def test_sparse_fft(self):
n = 4
e = int(round(n * (n - 1.0) / 2.0))
for i in xrange(e + 1):
for edges in kbits(e, i):
logging.info("%d 1s in %d edges." % (i, e))
f = Graph.from_edges(edges)
fft = super(Graph, f).fft().matrix
f = Graph.from_edges(edges)
graph_fft = f.sparse_fft().matrix
for fft_rho, gfft_rho in zip(fft, graph_fft):
assert_array_almost_equal(fft_rho, gfft_rho.todense())
def test_fft(self):
f = Graph.from_edges([0, 1, 1])
assert_array_almost_equal(f.f, [1, 1, 1, 1, 0, 0])
expected = [[[4]], [[0, 0], [1.73205, 1]], [[0]]]
for i, ex in enumerate(expected):
assert_array_almost_equal(f.fft().matrix[i].todense(),
np.array(ex))
def calculate_invariant(self, invariant_name, n=4, sparse=False, **kwargs):
iso_classes = {}
tolerance = 1.0
e = int(round(n * (n - 1.0) / 2.0))
for i in xrange(e + 1):
logging.info("%d 1s in %d edges." % (i, e))
for edges in kbits(e, i):
f = Graph.from_edges(edges)
invariant_value = getattr(f, invariant_name)(**kwargs)
if sparse:
invariant_value = [
inv.todense() for inv in invariant_value
]
found = False
for key, (fdash, value) in iso_classes.iteritems():
diff = np.sum([
np.linalg.norm(v1 - v2)
for v1, v2 in zip(invariant_value, value)
])
if diff < tolerance:
found = key
break
if not found:
key = unicode(invariant_value).encode("bz2")
iso_classes[key] = ([(f, invariant_value)],
invariant_value)
else:
fdash.append((f, invariant_value))
return iso_classes
def test_bispectrum_invariance(self):
n = 5
e = int(round(n * (n - 1.0) / 2.0))
for i in xrange(e + 1):
for edges in kbits(e, i):
logging.info("%d 1s in %d edges." % (i, e))
G = Graph.from_edges(edges)
bispectrum = G.bispectrum(idx=(0, 1))
for g in G.sn.generate():
Gdash = G.apply_permutation(g)
bispectrum_ = Gdash.bispectrum(idx=(0, 1))
for b_i in xrange(len(bispectrum)):
assert_array_almost_equal(bispectrum[b_i],
bispectrum_[b_i])
def test_large_fft(self):
f1 = Graph.erdos_renyi(n=15)
# fft = super(Graph, f1).fft().matrix
graph_fft = f1.sparse_fft().matrix
def setUp(self):
self.s3 = SymmetricGroup(3)
self.s4 = SymmetricGroup(4)
self.s5 = SymmetricGroup(5)
self.f1 = Graph.from_edges([0, 1, 1])
self.sigma = Permutation([2, 1, 0])
def test_large_bispectrum(self):
f1 = Graph.erdos_renyi(n=6)
p = f1.sn.random()
f2 = f1.apply_permutation(p)
for m1, m2 in zip(f1.bispectrum(), f2.bispectrum()):
assert_array_almost_equal(m1.todense(), m2.todense())
def test_power_spectrum_invariant(self):
f1 = Graph.erdos_renyi(7)
f2 = f1.apply_permutation(f1.sn.random())
for fm1, fm2 in zip(f1.power_spectrum(), f2.power_spectrum()):
assert_array_almost_equal(fm1.todense(), fm2.todense())