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

202 lines
7.2 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
from scipy.sparse.csgraph._flow import (
_add_reverse_edges, _make_edge_pointers, _make_tails
)
methods = ['edmonds_karp', 'dinic']
def test_raises_on_dense_input():
with pytest.raises(TypeError):
graph = np.array([[0, 1], [0, 0]])
maximum_flow(graph, 0, 1)
maximum_flow(graph, 0, 1, method='edmonds_karp')
def test_raises_on_csc_input():
with pytest.raises(TypeError):
graph = csc_matrix([[0, 1], [0, 0]])
maximum_flow(graph, 0, 1)
maximum_flow(graph, 0, 1, method='edmonds_karp')
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)
maximum_flow(graph, 0, 1, method='edmonds_karp')
def test_raises_on_non_square_input():
with pytest.raises(ValueError):
graph = csr_matrix([[0, 1, 2], [2, 1, 0]])
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)
maximum_flow(graph, 0, 0, method='edmonds_karp')
@pytest.mark.parametrize('method', methods)
@pytest.mark.parametrize('source', [-1, 2, 3])
def test_raises_when_source_is_out_of_bounds(source, method):
with pytest.raises(ValueError):
graph = csr_matrix([[0, 1], [0, 0]])
maximum_flow(graph, source, 1, method=method)
@pytest.mark.parametrize('method', methods)
@pytest.mark.parametrize('sink', [-1, 2, 3])
def test_raises_when_sink_is_out_of_bounds(sink, method):
with pytest.raises(ValueError):
graph = csr_matrix([[0, 1], [0, 0]])
maximum_flow(graph, 0, sink, method=method)
@pytest.mark.parametrize('method', methods)
def test_simple_graph(method):
# This graph looks as follows:
# (0) --5--> (1)
graph = csr_matrix([[0, 5], [0, 0]])
res = maximum_flow(graph, 0, 1, method=method)
assert res.flow_value == 5
expected_flow = np.array([[0, 5], [-5, 0]])
assert_array_equal(res.flow.toarray(), expected_flow)
@pytest.mark.parametrize('method', methods)
def test_bottle_neck_graph(method):
# 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, method=method)
assert res.flow_value == 3
expected_flow = np.array([[0, 3, 0], [-3, 0, 3], [0, -3, 0]])
assert_array_equal(res.flow.toarray(), expected_flow)
@pytest.mark.parametrize('method', methods)
def test_backwards_flow(method):
# 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, method=method)
assert res.flow_value == 20
expected_flow = 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.flow.toarray(), expected_flow)
@pytest.mark.parametrize('method', methods)
def test_example_from_clrs_chapter_26_1(method):
# 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, method=method)
assert res.flow_value == 23
expected_flow = 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.flow.toarray(), expected_flow)
@pytest.mark.parametrize('method', methods)
def test_disconnected_graph(method):
# 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, method=method)
assert res.flow_value == 0
expected_flow = np.zeros((4, 4), dtype=np.int32)
assert_array_equal(res.flow.toarray(), expected_flow)
@pytest.mark.parametrize('method', methods)
def test_add_reverse_edges_large_graph(method):
# Regression test for https://github.com/scipy/scipy/issues/14385
n = 100_000
indices = np.arange(1, n)
indptr = np.array(list(range(n)) + [n - 1])
data = np.ones(n - 1, dtype=np.int32)
graph = csr_matrix((data, indices, indptr), shape=(n, n))
res = maximum_flow(graph, 0, n - 1, method=method)
assert res.flow_value == 1
expected_flow = graph - graph.transpose()
assert_array_equal(res.flow.data, expected_flow.data)
assert_array_equal(res.flow.indices, expected_flow.indices)
assert_array_equal(res.flow.indptr, expected_flow.indptr)
@pytest.mark.parametrize("a,b_data_expected", [
([[]], []),
([[0], [0]], []),
([[1, 0, 2], [0, 0, 0], [0, 3, 0]], [1, 2, 0, 0, 3]),
([[9, 8, 7], [4, 5, 6], [0, 0, 0]], [9, 8, 7, 4, 5, 6, 0, 0])])
def test_add_reverse_edges(a, b_data_expected):
"""Test that the reversal of the edges of the input graph works
as expected.
"""
a = csr_matrix(a, dtype=np.int32, shape=(len(a), len(a)))
b = _add_reverse_edges(a)
assert_array_equal(b.data, b_data_expected)
@pytest.mark.parametrize("a,expected", [
([[]], []),
([[0]], []),
([[1]], [0]),
([[0, 1], [10, 0]], [1, 0]),
([[1, 0, 2], [0, 0, 3], [4, 5, 0]], [0, 3, 4, 1, 2])
])
def test_make_edge_pointers(a, expected):
a = csr_matrix(a, dtype=np.int32)
rev_edge_ptr = _make_edge_pointers(a)
assert_array_equal(rev_edge_ptr, expected)
@pytest.mark.parametrize("a,expected", [
([[]], []),
([[0]], []),
([[1]], [0]),
([[0, 1], [10, 0]], [0, 1]),
([[1, 0, 2], [0, 0, 3], [4, 5, 0]], [0, 0, 1, 2, 2])
])
def test_make_tails(a, expected):
a = csr_matrix(a, dtype=np.int32)
tails = _make_tails(a)
assert_array_equal(tails, expected)