def test_morlet_1d():
"""
Tests for Morlet wavelets:
- Make sure that it has exact zero mean
- Make sure that it has a fast decay in time
- Check that the maximal frequency is relatively close to xi,
up to 1% accuracy
"""
size_signal = [2**13]
Q_range = np.arange(1, 20, dtype=int)
for N in size_signal:
for Q in Q_range:
xi_max = compute_xi_max(Q)
xi_range = xi_max / np.power(2, np.arange(7))
for xi in xi_range:
sigma = compute_sigma_psi(xi, Q)
# get the morlet for these parameters
psi_f = morlet_1d(N, xi, sigma, normalize='l2')
# make sure that it has zero mean
assert np.isclose(psi_f[0], 0.)
# make sure that it has a fast decay in time
psi = np.fft.ifft(psi_f)
psi_abs = np.abs(psi)
assert np.min(psi_abs) / np.max(psi_abs) < 1e-4
# Check that the maximal frequency is relatively close to xi,
# up to 1 percent
k_max = np.argmax(np.abs(psi_f))
xi_emp = float(k_max) / float(N)
assert np.abs(xi_emp - xi) / xi < 1e-2
def test_get_max_dyadic_subsampling():
"""
Tests on the subsampling formula for wavelets, to check that the retained
value does not create aliasing (the wavelet should have decreased by
a relative value of 1e-2 at the border of the aliasing.)
"""
N = 2**12
Q_range = np.arange(1, 20, dtype=int)
J = 7
for Q in Q_range:
xi_max = compute_xi_max(Q)
xi_range = xi_max * np.power(0.5, np.arange(J * Q) / float(Q))
for xi in xi_range:
sigma = compute_sigma_psi(xi, Q)
j = get_max_dyadic_subsampling(xi, sigma)
if j > 0: # if there is subsampling
# compute the corresponding Morlet
psi_f = morlet_1d(N, xi, sigma)
# find the integer k such that
k = N // 2**(j + 1)
assert np.abs(psi_f[k]) / np.max(np.abs(psi_f)) < 1e-2
else:
# pass this case: we have detected that there cannot
# be any subsampling, and we assume that the filters are not
# aliased already
pass
def test_gauss_1d():
"""
Tests for Gabor low-pass
- Make sure that it has a fast decay in time
- Make sure that it is symmetric, up to 1e-7 absolute precision
"""
N = 2**13
J = 7
P_range = [1, 5]
sigma0 = 0.1
tol = 1e-7
for j in range(1, J + 1):
for P in P_range:
sigma_low = sigma0 / math.pow(2, j)
g_f = gauss_1d(N, sigma_low, P_max=P)
# check the symmetry of g_f
assert np.max(np.abs(g_f[1:N // 2] - g_f[N // 2 + 1:][::-1])) < tol
# make sure that it has a fast decay in time
phi = np.fft.ifft(g_f)
assert np.min(phi) > - tol
assert np.min(np.abs(phi)) / np.max(np.abs(phi)) < 1e-4
Q = 1
xi = compute_xi_max(Q)
sigma = compute_sigma_psi(xi, Q)
with pytest.raises(ValueError) as ve:
gauss_1d(N, xi, sigma, P_max=5.1)
assert "should be an int" in ve.value.args[0]
with pytest.raises(ValueError) as ve:
gauss_1d(N, xi, sigma, P_max=-5)
assert "should be non-negative" in ve.value.args[0]
def test_compute_xi_max():
"""
Tests that 0.25 <= xi_max(Q) <= 0.5, whatever Q
"""
Q_range = np.arange(1, 21, dtype=int)
for Q in Q_range:
xi_max = compute_xi_max(Q)
assert xi_max <= 0.5
assert xi_max >= 0.25
def test_morlet_1d():
"""
Tests for Morlet wavelets:
- Make sure that it has exact zero mean
- Make sure that it has a fast decay in time
- Check that the maximal frequency is relatively close to xi,
up to 1% accuracy
"""
size_signal = [2**13]
Q_range = np.arange(1, 20, dtype=int)
P_range = [1, 5]
for N in size_signal:
for Q in Q_range:
xi_max = compute_xi_max(Q)
xi_range = xi_max / np.power(2, np.arange(7))
for xi in xi_range:
for P in P_range:
sigma = compute_sigma_psi(xi, Q)
# get the morlet for these parameters
psi_f = morlet_1d(N, xi, sigma, normalize='l2', P_max=P)
# make sure that it has zero mean
assert np.isclose(psi_f[0], 0.)
# make sure that it has a fast decay in time
psi = np.fft.ifft(psi_f)
psi_abs = np.abs(psi)
assert np.min(psi_abs) / np.max(psi_abs) < 1e-3
# Check that the maximal frequency is relatively close to xi,
# up to 1 percent
k_max = np.argmax(np.abs(psi_f))
xi_emp = float(k_max) / float(N)
assert np.abs(xi_emp - xi) / xi < 1e-2
Q = 1
xi = compute_xi_max(Q)
sigma = compute_sigma_psi(xi, Q)
with pytest.raises(ValueError) as ve:
morlet_1d(size_signal[0], xi, sigma, P_max=5.1)
assert "should be an int" in ve.value.args[0]
with pytest.raises(ValueError) as ve:
morlet_1d(size_signal[0], xi, sigma, P_max=-5)
assert "should be non-negative" in ve.value.args[0]
