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- from itertools import product
- import numpy as np
- from numpy.testing import assert_array_equal, assert_equal
- import pytest
- from scipy.sparse import csr_matrix, coo_matrix, diags
- from scipy.sparse.csgraph import (
- maximum_bipartite_matching, min_weight_full_bipartite_matching
- )
- def test_maximum_bipartite_matching_raises_on_dense_input():
- with pytest.raises(TypeError):
- graph = np.array([[0, 1], [0, 0]])
- maximum_bipartite_matching(graph)
- def test_maximum_bipartite_matching_empty_graph():
- graph = csr_matrix((0, 0))
- x = maximum_bipartite_matching(graph, perm_type='row')
- y = maximum_bipartite_matching(graph, perm_type='column')
- expected_matching = np.array([])
- assert_array_equal(expected_matching, x)
- assert_array_equal(expected_matching, y)
- def test_maximum_bipartite_matching_empty_left_partition():
- graph = csr_matrix((2, 0))
- x = maximum_bipartite_matching(graph, perm_type='row')
- y = maximum_bipartite_matching(graph, perm_type='column')
- assert_array_equal(np.array([]), x)
- assert_array_equal(np.array([-1, -1]), y)
- def test_maximum_bipartite_matching_empty_right_partition():
- graph = csr_matrix((0, 3))
- x = maximum_bipartite_matching(graph, perm_type='row')
- y = maximum_bipartite_matching(graph, perm_type='column')
- assert_array_equal(np.array([-1, -1, -1]), x)
- assert_array_equal(np.array([]), y)
- def test_maximum_bipartite_matching_graph_with_no_edges():
- graph = csr_matrix((2, 2))
- x = maximum_bipartite_matching(graph, perm_type='row')
- y = maximum_bipartite_matching(graph, perm_type='column')
- assert_array_equal(np.array([-1, -1]), x)
- assert_array_equal(np.array([-1, -1]), y)
- def test_maximum_bipartite_matching_graph_that_causes_augmentation():
- # In this graph, column 1 is initially assigned to row 1, but it should be
- # reassigned to make room for row 2.
- graph = csr_matrix([[1, 1], [1, 0]])
- x = maximum_bipartite_matching(graph, perm_type='column')
- y = maximum_bipartite_matching(graph, perm_type='row')
- expected_matching = np.array([1, 0])
- assert_array_equal(expected_matching, x)
- assert_array_equal(expected_matching, y)
- def test_maximum_bipartite_matching_graph_with_more_rows_than_columns():
- graph = csr_matrix([[1, 1], [1, 0], [0, 1]])
- x = maximum_bipartite_matching(graph, perm_type='column')
- y = maximum_bipartite_matching(graph, perm_type='row')
- assert_array_equal(np.array([0, -1, 1]), x)
- assert_array_equal(np.array([0, 2]), y)
- def test_maximum_bipartite_matching_graph_with_more_columns_than_rows():
- graph = csr_matrix([[1, 1, 0], [0, 0, 1]])
- x = maximum_bipartite_matching(graph, perm_type='column')
- y = maximum_bipartite_matching(graph, perm_type='row')
- assert_array_equal(np.array([0, 2]), x)
- assert_array_equal(np.array([0, -1, 1]), y)
- def test_maximum_bipartite_matching_explicit_zeros_count_as_edges():
- data = [0, 0]
- indices = [1, 0]
- indptr = [0, 1, 2]
- graph = csr_matrix((data, indices, indptr), shape=(2, 2))
- x = maximum_bipartite_matching(graph, perm_type='row')
- y = maximum_bipartite_matching(graph, perm_type='column')
- expected_matching = np.array([1, 0])
- assert_array_equal(expected_matching, x)
- assert_array_equal(expected_matching, y)
- def test_maximum_bipartite_matching_feasibility_of_result():
- # This is a regression test for GitHub issue #11458
- data = np.ones(50, dtype=int)
- indices = [11, 12, 19, 22, 23, 5, 22, 3, 8, 10, 5, 6, 11, 12, 13, 5, 13,
- 14, 20, 22, 3, 15, 3, 13, 14, 11, 12, 19, 22, 23, 5, 22, 3, 8,
- 10, 5, 6, 11, 12, 13, 5, 13, 14, 20, 22, 3, 15, 3, 13, 14]
- indptr = [0, 5, 7, 10, 10, 15, 20, 22, 22, 23, 25, 30, 32, 35, 35, 40, 45,
- 47, 47, 48, 50]
- graph = csr_matrix((data, indices, indptr), shape=(20, 25))
- x = maximum_bipartite_matching(graph, perm_type='row')
- y = maximum_bipartite_matching(graph, perm_type='column')
- assert (x != -1).sum() == 13
- assert (y != -1).sum() == 13
- # Ensure that each element of the matching is in fact an edge in the graph.
- for u, v in zip(range(graph.shape[0]), y):
- if v != -1:
- assert graph[u, v]
- for u, v in zip(x, range(graph.shape[1])):
- if u != -1:
- assert graph[u, v]
- def test_matching_large_random_graph_with_one_edge_incident_to_each_vertex():
- np.random.seed(42)
- A = diags(np.ones(25), offsets=0, format='csr')
- rand_perm = np.random.permutation(25)
- rand_perm2 = np.random.permutation(25)
- Rrow = np.arange(25)
- Rcol = rand_perm
- Rdata = np.ones(25, dtype=int)
- Rmat = coo_matrix((Rdata, (Rrow, Rcol))).tocsr()
- Crow = rand_perm2
- Ccol = np.arange(25)
- Cdata = np.ones(25, dtype=int)
- Cmat = coo_matrix((Cdata, (Crow, Ccol))).tocsr()
- # Randomly permute identity matrix
- B = Rmat * A * Cmat
- # Row permute
- perm = maximum_bipartite_matching(B, perm_type='row')
- Rrow = np.arange(25)
- Rcol = perm
- Rdata = np.ones(25, dtype=int)
- Rmat = coo_matrix((Rdata, (Rrow, Rcol))).tocsr()
- C1 = Rmat * B
- # Column permute
- perm2 = maximum_bipartite_matching(B, perm_type='column')
- Crow = perm2
- Ccol = np.arange(25)
- Cdata = np.ones(25, dtype=int)
- Cmat = coo_matrix((Cdata, (Crow, Ccol))).tocsr()
- C2 = B * Cmat
- # Should get identity matrix back
- assert_equal(any(C1.diagonal() == 0), False)
- assert_equal(any(C2.diagonal() == 0), False)
- @pytest.mark.parametrize('num_rows,num_cols', [(0, 0), (2, 0), (0, 3)])
- def test_min_weight_full_matching_trivial_graph(num_rows, num_cols):
- biadjacency_matrix = csr_matrix((num_cols, num_rows))
- row_ind, col_ind = min_weight_full_bipartite_matching(biadjacency_matrix)
- assert len(row_ind) == 0
- assert len(col_ind) == 0
- @pytest.mark.parametrize('biadjacency_matrix',
- [
- [[1, 1, 1], [1, 0, 0], [1, 0, 0]],
- [[1, 1, 1], [0, 0, 1], [0, 0, 1]],
- [[1, 0, 0], [2, 0, 0]],
- [[0, 1, 0], [0, 2, 0]],
- [[1, 0], [2, 0], [5, 0]]
- ])
- def test_min_weight_full_matching_infeasible_problems(biadjacency_matrix):
- with pytest.raises(ValueError):
- min_weight_full_bipartite_matching(csr_matrix(biadjacency_matrix))
- def test_explicit_zero_causes_warning():
- with pytest.warns(UserWarning):
- biadjacency_matrix = csr_matrix(((2, 0, 3), (0, 1, 1), (0, 2, 3)))
- min_weight_full_bipartite_matching(biadjacency_matrix)
- # General test for linear sum assignment solvers to make it possible to rely
- # on the same tests for scipy.optimize.linear_sum_assignment.
- def linear_sum_assignment_assertions(
- solver, array_type, sign, test_case
- ):
- cost_matrix, expected_cost = test_case
- maximize = sign == -1
- cost_matrix = sign * array_type(cost_matrix)
- expected_cost = sign * np.array(expected_cost)
- row_ind, col_ind = solver(cost_matrix, maximize=maximize)
- assert_array_equal(row_ind, np.sort(row_ind))
- assert_array_equal(expected_cost,
- np.array(cost_matrix[row_ind, col_ind]).flatten())
- cost_matrix = cost_matrix.T
- row_ind, col_ind = solver(cost_matrix, maximize=maximize)
- assert_array_equal(row_ind, np.sort(row_ind))
- assert_array_equal(np.sort(expected_cost),
- np.sort(np.array(
- cost_matrix[row_ind, col_ind])).flatten())
- linear_sum_assignment_test_cases = product(
- [-1, 1],
- [
- # Square
- ([[400, 150, 400],
- [400, 450, 600],
- [300, 225, 300]],
- [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)
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