code: def _test_all_to_all_single(self, backend):
      store = c10d.FileStore(self.file_name, self.world_size)
      # This is required because these functions calls directly to the .dist and needs
      # the world to be initialized
      c10d.init_process_group(
          store=store,
          rank=self.rank,
          world_size=self.world_size,
          backend=backend,
      )
      device = torch.device(f"cuda:{self.rank}")
      row = (
          self.world_size * (self.rank + 1) * (self.world_size + 1) / 2
      )
      x = torch.ones(int(row), 5, device=device) * (self.rank + 1)
      x.requires_grad = True
      y = torch.empty_like(x)
      split_sizes = [
          (i + 1) * (self.rank + 1) for i in range(self.world_size)
      ]
      y = torch.distributed.nn.all_to_all_single(
          y,
          x,
          output_split_sizes=split_sizes,
          input_split_sizes=split_sizes,
      )
      expected = []
      for idx, tensor in enumerate(torch.split(x, split_sizes)):
          expected.append(torch.full_like(tensor, (idx + 1)))
      expected = torch.cat(expected)
      self.assertEqual(y, expected)
      z = y.sin().sum()
      z.backward()
      x_s = (
          (self.rank + 1) * torch.ones(int(row), 5, device=device)
      ).cos()
      self.assertEqual(x.grad, x_s)
  
imports: import os
  import sys
  import tempfile
  import torch
  import torch.distributed
  import torch.multiprocessing
  from torch.testing._internal.common_distributed import MultiProcessTestCase
  from torch.testing._internal.common_utils import load_tests, NO_MULTIPROCESSING_SPAWN
label_desc: Use image node_id 10 for calling the TestDistributedNNFunctions obj's underlying member method code with example usage: obj._test_all_to_all_single(backend) without return types