code: def test_gam_gradient():
      # test the gam gradient for the example polynomial
      np.random.seed(1)
      pol, y = polynomial_sample_data()
  
      alpha = 1
      smoother = pol.smoothers[0]
      gp = UnivariateGamPenalty(
          alpha=alpha, univariate_smoother=smoother
      )
  
      for _ in range(10):
          params = np.random.uniform(-2, 2, 4)
          params = np.array([1, 1, 1, 1])
          gam_grad = gp.deriv(params)
          grd = grad(params)
  
          assert_allclose(gam_grad, grd, rtol=1.0e-2, atol=1.0e-2)
  
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 7 for calling a global function with example usage: test_gam_gradient() without return types