def test_boundary_transform_1d(wavelet_str, data, level, boundary):
"""Ensure matrix fwt reconstructions are pywt compatible."""
data_torch = torch.from_numpy(data.astype(np.float64))
wavelet = pywt.Wavelet(wavelet_str)
matrix_wavedec = MatrixWavedec(wavelet, level=level, boundary=boundary)
coeffs = matrix_wavedec(data_torch)
matrix_waverec = MatrixWaverec(wavelet, boundary=boundary)
rec = matrix_waverec(coeffs)
rec_pywt = pywt.waverec(
pywt.wavedec(data_torch.numpy(), wavelet, mode="zero"), wavelet)
error = np.sum(np.abs(rec_pywt - rec.numpy()))
print(
"wavelet: {},".format(wavelet_str),
"level: {},".format(level),
"shape: {},".format(data.shape[-1]),
"error {:2.2e}".format(error),
)
assert np.allclose(rec.numpy(), rec_pywt)
# test the operator matrices
if not matrix_wavedec.padded and not matrix_waverec.padded:
test_mat = torch.sparse.mm(
matrix_waverec.sparse_ifwt_operator,
matrix_wavedec.sparse_fwt_operator,
)
assert np.allclose(test_mat.to_dense().numpy(),
np.eye(test_mat.shape[0]))
def test_fwt_ifwt_level_1():
"""Test the Haar case."""
wavelet = pywt.Wavelet("haar")
data2 = 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,
])
# level 1
coeffs = pywt.dwt(data2, wavelet)
print(coeffs[0], coeffs[1])
matrix_wavedec = MatrixWavedec(wavelet, 1)
coeffsmat1 = matrix_wavedec(torch.from_numpy(data2))
err1 = np.mean(np.abs(coeffs[0] - coeffsmat1[0].squeeze().numpy()))
err2 = np.mean(np.abs(coeffs[1] - coeffsmat1[1].squeeze().numpy()))
print(err1 < 0.00001, err2 < 0.00001)
assert err1 < 1e-6
assert err2 < 1e-6
def test_fwt_ifwt_mackey_haar():
"""Test the Haar case for a long signal."""
wavelet = pywt.Wavelet("haar")
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
generator = MackeyGenerator(batch_size=2,
tmax=512,
delta_t=1,
device=device)
wavelet = pywt.Wavelet("haar")
pt_data = torch.squeeze(generator())
coeffs_max = pywt.wavedec(pt_data.cpu().numpy(), wavelet, level=9)
matrix_wavedec = MatrixWavedec(wavelet, 9)
coeffs_mat_max = matrix_wavedec(pt_data)
test_lst = []
for test_no in range(9):
test_lst.append(
np.sum(
np.abs(coeffs_max[test_no] -
coeffs_mat_max[test_no].cpu().numpy())) < 0.001)
print(test_lst)
# test the inverse fwt.
matrix_waverec = MatrixWaverec(wavelet)
reconstructed_data = matrix_waverec(coeffs_mat_max)
err1 = torch.mean(torch.abs(pt_data - reconstructed_data))
print("abs ifwt reconstruction error", err1)
assert np.allclose(pt_data.cpu().numpy(), reconstructed_data.cpu().numpy())
def test_fwt_ifwt_mackey_db2():
"""Test the db2 case for a long signal."""
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
wavelet = pywt.Wavelet("db2")
generator = MackeyGenerator(batch_size=2,
tmax=512,
delta_t=1,
device=device)
pt_data = torch.squeeze(generator()).cpu()
matrix_wavedec = MatrixWavedec(wavelet, 4)
coeffs_mat_max = matrix_wavedec(pt_data)
matrix_waverec = MatrixWaverec(wavelet)
reconstructed_data = matrix_waverec(coeffs_mat_max)
err = torch.mean(torch.abs(pt_data - reconstructed_data))
print("reconstruction error:", err)
assert err < 1e-6
def test_fwt_ifwt_level_3():
"""Test the Haar level 3 case."""
wavelet = pywt.Wavelet("haar")
data2 = 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,
])
coeffs3 = pywt.wavedec(data2, wavelet, level=3)
matrix_wavedec = MatrixWavedec(wavelet, level=3)
coeffsmat3 = matrix_wavedec(torch.from_numpy(data2))
err1 = np.mean(np.abs(coeffs3[0] - coeffsmat3[0].squeeze().numpy()))
err2 = np.mean(np.abs(coeffs3[1] - coeffsmat3[1].squeeze().numpy()))
err3 = np.mean(np.abs(coeffs3[2] - coeffsmat3[2].squeeze().numpy()))
err4 = np.mean(np.abs(coeffs3[3] - coeffsmat3[3].squeeze().numpy()))
print(err1 < 1e-6, err2 < 1e-6, err3 < 1e-6, err4 < 1e-6)
assert err1 < 1e-6
assert err2 < 1e-6
assert err3 < 1e-6
assert err4 < 1e-6
matrix_waverec = MatrixWaverec(wavelet)
reconstructed_data = matrix_waverec(coeffsmat3)
err5 = torch.mean(torch.abs(torch.from_numpy(data2) - reconstructed_data))
print("abs ifwt 3 reconstruction error", err5)
assert np.allclose(data2, reconstructed_data.numpy())
def test_fwt_ifwt_level_2():
"""Test the Haar level two case."""
wavelet = pywt.Wavelet("haar")
data2 = 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,
18.0,
])
coeffs2 = pywt.wavedec(data2, wavelet, level=2, mode="zero")
matrix_wavedec = MatrixWavedec(wavelet, 2)
coeffsmat2 = matrix_wavedec(torch.from_numpy(data2))
err1 = np.mean(np.abs(coeffs2[0] - coeffsmat2[0].squeeze().numpy()))
err2 = np.mean(np.abs(coeffs2[1] - coeffsmat2[1].squeeze().numpy()))
err3 = np.mean(np.abs(coeffs2[2] - coeffsmat2[2].squeeze().numpy()))
print(
np.mean(np.abs(coeffs2[0] - coeffsmat2[0].squeeze().numpy())) < 1e-6,
np.mean(np.abs(coeffs2[1] - coeffsmat2[1].squeeze().numpy())) < 1e-6,
np.mean(np.abs(coeffs2[2] - coeffsmat2[2].squeeze().numpy())) < 1e-6,
)
assert err1 < 1e-6
assert err2 < 1e-6
assert err3 < 1e-6