code: def _init(
      self,
      batch_size,
      layers,
      dim,
      foreach: bool = True,
      fused: bool = False,
  ):
      torch.manual_seed(0)
      model = DummyModel(layers, dim).cuda()
      ddp_model = DDP(deepcopy(model), device_ids=[self.rank])
      optim = torch.optim.Adam(
          model.parameters(),
          lr=0.01,
          foreach=foreach,
          fused=fused,
          capturable=True,
      )
      ddp_optim = torch.optim.Adam(
          ddp_model.parameters(),
          lr=0.01,
          foreach=foreach,
          fused=fused,
          capturable=True,
      )
      batch = torch.randn(batch_size, dim).cuda()
  
      # materialize optimizer states
      out = model(batch)
      out.sum().backward()
      optim.step()
      optim.zero_grad()
  
      ddp_out = ddp_model(batch)
      ddp_out.sum().backward()
      ddp_optim.step()
      ddp_optim.zero_grad()
  
      self.assertEqual(ddp_out, out)
      self.assertEqual(
          list(ddp_model.parameters()), list(model.parameters())
      )
      return model, optim, ddp_model, ddp_optim
  
imports: import unittest
  from copy import deepcopy
  from functools import wraps
  from unittest.mock import MagicMock
  import torch
  import torch.nn
  from torch.distributed._spmd.api import compile
  from torch.distributed._spmd.gm_transformation import GraphModuleTransformation
  from torch.distributed._spmd.graph_optimization import _optimized_func, comm_fusion_with_concat, find_all_descendants, get_all_fused_optimizer_blocks, graph_optimization_pass, iter_move_grads_and_optimizers, remove_copy_from_optimizer, schedule_comm_wait, split_fused_optimizer
  from torch.distributed._spmd.graph_utils import find_node
  from torch.distributed._spmd.iter_graph_module import IterGraphModule
  from torch.nn.parallel import DistributedDataParallel
  from torch.testing._internal.common_distributed import skip_if_lt_x_gpu
  from torch.testing._internal.common_utils import run_tests, skipIfRocm
  from torch.testing._internal.distributed._tensor.common_dtensor import DTensorTestBase, with_comms
  from torch.utils._triton import has_triton
label_desc: Use image node_id 2 for calling the TransformationTest obj's underlying member method code with example usage: obj._init(batch_size, layers, dim, foreach, fused) and returns: model,  optim,  ddp_model,  ddp_optim