code: def knn_interpolate(
      x: torch.Tensor,
      pos_x: torch.Tensor,
      pos_y: torch.Tensor,
      batch_x: OptTensor = None,
      batch_y: OptTensor = None,
      k: int = 3,
      num_workers: int = 1,
  ):
      r"""The k-NN interpolation from the `"PointNet++: Deep Hierarchical
      Feature Learning on Point Sets in a Metric Space"
      <https://arxiv.org/abs/1706.02413>`_ paper.
  
      For each point :math:`y` with position :math:`\mathbf{p}(y)`, its
      interpolated features :math:`\mathbf{f}(y)` are given by
  
      .. math::
          \mathbf{f}(y) = \frac{\sum_{i=1}^k w(x_i) \mathbf{f}(x_i)}{\sum_{i=1}^k
          w(x_i)} \textrm{, where } w(x_i) = \frac{1}{d(\mathbf{p}(y),
          \mathbf{p}(x_i))^2}
  
      and :math:`\{ x_1, \ldots, x_k \}` denoting the :math:`k` nearest points
      to :math:`y`.
  
      Args:
          x (torch.Tensor): Node feature matrix
              :math:`\mathbf{X} \in \mathbb{R}^{N \times F}`.
          pos_x (torch.Tensor): Node position matrix
              :math:`\in \mathbb{R}^{N \times d}`.
          pos_y (torch.Tensor): Upsampled node position matrix
              :math:`\in \mathbb{R}^{M \times d}`.
          batch_x (torch.Tensor, optional): Batch vector
              :math:`\mathbf{b_x} \in {\{ 0, \ldots, B-1\}}^N`, which assigns
              each node from :math:`\mathbf{X}` to a specific example.
              (default: :obj:`None`)
          batch_y (torch.Tensor, optional): Batch vector
              :math:`\mathbf{b_y} \in {\{ 0, \ldots, B-1\}}^N`, which assigns
              each node from :math:`\mathbf{Y}` to a specific example.
              (default: :obj:`None`)
          k (int, optional): Number of neighbors. (default: :obj:`3`)
          num_workers (int, optional): Number of workers to use for computation.
              Has no effect in case :obj:`batch_x` or :obj:`batch_y` is not
              :obj:`None`, or the input lies on the GPU. (default: :obj:`1`)
      """
      with torch.no_grad():
          assign_index = knn(
              pos_x,
              pos_y,
              k,
              batch_x=batch_x,
              batch_y=batch_y,
              num_workers=num_workers,
          )
          y_idx, x_idx = assign_index[0], assign_index[1]
          diff = pos_x[x_idx] - pos_y[y_idx]
          squared_distance = (diff * diff).sum(dim=-1, keepdim=True)
          weights = 1.0 / torch.clamp(squared_distance, min=1e-16)
  
      y = scatter(
          x[x_idx] * weights, y_idx, 0, pos_y.size(0), reduce="sum"
      )
      y = y / scatter(weights, y_idx, 0, pos_y.size(0), reduce="sum")
  
      return y
  
imports: import torch
  from torch_geometric.nn import knn
  from torch_geometric.typing import OptTensor
  from torch_geometric.utils import scatter
label_desc: Use image node_id 1 for calling a global function with example usage: knn_interpolate(x, pos_x, pos_y, batch_x, batch_y, k, num_workers) and returns: y