code: def _forward(self, data: dict) -> dict:  # type: ignore
      for key in self.required_data_keys:
          KORNIA_CHECK(key in data, f"Missing key {key} in data")
      data0, data1 = data["image0"], data["image1"]
      kpts0, kpts1 = data0["keypoints"], data1["keypoints"]
      b, m, _ = kpts0.shape
      b, n, _ = kpts1.shape
      device = kpts0.device
      size0, size1 = data0.get("image_size"), data1.get("image_size")
      size0 = (
          size0
          if size0 is not None
          else data0["image"].shape[-2:][::-1]
      )
      size1 = (
          size1
          if size1 is not None
          else data1["image"].shape[-2:][::-1]
      )
  
      kpts0 = normalize_keypoints(kpts0, size0).clone()
      kpts1 = normalize_keypoints(kpts1, size1).clone()
      KORNIA_CHECK(torch.all(kpts0 >= -1).item() and torch.all(kpts0 <= 1).item(), "")  # type: ignore
      KORNIA_CHECK(torch.all(kpts1 >= -1).item() and torch.all(kpts1 <= 1).item(), "")  # type: ignore
      if self.conf.add_scale_ori:
          kpts0 = concatenate(
              [kpts0]
              + [data0[k].unsqueeze(-1) for k in ("scales", "oris")],
              -1,
          )
          kpts1 = concatenate(
              [kpts1]
              + [data1[k].unsqueeze(-1) for k in ("scales", "oris")],
              -1,
          )
      elif self.conf.add_laf:
          laf0 = scale_laf(data0["lafs"], self.conf.scale_coef)
          laf1 = scale_laf(data1["lafs"], self.conf.scale_coef)
          laf0 = laf_to_three_points(laf0)
          laf1 = laf_to_three_points(laf1)
          kpts0 = concatenate(
              [
                  kpts0,
                  normalize_keypoints(laf0[..., 0], size0)
                  .clone()
                  .to(kpts0.dtype),
                  normalize_keypoints(laf0[..., 1], size0)
                  .clone()
                  .to(kpts0.dtype),
              ],
              -1,
          )
          kpts1 = concatenate(
              [
                  kpts1,
                  normalize_keypoints(laf1[..., 0], size1)
                  .clone()
                  .to(kpts1.dtype),
                  normalize_keypoints(laf1[..., 1], size1)
                  .clone()
                  .to(kpts1.dtype),
              ],
              -1,
          )
  
      desc0 = data0["descriptors"].detach().contiguous()
      desc1 = data1["descriptors"].detach().contiguous()
  
      KORNIA_CHECK(
          desc0.shape[-1] == self.conf.input_dim,
          "Descriptor dimension does not match input dim in config",
      )
      KORNIA_CHECK(
          desc1.shape[-1] == self.conf.input_dim,
          "Descriptor dimension does not match input dim in config",
      )
  
      if torch.is_autocast_enabled():
          desc0 = desc0.half()
          desc1 = desc1.half()
  
      mask0, mask1 = None, None
      c = max(m, n)
      do_compile = self.static_lengths and c <= max(self.static_lengths)
      if do_compile:
          kn = min([k for k in self.static_lengths if k >= c])
          desc0, mask0 = pad_to_length(desc0, kn)
          desc1, mask1 = pad_to_length(desc1, kn)
          kpts0, _ = pad_to_length(kpts0, kn)
          kpts1, _ = pad_to_length(kpts1, kn)
      desc0 = self.input_proj(desc0)
      desc1 = self.input_proj(desc1)
      # cache positional embeddings
      encoding0 = self.posenc(kpts0)
      encoding1 = self.posenc(kpts1)
  
      # GNN + final_proj + assignment
      do_early_stop = self.conf.depth_confidence > 0
      do_point_pruning = (
          self.conf.width_confidence > 0 and not do_compile
      )
      pruning_th = self.pruning_min_kpts(device)
      if do_point_pruning:
          ind0 = arange(0, m, device=device)[None]
          ind1 = arange(0, n, device=device)[None]
          # We store the index of the layer at which pruning is detected.
          prune0 = ones_like(ind0)
          prune1 = ones_like(ind1)
      token0, token1 = None, None
      for i in range(self.conf.n_layers):
          desc0, desc1 = self.transformers[i](
              desc0,
              desc1,
              encoding0,
              encoding1,
              mask0=mask0,
              mask1=mask1,
          )
          if i == self.conf.n_layers - 1:
              continue  # no early stopping or adaptive width at last layer
  
          if do_early_stop:
              token0, token1 = self.token_confidence[i](desc0, desc1)
              if self.check_if_stop(
                  token0[..., :m, :], token1[..., :n, :], i, m + n
              ):
                  break
          if do_point_pruning and desc0.shape[-2] > pruning_th:
              scores0 = self.log_assignment[i].get_matchability(desc0)
              prunemask0 = self.get_pruning_mask(token0, scores0, i)  # type: ignore
              keep0 = where(prunemask0)[1]
              ind0 = ind0.index_select(1, keep0)
              desc0 = desc0.index_select(1, keep0)
              encoding0 = encoding0.index_select(-2, keep0)
              prune0[:, ind0] += 1
          if do_point_pruning and desc1.shape[-2] > pruning_th:
              scores1 = self.log_assignment[i].get_matchability(desc1)
              prunemask1 = self.get_pruning_mask(token1, scores1, i)  # type: ignore
              keep1 = where(prunemask1)[1]
              ind1 = ind1.index_select(1, keep1)
              desc1 = desc1.index_select(1, keep1)
              encoding1 = encoding1.index_select(-2, keep1)
              prune1[:, ind1] += 1
  
      desc0, desc1 = desc0[..., :m, :], desc1[..., :n, :]
      scores, _ = self.log_assignment[i](desc0, desc1)
      m0, m1, mscores0, mscores1 = filter_matches(
          scores, self.conf.filter_threshold
      )
      matches, mscores = [], []
      for k in range(b):
          valid = m0[k] > -1
          m_indices_0 = where(valid)[0]
          m_indices_1 = m0[k][valid]
          if do_point_pruning:
              m_indices_0 = ind0[k, m_indices_0]
              m_indices_1 = ind1[k, m_indices_1]
          matches.append(stack([m_indices_0, m_indices_1], -1))
          mscores.append(mscores0[k][valid])
  
      # TODO: Remove when hloc switches to the compact format.
      if do_point_pruning:
          m0_ = torch.full((b, m), -1, device=m0.device, dtype=m0.dtype)
          m1_ = torch.full((b, n), -1, device=m1.device, dtype=m1.dtype)
          m0_[:, ind0] = where(
              m0 == -1, -1, ind1.gather(1, m0.clamp(min=0))
          )
          m1_[:, ind1] = where(
              m1 == -1, -1, ind0.gather(1, m1.clamp(min=0))
          )
          mscores0_ = zeros((b, m), device=mscores0.device)
          mscores1_ = zeros((b, n), device=mscores1.device)
          mscores0_[:, ind0] = mscores0
          mscores1_[:, ind1] = mscores1
          m0, m1, mscores0, mscores1 = m0_, m1_, mscores0_, mscores1_
      else:
          prune0 = ones_like(mscores0) * self.conf.n_layers
          prune1 = ones_like(mscores1) * self.conf.n_layers
  
      pred = {
          "matches0": m0,
          "matches1": m1,
          "matching_scores0": mscores0,
          "matching_scores1": mscores1,
          "stop": i + 1,
          "matches": matches,
          "scores": mscores,
          "prune0": prune0,
          "prune1": prune1,
      }
  
      return pred
  
imports: import math
  import warnings
  from pathlib import Path
  from types import SimpleNamespace
  from typing import Any, Callable, ClassVar, Dict, List, Optional, Tuple
  import torch
  import torch.nn.functional
  from torch import nn
  from kornia.core import Module, ModuleList, Tensor, arange, concatenate, cos, einsum, ones, ones_like, sin, stack, where, zeros
  from kornia.core.check import KORNIA_CHECK
  from kornia.feature.laf import laf_to_three_points, scale_laf
label_desc: Use image node_id 4 for calling the LightGlue obj's underlying member method code with example usage: obj._forward(data) and returns: pred