Mercurial > repos > shellac > sam_consensus_v3
diff env/lib/python3.9/site-packages/networkx/algorithms/shortest_paths/tests/test_weighted.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
| author | shellac |
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| date | Mon, 22 Mar 2021 18:12:50 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/env/lib/python3.9/site-packages/networkx/algorithms/shortest_paths/tests/test_weighted.py Mon Mar 22 18:12:50 2021 +0000 @@ -0,0 +1,888 @@ +import pytest + +import networkx as nx +from networkx.utils import pairwise + + +def validate_path(G, s, t, soln_len, path, weight="weight"): + assert path[0] == s + assert path[-1] == t + + if callable(weight): + weight_f = weight + else: + if G.is_multigraph(): + + def weight_f(u, v, d): + return min(e.get(weight, 1) for e in d.values()) + + else: + + def weight_f(u, v, d): + return d.get(weight, 1) + + computed = sum(weight_f(u, v, G[u][v]) for u, v in pairwise(path)) + assert soln_len == computed + + +def validate_length_path(G, s, t, soln_len, length, path, weight="weight"): + assert soln_len == length + validate_path(G, s, t, length, path, weight=weight) + + +class WeightedTestBase: + """Base class for test classes that test functions for computing + shortest paths in weighted graphs. + + """ + + def setup(self): + """Creates some graphs for use in the unit tests.""" + cnlti = nx.convert_node_labels_to_integers + self.grid = cnlti(nx.grid_2d_graph(4, 4), first_label=1, ordering="sorted") + self.cycle = nx.cycle_graph(7) + self.directed_cycle = nx.cycle_graph(7, create_using=nx.DiGraph()) + self.XG = nx.DiGraph() + self.XG.add_weighted_edges_from( + [ + ("s", "u", 10), + ("s", "x", 5), + ("u", "v", 1), + ("u", "x", 2), + ("v", "y", 1), + ("x", "u", 3), + ("x", "v", 5), + ("x", "y", 2), + ("y", "s", 7), + ("y", "v", 6), + ] + ) + self.MXG = nx.MultiDiGraph(self.XG) + self.MXG.add_edge("s", "u", weight=15) + self.XG2 = nx.DiGraph() + self.XG2.add_weighted_edges_from( + [ + [1, 4, 1], + [4, 5, 1], + [5, 6, 1], + [6, 3, 1], + [1, 3, 50], + [1, 2, 100], + [2, 3, 100], + ] + ) + + self.XG3 = nx.Graph() + self.XG3.add_weighted_edges_from( + [[0, 1, 2], [1, 2, 12], [2, 3, 1], [3, 4, 5], [4, 5, 1], [5, 0, 10]] + ) + + self.XG4 = nx.Graph() + self.XG4.add_weighted_edges_from( + [ + [0, 1, 2], + [1, 2, 2], + [2, 3, 1], + [3, 4, 1], + [4, 5, 1], + [5, 6, 1], + [6, 7, 1], + [7, 0, 1], + ] + ) + self.MXG4 = nx.MultiGraph(self.XG4) + self.MXG4.add_edge(0, 1, weight=3) + self.G = nx.DiGraph() # no weights + self.G.add_edges_from( + [ + ("s", "u"), + ("s", "x"), + ("u", "v"), + ("u", "x"), + ("v", "y"), + ("x", "u"), + ("x", "v"), + ("x", "y"), + ("y", "s"), + ("y", "v"), + ] + ) + + +class TestWeightedPath(WeightedTestBase): + def test_dijkstra(self): + (D, P) = nx.single_source_dijkstra(self.XG, "s") + validate_path(self.XG, "s", "v", 9, P["v"]) + assert D["v"] == 9 + + validate_path( + self.XG, "s", "v", 9, nx.single_source_dijkstra_path(self.XG, "s")["v"] + ) + assert dict(nx.single_source_dijkstra_path_length(self.XG, "s"))["v"] == 9 + + validate_path( + self.XG, "s", "v", 9, nx.single_source_dijkstra(self.XG, "s")[1]["v"] + ) + validate_path( + self.MXG, "s", "v", 9, nx.single_source_dijkstra_path(self.MXG, "s")["v"] + ) + + GG = self.XG.to_undirected() + # make sure we get lower weight + # to_undirected might choose either edge with weight 2 or weight 3 + GG["u"]["x"]["weight"] = 2 + (D, P) = nx.single_source_dijkstra(GG, "s") + validate_path(GG, "s", "v", 8, P["v"]) + assert D["v"] == 8 # uses lower weight of 2 on u<->x edge + validate_path(GG, "s", "v", 8, nx.dijkstra_path(GG, "s", "v")) + assert nx.dijkstra_path_length(GG, "s", "v") == 8 + + validate_path(self.XG2, 1, 3, 4, nx.dijkstra_path(self.XG2, 1, 3)) + validate_path(self.XG3, 0, 3, 15, nx.dijkstra_path(self.XG3, 0, 3)) + assert nx.dijkstra_path_length(self.XG3, 0, 3) == 15 + validate_path(self.XG4, 0, 2, 4, nx.dijkstra_path(self.XG4, 0, 2)) + assert nx.dijkstra_path_length(self.XG4, 0, 2) == 4 + validate_path(self.MXG4, 0, 2, 4, nx.dijkstra_path(self.MXG4, 0, 2)) + validate_path( + self.G, "s", "v", 2, nx.single_source_dijkstra(self.G, "s", "v")[1] + ) + validate_path( + self.G, "s", "v", 2, nx.single_source_dijkstra(self.G, "s")[1]["v"] + ) + + validate_path(self.G, "s", "v", 2, nx.dijkstra_path(self.G, "s", "v")) + assert nx.dijkstra_path_length(self.G, "s", "v") == 2 + + # NetworkXError: node s not reachable from moon + pytest.raises(nx.NetworkXNoPath, nx.dijkstra_path, self.G, "s", "moon") + pytest.raises(nx.NetworkXNoPath, nx.dijkstra_path_length, self.G, "s", "moon") + + validate_path(self.cycle, 0, 3, 3, nx.dijkstra_path(self.cycle, 0, 3)) + validate_path(self.cycle, 0, 4, 3, nx.dijkstra_path(self.cycle, 0, 4)) + + assert nx.single_source_dijkstra(self.cycle, 0, 0) == (0, [0]) + + def test_bidirectional_dijkstra(self): + validate_length_path( + self.XG, "s", "v", 9, *nx.bidirectional_dijkstra(self.XG, "s", "v") + ) + validate_length_path( + self.G, "s", "v", 2, *nx.bidirectional_dijkstra(self.G, "s", "v") + ) + validate_length_path( + self.cycle, 0, 3, 3, *nx.bidirectional_dijkstra(self.cycle, 0, 3) + ) + validate_length_path( + self.cycle, 0, 4, 3, *nx.bidirectional_dijkstra(self.cycle, 0, 4) + ) + validate_length_path( + self.XG3, 0, 3, 15, *nx.bidirectional_dijkstra(self.XG3, 0, 3) + ) + validate_length_path( + self.XG4, 0, 2, 4, *nx.bidirectional_dijkstra(self.XG4, 0, 2) + ) + + # need more tests here + P = nx.single_source_dijkstra_path(self.XG, "s")["v"] + validate_path( + self.XG, + "s", + "v", + sum(self.XG[u][v]["weight"] for u, v in zip(P[:-1], P[1:])), + nx.dijkstra_path(self.XG, "s", "v"), + ) + + # check absent source + G = nx.path_graph(2) + pytest.raises(nx.NodeNotFound, nx.bidirectional_dijkstra, G, 3, 0) + + def test_weight_functions(self): + def heuristic(*z): + return hash(z) + + def getpath(pred, v, s): + return [v] if v == s else getpath(pred, pred[v], s) + [v] + + def goldberg_radzik(g, s, t, weight="weight"): + pred, dist = nx.goldberg_radzik(g, s, weight=weight) + dist = dist[t] + return dist, getpath(pred, t, s) + + def astar(g, s, t, weight="weight"): + path = nx.astar_path(g, s, t, heuristic, weight=weight) + dist = nx.astar_path_length(g, s, t, heuristic, weight=weight) + return dist, path + + def vlp(G, s, t, l, F, w): + res = F(G, s, t, weight=w) + validate_length_path(G, s, t, l, *res, weight=w) + + G = self.cycle + s = 6 + t = 4 + path = [6] + list(range(t + 1)) + + def weight(u, v, _): + return 1 + v ** 2 + + length = sum(weight(u, v, None) for u, v in pairwise(path)) + vlp(G, s, t, length, nx.bidirectional_dijkstra, weight) + vlp(G, s, t, length, nx.single_source_dijkstra, weight) + vlp(G, s, t, length, nx.single_source_bellman_ford, weight) + vlp(G, s, t, length, goldberg_radzik, weight) + vlp(G, s, t, length, astar, weight) + + def weight(u, v, _): + return 2 ** (u * v) + + length = sum(weight(u, v, None) for u, v in pairwise(path)) + vlp(G, s, t, length, nx.bidirectional_dijkstra, weight) + vlp(G, s, t, length, nx.single_source_dijkstra, weight) + vlp(G, s, t, length, nx.single_source_bellman_ford, weight) + vlp(G, s, t, length, goldberg_radzik, weight) + vlp(G, s, t, length, astar, weight) + + def test_bidirectional_dijkstra_no_path(self): + with pytest.raises(nx.NetworkXNoPath): + G = nx.Graph() + nx.add_path(G, [1, 2, 3]) + nx.add_path(G, [4, 5, 6]) + path = nx.bidirectional_dijkstra(G, 1, 6) + + def test_absent_source(self): + # the check is in _dijkstra_multisource, but this will provide + # regression testing against later changes to any of the "client" + # Dijkstra or Bellman-Ford functions + G = nx.path_graph(2) + for fn in ( + nx.dijkstra_path, + nx.dijkstra_path_length, + nx.single_source_dijkstra_path, + nx.single_source_dijkstra_path_length, + nx.single_source_dijkstra, + nx.dijkstra_predecessor_and_distance, + ): + pytest.raises(nx.NodeNotFound, fn, G, 3, 0) + + def test_dijkstra_predecessor1(self): + G = nx.path_graph(4) + assert nx.dijkstra_predecessor_and_distance(G, 0) == ( + {0: [], 1: [0], 2: [1], 3: [2]}, + {0: 0, 1: 1, 2: 2, 3: 3}, + ) + + def test_dijkstra_predecessor2(self): + # 4-cycle + G = nx.Graph([(0, 1), (1, 2), (2, 3), (3, 0)]) + pred, dist = nx.dijkstra_predecessor_and_distance(G, (0)) + assert pred[0] == [] + assert pred[1] == [0] + assert pred[2] in [[1, 3], [3, 1]] + assert pred[3] == [0] + assert dist == {0: 0, 1: 1, 2: 2, 3: 1} + + def test_dijkstra_predecessor3(self): + XG = nx.DiGraph() + XG.add_weighted_edges_from( + [ + ("s", "u", 10), + ("s", "x", 5), + ("u", "v", 1), + ("u", "x", 2), + ("v", "y", 1), + ("x", "u", 3), + ("x", "v", 5), + ("x", "y", 2), + ("y", "s", 7), + ("y", "v", 6), + ] + ) + (P, D) = nx.dijkstra_predecessor_and_distance(XG, "s") + assert P["v"] == ["u"] + assert D["v"] == 9 + (P, D) = nx.dijkstra_predecessor_and_distance(XG, "s", cutoff=8) + assert "v" not in D + + def test_single_source_dijkstra_path_length(self): + pl = nx.single_source_dijkstra_path_length + assert dict(pl(self.MXG4, 0))[2] == 4 + spl = pl(self.MXG4, 0, cutoff=2) + assert 2 not in spl + + def test_bidirectional_dijkstra_multigraph(self): + G = nx.MultiGraph() + G.add_edge("a", "b", weight=10) + G.add_edge("a", "b", weight=100) + dp = nx.bidirectional_dijkstra(G, "a", "b") + assert dp == (10, ["a", "b"]) + + def test_dijkstra_pred_distance_multigraph(self): + G = nx.MultiGraph() + G.add_edge("a", "b", key="short", foo=5, weight=100) + G.add_edge("a", "b", key="long", bar=1, weight=110) + p, d = nx.dijkstra_predecessor_and_distance(G, "a") + assert p == {"a": [], "b": ["a"]} + assert d == {"a": 0, "b": 100} + + def test_negative_edge_cycle(self): + G = nx.cycle_graph(5, create_using=nx.DiGraph()) + assert not nx.negative_edge_cycle(G) + G.add_edge(8, 9, weight=-7) + G.add_edge(9, 8, weight=3) + graph_size = len(G) + assert nx.negative_edge_cycle(G) + assert graph_size == len(G) + pytest.raises(ValueError, nx.single_source_dijkstra_path_length, G, 8) + pytest.raises(ValueError, nx.single_source_dijkstra, G, 8) + pytest.raises(ValueError, nx.dijkstra_predecessor_and_distance, G, 8) + G.add_edge(9, 10) + pytest.raises(ValueError, nx.bidirectional_dijkstra, G, 8, 10) + + def test_weight_function(self): + """Tests that a callable weight is interpreted as a weight + function instead of an edge attribute. + + """ + # Create a triangle in which the edge from node 0 to node 2 has + # a large weight and the other two edges have a small weight. + G = nx.complete_graph(3) + G.adj[0][2]["weight"] = 10 + G.adj[0][1]["weight"] = 1 + G.adj[1][2]["weight"] = 1 + # The weight function will take the multiplicative inverse of + # the weights on the edges. This way, weights that were large + # before now become small and vice versa. + + def weight(u, v, d): + return 1 / d["weight"] + + # The shortest path from 0 to 2 using the actual weights on the + # edges should be [0, 1, 2]. + distance, path = nx.single_source_dijkstra(G, 0, 2) + assert distance == 2 + assert path == [0, 1, 2] + # However, with the above weight function, the shortest path + # should be [0, 2], since that has a very small weight. + distance, path = nx.single_source_dijkstra(G, 0, 2, weight=weight) + assert distance == 1 / 10 + assert path == [0, 2] + + def test_all_pairs_dijkstra_path(self): + cycle = nx.cycle_graph(7) + p = dict(nx.all_pairs_dijkstra_path(cycle)) + assert p[0][3] == [0, 1, 2, 3] + + cycle[1][2]["weight"] = 10 + p = dict(nx.all_pairs_dijkstra_path(cycle)) + assert p[0][3] == [0, 6, 5, 4, 3] + + def test_all_pairs_dijkstra_path_length(self): + cycle = nx.cycle_graph(7) + pl = dict(nx.all_pairs_dijkstra_path_length(cycle)) + assert pl[0] == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1} + + cycle[1][2]["weight"] = 10 + pl = dict(nx.all_pairs_dijkstra_path_length(cycle)) + assert pl[0] == {0: 0, 1: 1, 2: 5, 3: 4, 4: 3, 5: 2, 6: 1} + + def test_all_pairs_dijkstra(self): + cycle = nx.cycle_graph(7) + out = dict(nx.all_pairs_dijkstra(cycle)) + assert out[0][0] == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1} + assert out[0][1][3] == [0, 1, 2, 3] + + cycle[1][2]["weight"] = 10 + out = dict(nx.all_pairs_dijkstra(cycle)) + assert out[0][0] == {0: 0, 1: 1, 2: 5, 3: 4, 4: 3, 5: 2, 6: 1} + assert out[0][1][3] == [0, 6, 5, 4, 3] + + +class TestDijkstraPathLength: + """Unit tests for the :func:`networkx.dijkstra_path_length` + function. + + """ + + def test_weight_function(self): + """Tests for computing the length of the shortest path using + Dijkstra's algorithm with a user-defined weight function. + + """ + # Create a triangle in which the edge from node 0 to node 2 has + # a large weight and the other two edges have a small weight. + G = nx.complete_graph(3) + G.adj[0][2]["weight"] = 10 + G.adj[0][1]["weight"] = 1 + G.adj[1][2]["weight"] = 1 + # The weight function will take the multiplicative inverse of + # the weights on the edges. This way, weights that were large + # before now become small and vice versa. + + def weight(u, v, d): + return 1 / d["weight"] + + # The shortest path from 0 to 2 using the actual weights on the + # edges should be [0, 1, 2]. However, with the above weight + # function, the shortest path should be [0, 2], since that has a + # very small weight. + length = nx.dijkstra_path_length(G, 0, 2, weight=weight) + assert length == 1 / 10 + + +class TestMultiSourceDijkstra: + """Unit tests for the multi-source dialect of Dijkstra's shortest + path algorithms. + + """ + + def test_no_sources(self): + with pytest.raises(ValueError): + nx.multi_source_dijkstra(nx.Graph(), {}) + + def test_path_no_sources(self): + with pytest.raises(ValueError): + nx.multi_source_dijkstra_path(nx.Graph(), {}) + + def test_path_length_no_sources(self): + with pytest.raises(ValueError): + nx.multi_source_dijkstra_path_length(nx.Graph(), {}) + + def test_absent_source(self): + G = nx.path_graph(2) + for fn in ( + nx.multi_source_dijkstra_path, + nx.multi_source_dijkstra_path_length, + nx.multi_source_dijkstra, + ): + pytest.raises(nx.NodeNotFound, fn, G, [3], 0) + + def test_two_sources(self): + edges = [(0, 1, 1), (1, 2, 1), (2, 3, 10), (3, 4, 1)] + G = nx.Graph() + G.add_weighted_edges_from(edges) + sources = {0, 4} + distances, paths = nx.multi_source_dijkstra(G, sources) + expected_distances = {0: 0, 1: 1, 2: 2, 3: 1, 4: 0} + expected_paths = {0: [0], 1: [0, 1], 2: [0, 1, 2], 3: [4, 3], 4: [4]} + assert distances == expected_distances + assert paths == expected_paths + + def test_simple_paths(self): + G = nx.path_graph(4) + lengths = nx.multi_source_dijkstra_path_length(G, [0]) + assert lengths == {n: n for n in G} + paths = nx.multi_source_dijkstra_path(G, [0]) + assert paths == {n: list(range(n + 1)) for n in G} + + +class TestBellmanFordAndGoldbergRadzik(WeightedTestBase): + def test_single_node_graph(self): + G = nx.DiGraph() + G.add_node(0) + assert nx.single_source_bellman_ford_path(G, 0) == {0: [0]} + assert nx.single_source_bellman_ford_path_length(G, 0) == {0: 0} + assert nx.single_source_bellman_ford(G, 0) == ({0: 0}, {0: [0]}) + assert nx.bellman_ford_predecessor_and_distance(G, 0) == ({0: []}, {0: 0}) + assert nx.goldberg_radzik(G, 0) == ({0: None}, {0: 0}) + + def test_absent_source_bellman_ford(self): + # the check is in _bellman_ford; this provides regression testing + # against later changes to "client" Bellman-Ford functions + G = nx.path_graph(2) + for fn in ( + nx.bellman_ford_predecessor_and_distance, + nx.bellman_ford_path, + nx.bellman_ford_path_length, + nx.single_source_bellman_ford_path, + nx.single_source_bellman_ford_path_length, + nx.single_source_bellman_ford, + ): + pytest.raises(nx.NodeNotFound, fn, G, 3, 0) + + def test_absent_source_goldberg_radzik(self): + with pytest.raises(nx.NodeNotFound): + G = nx.path_graph(2) + nx.goldberg_radzik(G, 3, 0) + + def test_negative_weight_cycle_heuristic(self): + G = nx.DiGraph() + G.add_edge(0, 1, weight=-1) + G.add_edge(1, 2, weight=-1) + G.add_edge(2, 3, weight=-1) + G.add_edge(3, 0, weight=3) + assert not nx.negative_edge_cycle(G, heuristic=True) + G.add_edge(2, 0, weight=1.999) + assert nx.negative_edge_cycle(G, heuristic=True) + G.edges[2, 0]["weight"] = 2 + assert not nx.negative_edge_cycle(G, heuristic=True) + + def test_negative_weight_cycle_consistency(self): + import random + + unif = random.uniform + for random_seed in range(2): # range(20): + random.seed(random_seed) + for density in [0.1, 0.9]: # .3, .7, .9]: + for N in [1, 10, 20]: # range(1, 60 - int(30 * density)): + for max_cost in [1, 90]: # [1, 10, 40, 90]: + G = nx.binomial_graph(N, density, seed=4, directed=True) + edges = ((u, v, unif(-1, max_cost)) for u, v in G.edges) + G.add_weighted_edges_from(edges) + + no_heuristic = nx.negative_edge_cycle(G, heuristic=False) + with_heuristic = nx.negative_edge_cycle(G, heuristic=True) + assert no_heuristic == with_heuristic + + def test_negative_weight_cycle(self): + G = nx.cycle_graph(5, create_using=nx.DiGraph()) + G.add_edge(1, 2, weight=-7) + for i in range(5): + pytest.raises( + nx.NetworkXUnbounded, nx.single_source_bellman_ford_path, G, i + ) + pytest.raises( + nx.NetworkXUnbounded, nx.single_source_bellman_ford_path_length, G, i + ) + pytest.raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford, G, i) + pytest.raises( + nx.NetworkXUnbounded, nx.bellman_ford_predecessor_and_distance, G, i + ) + pytest.raises(nx.NetworkXUnbounded, nx.goldberg_radzik, G, i) + G = nx.cycle_graph(5) # undirected Graph + G.add_edge(1, 2, weight=-3) + for i in range(5): + pytest.raises( + nx.NetworkXUnbounded, nx.single_source_bellman_ford_path, G, i + ) + pytest.raises( + nx.NetworkXUnbounded, nx.single_source_bellman_ford_path_length, G, i + ) + pytest.raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford, G, i) + pytest.raises( + nx.NetworkXUnbounded, nx.bellman_ford_predecessor_and_distance, G, i + ) + pytest.raises(nx.NetworkXUnbounded, nx.goldberg_radzik, G, i) + G = nx.DiGraph([(1, 1, {"weight": -1})]) + pytest.raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford_path, G, 1) + pytest.raises( + nx.NetworkXUnbounded, nx.single_source_bellman_ford_path_length, G, 1 + ) + pytest.raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford, G, 1) + pytest.raises( + nx.NetworkXUnbounded, nx.bellman_ford_predecessor_and_distance, G, 1 + ) + pytest.raises(nx.NetworkXUnbounded, nx.goldberg_radzik, G, 1) + # no negative cycle but negative weight + G = nx.cycle_graph(5, create_using=nx.DiGraph()) + G.add_edge(1, 2, weight=-3) + assert nx.single_source_bellman_ford_path(G, 0) == { + 0: [0], + 1: [0, 1], + 2: [0, 1, 2], + 3: [0, 1, 2, 3], + 4: [0, 1, 2, 3, 4], + } + assert nx.single_source_bellman_ford_path_length(G, 0) == { + 0: 0, + 1: 1, + 2: -2, + 3: -1, + 4: 0, + } + assert nx.single_source_bellman_ford(G, 0) == ( + {0: 0, 1: 1, 2: -2, 3: -1, 4: 0}, + {0: [0], 1: [0, 1], 2: [0, 1, 2], 3: [0, 1, 2, 3], 4: [0, 1, 2, 3, 4]}, + ) + assert nx.bellman_ford_predecessor_and_distance(G, 0) == ( + {0: [], 1: [0], 2: [1], 3: [2], 4: [3]}, + {0: 0, 1: 1, 2: -2, 3: -1, 4: 0}, + ) + assert nx.goldberg_radzik(G, 0) == ( + {0: None, 1: 0, 2: 1, 3: 2, 4: 3}, + {0: 0, 1: 1, 2: -2, 3: -1, 4: 0}, + ) + + def test_not_connected(self): + G = nx.complete_graph(6) + G.add_edge(10, 11) + G.add_edge(10, 12) + assert nx.single_source_bellman_ford_path(G, 0) == { + 0: [0], + 1: [0, 1], + 2: [0, 2], + 3: [0, 3], + 4: [0, 4], + 5: [0, 5], + } + assert nx.single_source_bellman_ford_path_length(G, 0) == { + 0: 0, + 1: 1, + 2: 1, + 3: 1, + 4: 1, + 5: 1, + } + assert nx.single_source_bellman_ford(G, 0) == ( + {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}, + {0: [0], 1: [0, 1], 2: [0, 2], 3: [0, 3], 4: [0, 4], 5: [0, 5]}, + ) + assert nx.bellman_ford_predecessor_and_distance(G, 0) == ( + {0: [], 1: [0], 2: [0], 3: [0], 4: [0], 5: [0]}, + {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}, + ) + assert nx.goldberg_radzik(G, 0) == ( + {0: None, 1: 0, 2: 0, 3: 0, 4: 0, 5: 0}, + {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}, + ) + + # not connected, with a component not containing the source that + # contains a negative cost cycle. + G = nx.complete_graph(6) + G.add_edges_from( + [ + ("A", "B", {"load": 3}), + ("B", "C", {"load": -10}), + ("C", "A", {"load": 2}), + ] + ) + assert nx.single_source_bellman_ford_path(G, 0, weight="load") == { + 0: [0], + 1: [0, 1], + 2: [0, 2], + 3: [0, 3], + 4: [0, 4], + 5: [0, 5], + } + assert nx.single_source_bellman_ford_path_length(G, 0, weight="load") == { + 0: 0, + 1: 1, + 2: 1, + 3: 1, + 4: 1, + 5: 1, + } + assert nx.single_source_bellman_ford(G, 0, weight="load") == ( + {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}, + {0: [0], 1: [0, 1], 2: [0, 2], 3: [0, 3], 4: [0, 4], 5: [0, 5]}, + ) + assert nx.bellman_ford_predecessor_and_distance(G, 0, weight="load") == ( + {0: [], 1: [0], 2: [0], 3: [0], 4: [0], 5: [0]}, + {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}, + ) + assert nx.goldberg_radzik(G, 0, weight="load") == ( + {0: None, 1: 0, 2: 0, 3: 0, 4: 0, 5: 0}, + {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}, + ) + + def test_multigraph(self): + assert nx.bellman_ford_path(self.MXG, "s", "v") == ["s", "x", "u", "v"] + assert nx.bellman_ford_path_length(self.MXG, "s", "v") == 9 + assert nx.single_source_bellman_ford_path(self.MXG, "s")["v"] == [ + "s", + "x", + "u", + "v", + ] + assert nx.single_source_bellman_ford_path_length(self.MXG, "s")["v"] == 9 + D, P = nx.single_source_bellman_ford(self.MXG, "s", target="v") + assert D == 9 + assert P == ["s", "x", "u", "v"] + P, D = nx.bellman_ford_predecessor_and_distance(self.MXG, "s") + assert P["v"] == ["u"] + assert D["v"] == 9 + P, D = nx.goldberg_radzik(self.MXG, "s") + assert P["v"] == "u" + assert D["v"] == 9 + assert nx.bellman_ford_path(self.MXG4, 0, 2) == [0, 1, 2] + assert nx.bellman_ford_path_length(self.MXG4, 0, 2) == 4 + assert nx.single_source_bellman_ford_path(self.MXG4, 0)[2] == [0, 1, 2] + assert nx.single_source_bellman_ford_path_length(self.MXG4, 0)[2] == 4 + D, P = nx.single_source_bellman_ford(self.MXG4, 0, target=2) + assert D == 4 + assert P == [0, 1, 2] + P, D = nx.bellman_ford_predecessor_and_distance(self.MXG4, 0) + assert P[2] == [1] + assert D[2] == 4 + P, D = nx.goldberg_radzik(self.MXG4, 0) + assert P[2] == 1 + assert D[2] == 4 + + def test_others(self): + assert nx.bellman_ford_path(self.XG, "s", "v") == ["s", "x", "u", "v"] + assert nx.bellman_ford_path_length(self.XG, "s", "v") == 9 + assert nx.single_source_bellman_ford_path(self.XG, "s")["v"] == [ + "s", + "x", + "u", + "v", + ] + assert nx.single_source_bellman_ford_path_length(self.XG, "s")["v"] == 9 + D, P = nx.single_source_bellman_ford(self.XG, "s", target="v") + assert D == 9 + assert P == ["s", "x", "u", "v"] + (P, D) = nx.bellman_ford_predecessor_and_distance(self.XG, "s") + assert P["v"] == ["u"] + assert D["v"] == 9 + (P, D) = nx.goldberg_radzik(self.XG, "s") + assert P["v"] == "u" + assert D["v"] == 9 + + def test_path_graph(self): + G = nx.path_graph(4) + assert nx.single_source_bellman_ford_path(G, 0) == { + 0: [0], + 1: [0, 1], + 2: [0, 1, 2], + 3: [0, 1, 2, 3], + } + assert nx.single_source_bellman_ford_path_length(G, 0) == { + 0: 0, + 1: 1, + 2: 2, + 3: 3, + } + assert nx.single_source_bellman_ford(G, 0) == ( + {0: 0, 1: 1, 2: 2, 3: 3}, + {0: [0], 1: [0, 1], 2: [0, 1, 2], 3: [0, 1, 2, 3]}, + ) + assert nx.bellman_ford_predecessor_and_distance(G, 0) == ( + {0: [], 1: [0], 2: [1], 3: [2]}, + {0: 0, 1: 1, 2: 2, 3: 3}, + ) + assert nx.goldberg_radzik(G, 0) == ( + {0: None, 1: 0, 2: 1, 3: 2}, + {0: 0, 1: 1, 2: 2, 3: 3}, + ) + assert nx.single_source_bellman_ford_path(G, 3) == { + 0: [3, 2, 1, 0], + 1: [3, 2, 1], + 2: [3, 2], + 3: [3], + } + assert nx.single_source_bellman_ford_path_length(G, 3) == { + 0: 3, + 1: 2, + 2: 1, + 3: 0, + } + assert nx.single_source_bellman_ford(G, 3) == ( + {0: 3, 1: 2, 2: 1, 3: 0}, + {0: [3, 2, 1, 0], 1: [3, 2, 1], 2: [3, 2], 3: [3]}, + ) + assert nx.bellman_ford_predecessor_and_distance(G, 3) == ( + {0: [1], 1: [2], 2: [3], 3: []}, + {0: 3, 1: 2, 2: 1, 3: 0}, + ) + assert nx.goldberg_radzik(G, 3) == ( + {0: 1, 1: 2, 2: 3, 3: None}, + {0: 3, 1: 2, 2: 1, 3: 0}, + ) + + def test_4_cycle(self): + # 4-cycle + G = nx.Graph([(0, 1), (1, 2), (2, 3), (3, 0)]) + dist, path = nx.single_source_bellman_ford(G, 0) + assert dist == {0: 0, 1: 1, 2: 2, 3: 1} + assert path[0] == [0] + assert path[1] == [0, 1] + assert path[2] in [[0, 1, 2], [0, 3, 2]] + assert path[3] == [0, 3] + + pred, dist = nx.bellman_ford_predecessor_and_distance(G, 0) + assert pred[0] == [] + assert pred[1] == [0] + assert pred[2] in [[1, 3], [3, 1]] + assert pred[3] == [0] + assert dist == {0: 0, 1: 1, 2: 2, 3: 1} + + pred, dist = nx.goldberg_radzik(G, 0) + assert pred[0] is None + assert pred[1] == 0 + assert pred[2] in [1, 3] + assert pred[3] == 0 + assert dist == {0: 0, 1: 1, 2: 2, 3: 1} + + def test_negative_weight(self): + G = nx.DiGraph() + G.add_nodes_from("abcd") + G.add_edge("a", "d", weight=0) + G.add_edge("a", "b", weight=1) + G.add_edge("b", "c", weight=-3) + G.add_edge("c", "d", weight=1) + + assert nx.bellman_ford_path(G, "a", "d") == ["a", "b", "c", "d"] + assert nx.bellman_ford_path_length(G, "a", "d") == -1 + + def test_zero_cycle_smoke(self): + D = nx.DiGraph() + D.add_weighted_edges_from([(0, 1, 1), (1, 2, 1), (2, 3, 1), (3, 1, -2)]) + + nx.bellman_ford_path(D, 1, 3) + nx.dijkstra_path(D, 1, 3) + nx.bidirectional_dijkstra(D, 1, 3) + # FIXME nx.goldberg_radzik(D, 1) + + +class TestJohnsonAlgorithm(WeightedTestBase): + def test_single_node_graph(self): + with pytest.raises(nx.NetworkXError): + G = nx.DiGraph() + G.add_node(0) + nx.johnson(G) + + def test_negative_cycle(self): + G = nx.DiGraph() + G.add_weighted_edges_from( + [ + ("0", "3", 3), + ("0", "1", -5), + ("1", "0", -5), + ("0", "2", 2), + ("1", "2", 4), + ("2", "3", 1), + ] + ) + pytest.raises(nx.NetworkXUnbounded, nx.johnson, G) + G = nx.Graph() + G.add_weighted_edges_from( + [ + ("0", "3", 3), + ("0", "1", -5), + ("1", "0", -5), + ("0", "2", 2), + ("1", "2", 4), + ("2", "3", 1), + ] + ) + pytest.raises(nx.NetworkXUnbounded, nx.johnson, G) + + def test_negative_weights(self): + G = nx.DiGraph() + G.add_weighted_edges_from( + [("0", "3", 3), ("0", "1", -5), ("0", "2", 2), ("1", "2", 4), ("2", "3", 1)] + ) + paths = nx.johnson(G) + assert paths == { + "1": {"1": ["1"], "3": ["1", "2", "3"], "2": ["1", "2"]}, + "0": { + "1": ["0", "1"], + "0": ["0"], + "3": ["0", "1", "2", "3"], + "2": ["0", "1", "2"], + }, + "3": {"3": ["3"]}, + "2": {"3": ["2", "3"], "2": ["2"]}, + } + + def test_unweighted_graph(self): + with pytest.raises(nx.NetworkXError): + G = nx.path_graph(5) + nx.johnson(G) + + def test_graphs(self): + validate_path(self.XG, "s", "v", 9, nx.johnson(self.XG)["s"]["v"]) + validate_path(self.MXG, "s", "v", 9, nx.johnson(self.MXG)["s"]["v"]) + validate_path(self.XG2, 1, 3, 4, nx.johnson(self.XG2)[1][3]) + validate_path(self.XG3, 0, 3, 15, nx.johnson(self.XG3)[0][3]) + validate_path(self.XG4, 0, 2, 4, nx.johnson(self.XG4)[0][2]) + validate_path(self.MXG4, 0, 2, 4, nx.johnson(self.MXG4)[0][2])