code: def check_gradient_correctness(kernel, X, Y, step_size=1e-4):
      X_grad = kernel.gradient_x(X, Y)
      num_grad = numerical_gradient(X, Y, kernel, step_size)
      assert_array_almost_equal(X_grad, num_grad, decimal=3)
  
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 4 for calling a global function with example usage: check_gradient_correctness(kernel, X, Y, step_size) without return types