code: def test_trainer():
      x = gluon.Parameter("x", shape=(10,))
      x.initialize(ctx=[mx.cpu(0), mx.cpu(1)], init="zeros")
      trainer = gluon.Trainer(
          [x], "sgd", {"learning_rate": 1.0, "momentum": 0.5}
      )
      with mx.autograd.record():
          for w in x.list_data():
              y = w + 1
              y.backward()
      trainer.step(1)
  
      assert (
          trainer._optimizer.param_dict == trainer._optimizer.param_dict
      )
      assert (x.data(mx.cpu(1)).asnumpy() == -2).all()
  
      x.lr_mult = 0.5
      with mx.autograd.record():
          for w in x.list_data():
              y = w + 1
              y.backward()
      trainer.step(1)
      assert (x.data(mx.cpu(1)).asnumpy() == -4).all()
  
      trainer.save_states("test_trainer.states")
      states = (
          deepcopy(trainer._kvstore._updater.states)
          if trainer._update_on_kvstore
          else deepcopy(trainer._updaters[0].states)
      )
      trainer.load_states("test_trainer.states")
      if trainer._update_on_kvstore:
          dict_equ(trainer._kvstore._updater.states, states)
          assert (
              trainer._optimizer == trainer._kvstore._updater.optimizer
          )
          # invalid usage of update and allreduce_grads if update_on_kvstore
          pytest.raises(AssertionError, trainer.update, 1)
          pytest.raises(AssertionError, trainer.allreduce_grads)
      else:
          for updater in trainer._updaters:
              dict_equ(updater.states, states)
          assert trainer._optimizer == trainer._updaters[0].optimizer
  
      x = gluon.Parameter("x", shape=(10,))
      x.initialize(ctx=[mx.cpu(0), mx.cpu(1)], init="zeros")
      trainer2 = gluon.Trainer(
          [x],
          "sgd",
          {"learning_rate": 1.0, "momentum": 0.5},
          update_on_kvstore=False,
      )
      with mx.autograd.record():
          for i, w in enumerate(x.list_data()):
              y = i * w
              y.backward()
      assert (
          x.grad(mx.cpu(0)).asnumpy() != x.grad(mx.cpu(1)).asnumpy()
      ).all()
      trainer2.allreduce_grads()
      assert (
          x.grad(mx.cpu(0)).asnumpy() == x.grad(mx.cpu(1)).asnumpy()
      ).all()
      trainer2.update(1)
  
      assert (x.data(mx.cpu(1)).asnumpy() == -1).all(), x.data(
          mx.cpu(1)
      ).asnumpy()
  
imports: import mxnet
  import unittest
  import os
  import numpy
  from mxnet import gluon
  from mxnet.gluon import nn
  from mxnet.test_utils import assert_almost_equal
  from common import assertRaises, xfail_when_nonstandard_decimal_separator
  from copy import deepcopy
  import pytest
label_desc: Use image node_id 5 for calling a global function with example usage: test_trainer() without return types