content: 
  
  
  __all__ = ['NBEATSx']
  
  
  from typing import Optional, Tuple
  
  import numpy as np
  import torch
  import torch.nn as nn
  
  from ..common._base_model import BaseModel
  from ..losses.pytorch import MAE
  
  
  class IdentityBasis(nn.Module):
      def __init__(self, backcast_size: int, forecast_size: int, out_features: int = 1):
          super().__init__()
          self.out_features = out_features
          self.forecast_size = forecast_size
          self.backcast_size = backcast_size
  
      def forward(self, theta: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
          backcast = theta[:, : self.backcast_size]
          forecast = theta[:, self.backcast_size :]
          forecast = forecast.reshape(len(forecast), -1, self.out_features)
          return backcast, forecast
  
  
  class TrendBasis(nn.Module):
      def __init__(
          self,
          degree_of_polynomial: int,
          backcast_size: int,
          forecast_size: int,
          out_features: int = 1,
      ):
          super().__init__()
          self.out_features = out_features
          polynomial_size = degree_of_polynomial + 1
          self.backcast_basis = nn.Parameter(
              torch.tensor(
                  np.concatenate(
                      [
                          np.power(
                              np.arange(backcast_size, dtype=float) / backcast_size, i
                          )[None, :]
                          for i in range(polynomial_size)
                      ]
                  ),
                  dtype=torch.float32,
              ),
              requires_grad=False,
          )
          self.forecast_basis = nn.Parameter(
              torch.tensor(
                  np.concatenate(
                      [
                          np.power(
                              np.arange(forecast_size, dtype=float) / forecast_size, i
                          )[None, :]
                          for i in range(polynomial_size)
                      ]
                  ),
                  dtype=torch.float32,
              ),
              requires_grad=False,
          )
  
      def forward(self, theta: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
          polynomial_size = self.forecast_basis.shape[0]  # [polynomial_size, L+H]
          backcast_theta = theta[:, :polynomial_size]
          forecast_theta = theta[:, polynomial_size:]
          forecast_theta = forecast_theta.reshape(
              len(forecast_theta), polynomial_size, -1
          )
          backcast = torch.einsum("bp,pt->bt", backcast_theta, self.backcast_basis)
          forecast = torch.einsum("bpq,pt->btq", forecast_theta, self.forecast_basis)
          return backcast, forecast
  
  
  class ExogenousBasis(nn.Module):
      # Reference: https://github.com/cchallu/nbeatsx
      def __init__(self, forecast_size: int):
          super().__init__()
          self.forecast_size = forecast_size
  
      def forward(
          self, theta: torch.Tensor, futr_exog: torch.Tensor
      ) -> Tuple[torch.Tensor, torch.Tensor]:
          backcast_basis = futr_exog[:, : -self.forecast_size, :].permute(0, 2, 1)
          forecast_basis = futr_exog[:, -self.forecast_size :, :].permute(0, 2, 1)
          cut_point = forecast_basis.shape[1]
          backcast_theta = theta[:, cut_point:]
          forecast_theta = theta[:, :cut_point].reshape(len(theta), cut_point, -1)
  
          backcast = torch.einsum("bp,bpt->bt", backcast_theta, backcast_basis)
          forecast = torch.einsum("bpq,bpt->btq", forecast_theta, forecast_basis)
  
          return backcast, forecast
  
  
  class SeasonalityBasis(nn.Module):
      def __init__(
          self,
          harmonics: int,
          backcast_size: int,
          forecast_size: int,
          out_features: int = 1,
      ):
          super().__init__()
          self.out_features = out_features
          frequency = np.append(
              np.zeros(1, dtype=float),
              np.arange(harmonics, harmonics / 2 * forecast_size, dtype=float)
              / harmonics,
          )[None, :]
          backcast_grid = (
              -2
              * np.pi
              * (np.arange(backcast_size, dtype=float)[:, None] / forecast_size)
              * frequency
          )
          forecast_grid = (
              2
              * np.pi
              * (np.arange(forecast_size, dtype=float)[:, None] / forecast_size)
              * frequency
          )
  
          backcast_cos_template = torch.tensor(
              np.transpose(np.cos(backcast_grid)), dtype=torch.float32
          )
          backcast_sin_template = torch.tensor(
              np.transpose(np.sin(backcast_grid)), dtype=torch.float32
          )
          backcast_template = torch.cat(
              [backcast_cos_template, backcast_sin_template], dim=0
          )
  
          forecast_cos_template = torch.tensor(
              np.transpose(np.cos(forecast_grid)), dtype=torch.float32
          )
          forecast_sin_template = torch.tensor(
              np.transpose(np.sin(forecast_grid)), dtype=torch.float32
          )
          forecast_template = torch.cat(
              [forecast_cos_template, forecast_sin_template], dim=0
          )
  
          self.backcast_basis = nn.Parameter(backcast_template, requires_grad=False)
          self.forecast_basis = nn.Parameter(forecast_template, requires_grad=False)
  
      def forward(self, theta: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
          harmonic_size = self.forecast_basis.shape[0]  # [harmonic_size, L+H]
          backcast_theta = theta[:, :harmonic_size]
          forecast_theta = theta[:, harmonic_size:]
          forecast_theta = forecast_theta.reshape(len(forecast_theta), harmonic_size, -1)
          backcast = torch.einsum("bp,pt->bt", backcast_theta, self.backcast_basis)
          forecast = torch.einsum("bpq,pt->btq", forecast_theta, self.forecast_basis)
          return backcast, forecast
  
  
  ACTIVATIONS = ["ReLU", "Softplus", "Tanh", "SELU", "LeakyReLU", "PReLU", "Sigmoid"]
  
  
  class NBEATSBlock(nn.Module):
      """
      N-BEATS block which takes a basis function as an argument.
      """
  
      def __init__(
          self,
          input_size: int,
          h: int,
          futr_input_size: int,
          hist_input_size: int,
          stat_input_size: int,
          n_theta: int,
          mlp_units: list,
          basis: nn.Module,
          dropout_prob: float,
          activation: str,
      ):
          """ """
          super().__init__()
  
          self.h = h
          self.dropout_prob = dropout_prob
          self.input_size = input_size
          self.futr_input_size = futr_input_size
          self.hist_input_size = hist_input_size
          self.stat_input_size = stat_input_size
  
          assert activation in ACTIVATIONS, f"{activation} is not in {ACTIVATIONS}"
          activ = getattr(nn, activation)()
  
          # Input vector for the block is
          # y_lags (input_size) + historical exogenous (hist_input_size*input_size) +
          # future exogenous (futr_input_size*input_size) + static exogenous (stat_input_size)
          # [ Y_[t-L:t], X_[t-L:t], F_[t-L:t+H], S ]
          input_size = (
              input_size
              + hist_input_size * input_size
              + futr_input_size * (input_size + h)
              + stat_input_size
          )
  
          hidden_layers = [
              nn.Linear(in_features=input_size, out_features=mlp_units[0][0])
          ]
          for layer in mlp_units:
              hidden_layers.append(nn.Linear(in_features=layer[0], out_features=layer[1]))
              hidden_layers.append(activ)
  
              if self.dropout_prob > 0:
                  hidden_layers.append(nn.Dropout(p=self.dropout_prob))
  
          output_layer = [nn.Linear(in_features=mlp_units[-1][1], out_features=n_theta)]
          layers = hidden_layers + output_layer
          self.layers = nn.Sequential(*layers)
          self.basis = basis
  
      def forward(
          self,
          insample_y: torch.Tensor,
          futr_exog: torch.Tensor,
          hist_exog: torch.Tensor,
          stat_exog: torch.Tensor,
      ) -> Tuple[torch.Tensor, torch.Tensor]:
          # Flatten MLP inputs [B, L+H, C] -> [B, (L+H)*C]
          # Contatenate [ Y_t, | X_{t-L},..., X_{t} | F_{t-L},..., F_{t+H} | S ]
          batch_size = len(insample_y)
          if self.hist_input_size > 0:
              insample_y = torch.cat(
                  (insample_y, hist_exog.reshape(batch_size, -1)), dim=1
              )
  
          if self.futr_input_size > 0:
              insample_y = torch.cat(
                  (insample_y, futr_exog.reshape(batch_size, -1)), dim=1
              )
  
          if self.stat_input_size > 0:
              insample_y = torch.cat(
                  (insample_y, stat_exog.reshape(batch_size, -1)), dim=1
              )
  
          # Compute local projection weights and projection
          theta = self.layers(insample_y)
  
          if isinstance(self.basis, ExogenousBasis):
              if self.futr_input_size > 0 and self.stat_input_size > 0:
                  futr_exog = torch.cat(
                      (
                          futr_exog,
                          stat_exog.unsqueeze(1).expand(-1, futr_exog.shape[1], -1),
                      ),
                      dim=2,
                  )
              elif self.futr_input_size > 0:
                  futr_exog = futr_exog
              elif self.stat_input_size > 0:
                  futr_exog = stat_exog.unsqueeze(1).expand(
                      -1, self.input_size + self.h, -1
                  )
              else:
                  raise (
                      ValueError(
                          "No stats or future exogenous. ExogenousBlock not supported."
                      )
                  )
              backcast, forecast = self.basis(theta, futr_exog)
              return backcast, forecast
          else:
              backcast, forecast = self.basis(theta)
              return backcast, forecast
  
  
  class NBEATSx(BaseModel):
      """NBEATSx
  
      The Neural Basis Expansion Analysis with Exogenous variables (NBEATSx) is a simple
      and effective deep learning architecture. It is built with a deep stack of MLPs with
      doubly residual connections. The NBEATSx architecture includes additional exogenous
      blocks, extending NBEATS capabilities and interpretability. With its interpretable
      version, NBEATSx decomposes its predictions on seasonality, trend, and exogenous effects.
  
      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].
          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.
          n_harmonics (int): Number of harmonic oscillations in the SeasonalityBasis [cos(i * t/n_harmonics), sin(i * t/n_harmonics)]. Note that it will only be used if 'seasonality' is in `stack_types`.
          n_polynomials (int): Number of polynomial terms for TrendBasis [1,t,...,t^n_poly]. Note that it will only be used if 'trend' is in `stack_types`.
          stack_types (List[str]): List of stack types. Subset from ['seasonality', 'trend', 'identity', 'exogenous'].
          n_blocks (List[int]): Number of blocks for each stack. Note that len(n_blocks) = len(stack_types).
          mlp_units (List[List[int]]): Structure of hidden layers for each stack type. Each internal list should contain the number of units of each hidden layer. Note that len(n_hidden) = len(stack_types).
          dropout_prob_theta (float): Float between (0, 1). Dropout for N-BEATS basis.
          activation (str): activation from ['ReLU', 'Softplus', 'Tanh', 'SELU', 'LeakyReLU', 'PReLU', 'Sigmoid'].
          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 initialization for replicability.
          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:
          - [Kin G. Olivares, Cristian Challu, Grzegorz Marcjasz, Rafał Weron, Artur Dubrawski (2021). "Neural basis expansion analysis with exogenous variables: Forecasting electricity prices with NBEATSx".](https://arxiv.org/abs/2104.05522)
      """
  
      # Class attributes
      EXOGENOUS_FUTR = True
      EXOGENOUS_HIST = True
      EXOGENOUS_STAT = True
      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,
          input_size,
          futr_exog_list=None,
          hist_exog_list=None,
          stat_exog_list=None,
          exclude_insample_y=False,
          n_harmonics=2,
          n_polynomials=2,
          stack_types: list = ["identity", "trend", "seasonality"],
          n_blocks: list = [1, 1, 1],
          mlp_units: list = 3 * [[512, 512]],
          dropout_prob_theta=0.0,
          activation="ReLU",
          shared_weights=False,
          loss=MAE(),
          valid_loss=None,
          max_steps: int = 1000,
          learning_rate: float = 1e-3,
          num_lr_decays: int = 3,
          early_stop_patience_steps: int = -1,
          val_check_steps: int = 100,
          batch_size=32,
          valid_batch_size: Optional[int] = None,
          windows_batch_size: int = 1024,
          inference_windows_batch_size: int = -1,
          start_padding_enabled: bool = 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,
      ):
          # Protect horizon collapsed seasonality and trend NBEATSx-i basis
          if h == 1 and (("seasonality" in stack_types) or ("trend" in stack_types)):
              raise Exception(
                  "Horizon `h=1` incompatible with `seasonality` or `trend` in stacks"
              )
  
          # Inherit BaseWindows class
          super(NBEATSx, self).__init__(
              h=h,
              input_size=input_size,
              futr_exog_list=futr_exog_list,
              hist_exog_list=hist_exog_list,
              stat_exog_list=stat_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
          blocks = self.create_stack(
              h=h,
              input_size=input_size,
              futr_input_size=self.futr_exog_size,
              hist_input_size=self.hist_exog_size,
              stat_input_size=self.stat_exog_size,
              stack_types=stack_types,
              n_blocks=n_blocks,
              mlp_units=mlp_units,
              dropout_prob_theta=dropout_prob_theta,
              activation=activation,
              shared_weights=shared_weights,
              n_polynomials=n_polynomials,
              n_harmonics=n_harmonics,
          )
          self.blocks = torch.nn.ModuleList(blocks)
  
      def create_stack(
          self,
          h,
          input_size,
          stack_types,
          n_blocks,
          mlp_units,
          dropout_prob_theta,
          activation,
          shared_weights,
          n_polynomials,
          n_harmonics,
          futr_input_size,
          hist_input_size,
          stat_input_size,
      ):
          block_list = []
          for i in range(len(stack_types)):
              for block_id in range(n_blocks[i]):
                  # Shared weights
                  if shared_weights and block_id > 0:
                      nbeats_block = block_list[-1]
                  else:
                      if stack_types[i] == "seasonality":
                          n_theta = (
                              2
                              * (self.loss.outputsize_multiplier + 1)
                              * int(np.ceil(n_harmonics / 2 * h) - (n_harmonics - 1))
                          )
                          basis = SeasonalityBasis(
                              harmonics=n_harmonics,
                              backcast_size=input_size,
                              forecast_size=h,
                              out_features=self.loss.outputsize_multiplier,
                          )
  
                      elif stack_types[i] == "trend":
                          n_theta = (self.loss.outputsize_multiplier + 1) * (
                              n_polynomials + 1
                          )
                          basis = TrendBasis(
                              degree_of_polynomial=n_polynomials,
                              backcast_size=input_size,
                              forecast_size=h,
                              out_features=self.loss.outputsize_multiplier,
                          )
  
                      elif stack_types[i] == "identity":
                          n_theta = input_size + self.loss.outputsize_multiplier * h
                          basis = IdentityBasis(
                              backcast_size=input_size,
                              forecast_size=h,
                              out_features=self.loss.outputsize_multiplier,
                          )
  
                      elif stack_types[i] == "exogenous":
                          if futr_input_size + stat_input_size > 0:
                              n_theta = 2 * (futr_input_size + stat_input_size)
                              basis = ExogenousBasis(forecast_size=h)
  
                      else:
                          raise ValueError(f"Block type {stack_types[i]} not found!")
  
                      nbeats_block = NBEATSBlock(
                          input_size=input_size,
                          h=h,
                          futr_input_size=futr_input_size,
                          hist_input_size=hist_input_size,
                          stat_input_size=stat_input_size,
                          n_theta=n_theta,
                          mlp_units=mlp_units,
                          basis=basis,
                          dropout_prob=dropout_prob_theta,
                          activation=activation,
                      )
  
                  # Select type of evaluation and apply it to all layers of block
                  block_list.append(nbeats_block)
  
          return block_list
  
      def forward(self, windows_batch):
          # Parse windows_batch
          insample_y = windows_batch["insample_y"].squeeze(-1)
          insample_mask = windows_batch["insample_mask"].squeeze(-1)
          futr_exog = windows_batch["futr_exog"]
          hist_exog = windows_batch["hist_exog"]
          stat_exog = windows_batch["stat_exog"]
  
          # NBEATSx' forward
          residuals = insample_y.flip(dims=(-1,))  # backcast init
          insample_mask = insample_mask.flip(dims=(-1,))
  
          forecast = insample_y[:, -1:, None]  # Level with Naive1
          block_forecasts = [forecast.repeat(1, self.h, 1)]
          for i, block in enumerate(self.blocks):
              backcast, block_forecast = block(
                  insample_y=residuals,
                  futr_exog=futr_exog,
                  hist_exog=hist_exog,
                  stat_exog=stat_exog,
              )
              residuals = (residuals - backcast) * insample_mask
              forecast = forecast + block_forecast
  
              if self.decompose_forecast:
                  block_forecasts.append(block_forecast)
  
          if self.decompose_forecast:
              # (n_batch, n_blocks, h)
              block_forecasts = torch.stack(block_forecasts)
              block_forecasts = block_forecasts.permute(1, 0, 2, 3)
              block_forecasts = block_forecasts.squeeze(-1)  # univariate output
              return block_forecasts
          else:
              return forecast
  