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| import torch | |
| import torch.nn as nn | |
| import torch.nn.functional as F | |
| import numpy as np | |
| from scipy import signal | |
| from scipy import special as ss | |
| device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu") | |
| def transition(N): | |
| Q = np.arange(N, dtype=np.float64) | |
| R = (2 * Q + 1)[:, None] # / theta | |
| j, i = np.meshgrid(Q, Q) | |
| A = np.where(i < j, -1, (-1.) ** (i - j + 1)) * R | |
| B = (-1.) ** Q[:, None] * R | |
| return A, B | |
| class HiPPO_LegT(nn.Module): | |
| def __init__(self, N, dt=1.0, discretization='bilinear'): | |
| """ | |
| N: the order of the HiPPO projection | |
| dt: discretization step size - should be roughly inverse to the length of the sequence | |
| """ | |
| super(HiPPO_LegT, self).__init__() | |
| self.N = N | |
| A, B = transition(N) | |
| C = np.ones((1, N)) | |
| D = np.zeros((1,)) | |
| A, B, _, _, _ = signal.cont2discrete((A, B, C, D), dt=dt, method=discretization) | |
| B = B.squeeze(-1) | |
| self.register_buffer('A', torch.Tensor(A).to(device)) | |
| self.register_buffer('B', torch.Tensor(B).to(device)) | |
| vals = np.arange(0.0, 1.0, dt) | |
| self.register_buffer('eval_matrix', torch.Tensor( | |
| ss.eval_legendre(np.arange(N)[:, None], 1 - 2 * vals).T).to(device)) | |
| def forward(self, inputs): | |
| """ | |
| inputs : (length, ...) | |
| output : (length, ..., N) where N is the order of the HiPPO projection | |
| """ | |
| c = torch.zeros(inputs.shape[:-1] + tuple([self.N])).to(device) | |
| cs = [] | |
| for f in inputs.permute([-1, 0, 1]): | |
| f = f.unsqueeze(-1) | |
| new = f @ self.B.unsqueeze(0) | |
| c = F.linear(c, self.A) + new | |
| cs.append(c) | |
| return torch.stack(cs, dim=0) | |
| def reconstruct(self, c): | |
| return (self.eval_matrix @ c.unsqueeze(-1)).squeeze(-1) | |
| class SpectralConv1d(nn.Module): | |
| def __init__(self, in_channels, out_channels, seq_len, ratio=0.5): | |
| """ | |
| 1D Fourier layer. It does FFT, linear transform, and Inverse FFT. | |
| """ | |
| super(SpectralConv1d, self).__init__() | |
| self.in_channels = in_channels | |
| self.out_channels = out_channels | |
| self.ratio = ratio | |
| self.modes = min(32, seq_len // 2) | |
| self.index = list(range(0, self.modes)) | |
| self.scale = (1 / (in_channels * out_channels)) | |
| self.weights_real = nn.Parameter( | |
| self.scale * torch.rand(in_channels, out_channels, len(self.index), dtype=torch.float)) | |
| self.weights_imag = nn.Parameter( | |
| self.scale * torch.rand(in_channels, out_channels, len(self.index), dtype=torch.float)) | |
| def compl_mul1d(self, order, x, weights_real, weights_imag): | |
| return torch.complex(torch.einsum(order, x.real, weights_real) - torch.einsum(order, x.imag, weights_imag), | |
| torch.einsum(order, x.real, weights_imag) + torch.einsum(order, x.imag, weights_real)) | |
| def forward(self, x): | |
| B, H, E, N = x.shape | |
| x_ft = torch.fft.rfft(x) | |
| out_ft = torch.zeros(B, H, self.out_channels, x.size(-1) // 2 + 1, device=x.device, dtype=torch.cfloat) | |
| a = x_ft[:, :, :, :self.modes] | |
| out_ft[:, :, :, :self.modes] = self.compl_mul1d("bjix,iox->bjox", a, self.weights_real, self.weights_imag) | |
| x = torch.fft.irfft(out_ft, n=x.size(-1)) | |
| return x | |
| class Model(nn.Module): | |
| """ | |
| Paper link: https://arxiv.org/abs/2205.08897 | |
| """ | |
| def __init__(self, configs): | |
| super(Model, self).__init__() | |
| self.task_name = configs.task_name | |
| self.configs = configs | |
| self.seq_len = configs.seq_len | |
| self.label_len = configs.label_len | |
| self.pred_len = configs.seq_len if configs.pred_len == 0 else configs.pred_len | |
| self.seq_len_all = self.seq_len + self.label_len | |
| self.layers = configs.e_layers | |
| self.enc_in = configs.enc_in | |
| self.e_layers = configs.e_layers | |
| # b, s, f means b, f | |
| self.affine_weight = nn.Parameter(torch.ones(1, 1, configs.enc_in)) | |
| self.affine_bias = nn.Parameter(torch.zeros(1, 1, configs.enc_in)) | |
| self.multiscale = [1, 2, 4] | |
| self.window_size = [256] | |
| configs.ratio = 0.5 | |
| self.legts = nn.ModuleList( | |
| [HiPPO_LegT(N=n, dt=1. / self.pred_len / i) for n in self.window_size for i in self.multiscale]) | |
| self.spec_conv_1 = nn.ModuleList([SpectralConv1d(in_channels=n, out_channels=n, | |
| seq_len=min(self.pred_len, self.seq_len), | |
| ratio=configs.ratio) for n in | |
| self.window_size for _ in range(len(self.multiscale))]) | |
| self.mlp = nn.Linear(len(self.multiscale) * len(self.window_size), 1) | |
| if self.task_name == 'imputation' or self.task_name == 'anomaly_detection': | |
| self.projection = nn.Linear( | |
| configs.d_model, configs.c_out, bias=True) | |
| if self.task_name == 'classification': | |
| self.act = F.gelu | |
| self.dropout = nn.Dropout(configs.dropout) | |
| self.projection = nn.Linear( | |
| configs.enc_in * configs.seq_len, configs.num_class) | |
| def forecast(self, x_enc, x_mark_enc, x_dec_true, x_mark_dec): | |
| # Normalization from Non-stationary Transformer | |
| means = x_enc.mean(1, keepdim=True).detach() | |
| x_enc = x_enc - means | |
| stdev = torch.sqrt(torch.var(x_enc, dim=1, keepdim=True, unbiased=False) + 1e-5).detach() | |
| x_enc /= stdev | |
| x_enc = x_enc * self.affine_weight + self.affine_bias | |
| x_decs = [] | |
| jump_dist = 0 | |
| for i in range(0, len(self.multiscale) * len(self.window_size)): | |
| x_in_len = self.multiscale[i % len(self.multiscale)] * self.pred_len | |
| x_in = x_enc[:, -x_in_len:] | |
| legt = self.legts[i] | |
| x_in_c = legt(x_in.transpose(1, 2)).permute([1, 2, 3, 0])[:, :, :, jump_dist:] | |
| out1 = self.spec_conv_1[i](x_in_c) | |
| if self.seq_len >= self.pred_len: | |
| x_dec_c = out1.transpose(2, 3)[:, :, self.pred_len - 1 - jump_dist, :] | |
| else: | |
| x_dec_c = out1.transpose(2, 3)[:, :, -1, :] | |
| x_dec = x_dec_c @ legt.eval_matrix[-self.pred_len:, :].T | |
| x_decs.append(x_dec) | |
| x_dec = torch.stack(x_decs, dim=-1) | |
| x_dec = self.mlp(x_dec).squeeze(-1).permute(0, 2, 1) | |
| # De-Normalization from Non-stationary Transformer | |
| x_dec = x_dec - self.affine_bias | |
| x_dec = x_dec / (self.affine_weight + 1e-10) | |
| x_dec = x_dec * stdev | |
| x_dec = x_dec + means | |
| return x_dec | |
| def imputation(self, x_enc, x_mark_enc, x_dec, x_mark_dec, mask): | |
| # Normalization from Non-stationary Transformer | |
| means = x_enc.mean(1, keepdim=True).detach() | |
| x_enc = x_enc - means | |
| stdev = torch.sqrt(torch.var(x_enc, dim=1, keepdim=True, unbiased=False) + 1e-5).detach() | |
| x_enc /= stdev | |
| x_enc = x_enc * self.affine_weight + self.affine_bias | |
| x_decs = [] | |
| jump_dist = 0 | |
| for i in range(0, len(self.multiscale) * len(self.window_size)): | |
| x_in_len = self.multiscale[i % len(self.multiscale)] * self.pred_len | |
| x_in = x_enc[:, -x_in_len:] | |
| legt = self.legts[i] | |
| x_in_c = legt(x_in.transpose(1, 2)).permute([1, 2, 3, 0])[:, :, :, jump_dist:] | |
| out1 = self.spec_conv_1[i](x_in_c) | |
| if self.seq_len >= self.pred_len: | |
| x_dec_c = out1.transpose(2, 3)[:, :, self.pred_len - 1 - jump_dist, :] | |
| else: | |
| x_dec_c = out1.transpose(2, 3)[:, :, -1, :] | |
| x_dec = x_dec_c @ legt.eval_matrix[-self.pred_len:, :].T | |
| x_decs.append(x_dec) | |
| x_dec = torch.stack(x_decs, dim=-1) | |
| x_dec = self.mlp(x_dec).squeeze(-1).permute(0, 2, 1) | |
| # De-Normalization from Non-stationary Transformer | |
| x_dec = x_dec - self.affine_bias | |
| x_dec = x_dec / (self.affine_weight + 1e-10) | |
| x_dec = x_dec * stdev | |
| x_dec = x_dec + means | |
| return x_dec | |
| def anomaly_detection(self, x_enc): | |
| # Normalization from Non-stationary Transformer | |
| means = x_enc.mean(1, keepdim=True).detach() | |
| x_enc = x_enc - means | |
| stdev = torch.sqrt(torch.var(x_enc, dim=1, keepdim=True, unbiased=False) + 1e-5).detach() | |
| x_enc /= stdev | |
| x_enc = x_enc * self.affine_weight + self.affine_bias | |
| x_decs = [] | |
| jump_dist = 0 | |
| for i in range(0, len(self.multiscale) * len(self.window_size)): | |
| x_in_len = self.multiscale[i % len(self.multiscale)] * self.pred_len | |
| x_in = x_enc[:, -x_in_len:] | |
| legt = self.legts[i] | |
| x_in_c = legt(x_in.transpose(1, 2)).permute([1, 2, 3, 0])[:, :, :, jump_dist:] | |
| out1 = self.spec_conv_1[i](x_in_c) | |
| if self.seq_len >= self.pred_len: | |
| x_dec_c = out1.transpose(2, 3)[:, :, self.pred_len - 1 - jump_dist, :] | |
| else: | |
| x_dec_c = out1.transpose(2, 3)[:, :, -1, :] | |
| x_dec = x_dec_c @ legt.eval_matrix[-self.pred_len:, :].T | |
| x_decs.append(x_dec) | |
| x_dec = torch.stack(x_decs, dim=-1) | |
| x_dec = self.mlp(x_dec).squeeze(-1).permute(0, 2, 1) | |
| # De-Normalization from Non-stationary Transformer | |
| x_dec = x_dec - self.affine_bias | |
| x_dec = x_dec / (self.affine_weight + 1e-10) | |
| x_dec = x_dec * stdev | |
| x_dec = x_dec + means | |
| return x_dec | |
| def classification(self, x_enc, x_mark_enc): | |
| x_enc = x_enc * self.affine_weight + self.affine_bias | |
| x_decs = [] | |
| jump_dist = 0 | |
| for i in range(0, len(self.multiscale) * len(self.window_size)): | |
| x_in_len = self.multiscale[i % len(self.multiscale)] * self.pred_len | |
| x_in = x_enc[:, -x_in_len:] | |
| legt = self.legts[i] | |
| x_in_c = legt(x_in.transpose(1, 2)).permute([1, 2, 3, 0])[:, :, :, jump_dist:] | |
| out1 = self.spec_conv_1[i](x_in_c) | |
| if self.seq_len >= self.pred_len: | |
| x_dec_c = out1.transpose(2, 3)[:, :, self.pred_len - 1 - jump_dist, :] | |
| else: | |
| x_dec_c = out1.transpose(2, 3)[:, :, -1, :] | |
| x_dec = x_dec_c @ legt.eval_matrix[-self.pred_len:, :].T | |
| x_decs.append(x_dec) | |
| x_dec = torch.stack(x_decs, dim=-1) | |
| x_dec = self.mlp(x_dec).squeeze(-1).permute(0, 2, 1) | |
| # Output from Non-stationary Transformer | |
| output = self.act(x_dec) | |
| output = self.dropout(output) | |
| output = output * x_mark_enc.unsqueeze(-1) | |
| output = output.reshape(output.shape[0], -1) | |
| output = self.projection(output) | |
| return output | |
| def forward(self, x_enc, x_mark_enc, x_dec, x_mark_dec, mask=None): | |
| if self.task_name == 'long_term_forecast' or self.task_name == 'short_term_forecast': | |
| dec_out = self.forecast(x_enc, x_mark_enc, x_dec, x_mark_dec) | |
| return dec_out[:, -self.pred_len:, :] # [B, L, D] | |
| if self.task_name == 'imputation': | |
| dec_out = self.imputation(x_enc, x_mark_enc, x_dec, x_mark_dec, mask) | |
| return dec_out # [B, L, D] | |
| if self.task_name == 'anomaly_detection': | |
| dec_out = self.anomaly_detection(x_enc) | |
| return dec_out # [B, L, D] | |
| if self.task_name == 'classification': | |
| dec_out = self.classification(x_enc, x_mark_enc) | |
| return dec_out # [B, N] | |
| return None | |