295 lines
12 KiB
Python
295 lines
12 KiB
Python
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from itertools import product
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import numpy as np
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from numpy.testing import assert_array_equal, assert_equal
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import pytest
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from scipy.sparse import csr_matrix, coo_matrix, diags
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from scipy.sparse.csgraph import (
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maximum_bipartite_matching, min_weight_full_bipartite_matching
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)
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def test_maximum_bipartite_matching_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_bipartite_matching(graph)
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def test_maximum_bipartite_matching_empty_graph():
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graph = csr_matrix((0, 0))
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x = maximum_bipartite_matching(graph, perm_type='row')
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y = maximum_bipartite_matching(graph, perm_type='column')
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expected_matching = np.array([])
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assert_array_equal(expected_matching, x)
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assert_array_equal(expected_matching, y)
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def test_maximum_bipartite_matching_empty_left_partition():
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graph = csr_matrix((2, 0))
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x = maximum_bipartite_matching(graph, perm_type='row')
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y = maximum_bipartite_matching(graph, perm_type='column')
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assert_array_equal(np.array([]), x)
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assert_array_equal(np.array([-1, -1]), y)
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def test_maximum_bipartite_matching_empty_right_partition():
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graph = csr_matrix((0, 3))
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x = maximum_bipartite_matching(graph, perm_type='row')
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y = maximum_bipartite_matching(graph, perm_type='column')
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assert_array_equal(np.array([-1, -1, -1]), x)
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assert_array_equal(np.array([]), y)
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def test_maximum_bipartite_matching_graph_with_no_edges():
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graph = csr_matrix((2, 2))
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x = maximum_bipartite_matching(graph, perm_type='row')
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y = maximum_bipartite_matching(graph, perm_type='column')
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assert_array_equal(np.array([-1, -1]), x)
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assert_array_equal(np.array([-1, -1]), y)
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def test_maximum_bipartite_matching_graph_that_causes_augmentation():
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# In this graph, column 1 is initially assigned to row 1, but it should be
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# reassigned to make room for row 2.
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graph = csr_matrix([[1, 1], [1, 0]])
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x = maximum_bipartite_matching(graph, perm_type='column')
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y = maximum_bipartite_matching(graph, perm_type='row')
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expected_matching = np.array([1, 0])
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assert_array_equal(expected_matching, x)
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assert_array_equal(expected_matching, y)
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def test_maximum_bipartite_matching_graph_with_more_rows_than_columns():
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graph = csr_matrix([[1, 1], [1, 0], [0, 1]])
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x = maximum_bipartite_matching(graph, perm_type='column')
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y = maximum_bipartite_matching(graph, perm_type='row')
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assert_array_equal(np.array([0, -1, 1]), x)
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assert_array_equal(np.array([0, 2]), y)
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def test_maximum_bipartite_matching_graph_with_more_columns_than_rows():
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graph = csr_matrix([[1, 1, 0], [0, 0, 1]])
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x = maximum_bipartite_matching(graph, perm_type='column')
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y = maximum_bipartite_matching(graph, perm_type='row')
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assert_array_equal(np.array([0, 2]), x)
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assert_array_equal(np.array([0, -1, 1]), y)
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def test_maximum_bipartite_matching_explicit_zeros_count_as_edges():
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data = [0, 0]
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indices = [1, 0]
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indptr = [0, 1, 2]
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graph = csr_matrix((data, indices, indptr), shape=(2, 2))
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x = maximum_bipartite_matching(graph, perm_type='row')
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y = maximum_bipartite_matching(graph, perm_type='column')
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expected_matching = np.array([1, 0])
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assert_array_equal(expected_matching, x)
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assert_array_equal(expected_matching, y)
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def test_maximum_bipartite_matching_feasibility_of_result():
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# This is a regression test for GitHub issue #11458
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data = np.ones(50, dtype=int)
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indices = [11, 12, 19, 22, 23, 5, 22, 3, 8, 10, 5, 6, 11, 12, 13, 5, 13,
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14, 20, 22, 3, 15, 3, 13, 14, 11, 12, 19, 22, 23, 5, 22, 3, 8,
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10, 5, 6, 11, 12, 13, 5, 13, 14, 20, 22, 3, 15, 3, 13, 14]
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indptr = [0, 5, 7, 10, 10, 15, 20, 22, 22, 23, 25, 30, 32, 35, 35, 40, 45,
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47, 47, 48, 50]
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graph = csr_matrix((data, indices, indptr), shape=(20, 25))
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x = maximum_bipartite_matching(graph, perm_type='row')
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y = maximum_bipartite_matching(graph, perm_type='column')
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assert (x != -1).sum() == 13
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assert (y != -1).sum() == 13
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# Ensure that each element of the matching is in fact an edge in the graph.
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for u, v in zip(range(graph.shape[0]), y):
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if v != -1:
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assert graph[u, v]
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for u, v in zip(x, range(graph.shape[1])):
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if u != -1:
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assert graph[u, v]
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def test_matching_large_random_graph_with_one_edge_incident_to_each_vertex():
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np.random.seed(42)
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A = diags(np.ones(25), offsets=0, format='csr')
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rand_perm = np.random.permutation(25)
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rand_perm2 = np.random.permutation(25)
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Rrow = np.arange(25)
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Rcol = rand_perm
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Rdata = np.ones(25, dtype=int)
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Rmat = coo_matrix((Rdata, (Rrow, Rcol))).tocsr()
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Crow = rand_perm2
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Ccol = np.arange(25)
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Cdata = np.ones(25, dtype=int)
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Cmat = coo_matrix((Cdata, (Crow, Ccol))).tocsr()
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# Randomly permute identity matrix
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B = Rmat * A * Cmat
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# Row permute
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perm = maximum_bipartite_matching(B, perm_type='row')
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Rrow = np.arange(25)
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Rcol = perm
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Rdata = np.ones(25, dtype=int)
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Rmat = coo_matrix((Rdata, (Rrow, Rcol))).tocsr()
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C1 = Rmat * B
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# Column permute
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perm2 = maximum_bipartite_matching(B, perm_type='column')
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Crow = perm2
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Ccol = np.arange(25)
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Cdata = np.ones(25, dtype=int)
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Cmat = coo_matrix((Cdata, (Crow, Ccol))).tocsr()
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C2 = B * Cmat
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# Should get identity matrix back
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assert_equal(any(C1.diagonal() == 0), False)
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assert_equal(any(C2.diagonal() == 0), False)
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@pytest.mark.parametrize('num_rows,num_cols', [(0, 0), (2, 0), (0, 3)])
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def test_min_weight_full_matching_trivial_graph(num_rows, num_cols):
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biadjacency_matrix = csr_matrix((num_cols, num_rows))
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row_ind, col_ind = min_weight_full_bipartite_matching(biadjacency_matrix)
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assert len(row_ind) == 0
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assert len(col_ind) == 0
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@pytest.mark.parametrize('biadjacency_matrix',
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[
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[[1, 1, 1], [1, 0, 0], [1, 0, 0]],
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[[1, 1, 1], [0, 0, 1], [0, 0, 1]],
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[[1, 0, 0, 1], [1, 1, 0, 1], [0, 0, 0, 0]],
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[[1, 0, 0], [2, 0, 0]],
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[[0, 1, 0], [0, 2, 0]],
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[[1, 0], [2, 0], [5, 0]]
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])
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def test_min_weight_full_matching_infeasible_problems(biadjacency_matrix):
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with pytest.raises(ValueError):
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min_weight_full_bipartite_matching(csr_matrix(biadjacency_matrix))
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def test_min_weight_full_matching_large_infeasible():
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# Regression test for GitHub issue #17269
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a = np.asarray([
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001],
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[0.0, 0.11687445, 0.0, 0.0, 0.01319788, 0.07509257, 0.0,
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0.0, 0.0, 0.74228317, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.81087935, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.8408466, 0.0, 0.0, 0.0, 0.0, 0.01194389,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.82994211, 0.0, 0.0, 0.0, 0.11468516, 0.0, 0.0, 0.0,
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0.11173505, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 0.0],
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[0.18796507, 0.0, 0.04002318, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75883335,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.71545464, 0.0, 0.0, 0.0, 0.0, 0.0, 0.02748488,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.78470564, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.14829198,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.10870609, 0.0, 0.0, 0.0, 0.8918677, 0.0, 0.0, 0.0, 0.06306644,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
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0.63844085, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7442354, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09850549, 0.0, 0.0, 0.18638258,
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0.2769244, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.73182464, 0.0, 0.0, 0.46443561,
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0.38589284, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
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[0.29510278, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09666032, 0.0,
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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
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])
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with pytest.raises(ValueError, match='no full matching exists'):
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min_weight_full_bipartite_matching(csr_matrix(a))
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def test_explicit_zero_causes_warning():
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with pytest.warns(UserWarning):
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biadjacency_matrix = csr_matrix(((2, 0, 3), (0, 1, 1), (0, 2, 3)))
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min_weight_full_bipartite_matching(biadjacency_matrix)
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# General test for linear sum assignment solvers to make it possible to rely
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# on the same tests for scipy.optimize.linear_sum_assignment.
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def linear_sum_assignment_assertions(
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solver, array_type, sign, test_case
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):
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cost_matrix, expected_cost = test_case
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maximize = sign == -1
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cost_matrix = sign * array_type(cost_matrix)
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expected_cost = sign * np.array(expected_cost)
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row_ind, col_ind = solver(cost_matrix, maximize=maximize)
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assert_array_equal(row_ind, np.sort(row_ind))
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assert_array_equal(expected_cost,
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np.array(cost_matrix[row_ind, col_ind]).flatten())
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cost_matrix = cost_matrix.T
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row_ind, col_ind = solver(cost_matrix, maximize=maximize)
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assert_array_equal(row_ind, np.sort(row_ind))
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assert_array_equal(np.sort(expected_cost),
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np.sort(np.array(
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cost_matrix[row_ind, col_ind])).flatten())
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linear_sum_assignment_test_cases = product(
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[-1, 1],
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[
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# Square
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([[400, 150, 400],
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[400, 450, 600],
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[300, 225, 300]],
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|
[150, 400, 300]),
|
||
|
|
|
||
|
|
# Rectangular variant
|
||
|
|
([[400, 150, 400, 1],
|
||
|
|
[400, 450, 600, 2],
|
||
|
|
[300, 225, 300, 3]],
|
||
|
|
[150, 2, 300]),
|
||
|
|
|
||
|
|
([[10, 10, 8],
|
||
|
|
[9, 8, 1],
|
||
|
|
[9, 7, 4]],
|
||
|
|
[10, 1, 7]),
|
||
|
|
|
||
|
|
# Square
|
||
|
|
([[10, 10, 8, 11],
|
||
|
|
[9, 8, 1, 1],
|
||
|
|
[9, 7, 4, 10]],
|
||
|
|
[10, 1, 4]),
|
||
|
|
|
||
|
|
# Rectangular variant
|
||
|
|
([[10, float("inf"), float("inf")],
|
||
|
|
[float("inf"), float("inf"), 1],
|
||
|
|
[float("inf"), 7, float("inf")]],
|
||
|
|
[10, 1, 7])
|
||
|
|
])
|
||
|
|
|
||
|
|
|
||
|
|
@pytest.mark.parametrize('sign,test_case', linear_sum_assignment_test_cases)
|
||
|
|
def test_min_weight_full_matching_small_inputs(sign, test_case):
|
||
|
|
linear_sum_assignment_assertions(
|
||
|
|
min_weight_full_bipartite_matching, csr_matrix, sign, test_case)
|