ai-content-maker/.venv/Lib/site-packages/scipy/sparse/csgraph/tests/test_matching.py

295 lines
12 KiB
Python

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, 1], [1, 1, 0, 1], [0, 0, 0, 0]],
[[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_min_weight_full_matching_large_infeasible():
# Regression test for GitHub issue #17269
a = np.asarray([
[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, 0.001, 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, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.001, 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, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.001, 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, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 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, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 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, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 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, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 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,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 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, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001],
[0.0, 0.11687445, 0.0, 0.0, 0.01319788, 0.07509257, 0.0,
0.0, 0.0, 0.74228317, 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, 0.0, 0.0, 0.81087935, 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, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.8408466, 0.0, 0.0, 0.0, 0.0, 0.01194389,
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, 0.82994211, 0.0, 0.0, 0.0, 0.11468516, 0.0, 0.0, 0.0,
0.11173505, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0],
[0.18796507, 0.0, 0.04002318, 0.0, 0.0, 0.0, 0.0, 0.0, 0.75883335,
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],
[0.0, 0.0, 0.71545464, 0.0, 0.0, 0.0, 0.0, 0.0, 0.02748488,
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],
[0.78470564, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.14829198,
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],
[0.0, 0.10870609, 0.0, 0.0, 0.0, 0.8918677, 0.0, 0.0, 0.0, 0.06306644,
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, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.63844085, 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, 0.0, 0.0, 0.7442354, 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, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09850549, 0.0, 0.0, 0.18638258,
0.2769244, 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, 0.0, 0.0, 0.0, 0.0, 0.73182464, 0.0, 0.0, 0.46443561,
0.38589284, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.29510278, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09666032, 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]
])
with pytest.raises(ValueError, match='no full matching exists'):
min_weight_full_bipartite_matching(csr_matrix(a))
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)