code: def test_main(self):
      for module in self.modules.values():
          closure = ForwardBackwardClosure(
              module, module.free_parameters
          )
  
          # Test __init__
          closure = ForwardBackwardClosure(
              module, module.free_parameters
          )
          self.assertEqual(module.free_parameters, closure.parameters)
          self.assertIsInstance(closure.context_manager, partial)
          self.assertEqual(closure.context_manager.func, zero_grad_ctx)
  
          # Test return values
          value, (dw, dx, dd) = closure()
          self.assertTrue(value.equal(module()))
          self.assertTrue(dw.equal(module.x))
          self.assertTrue(dx.equal(module.w))
          self.assertEqual(dd, None)
  
          # Test `callback`` and `reducer``
          closure = ForwardBackwardClosure(
              module, module.free_parameters
          )
          mock_reducer = MagicMock(return_value=closure.forward())
          mock_callback = MagicMock()
          closure = ForwardBackwardClosure(
              forward=module,
              parameters=module.free_parameters,
              reducer=mock_reducer,
              callback=mock_callback,
          )
          value, grads = closure()
          mock_reducer.assert_called_once_with(value)
          mock_callback.assert_called_once_with(value, grads)
  
          # Test `backward`` and `context_manager`
          closure = ForwardBackwardClosure(
              forward=module,
              parameters=module.free_parameters,
              backward=partial(
                  torch.Tensor.backward, retain_graph=True
              ),
              context_manager=nullcontext,
          )
          _, (
              dw,
              dx,
              dd,
          ) = closure()  # x2 because `grad` is no longer zeroed
          self.assertTrue(dw.equal(2 * module.x))
          self.assertTrue(dx.equal(2 * module.w))
          self.assertEqual(dd, None)
  
imports: from contextlib import nullcontext
  from functools import partial
  from typing import Dict
  from unittest.mock import MagicMock
  import numpy
  import torch
  from botorch.optim.closures.core import ForwardBackwardClosure, get_tensors_as_ndarray_1d, NdarrayOptimizationClosure
  from botorch.optim.utils import as_ndarray
  from botorch.utils.context_managers import zero_grad_ctx
  from botorch.utils.testing import BotorchTestCase
  from linear_operator.utils.errors import NanError, NotPSDError
  from torch.nn import Module, Parameter
label_desc: Use image node_id 2 for calling the TestForwardBackwardClosure obj's underlying member method code with example usage: obj.test_main() without return types