code: def cot_laplacian(
      verts: torch.Tensor, faces: torch.Tensor, eps: float = 1e-12
  ) -> Tuple[torch.Tensor, torch.Tensor]:
      """
      Returns the Laplacian matrix with cotangent weights and the inverse of the
      face areas.
  
      Args:
          verts: tensor of shape (V, 3) containing the vertices of the graph
          faces: tensor of shape (F, 3) containing the vertex indices of each face
      Returns:
          2-element tuple containing
          - **L**: Sparse FloatTensor of shape (V,V) for the Laplacian matrix.
             Here, L[i, j] = cot a_ij + cot b_ij iff (i, j) is an edge in meshes.
             See the description above for more clarity.
          - **inv_areas**: FloatTensor of shape (V,) containing the inverse of sum of
             face areas containing each vertex
      """
      V, F = verts.shape[0], faces.shape[0]
  
      face_verts = verts[faces]
      v0, v1, v2 = face_verts[:, 0], face_verts[:, 1], face_verts[:, 2]
  
      # Side lengths of each triangle, of shape (sum(F_n),)
      # A is the side opposite v1, B is opposite v2, and C is opposite v3
      A = (v1 - v2).norm(dim=1)
      B = (v0 - v2).norm(dim=1)
      C = (v0 - v1).norm(dim=1)
  
      # Area of each triangle (with Heron's formula); shape is (sum(F_n),)
      s = 0.5 * (A + B + C)
      # note that the area can be negative (close to 0) causing nans after sqrt()
      # we clip it to a small positive value
      # pyre-fixme[16]: `float` has no attribute `clamp_`.
      area = (s * (s - A) * (s - B) * (s - C)).clamp_(min=eps).sqrt()
  
      # Compute cotangents of angles, of shape (sum(F_n), 3)
      A2, B2, C2 = A * A, B * B, C * C
      cota = (B2 + C2 - A2) / area
      cotb = (A2 + C2 - B2) / area
      cotc = (A2 + B2 - C2) / area
      cot = torch.stack([cota, cotb, cotc], dim=1)
      cot /= 4.0
  
      # Construct a sparse matrix by basically doing:
      # L[v1, v2] = cota
      # L[v2, v0] = cotb
      # L[v0, v1] = cotc
      ii = faces[:, [1, 2, 0]]
      jj = faces[:, [2, 0, 1]]
      idx = torch.stack([ii, jj], dim=0).view(2, F * 3)
      # pyre-fixme[16]: Module `sparse` has no attribute `FloatTensor`.
      L = torch.sparse.FloatTensor(idx, cot.view(-1), (V, V))
  
      # Make it symmetric; this means we are also setting
      # L[v2, v1] = cota
      # L[v0, v2] = cotb
      # L[v1, v0] = cotc
      L += L.t()
  
      # For each vertex, compute the sum of areas for triangles containing it.
      idx = faces.view(-1)
      inv_areas = torch.zeros(
          V, dtype=torch.float32, device=verts.device
      )
      val = torch.stack([area] * 3, dim=1).view(-1)
      inv_areas.scatter_add_(0, idx, val)
      idx = inv_areas > 0
      # pyre-fixme[58]: `/` is not supported for operand types `float` and `Tensor`.
      inv_areas[idx] = 1.0 / inv_areas[idx]
      inv_areas = inv_areas.view(-1, 1)
  
      return L, inv_areas
  
imports: from typing import Tuple
  import torch
label_desc: Use image node_id 2 for calling a global function with example usage: cot_laplacian(verts, faces, eps) and returns: L,  inv_areas