docstr: Forward pass.
  
  u: (B H L) if self.transposed else (B L H)
  state: (H N) never needed unless you know what you're doing
  
  Returns: same shape as u
docstr_tok: ["Forward","pass",".","u",":","(","B","H","L",")","if","self.transposed","else","(","B","L","H",")","state",":","(","H","N",")","never","needed","unless","you","know","what","you","'re","doing","Returns",":","same","shape","as","u"]
code: def forward(self, u, state=None, rate=1.0, lengths=None, **kwargs):
      """Forward pass.
  
      u: (B H L) if self.transposed else (B L H)
      state: (H N) never needed unless you know what you're doing
  
      Returns: same shape as u
      """
      if not self.transposed:
          u = u.transpose(-1, -2)
      L = u.size(-1)
  
      # Mask out padding tokens
      if isinstance(lengths, int):
          if lengths != L:
              lengths = torch.tensor(
                  lengths, dtype=torch.long, device=u.device
              )
          else:
              lengths = None
      if lengths is not None:
          if lengths.ndim == 0:
              lengths = lengths.unsqueeze(0)
          assert (
              isinstance(lengths, torch.Tensor)
              and lengths.ndim == 1
              and lengths.size(0) in [1, u.size(0)]
          ), print(f"l:{lengths.ndim}, {lengths.size()}, {u.size()}")
          mask = torch.where(
              torch.arange(L, device=lengths.device)
              < lengths[:, None, None],
              1.0,
              0.0,
          )
          u = u * mask
  
      if self.gate is not None:
          v = self.input_gate(u)
      if self.bottleneck is not None:
          u = self.input_linear(u)
  
      # Compute SS Kernel
      L_kernel = L if self.L is None else min(L, round(self.L / rate))
      k, k_state = self.kernel(
          L=L_kernel, rate=rate, state=state
      )  # (C H L) (B C H L)
  
      # Convolution
      if self.bidirectional:
          k0, k1 = rearrange(k, "(s c) h l -> s c h l", s=2)
          k = F.pad(k0, (0, L)) + F.pad(k1.flip(-1), (L, 0))
      k_f = torch.fft.rfft(k, n=L_kernel + L)  # (C H L)
      u_f = torch.fft.rfft(u, n=L_kernel + L)  # (B H L)
      y_f = contract("bhl,chl->bchl", u_f, k_f)
      y = torch.fft.irfft(y_f, n=L_kernel + L)[..., :L]  # (B C H L)
  
      # Compute D term in state space equation - essentially a skip connection
      y = y + contract("bhl,ch->bchl", u, self.D)
  
      # Compute state update
      if state is not None:
          assert (
              not self.bidirectional
          ), "Bidirectional not supported with state forwarding"
          y = y + k_state  #
          next_state = self.kernel.forward_state(u, state)
      else:
          next_state = None
  
      # Optional hyper-network multiplication
      if self.hyper:
          y, yh = rearrange(y, "b (s c) h l -> s b c h l", s=2)
          y = self.hyper_activation(yh) * y
  
      # Reshape to flatten channels
      y = rearrange(y, "... c h l -> ... (c h) l")
  
      y = self.dropout(self.activation(y))
  
      if not self.transposed:
          y = y.transpose(-1, -2)
  
      y = self.output_linear(y)
  
      if self.gate is not None:
          if not self.transposed:
              v = v.transpose(-1, -2)
          y = self.output_gate(y * v)
  
      return y, next_state
  
imports: import logging
  import math
  import os
  from functools import wraps
  from typing import Any, Callable, Optional
  import numpy
  import opt_einsum
  import torch
  import torch.nn
  import torch.nn.functional
  from einops import rearrange, repeat
  from espnet2.asr.state_spaces.components import Activation, DropoutNd, LinearActivation
label_desc: Use image node_id 2 for calling the S4 obj's underlying member method code with example usage: obj.forward(u, state, rate, lengths) and returns: y,  next_state