlp(G, s, t, length, nx.bidirectional_dijkstra, weight) |
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240 vlp(G, s, t, length, nx.single_source_dijkstra, weight) |
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241 vlp(G, s, t, length, nx.single_source_bellman_ford, weight) |
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242 vlp(G, s, t, length, goldberg_radzik, weight) |
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243 vlp(G, s, t, length, astar, weight) |
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244 |
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245 def test_bidirectional_dijkstra_no_path(self): |
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246 with pytest.raises(nx.NetworkXNoPath): |
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247 G = nx.Graph() |
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248 nx.add_path(G, [1, 2, 3]) |
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249 nx.add_path(G, [4, 5, 6]) |
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250 path = nx.bidirectional_dijkstra(G, 1, 6) |
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251 |
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252 def test_absent_source(self): |
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253 # the check is in _dijkstra_multisource, but this will provide |
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254 # regression testing against later changes to any of the "client" |
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255 # Dijkstra or Bellman-Ford functions |
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256 G = nx.path_graph(2) |
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257 for fn in ( |
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258 nx.dijkstra_path, |
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259 nx.dijkstra_path_length, |
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260 nx.single_source_dijkstra_path, |
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261 nx.single_source_dijkstra_path_length, |
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262 nx.single_source_dijkstra, |
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263 nx.dijkstra_predecessor_and_distance, |
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264 ): |
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265 pytest.raises(nx.NodeNotFound, fn, G, 3, 0) |
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266 |
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267 def test_dijkstra_predecessor1(self): |
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268 G = nx.path_graph(4) |
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269 assert nx.dijkstra_predecessor_and_distance(G, 0) == ( |
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270 {0: [], 1: [0], 2: [1], 3: [2]}, |
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271 {0: 0, 1: 1, 2: 2, 3: 3}, |
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272 ) |
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273 |
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274 def test_dijkstra_predecessor2(self): |
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275 # 4-cycle |
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276 G = nx.Graph([(0, 1), (1, 2), (2, 3), (3, 0)]) |
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277 pred, dist = nx.dijkstra_predecessor_and_distance(G, (0)) |
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278 assert pred[0] == [] |
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279 assert pred[1] == [0] |
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280 assert pred[2] in [[1, 3], [3, 1]] |
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281 assert pred[3] == [0] |
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282 assert dist == {0: 0, 1: 1, 2: 2, 3: 1} |
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283 |
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284 def test_dijkstra_predecessor3(self): |
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285 XG = nx.DiGraph() |
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286 XG.add_weighted_edges_from( |
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287 [ |
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288 ("s", "u", 10), |
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289 ("s", "x", 5), |
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290 ("u", "v", 1), |
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291 ("u", "x", 2), |
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292 ("v", "y", 1), |
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293 ("x", "u", 3), |
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294 ("x", "v", 5), |
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295 ("x", "y", 2), |
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296 ("y", "s", 7), |
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297 ("y", "v", 6), |
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298 ] |
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299 ) |
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300 (P, D) = nx.dijkstra_predecessor_and_distance(XG, "s") |
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301 assert P["v"] == ["u"] |
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302 assert D["v"] == 9 |
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303 (P, D) = nx.dijkstra_predecessor_and_distance(XG, "s", cutoff=8) |
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304 assert "v" not in D |
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305 |
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306 def test_single_source_dijkstra_path_length(self): |
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307 pl = nx.single_source_dijkstra_path_length |
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308 assert dict(pl(self.MXG4, 0))[2] == 4 |
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309 spl = pl(self.MXG4, 0, cutoff=2) |
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310 assert 2 not in spl |
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311 |
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312 def test_bidirectional_dijkstra_multigraph(self): |
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313 G = nx.MultiGraph() |
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314 G.add_edge("a", "b", weight=10) |
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315 G.add_edge("a", "b", weight=100) |
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316 dp = nx.bidirectional_dijkstra(G, "a", "b") |
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317 assert dp == (10, ["a", "b"]) |
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318 |
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319 def test_dijkstra_pred_distance_multigraph(self): |
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320 G = nx.MultiGraph() |
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321 G.add_edge("a", "b", key="short", foo=5, weight=100) |
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322 G.add_edge("a", "b", key="long", bar=1, weight=110) |
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323 p, d = nx.dijkstra_predecessor_and_distance(G, "a") |
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324 assert p == {"a": [], "b": ["a"]} |
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325 assert d == {"a": 0, "b": 100} |
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326 |
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327 def test_negative_edge_cycle(self): |
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328 G = nx.cycle_graph(5, create_using=nx.DiGraph()) |
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329 assert not nx.negative_edge_cycle(G) |
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330 G.add_edge(8, 9, weight=-7) |
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331 G.add_edge(9, 8, weight=3) |
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332 graph_size = len(G) |
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333 assert nx.negative_edge_cycle(G) |
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334 assert graph_size == len(G) |
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335 pytest.raises(ValueError, nx.single_source_dijkstra_path_length, G, 8) |
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336 pytest.raises(ValueError, nx.single_source_dijkstra, G, 8) |
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337 pytest.raises(ValueError, nx.dijkstra_predecessor_and_distance, G, 8) |
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338 G.add_edge(9, 10) |
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339 pytest.raises(ValueError, nx.bidirectional_dijkstra, G, 8, 10) |
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340 |
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341 def test_weight_function(self): |
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342 """Tests that a callable weight is interpreted as a weight |
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343 function instead of an edge attribute. |
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344 |
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345 """ |
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346 # Create a triangle in which the edge from node 0 to node 2 has |
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347 # a large weight and the other two edges have a small weight. |
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348 G = nx.complete_graph(3) |
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349 G.adj[0][2]["weight"] = 10 |
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350 G.adj[0][1]["weight"] = 1 |
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351 G.adj[1][2]["weight"] = 1 |
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352 # The weight function will take the multiplicative inverse of |
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353 # the weights on the edges. This way, weights that were large |
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354 # before now become small and vice versa. |
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355 |
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356 def weight(u, v, d): |
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357 return 1 / d["weight"] |
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358 |
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359 # The shortest path from 0 to 2 using the actual weights on the |
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360 # edges should be [0, 1, 2]. |
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361 distance, path = nx.single_source_dijkstra(G, 0, 2) |
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362 assert distance == 2 |
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363 assert path == [0, 1, 2] |
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364 # However, with the above weight function, the shortest path |
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365 # should be [0, 2], since that has a very small weight. |
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366 distance, path = nx.single_source_dijkstra(G, 0, 2, weight=weight) |
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367 assert distance == 1 / 10 |
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368 assert path == [0, 2] |
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369 |
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370 def test_all_pairs_dijkstra_path(self): |
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371 cycle = nx.cycle_graph(7) |
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372 p = dict(nx.all_pairs_dijkstra_path(cycle)) |
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373 assert p[0][3] == [0, 1, 2, 3] |
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374 |
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375 cycle[1][2]["weight"] = 10 |
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376 p = dict(nx.all_pairs_dijkstra_path(cycle)) |
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377 assert p[0][3] == [0, 6, 5, 4, 3] |
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378 |
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379 def test_all_pairs_dijkstra_path_length(self): |
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380 cycle = nx.cycle_graph(7) |
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381 pl = dict(nx.all_pairs_dijkstra_path_length(cycle)) |
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382 assert pl[0] == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1} |
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383 |
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384 cycle[1][2]["weight"] = 10 |
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385 pl = dict(nx.all_pairs_dijkstra_path_length(cycle)) |
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386 assert pl[0] == {0: 0, 1: 1, 2: 5, 3: 4, 4: 3, 5: 2, 6: 1} |
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387 |
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388 def test_all_pairs_dijkstra(self): |
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389 cycle = nx.cycle_graph(7) |
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390 out = dict(nx.all_pairs_dijkstra(cycle)) |
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391 assert out[0][0] == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1} |
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392 assert out[0][1][3] == [0, 1, 2, 3] |
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393 |
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394 cycle[1][2]["weight"] = 10 |
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395 out = dict(nx.all_pairs_dijkstra(cycle)) |
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396 assert out[0][0] == {0: 0, 1: 1, 2: 5, 3: 4, 4: 3, 5: 2, 6: 1} |
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397 assert out[0][1][3] == [0, 6, 5, 4, 3] |
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398 |
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399 |
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400 class TestDijkstraPathLength: |
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401 """Unit tests for the :func:`networkx.dijkstra_path_length` |
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402 function. |
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403 |
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404 """ |
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405 |
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406 def test_weight_function(self): |
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407 """Tests for computing the length of the shortest path using |
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408 Dijkstra's algorithm with a user-defined weight function. |
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409 |
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410 """ |
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411 # Create a triangle in which the edge from node 0 to node 2 has |
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412 # a large weight and the other two edges have a small weight. |
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413 G = nx.complete_graph(3) |
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414 G.adj[0][2]["weight"] = 10 |
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415 G.adj[0][1]["weight"] = 1 |
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416 G.adj[1][2]["weight"] = 1 |
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417 # The weight function will take the multiplicative inverse of |
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418 # the weights on the edges. This way, weights that were large |
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419 # before now become small and vice versa. |
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420 |
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421 def weight(u, v, d): |
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422 return 1 / d["weight"] |
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423 |
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424 # The shortest path from 0 to 2 using the actual weights on the |
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425 # edges should be [0, 1, 2]. However, with the above weight |
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426 # function, the shortest path should be [0, 2], since that has a |
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427 # very small weight. |
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428 length = nx.dijkstra_path_length(G, 0, 2, weight=weight) |
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429 assert length == 1 / 10 |
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430 |
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431 |
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432 class TestMultiSourceDijkstra: |
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433 """Unit tests for the multi-source dialect of Dijkstra's shortest |
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434 path algorithms. |
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435 |
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436 """ |
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437 |
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438 def test_no_sources(self): |
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439 with pytest.raises(ValueError): |
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440 nx.multi_source_dijkstra(nx.Graph(), {}) |
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441 |
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442 def test_path_no_sources(self): |
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443 with pytest.raises(ValueError): |
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444 nx.multi_source_dijkstra_path(nx.Graph(), {}) |
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445 |
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446 def test_path_length_no_sources(self): |
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447 with pytest.raises(ValueError): |
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448 nx.multi_source_dijkstra_path_length(nx.Graph(), {}) |
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449 |
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450 def test_absent_source(self): |
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451 G = nx.path_graph(2) |
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452 for fn in ( |
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453 nx.multi_source_dijkstra_path, |
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454 nx.multi_source_dijkstra_path_length, |
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455 nx.multi_source_dijkstra, |
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456 ): |
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457 pytest.raises(nx.NodeNotFound, fn, G, [3], 0) |
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458 |
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459 def test_two_sources(self): |
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460 edges = [(0, 1, 1), (1, 2, 1), (2, 3, 10), (3, 4, 1)] |
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461 G = nx.Graph() |
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462 G.add_weighted_edges_from(edges) |
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463 sources = {0, 4} |
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464 distances, paths = nx.multi_source_dijkstra(G, sources) |
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465 expected_distances = {0: 0, 1: 1, 2: 2, 3: 1, 4: 0} |
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466 expected_paths = {0: [0], 1: [0, 1], 2: [0, 1, 2], 3: [4, 3], 4: [4]} |
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467 assert distances == expected_distances |
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468 assert paths == expected_paths |
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469 |
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470 def test_simple_paths(self): |
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471 G = nx.path_graph(4) |
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472 lengths = nx.multi_source_dijkstra_path_length(G, [0]) |
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473 assert lengths == {n: n for n in G} |
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474 paths = nx.multi_source_dijkstra_path(G, [0]) |
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475 assert paths == {n: list(range(n + 1)) for n in G} |
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476 |
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477 |
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478 class TestBellmanFordAndGoldbergRadzik(WeightedTestBase): |
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479 def test_single_node_graph(self): |
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480 G = nx.DiGraph() |
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481 G.add_node(0) |
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482 assert nx.single_source_bellman_ford_path(G, 0) == {0: [0]} |
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483 assert nx.single_source_bellman_ford_path_length(G, 0) == {0: 0} |
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484 assert nx.single_source_bellman_ford(G, 0) == ({0: 0}, {0: [0]}) |
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485 assert nx.bellman_ford_predecessor_and_distance(G, 0) == ({0: []}, {0: 0}) |
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486 assert nx.goldberg_radzik(G, 0) == ({0: None}, {0: 0}) |
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487 |
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488 def test_absent_source_bellman_ford(self): |
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489 # the check is in _bellman_ford; this provides regression testing |
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490 # against later changes to "client" Bellman-Ford functions |
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491 G = nx.path_graph(2) |
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492 for fn in ( |
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493 nx.bellman_ford_predecessor_and_distance, |
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494 nx.bellman_ford_path, |
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495 nx.bellman_ford_path_length, |
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496 nx.single_source_bellman_ford_path, |
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497 nx.single_source_bellman_ford_path_length, |
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498 nx.single_source_bellman_ford, |
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499 ): |
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500 pytest.raises(nx.NodeNotFound, fn, G, 3, 0) |
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501 |
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502 def test_absent_source_goldberg_radzik(self): |
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503 with pytest.raises(nx.NodeNotFound): |
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504 G = nx.path_graph(2) |
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505 nx.goldberg_radzik(G, 3, 0) |
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506 |
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507 def test_negative_weight_cycle_heuristic(self): |
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508 G = nx.DiGraph() |
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509 G.add_edge(0, 1, weight=-1) |
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510 G.add_edge(1, 2, weight=-1) |
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511 G.add_edge(2, 3, weight=-1) |
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512 G.add_edge(3, 0, weight=3) |
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513 assert not nx.negative_edge_cycle(G, heuristic=True) |
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514 G.add_edge(2, 0, weight=1.999) |
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515 assert nx.negative_edge_cycle(G, heuristic=True) |
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516 G.edges[2, 0]["weight"] = 2 |
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517 assert not nx.negative_edge_cycle(G, heuristic=True) |
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518 |
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519 def test_negative_weight_cycle_consistency(self): |
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520 import random |
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521 |
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522 unif = random.uniform |
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523 for random_seed in range(2): # range(20): |
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524 random.seed(random_seed) |
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525 for density in [0.1, 0.9]: # .3, .7, .9]: |
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526 for N in [1, 10, 20]: # range(1, 60 - int(30 * density)): |
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527 for max_cost in [1, 90]: # [1, 10, 40, 90]: |
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528 G = nx.binomial_graph(N, density, seed=4, directed=True) |
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529 edges = ((u, v, unif(-1, max_cost)) for u, v in G.edges) |
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530 G.add_weighted_edges_from(edges) |
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531 |
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532 no_heuristic = nx.negative_edge_cycle(G, heuristic=False) |
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533 with_heuristic = nx.negative_edge_cycle(G, heuristic=True) |
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534 assert no_heuristic == with_heuristic |
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535 |
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536 def test_negative_weight_cycle(self): |
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537 G = nx.cycle_graph(5, create_using=nx.DiGraph()) |
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538 G.add_edge(1, 2, weight=-7) |
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539 for i in range(5): |
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540 pytest.raises( |
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541 nx.NetworkXUnbounded, nx.single_source_bellman_ford_path, G, i |
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542 ) |
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543 pytest.raises( |
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544 nx.NetworkXUnbounded, nx.single_source_bellman_ford_path_length, G, i |
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545 ) |
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546 pytest.raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford, G, i) |
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547 pytest.raises( |
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548 nx.NetworkXUnbounded, nx.bellman_ford_predecessor_and_distance, G, i |
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549 ) |
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550 pytest.raises(nx.NetworkXUnbounded, nx.goldberg_radzik, G, i) |
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551 G = nx.cycle_graph(5) # undirected Graph |
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552 G.add_edge(1, 2, weight=-3) |
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553 for i in range(5): |
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554 pytest.raises( |
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555 nx.NetworkXUnbounded, nx.single_source_bellman_ford_path, G, i |
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556 ) |
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557 pytest.raises( |
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558 nx.NetworkXUnbounded, nx.single_source_bellman_ford_path_length, G, i |
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559 ) |
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560 pytest.raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford, G, i) |
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561 pytest.raises( |
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562 nx.NetworkXUnbounded, nx.bellman_ford_predecessor_and_distance, G, i |
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563 ) |
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564 pytest.raises(nx.NetworkXUnbounded, nx.goldberg_radzik, G, i) |
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565 G = nx.DiGraph([(1, 1, {"weight": -1})]) |
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566 pytest.raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford_path, G, 1) |
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567 pytest.raises( |
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568 nx.NetworkXUnbounded, nx.single_source_bellman_ford_path_length, G, 1 |
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569 ) |
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570 pytest.raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford, G, 1) |
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571 pytest.raises( |
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572 nx.NetworkXUnbounded, nx.bellman_ford_predecessor_and_distance, G, 1 |
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573 ) |
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574 pytest.raises(nx.NetworkXUnbounded, nx.goldberg_radzik, G, 1) |
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575 # no negative cycle but negative weight |
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576 G = nx.cycle_graph(5, create_using=nx.DiGraph()) |
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577 G.add_edge(1, 2, weight=-3) |
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578 assert nx.single_source_bellman_ford_path(G, 0) == { |
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579 0: [0], |
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580 1: [0, 1], |
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581 2: [0, 1, 2], |
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582 3: [0, 1, 2, 3], |
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583 4: [0, 1, 2, 3, 4], |
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584 } |
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585 assert nx.single_source_bellman_ford_path_length(G, 0) == { |
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586 0: 0, |
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587 1: 1, |
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588 2: -2, |
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589 3: -1, |
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590 4: 0, |
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591 } |
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592 assert nx.single_source_bellman_ford(G, 0) == ( |
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593 {0: 0, 1: 1, 2: -2, 3: -1, 4: 0}, |
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594 {0: [0], 1: [0, 1], 2: [0, 1, 2], 3: [0, 1, 2, 3], 4: [0, 1, 2, 3, 4]}, |
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595 ) |
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596 assert nx.bellman_ford_predecessor_and_distance(G, 0) == ( |
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597 {0: [], 1: [0], 2: [1], 3: [2], 4: [3]}, |
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598 {0: 0, 1: 1, 2: -2, 3: -1, 4: 0}, |
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599 ) |
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600 assert nx.goldberg_radzik(G, 0) == ( |
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601 {0: None, 1: 0, 2: 1, 3: 2, 4: 3}, |
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602 {0: 0, 1: 1, 2: -2, 3: -1, 4: 0}, |
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603 ) |
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604 |
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605 def test_not_connected(self): |
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606 G = nx.complete_graph(6) |
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607 G.add_edge(10, 11) |
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608 G.add_edge(10, 12) |
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609 assert nx.single_source_bellman_ford_path(G, 0) == { |
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610 0: [0], |
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611 1: [0, 1], |
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612 2: [0, 2], |
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613 3: [0, 3], |
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614 4: [0, 4], |
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615 5: [0, 5], |
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616 } |
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617 assert nx.single_source_bellman_ford_path_length(G, 0) == { |
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618 0: 0, |
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619 1: 1, |
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620 2: 1, |
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621 3: 1, |
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622 4: 1, |
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623 5: 1, |
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624 } |
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625 assert nx.single_source_bellman_ford(G, 0) == ( |
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626 {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}, |
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627 {0: [0], 1: [0, 1], 2: [0, 2], 3: [0, 3], 4: [0, 4], 5: [0, 5]}, |
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628 ) |
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629 assert nx.bellman_ford_predecessor_and_distance(G, 0) == ( |
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630 {0: [], 1: [0], 2: [0], 3: [0], 4: [0], 5: [0]}, |
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631 {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}, |
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632 ) |
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633 assert nx.goldberg_radzik(G, 0) == ( |
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634 {0: None, 1: 0, 2: 0, 3: 0, 4: 0, 5: 0}, |
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635 {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}, |
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636 ) |
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637 |
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638 # not connected, with a component not containing the source that |
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639 # contains a negative cost cycle. |
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640 G = nx.complete_graph(6) |
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641 G.add_edges_from( |
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642 [ |
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643 ("A", "B", {"load": 3}), |
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644 ("B", "C", {"load": -10}), |
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645 ("C", "A", {"load": 2}), |
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646 ] |
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647 ) |
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648 assert nx.single_source_bellman_ford_path(G, 0, weight="load") == { |
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649 0: [0], |
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650 1: [0, 1], |
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651 2: [0, 2], |
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652 3: [0, 3], |
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653 4: [0, 4], |
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654 5: [0, 5], |
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655 } |
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656 assert nx.single_source_bellman_ford_path_length(G, 0, weight="load") == { |
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657 0: 0, |
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658 1: 1, |
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659 2: 1, |
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660 3: 1, |
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661 4: 1, |
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662 5: 1, |
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663 } |
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664 assert nx.single_source_bellman_ford(G, 0, weight="load") == ( |
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665 {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}, |
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666 {0: [0], 1: [0, 1], 2: [0, 2], 3: [0, 3], 4: [0, 4], 5: [0, 5]}, |
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667 ) |
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668 assert nx.bellman_ford_predecessor_and_distance(G, 0, weight="load") == ( |
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669 {0: [], 1: [0], 2: [0], 3: [0], 4: [0], 5: [0]}, |
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670 {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}, |
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671 ) |
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672 assert nx.goldberg_radzik(G, 0, weight="load") == ( |
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673 {0: None, 1: 0, 2: 0, 3: 0, 4: 0, 5: 0}, |
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674 {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}, |
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675 ) |
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676 |
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677 def test_multigraph(self): |
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678 assert nx.bellman_ford_path(self.MXG, "s", "v") == ["s", "x", "u", "v"] |
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679 assert nx.bellman_ford_path_length(self.MXG, "s", "v") == 9 |
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680 assert nx.single_source_bellman_ford_path(self.MXG, "s")["v"] == [ |
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681 "s", |
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682 "x", |
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683 "u", |
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684 "v", |
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685 ] |
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686 assert nx.single_source_bellman_ford_path_length(self.MXG, "s")["v"] == 9 |
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687 D, P = nx.single_source_bellman_ford(self.MXG, "s", target="v") |
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688 assert D == 9 |
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689 assert P == ["s", "x", "u", "v"] |
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690 P, D = nx.bellman_ford_predecessor_and_distance(self.MXG, "s") |
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691 assert P["v"] == ["u"] |
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692 assert D["v"] == 9 |
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693 P, D = nx.goldberg_radzik(self.MXG, "s") |
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694 assert P["v"] == "u" |
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695 assert D["v"] == 9 |
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696 assert nx.bellman_ford_path(self.MXG4, 0, 2) == [0, 1, 2] |
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697 assert nx.bellman_ford_path_length(self.MXG4, 0, 2) == 4 |
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698 assert nx.single_source_bellman_ford_path(self.MXG4, 0)[2] == [0, 1, 2] |
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699 assert nx.single_source_bellman_ford_path_length(self.MXG4, 0)[2] == 4 |
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700 D, P = nx.single_source_bellman_ford(self.MXG4, 0, target=2) |
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701 assert D == 4 |
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702 assert P == [0, 1, 2] |
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703 P, D = nx.bellman_ford_predecessor_and_distance(self.MXG4, 0) |
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704 assert P[2] == [1] |
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705 assert D[2] == 4 |
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706 P, D = nx.goldberg_radzik(self.MXG4, 0) |
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707 assert P[2] == 1 |
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708 assert D[2] == 4 |
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709 |
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710 def test_others(self): |
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711 assert nx.bellman_ford_path(self.XG, "s", "v") == ["s", "x", "u", "v"] |
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712 assert nx.bellman_ford_path_length(self.XG, "s", "v") == 9 |
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713 assert nx.single_source_bellman_ford_path(self.XG, "s")["v"] == [ |
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714 "s", |
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715 "x", |
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716 "u", |
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717 "v", |
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718 ] |
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719 assert nx.single_source_bellman_ford_path_length(self.XG, "s")["v"] == 9 |
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720 D, P = nx.single_source_bellman_ford(self.XG, "s", target="v") |
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721 assert D == 9 |
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722 assert P == ["s", "x", "u", "v"] |
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723 (P, D) = nx.bellman_ford_predecessor_and_distance(self.XG, "s") |
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724 assert P["v"] == ["u"] |
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725 assert D["v"] == 9 |
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726 (P, D) = nx.goldberg_radzik(self.XG, "s") |
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727 assert P["v"] == "u" |
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728 assert D["v"] == 9 |
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729 |
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730 def test_path_graph(self): |
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731 G = nx.path_graph(4) |
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732 assert nx.single_source_bellman_ford_path(G, 0) == { |
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733 0: [0], |
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734 1: [0, 1], |
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735 2: [0, 1, 2], |
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736 3: [0, 1, 2, 3], |
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737 } |
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738 assert nx.single_source_bellman_ford_path_length(G, 0) == { |
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739 0: 0, |
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740 1: 1, |
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741 2: 2, |
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742 3: 3, |
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743 } |
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744 assert nx.single_source_bellman_ford(G, 0) == ( |
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745 {0: 0, 1: 1, 2: 2, 3: 3}, |
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746 {0: [0], 1: [0, 1], 2: [0, 1, 2], 3: [0, 1, 2, 3]}, |
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747 ) |
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748 assert nx.bellman_ford_predecessor_and_distance(G, 0) == ( |
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749 {0: [], 1: [0], 2: [1], 3: [2]}, |
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750 {0: 0, 1: 1, 2: 2, 3: 3}, |
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751 ) |
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752 assert nx.goldberg_radzik(G, 0) == ( |
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753 {0: None, 1: 0, 2: 1, 3: 2}, |
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754 {0: 0, 1: 1, 2: 2, 3: 3}, |
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755 ) |
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756 assert nx.single_source_bellman_ford_path(G, 3) == { |
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757 0: [3, 2, 1, 0], |
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758 1: [3, 2, 1], |
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759 2: [3, 2], |
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760 3: [3], |
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761 } |
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762 assert nx.single_source_bellman_ford_path_length(G, 3) == { |
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763 0: 3, |
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764 1: 2, |
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765 2: 1, |
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766 3: 0, |
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767 } |
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768 assert nx.single_source_bellman_ford(G, 3) == ( |
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769 {0: 3, 1: 2, 2: 1, 3: 0}, |
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770 {0: [3, 2, 1, 0], 1: [3, 2, 1], 2: [3, 2], 3: [3]}, |
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771 ) |
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772 assert nx.bellman_ford_predecessor_and_distance(G, 3) == ( |
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773 {0: [1], 1: [2], 2: [3], 3: []}, |
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774 {0: 3, 1: 2, 2: 1, 3: 0}, |
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775 ) |
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776 assert nx.goldberg_radzik(G, 3) == ( |
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777 {0: 1, 1: 2, 2: 3, 3: None}, |
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778 {0: 3, 1: 2, 2: 1, 3: 0}, |
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779 ) |
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780 |
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781 def test_4_cycle(self): |
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782 # 4-cycle |
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783 G = nx.Graph([(0, 1), (1, 2), (2, 3), (3, 0)]) |
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784 dist, path = nx.single_source_bellman_ford(G, 0) |
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785 assert dist == {0: 0, 1: 1, 2: 2, 3: 1} |
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786 assert path[0] == [0] |
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787 assert path[1] == [0, 1] |
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788 assert path[2] in [[0, 1, 2], [0, 3, 2]] |
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789 assert path[3] == [0, 3] |
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790 |
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791 pred, dist = nx.bellman_ford_predecessor_and_distance(G, 0) |
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792 assert pred[0] == [] |
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793 assert pred[1] == [0] |
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794 assert pred[2] in [[1, 3], [3, 1]] |
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795 assert pred[3] == [0] |
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796 assert dist == {0: 0, 1: 1, 2: 2, 3: 1} |
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797 |
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798 pred, dist = nx.goldberg_radzik(G, 0) |
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799 assert pred[0] is None |
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800 assert pred[1] == 0 |
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801 assert pred[2] in [1, 3] |
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802 assert pred[3] == 0 |
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803 assert dist == {0: 0, 1: 1, 2: 2, 3: 1} |
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804 |
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805 def test_negative_weight(self): |
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806 G = nx.DiGraph() |
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807 G.add_nodes_from("abcd") |
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808 G.add_edge("a", "d", weight=0) |
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809 G.add_edge("a", "b", weight=1) |
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810 G.add_edge("b", "c", weight=-3) |
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811 G.add_edge("c", "d", weight=1) |
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812 |
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813 assert nx.bellman_ford_path(G, "a", "d") == ["a", "b", "c", "d"] |
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814 assert nx.bellman_ford_path_length(G, "a", "d") == -1 |
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815 |
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816 def test_zero_cycle_smoke(self): |
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817 D = nx.DiGraph() |
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818 D.add_weighted_edges_from([(0, 1, 1), (1, 2, 1), (2, 3, 1), (3, 1, -2)]) |
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819 |
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820 nx.bellman_ford_path(D, 1, 3) |
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821 nx.dijkstra_path(D, 1, 3) |
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822 nx.bidirectional_dijkstra(D, 1, 3) |
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823 # FIXME nx.goldberg_radzik(D, 1) |
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824 |
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825 |
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826 class TestJohnsonAlgorithm(WeightedTestBase): |
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827 def test_single_node_graph(self): |
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828 with pytest.raises(nx.NetworkXError): |
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829 G = nx.DiGraph() |
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830 G.add_node(0) |
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831 nx.johnson(G) |
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832 |
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833 def test_negative_cycle(self): |
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834 G = nx.DiGraph() |
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835 G.add_weighted_edges_from( |
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836 [ |
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837 ("0", "3", 3), |
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838 ("0", "1", -5), |
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839 ("1", "0", -5), |
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840 ("0", "2", 2), |
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841 ("1", "2", 4), |
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842 ("2", "3", 1), |
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843 ] |
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844 ) |
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845 pytest.raises(nx.NetworkXUnbounded, nx.johnson, G) |
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846 G = nx.Graph() |
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847 G.add_weighted_edges_from( |
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848 [ |
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849 ("0", "3", 3), |
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850 ("0", "1", -5), |
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851 ("1", "0", -5), |
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852 ("0", "2", 2), |
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853 ("1", "2", 4), |
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854 ("2", "3", 1), |
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855 ] |
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856 ) |
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857 pytest.raises(nx.NetworkXUnbounded, nx.johnson, G) |
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858 |
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859 def test_negative_weights(self): |
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860 G = nx.DiGraph() |
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861 G.add_weighted_edges_from( |
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862 [("0", "3", 3), ("0", "1", -5), ("0", "2", 2), ("1", "2", 4), ("2", "3", 1)] |
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863 ) |
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864 paths = nx.johnson(G) |
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865 assert paths == { |
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866 "1": {"1": ["1"], "3": ["1", "2", "3"], "2": ["1", "2"]}, |
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867 "0": { |
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868 "1": ["0", "1"], |
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869 "0": ["0"], |
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870 "3": ["0", "1", "2", "3"], |
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871 "2": ["0", "1", "2"], |
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872 }, |
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873 "3": {"3": ["3"]}, |
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874 "2": {"3": ["2", "3"], "2": ["2"]}, |
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875 } |
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876 |
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877 def test_unweighted_graph(self): |
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878 with pytest.raises(nx.NetworkXError): |
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879 G = nx.path_graph(5) |
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880 nx.johnson(G) |
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881 |
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882 def test_graphs(self): |
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883 validate_path(self.XG, "s", "v", 9, nx.johnson(self.XG)["s"]["v"]) |
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884 validate_path(self.MXG, "s", "v", 9, nx.johnson(self.MXG)["s"]["v"]) |
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885 validate_path(self.XG2, 1, 3, 4, nx.johnson(self.XG2)[1][3]) |
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886 validate_path(self.XG3, 0, 3, 15, nx.johnson(self.XG3)[0][3]) |
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887 validate_path(self.XG4, 0, 2, 4, nx.johnson(self.XG4)[0][2]) |
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888 validate_path(self.MXG4, 0, 2, 4, nx.johnson(self.MXG4)[0][2]) |