content: 
  
  
  __all__ = ['NBEATS']
  
  
  import warnings
  from typing import Optional, Tuple
  
  import numpy as np
  import torch
  import torch.nn as nn
  from numpy.polynomial.chebyshev import Chebyshev
  from numpy.polynomial.legendre import Legendre
  from scipy.interpolate import BSpline
  
  from ..common._base_model import BaseModel
  from ..losses.pytorch import MAE
  
  
  def generate_legendre_basis(length, n_basis):
      """
      Generates Legendre polynomial basis functions.
  
      Args:
          length (int): Number of data points.
          n_basis (int): Number of basis functions to generate.
  
      Returns:
          legendre_basis (ndarray): An array of Legendre basis functions.
      """
      x = np.linspace(-1, 1, length)  # Legendre polynomials are defined on [-1, 1]
      legendre_basis = np.zeros((length, n_basis))
      for i in range(n_basis):
          # Legendre polynomial of degree i
          P_i = Legendre.basis(i)
          legendre_basis[:, i] = P_i(x)
      return legendre_basis
  
  
  def generate_polynomial_basis(length, n_basis):
      """
      Generates standard polynomial basis functions.
  
      Args:
          length (int): Number of data points.
          n_basis (int): Number of polynomial functions to generate.
  
      Returns:
          poly_basis (ndarray): An array of polynomial basis functions.
      """
      return np.concatenate(
          [
              np.power(np.arange(length, dtype=float) / length, i)[None, :]
              for i in range(n_basis)
          ]
      ).T
  
  
  def generate_changepoint_basis(length, n_basis):
      """
      Generates changepoint basis functions with automatically spaced changepoints.
  
      Args:
          length (int): Number of data points.
          n_basis (int): Number of changepoint functions to generate.
  
      Returns:
          changepoint_basis (ndarray): An array of changepoint basis functions.
      """
      x = np.linspace(0, 1, length)[:, None]  # Shape: (length, 1)
      changepoint_locations = np.linspace(0, 1, n_basis + 1)[1:][
          None, :
      ]  # Shape: (1, n_basis)
      return np.maximum(0, x - changepoint_locations)
  
  
  def generate_piecewise_linear_basis(length, n_basis):
      """
      Generates piecewise linear basis functions (linear splines).
  
      Args:
          length (int): Number of data points.
          n_basis (int): Number of piecewise linear basis functions to generate.
  
      Returns:
          pw_linear_basis (ndarray): An array of piecewise linear basis functions.
      """
      x = np.linspace(0, 1, length)
      knots = np.linspace(0, 1, n_basis + 1)
      pw_linear_basis = np.zeros((length, n_basis))
      for i in range(1, n_basis):
          pw_linear_basis[:, i] = np.maximum(
              0,
              np.minimum(
                  (x - knots[i - 1]) / (knots[i] - knots[i - 1]),
                  (knots[i + 1] - x) / (knots[i + 1] - knots[i]),
              ),
          )
      return pw_linear_basis
  
  
  def generate_linear_hat_basis(length, n_basis):
      x = np.linspace(0, 1, length)[:, None]  # Shape: (length, 1)
      centers = np.linspace(0, 1, n_basis)[None, :]  # Shape: (1, n_basis)
      width = 1.0 / (n_basis - 1)
  
      # Create triangular functions using piecewise linear equations
      return np.maximum(0, 1 - np.abs(x - centers) / width)
  
  
  def generate_spline_basis(length, n_basis):
      """
      Generates cubic spline basis functions.
  
      Args:
          length (int): Number of data points.
          n_basis (int): Number of basis functions.
  
      Returns:
          spline_basis (ndarray): An array of cubic spline basis functions.
      """
      if n_basis < 4:
          raise ValueError(
              f"To use the spline basis, n_basis must be set to 4 or more. Current value is {n_basis}"
          )
      x = np.linspace(0, 1, length)
      knots = np.linspace(0, 1, n_basis - 2)
      t = np.concatenate(([0, 0, 0], knots, [1, 1, 1]))
      degree = 3
      # Create basis coefficient matrix once
      coefficients = np.eye(n_basis)
      # Create single BSpline object with all coefficients
      spline = BSpline(t, coefficients.T, degree)
      return spline(x)
  
  
  def generate_chebyshev_basis(length, n_basis):
      """
      Generates Chebyshev polynomial basis functions.
  
      Args:
          length (int): Number of data points.
          n_basis (int): Number of Chebyshev polynomials to generate.
  
      Returns:
          chebyshev_basis (ndarray): An array of Chebyshev polynomial basis functions.
      """
      x = np.linspace(-1, 1, length)
      chebyshev_basis = np.zeros((length, n_basis))
      for i in range(n_basis):
          T_i = Chebyshev.basis(i)
          chebyshev_basis[:, i] = T_i(x)
      return chebyshev_basis
  
  
  def get_basis(length, n_basis, basis):
      basis_dict = {
          "legendre": generate_legendre_basis,
          "polynomial": generate_polynomial_basis,
          "changepoint": generate_changepoint_basis,
          "piecewise_linear": generate_piecewise_linear_basis,
          "linear_hat": generate_linear_hat_basis,
          "spline": generate_spline_basis,
          "chebyshev": generate_chebyshev_basis,
      }
      return basis_dict[basis](length, n_basis + 1)
  
  
  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,
          n_basis: int,
          backcast_size: int,
          forecast_size: int,
          out_features: int = 1,
          basis="polynomial",
      ):
          super().__init__()
          self.out_features = out_features
          self.backcast_basis = nn.Parameter(
              torch.tensor(
                  get_basis(backcast_size, n_basis, basis).T, dtype=torch.float32
              ),
              requires_grad=False,
          )
          self.forecast_basis = nn.Parameter(
              torch.tensor(
                  get_basis(forecast_size, n_basis, basis).T, 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 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,
          n_theta: int,
          mlp_units: list,
          basis: nn.Module,
          dropout_prob: float,
          activation: str,
      ):
          super().__init__()
  
          self.dropout_prob = dropout_prob
  
          assert activation in ACTIVATIONS, f"{activation} is not in {ACTIVATIONS}"
          activ = getattr(nn, activation)()
  
          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:
                  raise NotImplementedError("dropout")
  
          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) -> Tuple[torch.Tensor, torch.Tensor]:
          # Compute local projection weights and projection
          theta = self.layers(insample_y)
          backcast, forecast = self.basis(theta)
          return backcast, forecast
  
  
  class NBEATS(BaseModel):
      """NBEATS
  
      The Neural Basis Expansion Analysis for Time Series (NBEATS), is a simple and yet
      effective architecture, it is built with a deep stack of MLPs with the doubly
      residual connections. It has a generic and interpretable architecture depending
      on the blocks it uses. Its interpretable architecture is recommended for scarce
      data settings, as it regularizes its predictions through projections unto harmonic
      and trend basis well-suited for most forecasting tasks.
  
      **Parameters:**
      `h`: int, forecast horizon.
      `input_size`: int, considered autorregresive inputs (lags), y=[1,2,3,4] input_size=2 -> lags=[1,2].
      `n_harmonics`: int, Number of harmonic terms for seasonality stack type. Note that len(n_harmonics) = len(stack_types). Note that it will only be used if a seasonality stack is used.
      `n_polynomials`: int, DEPRECATED - polynomial degree for trend stack. Note that len(n_polynomials) = len(stack_types). Note that it will only be used if a trend stack is used.
      `basis`: str, Type of basis function to use in the trend stack. Choose one from ['legendre', 'polynomial', 'changepoint', 'piecewise_linear', 'linear_hat', 'spline', 'chebyshev']
      `n_basis`: int, the degree of the basis function for the trend stack. Note that it will only be used if a trend stack is used.
      `stack_types`: List[str], List of stack types. Subset from ['seasonality', 'trend', 'identity'].
      `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'].
      `shared_weights`: bool, If True, all blocks within each stack will share parameters. 
      `loss`: PyTorch module, instantiated train loss class from [losses collection](./losses.pytorch).
      `valid_loss`: PyTorch module=`loss`, instantiated valid loss class from [losses collection](./losses.pytorch).
      `max_steps`: int=1000, maximum number of training steps.
      `learning_rate`: float=1e-3, Learning rate between (0, 1).
      `num_lr_decays`: int=3, Number of learning rate decays, evenly distributed across max_steps.
      `early_stop_patience_steps`: int=-1, Number of validation iterations before early stopping.
      `val_check_steps`: int=100, Number of training steps between every validation loss check.
      `batch_size`: int=32, number of different series in each batch.
      `valid_batch_size`: int=None, number of different series in each validation and test batch, if None uses batch_size.
      `windows_batch_size`: int=1024, number of windows to sample in each training batch, default uses all.
      `inference_windows_batch_size`: int=-1, number of windows to sample in each inference batch, -1 uses all.
      `start_padding_enabled`: bool=False, 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]]=0.0, 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=1, step size between each window of temporal data.
      `scaler_type`: str='identity', 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=False, 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:**
      -[Boris N. Oreshkin, Dmitri Carpov, Nicolas Chapados, Yoshua Bengio (2019).
      "N-BEATS: Neural basis expansion analysis for interpretable time series forecasting".](https://arxiv.org/abs/1905.10437)
      """
  
      # Class attributes
      EXOGENOUS_FUTR = False
      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,
          input_size,
          n_harmonics: int = 2,
          n_polynomials: Optional[int] = None,
          n_basis: int = 2,
          basis: str = "polynomial",
          stack_types: list = ["identity", "trend", "seasonality"],
          n_blocks: list = [1, 1, 1],
          mlp_units: list = 3 * [[512, 512]],
          dropout_prob_theta: float = 0.0,
          activation: str = "ReLU",
          shared_weights: bool = 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: int = 32,
          valid_batch_size: Optional[int] = None,
          windows_batch_size: int = 1024,
          inference_windows_batch_size: int = -1,
          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,
      ):
  
          # 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(NBEATS, self).__init__(
              h=h,
              input_size=input_size,
              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,
              windows_batch_size=windows_batch_size,
              valid_batch_size=valid_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,
              drop_last_loader=drop_last_loader,
              alias=alias,
              random_seed=random_seed,
              optimizer=optimizer,
              optimizer_kwargs=optimizer_kwargs,
              lr_scheduler=lr_scheduler,
              lr_scheduler_kwargs=lr_scheduler_kwargs,
              dataloader_kwargs=dataloader_kwargs,
              **trainer_kwargs,
          )
  
          # Raise deprecation warning
          if n_polynomials is not None:
              warnings.warn(
                  "The parameter n_polynomials will be deprecated in favor of n_basis and basis and it is currently ignored.\n"
                  "The basis parameter defines the basis function to be used in the trend stack.\n"
                  "The n_basis defines the degree of the basis function used in the trend stack.",
                  DeprecationWarning,
              )
  
          # Architecture
          blocks = self.create_stack(
              h=h,
              input_size=input_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_harmonics=n_harmonics,
              n_basis=n_basis,
              basis_type=basis,
          )
          self.blocks = torch.nn.ModuleList(blocks)
  
      def create_stack(
          self,
          stack_types,
          n_blocks,
          input_size,
          h,
          mlp_units,
          dropout_prob_theta,
          activation,
          shared_weights,
          n_harmonics,
          n_basis,
          basis_type,
      ):
  
          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_basis + 1)
                          basis = TrendBasis(
                              n_basis=n_basis,
                              backcast_size=input_size,
                              forecast_size=h,
                              out_features=self.loss.outputsize_multiplier,
                              basis=basis_type,
                          )
  
                      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,
                          )
                      else:
                          raise ValueError(f"Block type {stack_types[i]} not found!")
  
                      nbeats_block = NBEATSBlock(
                          input_size=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)
  
          # NBEATS' 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)
              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, out_features)
              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
  