code: def test(
      self,
      param_persistence_threshold: int,
      contiguous_gradients: bool,
      offload_optimizer: bool,
      zero_grad: bool,
      prefetching: bool,
  ) -> None:
      if offload_optimizer and not contiguous_gradients:
          return
  
      m = 3
      n = 5
      weights = [
          Parameter(torch.zeros((m, n), dtype=torch.float32))
          for _ in range(3)
      ]
      model = EltwiseMultiplicationTestNetwork(*weights)
      prefetch_bucket_size = sum(
          [p.numel() for p in model.parameters(recurse=True)]
      )
      cfg = {
          "train_micro_batch_size_per_gpu": 1,
          "zero_optimization": {
              "stage": 3,
              "stage3_max_reuse_distance": 0,
              "stage3_param_persistence_threshold": param_persistence_threshold,
              "contiguous_gradients": contiguous_gradients,
              "stage3_prefetch_bucket_size": prefetch_bucket_size
              if prefetching
              else 0,
          },
          "optimizer": {"type": "Adam", "params": {"lr": 1.0}},
          "bf16": {
              "enabled": True,
              "loss_scale": 1.0,
          },
      }
  
      if offload_optimizer:
          cfg["zero_optimization"]["offload_optimizer"] = {
              "device": "cpu",
              "pin_memory": True,
          }
  
      ds_engine = _ds_initialize_for_param_partitioning_testing(
          model, cfg
      )
      for i, weight in enumerate(weights):
          weight.ds_tensor.data = torch.full_like(
              weight.ds_tensor.data, (i + 1) * (1 + dist.get_rank())
          )
  
      def create_tensor(vals):
          return torch.as_tensor(
              vals, dtype=torch.bfloat16, device=ds_engine.device
          )
  
      expected_hidden1 = create_tensor(
          [
              [1, 1, 1, 1, 1],
              [1, 1, 1, 2, 2],
              [2, 2, 2, 2, 2],
          ]
      )
      expected_hidden2 = create_tensor(
          [
              [2, 2, 2, 2, 2],
              [2, 2, 2, 8, 8],
              [8, 8, 8, 8, 8],
          ]
      )
      expected_yhat = create_tensor(
          [[6, 6, 6, 6, 6], [6, 6, 6, 48, 48], [48, 48, 48, 48, 48]]
      )
      expected_loss = create_tensor(
          [
              [5, 5, 5, 5, 5],
              [5, 5, 5, 47, 47],
              [47, 47, 47, 47, 47],
          ]
      )
  
      for train_iter in range(3):
          _assert_partition_status(
              ds_engine, {ZeroParamStatus.NOT_AVAILABLE}
          )
          activations = ds_engine(
              x=torch.ones(
                  (m, n), dtype=torch.bfloat16, device=ds_engine.device
              ),
              y=torch.ones(
                  (m, n), dtype=torch.bfloat16, device=ds_engine.device
              ),
              use_module_trace=train_iter > 0,
              param_prefetching=prefetching and train_iter > 0,
          )
          assert torch.allclose(
              activations["hidden1"], expected_hidden1
          )
          assert torch.allclose(
              activations["hidden2"], expected_hidden2
          )
          assert torch.allclose(activations["y_hat"], expected_yhat)
          assert torch.allclose(activations["loss"], expected_loss)
  
          ds_engine.backward(activations["loss"].sum())
          _assert_partition_status(
              ds_engine, {ZeroParamStatus.NOT_AVAILABLE}
          )
  
          # check the gradients
          grad_partitions = (
              ds_engine.optimizer.get_fp32_grad_partitions()
          )
          assert set(grad_partitions.keys()) == {
              0
          }, f"should have one parameter group but got {len(grad_partitions)}"
          assert set(grad_partitions[0].keys()) == {0, 1, 2}
          dloss_wrt_layer1 = grad_partitions[0][0]
          dloss_wrt_layer2 = grad_partitions[0][1]
          dloss_wrt_layer3 = grad_partitions[0][2]
  
          # layer1 = [..., 1, 2, ...]
          # layer2 = [..., 2, 4, ...]
          # layer3 = [..., 3, 6, ...]
          # dloss_wrt_layer3 = hidden2
          # dloss_wrt_layer2 = layer3 * hidden1
          # dloss_wrt_layer1 = layer3 * layer2 * x
  
          expected_grad_dtype = (
              torch.float32 if offload_optimizer else torch.bfloat16
          )
  
          grad_multiplier = 1 if zero_grad else (train_iter + 1)
          if dist.get_rank() == 0:
              assert torch.allclose(
                  dloss_wrt_layer3.cuda(),
                  grad_multiplier
                  * create_tensor([2] * 8).to(expected_grad_dtype),
              )
              assert torch.allclose(
                  dloss_wrt_layer2.cuda(),
                  grad_multiplier
                  * create_tensor([3 * 1] * 8).to(expected_grad_dtype),
              )
              assert torch.allclose(
                  dloss_wrt_layer1.cuda(),
                  grad_multiplier
                  * create_tensor([3 * 2 * 1] * 8).to(
                      expected_grad_dtype
                  ),
              )
          elif dist.get_rank() == 1:
              # parameters dont split evenly across ranks so rank 1 has a zero-padded
              # partition
              assert torch.allclose(
                  dloss_wrt_layer3.cuda(),
                  grad_multiplier
                  * create_tensor(([8] * 7) + [0]).to(
                      expected_grad_dtype
                  ),
              )
              assert torch.allclose(
                  dloss_wrt_layer2.cuda(),
                  grad_multiplier
                  * create_tensor(([6 * 2] * 7) + [0]).to(
                      expected_grad_dtype
                  ),
              )
              assert torch.allclose(
                  dloss_wrt_layer1.cuda(),
                  grad_multiplier
                  * create_tensor(([6 * 4 * 1] * 7) + [0]).to(
                      expected_grad_dtype
                  ),
              )
          else:
              raise RuntimeError("test has world size of two")
  
          if zero_grad:
              ds_engine.optimizer.zero_grad()
  
      # TODO. add testing for this - for now we just call it to make sure it
      # doesn't throw
      ds_engine.optimizer.step()
      _assert_partition_status(
          ds_engine, {ZeroParamStatus.NOT_AVAILABLE}
      )
  
imports: import math
  from typing import Dict, List, Set
  import pytest
  import deepspeed.comm
  import torch
  from torch import Tensor
  from torch.nn import Linear, Module
  from torch.nn.modules.container import ModuleList
  from torch.nn.modules.loss import L1Loss
  from torch.nn.parameter import Parameter
  from unit.common import DistributedTest
  from unit.simple_model import SimpleModel, random_dataloader
  import deepspeed
  from deepspeed.runtime.engine import DeepSpeedEngine
  from deepspeed.runtime.zero.partition_parameters import ZeroParamStatus
  from deepspeed.utils.zero_to_fp32 import load_state_dict_from_zero_checkpoint
label_desc: Use image node_id 1 for calling the TestZero3ParamPartitioningBaseBF16 obj's underlying member method code with example usage: obj.test(param_persistence_threshold, contiguous_gradients, offload_optimizer, zero_grad, prefetching) and returns: torch