code: def svd_pe(g, k, padding=False, random_flip=True):
      r"""SVD-based Positional Encoding, as introduced in
      `Global Self-Attention as a Replacement for Graph Convolution
      <https://arxiv.org/pdf/2108.03348.pdf>`__
  
      This function computes the largest :math:`k` singular values and
      corresponding left and right singular vectors to form positional encodings.
  
      Parameters
      ----------
      g : DGLGraph
          A DGLGraph to be encoded, which must be a homogeneous one.
      k : int
          Number of largest singular values and corresponding singular vectors
          used for positional encoding.
      padding : bool, optional
          If False, raise an error when :math:`k > N`,
          where :math:`N` is the number of nodes in :attr:`g`.
          If True, add zero paddings in the end of encoding vectors when
          :math:`k > N`.
          Default : False.
      random_flip : bool, optional
          If True, randomly flip the signs of encoding vectors.
          Proposed to be activated during training for better generalization.
          Default : True.
  
      Returns
      -------
      Tensor
          Return SVD-based positional encodings of shape :math:`(N, 2k)`.
  
      Example
      -------
      >>> import dgl
  
      >>> g = dgl.graph(([0,1,2,3,4,2,3,1,4,0], [2,3,1,4,0,0,1,2,3,4]))
      >>> dgl.svd_pe(g, k=2, padding=False, random_flip=True)
      tensor([[-6.3246e-01, -1.1373e-07, -6.3246e-01,  0.0000e+00],
              [-6.3246e-01,  7.6512e-01, -6.3246e-01, -7.6512e-01],
              [ 6.3246e-01,  4.7287e-01,  6.3246e-01, -4.7287e-01],
              [-6.3246e-01, -7.6512e-01, -6.3246e-01,  7.6512e-01],
              [ 6.3246e-01, -4.7287e-01,  6.3246e-01,  4.7287e-01]])
      """
      n = g.num_nodes()
      if not padding and n < k:
          raise ValueError(
              "The number of singular values k must be no greater than the "
              "number of nodes n, but "
              + f"got {k} and {n} respectively."
          )
      a = g.adj_external(ctx=g.device, scipy_fmt="coo").toarray()
      u, d, vh = scipy.linalg.svd(a)
      v = vh.transpose()
      m = min(n, k)
      topm_u = u[:, 0:m]
      topm_v = v[:, 0:m]
      topm_sqrt_d = sparse.diags(np.sqrt(d[0:m]))
      encoding = np.concatenate(
          ((topm_u @ topm_sqrt_d), (topm_v @ topm_sqrt_d)), axis=1
      )
      # randomly flip row vectors
      if random_flip:
          rand_sign = 2 * (np.random.rand(n) > 0.5) - 1
          flipped_encoding = F.tensor(
              rand_sign[:, np.newaxis] * encoding, dtype=F.float32
          )
      else:
          flipped_encoding = F.tensor(encoding, dtype=F.float32)
  
      if n < k:
          zero_padding = F.zeros(
              [n, 2 * (k - n)],
              dtype=F.float32,
              ctx=F.context(flipped_encoding),
          )
          flipped_encoding = F.cat(
              [flipped_encoding, zero_padding], dim=1
          )
  
      return flipped_encoding
  
imports: import copy
  from collections.abc import Iterable, Mapping
  import numpy
  import scipy.sparse
  import scipy.sparse.linalg
  from ..utils import version
  from ..None import backend, batch, convert, function, ndarray, subgraph, utils
  from .._ffi.function import _init_api
  from ..base import dgl_warning, DGLError, EID, NID
  from ..frame import Frame
  from ..heterograph import DGLGraph
  from ..heterograph_index import create_heterograph_from_relations, create_metagraph_index
  from ..partition import metis_partition, metis_partition_assignment, partition_graph_with_halo
  from ..sampling.neighbor import sample_neighbors
label_desc: Use image node_id 45 for calling a global function with example usage: svd_pe(g, k, padding, random_flip) and returns: flipped_encoding