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)