code: def test_gam_hessian():
      # test the deriv2 method of the gam penalty
      np.random.seed(1)
      pol, y = polynomial_sample_data()
      univ_pol = pol.smoothers[0]
      alpha = 1
      gp = UnivariateGamPenalty(
          alpha=alpha, univariate_smoother=univ_pol
      )
  
      for _ in range(10):
          params = np.random.randint(-2, 2, 5)
          gam_der2 = gp.deriv2(params)
          hess = hessian(params)
          hess = np.flipud(hess)
          hess = np.fliplr(hess)
          assert_allclose(gam_der2, hess, atol=1.0e-13, rtol=1.0e-3)
  
imports: import os
  import numpy
  from numpy.testing import assert_allclose
  import pandas
  from scipy.linalg import block_diag
  import pytest
  from statsmodels.tools.linalg import matrix_sqrt
  from statsmodels.gam.smooth_basis import UnivariatePolynomialSmoother, PolynomialSmoother, BSplines, GenericSmoothers, UnivariateCubicSplines, CyclicCubicSplines
  from statsmodels.gam.generalized_additive_model import GLMGam, LogitGam, make_augmented_matrix, penalized_wls
  from statsmodels.gam.gam_cross_validation.gam_cross_validation import MultivariateGAMCV, MultivariateGAMCVPath, _split_train_test_smoothers
  from statsmodels.gam.gam_penalties import UnivariateGamPenalty, MultivariateGamPenalty
  from statsmodels.gam.gam_cross_validation.cross_validators import KFold
  from statsmodels.genmod.generalized_linear_model import GLM
  from statsmodels.genmod.families.family import Gaussian
  from statsmodels.genmod.generalized_linear_model import lm
label_desc: Use image node_id 8 for calling a global function with example usage: test_gam_hessian() without return types