code: def test_posterior_bo_integration__predict_f(
      register_posterior_bo_integration_test: Callable[
          [AbstractPosterior], None
      ],
      _model_factory: _ModelFactory[Any],
      _data: Tuple[tf.Variable, tf.Variable],
      _extend_data: Callable[[GPModel], Iterator[int]],
      _X_new: tf.Tensor,
  ) -> None:
      """
      Check that data added incrementally is correctly reflected in `predict_f`.
      """
      _X, Y = _data
      n_rows_new = _X_new.shape[0]
      n_outputs = Y.shape[1]
  
      model = _model_factory.create_model(_data)
      posterior = model.posterior(PrecomputeCacheType.VARIABLE)
      register_posterior_bo_integration_test(posterior)
      if _COMPILE:
          predict_f = tf.function(
              lambda Xnew: posterior.predict_f(Xnew)
          )
      else:
          predict_f = posterior.predict_f
  
      for _ in _extend_data(model):
          posterior.update_cache()
          compiled_mean, compiled_var = predict_f(_X_new)
  
          np.testing.assert_equal(
              (n_rows_new, n_outputs), compiled_mean.shape
          )
          np.testing.assert_equal(
              (n_rows_new, n_outputs), compiled_var.shape
          )
  
          eager_model = _model_factory.create_model(_data)
          eager_mean, eager_var = eager_model.predict_f(_X_new)
  
          np.testing.assert_allclose(
              eager_mean,
              compiled_mean,
              rtol=_model_factory.rtol,
              atol=_model_factory.atol,
          )
          np.testing.assert_allclose(
              eager_var,
              compiled_var,
              rtol=_model_factory.rtol,
              atol=_model_factory.atol,
          )
  
imports: from typing import Any, Callable, DefaultDict, Generic, Iterator, List, Set, Tuple, Type, TypeVar, cast
  import numpy
  import pytest
  import tensorflow
  from _pytest.fixtures import SubRequest
  from check_shapes import check_shapes
  import gpflow
  from gpflow.base import RegressionData
  from gpflow.config import default_float
  from gpflow.inducing_variables import InducingPoints, InducingVariables
  from gpflow.kernels import Kernel, Matern52
  from gpflow.likelihoods import Exponential, Likelihood
  from gpflow.models import GPR, SGPR, SVGP, VGP, GPModel, training_loss_closure
  from gpflow.models.vgp import update_vgp_data
  from gpflow.posteriors import AbstractPosterior, PrecomputeCacheType
label_desc: Use image node_id 22 for calling a global function with example usage: test_posterior_bo_integration__predict_f(register_posterior_bo_integration_test, _model_factory, _data, _extend_data, _X_new) without return types