code: def find_all_index(
      self, ragged_lat, ctc_graph, dense_fsa_vec, arc_map_a, arc_map_b
  ):
      # This function finds the index of (b, t, u, d) for each arc and each state
      num_fsas = len(ctc_graph.arcs.row_splits(1)) - 1
  
      # Arc part
      ctc_graph_arcs = ctc_graph.as_dict()["arcs"][
          2 * num_fsas + 4 :
      ].view(-1, 4)
      arc_u_idx = ctc_graph_arcs[:, 1].long()
      arc_u_idx = arc_u_idx[arc_map_a.long()]
  
      arc_k_idx = ctc_graph_arcs[:, 2].long()
      arc_k_idx = arc_k_idx[arc_map_a.long()]
  
      arc_boundaries = (
          ctc_graph.arcs.shape()
          .row_splits(2)
          .long()[ctc_graph.arcs.shape().row_splits(1).long()]
      )
      arc_ids = torch.arange(
          ctc_graph.num_arcs, device=ctc_graph.device
      )
      arc_b_idx = (
          torch.bucketize(arc_ids, arc_boundaries, right=True) - 1
      )
      arc_b_idx = arc_b_idx[arc_map_a.long()]
  
      arc_t_idx = arc_map_b // dense_fsa_vec.scores.size(1)
      duration = dense_fsa_vec.duration + 1
      t_shift = torch.zeros(
          num_fsas + 1, dtype=duration.dtype, device=ctc_graph.device
      )
      t_shift[1:] = torch.cumsum(duration, dim=0)
      arc_t_idx = (arc_t_idx - t_shift[arc_b_idx]).long()
  
      # State part
      lats = k2.Fsa(ragged_lat)
      arc2state = lats._get_entering_arcs(
          False
      ).long()  # encoming arc_id for start state is -1
      start_state_id = lats.arcs.row_splits(1)[:-1].long()
  
      state_u_idx, state_t_idx, state_k_idx, state_b_idx = (
          arc_u_idx[arc2state],
          arc_t_idx[arc2state],
          arc_k_idx[arc2state],
          arc_b_idx[arc2state],
      )
  
      # Post-process:
      # A. Start and end states are the super-nodes. make the redundancy.
      # B. Correct the values on start states.
      # C. Clip k_idx to avoid any negative value.
      state_u_idx, state_t_idx = state_u_idx + 1, state_t_idx + 1
  
      state_t_idx[start_state_id], state_u_idx[start_state_id] = 0, 0
      state_b_idx[start_state_id] = torch.arange(
          num_fsas, device=ctc_graph.device
      )
      state_k_idx, arc_k_idx = torch.clip(
          state_k_idx, min=0
      ), torch.clip(arc_k_idx, min=0)
  
      return (arc_u_idx, arc_t_idx, arc_k_idx, arc_b_idx), (
          state_u_idx,
          state_t_idx,
          state_k_idx,
          state_b_idx,
      )
  
file_path: espnet/espnet2/asr/bayes_risk_ctc.py
imports: import logging
  import _k2
  import k2
  import torch
label_desc: Use image node_id 5 for calling the BayesRiskCTC obj's underlying member method code with example usage: obj.find_all_index(ragged_lat, ctc_graph, dense_fsa_vec, arc_map_a, arc_map_b) and returns: arc_u_idx,  arc_t_idx,  arc_k_idx,  arc_b_idx,  state_u_idx,  state_t_idx,  state_k_idx,  state_b_idx