code: def fourier_encode_dist(x, num_encodings=4, include_self=True):
      """
      Fourier encode the input tensor `x` based on the specified number of encodings.
  
      This function applies a Fourier encoding to the input tensor `x` by dividing
      it by a range of scales (2^i for i in range(num_encodings)) and then
      concatenating the sine and cosine of the scaled values. Optionally, the
      original input tensor can be included in the output.
  
      Parameters
      ----------
      x : torch.Tensor
          Input tensor to be Fourier encoded.
      num_encodings : int, optional, default=4
          Number of Fourier encodings to apply.
      include_self : bool, optional, default=True
          Whether to include the original input tensor in the output.
  
      Returns
      -------
      torch.Tensor
          Fourier encoded tensor.
  
      Examples
      --------
      >>> import torch
      >>> x = torch.tensor([1.0, 2.0, 3.0])
      >>> encoded_x = fourier_encode_dist(x, num_encodings=4, include_self=True)
      """
      x = x.unsqueeze(-1)
      device, dtype, orig_x = x.device, x.dtype, x
      scales = 2 ** torch.arange(
          num_encodings, device=device, dtype=dtype
      )
      x = x / scales
      x = torch.cat([x.sin(), x.cos()], dim=-1)
      x = torch.cat((x, orig_x), dim=-1) if include_self else x
      return x.squeeze()
  
file_path: deepchem/deepchem/utils/graph_utils.py
imports: import numpy
label_desc: Use image node_id 1 for calling a global function with example usage: fourier_encode_dist(x, num_encodings, include_) and returns: x