Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/centrality/tests/test_trophic.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 """Test trophic levels, trophic differences and trophic coherence |
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2 """ |
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3 import pytest |
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4 |
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5 np = pytest.importorskip("numpy") |
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6 |
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7 import networkx as nx |
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8 from networkx.testing import almost_equal |
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9 |
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10 |
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11 def test_trophic_levels(): |
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12 """Trivial example |
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13 """ |
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14 G = nx.DiGraph() |
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15 G.add_edge("a", "b") |
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16 G.add_edge("b", "c") |
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17 |
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18 d = nx.trophic_levels(G) |
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19 assert d == {"a": 1, "b": 2, "c": 3} |
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20 |
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21 |
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22 def test_trophic_levels_levine(): |
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23 """Example from Figure 5 in Stephen Levine (1980) J. theor. Biol. 83, |
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24 195-207 |
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25 """ |
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26 S = nx.DiGraph() |
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27 S.add_edge(1, 2, weight=1.0) |
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28 S.add_edge(1, 3, weight=0.2) |
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29 S.add_edge(1, 4, weight=0.8) |
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30 S.add_edge(2, 3, weight=0.2) |
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31 S.add_edge(2, 5, weight=0.3) |
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32 S.add_edge(4, 3, weight=0.6) |
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33 S.add_edge(4, 5, weight=0.7) |
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34 S.add_edge(5, 4, weight=0.2) |
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35 |
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36 # save copy for later, test intermediate implementation details first |
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37 S2 = S.copy() |
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38 |
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39 # drop nodes of in-degree zero |
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40 z = [nid for nid, d in S.in_degree if d == 0] |
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41 for nid in z: |
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42 S.remove_node(nid) |
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43 |
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44 # find adjacency matrix |
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45 q = nx.linalg.graphmatrix.adjacency_matrix(S).T |
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46 |
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47 # fmt: off |
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48 expected_q = np.array([ |
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49 [0, 0, 0., 0], |
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50 [0.2, 0, 0.6, 0], |
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51 [0, 0, 0, 0.2], |
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52 [0.3, 0, 0.7, 0] |
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53 ]) |
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54 # fmt: on |
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55 assert np.array_equal(q.todense(), expected_q) |
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56 |
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57 # must be square, size of number of nodes |
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58 assert len(q.shape) == 2 |
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59 assert q.shape[0] == q.shape[1] |
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60 assert q.shape[0] == len(S) |
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61 |
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62 nn = q.shape[0] |
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63 |
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64 i = np.eye(nn) |
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65 n = np.linalg.inv(i - q) |
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66 y = np.dot(np.asarray(n), np.ones(nn)) |
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67 |
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68 expected_y = np.array([1, 2.07906977, 1.46511628, 2.3255814]) |
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69 assert np.allclose(y, expected_y) |
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70 |
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71 expected_d = {1: 1, 2: 2, 3: 3.07906977, 4: 2.46511628, 5: 3.3255814} |
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72 |
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73 d = nx.trophic_levels(S2) |
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74 |
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75 for nid, level in d.items(): |
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76 expected_level = expected_d[nid] |
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77 assert almost_equal(expected_level, level) |
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78 |
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79 |
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80 def test_trophic_levels_simple(): |
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81 matrix_a = np.array([[0, 0], [1, 0]]) |
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82 G = nx.from_numpy_array(matrix_a, create_using=nx.DiGraph) |
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83 d = nx.trophic_levels(G) |
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84 assert almost_equal(d[0], 2) |
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85 assert almost_equal(d[1], 1) |
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86 |
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87 |
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88 def test_trophic_levels_more_complex(): |
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89 # fmt: off |
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90 matrix = np.array([ |
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91 [0, 1, 0, 0], |
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92 [0, 0, 1, 0], |
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93 [0, 0, 0, 1], |
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94 [0, 0, 0, 0] |
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95 ]) |
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96 # fmt: on |
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97 G = nx.from_numpy_array(matrix, create_using=nx.DiGraph) |
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98 d = nx.trophic_levels(G) |
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99 expected_result = [1, 2, 3, 4] |
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100 for ind in range(4): |
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101 assert almost_equal(d[ind], expected_result[ind]) |
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102 |
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103 # fmt: off |
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104 matrix = np.array([ |
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105 [0, 1, 1, 0], |
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106 [0, 0, 1, 1], |
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107 [0, 0, 0, 1], |
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108 [0, 0, 0, 0] |
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109 ]) |
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110 # fmt: on |
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111 G = nx.from_numpy_array(matrix, create_using=nx.DiGraph) |
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112 d = nx.trophic_levels(G) |
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113 |
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114 expected_result = [1, 2, 2.5, 3.25] |
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115 print("Calculated result: ", d) |
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116 print("Expected Result: ", expected_result) |
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117 |
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118 for ind in range(4): |
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119 assert almost_equal(d[ind], expected_result[ind]) |
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120 |
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121 |
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122 def test_trophic_levels_even_more_complex(): |
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123 # fmt: off |
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124 # Another, bigger matrix |
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125 matrix = np.array([ |
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126 [0, 0, 0, 0, 0], |
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127 [0, 1, 0, 1, 0], |
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128 [1, 0, 0, 0, 0], |
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129 [0, 1, 0, 0, 0], |
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130 [0, 0, 0, 1, 0] |
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131 ]) |
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132 # Generated this linear system using pen and paper: |
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133 K = np.array([ |
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134 [1, 0, -1, 0, 0], |
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135 [0, 0.5, 0, -0.5, 0], |
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136 [0, 0, 1, 0, 0], |
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137 [0, -0.5, 0, 1, -0.5], |
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138 [0, 0, 0, 0, 1], |
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139 ]) |
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140 # fmt: on |
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141 result_1 = np.ravel(np.matmul(np.linalg.inv(K), np.ones(5))) |
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142 G = nx.from_numpy_array(matrix, create_using=nx.DiGraph) |
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143 result_2 = nx.trophic_levels(G) |
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144 |
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145 for ind in range(5): |
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146 assert almost_equal(result_1[ind], result_2[ind]) |
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147 |
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148 |
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149 def test_trophic_levels_singular_matrix(): |
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150 """Should raise an error with graphs with only non-basal nodes |
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151 """ |
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152 matrix = np.identity(4) |
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153 G = nx.from_numpy_array(matrix, create_using=nx.DiGraph) |
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154 with pytest.raises(nx.NetworkXError) as e: |
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155 nx.trophic_levels(G) |
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156 msg = ( |
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157 "Trophic levels are only defined for graphs where every node " |
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158 + "has a path from a basal node (basal nodes are nodes with no " |
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159 + "incoming edges)." |
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160 ) |
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161 assert msg in str(e.value) |
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162 |
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163 |
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164 def test_trophic_levels_singular_with_basal(): |
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165 """Should fail to compute if there are any parts of the graph which are not |
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166 reachable from any basal node (with in-degree zero). |
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167 """ |
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168 G = nx.DiGraph() |
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169 # a has in-degree zero |
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170 G.add_edge("a", "b") |
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171 |
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172 # b is one level above a, c and d |
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173 G.add_edge("c", "b") |
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174 G.add_edge("d", "b") |
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175 |
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176 # c and d form a loop, neither are reachable from a |
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177 G.add_edge("c", "d") |
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178 G.add_edge("d", "c") |
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179 |
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180 with pytest.raises(nx.NetworkXError) as e: |
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181 nx.trophic_levels(G) |
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182 msg = ( |
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183 "Trophic levels are only defined for graphs where every node " |
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184 + "has a path from a basal node (basal nodes are nodes with no " |
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185 + "incoming edges)." |
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186 ) |
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187 assert msg in str(e.value) |
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188 |
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189 # if self-loops are allowed, smaller example: |
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190 G = nx.DiGraph() |
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191 G.add_edge("a", "b") # a has in-degree zero |
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192 G.add_edge("c", "b") # b is one level above a and c |
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193 G.add_edge("c", "c") # c has a self-loop |
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194 with pytest.raises(nx.NetworkXError) as e: |
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195 nx.trophic_levels(G) |
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196 msg = ( |
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197 "Trophic levels are only defined for graphs where every node " |
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198 + "has a path from a basal node (basal nodes are nodes with no " |
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199 + "incoming edges)." |
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200 ) |
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201 assert msg in str(e.value) |
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202 |
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203 |
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204 def test_trophic_differences(): |
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205 matrix_a = np.array([[0, 1], [0, 0]]) |
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206 G = nx.from_numpy_array(matrix_a, create_using=nx.DiGraph) |
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207 diffs = nx.trophic_differences(G) |
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208 assert almost_equal(diffs[(0, 1)], 1) |
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209 |
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210 # fmt: off |
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211 matrix_b = np.array([ |
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212 [0, 1, 1, 0], |
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213 [0, 0, 1, 1], |
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214 [0, 0, 0, 1], |
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215 [0, 0, 0, 0] |
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216 ]) |
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217 # fmt: on |
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218 G = nx.from_numpy_array(matrix_b, create_using=nx.DiGraph) |
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219 diffs = nx.trophic_differences(G) |
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220 |
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221 assert almost_equal(diffs[(0, 1)], 1) |
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222 assert almost_equal(diffs[(0, 2)], 1.5) |
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223 assert almost_equal(diffs[(1, 2)], 0.5) |
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224 assert almost_equal(diffs[(1, 3)], 1.25) |
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225 assert almost_equal(diffs[(2, 3)], 0.75) |
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226 |
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227 |
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228 def test_trophic_incoherence_parameter_no_cannibalism(): |
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229 matrix_a = np.array([[0, 1], [0, 0]]) |
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230 G = nx.from_numpy_array(matrix_a, create_using=nx.DiGraph) |
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231 q = nx.trophic_incoherence_parameter(G, cannibalism=False) |
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232 assert almost_equal(q, 0) |
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233 |
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234 # fmt: off |
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235 matrix_b = np.array([ |
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236 [0, 1, 1, 0], |
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237 [0, 0, 1, 1], |
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238 [0, 0, 0, 1], |
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239 [0, 0, 0, 0] |
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240 ]) |
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241 # fmt: on |
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242 G = nx.from_numpy_array(matrix_b, create_using=nx.DiGraph) |
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243 q = nx.trophic_incoherence_parameter(G, cannibalism=False) |
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244 assert almost_equal(q, np.std([1, 1.5, 0.5, 0.75, 1.25])) |
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245 |
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246 # fmt: off |
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247 matrix_c = np.array([ |
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248 [0, 1, 1, 0], |
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249 [0, 1, 1, 1], |
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250 [0, 0, 0, 1], |
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251 [0, 0, 0, 1] |
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252 ]) |
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253 # fmt: on |
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254 G = nx.from_numpy_array(matrix_c, create_using=nx.DiGraph) |
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255 q = nx.trophic_incoherence_parameter(G, cannibalism=False) |
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256 # Ignore the -link |
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257 assert almost_equal(q, np.std([1, 1.5, 0.5, 0.75, 1.25])) |
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258 |
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259 # no self-loops case |
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260 # fmt: off |
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261 matrix_d = np.array([ |
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262 [0, 1, 1, 0], |
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263 [0, 0, 1, 1], |
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264 [0, 0, 0, 1], |
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265 [0, 0, 0, 0] |
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266 ]) |
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267 # fmt: on |
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268 G = nx.from_numpy_array(matrix_d, create_using=nx.DiGraph) |
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269 q = nx.trophic_incoherence_parameter(G, cannibalism=False) |
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270 # Ignore the -link |
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271 assert almost_equal(q, np.std([1, 1.5, 0.5, 0.75, 1.25])) |
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272 |
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273 |
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274 def test_trophic_incoherence_parameter_cannibalism(): |
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275 matrix_a = np.array([[0, 1], [0, 0]]) |
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276 G = nx.from_numpy_array(matrix_a, create_using=nx.DiGraph) |
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277 q = nx.trophic_incoherence_parameter(G, cannibalism=True) |
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278 assert almost_equal(q, 0) |
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279 |
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280 # fmt: off |
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281 matrix_b = np.array([ |
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282 [0, 0, 0, 0, 0], |
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283 [0, 1, 0, 1, 0], |
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284 [1, 0, 0, 0, 0], |
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285 [0, 1, 0, 0, 0], |
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286 [0, 0, 0, 1, 0] |
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287 ]) |
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288 # fmt: on |
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289 G = nx.from_numpy_array(matrix_b, create_using=nx.DiGraph) |
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290 q = nx.trophic_incoherence_parameter(G, cannibalism=True) |
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291 assert almost_equal(q, 2) |
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292 |
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293 # fmt: off |
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294 matrix_c = np.array([ |
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295 [0, 1, 1, 0], |
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296 [0, 0, 1, 1], |
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297 [0, 0, 0, 1], |
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298 [0, 0, 0, 0] |
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299 ]) |
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300 # fmt: on |
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301 G = nx.from_numpy_array(matrix_c, create_using=nx.DiGraph) |
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302 q = nx.trophic_incoherence_parameter(G, cannibalism=True) |
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303 # Ignore the -link |
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304 assert almost_equal(q, np.std([1, 1.5, 0.5, 0.75, 1.25])) |