code: def test_fixed_noise_fantasy_updates(self, cuda=False):
      train_x, test_x, train_y, test_y = self._get_data(cuda=cuda)
      noise = torch.full_like(train_y, 2e-4)
      test_noise = torch.full_like(test_y, 3e-4)
  
      likelihood = FixedNoiseGaussianLikelihood(noise)
      gp_model = ExactGPModel(train_x, train_y, likelihood)
      mll = gpytorch.ExactMarginalLogLikelihood(likelihood, gp_model)
      gp_model.covar_module.base_kernel.initialize(lengthscale=exp(1))
      gp_model.mean_module.initialize(constant=0)
  
      if cuda:
          gp_model.cuda()
          likelihood.cuda()
  
      # Find optimal model hyperparameters
      gp_model.train()
      likelihood.train()
      optimizer = optim.Adam(gp_model.parameters(), lr=0.15)
      for _ in range(50):
          optimizer.zero_grad()
          with gpytorch.settings.debug(False):
              output = gp_model(train_x)
          loss = -mll(output, train_y)
          loss.backward()
          optimizer.step()
  
      for param in gp_model.parameters():
          self.assertTrue(param.grad is not None)
          self.assertGreater(param.grad.norm().item(), 0)
      optimizer.step()
  
      train_x.requires_grad = True
      gp_model.set_train_data(train_x, train_y)
      with gpytorch.settings.fast_pred_var(), gpytorch.settings.detach_test_caches(
          False
      ):
          # Test the model
          gp_model.eval()
          likelihood.eval()
          test_function_predictions = likelihood(
              gp_model(test_x), noise=test_noise
          )
          test_function_predictions.mean.sum().backward()
  
          real_fant_x_grad = train_x.grad[5:].clone()
          train_x.grad = None
          train_x.requires_grad = False
          gp_model.set_train_data(train_x, train_y)
  
          # Cut data down, and then add back via the fantasy interface
          gp_model.set_train_data(
              train_x[:5], train_y[:5], strict=False
          )
          gp_model.likelihood.noise_covar = FixedGaussianNoise(
              noise=noise[:5]
          )
          likelihood(gp_model(test_x), noise=test_noise)
  
          fantasy_x = train_x[5:].clone().detach().requires_grad_(True)
          fant_model = gp_model.get_fantasy_model(
              fantasy_x, train_y[5:], noise=noise[5:]
          )
  
          fant_function_predictions = likelihood(
              fant_model(test_x), noise=test_noise
          )
  
          self.assertAllClose(
              test_function_predictions.mean,
              fant_function_predictions.mean,
              atol=1e-4,
          )
  
          fant_function_predictions.mean.sum().backward()
          self.assertTrue(fantasy_x.grad is not None)
  
          relative_error = (
              torch.norm(real_fant_x_grad - fantasy_x.grad)
              / fantasy_x.grad.norm()
          )
          self.assertLess(relative_error, 15e-1)
  
imports: import unittest
  from math import exp, pi
  import torch
  from torch import optim
  import gpytorch
  from gpytorch.distributions import MultivariateNormal
  from gpytorch.kernels import RBFKernel, ScaleKernel
  from gpytorch.likelihoods import FixedNoiseGaussianLikelihood
  from gpytorch.likelihoods.noise_models import FixedGaussianNoise
  from gpytorch.means import ConstantMean
  from gpytorch.priors import SmoothedBoxPrior
  from gpytorch.test.base_test_case import BaseTestCase
  from gpytorch.test.utils import least_used_cuda_device
label_desc: Use image node_id 3 for calling the TestFixedNoiseFantasies obj's underlying member method code with example usage: obj.test_fixed_noise_fantasy_updates(cuda) without return types