def test_conv_fwt():
"""Test multiple convolution fwt, for various levels and padding options."""
generator = MackeyGenerator(batch_size=2,
tmax=128,
delta_t=1,
device="cpu")
mackey_data_1 = torch.squeeze(generator())
for level in [1, 2, 3, None]:
for wavelet_string in ["db1", "db2", "db3", "db4", "db5"]:
for mode in ["reflect", "zero"]:
wavelet = pywt.Wavelet(wavelet_string)
ptcoeff = wavedec(mackey_data_1,
wavelet,
level=level,
mode=mode)
pycoeff = pywt.wavedec(mackey_data_1[0, :].numpy(),
wavelet,
level=level,
mode=mode)
cptcoeff = torch.cat(ptcoeff, -1)[0, :]
cpycoeff = np.concatenate(pycoeff, -1)
err = np.mean(np.abs(cpycoeff - cptcoeff.numpy()))
print(
"db5 coefficient error scale 3:",
err,
["ok" if err < 1e-4 else "failed!"],
"mode",
mode,
)
assert np.allclose(cptcoeff.numpy(), cpycoeff, atol=1e-6)
res = waverec(
wavedec(mackey_data_1, wavelet, level=3, mode=mode),
wavelet,
)
err = torch.mean(torch.abs(mackey_data_1 - res)).numpy()
print(
"db5 reconstruction error scale 3:",
err,
["ok" if err < 1e-4 else "failed!"],
"mode",
mode,
)
assert np.allclose(mackey_data_1.numpy(), res.numpy())
res = waverec(
wavedec(mackey_data_1, wavelet, level=4, mode=mode),
wavelet,
)
err = torch.mean(torch.abs(mackey_data_1 - res)).numpy()
print(
"db5 reconstruction error scale 4:",
err,
["ok" if err < 1e-4 else "failed!"],
"mode",
mode,
)
assert np.allclose(mackey_data_1.numpy(), res.numpy())
def test_conv_fwt_db5_lvl3():
"""Test a third level db5 conv-fwt."""
generator = MackeyGenerator(batch_size=2,
tmax=128,
delta_t=1,
device="cpu")
mackey_data_1 = torch.squeeze(generator())
wavelet = pywt.Wavelet("db5")
for mode in ["reflect", "zero"]:
ptcoeff = wavedec(mackey_data_1, wavelet, level=3, mode=mode)
pycoeff = pywt.wavedec(mackey_data_1[0, :].numpy(),
wavelet,
level=3,
mode=mode)
cptcoeff = torch.cat(ptcoeff, -1)[0, :]
cpycoeff = np.concatenate(pycoeff, -1)
err = np.mean(np.abs(cpycoeff - cptcoeff.numpy()))
print(
"db5 coefficient error scale 3:",
err,
["ok" if err < 1e-4 else "failed!"],
"mode",
mode,
)
assert np.allclose(cpycoeff, cptcoeff.numpy(), atol=1e-6)
res = waverec(wavedec(mackey_data_1, wavelet, level=3, mode=mode),
wavelet)
err = torch.mean(torch.abs(mackey_data_1 - res)).numpy()
print(
"db5 reconstruction error scale 3:",
err,
["ok" if err < 1e-4 else "failed!"],
"mode",
mode,
)
assert np.allclose(mackey_data_1.numpy(), res.numpy())
res = waverec(wavedec(mackey_data_1, wavelet, level=4, mode=mode),
wavelet)
err = torch.mean(torch.abs(mackey_data_1 - res)).numpy()
print(
"db5 reconstruction error scale 4:",
err,
["ok" if err < 1e-4 else "failed!"],
"mode",
mode,
)
assert np.allclose(mackey_data_1.numpy(), res.numpy())
def test_conv_fwt_haar_lvl2_odd():
"""Test an odd Haar wavelet convolution fwt."""
data = np.array([
1.0,
2.0,
3.0,
4.0,
5.0,
6.0,
7.0,
8.0,
9.0,
10.0,
11.0,
12.0,
13.0,
14.0,
15.0,
16.0,
17.0,
])
wavelet = pywt.Wavelet("haar")
pycoeff = pywt.wavedec(data, wavelet, level=2, mode="reflect")
pywt_coeffs = np.concatenate(pycoeff)
ptcoeff = wavedec(torch.from_numpy(data), wavelet, level=2, mode="reflect")
ptwt_coeffs = torch.cat(ptcoeff, -1)[0, :].numpy()
assert np.allclose(pywt_coeffs, ptwt_coeffs)
rec = waverec(ptcoeff, wavelet)
assert np.allclose(data, rec[:, :-1].numpy())
def test_conv_fwt_db2_lvl1():
"""Test a second level db2 conv-fwt."""
data = np.array([
1.0,
2.0,
3.0,
4.0,
5.0,
6.0,
7.0,
8.0,
9.0,
10.0,
11.0,
12.0,
13.0,
14.0,
15.0,
16.0,
])
# ------------------------- db2 wavelet tests ----------------------------
wavelet = pywt.Wavelet("db2")
coeffs = pywt.wavedec(data, wavelet, level=1, mode="reflect")
coeffs2 = wavedec(torch.from_numpy(data), wavelet, level=1, mode="reflect")
ccoeffs = np.concatenate(coeffs, -1)
ccoeffs2 = torch.cat(coeffs2, -1).numpy()
err = np.mean(np.abs(ccoeffs - ccoeffs2))
print("db2 coefficient error scale 1:", err,
["ok" if err < 1e-4 else "failed!"])
assert np.allclose(ccoeffs, ccoeffs2, atol=1e-6)
rec = waverec(coeffs2, wavelet)
err = np.mean(np.abs(data - rec.numpy()))
print("db2 reconstruction error scale 1:", err,
["ok" if err < 1e-4 else "failed!"])
assert np.allclose(data, rec.numpy())
def wavelet_reconstruction(self, x):
"""Reconstruction from a tensor input.
Args:
x (torch.Tensor): Analysis coefficient tensor.
Returns:
torch.Tensor: Input reconstruction.
"""
coeff_lst = []
start = 0
# turn tensor into list
for s in range(self.scales + 1):
stop = start + self.coefficient_len_lst[::-1][s]
coeff_lst.append(x[..., start:stop])
start = self.coefficient_len_lst[s]
y = waverec(coeff_lst, self.wavelet)
return y
def test_orth_wavelet():
"""Test an orthogonal wavelet fwt."""
generator = MackeyGenerator(batch_size=2, tmax=64, delta_t=1, device="cpu")
mackey_data_1 = torch.squeeze(generator())
# orthogonal wavelet object test
wavelet = pywt.Wavelet("db5")
orthwave = SoftOrthogonalWavelet(
torch.tensor(wavelet.rec_lo),
torch.tensor(wavelet.rec_hi),
torch.tensor(wavelet.dec_lo),
torch.tensor(wavelet.dec_hi),
)
res = waverec(wavedec(mackey_data_1, orthwave), orthwave)
err = torch.mean(torch.abs(mackey_data_1 - res.detach())).numpy()
print("orth reconstruction error scale 4:", err,
["ok" if err < 1e-4 else "failed!"])
assert np.allclose(res.detach().numpy(), mackey_data_1.numpy())
def test_conv_fwt_haar_lvl4():
"""Test a fourth level Haar wavelet conv-fwt."""
generator = MackeyGenerator(batch_size=2, tmax=64, delta_t=1, device="cpu")
mackey_data_1 = torch.squeeze(generator())
wavelet = pywt.Wavelet("haar")
ptcoeff = wavedec(mackey_data_1, wavelet, level=4)
pycoeff = pywt.wavedec(mackey_data_1[0, :].numpy(), wavelet, level=4)
ptwt_coeff = torch.cat(ptcoeff, -1)[0, :].numpy()
pywt_coeff = np.concatenate(pycoeff)
err = np.mean(np.abs(pywt_coeff - ptwt_coeff))
print("haar coefficient error scale 4:", err,
["ok" if err < 1e-4 else "failed!"])
assert np.allclose(pywt_coeff, ptwt_coeff, atol=1e-06)
reconstruction = waverec(wavedec(mackey_data_1, wavelet), wavelet)
err = torch.mean(torch.abs(mackey_data_1 - reconstruction)).numpy()
print("haar reconstruction error scale 4:", err,
["ok" if err < 1e-4 else "failed!"])
assert np.allclose(reconstruction.numpy(), mackey_data_1.numpy())
def test_conv_fwt_haar_lvl2():
"""Test Haar wavelet level two conv fwt."""
data = np.array([
1.0,
2.0,
3.0,
4.0,
5.0,
6.0,
7.0,
8.0,
9.0,
10.0,
11.0,
12.0,
13.0,
14.0,
15.0,
16.0,
])
wavelet = pywt.Wavelet("haar")
coeffs = pywt.wavedec(data, wavelet, level=2)
coeffs2 = wavedec(torch.from_numpy(data), wavelet, level=2)
assert len(coeffs) == len(coeffs2)
pywt_coeffs = np.concatenate(coeffs)
ptwt_coeffs = torch.cat(coeffs2, -1).squeeze().numpy()
err = np.mean(np.abs(pywt_coeffs - ptwt_coeffs))
print("haar coefficient error scale 2", err,
["ok" if err < 1e-6 else "failed!"])
assert np.allclose(pywt_coeffs, ptwt_coeffs)
rec = waverec(coeffs2, wavelet).squeeze().numpy()
err = np.mean(np.abs((data - rec)))
print("haar reconstruction error scale 2", err,
["ok" if err < 1e-6 else "failed!"])
assert np.allclose(data, rec)