code: def test_posterior_update_cache_with_variables_update_value(
      q_sqrt_factory: QSqrtFactory, whiten: bool
  ) -> None:
      # setup posterior
      kernel = gpflow.kernels.SquaredExponential()
      inducing_variable = inducingpoint_wrapper(
          np.random.randn(NUM_INDUCING_POINTS, INPUT_DIMS)
      )
  
      q_mu = tf.Variable(np.random.randn(NUM_INDUCING_POINTS, 1))
  
      initial_q_sqrt = q_sqrt_factory(NUM_INDUCING_POINTS, 1)
      if initial_q_sqrt is not None:
          q_sqrt = tf.Variable(initial_q_sqrt)
      else:
          q_sqrt = initial_q_sqrt
  
      posterior = IndependentPosteriorSingleOutput(
          kernel=kernel,
          inducing_variable=inducing_variable,
          q_mu=q_mu,
          q_sqrt=q_sqrt,
          whiten=whiten,
          precompute_cache=PrecomputeCacheType.TENSOR,
      )
      assert posterior.cache
      initial_alpha, initial_Qinv = posterior.cache
  
      posterior.update_cache(PrecomputeCacheType.VARIABLE)
  
      # ensure the values of alpha and Qinv will change
      q_mu.assign_add(tf.ones_like(q_mu))
      if initial_q_sqrt is not None:
          q_sqrt.assign_add(tf.ones_like(q_sqrt))
      posterior.update_cache(PrecomputeCacheType.VARIABLE)
  
      # assert that the values have changed
      assert posterior.cache
      alpha, Qinv = posterior.cache
      assert not np.allclose(initial_alpha, tf.convert_to_tensor(alpha))
      if initial_q_sqrt is not None:
          assert not np.allclose(
              initial_Qinv, tf.convert_to_tensor(Qinv)
          )
  
imports: from typing import Any, Callable, DefaultDict, Optional, Set, Type, cast
  import numpy
  import pytest
  import tensorflow
  from _pytest.fixtures import SubRequest
  from check_shapes import check_shapes
  import gpflow
  import gpflow.ci_utils
  from gpflow.base import TensorType
  from gpflow.conditionals import conditional
  from gpflow.inducing_variables import InducingPoints, InducingVariables
  from gpflow.kernels import Kernel
  from gpflow.likelihoods import Gaussian
  from gpflow.mean_functions import Zero
  from gpflow.models.util import inducingpoint_wrapper
  from gpflow.posteriors import AbstractPosterior, FallbackIndependentLatentPosterior, FullyCorrelatedPosterior, GPRPosterior, IndependentPosteriorMultiOutput, IndependentPosteriorSingleOutput, LinearCoregionalizationPosterior, PrecomputeCacheType, SGPRPosterior, VGPPosterior, create_posterior
label_desc: Use image node_id 22 for calling a global function with example usage: test_posterior_update_cache_with_variables_update_value(q_sqrt_factory, whiten) without return types