145 lines
5 KiB
Python
145 lines
5 KiB
Python
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
|
|
|
|
|
|
def test_raises_on_dense_input():
|
|
with pytest.raises(TypeError):
|
|
graph = np.array([[0, 1], [0, 0]])
|
|
maximum_bipartite_matching(graph)
|
|
|
|
|
|
def test_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_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_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_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_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_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_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_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_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_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)
|