code: def test_gradient_finiteness(random_state, kernel):
      """
      When x is the same as X_train, gradients might become undefined because
      they are divided by d(x, X_train).
      Check they are equal to numerical gradients at such points.
      """
      rng = np.random.RandomState(random_state)
      X = rng.randn(5).tolist()
      Y = [X]
      check_gradient_correctness(kernel, X, Y, 1e-6)
  
imports: import numpy
  from scipy import optimize
  from scipy.spatial.distance import pdist, squareform
  from numpy.testing import assert_array_almost_equal
  from numpy.testing import assert_array_equal
  import pytest
  from skopt.learning.gaussian_process import GaussianProcessRegressor
  from skopt.learning.gaussian_process.kernels import ConstantKernel
  from skopt.learning.gaussian_process.kernels import DotProduct
  from skopt.learning.gaussian_process.kernels import ExpSineSquared
  from skopt.learning.gaussian_process.kernels import HammingKernel
  from skopt.learning.gaussian_process.kernels import Matern
  from skopt.learning.gaussian_process.kernels import RationalQuadratic
  from skopt.learning.gaussian_process.kernels import RBF
  from skopt.learning.gaussian_process.kernels import WhiteKernel
label_desc: Use image node_id 6 for calling a global function with example usage: test_gradient_finiteness(random_state, kernel) without return types