125 lines
4.6 KiB
Python
125 lines
4.6 KiB
Python
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import numpy as np
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from numpy.testing import assert_array_equal
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import pytest
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from scipy.sparse import csr_matrix, csc_matrix
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from scipy.sparse.csgraph import maximum_flow
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def test_raises_on_dense_input():
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with pytest.raises(TypeError):
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graph = np.array([[0, 1], [0, 0]])
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maximum_flow(graph, 0, 1)
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def test_raises_on_csc_input():
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with pytest.raises(TypeError):
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graph = csc_matrix([[0, 1], [0, 0]])
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maximum_flow(graph, 0, 1)
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def test_raises_on_floating_point_input():
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with pytest.raises(ValueError):
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graph = csr_matrix([[0, 1.5], [0, 0]], dtype=np.float64)
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maximum_flow(graph, 0, 1)
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def test_raises_when_source_is_sink():
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with pytest.raises(ValueError):
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graph = csr_matrix([[0, 1], [0, 0]])
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maximum_flow(graph, 0, 0)
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@pytest.mark.parametrize('source', [-1, 2, 3])
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def test_raises_when_source_is_out_of_bounds(source):
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with pytest.raises(ValueError):
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graph = csr_matrix([[0, 1], [0, 0]])
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maximum_flow(graph, source, 1)
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@pytest.mark.parametrize('sink', [-1, 2, 3])
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def test_raises_when_sink_is_out_of_bounds(sink):
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with pytest.raises(ValueError):
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graph = csr_matrix([[0, 1], [0, 0]])
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maximum_flow(graph, 0, sink)
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def test_simple_graph():
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# This graph looks as follows:
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# (0) --5--> (1)
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graph = csr_matrix([[0, 5], [0, 0]])
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res = maximum_flow(graph, 0, 1)
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assert res.flow_value == 5
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expected_residual = np.array([[0, 5], [-5, 0]])
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assert_array_equal(res.residual.toarray(), expected_residual)
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def test_bottle_neck_graph():
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# This graph cannot use the full capacity between 0 and 1:
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# (0) --5--> (1) --3--> (2)
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graph = csr_matrix([[0, 5, 0], [0, 0, 3], [0, 0, 0]])
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res = maximum_flow(graph, 0, 2)
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assert res.flow_value == 3
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expected_residual = np.array([[0, 3, 0], [-3, 0, 3], [0, -3, 0]])
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assert_array_equal(res.residual.toarray(), expected_residual)
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def test_backwards_flow():
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# This example causes backwards flow between vertices 3 and 4,
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# and so this test ensures that we handle that accordingly. See
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# https://stackoverflow.com/q/38843963/5085211
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# for more information.
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graph = csr_matrix([[0, 10, 0, 0, 10, 0, 0, 0],
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[0, 0, 10, 0, 0, 0, 0, 0],
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[0, 0, 0, 10, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, 10],
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[0, 0, 0, 10, 0, 10, 0, 0],
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[0, 0, 0, 0, 0, 0, 10, 0],
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[0, 0, 0, 0, 0, 0, 0, 10],
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[0, 0, 0, 0, 0, 0, 0, 0]])
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res = maximum_flow(graph, 0, 7)
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assert res.flow_value == 20
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expected_residual = np.array([[0, 10, 0, 0, 10, 0, 0, 0],
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[-10, 0, 10, 0, 0, 0, 0, 0],
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[0, -10, 0, 10, 0, 0, 0, 0],
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[0, 0, -10, 0, 0, 0, 0, 10],
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[-10, 0, 0, 0, 0, 10, 0, 0],
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[0, 0, 0, 0, -10, 0, 10, 0],
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[0, 0, 0, 0, 0, -10, 0, 10],
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[0, 0, 0, -10, 0, 0, -10, 0]])
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assert_array_equal(res.residual.toarray(), expected_residual)
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def test_example_from_clrs_chapter_26_1():
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# See page 659 in CLRS second edition, but note that the maximum flow
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# we find is slightly different than the one in CLRS; we push a flow of
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# 12 to v_1 instead of v_2.
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graph = csr_matrix([[0, 16, 13, 0, 0, 0],
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[0, 0, 10, 12, 0, 0],
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[0, 4, 0, 0, 14, 0],
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[0, 0, 9, 0, 0, 20],
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[0, 0, 0, 7, 0, 4],
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[0, 0, 0, 0, 0, 0]])
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res = maximum_flow(graph, 0, 5)
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assert res.flow_value == 23
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expected_residual = np.array([[0, 12, 11, 0, 0, 0],
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[-12, 0, 0, 12, 0, 0],
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[-11, 0, 0, 0, 11, 0],
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[0, -12, 0, 0, -7, 19],
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[0, 0, -11, 7, 0, 4],
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[0, 0, 0, -19, -4, 0]])
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assert_array_equal(res.residual.toarray(), expected_residual)
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def test_disconnected_graph():
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# This tests the following disconnected graph:
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# (0) --5--> (1) (2) --3--> (3)
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graph = csr_matrix([[0, 5, 0, 0],
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[0, 0, 0, 0],
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[0, 0, 9, 3],
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[0, 0, 0, 0]])
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res = maximum_flow(graph, 0, 3)
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assert res.flow_value == 0
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expected_residual = np.zeros((4, 4), dtype=np.int32)
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assert_array_equal(res.residual.toarray(), expected_residual)
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