209 lines
7.4 KiB
Python
209 lines
7.4 KiB
Python
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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from scipy.sparse.csgraph._flow import (
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_add_reverse_edges, _make_edge_pointers, _make_tails
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)
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methods = ['edmonds_karp', 'dinic']
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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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maximum_flow(graph, 0, 1, method='edmonds_karp')
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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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maximum_flow(graph, 0, 1, method='edmonds_karp')
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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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maximum_flow(graph, 0, 1, method='edmonds_karp')
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def test_raises_on_non_square_input():
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with pytest.raises(ValueError):
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graph = csr_matrix([[0, 1, 2], [2, 1, 0]])
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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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maximum_flow(graph, 0, 0, method='edmonds_karp')
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@pytest.mark.parametrize('method', methods)
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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, method):
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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, method=method)
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@pytest.mark.parametrize('method', methods)
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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, method):
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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, method=method)
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@pytest.mark.parametrize('method', methods)
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def test_simple_graph(method):
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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, method=method)
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assert res.flow_value == 5
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expected_flow = np.array([[0, 5], [-5, 0]])
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assert_array_equal(res.flow.toarray(), expected_flow)
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@pytest.mark.parametrize('method', methods)
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def test_bottle_neck_graph(method):
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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, method=method)
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assert res.flow_value == 3
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expected_flow = np.array([[0, 3, 0], [-3, 0, 3], [0, -3, 0]])
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assert_array_equal(res.flow.toarray(), expected_flow)
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@pytest.mark.parametrize('method', methods)
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def test_backwards_flow(method):
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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, method=method)
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assert res.flow_value == 20
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expected_flow = 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.flow.toarray(), expected_flow)
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@pytest.mark.parametrize('method', methods)
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def test_example_from_clrs_chapter_26_1(method):
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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, method=method)
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assert res.flow_value == 23
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expected_flow = 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.flow.toarray(), expected_flow)
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@pytest.mark.parametrize('method', methods)
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def test_disconnected_graph(method):
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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, method=method)
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assert res.flow_value == 0
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expected_flow = np.zeros((4, 4), dtype=np.int32)
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assert_array_equal(res.flow.toarray(), expected_flow)
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@pytest.mark.parametrize('method', methods)
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def test_add_reverse_edges_large_graph(method):
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# Regression test for https://github.com/scipy/scipy/issues/14385
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n = 100_000
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indices = np.arange(1, n)
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indptr = np.array(list(range(n)) + [n - 1])
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data = np.ones(n - 1, dtype=np.int32)
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graph = csr_matrix((data, indices, indptr), shape=(n, n))
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res = maximum_flow(graph, 0, n - 1, method=method)
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assert res.flow_value == 1
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expected_flow = graph - graph.transpose()
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assert_array_equal(res.flow.data, expected_flow.data)
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assert_array_equal(res.flow.indices, expected_flow.indices)
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assert_array_equal(res.flow.indptr, expected_flow.indptr)
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def test_residual_raises_deprecation_warning():
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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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with pytest.deprecated_call():
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res.residual
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@pytest.mark.parametrize("a,b_data_expected", [
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([[]], []),
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([[0], [0]], []),
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([[1, 0, 2], [0, 0, 0], [0, 3, 0]], [1, 2, 0, 0, 3]),
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([[9, 8, 7], [4, 5, 6], [0, 0, 0]], [9, 8, 7, 4, 5, 6, 0, 0])])
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def test_add_reverse_edges(a, b_data_expected):
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"""Test that the reversal of the edges of the input graph works
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as expected.
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"""
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a = csr_matrix(a, dtype=np.int32, shape=(len(a), len(a)))
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b = _add_reverse_edges(a)
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assert_array_equal(b.data, b_data_expected)
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@pytest.mark.parametrize("a,expected", [
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([[]], []),
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([[0]], []),
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([[1]], [0]),
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([[0, 1], [10, 0]], [1, 0]),
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([[1, 0, 2], [0, 0, 3], [4, 5, 0]], [0, 3, 4, 1, 2])
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])
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def test_make_edge_pointers(a, expected):
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a = csr_matrix(a, dtype=np.int32)
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rev_edge_ptr = _make_edge_pointers(a)
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assert_array_equal(rev_edge_ptr, expected)
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@pytest.mark.parametrize("a,expected", [
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([[]], []),
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([[0]], []),
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([[1]], [0]),
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([[0, 1], [10, 0]], [0, 1]),
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([[1, 0, 2], [0, 0, 3], [4, 5, 0]], [0, 0, 1, 2, 2])
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])
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def test_make_tails(a, expected):
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a = csr_matrix(a, dtype=np.int32)
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tails = _make_tails(a)
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assert_array_equal(tails, expected)
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