Mercurial > repos > shellac > sam_consensus_v3
view env/lib/python3.9/site-packages/networkx/linalg/tests/test_laplacian.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
| author | shellac |
|---|---|
| date | Mon, 22 Mar 2021 18:12:50 +0000 |
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import pytest np = pytest.importorskip("numpy") npt = pytest.importorskip("numpy.testing") pytest.importorskip("scipy") import networkx as nx from networkx.generators.degree_seq import havel_hakimi_graph from networkx.generators.expanders import margulis_gabber_galil_graph class TestLaplacian: @classmethod def setup_class(cls): deg = [3, 2, 2, 1, 0] cls.G = havel_hakimi_graph(deg) cls.WG = nx.Graph( (u, v, {"weight": 0.5, "other": 0.3}) for (u, v) in cls.G.edges() ) cls.WG.add_node(4) cls.MG = nx.MultiGraph(cls.G) # Graph with clsloops cls.Gsl = cls.G.copy() for node in cls.Gsl.nodes(): cls.Gsl.add_edge(node, node) def test_laplacian(self): "Graph Laplacian" # fmt: off NL = np.array([[3, -1, -1, -1, 0], [-1, 2, -1, 0, 0], [-1, -1, 2, 0, 0], [-1, 0, 0, 1, 0], [0, 0, 0, 0, 0]]) # fmt: on WL = 0.5 * NL OL = 0.3 * NL npt.assert_equal(nx.laplacian_matrix(self.G).todense(), NL) npt.assert_equal(nx.laplacian_matrix(self.MG).todense(), NL) npt.assert_equal( nx.laplacian_matrix(self.G, nodelist=[0, 1]).todense(), np.array([[1, -1], [-1, 1]]), ) npt.assert_equal(nx.laplacian_matrix(self.WG).todense(), WL) npt.assert_equal(nx.laplacian_matrix(self.WG, weight=None).todense(), NL) npt.assert_equal(nx.laplacian_matrix(self.WG, weight="other").todense(), OL) def test_normalized_laplacian(self): "Generalized Graph Laplacian" # fmt: off G = np.array([[ 1. , -0.408, -0.408, -0.577, 0.], [-0.408, 1. , -0.5 , 0. , 0.], [-0.408, -0.5 , 1. , 0. , 0.], [-0.577, 0. , 0. , 1. , 0.], [ 0. , 0. , 0. , 0. , 0.]]) GL = np.array([[1.00, -0.408, -0.408, -0.577, 0.00], [-0.408, 1.00, -0.50, 0.00, 0.00], [-0.408, -0.50, 1.00, 0.00, 0.00], [-0.577, 0.00, 0.00, 1.00, 0.00], [0.00, 0.00, 0.00, 0.00, 0.00]]) Lsl = np.array([[0.75, -0.2887, -0.2887, -0.3536, 0.], [-0.2887, 0.6667, -0.3333, 0., 0.], [-0.2887, -0.3333, 0.6667, 0., 0.], [-0.3536, 0., 0., 0.5, 0.], [0., 0., 0., 0., 0.]]) # fmt: on npt.assert_almost_equal( nx.normalized_laplacian_matrix(self.G, nodelist=range(5)).todense(), G, decimal=3, ) npt.assert_almost_equal( nx.normalized_laplacian_matrix(self.G).todense(), GL, decimal=3 ) npt.assert_almost_equal( nx.normalized_laplacian_matrix(self.MG).todense(), GL, decimal=3 ) npt.assert_almost_equal( nx.normalized_laplacian_matrix(self.WG).todense(), GL, decimal=3 ) npt.assert_almost_equal( nx.normalized_laplacian_matrix(self.WG, weight="other").todense(), GL, decimal=3, ) npt.assert_almost_equal( nx.normalized_laplacian_matrix(self.Gsl).todense(), Lsl, decimal=3 ) def test_directed_laplacian(self): "Directed Laplacian" # Graph used as an example in Sec. 4.1 of Langville and Meyer, # "Google's PageRank and Beyond". The graph contains dangling nodes, so # the pagerank random walk is selected by directed_laplacian G = nx.DiGraph() G.add_edges_from( ( (1, 2), (1, 3), (3, 1), (3, 2), (3, 5), (4, 5), (4, 6), (5, 4), (5, 6), (6, 4), ) ) # fmt: off GL = np.array([[0.9833, -0.2941, -0.3882, -0.0291, -0.0231, -0.0261], [-0.2941, 0.8333, -0.2339, -0.0536, -0.0589, -0.0554], [-0.3882, -0.2339, 0.9833, -0.0278, -0.0896, -0.0251], [-0.0291, -0.0536, -0.0278, 0.9833, -0.4878, -0.6675], [-0.0231, -0.0589, -0.0896, -0.4878, 0.9833, -0.2078], [-0.0261, -0.0554, -0.0251, -0.6675, -0.2078, 0.9833]]) # fmt: on L = nx.directed_laplacian_matrix(G, alpha=0.9, nodelist=sorted(G)) npt.assert_almost_equal(L, GL, decimal=3) # Make the graph strongly connected, so we can use a random and lazy walk G.add_edges_from(((2, 5), (6, 1))) # fmt: off GL = np.array([[1., -0.3062, -0.4714, 0., 0., -0.3227], [-0.3062, 1., -0.1443, 0., -0.3162, 0.], [-0.4714, -0.1443, 1., 0., -0.0913, 0.], [0., 0., 0., 1., -0.5, -0.5], [0., -0.3162, -0.0913, -0.5, 1., -0.25], [-0.3227, 0., 0., -0.5, -0.25, 1.]]) # fmt: on L = nx.directed_laplacian_matrix( G, alpha=0.9, nodelist=sorted(G), walk_type="random" ) npt.assert_almost_equal(L, GL, decimal=3) # fmt: off GL = np.array([[0.5, -0.1531, -0.2357, 0., 0., -0.1614], [-0.1531, 0.5, -0.0722, 0., -0.1581, 0.], [-0.2357, -0.0722, 0.5, 0., -0.0456, 0.], [0., 0., 0., 0.5, -0.25, -0.25], [0., -0.1581, -0.0456, -0.25, 0.5, -0.125], [-0.1614, 0., 0., -0.25, -0.125, 0.5]]) # fmt: on L = nx.directed_laplacian_matrix( G, alpha=0.9, nodelist=sorted(G), walk_type="lazy" ) npt.assert_almost_equal(L, GL, decimal=3) def test_directed_combinatorial_laplacian(self): "Directed combinatorial Laplacian" # Graph used as an example in Sec. 4.1 of Langville and Meyer, # "Google's PageRank and Beyond". The graph contains dangling nodes, so # the pagerank random walk is selected by directed_laplacian G = nx.DiGraph() G.add_edges_from( ( (1, 2), (1, 3), (3, 1), (3, 2), (3, 5), (4, 5), (4, 6), (5, 4), (5, 6), (6, 4), ) ) # fmt: off GL = np.array([[0.0366, -0.0132, -0.0153, -0.0034, -0.0020, -0.0027], [-0.0132, 0.0450, -0.0111, -0.0076, -0.0062, -0.0069], [-0.0153, -0.0111, 0.0408, -0.0035, -0.0083, -0.0027], [-0.0034, -0.0076, -0.0035, 0.3688, -0.1356, -0.2187], [-0.0020, -0.0062, -0.0083, -0.1356, 0.2026, -0.0505], [-0.0027, -0.0069, -0.0027, -0.2187, -0.0505, 0.2815]]) # fmt: on L = nx.directed_combinatorial_laplacian_matrix(G, alpha=0.9, nodelist=sorted(G)) npt.assert_almost_equal(L, GL, decimal=3) # Make the graph strongly connected, so we can use a random and lazy walk G.add_edges_from(((2, 5), (6, 1))) # fmt: off GL = np.array([[0.1395, -0.0349, -0.0465, 0, 0, -0.0581], [-0.0349, 0.0930, -0.0116, 0, -0.0465, 0], [-0.0465, -0.0116, 0.0698, 0, -0.0116, 0], [0, 0, 0, 0.2326, -0.1163, -0.1163], [0, -0.0465, -0.0116, -0.1163, 0.2326, -0.0581], [-0.0581, 0, 0, -0.1163, -0.0581, 0.2326]]) # fmt: on L = nx.directed_combinatorial_laplacian_matrix( G, alpha=0.9, nodelist=sorted(G), walk_type="random" ) npt.assert_almost_equal(L, GL, decimal=3) # fmt: off GL = np.array([[0.0698, -0.0174, -0.0233, 0, 0, -0.0291], [-0.0174, 0.0465, -0.0058, 0, -0.0233, 0], [-0.0233, -0.0058, 0.0349, 0, -0.0058, 0], [0, 0, 0, 0.1163, -0.0581, -0.0581], [0, -0.0233, -0.0058, -0.0581, 0.1163, -0.0291], [-0.0291, 0, 0, -0.0581, -0.0291, 0.1163]]) # fmt: on L = nx.directed_combinatorial_laplacian_matrix( G, alpha=0.9, nodelist=sorted(G), walk_type="lazy" ) npt.assert_almost_equal(L, GL, decimal=3) E = nx.DiGraph(margulis_gabber_galil_graph(2)) L = nx.directed_combinatorial_laplacian_matrix(E) # fmt: off expected = np.array( [[ 0.16666667, -0.08333333, -0.08333333, 0. ], [-0.08333333, 0.16666667, 0. , -0.08333333], [-0.08333333, 0. , 0.16666667, -0.08333333], [ 0. , -0.08333333, -0.08333333, 0.16666667]] ) # fmt: on npt.assert_almost_equal(L, expected, decimal=6) with pytest.raises(nx.NetworkXError): nx.directed_combinatorial_laplacian_matrix( G, walk_type="pagerank", alpha=100 ) with pytest.raises(nx.NetworkXError): nx.directed_combinatorial_laplacian_matrix(G, walk_type="silly")