content: 
  
  
  __all__ = ['LayerNorm', 'AutoCorrelationLayer', 'EncoderLayer', 'Encoder', 'DecoderLayer', 'Decoder', 'get_frequency_modes',
             'FourierBlock', 'FourierCrossAttention', 'FEDformer']
  
  
  from typing import Optional
  
  import numpy as np
  import torch
  import torch.nn as nn
  import torch.nn.functional as F
  
  from ..common._base_model import BaseModel
  from ..common._modules import DataEmbedding, SeriesDecomp
  from ..losses.pytorch import MAE
  
  
  class LayerNorm(nn.Module):
      """
      Special designed layernorm for the seasonal part
      """
  
      def __init__(self, channels):
          super(LayerNorm, self).__init__()
          self.layernorm = nn.LayerNorm(channels)
  
      def forward(self, x):
          x_hat = self.layernorm(x)
          bias = torch.mean(x_hat, dim=1).unsqueeze(1).repeat(1, x.shape[1], 1)
          return x_hat - bias
  
  
  class AutoCorrelationLayer(nn.Module):
      """
      Auto Correlation Layer
      """
  
      def __init__(self, correlation, hidden_size, n_head, d_keys=None, d_values=None):
          super(AutoCorrelationLayer, self).__init__()
  
          d_keys = d_keys or (hidden_size // n_head)
          d_values = d_values or (hidden_size // n_head)
  
          self.inner_correlation = correlation
          self.query_projection = nn.Linear(hidden_size, d_keys * n_head)
          self.key_projection = nn.Linear(hidden_size, d_keys * n_head)
          self.value_projection = nn.Linear(hidden_size, d_values * n_head)
          self.out_projection = nn.Linear(d_values * n_head, hidden_size)
          self.n_head = n_head
  
      def forward(self, queries, keys, values, attn_mask):
          B, L, _ = queries.shape
          _, S, _ = keys.shape
          H = self.n_head
  
          queries = self.query_projection(queries).view(B, L, H, -1)
          keys = self.key_projection(keys).view(B, S, H, -1)
          values = self.value_projection(values).view(B, S, H, -1)
  
          out, attn = self.inner_correlation(queries, keys, values, attn_mask)
          out = out.view(B, L, -1)
  
          return self.out_projection(out), attn
  
  
  class EncoderLayer(nn.Module):
      """
      FEDformer encoder layer with the progressive decomposition architecture
      """
  
      def __init__(
          self,
          attention,
          hidden_size,
          conv_hidden_size=None,
          MovingAvg=25,
          dropout=0.1,
          activation="relu",
      ):
          super(EncoderLayer, self).__init__()
          conv_hidden_size = conv_hidden_size or 4 * hidden_size
          self.attention = attention
          self.conv1 = nn.Conv1d(
              in_channels=hidden_size,
              out_channels=conv_hidden_size,
              kernel_size=1,
              bias=False,
          )
          self.conv2 = nn.Conv1d(
              in_channels=conv_hidden_size,
              out_channels=hidden_size,
              kernel_size=1,
              bias=False,
          )
          self.decomp1 = SeriesDecomp(MovingAvg)
          self.decomp2 = SeriesDecomp(MovingAvg)
          self.dropout = nn.Dropout(dropout)
          self.activation = F.relu if activation == "relu" else F.gelu
  
      def forward(self, x, attn_mask=None):
          new_x, attn = self.attention(x, x, x, attn_mask=attn_mask)
          x = x + self.dropout(new_x)
          x, _ = self.decomp1(x)
          y = x
          y = self.dropout(self.activation(self.conv1(y.transpose(-1, 1))))
          y = self.dropout(self.conv2(y).transpose(-1, 1))
          res, _ = self.decomp2(x + y)
          return res, attn
  
  
  class Encoder(nn.Module):
      """
      FEDformer encoder
      """
  
      def __init__(self, attn_layers, conv_layers=None, norm_layer=None):
          super(Encoder, self).__init__()
          self.attn_layers = nn.ModuleList(attn_layers)
          self.conv_layers = (
              nn.ModuleList(conv_layers) if conv_layers is not None else None
          )
          self.norm = norm_layer
  
      def forward(self, x, attn_mask=None):
          attns = []
          if self.conv_layers is not None:
              for attn_layer, conv_layer in zip(self.attn_layers, self.conv_layers):
                  x, attn = attn_layer(x, attn_mask=attn_mask)
                  x = conv_layer(x)
                  attns.append(attn)
              x, attn = self.attn_layers[-1](x)
              attns.append(attn)
          else:
              for attn_layer in self.attn_layers:
                  x, attn = attn_layer(x, attn_mask=attn_mask)
                  attns.append(attn)
  
          if self.norm is not None:
              x = self.norm(x)
  
          return x, attns
  
  
  class DecoderLayer(nn.Module):
      """
      FEDformer decoder layer with the progressive decomposition architecture
      """
  
      def __init__(
          self,
          self_attention,
          cross_attention,
          hidden_size,
          c_out,
          conv_hidden_size=None,
          MovingAvg=25,
          dropout=0.1,
          activation="relu",
      ):
          super(DecoderLayer, self).__init__()
          conv_hidden_size = conv_hidden_size or 4 * hidden_size
          self.self_attention = self_attention
          self.cross_attention = cross_attention
          self.conv1 = nn.Conv1d(
              in_channels=hidden_size,
              out_channels=conv_hidden_size,
              kernel_size=1,
              bias=False,
          )
          self.conv2 = nn.Conv1d(
              in_channels=conv_hidden_size,
              out_channels=hidden_size,
              kernel_size=1,
              bias=False,
          )
          self.decomp1 = SeriesDecomp(MovingAvg)
          self.decomp2 = SeriesDecomp(MovingAvg)
          self.decomp3 = SeriesDecomp(MovingAvg)
          self.dropout = nn.Dropout(dropout)
          self.projection = nn.Conv1d(
              in_channels=hidden_size,
              out_channels=c_out,
              kernel_size=3,
              stride=1,
              padding=1,
              padding_mode="circular",
              bias=False,
          )
          self.activation = F.relu if activation == "relu" else F.gelu
  
      def forward(self, x, cross, x_mask=None, cross_mask=None):
          x = x + self.dropout(self.self_attention(x, x, x, attn_mask=x_mask)[0])
          x, trend1 = self.decomp1(x)
          x = x + self.dropout(
              self.cross_attention(x, cross, cross, attn_mask=cross_mask)[0]
          )
          x, trend2 = self.decomp2(x)
          y = x
          y = self.dropout(self.activation(self.conv1(y.transpose(-1, 1))))
          y = self.dropout(self.conv2(y).transpose(-1, 1))
          x, trend3 = self.decomp3(x + y)
  
          residual_trend = trend1 + trend2 + trend3
          residual_trend = self.projection(residual_trend.permute(0, 2, 1)).transpose(
              1, 2
          )
          return x, residual_trend
  
  
  class Decoder(nn.Module):
      """
      FEDformer decoder
      """
  
      def __init__(self, layers, norm_layer=None, projection=None):
          super(Decoder, self).__init__()
          self.layers = nn.ModuleList(layers)
          self.norm = norm_layer
          self.projection = projection
  
      def forward(self, x, cross, x_mask=None, cross_mask=None, trend=None):
          for layer in self.layers:
              x, residual_trend = layer(x, cross, x_mask=x_mask, cross_mask=cross_mask)
              trend = trend + residual_trend
  
          if self.norm is not None:
              x = self.norm(x)
  
          if self.projection is not None:
              x = self.projection(x)
          return x, trend
  
  
  def get_frequency_modes(seq_len, modes=64, mode_select_method="random"):
      """
      Get modes on frequency domain:
          'random' for sampling randomly
          'else' for sampling the lowest modes;
      """
      modes = min(modes, seq_len // 2)
      if mode_select_method == "random":
          index = list(range(0, seq_len // 2))
          np.random.shuffle(index)
          index = index[:modes]
      else:
          index = list(range(0, modes))
      index.sort()
      return index
  
  
  class FourierBlock(nn.Module):
      """
      Fourier block
      """
  
      def __init__(
          self, in_channels, out_channels, seq_len, modes=0, mode_select_method="random"
      ):
          super(FourierBlock, self).__init__()
          # get modes on frequency domain
          self.index = get_frequency_modes(
              seq_len, modes=modes, mode_select_method=mode_select_method
          )
  
          self.scale = 1 / (in_channels * out_channels)
          self.weights1 = nn.Parameter(
              self.scale
              * torch.rand(
                  8,
                  in_channels // 8,
                  out_channels // 8,
                  len(self.index),
                  dtype=torch.cfloat,
              )
          )
  
      # Complex multiplication
      def compl_mul1d(self, input, weights):
          # (batch, in_channel, x ), (in_channel, out_channel, x) -> (batch, out_channel, x)
          return torch.einsum("bhi,hio->bho", input, weights)
  
      def forward(self, q, k, v, mask):
          # size = [B, L, H, E]
          B, L, H, E = q.shape
  
          x = q.permute(0, 2, 3, 1)
          # Compute Fourier coefficients
          x_ft = torch.fft.rfft(x, dim=-1)
          # Perform Fourier neural operations
          out_ft = torch.zeros(B, H, E, L // 2 + 1, device=x.device, dtype=torch.cfloat)
          for wi, i in enumerate(self.index):
              out_ft[:, :, :, wi] = self.compl_mul1d(
                  x_ft[:, :, :, i], self.weights1[:, :, :, wi]
              )
          # Return to time domain
          x = torch.fft.irfft(out_ft, n=x.size(-1))
          return (x, None)
  
  
  class FourierCrossAttention(nn.Module):
      """
      Fourier Cross Attention layer
      """
  
      def __init__(
          self,
          in_channels,
          out_channels,
          seq_len_q,
          seq_len_kv,
          modes=64,
          mode_select_method="random",
          activation="tanh",
          policy=0,
      ):
          super(FourierCrossAttention, self).__init__()
          self.activation = activation
          self.in_channels = in_channels
          self.out_channels = out_channels
          # get modes for queries and keys (& values) on frequency domain
          self.index_q = get_frequency_modes(
              seq_len_q, modes=modes, mode_select_method=mode_select_method
          )
          self.index_kv = get_frequency_modes(
              seq_len_kv, modes=modes, mode_select_method=mode_select_method
          )
  
          self.scale = 1 / (in_channels * out_channels)
          self.weights1 = nn.Parameter(
              self.scale
              * torch.rand(
                  8,
                  in_channels // 8,
                  out_channels // 8,
                  len(self.index_q),
                  dtype=torch.cfloat,
              )
          )
  
      # Complex multiplication
      def compl_mul1d(self, input, weights):
          # (batch, in_channel, x ), (in_channel, out_channel, x) -> (batch, out_channel, x)
          return torch.einsum("bhi,hio->bho", input, weights)
  
      def forward(self, q, k, v, mask):
          # size = [B, L, H, E]
          B, L, H, E = q.shape
          xq = q.permute(0, 2, 3, 1)  # size = [B, H, E, L]
          xk = k.permute(0, 2, 3, 1)
          # xv = v.permute(0, 2, 3, 1)
  
          # Compute Fourier coefficients
          xq_ft_ = torch.zeros(
              B, H, E, len(self.index_q), device=xq.device, dtype=torch.cfloat
          )
          xq_ft = torch.fft.rfft(xq, dim=-1)
          for i, j in enumerate(self.index_q):
              xq_ft_[:, :, :, i] = xq_ft[:, :, :, j]
          xk_ft_ = torch.zeros(
              B, H, E, len(self.index_kv), device=xq.device, dtype=torch.cfloat
          )
          xk_ft = torch.fft.rfft(xk, dim=-1)
          for i, j in enumerate(self.index_kv):
              xk_ft_[:, :, :, i] = xk_ft[:, :, :, j]
  
          # Attention mechanism on frequency domain
          xqk_ft = torch.einsum("bhex,bhey->bhxy", xq_ft_, xk_ft_)
          if self.activation == "tanh":
              xqk_ft = xqk_ft.tanh()
          elif self.activation == "softmax":
              xqk_ft = torch.softmax(abs(xqk_ft), dim=-1)
              xqk_ft = torch.complex(xqk_ft, torch.zeros_like(xqk_ft))
          else:
              raise Exception(
                  "{} actiation function is not implemented".format(self.activation)
              )
          xqkv_ft = torch.einsum("bhxy,bhey->bhex", xqk_ft, xk_ft_)
          xqkvw = torch.einsum("bhex,heox->bhox", xqkv_ft, self.weights1)
          out_ft = torch.zeros(B, H, E, L // 2 + 1, device=xq.device, dtype=torch.cfloat)
          for i, j in enumerate(self.index_q):
              out_ft[:, :, :, j] = xqkvw[:, :, :, i]
  
          # Return to time domain
          out = torch.fft.irfft(
              out_ft / self.in_channels / self.out_channels, n=xq.size(-1)
          )
          return (out, None)
  
  
  class FEDformer(BaseModel):
      """FEDformer
  
      The FEDformer model tackles the challenge of finding reliable dependencies on intricate temporal patterns of long-horizon forecasting.
  
      The architecture has the following distinctive features:
      - In-built progressive decomposition in trend and seasonal components based on a moving average filter.
      - Frequency Enhanced Block and Frequency Enhanced Attention to perform attention in the sparse representation on basis such as Fourier transform.
      - Classic encoder-decoder proposed by Vaswani et al. (2017) with a multi-head attention mechanism.
  
      The FEDformer model utilizes a three-component approach to define its embedding:
      - It employs encoded autoregressive features obtained from a convolution network.
      - Absolute positional embeddings obtained from calendar features are utilized.
  
      Args:
          h (int): forecast horizon.
          input_size (int): maximum sequence length for truncated train backpropagation.
          stat_exog_list (List[str]): static exogenous columns.
          hist_exog_list (List[str]): historic exogenous columns.
          futr_exog_list (List[str]): future exogenous columns.
          decoder_input_size_multiplier (float): multiplier for the input size of the decoder.
          version (str): version of the model.
          modes (int): number of modes for the Fourier block.
          mode_select (str): method to select the modes for the Fourier block.
          hidden_size (int): units of embeddings and encoders.
          dropout (float): dropout throughout Autoformer architecture.
          n_head (int): controls number of multi-head's attention.
          conv_hidden_size (int): channels of the convolutional encoder.
          activation (str): activation from ['ReLU', 'Softplus', 'Tanh', 'SELU', 'LeakyReLU', 'PReLU', 'Sigmoid', 'GELU'].
          encoder_layers (int): number of layers for the TCN encoder.
          decoder_layers (int): number of layers for the MLP decoder.
          MovingAvg_window (int): window size for the moving average filter.
          loss (PyTorch module): instantiated train loss class from [losses collection](./losses.pytorch).
          valid_loss (PyTorch module): instantiated validation 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.
          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 (int):  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:
          - [Tian Zhou, et al. "FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting" Proceedings of the AAAI conference on artificial intelligence. Vol. 37. No. 9. 2023."](https://arxiv.org/abs/2201.12740)
  
      """
  
      # Class attributes
      EXOGENOUS_FUTR = True
      EXOGENOUS_HIST = False
      EXOGENOUS_STAT = False
      MULTIVARIATE = False  # 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: int,
          input_size: int,
          stat_exog_list=None,
          hist_exog_list=None,
          futr_exog_list=None,
          decoder_input_size_multiplier: float = 0.5,
          version: str = "Fourier",
          modes: int = 64,
          mode_select: str = "random",
          hidden_size: int = 128,
          dropout: float = 0.05,
          n_head: int = 8,
          conv_hidden_size: int = 32,
          activation: str = "gelu",
          encoder_layers: int = 2,
          decoder_layers: int = 1,
          MovingAvg_window: int = 25,
          loss=MAE(),
          valid_loss=None,
          max_steps: int = 5000,
          learning_rate: float = 1e-4,
          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=1024,
          inference_windows_batch_size=1024,
          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(FEDformer, self).__init__(
              h=h,
              input_size=input_size,
              stat_exog_list=stat_exog_list,
              hist_exog_list=hist_exog_list,
              futr_exog_list=futr_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,
          )
          # Architecture
          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)"
              )
  
          if activation not in ["relu", "gelu"]:
              raise Exception(f"Check activation={activation}")
  
          if n_head != 8:
              raise Exception("n_head must be 8")
  
          if version not in ["Fourier"]:
              raise Exception("Only Fourier version is supported currently.")
  
          self.c_out = self.loss.outputsize_multiplier
          self.output_attention = False
          self.enc_in = 1
          self.dec_in = 1
  
          self.decomp = SeriesDecomp(MovingAvg_window)
  
          # Embedding
          self.enc_embedding = DataEmbedding(
              c_in=self.enc_in,
              exog_input_size=self.futr_exog_size,
              hidden_size=hidden_size,
              pos_embedding=False,
              dropout=dropout,
          )
          self.dec_embedding = DataEmbedding(
              self.dec_in,
              exog_input_size=self.futr_exog_size,
              hidden_size=hidden_size,
              pos_embedding=False,
              dropout=dropout,
          )
  
          encoder_self_att = FourierBlock(
              in_channels=hidden_size,
              out_channels=hidden_size,
              seq_len=input_size,
              modes=modes,
              mode_select_method=mode_select,
          )
          decoder_self_att = FourierBlock(
              in_channels=hidden_size,
              out_channels=hidden_size,
              seq_len=input_size // 2 + self.h,
              modes=modes,
              mode_select_method=mode_select,
          )
          decoder_cross_att = FourierCrossAttention(
              in_channels=hidden_size,
              out_channels=hidden_size,
              seq_len_q=input_size // 2 + self.h,
              seq_len_kv=input_size,
              modes=modes,
              mode_select_method=mode_select,
          )
  
          self.encoder = Encoder(
              [
                  EncoderLayer(
                      AutoCorrelationLayer(encoder_self_att, hidden_size, n_head),
                      hidden_size=hidden_size,
                      conv_hidden_size=conv_hidden_size,
                      MovingAvg=MovingAvg_window,
                      dropout=dropout,
                      activation=activation,
                  )
                  for l in range(encoder_layers)
              ],
              norm_layer=LayerNorm(hidden_size),
          )
          # Decoder
          self.decoder = Decoder(
              [
                  DecoderLayer(
                      AutoCorrelationLayer(decoder_self_att, hidden_size, n_head),
                      AutoCorrelationLayer(decoder_cross_att, hidden_size, n_head),
                      hidden_size=hidden_size,
                      c_out=self.c_out,
                      conv_hidden_size=conv_hidden_size,
                      MovingAvg=MovingAvg_window,
                      dropout=dropout,
                      activation=activation,
                  )
                  for l in range(decoder_layers)
              ],
              norm_layer=LayerNorm(hidden_size),
              projection=nn.Linear(hidden_size, self.c_out, bias=True),
          )
  
      def forward(self, windows_batch):
          # Parse windows_batch
          insample_y = windows_batch["insample_y"]
          futr_exog = windows_batch["futr_exog"]
  
          # Parse inputs
          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
  
          x_dec = torch.zeros(
              size=(len(insample_y), self.h, self.dec_in), device=insample_y.device
          )
          x_dec = torch.cat([insample_y[:, -self.label_len :, :], x_dec], dim=1)
  
          # decomp init
          mean = torch.mean(insample_y, dim=1).unsqueeze(1).repeat(1, self.h, 1)
          zeros = torch.zeros(
              [x_dec.shape[0], self.h, x_dec.shape[2]], device=insample_y.device
          )
          seasonal_init, trend_init = self.decomp(insample_y)
          # decoder input
          trend_init = torch.cat([trend_init[:, -self.label_len :, :], mean], dim=1)
          seasonal_init = torch.cat(
              [seasonal_init[:, -self.label_len :, :], zeros], dim=1
          )
          # enc
          enc_out = self.enc_embedding(insample_y, x_mark_enc)
          enc_out, attns = self.encoder(enc_out, attn_mask=None)
          # dec
          dec_out = self.dec_embedding(seasonal_init, x_mark_dec)
          seasonal_part, trend_part = self.decoder(
              dec_out, enc_out, x_mask=None, cross_mask=None, trend=trend_init
          )
          # final
          dec_out = trend_part + seasonal_part
          forecast = dec_out[:, -self.h :]
  
          return forecast
  