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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
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