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from contextlib import contextmanager
from math import sqrt
import networkx as nx
from nose import SkipTest
from nose.tools import *
methods = ('tracemin_pcg', 'tracemin_chol', 'tracemin_lu', 'lanczos', 'lobpcg')
try:
from numpy.random import get_state, seed, set_state, shuffle
@contextmanager
def save_random_state():
state = get_state()
try:
yield
finally:
set_state(state)
def preserve_random_state(func):
def wrapper(*args, **kwargs):
with save_random_state():
seed(1234567890)
return func(*args, **kwargs)
wrapper.__name__ = func.__name__
return wrapper
except ImportError:
@contextmanager
def save_random_state():
yield
def preserve_random_state(func):
return func
def check_eigenvector(A, l, x):
nx = numpy.linalg.norm(x)
# Check zeroness.
assert_not_almost_equal(nx, 0)
y = A * x
ny = numpy.linalg.norm(y)
# Check collinearity.
assert_almost_equal(numpy.dot(x, y), nx * ny)
# Check eigenvalue.
assert_almost_equal(ny, l * nx)
class TestAlgebraicConnectivity(object):
numpy = 1
@classmethod
def setupClass(cls):
global numpy
try:
import numpy.linalg
import scipy.sparse
except ImportError:
raise SkipTest('SciPy not available.')
@preserve_random_state
def test_directed(self):
G = nx.DiGraph()
for method in self._methods:
assert_raises(nx.NetworkXNotImplemented, nx.algebraic_connectivity,
G, method=method)
assert_raises(nx.NetworkXNotImplemented, nx.fiedler_vector, G,
method=method)
@preserve_random_state
def test_null_and_singleton(self):
G = nx.Graph()
for method in self._methods:
assert_raises(nx.NetworkXError, nx.algebraic_connectivity, G,
method=method)
assert_raises(nx.NetworkXError, nx.fiedler_vector, G,
method=method)
G.add_edge(0, 0)
for method in self._methods:
assert_raises(nx.NetworkXError, nx.algebraic_connectivity, G,
method=method)
assert_raises(nx.NetworkXError, nx.fiedler_vector, G,
method=method)
@preserve_random_state
def test_disconnected(self):
G = nx.Graph()
G.add_nodes_from(range(2))
for method in self._methods:
assert_equal(nx.algebraic_connectivity(G), 0)
assert_raises(nx.NetworkXError, nx.fiedler_vector, G,
method=method)
G.add_edge(0, 1, weight=0)
for method in self._methods:
assert_equal(nx.algebraic_connectivity(G), 0)
assert_raises(nx.NetworkXError, nx.fiedler_vector, G,
method=method)
@preserve_random_state
def test_unrecognized_method(self):
G = nx.path_graph(4)
assert_raises(nx.NetworkXError, nx.algebraic_connectivity, G,
method='unknown')
assert_raises(nx.NetworkXError, nx.fiedler_vector, G, method='unknown')
@preserve_random_state
def test_two_nodes(self):
G = nx.Graph()
G.add_edge(0, 1, weight=1)
A = nx.laplacian_matrix(G)
for method in self._methods:
assert_almost_equal(nx.algebraic_connectivity(
G, tol=1e-12, method=method), 2)
x = nx.fiedler_vector(G, tol=1e-12, method=method)
check_eigenvector(A, 2, x)
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')
for method in self._methods:
assert_almost_equal(nx.algebraic_connectivity(
G, weight='spam', tol=1e-12, method=method), 6)
x = nx.fiedler_vector(G, weight='spam', tol=1e-12, method=method)
check_eigenvector(A, 6, x)
@preserve_random_state
def test_path(self):
G = nx.path_graph(8)
A = nx.laplacian_matrix(G)
sigma = 2 - sqrt(2 + sqrt(2))
for method in self._methods:
assert_almost_equal(nx.algebraic_connectivity(
G, tol=1e-12, method=method), sigma)
x = nx.fiedler_vector(G, tol=1e-12, method=method)
check_eigenvector(A, sigma, x)
@preserve_random_state
def test_cycle(self):
G = nx.cycle_graph(8)
A = nx.laplacian_matrix(G)
sigma = 2 - sqrt(2)
for method in self._methods:
assert_almost_equal(nx.algebraic_connectivity(
G, tol=1e-12, method=method), sigma)
x = nx.fiedler_vector(G, tol=1e-12, method=method)
check_eigenvector(A, sigma, x)
@preserve_random_state
def test_buckminsterfullerene(self):
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)])
for normalized in (False, True):
if not normalized:
A = nx.laplacian_matrix(G)
sigma = 0.2434017461399311
else:
A = nx.normalized_laplacian_matrix(G)
sigma = 0.08113391537997749
for method in methods:
try:
assert_almost_equal(nx.algebraic_connectivity(
G, normalized=normalized, tol=1e-12, method=method),
sigma)
x = nx.fiedler_vector(G, normalized=normalized, tol=1e-12,
method=method)
check_eigenvector(A, sigma, x)
except nx.NetworkXError as e:
if e.args not in (('Cholesky solver unavailable.',),
('LU solver unavailable.',)):
raise
_methods = ('tracemin', 'lanczos', 'lobpcg')
class TestSpectralOrdering(object):
numpy = 1
@classmethod
def setupClass(cls):
global numpy
try:
import numpy.linalg
import scipy.sparse
except ImportError:
raise SkipTest('SciPy not available.')
@preserve_random_state
def test_nullgraph(self):
for graph in (nx.Graph, nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph):
G = graph()
assert_raises(nx.NetworkXError, nx.spectral_ordering, G)
@preserve_random_state
def test_singleton(self):
for graph in (nx.Graph, nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph):
G = graph()
G.add_node('x')
assert_equal(nx.spectral_ordering(G), ['x'])
G.add_edge('x', 'x', weight=33)
G.add_edge('x', 'x', weight=33)
assert_equal(nx.spectral_ordering(G), ['x'])
@preserve_random_state
def test_unrecognized_method(self):
G = nx.path_graph(4)
assert_raises(nx.NetworkXError, nx.spectral_ordering, G,
method='unknown')
@preserve_random_state
def test_three_nodes(self):
G = nx.Graph()
G.add_weighted_edges_from([(1, 2, 1), (1, 3, 2), (2, 3, 1)],
weight='spam')
for method in self._methods:
order = nx.spectral_ordering(G, weight='spam', method=method)
assert_equal(set(order), set(G))
ok_(set([1, 3]) in (set(order[:-1]), set(order[1:])))
G = nx.MultiDiGraph()
G.add_weighted_edges_from([(1, 2, 1), (1, 3, 2), (2, 3, 1), (2, 3, 2)])
for method in self._methods:
order = nx.spectral_ordering(G, method=method)
assert_equal(set(order), set(G))
ok_(set([2, 3]) in (set(order[:-1]), set(order[1:])))
@preserve_random_state
def test_path(self):
path = list(range(10))
shuffle(path)
G = nx.Graph()
G.add_path(path)
for method in self._methods:
order = nx.spectral_ordering(G, method=method)
ok_(order in [path, list(reversed(path))])
@preserve_random_state
def test_disconnected(self):
G = nx.Graph()
G.add_path(range(0, 10, 2))
G.add_path(range(1, 10, 2))
for method in self._methods:
order = nx.spectral_ordering(G, method=method)
assert_equal(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))]
ok_(order[:5] in seqs)
ok_(order[5:] in seqs)
@preserve_random_state
def test_cycle(self):
path = list(range(10))
G = nx.Graph()
G.add_path(path, weight=5)
G.add_edge(path[-1], path[0], weight=1)
A = nx.laplacian_matrix(G).todense()
for normalized in (False, True):
for method in methods:
try:
order = nx.spectral_ordering(G, normalized=normalized,
method=method)
except nx.NetworkXError as e:
if e.args not in (('Cholesky solver unavailable.',),
('LU solver unavailable.',)):
raise
else:
if not normalized:
ok_(order in [[1, 2, 0, 3, 4, 5, 6, 9, 7, 8],
[8, 7, 9, 6, 5, 4, 3, 0, 2, 1]])
else:
ok_(order in [[1, 2, 3, 0, 4, 5, 9, 6, 7, 8],
[8, 7, 6, 9, 5, 4, 0, 3, 2, 1]])
_methods = ('tracemin', 'lanczos', 'lobpcg')
|
