content: 
  
  
  __all__ = ['AutoCorrelation', 'AutoCorrelationLayer', 'LayerNorm', 'EncoderLayer', 'Encoder', 'DecoderLayer', 'Decoder',
             'Autoformer']
  
  
  import math
  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 AutoCorrelation(nn.Module):
      """
      AutoCorrelation Mechanism with the following two phases:
      (1) period-based dependencies discovery
      (2) time delay aggregation
      This block can replace the self-attention family mechanism seamlessly.
      """
  
      def __init__(
          self,
          mask_flag=True,
          factor=1,
          scale=None,
          attention_dropout=0.1,
          output_attention=False,
      ):
          super(AutoCorrelation, self).__init__()
          self.factor = factor
          self.scale = scale
          self.mask_flag = mask_flag
          self.output_attention = output_attention
          self.dropout = nn.Dropout(attention_dropout)
  
      def time_delay_agg_training(self, values, corr):
          """
          SpeedUp version of Autocorrelation (a batch-normalization style design)
          This is for the training phase.
          """
          head = values.shape[1]
          channel = values.shape[2]
          length = values.shape[3]
          # find top k
          top_k = int(self.factor * math.log(length))
          mean_value = torch.mean(torch.mean(corr, dim=1), dim=1)
          index = torch.topk(torch.mean(mean_value, dim=0), top_k, dim=-1)[1]
          weights = torch.stack([mean_value[:, index[i]] for i in range(top_k)], dim=-1)
          # update corr
          tmp_corr = torch.softmax(weights, dim=-1)
          # aggregation
          tmp_values = values
          delays_agg = torch.zeros_like(values, dtype=torch.float, device=values.device)
          for i in range(top_k):
              pattern = torch.roll(tmp_values, -int(index[i]), -1)
              delays_agg = delays_agg + pattern * (
                  tmp_corr[:, i]
                  .unsqueeze(1)
                  .unsqueeze(1)
                  .unsqueeze(1)
                  .repeat(1, head, channel, length)
              )
          return delays_agg
  
      def time_delay_agg_inference(self, values, corr):
          """
          SpeedUp version of Autocorrelation (a batch-normalization style design)
          This is for the inference phase.
          """
          batch = values.shape[0]
          head = values.shape[1]
          channel = values.shape[2]
          length = values.shape[3]
          # index init
          init_index = (
              torch.arange(length, device=values.device)
              .unsqueeze(0)
              .unsqueeze(0)
              .unsqueeze(0)
              .repeat(batch, head, channel, 1)
          )
          # find top k
          top_k = int(self.factor * math.log(length))
          mean_value = torch.mean(torch.mean(corr, dim=1), dim=1)
          weights = torch.topk(mean_value, top_k, dim=-1)[0]
          delay = torch.topk(mean_value, top_k, dim=-1)[1]
          # update corr
          tmp_corr = torch.softmax(weights, dim=-1)
          # aggregation
          tmp_values = values.repeat(1, 1, 1, 2)
          delays_agg = torch.zeros_like(values, dtype=torch.float, device=values.device)
          for i in range(top_k):
              tmp_delay = init_index + delay[:, i].unsqueeze(1).unsqueeze(1).unsqueeze(
                  1
              ).repeat(1, head, channel, length)
              pattern = torch.gather(tmp_values, dim=-1, index=tmp_delay)
              delays_agg = delays_agg + pattern * (
                  tmp_corr[:, i]
                  .unsqueeze(1)
                  .unsqueeze(1)
                  .unsqueeze(1)
                  .repeat(1, head, channel, length)
              )
          return delays_agg
  
      def time_delay_agg_full(self, values, corr):
          """
          Standard version of Autocorrelation
          """
          batch = values.shape[0]
          head = values.shape[1]
          channel = values.shape[2]
          length = values.shape[3]
          # index init
          init_index = (
              torch.arange(length, device=values.device)
              .unsqueeze(0)
              .unsqueeze(0)
              .unsqueeze(0)
              .repeat(batch, head, channel, 1)
          )
          # find top k
          top_k = int(self.factor * math.log(length))
          weights = torch.topk(corr, top_k, dim=-1)[0]
          delay = torch.topk(corr, top_k, dim=-1)[1]
          # update corr
          tmp_corr = torch.softmax(weights, dim=-1)
          # aggregation
          tmp_values = values.repeat(1, 1, 1, 2)
          delays_agg = torch.zeros_like(values, dtype=torch.float, device=values.device)
          for i in range(top_k):
              tmp_delay = init_index + delay[..., i].unsqueeze(-1)
              pattern = torch.gather(tmp_values, dim=-1, index=tmp_delay)
              delays_agg = delays_agg + pattern * (tmp_corr[..., i].unsqueeze(-1))
          return delays_agg
  
      def forward(self, queries, keys, values, attn_mask):
          B, L, H, E = queries.shape
          _, S, _, D = values.shape
          if L > S:
              zeros = torch.zeros_like(
                  queries[:, : (L - S), :], dtype=torch.float, device=queries.device
              )
              values = torch.cat([values, zeros], dim=1)
              keys = torch.cat([keys, zeros], dim=1)
          else:
              values = values[:, :L, :, :]
              keys = keys[:, :L, :, :]
  
          # period-based dependencies
          q_fft = torch.fft.rfft(queries.permute(0, 2, 3, 1).contiguous(), dim=-1)
          k_fft = torch.fft.rfft(keys.permute(0, 2, 3, 1).contiguous(), dim=-1)
          res = q_fft * torch.conj(k_fft)
          corr = torch.fft.irfft(res, dim=-1)
  
          # time delay agg
          if self.training:
              V = self.time_delay_agg_training(
                  values.permute(0, 2, 3, 1).contiguous(), corr
              ).permute(0, 3, 1, 2)
          else:
              V = self.time_delay_agg_inference(
                  values.permute(0, 2, 3, 1).contiguous(), corr
              ).permute(0, 3, 1, 2)
  
          if self.output_attention:
              return (V.contiguous(), corr.permute(0, 3, 1, 2))
          else:
              return (V.contiguous(), None)
  
  
  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 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 EncoderLayer(nn.Module):
      """
      Autoformer 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):
      """
      Autoformer 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):
      """
      Autoformer 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):
      """
      Autoformer 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
  
  
  class Autoformer(BaseModel):
      """Autoformer
  
      The Autoformer 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 compontents based on a moving average filter.
      - Auto-Correlation mechanism that discovers the period-based dependencies by
      calculating the autocorrelation and aggregating similar sub-series based on the periodicity.
      - Classic encoder-decoder proposed by Vaswani et al. (2017) with a multi-head attention mechanism.
  
      The Autoformer 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. Default -1 uses all history.
          futr_exog_list (str list): future exogenous columns.
          hist_exog_list (str list): historic exogenous columns.
          stat_exog_list (str list): static exogenous columns.
          exclude_insample_y (bool): the model skips the autoregressive features y[t-input_size:t] if True.
          decoder_input_size_multiplier (float): .
          hidden_size (int): units of embeddings and encoders.
          n_head (int): controls number of multi-head's attention.
          dropout (float): dropout throughout Autoformer architecture.
          factor (int): Probsparse attention factor.
          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:
          - [Wu, Haixu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. "Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting"](https://proceedings.neurips.cc/paper/2021/hash/bcc0d400288793e8bdcd7c19a8ac0c2b-Abstract.html)
      """
  
      # 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,
          exclude_insample_y=False,
          decoder_input_size_multiplier: float = 0.5,
          hidden_size: int = 128,
          dropout: float = 0.05,
          factor: int = 3,
          n_head: int = 4,
          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(Autoformer, 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,
              exclude_insample_y=exclude_insample_y,
              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}")
  
          self.c_out = self.loss.outputsize_multiplier
          self.output_attention = False
          self.enc_in = 1
          self.dec_in = 1
  
          # Decomposition
          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.encoder = Encoder(
              [
                  EncoderLayer(
                      AutoCorrelationLayer(
                          AutoCorrelation(
                              False,
                              factor,
                              attention_dropout=dropout,
                              output_attention=self.output_attention,
                          ),
                          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(
                          AutoCorrelation(
                              True,
                              factor,
                              attention_dropout=dropout,
                              output_attention=False,
                          ),
                          hidden_size,
                          n_head,
                      ),
                      AutoCorrelationLayer(
                          AutoCorrelation(
                              False,
                              factor,
                              attention_dropout=dropout,
                              output_attention=False,
                          ),
                          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, 1), 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
  