def test_filter(self, n_filters=5):
g = filters.MexicanHat(self._G, n_filters)
s1 = self._rs.uniform(size=self._G.N)
s2 = s1.reshape((self._G.N, 1))
s3 = g.filter(s1)
s4 = g.filter(s2)
s5 = g.analyze(s1)
assert s3.shape == (self._G.N, n_filters)
np.testing.assert_allclose(s3, s4)
np.testing.assert_allclose(s3, s5)
s1 = self._rs.uniform(size=(self._G.N, 4))
s2 = s1.reshape((self._G.N, 4, 1))
s3 = g.filter(s1)
s4 = g.filter(s2)
s5 = g.analyze(s1)
assert s3.shape == (self._G.N, 4, n_filters)
np.testing.assert_allclose(s3, s4)
np.testing.assert_allclose(s3, s5)
s1 = self._rs.uniform(size=(self._G.N, n_filters))
s2 = s1.reshape((self._G.N, 1, n_filters))
s3 = g.filter(s1)
s4 = g.filter(s2)
s5 = g.synthesize(s1)
assert s3.shape == (self._G.N, )
np.testing.assert_allclose(s3, s4)
np.testing.assert_allclose(s3, s5)
s1 = self._rs.uniform(size=(self._G.N, 10, n_filters))
s3 = g.filter(s1)
s5 = g.synthesize(s1)
assert s3.shape == (self._G.N, 10)
np.testing.assert_allclose(s3, s5)
def test_complement(self, frame_bound=2.5):
"""Any filter bank becomes tight upon addition of their complement."""
g = filters.MexicanHat(self._G)
g += g.complement(frame_bound)
A, B = g.estimate_frame_bounds()
np.testing.assert_allclose(A, frame_bound)
np.testing.assert_allclose(B, frame_bound)
def test_mexicanhat(self):
f = filters.MexicanHat(self._G, Nf=5, normalize=False)
self._test_methods(f, tight=False)
f = filters.MexicanHat(self._G, Nf=4, normalize=True)
self._test_methods(f, tight=False)
DELTA = 255
s = g.localize(DELTA)
fig = plt.figure(figsize=(10, 2.5))
for i in range(4):
ax = fig.add_subplot(1, 4, i + 1, projection='3d')
G.plot_signal(s[:, i], ax=ax)
_ = ax.set_title('Wavelet {}'.format(i + 1))
ax.set_axis_off()
fig.tight_layout()
plt.show()
# Mexican hat wavelets on a torus
G = graphs.Torus()
G.estimate_lmax()
g = filters.MexicanHat(G, Nf=6)
fig, ax = plt.subplots(figsize=(10, 5))
g.plot(ax=ax)
_ = ax.set_title('Filter bank of Mexican Hat wavelets')
DELTA = 255
s = g.localize(DELTA)
fig = plt.figure(figsize=(10, 2.5))
for i in range(4):
ax = fig.add_subplot(1, 4, i + 1, projection='3d')
G.plot_signal(s[:, i], ax=ax)
_ = ax.set_title('Wavelet {}'.format(i + 1))
ax.set_axis_off()
fig.tight_layout()
plt.show()