diff options
Diffstat (limited to '.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_mincost.py')
| -rw-r--r-- | .venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_mincost.py | 476 |
1 files changed, 476 insertions, 0 deletions
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_mincost.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_mincost.py new file mode 100644 index 00000000..5b1794b1 --- /dev/null +++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/flow/tests/test_mincost.py @@ -0,0 +1,476 @@ +import bz2 +import importlib.resources +import os +import pickle + +import pytest + +import networkx as nx + + +class TestMinCostFlow: + def test_simple_digraph(self): + G = nx.DiGraph() + G.add_node("a", demand=-5) + G.add_node("d", demand=5) + G.add_edge("a", "b", weight=3, capacity=4) + G.add_edge("a", "c", weight=6, capacity=10) + G.add_edge("b", "d", weight=1, capacity=9) + G.add_edge("c", "d", weight=2, capacity=5) + flowCost, H = nx.network_simplex(G) + soln = {"a": {"b": 4, "c": 1}, "b": {"d": 4}, "c": {"d": 1}, "d": {}} + assert flowCost == 24 + assert nx.min_cost_flow_cost(G) == 24 + assert H == soln + assert nx.min_cost_flow(G) == soln + assert nx.cost_of_flow(G, H) == 24 + + flowCost, H = nx.capacity_scaling(G) + assert flowCost == 24 + assert nx.cost_of_flow(G, H) == 24 + assert H == soln + + def test_negcycle_infcap(self): + G = nx.DiGraph() + G.add_node("s", demand=-5) + G.add_node("t", demand=5) + G.add_edge("s", "a", weight=1, capacity=3) + G.add_edge("a", "b", weight=3) + G.add_edge("c", "a", weight=-6) + G.add_edge("b", "d", weight=1) + G.add_edge("d", "c", weight=-2) + G.add_edge("d", "t", weight=1, capacity=3) + pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G) + pytest.raises(nx.NetworkXUnbounded, nx.capacity_scaling, G) + + def test_sum_demands_not_zero(self): + G = nx.DiGraph() + G.add_node("s", demand=-5) + G.add_node("t", demand=4) + G.add_edge("s", "a", weight=1, capacity=3) + G.add_edge("a", "b", weight=3) + G.add_edge("a", "c", weight=-6) + G.add_edge("b", "d", weight=1) + G.add_edge("c", "d", weight=-2) + G.add_edge("d", "t", weight=1, capacity=3) + pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G) + pytest.raises(nx.NetworkXUnfeasible, nx.capacity_scaling, G) + + def test_no_flow_satisfying_demands(self): + G = nx.DiGraph() + G.add_node("s", demand=-5) + G.add_node("t", demand=5) + G.add_edge("s", "a", weight=1, capacity=3) + G.add_edge("a", "b", weight=3) + G.add_edge("a", "c", weight=-6) + G.add_edge("b", "d", weight=1) + G.add_edge("c", "d", weight=-2) + G.add_edge("d", "t", weight=1, capacity=3) + pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G) + pytest.raises(nx.NetworkXUnfeasible, nx.capacity_scaling, G) + + def test_transshipment(self): + G = nx.DiGraph() + G.add_node("a", demand=1) + G.add_node("b", demand=-2) + G.add_node("c", demand=-2) + G.add_node("d", demand=3) + G.add_node("e", demand=-4) + G.add_node("f", demand=-4) + G.add_node("g", demand=3) + G.add_node("h", demand=2) + G.add_node("r", demand=3) + G.add_edge("a", "c", weight=3) + G.add_edge("r", "a", weight=2) + G.add_edge("b", "a", weight=9) + G.add_edge("r", "c", weight=0) + G.add_edge("b", "r", weight=-6) + G.add_edge("c", "d", weight=5) + G.add_edge("e", "r", weight=4) + G.add_edge("e", "f", weight=3) + G.add_edge("h", "b", weight=4) + G.add_edge("f", "d", weight=7) + G.add_edge("f", "h", weight=12) + G.add_edge("g", "d", weight=12) + G.add_edge("f", "g", weight=-1) + G.add_edge("h", "g", weight=-10) + flowCost, H = nx.network_simplex(G) + soln = { + "a": {"c": 0}, + "b": {"a": 0, "r": 2}, + "c": {"d": 3}, + "d": {}, + "e": {"r": 3, "f": 1}, + "f": {"d": 0, "g": 3, "h": 2}, + "g": {"d": 0}, + "h": {"b": 0, "g": 0}, + "r": {"a": 1, "c": 1}, + } + assert flowCost == 41 + assert nx.min_cost_flow_cost(G) == 41 + assert H == soln + assert nx.min_cost_flow(G) == soln + assert nx.cost_of_flow(G, H) == 41 + + flowCost, H = nx.capacity_scaling(G) + assert flowCost == 41 + assert nx.cost_of_flow(G, H) == 41 + assert H == soln + + def test_max_flow_min_cost(self): + G = nx.DiGraph() + G.add_edge("s", "a", bandwidth=6) + G.add_edge("s", "c", bandwidth=10, cost=10) + G.add_edge("a", "b", cost=6) + G.add_edge("b", "d", bandwidth=8, cost=7) + G.add_edge("c", "d", cost=10) + G.add_edge("d", "t", bandwidth=5, cost=5) + soln = { + "s": {"a": 5, "c": 0}, + "a": {"b": 5}, + "b": {"d": 5}, + "c": {"d": 0}, + "d": {"t": 5}, + "t": {}, + } + flow = nx.max_flow_min_cost(G, "s", "t", capacity="bandwidth", weight="cost") + assert flow == soln + assert nx.cost_of_flow(G, flow, weight="cost") == 90 + + G.add_edge("t", "s", cost=-100) + flowCost, flow = nx.capacity_scaling(G, capacity="bandwidth", weight="cost") + G.remove_edge("t", "s") + assert flowCost == -410 + assert flow["t"]["s"] == 5 + del flow["t"]["s"] + assert flow == soln + assert nx.cost_of_flow(G, flow, weight="cost") == 90 + + def test_digraph1(self): + # From Bradley, S. P., Hax, A. C. and Magnanti, T. L. Applied + # Mathematical Programming. Addison-Wesley, 1977. + G = nx.DiGraph() + G.add_node(1, demand=-20) + G.add_node(4, demand=5) + G.add_node(5, demand=15) + G.add_edges_from( + [ + (1, 2, {"capacity": 15, "weight": 4}), + (1, 3, {"capacity": 8, "weight": 4}), + (2, 3, {"weight": 2}), + (2, 4, {"capacity": 4, "weight": 2}), + (2, 5, {"capacity": 10, "weight": 6}), + (3, 4, {"capacity": 15, "weight": 1}), + (3, 5, {"capacity": 5, "weight": 3}), + (4, 5, {"weight": 2}), + (5, 3, {"capacity": 4, "weight": 1}), + ] + ) + flowCost, H = nx.network_simplex(G) + soln = { + 1: {2: 12, 3: 8}, + 2: {3: 8, 4: 4, 5: 0}, + 3: {4: 11, 5: 5}, + 4: {5: 10}, + 5: {3: 0}, + } + assert flowCost == 150 + assert nx.min_cost_flow_cost(G) == 150 + assert H == soln + assert nx.min_cost_flow(G) == soln + assert nx.cost_of_flow(G, H) == 150 + + flowCost, H = nx.capacity_scaling(G) + assert flowCost == 150 + assert H == soln + assert nx.cost_of_flow(G, H) == 150 + + def test_digraph2(self): + # Example from ticket #430 from mfrasca. Original source: + # http://www.cs.princeton.edu/courses/archive/spr03/cs226/lectures/mincost.4up.pdf, slide 11. + G = nx.DiGraph() + G.add_edge("s", 1, capacity=12) + G.add_edge("s", 2, capacity=6) + G.add_edge("s", 3, capacity=14) + G.add_edge(1, 2, capacity=11, weight=4) + G.add_edge(2, 3, capacity=9, weight=6) + G.add_edge(1, 4, capacity=5, weight=5) + G.add_edge(1, 5, capacity=2, weight=12) + G.add_edge(2, 5, capacity=4, weight=4) + G.add_edge(2, 6, capacity=2, weight=6) + G.add_edge(3, 6, capacity=31, weight=3) + G.add_edge(4, 5, capacity=18, weight=4) + G.add_edge(5, 6, capacity=9, weight=5) + G.add_edge(4, "t", capacity=3) + G.add_edge(5, "t", capacity=7) + G.add_edge(6, "t", capacity=22) + flow = nx.max_flow_min_cost(G, "s", "t") + soln = { + 1: {2: 6, 4: 5, 5: 1}, + 2: {3: 6, 5: 4, 6: 2}, + 3: {6: 20}, + 4: {5: 2, "t": 3}, + 5: {6: 0, "t": 7}, + 6: {"t": 22}, + "s": {1: 12, 2: 6, 3: 14}, + "t": {}, + } + assert flow == soln + + G.add_edge("t", "s", weight=-100) + flowCost, flow = nx.capacity_scaling(G) + G.remove_edge("t", "s") + assert flow["t"]["s"] == 32 + assert flowCost == -3007 + del flow["t"]["s"] + assert flow == soln + assert nx.cost_of_flow(G, flow) == 193 + + def test_digraph3(self): + """Combinatorial Optimization: Algorithms and Complexity, + Papadimitriou Steiglitz at page 140 has an example, 7.1, but that + admits multiple solutions, so I alter it a bit. From ticket #430 + by mfrasca.""" + + G = nx.DiGraph() + G.add_edge("s", "a") + G["s"]["a"].update({0: 2, 1: 4}) + G.add_edge("s", "b") + G["s"]["b"].update({0: 2, 1: 1}) + G.add_edge("a", "b") + G["a"]["b"].update({0: 5, 1: 2}) + G.add_edge("a", "t") + G["a"]["t"].update({0: 1, 1: 5}) + G.add_edge("b", "a") + G["b"]["a"].update({0: 1, 1: 3}) + G.add_edge("b", "t") + G["b"]["t"].update({0: 3, 1: 2}) + + "PS.ex.7.1: testing main function" + sol = nx.max_flow_min_cost(G, "s", "t", capacity=0, weight=1) + flow = sum(v for v in sol["s"].values()) + assert 4 == flow + assert 23 == nx.cost_of_flow(G, sol, weight=1) + assert sol["s"] == {"a": 2, "b": 2} + assert sol["a"] == {"b": 1, "t": 1} + assert sol["b"] == {"a": 0, "t": 3} + assert sol["t"] == {} + + G.add_edge("t", "s") + G["t"]["s"].update({1: -100}) + flowCost, sol = nx.capacity_scaling(G, capacity=0, weight=1) + G.remove_edge("t", "s") + flow = sum(v for v in sol["s"].values()) + assert 4 == flow + assert sol["t"]["s"] == 4 + assert flowCost == -377 + del sol["t"]["s"] + assert sol["s"] == {"a": 2, "b": 2} + assert sol["a"] == {"b": 1, "t": 1} + assert sol["b"] == {"a": 0, "t": 3} + assert sol["t"] == {} + assert nx.cost_of_flow(G, sol, weight=1) == 23 + + def test_zero_capacity_edges(self): + """Address issue raised in ticket #617 by arv.""" + G = nx.DiGraph() + G.add_edges_from( + [ + (1, 2, {"capacity": 1, "weight": 1}), + (1, 5, {"capacity": 1, "weight": 1}), + (2, 3, {"capacity": 0, "weight": 1}), + (2, 5, {"capacity": 1, "weight": 1}), + (5, 3, {"capacity": 2, "weight": 1}), + (5, 4, {"capacity": 0, "weight": 1}), + (3, 4, {"capacity": 2, "weight": 1}), + ] + ) + G.nodes[1]["demand"] = -1 + G.nodes[2]["demand"] = -1 + G.nodes[4]["demand"] = 2 + + flowCost, H = nx.network_simplex(G) + soln = {1: {2: 0, 5: 1}, 2: {3: 0, 5: 1}, 3: {4: 2}, 4: {}, 5: {3: 2, 4: 0}} + assert flowCost == 6 + assert nx.min_cost_flow_cost(G) == 6 + assert H == soln + assert nx.min_cost_flow(G) == soln + assert nx.cost_of_flow(G, H) == 6 + + flowCost, H = nx.capacity_scaling(G) + assert flowCost == 6 + assert H == soln + assert nx.cost_of_flow(G, H) == 6 + + def test_digon(self): + """Check if digons are handled properly. Taken from ticket + #618 by arv.""" + nodes = [(1, {}), (2, {"demand": -4}), (3, {"demand": 4})] + edges = [ + (1, 2, {"capacity": 3, "weight": 600000}), + (2, 1, {"capacity": 2, "weight": 0}), + (2, 3, {"capacity": 5, "weight": 714285}), + (3, 2, {"capacity": 2, "weight": 0}), + ] + G = nx.DiGraph(edges) + G.add_nodes_from(nodes) + flowCost, H = nx.network_simplex(G) + soln = {1: {2: 0}, 2: {1: 0, 3: 4}, 3: {2: 0}} + assert flowCost == 2857140 + assert nx.min_cost_flow_cost(G) == 2857140 + assert H == soln + assert nx.min_cost_flow(G) == soln + assert nx.cost_of_flow(G, H) == 2857140 + + flowCost, H = nx.capacity_scaling(G) + assert flowCost == 2857140 + assert H == soln + assert nx.cost_of_flow(G, H) == 2857140 + + def test_deadend(self): + """Check if one-node cycles are handled properly. Taken from ticket + #2906 from @sshraven.""" + G = nx.DiGraph() + + G.add_nodes_from(range(5), demand=0) + G.nodes[4]["demand"] = -13 + G.nodes[3]["demand"] = 13 + + G.add_edges_from([(0, 2), (0, 3), (2, 1)], capacity=20, weight=0.1) + pytest.raises(nx.NetworkXUnfeasible, nx.min_cost_flow, G) + + def test_infinite_capacity_neg_digon(self): + """An infinite capacity negative cost digon results in an unbounded + instance.""" + nodes = [(1, {}), (2, {"demand": -4}), (3, {"demand": 4})] + edges = [ + (1, 2, {"weight": -600}), + (2, 1, {"weight": 0}), + (2, 3, {"capacity": 5, "weight": 714285}), + (3, 2, {"capacity": 2, "weight": 0}), + ] + G = nx.DiGraph(edges) + G.add_nodes_from(nodes) + pytest.raises(nx.NetworkXUnbounded, nx.network_simplex, G) + pytest.raises(nx.NetworkXUnbounded, nx.capacity_scaling, G) + + def test_finite_capacity_neg_digon(self): + """The digon should receive the maximum amount of flow it can handle. + Taken from ticket #749 by @chuongdo.""" + G = nx.DiGraph() + G.add_edge("a", "b", capacity=1, weight=-1) + G.add_edge("b", "a", capacity=1, weight=-1) + min_cost = -2 + assert nx.min_cost_flow_cost(G) == min_cost + + flowCost, H = nx.capacity_scaling(G) + assert flowCost == -2 + assert H == {"a": {"b": 1}, "b": {"a": 1}} + assert nx.cost_of_flow(G, H) == -2 + + def test_multidigraph(self): + """Multidigraphs are acceptable.""" + G = nx.MultiDiGraph() + G.add_weighted_edges_from([(1, 2, 1), (2, 3, 2)], weight="capacity") + flowCost, H = nx.network_simplex(G) + assert flowCost == 0 + assert H == {1: {2: {0: 0}}, 2: {3: {0: 0}}, 3: {}} + + flowCost, H = nx.capacity_scaling(G) + assert flowCost == 0 + assert H == {1: {2: {0: 0}}, 2: {3: {0: 0}}, 3: {}} + + def test_negative_selfloops(self): + """Negative selfloops should cause an exception if uncapacitated and + always be saturated otherwise. + """ + G = nx.DiGraph() + G.add_edge(1, 1, weight=-1) + pytest.raises(nx.NetworkXUnbounded, nx.network_simplex, G) + pytest.raises(nx.NetworkXUnbounded, nx.capacity_scaling, G) + G[1][1]["capacity"] = 2 + flowCost, H = nx.network_simplex(G) + assert flowCost == -2 + assert H == {1: {1: 2}} + flowCost, H = nx.capacity_scaling(G) + assert flowCost == -2 + assert H == {1: {1: 2}} + + G = nx.MultiDiGraph() + G.add_edge(1, 1, "x", weight=-1) + G.add_edge(1, 1, "y", weight=1) + pytest.raises(nx.NetworkXUnbounded, nx.network_simplex, G) + pytest.raises(nx.NetworkXUnbounded, nx.capacity_scaling, G) + G[1][1]["x"]["capacity"] = 2 + flowCost, H = nx.network_simplex(G) + assert flowCost == -2 + assert H == {1: {1: {"x": 2, "y": 0}}} + flowCost, H = nx.capacity_scaling(G) + assert flowCost == -2 + assert H == {1: {1: {"x": 2, "y": 0}}} + + def test_bone_shaped(self): + # From #1283 + G = nx.DiGraph() + G.add_node(0, demand=-4) + G.add_node(1, demand=2) + G.add_node(2, demand=2) + G.add_node(3, demand=4) + G.add_node(4, demand=-2) + G.add_node(5, demand=-2) + G.add_edge(0, 1, capacity=4) + G.add_edge(0, 2, capacity=4) + G.add_edge(4, 3, capacity=4) + G.add_edge(5, 3, capacity=4) + G.add_edge(0, 3, capacity=0) + flowCost, H = nx.network_simplex(G) + assert flowCost == 0 + assert H == {0: {1: 2, 2: 2, 3: 0}, 1: {}, 2: {}, 3: {}, 4: {3: 2}, 5: {3: 2}} + flowCost, H = nx.capacity_scaling(G) + assert flowCost == 0 + assert H == {0: {1: 2, 2: 2, 3: 0}, 1: {}, 2: {}, 3: {}, 4: {3: 2}, 5: {3: 2}} + + def test_exceptions(self): + G = nx.Graph() + pytest.raises(nx.NetworkXNotImplemented, nx.network_simplex, G) + pytest.raises(nx.NetworkXNotImplemented, nx.capacity_scaling, G) + G = nx.MultiGraph() + pytest.raises(nx.NetworkXNotImplemented, nx.network_simplex, G) + pytest.raises(nx.NetworkXNotImplemented, nx.capacity_scaling, G) + G = nx.DiGraph() + pytest.raises(nx.NetworkXError, nx.network_simplex, G) + # pytest.raises(nx.NetworkXError, nx.capacity_scaling, G) + G.add_node(0, demand=float("inf")) + pytest.raises(nx.NetworkXError, nx.network_simplex, G) + pytest.raises(nx.NetworkXUnfeasible, nx.capacity_scaling, G) + G.nodes[0]["demand"] = 0 + G.add_node(1, demand=0) + G.add_edge(0, 1, weight=-float("inf")) + pytest.raises(nx.NetworkXError, nx.network_simplex, G) + pytest.raises(nx.NetworkXUnfeasible, nx.capacity_scaling, G) + G[0][1]["weight"] = 0 + G.add_edge(0, 0, weight=float("inf")) + pytest.raises(nx.NetworkXError, nx.network_simplex, G) + # pytest.raises(nx.NetworkXError, nx.capacity_scaling, G) + G[0][0]["weight"] = 0 + G[0][1]["capacity"] = -1 + pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G) + # pytest.raises(nx.NetworkXUnfeasible, nx.capacity_scaling, G) + G[0][1]["capacity"] = 0 + G[0][0]["capacity"] = -1 + pytest.raises(nx.NetworkXUnfeasible, nx.network_simplex, G) + # pytest.raises(nx.NetworkXUnfeasible, nx.capacity_scaling, G) + + def test_large(self): + fname = ( + importlib.resources.files("networkx.algorithms.flow.tests") + / "netgen-2.gpickle.bz2" + ) + with bz2.BZ2File(fname, "rb") as f: + G = pickle.load(f) + flowCost, flowDict = nx.network_simplex(G) + assert 6749969302 == flowCost + assert 6749969302 == nx.cost_of_flow(G, flowDict) + flowCost, flowDict = nx.capacity_scaling(G) + assert 6749969302 == flowCost + assert 6749969302 == nx.cost_of_flow(G, flowDict) |