125 lines
4.6 KiB
Python
125 lines
4.6 KiB
Python
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
|
|
|
|
|
|
def test_raises_on_dense_input():
|
|
with pytest.raises(TypeError):
|
|
graph = np.array([[0, 1], [0, 0]])
|
|
maximum_flow(graph, 0, 1)
|
|
|
|
|
|
def test_raises_on_csc_input():
|
|
with pytest.raises(TypeError):
|
|
graph = csc_matrix([[0, 1], [0, 0]])
|
|
maximum_flow(graph, 0, 1)
|
|
|
|
|
|
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)
|
|
|
|
|
|
def test_raises_when_source_is_sink():
|
|
with pytest.raises(ValueError):
|
|
graph = csr_matrix([[0, 1], [0, 0]])
|
|
maximum_flow(graph, 0, 0)
|
|
|
|
|
|
@pytest.mark.parametrize('source', [-1, 2, 3])
|
|
def test_raises_when_source_is_out_of_bounds(source):
|
|
with pytest.raises(ValueError):
|
|
graph = csr_matrix([[0, 1], [0, 0]])
|
|
maximum_flow(graph, source, 1)
|
|
|
|
|
|
@pytest.mark.parametrize('sink', [-1, 2, 3])
|
|
def test_raises_when_sink_is_out_of_bounds(sink):
|
|
with pytest.raises(ValueError):
|
|
graph = csr_matrix([[0, 1], [0, 0]])
|
|
maximum_flow(graph, 0, sink)
|
|
|
|
|
|
def test_simple_graph():
|
|
# This graph looks as follows:
|
|
# (0) --5--> (1)
|
|
graph = csr_matrix([[0, 5], [0, 0]])
|
|
res = maximum_flow(graph, 0, 1)
|
|
assert res.flow_value == 5
|
|
expected_residual = np.array([[0, 5], [-5, 0]])
|
|
assert_array_equal(res.residual.toarray(), expected_residual)
|
|
|
|
|
|
def test_bottle_neck_graph():
|
|
# 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)
|
|
assert res.flow_value == 3
|
|
expected_residual = np.array([[0, 3, 0], [-3, 0, 3], [0, -3, 0]])
|
|
assert_array_equal(res.residual.toarray(), expected_residual)
|
|
|
|
|
|
def test_backwards_flow():
|
|
# 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)
|
|
assert res.flow_value == 20
|
|
expected_residual = 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.residual.toarray(), expected_residual)
|
|
|
|
|
|
def test_example_from_clrs_chapter_26_1():
|
|
# 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)
|
|
assert res.flow_value == 23
|
|
expected_residual = 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.residual.toarray(), expected_residual)
|
|
|
|
|
|
def test_disconnected_graph():
|
|
# 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)
|
|
assert res.flow_value == 0
|
|
expected_residual = np.zeros((4, 4), dtype=np.int32)
|
|
assert_array_equal(res.residual.toarray(), expected_residual)
|