code: def test_adam_w(self, backend_config):
      xp = backend_config.xp
      device = backend_config.device
  
      link = chainer.Link(x=(1,))
      link.to_device(device)
  
      opt = optimizers.Adam(eta=0.5, weight_decay_rate=0.1)
      opt.setup(link)
  
      link.x.data.fill(1)
      link.x.grad = device.send(xp.ones_like(link.x.data))
  
      opt.update()
  
      # compare against the value computed with v5 impl
      testing.assert_allclose(
          link.x.data, np.array([0.9495]), atol=1e-7, rtol=1e-7
      )
  
imports: import pickle
  import unittest
  import numpy
  import six
  import chainer
  from chainer import functions
  from chainer import optimizers
  from chainer import testing
label_desc: Use image node_id 1 for calling the TestAdamW obj's underlying member method code with example usage: obj.test_adam_w(backend_config) without return types