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|
from math import sqrt
import pytest
np = pytest.importorskip("numpy")
import networkx as nx
methods = ("tracemin_pcg", "tracemin_lu", "lanczos", "lobpcg")
def test_algebraic_connectivity_tracemin_chol():
"""Test that "tracemin_chol" raises an exception."""
pytest.importorskip("scipy")
G = nx.barbell_graph(5, 4)
with pytest.raises(nx.NetworkXError):
nx.algebraic_connectivity(G, method="tracemin_chol")
def test_fiedler_vector_tracemin_chol():
"""Test that "tracemin_chol" raises an exception."""
pytest.importorskip("scipy")
G = nx.barbell_graph(5, 4)
with pytest.raises(nx.NetworkXError):
nx.fiedler_vector(G, method="tracemin_chol")
def test_spectral_ordering_tracemin_chol():
"""Test that "tracemin_chol" raises an exception."""
pytest.importorskip("scipy")
G = nx.barbell_graph(5, 4)
with pytest.raises(nx.NetworkXError):
nx.spectral_ordering(G, method="tracemin_chol")
def test_fiedler_vector_tracemin_unknown():
"""Test that "tracemin_unknown" raises an exception."""
pytest.importorskip("scipy")
G = nx.barbell_graph(5, 4)
L = nx.laplacian_matrix(G)
X = np.asarray(np.random.normal(size=(1, L.shape[0]))).T
with pytest.raises(nx.NetworkXError, match="Unknown linear system solver"):
nx.linalg.algebraicconnectivity._tracemin_fiedler(
L, X, normalized=False, tol=1e-8, method="tracemin_unknown"
)
def test_spectral_bisection():
pytest.importorskip("scipy")
G = nx.barbell_graph(3, 0)
C = nx.spectral_bisection(G)
assert C == ({0, 1, 2}, {3, 4, 5})
mapping = dict(enumerate("badfec"))
G = nx.relabel_nodes(G, mapping)
C = nx.spectral_bisection(G)
assert C == (
{mapping[0], mapping[1], mapping[2]},
{mapping[3], mapping[4], mapping[5]},
)
def check_eigenvector(A, l, x):
nx = np.linalg.norm(x)
# Check zeroness.
assert nx != pytest.approx(0, abs=1e-07)
y = A @ x
ny = np.linalg.norm(y)
# Check collinearity.
assert x @ y == pytest.approx(nx * ny, abs=1e-7)
# Check eigenvalue.
assert ny == pytest.approx(l * nx, abs=1e-7)
class TestAlgebraicConnectivity:
@pytest.mark.parametrize("method", methods)
def test_directed(self, method):
G = nx.DiGraph()
pytest.raises(
nx.NetworkXNotImplemented, nx.algebraic_connectivity, G, method=method
)
pytest.raises(nx.NetworkXNotImplemented, nx.fiedler_vector, G, method=method)
@pytest.mark.parametrize("method", methods)
def test_null_and_singleton(self, method):
G = nx.Graph()
pytest.raises(nx.NetworkXError, nx.algebraic_connectivity, G, method=method)
pytest.raises(nx.NetworkXError, nx.fiedler_vector, G, method=method)
G.add_edge(0, 0)
pytest.raises(nx.NetworkXError, nx.algebraic_connectivity, G, method=method)
pytest.raises(nx.NetworkXError, nx.fiedler_vector, G, method=method)
@pytest.mark.parametrize("method", methods)
def test_disconnected(self, method):
G = nx.Graph()
G.add_nodes_from(range(2))
assert nx.algebraic_connectivity(G) == 0
pytest.raises(nx.NetworkXError, nx.fiedler_vector, G, method=method)
G.add_edge(0, 1, weight=0)
assert nx.algebraic_connectivity(G) == 0
pytest.raises(nx.NetworkXError, nx.fiedler_vector, G, method=method)
def test_unrecognized_method(self):
pytest.importorskip("scipy")
G = nx.path_graph(4)
pytest.raises(nx.NetworkXError, nx.algebraic_connectivity, G, method="unknown")
pytest.raises(nx.NetworkXError, nx.fiedler_vector, G, method="unknown")
@pytest.mark.parametrize("method", methods)
def test_two_nodes(self, method):
pytest.importorskip("scipy")
G = nx.Graph()
G.add_edge(0, 1, weight=1)
A = nx.laplacian_matrix(G)
assert nx.algebraic_connectivity(G, tol=1e-12, method=method) == pytest.approx(
2, abs=1e-7
)
x = nx.fiedler_vector(G, tol=1e-12, method=method)
check_eigenvector(A, 2, x)
@pytest.mark.parametrize("method", methods)
def test_two_nodes_multigraph(self, method):
pytest.importorskip("scipy")
G = nx.MultiGraph()
G.add_edge(0, 0, spam=1e8)
G.add_edge(0, 1, spam=1)
G.add_edge(0, 1, spam=-2)
A = -3 * nx.laplacian_matrix(G, weight="spam")
assert nx.algebraic_connectivity(
G, weight="spam", tol=1e-12, method=method
) == pytest.approx(6, abs=1e-7)
x = nx.fiedler_vector(G, weight="spam", tol=1e-12, method=method)
check_eigenvector(A, 6, x)
def test_abbreviation_of_method(self):
pytest.importorskip("scipy")
G = nx.path_graph(8)
A = nx.laplacian_matrix(G)
sigma = 2 - sqrt(2 + sqrt(2))
ac = nx.algebraic_connectivity(G, tol=1e-12, method="tracemin")
assert ac == pytest.approx(sigma, abs=1e-7)
x = nx.fiedler_vector(G, tol=1e-12, method="tracemin")
check_eigenvector(A, sigma, x)
@pytest.mark.parametrize("method", methods)
def test_path(self, method):
pytest.importorskip("scipy")
G = nx.path_graph(8)
A = nx.laplacian_matrix(G)
sigma = 2 - sqrt(2 + sqrt(2))
ac = nx.algebraic_connectivity(G, tol=1e-12, method=method)
assert ac == pytest.approx(sigma, abs=1e-7)
x = nx.fiedler_vector(G, tol=1e-12, method=method)
check_eigenvector(A, sigma, x)
@pytest.mark.parametrize("method", methods)
def test_problematic_graph_issue_2381(self, method):
pytest.importorskip("scipy")
G = nx.path_graph(4)
G.add_edges_from([(4, 2), (5, 1)])
A = nx.laplacian_matrix(G)
sigma = 0.438447187191
ac = nx.algebraic_connectivity(G, tol=1e-12, method=method)
assert ac == pytest.approx(sigma, abs=1e-7)
x = nx.fiedler_vector(G, tol=1e-12, method=method)
check_eigenvector(A, sigma, x)
@pytest.mark.parametrize("method", methods)
def test_cycle(self, method):
pytest.importorskip("scipy")
G = nx.cycle_graph(8)
A = nx.laplacian_matrix(G)
sigma = 2 - sqrt(2)
ac = nx.algebraic_connectivity(G, tol=1e-12, method=method)
assert ac == pytest.approx(sigma, abs=1e-7)
x = nx.fiedler_vector(G, tol=1e-12, method=method)
check_eigenvector(A, sigma, x)
@pytest.mark.parametrize("method", methods)
def test_seed_argument(self, method):
pytest.importorskip("scipy")
G = nx.cycle_graph(8)
A = nx.laplacian_matrix(G)
sigma = 2 - sqrt(2)
ac = nx.algebraic_connectivity(G, tol=1e-12, method=method, seed=1)
assert ac == pytest.approx(sigma, abs=1e-7)
x = nx.fiedler_vector(G, tol=1e-12, method=method, seed=1)
check_eigenvector(A, sigma, x)
@pytest.mark.parametrize(
("normalized", "sigma", "laplacian_fn"),
(
(False, 0.2434017461399311, nx.laplacian_matrix),
(True, 0.08113391537997749, nx.normalized_laplacian_matrix),
),
)
@pytest.mark.parametrize("method", methods)
def test_buckminsterfullerene(self, normalized, sigma, laplacian_fn, method):
pytest.importorskip("scipy")
G = nx.Graph(
[
(1, 10),
(1, 41),
(1, 59),
(2, 12),
(2, 42),
(2, 60),
(3, 6),
(3, 43),
(3, 57),
(4, 8),
(4, 44),
(4, 58),
(5, 13),
(5, 56),
(5, 57),
(6, 10),
(6, 31),
(7, 14),
(7, 56),
(7, 58),
(8, 12),
(8, 32),
(9, 23),
(9, 53),
(9, 59),
(10, 15),
(11, 24),
(11, 53),
(11, 60),
(12, 16),
(13, 14),
(13, 25),
(14, 26),
(15, 27),
(15, 49),
(16, 28),
(16, 50),
(17, 18),
(17, 19),
(17, 54),
(18, 20),
(18, 55),
(19, 23),
(19, 41),
(20, 24),
(20, 42),
(21, 31),
(21, 33),
(21, 57),
(22, 32),
(22, 34),
(22, 58),
(23, 24),
(25, 35),
(25, 43),
(26, 36),
(26, 44),
(27, 51),
(27, 59),
(28, 52),
(28, 60),
(29, 33),
(29, 34),
(29, 56),
(30, 51),
(30, 52),
(30, 53),
(31, 47),
(32, 48),
(33, 45),
(34, 46),
(35, 36),
(35, 37),
(36, 38),
(37, 39),
(37, 49),
(38, 40),
(38, 50),
(39, 40),
(39, 51),
(40, 52),
(41, 47),
(42, 48),
(43, 49),
(44, 50),
(45, 46),
(45, 54),
(46, 55),
(47, 54),
(48, 55),
]
)
A = laplacian_fn(G)
try:
assert nx.algebraic_connectivity(
G, normalized=normalized, tol=1e-12, method=method
) == pytest.approx(sigma, abs=1e-7)
x = nx.fiedler_vector(G, normalized=normalized, tol=1e-12, method=method)
check_eigenvector(A, sigma, x)
except nx.NetworkXError as err:
if err.args not in (
("Cholesky solver unavailable.",),
("LU solver unavailable.",),
):
raise
class TestSpectralOrdering:
_graphs = (nx.Graph, nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)
@pytest.mark.parametrize("graph", _graphs)
def test_nullgraph(self, graph):
G = graph()
pytest.raises(nx.NetworkXError, nx.spectral_ordering, G)
@pytest.mark.parametrize("graph", _graphs)
def test_singleton(self, graph):
G = graph()
G.add_node("x")
assert nx.spectral_ordering(G) == ["x"]
G.add_edge("x", "x", weight=33)
G.add_edge("x", "x", weight=33)
assert nx.spectral_ordering(G) == ["x"]
def test_unrecognized_method(self):
G = nx.path_graph(4)
pytest.raises(nx.NetworkXError, nx.spectral_ordering, G, method="unknown")
@pytest.mark.parametrize("method", methods)
def test_three_nodes(self, method):
pytest.importorskip("scipy")
G = nx.Graph()
G.add_weighted_edges_from([(1, 2, 1), (1, 3, 2), (2, 3, 1)], weight="spam")
order = nx.spectral_ordering(G, weight="spam", method=method)
assert set(order) == set(G)
assert {1, 3} in (set(order[:-1]), set(order[1:]))
@pytest.mark.parametrize("method", methods)
def test_three_nodes_multigraph(self, method):
pytest.importorskip("scipy")
G = nx.MultiDiGraph()
G.add_weighted_edges_from([(1, 2, 1), (1, 3, 2), (2, 3, 1), (2, 3, 2)])
order = nx.spectral_ordering(G, method=method)
assert set(order) == set(G)
assert {2, 3} in (set(order[:-1]), set(order[1:]))
@pytest.mark.parametrize("method", methods)
def test_path(self, method):
pytest.importorskip("scipy")
path = list(range(10))
np.random.shuffle(path)
G = nx.Graph()
nx.add_path(G, path)
order = nx.spectral_ordering(G, method=method)
assert order in [path, list(reversed(path))]
@pytest.mark.parametrize("method", methods)
def test_seed_argument(self, method):
pytest.importorskip("scipy")
path = list(range(10))
np.random.shuffle(path)
G = nx.Graph()
nx.add_path(G, path)
order = nx.spectral_ordering(G, method=method, seed=1)
assert order in [path, list(reversed(path))]
@pytest.mark.parametrize("method", methods)
def test_disconnected(self, method):
pytest.importorskip("scipy")
G = nx.Graph()
nx.add_path(G, range(0, 10, 2))
nx.add_path(G, range(1, 10, 2))
order = nx.spectral_ordering(G, method=method)
assert set(order) == set(G)
seqs = [
list(range(0, 10, 2)),
list(range(8, -1, -2)),
list(range(1, 10, 2)),
list(range(9, -1, -2)),
]
assert order[:5] in seqs
assert order[5:] in seqs
@pytest.mark.parametrize(
("normalized", "expected_order"),
(
(False, [[1, 2, 0, 3, 4, 5, 6, 9, 7, 8], [8, 7, 9, 6, 5, 4, 3, 0, 2, 1]]),
(True, [[1, 2, 3, 0, 4, 5, 9, 6, 7, 8], [8, 7, 6, 9, 5, 4, 0, 3, 2, 1]]),
),
)
@pytest.mark.parametrize("method", methods)
def test_cycle(self, normalized, expected_order, method):
pytest.importorskip("scipy")
path = list(range(10))
G = nx.Graph()
nx.add_path(G, path, weight=5)
G.add_edge(path[-1], path[0], weight=1)
A = nx.laplacian_matrix(G).todense()
order = nx.spectral_ordering(G, normalized=normalized, method=method)
assert order in expected_order
|
