code: def test_predict_with_actual_values(self):
      X = np.array(
          [
              [0.0, 0.0, 0.0],
              [0.0, 0.0, 1.0],
              [0.0, 1.0, 0.0],
              [0.0, 1.0, 1.0],
              [1.0, 0.0, 0.0],
              [1.0, 0.0, 1.0],
              [1.0, 1.0, 0.0],
              [1.0, 1.0, 1.0],
          ],
          dtype=np.float64,
      )
      y = np.array(
          [
              [0.1],
              [0.2],
              [9],
              [9.2],
              [100.0],
              [100.2],
              [109.0],
              [109.2],
          ],
          dtype=np.float64,
      )
      rs = np.random.RandomState(1)
      model = get_gp(3, rs)
      model.train(
          np.vstack((X, X, X, X, X, X, X, X)),
          np.vstack((y, y, y, y, y, y, y, y)),
      )
  
      self.assertEqual(model.is_trained, True)
  
      mu_hat, var_hat = model.predict(X)
      for y_i, y_hat_i, mu_hat_i in zip(
          y.reshape((1, -1)).flatten(),
          mu_hat.reshape((1, -1)).flatten(),
          var_hat.reshape((1, -1)).flatten(),
      ):
          self.assertAlmostEqual(y_hat_i, y_i, delta=2)
          self.assertAlmostEqual(mu_hat_i, 0, delta=2)
  
      # Regression test that performance does not drastically decrease in the near future
      mu_hat, var_hat = model.predict(np.array([[10.0, 10.0, 10.0]]))
  
      self.assertAlmostEqual(mu_hat[0][0], 54.612500000000004)
      # There's a slight difference between my local installation and travis
      self.assertLess(abs(var_hat[0][0] - 1017.1374468449195), 15)
  
      # test other covariance results
      _, var_fc = model.predict(X, cov_return_type="full")
      self.assertEqual(var_fc.shape, (8, 8))
      _, var_sd = model.predict(X, cov_return_type="std")
      self.assertEqual(var_sd.shape, (8, 1))
      _, var_no = model.predict(
          np.array([[10.0, 10.0, 10.0]]), cov_return_type=None
      )
      self.assertIsNone(var_no)
      # check values
      _, var_fc = model.predict(
          np.array([[10.0, 10.0, 10.0]]), cov_return_type="full"
      )
      self.assertAlmostEqual(var_fc[0][0], var_hat[0][0])
      _, var_sd = model.predict(
          np.array([[10.0, 10.0, 10.0]]), cov_return_type="std"
      )
      self.assertAlmostEqual(var_sd[0][0] ** 2, var_hat[0][0])
  
      _, var_fc = model.predict(
          np.array([[10.0, 10.0, 10.0], [5.0, 5.0, 5.0]]),
          cov_return_type="full",
      )
      self.assertEqual(var_fc.shape, (2, 2))
  
imports: import unittest.mock
  import numpy
  import pyro
  import torch
  from botorch.models.kernels.categorical import CategoricalKernel
  from gpytorch.constraints.constraints import Interval
  from gpytorch.kernels import MaternKernel, ProductKernel, ScaleKernel
  from gpytorch.likelihoods.gaussian_likelihood import GaussianLikelihood
  from gpytorch.mlls.exact_marginal_log_likelihood import ExactMarginalLogLikelihood
  from gpytorch.models.exact_gp import ExactGP
  from gpytorch.priors import HorseshoePrior, LogNormalPrior, UniformPrior
  from gpytorch.utils.errors import NotPSDError
  from smac.configspace import CategoricalHyperparameter, ConfigurationSpace, UniformFloatHyperparameter
  from smac.model.gaussian_process.gpytorch_gaussian_process import GPyTorchGaussianProcess
  from ._test_gp import TestGP, get_cat_data, get_cont_data
label_desc: Use image node_id 8 for calling the TestGPGPyTorch obj's underlying member method code with example usage: obj.test_predict_with_actual_values() without return types