code: def test_GaussianProcess_std(self):
      X = np.atleast_2d([1.0, 3.0, 5.0, 6.0, 7.0, 8.0]).T
      y = np.sin(X).ravel()
      df = pdml.ModelFrame(X, target=y)
  
      k1 = df.gp.kernels.ConstantKernel(
          1.0, (1e-3, 1e3)
      ) * df.gp.kernels.RBF(10, (1e-2, 1e2))
      g1 = df.gp.GaussianProcessRegressor(
          kernel=k1,
          n_restarts_optimizer=9,
          random_state=self.random_state,
      )
  
      k2 = gp.kernels.ConstantKernel(1.0, (1e-3, 1e3)) * gp.kernels.RBF(
          10, (1e-2, 1e2)
      )
      g2 = gp.GaussianProcessRegressor(
          kernel=k2,
          n_restarts_optimizer=9,
          random_state=self.random_state,
      )
  
      g1.fit(X, y)
      g2.fit(X, y)
  
      x = np.atleast_2d(np.linspace(0, 10, 1000)).T
      tdf = pdml.ModelFrame(x)
  
      y_result, std_result = tdf.predict(g1, return_std=True)
      y_expected, std_expected = g2.predict(x, return_std=True)
  
      self.assertIsInstance(y_result, pdml.ModelSeries)
      tm.assert_index_equal(y_result.index, tdf.index)
  
      self.assertIsInstance(std_result, pdml.ModelSeries)
      tm.assert_index_equal(std_result.index, tdf.index)
  
      self.assert_numpy_array_almost_equal(y_result.values, y_expected)
      self.assert_numpy_array_almost_equal(
          std_result.values, std_expected
      )
  
file_path: pandas-ml/pandas_ml/skaccessors/test/test_gaussian_process.py
imports: import numpy
  import sklearn.gaussian_process
  import pandas_ml
  import pandas_ml.util.testing
label_desc: Use image node_id 8 for calling the TestGaussianProcess obj's underlying member method code with example usage: obj.test_GaussianProcess_std() without return types