content: 
  
  
  __all__ = ['WaveKANLayer', 'TaylorKANLayer', 'JacobiKANLayer', 'RMoK']
  
  
  import math
  from typing import Optional
  
  import torch
  import torch.nn as nn
  import torch.nn.functional as F
  
  from ..common._base_model import BaseModel
  from ..common._modules import RevINMultivariate
  from ..losses.pytorch import MAE
  
  
  class WaveKANLayer(nn.Module):
      """This is a sample code for the simulations of the paper:
      Bozorgasl, Zavareh and Chen, Hao, Wav-KAN: Wavelet Kolmogorov-Arnold Networks (May, 2024)
  
      https://arxiv.org/abs/2405.12832
      and also available at:
      https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4835325
      We used efficient KAN notation and some part of the code:+
  
      """
  
      def __init__(
          self,
          in_features,
          out_features,
          wavelet_type="mexican_hat",
          with_bn=True,
          device="cpu",
      ):
          super(WaveKANLayer, self).__init__()
          self.in_features = in_features
          self.out_features = out_features
          self.wavelet_type = wavelet_type
          self.with_bn = with_bn
  
          # Parameters for wavelet transformation
          self.scale = nn.Parameter(torch.ones(out_features, in_features))
          self.translation = nn.Parameter(torch.zeros(out_features, in_features))
  
          # self.weight1 is not used; you may use it for weighting base activation and adding it like Spl-KAN paper
          self.weight1 = nn.Parameter(torch.Tensor(out_features, in_features))
          self.wavelet_weights = nn.Parameter(torch.Tensor(out_features, in_features))
  
          nn.init.kaiming_uniform_(self.wavelet_weights, a=math.sqrt(5))
          nn.init.kaiming_uniform_(self.weight1, a=math.sqrt(5))
  
          # Base activation function #not used for this experiment
          self.base_activation = nn.SiLU()
  
          # Batch normalization
          if self.with_bn:
              self.bn = nn.BatchNorm1d(out_features)
  
      def wavelet_transform(self, x):
          if x.dim() == 2:
              x_expanded = x.unsqueeze(1)
          else:
              x_expanded = x
  
          translation_expanded = self.translation.unsqueeze(0).expand(x.size(0), -1, -1)
          scale_expanded = self.scale.unsqueeze(0).expand(x.size(0), -1, -1)
          x_scaled = (x_expanded - translation_expanded) / scale_expanded
  
          # Implementation of different wavelet types
          if self.wavelet_type == "mexican_hat":
              term1 = (x_scaled**2) - 1
              term2 = torch.exp(-0.5 * x_scaled**2)
              wavelet = (2 / (math.sqrt(3) * math.pi**0.25)) * term1 * term2
              wavelet_weighted = wavelet * self.wavelet_weights.unsqueeze(0).expand_as(
                  wavelet
              )
              wavelet_output = wavelet_weighted.sum(dim=2)
          elif self.wavelet_type == "morlet":
              omega0 = 5.0  # Central frequency
              real = torch.cos(omega0 * x_scaled)
              envelope = torch.exp(-0.5 * x_scaled**2)
              wavelet = envelope * real
              wavelet_weighted = wavelet * self.wavelet_weights.unsqueeze(0).expand_as(
                  wavelet
              )
              wavelet_output = wavelet_weighted.sum(dim=2)
  
          elif self.wavelet_type == "dog":
              # Implementing Derivative of Gaussian Wavelet
              dog = -x_scaled * torch.exp(-0.5 * x_scaled**2)
              wavelet = dog
              wavelet_weighted = wavelet * self.wavelet_weights.unsqueeze(0).expand_as(
                  wavelet
              )
              wavelet_output = wavelet_weighted.sum(dim=2)
          elif self.wavelet_type == "meyer":
              # Implement Meyer Wavelet here
              # Constants for the Meyer wavelet transition boundaries
              v = torch.abs(x_scaled)
              pi = math.pi
  
              def meyer_aux(v):
                  return torch.where(
                      v <= 1 / 2,
                      torch.ones_like(v),
                      torch.where(
                          v >= 1, torch.zeros_like(v), torch.cos(pi / 2 * nu(2 * v - 1))
                      ),
                  )
  
              def nu(t):
                  return t**4 * (35 - 84 * t + 70 * t**2 - 20 * t**3)
  
              # Meyer wavelet calculation using the auxiliary function
              wavelet = torch.sin(pi * v) * meyer_aux(v)
              wavelet_weighted = wavelet * self.wavelet_weights.unsqueeze(0).expand_as(
                  wavelet
              )
              wavelet_output = wavelet_weighted.sum(dim=2)
          elif self.wavelet_type == "shannon":
              # Windowing the sinc function to limit its support
              pi = math.pi
              sinc = torch.sinc(x_scaled / pi)  # sinc(x) = sin(pi*x) / (pi*x)
  
              # Applying a Hamming window to limit the infinite support of the sinc function
              window = torch.hamming_window(
                  x_scaled.size(-1),
                  periodic=False,
                  dtype=x_scaled.dtype,
                  device=x_scaled.device,
              )
              # Shannon wavelet is the product of the sinc function and the window
              wavelet = sinc * window
              wavelet_weighted = wavelet * self.wavelet_weights.unsqueeze(0).expand_as(
                  wavelet
              )
              wavelet_output = wavelet_weighted.sum(dim=2)
              # You can try many more wavelet types ...
          else:
              raise ValueError("Unsupported wavelet type")
  
          return wavelet_output
  
      def forward(self, x):
          wavelet_output = self.wavelet_transform(x)
          # You may like test the cases like Spl-KAN
          # wav_output = F.linear(wavelet_output, self.weight)
          # base_output = F.linear(self.base_activation(x), self.weight1)
  
          # base_output = F.linear(x, self.weight1)
          combined_output = wavelet_output  # + base_output
  
          # Apply batch normalization
          if self.with_bn:
              return self.bn(combined_output)
          else:
              return combined_output
  
  
  class TaylorKANLayer(nn.Module):
      """
      https://github.com/Muyuzhierchengse/TaylorKAN/
      """
  
      def __init__(self, input_dim, out_dim, order, addbias=True):
          super(TaylorKANLayer, self).__init__()
          self.input_dim = input_dim
          self.out_dim = out_dim
          self.order = order
          self.addbias = addbias
  
          self.coeffs = nn.Parameter(torch.randn(out_dim, input_dim, order) * 0.01)
          if self.addbias:
              self.bias = nn.Parameter(torch.zeros(1, out_dim))
  
      def forward(self, x):
          shape = x.shape
          outshape = shape[0:-1] + (self.out_dim,)
          x = torch.reshape(x, (-1, self.input_dim))
          x_expanded = x.unsqueeze(1).expand(-1, self.out_dim, -1)
  
          y = torch.zeros((x.shape[0], self.out_dim), device=x.device)
  
          for i in range(self.order):
              term = (x_expanded**i) * self.coeffs[:, :, i]
              y += term.sum(dim=-1)
  
          if self.addbias:
              y += self.bias
  
          y = torch.reshape(y, outshape)
          return y
  
  
  class JacobiKANLayer(nn.Module):
      """
      https://github.com/SpaceLearner/JacobiKAN/blob/main/JacobiKANLayer.py
      """
  
      def __init__(self, input_dim, output_dim, degree, a=1.0, b=1.0):
          super(JacobiKANLayer, self).__init__()
          self.inputdim = input_dim
          self.outdim = output_dim
          self.a = a
          self.b = b
          self.degree = degree
  
          self.jacobi_coeffs = nn.Parameter(
              torch.empty(input_dim, output_dim, degree + 1)
          )
  
          nn.init.normal_(
              self.jacobi_coeffs, mean=0.0, std=1 / (input_dim * (degree + 1))
          )
  
      def forward(self, x):
          x = torch.reshape(x, (-1, self.inputdim))  # shape = (batch_size, inputdim)
          # Since Jacobian polynomial is defined in [-1, 1]
          # We need to normalize x to [-1, 1] using tanh
          x = torch.tanh(x)
          # Initialize Jacobian polynomial tensors
          jacobi = torch.ones(x.shape[0], self.inputdim, self.degree + 1, device=x.device)
          if (
              self.degree > 0
          ):  ## degree = 0: jacobi[:, :, 0] = 1 (already initialized) ; degree = 1: jacobi[:, :, 1] = x ; d
              jacobi[:, :, 1] = ((self.a - self.b) + (self.a + self.b + 2) * x) / 2
          for i in range(2, self.degree + 1):
              theta_k = (
                  (2 * i + self.a + self.b)
                  * (2 * i + self.a + self.b - 1)
                  / (2 * i * (i + self.a + self.b))
              )
              theta_k1 = (
                  (2 * i + self.a + self.b - 1)
                  * (self.a * self.a - self.b * self.b)
                  / (2 * i * (i + self.a + self.b) * (2 * i + self.a + self.b - 2))
              )
              theta_k2 = (
                  (i + self.a - 1)
                  * (i + self.b - 1)
                  * (2 * i + self.a + self.b)
                  / (i * (i + self.a + self.b) * (2 * i + self.a + self.b - 2))
              )
              jacobi[:, :, i] = (theta_k * x + theta_k1) * jacobi[
                  :, :, i - 1
              ].clone() - theta_k2 * jacobi[
                  :, :, i - 2
              ].clone()  # 2 * x * jacobi[:, :, i - 1].clone() - jacobi[:, :, i - 2].clone()
          # Compute the Jacobian interpolation
          y = torch.einsum(
              "bid,iod->bo", jacobi, self.jacobi_coeffs
          )  # shape = (batch_size, outdim)
          y = y.view(-1, self.outdim)
          return y
  
  
  class RMoK(BaseModel):
      """Reversible Mixture of KAN
  
  
      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.
          taylor_order (int): order of the Taylor polynomial.
          jacobi_degree (int): degree of the Jacobi polynomial.
          wavelet_function (str): wavelet function to use in the WaveKAN. Choose from ["mexican_hat", "morlet", "dog", "meyer", "shannon"]
          dropout (float): dropout rate.
          revin_affine (bool): bool to use affine in RevIn.
          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 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:
          - [Xiao Han, Xinfeng Zhang, Yiling Wu, Zhenduo Zhang, Zhe Wu."KAN4TSF: Are KAN and KAN-based models Effective for Time Series Forecasting?". arXiv.](https://arxiv.org/abs/2408.11306)
      """
  
      # 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: int,
          futr_exog_list=None,
          hist_exog_list=None,
          stat_exog_list=None,
          taylor_order: int = 3,
          jacobi_degree: int = 6,
          wavelet_function: str = "mexican_hat",
          dropout: float = 0.1,
          revin_affine: bool = True,
          loss=MAE(),
          valid_loss=None,
          max_steps: int = 1000,
          learning_rate: float = 1e-3,
          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=32,
          inference_windows_batch_size=32,
          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(RMoK, self).__init__(
              h=h,
              input_size=input_size,
              n_series=n_series,
              futr_exog_list=hist_exog_list,
              hist_exog_list=stat_exog_list,
              stat_exog_list=futr_exog_list,
              loss=loss,
              valid_loss=valid_loss,
              max_steps=max_steps,
              learning_rate=learning_rate,
              num_lr_decays=num_lr_decays,
              early_stop_patience_steps=early_stop_patience_steps,
              val_check_steps=val_check_steps,
              batch_size=batch_size,
              valid_batch_size=valid_batch_size,
              windows_batch_size=windows_batch_size,
              inference_windows_batch_size=inference_windows_batch_size,
              start_padding_enabled=start_padding_enabled,
              training_data_availability_threshold=training_data_availability_threshold,
              step_size=step_size,
              scaler_type=scaler_type,
              random_seed=random_seed,
              drop_last_loader=drop_last_loader,
              alias=alias,
              optimizer=optimizer,
              optimizer_kwargs=optimizer_kwargs,
              lr_scheduler=lr_scheduler,
              lr_scheduler_kwargs=lr_scheduler_kwargs,
              dataloader_kwargs=dataloader_kwargs,
              **trainer_kwargs
          )
  
          self.input_size = input_size
          self.h = h
          self.n_series = n_series
          self.dropout = nn.Dropout(dropout)
          self.revin_affine = revin_affine
  
          self.taylor_order = taylor_order
          self.jacobi_degree = jacobi_degree
          self.wavelet_function = wavelet_function
  
          self.experts = nn.ModuleList(
              [
                  TaylorKANLayer(
                      self.input_size,
                      self.h * self.loss.outputsize_multiplier,
                      order=self.taylor_order,
                      addbias=True,
                  ),
                  JacobiKANLayer(
                      self.input_size,
                      self.h * self.loss.outputsize_multiplier,
                      degree=self.jacobi_degree,
                  ),
                  WaveKANLayer(
                      self.input_size,
                      self.h * self.loss.outputsize_multiplier,
                      wavelet_type=self.wavelet_function,
                  ),
                  nn.Linear(self.input_size, self.h * self.loss.outputsize_multiplier),
              ]
          )
  
          self.num_experts = len(self.experts)
          self.gate = nn.Linear(self.input_size, self.num_experts)
          self.softmax = nn.Softmax(dim=-1)
          self.rev = RevINMultivariate(self.n_series, affine=self.revin_affine)
  
      def forward(self, windows_batch):
          insample_y = windows_batch["insample_y"]
          B, L, N = insample_y.shape
          x = self.rev(insample_y, "norm")
          x = self.dropout(x).transpose(1, 2).reshape(B * N, L)
  
          score = F.softmax(self.gate(x), dim=-1)
          expert_outputs = torch.stack(
              [self.experts[i](x) for i in range(self.num_experts)], dim=-1
          )
  
          y_pred = (
              torch.einsum("BLE, BE -> BL", expert_outputs, score)
              .reshape(B, N, self.h * self.loss.outputsize_multiplier)
              .permute(0, 2, 1)
          )
          y_pred = self.rev(y_pred, "denorm")
          y_pred = y_pred.reshape(B, self.h, -1)
  
          return y_pred
  