content: 
  
  
  __all__ = ['GLU', 'StockBlockLayer', 'StemGNN']
  
  
  from typing import Optional
  
  import torch
  import torch.nn as nn
  import torch.nn.functional as F
  
  from ..common._base_model import BaseModel
  from ..losses.pytorch import MAE
  
  
  class GLU(nn.Module):
      """
      GLU
      """
  
      def __init__(self, input_channel, output_channel):
          super(GLU, self).__init__()
          self.linear_left = nn.Linear(input_channel, output_channel)
          self.linear_right = nn.Linear(input_channel, output_channel)
  
      def forward(self, x):
          return torch.mul(self.linear_left(x), torch.sigmoid(self.linear_right(x)))
  
  
  class StockBlockLayer(nn.Module):
      """
      StockBlockLayer
      """
  
      def __init__(self, time_step, unit, multi_layer, stack_cnt=0):
          super(StockBlockLayer, self).__init__()
          self.time_step = time_step
          self.unit = unit
          self.stack_cnt = stack_cnt
          self.multi = multi_layer
          self.weight = nn.Parameter(
              torch.Tensor(
                  1, 3 + 1, 1, self.time_step * self.multi, self.multi * self.time_step
              )
          )  # [K+1, 1, in_c, out_c]
          nn.init.xavier_normal_(self.weight)
          self.forecast = nn.Linear(
              self.time_step * self.multi, self.time_step * self.multi
          )
          self.forecast_result = nn.Linear(self.time_step * self.multi, self.time_step)
          if self.stack_cnt == 0:
              self.backcast = nn.Linear(self.time_step * self.multi, self.time_step)
          self.backcast_short_cut = nn.Linear(self.time_step, self.time_step)
          self.relu = nn.ReLU()
          self.GLUs = nn.ModuleList()
          self.output_channel = 4 * self.multi
          for i in range(3):
              if i == 0:
                  self.GLUs.append(
                      GLU(self.time_step * 4, self.time_step * self.output_channel)
                  )
                  self.GLUs.append(
                      GLU(self.time_step * 4, self.time_step * self.output_channel)
                  )
              elif i == 1:
                  self.GLUs.append(
                      GLU(
                          self.time_step * self.output_channel,
                          self.time_step * self.output_channel,
                      )
                  )
                  self.GLUs.append(
                      GLU(
                          self.time_step * self.output_channel,
                          self.time_step * self.output_channel,
                      )
                  )
              else:
                  self.GLUs.append(
                      GLU(
                          self.time_step * self.output_channel,
                          self.time_step * self.output_channel,
                      )
                  )
                  self.GLUs.append(
                      GLU(
                          self.time_step * self.output_channel,
                          self.time_step * self.output_channel,
                      )
                  )
  
      def spe_seq_cell(self, input):
          batch_size, k, input_channel, node_cnt, time_step = input.size()
          input = input.view(batch_size, -1, node_cnt, time_step)
          ffted = torch.view_as_real(torch.fft.fft(input, dim=1))
          real = (
              ffted[..., 0]
              .permute(0, 2, 1, 3)
              .contiguous()
              .reshape(batch_size, node_cnt, -1)
          )
          img = (
              ffted[..., 1]
              .permute(0, 2, 1, 3)
              .contiguous()
              .reshape(batch_size, node_cnt, -1)
          )
          for i in range(3):
              real = self.GLUs[i * 2](real)
              img = self.GLUs[2 * i + 1](img)
          real = (
              real.reshape(batch_size, node_cnt, 4, -1).permute(0, 2, 1, 3).contiguous()
          )
          img = img.reshape(batch_size, node_cnt, 4, -1).permute(0, 2, 1, 3).contiguous()
          time_step_as_inner = torch.cat([real.unsqueeze(-1), img.unsqueeze(-1)], dim=-1)
          iffted = torch.fft.irfft(
              torch.view_as_complex(time_step_as_inner),
              n=time_step_as_inner.shape[1],
              dim=1,
          )
          return iffted
  
      def forward(self, x, mul_L):
          mul_L = mul_L.unsqueeze(1)
          x = x.unsqueeze(1)
          gfted = torch.matmul(mul_L, x)
          gconv_input = self.spe_seq_cell(gfted).unsqueeze(2)
          igfted = torch.matmul(gconv_input, self.weight)
          igfted = torch.sum(igfted, dim=1)
          forecast_source = torch.sigmoid(self.forecast(igfted).squeeze(1))
          forecast = self.forecast_result(forecast_source)
          if self.stack_cnt == 0:
              backcast_short = self.backcast_short_cut(x).squeeze(1)
              backcast_source = torch.sigmoid(self.backcast(igfted) - backcast_short)
          else:
              backcast_source = None
          return forecast, backcast_source
  
  
  class StemGNN(BaseModel):
      """StemGNN
  
      The Spectral Temporal Graph Neural Network (`StemGNN`) is a Graph-based multivariate
      time-series forecasting model. `StemGNN` jointly learns temporal dependencies and
      inter-series correlations in the spectral domain, by combining Graph Fourier Transform (GFT)
      and Discrete Fourier Transform (DFT).
  
      Args:
          h (int): Forecast horizon.
          input_size (int): autorregresive inputs size, y=[1,2,3,4] input_size=2 -> y_[t-2:t]=[1,2].
          n_series (int): number of time-series.
          futr_exog_list (str list): future exogenous columns.
          hist_exog_list (str list): historic exogenous columns.
          stat_exog_list (str list): static exogenous columns.
          n_stacks (int): number of stacks in the model.
          multi_layer (int): multiplier for FC hidden size on StemGNN blocks.
          dropout_rate (float): dropout rate.
          leaky_rate (float): alpha for LeakyReLU layer on Latent Correlation layer.
          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 windows in each batch.
          valid_batch_size (int): number of different series in each validation and test batch, if None uses batch_size.
          windows_batch_size (int): number of windows to sample in each training batch, default uses all.
          inference_windows_batch_size (int): number of windows to sample in each inference batch, -1 uses all.
          start_padding_enabled (bool): if True, the model will pad the time series with zeros at the beginning, by input size.
          training_data_availability_threshold (Union[float, List[float]]): minimum fraction of valid data points required for training windows. Single float applies to both insample and outsample; list of two floats specifies [insample_fraction, outsample_fraction]. Default 0.0 allows windows with only 1 valid data point (current behavior).
          step_size (int): step size between each window of temporal data.
          scaler_type (str): type of scaler for temporal inputs normalization see [temporal scalers](https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/common/_scalers.py).
          random_seed (int): random_seed for pytorch initializer and numpy generators.
          drop_last_loader (bool): if True `TimeSeriesDataLoader` drops last non-full batch.
          alias (str): optional,  Custom name of the model.
          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).
      """
  
      # Class attributes
      EXOGENOUS_FUTR = False
      EXOGENOUS_HIST = False
      EXOGENOUS_STAT = False
      MULTIVARIATE = True  # If the model produces multivariate forecasts (True) or univariate (False)
      RECURRENT = (
          False  # If the model produces forecasts recursively (True) or direct (False)
      )
  
      def __init__(
          self,
          h,
          input_size,
          n_series,
          futr_exog_list=None,
          hist_exog_list=None,
          stat_exog_list=None,
          exclude_insample_y=False,
          n_stacks=2,
          multi_layer: int = 5,
          dropout_rate: float = 0.5,
          leaky_rate: float = 0.2,
          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=32,
          inference_windows_batch_size=32,
          start_padding_enabled=False,
          training_data_availability_threshold=0.0,
          step_size: int = 1,
          scaler_type: str = "robust",
          random_seed: int = 1,
          drop_last_loader=False,
          alias: Optional[str] = None,
          optimizer=None,
          optimizer_kwargs=None,
          lr_scheduler=None,
          lr_scheduler_kwargs=None,
          dataloader_kwargs=None,
          **trainer_kwargs
      ):
  
          # Inherit BaseMultivariate class
          super(StemGNN, self).__init__(
              h=h,
              input_size=input_size,
              n_series=n_series,
              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
          )
          # Quick fix for now, fix the model later.
          if n_stacks != 2:
              raise Exception("StemGNN currently only supports n_stacks=2.")
  
          self.unit = n_series
          self.stack_cnt = n_stacks
          self.alpha = leaky_rate
          self.time_step = input_size
          self.horizon = h
          self.h = h
  
          self.weight_key = nn.Parameter(torch.zeros(size=(self.unit, 1)))
          nn.init.xavier_uniform_(self.weight_key.data, gain=1.414)
          self.weight_query = nn.Parameter(torch.zeros(size=(self.unit, 1)))
          nn.init.xavier_uniform_(self.weight_query.data, gain=1.414)
          self.GRU = nn.GRU(self.time_step, self.unit)
          self.multi_layer = multi_layer
          self.stock_block = nn.ModuleList()
          self.stock_block.extend(
              [
                  StockBlockLayer(
                      self.time_step, self.unit, self.multi_layer, stack_cnt=i
                  )
                  for i in range(self.stack_cnt)
              ]
          )
          self.fc = nn.Sequential(
              nn.Linear(int(self.time_step), int(self.time_step)),
              nn.LeakyReLU(),
              nn.Linear(
                  int(self.time_step), self.horizon * self.loss.outputsize_multiplier
              ),
          )
          self.leakyrelu = nn.LeakyReLU(self.alpha)
          self.dropout = nn.Dropout(p=dropout_rate)
  
      def get_laplacian(self, graph, normalize):
          """
          return the laplacian of the graph.
          :param graph: the graph structure without self loop, [N, N].
          :param normalize: whether to used the normalized laplacian.
          :return: graph laplacian.
          """
          if normalize:
              D = torch.diag(torch.sum(graph, dim=-1) ** (-1 / 2))
              L = torch.eye(
                  graph.size(0), device=graph.device, dtype=graph.dtype
              ) - torch.mm(torch.mm(D, graph), D)
          else:
              D = torch.diag(torch.sum(graph, dim=-1))
              L = D - graph
          return L
  
      def cheb_polynomial(self, laplacian):
          """
          Compute the Chebyshev Polynomial, according to the graph laplacian.
          :param laplacian: the graph laplacian, [N, N].
          :return: the multi order Chebyshev laplacian, [K, N, N].
          """
          N = laplacian.size(0)  # [N, N]
          laplacian = laplacian.unsqueeze(0)
          first_laplacian = torch.zeros(
              [1, N, N], device=laplacian.device, dtype=torch.float
          )
          second_laplacian = laplacian
          third_laplacian = (
              2 * torch.matmul(laplacian, second_laplacian)
          ) - first_laplacian
          forth_laplacian = (
              2 * torch.matmul(laplacian, third_laplacian) - second_laplacian
          )
          multi_order_laplacian = torch.cat(
              [first_laplacian, second_laplacian, third_laplacian, forth_laplacian], dim=0
          )
          return multi_order_laplacian
  
      def latent_correlation_layer(self, x):
          input, _ = self.GRU(x.permute(2, 0, 1).contiguous())
          input = input.permute(1, 0, 2).contiguous()
          attention = self.self_graph_attention(input)
          attention = torch.mean(attention, dim=0)
          degree = torch.sum(attention, dim=1)
          # laplacian is sym or not
          attention = 0.5 * (attention + attention.T)
          degree_l = torch.diag(degree)
          diagonal_degree_hat = torch.diag(1 / (torch.sqrt(degree) + 1e-7))
          laplacian = torch.matmul(
              diagonal_degree_hat, torch.matmul(degree_l - attention, diagonal_degree_hat)
          )
          mul_L = self.cheb_polynomial(laplacian)
          return mul_L, attention
  
      def self_graph_attention(self, input):
          input = input.permute(0, 2, 1).contiguous()
          bat, N, fea = input.size()
          key = torch.matmul(input, self.weight_key)
          query = torch.matmul(input, self.weight_query)
          data = key.repeat(1, 1, N).view(bat, N * N, 1) + query.repeat(1, N, 1)
          data = data.squeeze(2)
          data = data.view(bat, N, -1)
          data = self.leakyrelu(data)
          attention = F.softmax(data, dim=2)
          attention = self.dropout(attention)
          return attention
  
      def graph_fft(self, input, eigenvectors):
          return torch.matmul(eigenvectors, input)
  
      def forward(self, windows_batch):
          # Parse batch
          x = windows_batch["insample_y"]
          batch_size = x.shape[0]
  
          mul_L, attention = self.latent_correlation_layer(x)
          X = x.unsqueeze(1).permute(0, 1, 3, 2).contiguous()
          result = []
          for stack_i in range(self.stack_cnt):
              forecast, X = self.stock_block[stack_i](X, mul_L)
              result.append(forecast)
          forecast = result[0] + result[1]
          forecast = self.fc(forecast)
  
          forecast = forecast.permute(0, 2, 1).contiguous()
          forecast = forecast.reshape(
              batch_size, self.h, self.loss.outputsize_multiplier * self.n_series
          )
  
          return forecast
  