import numpy as np from numpy.testing import assert_array_equal import pytest from scipy.sparse import csr_matrix, csc_matrix from scipy.sparse.csgraph import maximum_flow from scipy.sparse.csgraph._flow import ( _add_reverse_edges, _make_edge_pointers, _make_tails ) methods = ['edmonds_karp', 'dinic'] def test_raises_on_dense_input(): with pytest.raises(TypeError): graph = np.array([[0, 1], [0, 0]]) maximum_flow(graph, 0, 1) maximum_flow(graph, 0, 1, method='edmonds_karp') def test_raises_on_csc_input(): with pytest.raises(TypeError): graph = csc_matrix([[0, 1], [0, 0]]) maximum_flow(graph, 0, 1) maximum_flow(graph, 0, 1, method='edmonds_karp') def test_raises_on_floating_point_input(): with pytest.raises(ValueError): graph = csr_matrix([[0, 1.5], [0, 0]], dtype=np.float64) maximum_flow(graph, 0, 1) maximum_flow(graph, 0, 1, method='edmonds_karp') def test_raises_on_non_square_input(): with pytest.raises(ValueError): graph = csr_matrix([[0, 1, 2], [2, 1, 0]]) maximum_flow(graph, 0, 1) def test_raises_when_source_is_sink(): with pytest.raises(ValueError): graph = csr_matrix([[0, 1], [0, 0]]) maximum_flow(graph, 0, 0) maximum_flow(graph, 0, 0, method='edmonds_karp') @pytest.mark.parametrize('method', methods) @pytest.mark.parametrize('source', [-1, 2, 3]) def test_raises_when_source_is_out_of_bounds(source, method): with pytest.raises(ValueError): graph = csr_matrix([[0, 1], [0, 0]]) maximum_flow(graph, source, 1, method=method) @pytest.mark.parametrize('method', methods) @pytest.mark.parametrize('sink', [-1, 2, 3]) def test_raises_when_sink_is_out_of_bounds(sink, method): with pytest.raises(ValueError): graph = csr_matrix([[0, 1], [0, 0]]) maximum_flow(graph, 0, sink, method=method) @pytest.mark.parametrize('method', methods) def test_simple_graph(method): # This graph looks as follows: # (0) --5--> (1) graph = csr_matrix([[0, 5], [0, 0]]) res = maximum_flow(graph, 0, 1, method=method) assert res.flow_value == 5 expected_flow = np.array([[0, 5], [-5, 0]]) assert_array_equal(res.flow.toarray(), expected_flow) @pytest.mark.parametrize('method', methods) def test_bottle_neck_graph(method): # This graph cannot use the full capacity between 0 and 1: # (0) --5--> (1) --3--> (2) graph = csr_matrix([[0, 5, 0], [0, 0, 3], [0, 0, 0]]) res = maximum_flow(graph, 0, 2, method=method) assert res.flow_value == 3 expected_flow = np.array([[0, 3, 0], [-3, 0, 3], [0, -3, 0]]) assert_array_equal(res.flow.toarray(), expected_flow) @pytest.mark.parametrize('method', methods) def test_backwards_flow(method): # This example causes backwards flow between vertices 3 and 4, # and so this test ensures that we handle that accordingly. See # https://stackoverflow.com/q/38843963/5085211 # for more information. graph = csr_matrix([[0, 10, 0, 0, 10, 0, 0, 0], [0, 0, 10, 0, 0, 0, 0, 0], [0, 0, 0, 10, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 10], [0, 0, 0, 10, 0, 10, 0, 0], [0, 0, 0, 0, 0, 0, 10, 0], [0, 0, 0, 0, 0, 0, 0, 10], [0, 0, 0, 0, 0, 0, 0, 0]]) res = maximum_flow(graph, 0, 7, method=method) assert res.flow_value == 20 expected_flow = np.array([[0, 10, 0, 0, 10, 0, 0, 0], [-10, 0, 10, 0, 0, 0, 0, 0], [0, -10, 0, 10, 0, 0, 0, 0], [0, 0, -10, 0, 0, 0, 0, 10], [-10, 0, 0, 0, 0, 10, 0, 0], [0, 0, 0, 0, -10, 0, 10, 0], [0, 0, 0, 0, 0, -10, 0, 10], [0, 0, 0, -10, 0, 0, -10, 0]]) assert_array_equal(res.flow.toarray(), expected_flow) @pytest.mark.parametrize('method', methods) def test_example_from_clrs_chapter_26_1(method): # See page 659 in CLRS second edition, but note that the maximum flow # we find is slightly different than the one in CLRS; we push a flow of # 12 to v_1 instead of v_2. graph = csr_matrix([[0, 16, 13, 0, 0, 0], [0, 0, 10, 12, 0, 0], [0, 4, 0, 0, 14, 0], [0, 0, 9, 0, 0, 20], [0, 0, 0, 7, 0, 4], [0, 0, 0, 0, 0, 0]]) res = maximum_flow(graph, 0, 5, method=method) assert res.flow_value == 23 expected_flow = np.array([[0, 12, 11, 0, 0, 0], [-12, 0, 0, 12, 0, 0], [-11, 0, 0, 0, 11, 0], [0, -12, 0, 0, -7, 19], [0, 0, -11, 7, 0, 4], [0, 0, 0, -19, -4, 0]]) assert_array_equal(res.flow.toarray(), expected_flow) @pytest.mark.parametrize('method', methods) def test_disconnected_graph(method): # This tests the following disconnected graph: # (0) --5--> (1) (2) --3--> (3) graph = csr_matrix([[0, 5, 0, 0], [0, 0, 0, 0], [0, 0, 9, 3], [0, 0, 0, 0]]) res = maximum_flow(graph, 0, 3, method=method) assert res.flow_value == 0 expected_flow = np.zeros((4, 4), dtype=np.int32) assert_array_equal(res.flow.toarray(), expected_flow) @pytest.mark.parametrize('method', methods) def test_add_reverse_edges_large_graph(method): # Regression test for https://github.com/scipy/scipy/issues/14385 n = 100_000 indices = np.arange(1, n) indptr = np.array(list(range(n)) + [n - 1]) data = np.ones(n - 1, dtype=np.int32) graph = csr_matrix((data, indices, indptr), shape=(n, n)) res = maximum_flow(graph, 0, n - 1, method=method) assert res.flow_value == 1 expected_flow = graph - graph.transpose() assert_array_equal(res.flow.data, expected_flow.data) assert_array_equal(res.flow.indices, expected_flow.indices) assert_array_equal(res.flow.indptr, expected_flow.indptr) @pytest.mark.parametrize("a,b_data_expected", [ ([[]], []), ([[0], [0]], []), ([[1, 0, 2], [0, 0, 0], [0, 3, 0]], [1, 2, 0, 0, 3]), ([[9, 8, 7], [4, 5, 6], [0, 0, 0]], [9, 8, 7, 4, 5, 6, 0, 0])]) def test_add_reverse_edges(a, b_data_expected): """Test that the reversal of the edges of the input graph works as expected. """ a = csr_matrix(a, dtype=np.int32, shape=(len(a), len(a))) b = _add_reverse_edges(a) assert_array_equal(b.data, b_data_expected) @pytest.mark.parametrize("a,expected", [ ([[]], []), ([[0]], []), ([[1]], [0]), ([[0, 1], [10, 0]], [1, 0]), ([[1, 0, 2], [0, 0, 3], [4, 5, 0]], [0, 3, 4, 1, 2]) ]) def test_make_edge_pointers(a, expected): a = csr_matrix(a, dtype=np.int32) rev_edge_ptr = _make_edge_pointers(a) assert_array_equal(rev_edge_ptr, expected) @pytest.mark.parametrize("a,expected", [ ([[]], []), ([[0]], []), ([[1]], [0]), ([[0, 1], [10, 0]], [0, 1]), ([[1, 0, 2], [0, 0, 3], [4, 5, 0]], [0, 0, 1, 2, 2]) ]) def test_make_tails(a, expected): a = csr_matrix(a, dtype=np.int32) tails = _make_tails(a) assert_array_equal(tails, expected)