code: def test_multivariate_gam_cv_path():
      def sample_metric(y1, y2):
          return np.linalg.norm(y1 - y2) / len(y1)
  
      cur_dir = os.path.dirname(os.path.abspath(__file__))
      file_path = os.path.join(
          cur_dir, "results", "prediction_from_mgcv.csv"
      )
  
      data_from_r = pd.read_csv(file_path)
  
      # dataset used to train the R model
      x = data_from_r.x.values
      y = data_from_r.y.values
      se_from_mgcv = data_from_r.y_est_se  # noqa: F841
      y_mgcv = data_from_r.y_mgcv_gcv  # noqa: F841
  
      df = [10]
      degree = [6]
  
      bsplines = BSplines(
          x, degree=degree, df=df, include_intercept=True
      )
  
      gam = GLMGam
      alphas = [np.linspace(0, 2, 10)]
      k = 3
      cv = KFold(k_folds=k, shuffle=True)
  
      # Note: kfold cv uses random shuffle
      np.random.seed(123)
      gam_cv = MultivariateGAMCVPath(
          smoother=bsplines,
          alphas=alphas,
          gam=gam,
          cost=sample_metric,
          endog=y,
          exog=None,
          cv_iterator=cv,
      )
      gam_cv_res = gam_cv.fit()  # noqa: F841
  
      glm_gam = GLMGam(y, smoother=bsplines, alpha=gam_cv.alpha_cv)
      res_glm_gam = glm_gam.fit(
          method="irls", max_start_irls=0, disp=1, maxiter=10000
      )
      y_est = res_glm_gam.predict(bsplines.basis)
  
      # plt.plot(x, y, '.', label='y')
      # plt.plot(x, y_est, '.', label='y est')
      # plt.plot(x, y_mgcv, '.', label='y mgcv')
      # plt.legend()
      # plt.show()
  
      # The test compares to result obtained with GCV and not KFOLDS CV.
      # This is because MGCV does not support KFOLD CV
      assert_allclose(
          data_from_r.y_mgcv_gcv, y_est, atol=1.0e-1, rtol=1.0e-1
      )
  
      # Note: kfold cv uses random shuffle
      np.random.seed(123)
      alpha_cv, res_cv = glm_gam.select_penweight_kfold(
          alphas=alphas, k_folds=3
      )
      assert_allclose(alpha_cv, gam_cv.alpha_cv, rtol=1e-12)
  
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 17 for calling a global function with example usage: test_multivariate_gam_cv_path() and returns: unknown