code: def test_sgpr_mean_abs_error(self, cuda=False):
      # Suppress numerical warnings
      warnings.simplefilter("ignore", NumericalWarning)
  
      train_x, train_y, test_x, test_y = make_data(cuda=cuda)
      likelihood = GaussianLikelihood()
      gp_model = GPRegressionModel(train_x, train_y, likelihood)
      mll = gpytorch.mlls.ExactMarginalLogLikelihood(
          likelihood, gp_model
      )
  
      if cuda:
          gp_model = gp_model.cuda()
          likelihood = likelihood.cuda()
  
      # Mock cholesky
      _wrapped_cholesky = MagicMock(wraps=torch.linalg.cholesky_ex)
      with patch(
          "torch.linalg.cholesky_ex", new=_wrapped_cholesky
      ) as cholesky_mock:
          # Optimize the model
          gp_model.train()
          likelihood.train()
  
          optimizer = optim.Adam(gp_model.parameters(), lr=0.1)
          for _ in range(30):
              optimizer.zero_grad()
              output = gp_model(train_x)
              loss = -mll(output, train_y)
              loss.backward()
              optimizer.step()
  
              # Check that we have the right LinearOperator type
              kernel = likelihood(
                  gp_model(train_x)
              ).lazy_covariance_matrix.evaluate_kernel()
              self.assertIsInstance(
                  kernel,
                  linear_operator.operators.LowRankRootAddedDiagLinearOperator,
              )
  
          for param in gp_model.parameters():
              self.assertTrue(param.grad is not None)
              self.assertGreater(param.grad.norm().item(), 0)
  
          # Test the model
          gp_model.eval()
          likelihood.eval()
  
          test_preds = likelihood(gp_model(test_x)).mean
          mean_abs_error = torch.mean(torch.abs(test_y - test_preds))
          cholesky_mock.assert_called()  # We SHOULD call Cholesky...
          for chol_arg in cholesky_mock.call_args_list:
              first_arg = chol_arg[0][0]
              self.assertTrue(torch.is_tensor(first_arg))
              self.assertTrue(
                  first_arg.size(-1)
                  == gp_model.covar_module.inducing_points.size(-2)
              )
  
      self.assertLess(mean_abs_error.squeeze().item(), 0.1)
  
      # Test variances
      test_vars = likelihood(gp_model(test_x)).variance
      self.assertAllClose(
          test_vars,
          likelihood(gp_model(test_x)).covariance_matrix.diagonal(
              dim1=-1, dim2=-2
          ),
      )
      self.assertGreater(
          test_vars.min().item() + 0.1, likelihood.noise.item()
      )
      self.assertLess(
          test_vars.max().item() - 0.05,
          likelihood.noise.item()
          + gp_model.covar_module.base_kernel.outputscale.item(),
      )
  
      # Test on training data
      test_outputs = likelihood(gp_model(train_x))
      self.assertLess((test_outputs.mean - train_y).max().item(), 0.1)
      self.assertLess(
          test_outputs.variance.max().item(),
          likelihood.noise.item() * 2,
      )
  
imports: import os
  import random
  import unittest
  import warnings
  from math import exp, pi
  from unittest.mock import MagicMock, patch
  import linear_operator
  import torch
  from torch import optim
  import gpytorch
  from gpytorch.distributions import MultivariateNormal
  from gpytorch.kernels import InducingPointKernel, RBFKernel, ScaleKernel
  from gpytorch.likelihoods import GaussianLikelihood
  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
  from gpytorch.utils.warnings import NumericalWarning
label_desc: Use image node_id 3 for calling the TestSGPRRegression obj's underlying member method code with example usage: obj.test_sgpr_mean_abs_error(cuda) without return types