code: def test_gpt_posterior_settings(self):
      for propagate_grads in (False, True):
          with settings.propagate_grads(propagate_grads):
              with gpt_posterior_settings():
                  self.assertTrue(gpt_settings.debug.off())
                  self.assertTrue(gpt_settings.fast_pred_var.on())
                  if settings.propagate_grads.off():
                      self.assertTrue(
                          gpt_settings.detach_test_caches.on()
                      )
                  else:
                      self.assertTrue(
                          gpt_settings.detach_test_caches.off()
                      )
  
imports: import warnings
  import torch
  from botorch import settings
  from botorch.exceptions import InputDataError, InputDataWarning
  from botorch.models.utils import add_output_dim, check_min_max_scaling, check_no_nans, check_standardization, fantasize, gpt_posterior_settings, multioutput_to_batch_mode_transform, validate_input_scaling
  from botorch.models.utils.assorted import consolidate_duplicates, detect_duplicates
  from botorch.utils.testing import BotorchTestCase
  from gpytorch import settings
label_desc: Use image node_id 1 for calling the TestGPTPosteriorSettings obj's underlying member method code with example usage: obj.test_gpt_posterior_settings() without return types