content: 
  
  
  __all__ = ['DataEmbedding_wo_pos', 'DFT_series_decomp', 'MultiScaleSeasonMixing', 'MultiScaleTrendMixing',
             'PastDecomposableMixing', 'TimeMixer']
  
  
  import math
  from typing import Optional
  
  import numpy as np
  import torch
  import torch.nn as nn
  
  from neuralforecast.common._modules import (
      PositionalEmbedding,
      RevIN,
      SeriesDecomp,
      TemporalEmbedding,
      TokenEmbedding,
  )
  
  from ..common._base_model import BaseModel
  from ..losses.pytorch import MAE
  
  
  class DataEmbedding_wo_pos(nn.Module):
      """
      DataEmbedding_wo_pos
      """
  
      def __init__(self, c_in, d_model, dropout=0.1, embed_type="fixed", freq="h"):
          super(DataEmbedding_wo_pos, self).__init__()
  
          self.value_embedding = TokenEmbedding(c_in=c_in, hidden_size=d_model)
          self.position_embedding = PositionalEmbedding(hidden_size=d_model)
          self.temporal_embedding = TemporalEmbedding(
              d_model=d_model, embed_type=embed_type, freq=freq
          )
          self.dropout = nn.Dropout(p=dropout)
  
      def forward(self, x, x_mark):
          if x is None and x_mark is not None:
              return self.temporal_embedding(x_mark)
          if x_mark is None:
              x = self.value_embedding(x)
          else:
              x = self.value_embedding(x) + self.temporal_embedding(x_mark)
          return self.dropout(x)
  
  
  class DFT_series_decomp(nn.Module):
      """
      Series decomposition block
      """
  
      def __init__(self, top_k):
          super(DFT_series_decomp, self).__init__()
          self.top_k = top_k
  
      def forward(self, x):
          xf = torch.fft.rfft(x)
          freq = abs(xf)
          freq[0] = 0
          top_k_freq, top_list = torch.topk(freq, self.top_k)
          xf[freq <= top_k_freq.min()] = 0
          x_season = torch.fft.irfft(xf)
          x_trend = x - x_season
          return x_season, x_trend
  
  
  class MultiScaleSeasonMixing(nn.Module):
      """
      Bottom-up mixing season pattern
      """
  
      def __init__(self, seq_len, down_sampling_window, down_sampling_layers):
          super(MultiScaleSeasonMixing, self).__init__()
  
          self.down_sampling_layers = torch.nn.ModuleList(
              [
                  nn.Sequential(
                      torch.nn.Linear(
                          math.ceil(seq_len // (down_sampling_window**i)),
                          math.ceil(seq_len // (down_sampling_window ** (i + 1))),
                      ),
                      nn.GELU(),
                      torch.nn.Linear(
                          math.ceil(seq_len // (down_sampling_window ** (i + 1))),
                          math.ceil(seq_len // (down_sampling_window ** (i + 1))),
                      ),
                  )
                  for i in range(down_sampling_layers)
              ]
          )
  
      def forward(self, season_list):
  
          # mixing high->low
          out_high = season_list[0]
          out_low = season_list[1]
          out_season_list = [out_high.permute(0, 2, 1)]
  
          for i in range(len(season_list) - 1):
              out_low_res = self.down_sampling_layers[i](out_high)
              out_low = out_low + out_low_res
              out_high = out_low
              if i + 2 <= len(season_list) - 1:
                  out_low = season_list[i + 2]
              out_season_list.append(out_high.permute(0, 2, 1))
  
          return out_season_list
  
  
  class MultiScaleTrendMixing(nn.Module):
      """
      Top-down mixing trend pattern
      """
  
      def __init__(self, seq_len, down_sampling_window, down_sampling_layers):
          super(MultiScaleTrendMixing, self).__init__()
  
          self.up_sampling_layers = torch.nn.ModuleList(
              [
                  nn.Sequential(
                      torch.nn.Linear(
                          math.ceil(seq_len / (down_sampling_window ** (i + 1))),
                          math.ceil(seq_len / (down_sampling_window**i)),
                      ),
                      nn.GELU(),
                      torch.nn.Linear(
                          math.ceil(seq_len / (down_sampling_window**i)),
                          math.ceil(seq_len / (down_sampling_window**i)),
                      ),
                  )
                  for i in reversed(range(down_sampling_layers))
              ]
          )
  
      def forward(self, trend_list):
  
          # mixing low->high
          trend_list_reverse = trend_list.copy()
          trend_list_reverse.reverse()
          out_low = trend_list_reverse[0]
          out_high = trend_list_reverse[1]
          out_trend_list = [out_low.permute(0, 2, 1)]
  
          for i in range(len(trend_list_reverse) - 1):
              out_high_res = self.up_sampling_layers[i](out_low)
              out_high = out_high + out_high_res
              out_low = out_high
              if i + 2 <= len(trend_list_reverse) - 1:
                  out_high = trend_list_reverse[i + 2]
              out_trend_list.append(out_low.permute(0, 2, 1))
  
          out_trend_list.reverse()
          return out_trend_list
  
  
  class PastDecomposableMixing(nn.Module):
      """
      PastDecomposableMixing
      """
  
      def __init__(
          self,
          seq_len,
          pred_len,
          down_sampling_window,
          down_sampling_layers,
          d_model,
          dropout,
          channel_independence,
          decomp_method,
          d_ff,
          moving_avg,
          top_k,
      ):
          super(PastDecomposableMixing, self).__init__()
          self.seq_len = seq_len
          self.pred_len = pred_len
          self.down_sampling_window = down_sampling_window
          self.down_sampling_layers = down_sampling_layers
  
          self.layer_norm = nn.LayerNorm(d_model)
          self.dropout = nn.Dropout(dropout)
          self.channel_independence = channel_independence
  
          if decomp_method == "moving_avg":
              self.decompsition = SeriesDecomp(moving_avg)
          elif decomp_method == "dft_decomp":
              self.decompsition = DFT_series_decomp(top_k)
          else:
              raise ValueError("decompsition is error")
  
          if self.channel_independence == 0:
              self.cross_layer = nn.Sequential(
                  nn.Linear(in_features=d_model, out_features=d_ff),
                  nn.GELU(),
                  nn.Linear(in_features=d_ff, out_features=d_model),
              )
  
          # Mixing season
          self.mixing_multi_scale_season = MultiScaleSeasonMixing(
              self.seq_len, self.down_sampling_window, self.down_sampling_layers
          )
  
          # Mxing trend
          self.mixing_multi_scale_trend = MultiScaleTrendMixing(
              self.seq_len, self.down_sampling_window, self.down_sampling_layers
          )
  
          self.out_cross_layer = nn.Sequential(
              nn.Linear(in_features=d_model, out_features=d_ff),
              nn.GELU(),
              nn.Linear(in_features=d_ff, out_features=d_model),
          )
  
      def forward(self, x_list):
          length_list = []
          for x in x_list:
              _, T, _ = x.size()
              length_list.append(T)
  
          # Decompose to obtain the season and trend
          season_list = []
          trend_list = []
          for x in x_list:
              season, trend = self.decompsition(x)
              if self.channel_independence == 0:
                  season = self.cross_layer(season)
                  trend = self.cross_layer(trend)
              season_list.append(season.permute(0, 2, 1))
              trend_list.append(trend.permute(0, 2, 1))
  
          # bottom-up season mixing
          out_season_list = self.mixing_multi_scale_season(season_list)
          # top-down trend mixing
          out_trend_list = self.mixing_multi_scale_trend(trend_list)
  
          out_list = []
          for ori, out_season, out_trend, length in zip(
              x_list, out_season_list, out_trend_list, length_list
          ):
              out = out_season + out_trend
              if self.channel_independence:
                  out = ori + self.out_cross_layer(out)
              out_list.append(out[:, :length, :])
          return out_list
  
  
  class TimeMixer(BaseModel):
      """TimeMixer
      Args:
          h (int): Forecast horizon.
          input_size (int): autorregresive inputs size, y=[1,2,3,4] input_size=2 -> y_[t-2:t]=[1,2].
          n_series (int): number of time-series.
          stat_exog_list (list): static exogenous columns.
          hist_exog_list (list): historic exogenous columns.
          futr_exog_list (list): future exogenous columns.
          d_model (int): dimension of the model.
          d_ff (int): dimension of the fully-connected network.
          dropout (float): dropout rate.
          e_layers (int): number of encoder layers.
          top_k (int): number of selected frequencies.
          decomp_method (str): method of series decomposition [moving_avg, dft_decomp].
          moving_avg (int): window size of moving average.
          channel_independence (int): 0: channel dependence, 1: channel independence.
          down_sampling_layers (int): number of downsampling layers.
          down_sampling_window (int): size of downsampling window.
          down_sampling_method (str): down sampling method [avg, max, conv].
          use_norm (bool): whether to normalize or not.
          decoder_input_size_multiplier (float): 0.5.
          loss (PyTorch module): instantiated train loss class from [losses collection](./losses.pytorch).
          valid_loss (PyTorch module): instantiated valid loss class from [losses collection](./losses.pytorch).
          max_steps (int): maximum number of training steps.
          learning_rate (float): Learning rate between (0, 1).
          num_lr_decays (int): Number of learning rate decays, evenly distributed across max_steps.
          early_stop_patience_steps (int): Number of validation iterations before early stopping.
          val_check_steps (int): Number of training steps between every validation loss check.
          batch_size (int): number of different series in each batch.
          valid_batch_size (int): number of different series in each validation and test batch, if None uses batch_size.
          windows_batch_size (int): number of windows to sample in each training batch, default uses all.
          inference_windows_batch_size (int): number of windows to sample in each inference batch, -1 uses all.
          start_padding_enabled (bool): if True, the model will pad the time series with zeros at the beginning, by input size.
          training_data_availability_threshold (Union[float, List[float]]): minimum fraction of valid data points required for training windows. Single float applies to both insample and outsample; list of two floats specifies [insample_fraction, outsample_fraction]. Default 0.0 allows windows with only 1 valid data point (current behavior).
          step_size (int): step size between each window of temporal data.
          scaler_type (str): type of scaler for temporal inputs normalization see [temporal scalers](https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/common/_scalers.py).
          random_seed (int): random_seed for pytorch initializer and numpy generators.
          drop_last_loader (bool): if True `TimeSeriesDataLoader` drops last non-full batch.
          alias (str): optional,  Custom name of the model.
          optimizer (Subclass of 'torch.optim.Optimizer'): optional, user specified optimizer instead of the default choice (Adam).
          optimizer_kwargs (dict): optional, list of parameters used by the user specified `optimizer`.
          lr_scheduler (Subclass of 'torch.optim.lr_scheduler.LRScheduler'): optional, user specified lr_scheduler instead of the default choice (StepLR).
          lr_scheduler_kwargs (dict): optional, list of parameters used by the user specified `lr_scheduler`.
          dataloader_kwargs (dict): optional, list of parameters passed into the PyTorch Lightning dataloader by the `TimeSeriesDataLoader`.
          **trainer_kwargs (keyword): trainer arguments inherited from [PyTorch Lighning's trainer](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).
  
      References:
          - [Shiyu Wang, Haixu Wu, Xiaoming Shi, Tengge Hu, Huakun Luo, Lintao Ma, James Y. Zhang, Jun Zhou."TimeMixer: Decomposable Multiscale Mixing For Time Series Forecasting"](https://openreview.net/pdf?id=7oLshfEIC2)
      """
  
      # Class attributes
      EXOGENOUS_FUTR = False
      EXOGENOUS_HIST = False
      EXOGENOUS_STAT = False
      MULTIVARIATE = True  # If the model produces multivariate forecasts (True) or univariate (False)
      RECURRENT = (
          False  # If the model produces forecasts recursively (True) or direct (False)
      )
  
      def __init__(
          self,
          h,
          input_size,
          n_series,
          stat_exog_list=None,
          hist_exog_list=None,
          futr_exog_list=None,
          d_model: int = 32,
          d_ff: int = 32,
          dropout: float = 0.1,
          e_layers: int = 4,
          top_k: int = 5,
          decomp_method: str = "moving_avg",
          moving_avg: int = 25,
          channel_independence: int = 0,
          down_sampling_layers: int = 1,
          down_sampling_window: int = 2,
          down_sampling_method: str = "avg",
          use_norm: bool = True,
          decoder_input_size_multiplier: float = 0.5,
          loss=MAE(),
          valid_loss=None,
          max_steps: int = 1000,
          learning_rate: float = 1e-3,
          num_lr_decays: int = -1,
          early_stop_patience_steps: int = -1,
          val_check_steps: int = 100,
          batch_size: int = 32,
          valid_batch_size: Optional[int] = None,
          windows_batch_size=32,
          inference_windows_batch_size=32,
          start_padding_enabled=False,
          training_data_availability_threshold=0.0,
          step_size: int = 1,
          scaler_type: str = "identity",
          random_seed: int = 1,
          drop_last_loader: bool = False,
          alias: Optional[str] = None,
          optimizer=None,
          optimizer_kwargs=None,
          lr_scheduler=None,
          lr_scheduler_kwargs=None,
          dataloader_kwargs=None,
          **trainer_kwargs,
      ):
  
          super(TimeMixer, self).__init__(
              h=h,
              input_size=input_size,
              n_series=n_series,
              stat_exog_list=stat_exog_list,
              futr_exog_list=futr_exog_list,
              hist_exog_list=hist_exog_list,
              loss=loss,
              valid_loss=valid_loss,
              max_steps=max_steps,
              learning_rate=learning_rate,
              num_lr_decays=num_lr_decays,
              early_stop_patience_steps=early_stop_patience_steps,
              val_check_steps=val_check_steps,
              batch_size=batch_size,
              valid_batch_size=valid_batch_size,
              windows_batch_size=windows_batch_size,
              inference_windows_batch_size=inference_windows_batch_size,
              start_padding_enabled=start_padding_enabled,
              training_data_availability_threshold=training_data_availability_threshold,
              step_size=step_size,
              scaler_type=scaler_type,
              random_seed=random_seed,
              drop_last_loader=drop_last_loader,
              alias=alias,
              optimizer=optimizer,
              optimizer_kwargs=optimizer_kwargs,
              lr_scheduler=lr_scheduler,
              lr_scheduler_kwargs=lr_scheduler_kwargs,
              dataloader_kwargs=dataloader_kwargs,
              **trainer_kwargs,
          )
  
          self.label_len = int(np.ceil(input_size * decoder_input_size_multiplier))
          if (self.label_len >= input_size) or (self.label_len <= 0):
              raise Exception(
                  f"Check decoder_input_size_multiplier={decoder_input_size_multiplier}, range (0,1)"
              )
  
          self.h = h
          self.input_size = input_size
          self.e_layers = e_layers
          self.d_model = d_model
          self.d_ff = d_ff
          self.dropout = dropout
          self.top_k = top_k
  
          self.use_norm = use_norm
  
          self.use_future_temporal_feature = 0
          if futr_exog_list is not None:
              self.use_future_temporal_feature = 1
  
          self.decomp_method = decomp_method
          self.moving_avg = moving_avg
          self.channel_independence = channel_independence
  
          self.down_sampling_layers = down_sampling_layers
          self.down_sampling_window = down_sampling_window
          self.down_sampling_method = down_sampling_method
  
          self.pdm_blocks = nn.ModuleList(
              [
                  PastDecomposableMixing(
                      self.input_size,
                      self.h,
                      self.down_sampling_window,
                      self.down_sampling_layers,
                      self.d_model,
                      self.dropout,
                      self.channel_independence,
                      self.decomp_method,
                      self.d_ff,
                      self.moving_avg,
                      self.top_k,
                  )
                  for _ in range(self.e_layers)
              ]
          )
  
          self.preprocess = SeriesDecomp(self.moving_avg)
          self.enc_in = n_series
          self.c_out = n_series
  
          if self.channel_independence == 1:
              self.enc_embedding = DataEmbedding_wo_pos(1, self.d_model, self.dropout)
          else:
              self.enc_embedding = DataEmbedding_wo_pos(
                  self.enc_in, self.d_model, self.dropout
              )
  
          self.normalize_layers = torch.nn.ModuleList(
              [
                  RevIN(
                      self.enc_in, affine=True, non_norm=False if self.use_norm else True
                  )
                  for i in range(self.down_sampling_layers + 1)
              ]
          )
  
          self.predict_layers = torch.nn.ModuleList(
              [
                  torch.nn.Linear(
                      math.ceil(self.input_size // (self.down_sampling_window**i)),
                      self.h,
                  )
                  for i in range(self.down_sampling_layers + 1)
              ]
          )
  
          if self.channel_independence == 1:
              self.projection_layer = nn.Linear(self.d_model, 1, bias=True)
          else:
              self.projection_layer = nn.Linear(self.d_model, self.c_out, bias=True)
  
              self.out_res_layers = torch.nn.ModuleList(
                  [
                      torch.nn.Linear(
                          self.input_size // (self.down_sampling_window**i),
                          self.input_size // (self.down_sampling_window**i),
                      )
                      for i in range(self.down_sampling_layers + 1)
                  ]
              )
  
              self.regression_layers = torch.nn.ModuleList(
                  [
                      torch.nn.Linear(
                          self.input_size // (self.down_sampling_window**i),
                          self.h,
                      )
                      for i in range(self.down_sampling_layers + 1)
                  ]
              )
  
          if self.loss.outputsize_multiplier > 1:
              self.distr_output = nn.Linear(
                  self.n_series, self.n_series * self.loss.outputsize_multiplier
              )
  
      def out_projection(self, dec_out, i, out_res):
          dec_out = self.projection_layer(dec_out)
          out_res = out_res.permute(0, 2, 1)
          out_res = self.out_res_layers[i](out_res)
          out_res = self.regression_layers[i](out_res).permute(0, 2, 1)
          dec_out = dec_out + out_res
          return dec_out
  
      def pre_enc(self, x_list):
          if self.channel_independence == 1:
              return (x_list, None)
          else:
              out1_list = []
              out2_list = []
              for x in x_list:
                  x_1, x_2 = self.preprocess(x)
                  out1_list.append(x_1)
                  out2_list.append(x_2)
              return (out1_list, out2_list)
  
      def __multi_scale_process_inputs(self, x_enc, x_mark_enc):
          if self.down_sampling_method == "max":
              down_pool = torch.nn.MaxPool1d(
                  self.down_sampling_window, return_indices=False
              )
          elif self.down_sampling_method == "avg":
              down_pool = torch.nn.AvgPool1d(self.down_sampling_window)
          elif self.down_sampling_method == "conv":
              padding = 1
              down_pool = nn.Conv1d(
                  in_channels=self.enc_in,
                  out_channels=self.enc_in,
                  kernel_size=3,
                  padding=padding,
                  stride=self.down_sampling_window,
                  padding_mode="circular",
                  bias=False,
              )
          else:
              return x_enc, x_mark_enc
          # B,T,C -> B,C,T
          x_enc = x_enc.permute(0, 2, 1)
  
          x_enc_ori = x_enc
          x_mark_enc_mark_ori = x_mark_enc
  
          x_enc_sampling_list = []
          x_mark_sampling_list = []
          x_enc_sampling_list.append(x_enc.permute(0, 2, 1))
          x_mark_sampling_list.append(x_mark_enc)
  
          for i in range(self.down_sampling_layers):
              x_enc_sampling = down_pool(x_enc_ori)
  
              x_enc_sampling_list.append(x_enc_sampling.permute(0, 2, 1))
              x_enc_ori = x_enc_sampling
  
              if x_mark_enc_mark_ori is not None:
                  x_mark_sampling_list.append(
                      x_mark_enc_mark_ori[:, :: self.down_sampling_window, :]
                  )
                  x_mark_enc_mark_ori = x_mark_enc_mark_ori[
                      :, :: self.down_sampling_window, :
                  ]
  
          x_enc = x_enc_sampling_list
          if x_mark_enc_mark_ori is not None:
              x_mark_enc = x_mark_sampling_list
          else:
              x_mark_enc = x_mark_enc
  
          return x_enc, x_mark_enc
  
      def forecast(self, x_enc, x_mark_enc, x_mark_dec):
  
          if self.use_future_temporal_feature:
              if self.channel_independence == 1:
                  B, T, N = x_enc.size()
                  x_mark_dec = x_mark_dec.repeat(N, 1, 1)
                  self.x_mark_dec = self.enc_embedding(None, x_mark_dec)
              else:
                  self.x_mark_dec = self.enc_embedding(None, x_mark_dec)
  
          x_enc, x_mark_enc = self.__multi_scale_process_inputs(x_enc, x_mark_enc)
  
          x_list = []
          x_mark_list = []
          if x_mark_enc is not None:
              for i, x, x_mark in zip(range(len(x_enc)), x_enc, x_mark_enc):
                  B, T, N = x.size()
                  x = self.normalize_layers[i](x, "norm")
                  if self.channel_independence == 1:
                      x = x.permute(0, 2, 1).contiguous().reshape(B * N, T, 1)
                      x_mark = x_mark.repeat(N, 1, 1)
                  x_list.append(x)
                  x_mark_list.append(x_mark)
          else:
              for i, x in zip(
                  range(len(x_enc)),
                  x_enc,
              ):
                  B, T, N = x.size()
                  x = self.normalize_layers[i](x, "norm")
                  if self.channel_independence == 1:
                      x = x.permute(0, 2, 1).contiguous().reshape(B * N, T, 1)
                  x_list.append(x)
  
          # embedding
          enc_out_list = []
          x_list = self.pre_enc(x_list)
          if x_mark_enc is not None:
              for i, x, x_mark in zip(range(len(x_list[0])), x_list[0], x_mark_list):
                  enc_out = self.enc_embedding(x, x_mark)  # [B,T,C]
                  enc_out_list.append(enc_out)
          else:
              for i, x in zip(range(len(x_list[0])), x_list[0]):
                  enc_out = self.enc_embedding(x, None)  # [B,T,C]
                  enc_out_list.append(enc_out)
  
          # Past Decomposable Mixing as encoder for past
          for i in range(self.e_layers):
              enc_out_list = self.pdm_blocks[i](enc_out_list)
  
          # Future Multipredictor Mixing as decoder for future
          dec_out_list = self.future_multi_mixing(B, enc_out_list, x_list)
  
          dec_out = torch.stack(dec_out_list, dim=-1).sum(-1)
          dec_out = self.normalize_layers[0](dec_out, "denorm")
          return dec_out
  
      def future_multi_mixing(self, B, enc_out_list, x_list):
          dec_out_list = []
          if self.channel_independence == 1:
              x_list = x_list[0]
              for i, enc_out in zip(range(len(x_list)), enc_out_list):
                  dec_out = self.predict_layers[i](enc_out.permute(0, 2, 1)).permute(
                      0, 2, 1
                  )  # align temporal dimension
                  if self.use_future_temporal_feature:
                      dec_out = dec_out + self.x_mark_dec
                      dec_out = self.projection_layer(dec_out)
                  else:
                      dec_out = self.projection_layer(dec_out)
                  dec_out = (
                      dec_out.reshape(B, self.c_out, self.h).permute(0, 2, 1).contiguous()
                  )
                  dec_out_list.append(dec_out)
  
          else:
              for i, enc_out, out_res in zip(
                  range(len(x_list[0])), enc_out_list, x_list[1]
              ):
                  dec_out = self.predict_layers[i](enc_out.permute(0, 2, 1)).permute(
                      0, 2, 1
                  )  # align temporal dimension
                  dec_out = self.out_projection(dec_out, i, out_res)
                  dec_out_list.append(dec_out)
  
          return dec_out_list
  
      def forward(self, windows_batch):
          insample_y = windows_batch["insample_y"]
          futr_exog = windows_batch["futr_exog"]
  
          if self.futr_exog_size > 0:
              x_mark_enc = futr_exog[:, :, : self.input_size, :]
              x_mark_dec = futr_exog[:, :, -(self.label_len + self.h) :, :]
          else:
              x_mark_enc = None
              x_mark_dec = None
  
          y_pred = self.forecast(insample_y, x_mark_enc, x_mark_dec)
          y_pred = y_pred[:, -self.h :, :]
          if self.loss.outputsize_multiplier > 1:
              y_pred = self.distr_output(y_pred)
  
          return y_pred
  