code: def test_iterated_integrability_tensor_derivative_parallel_vec(
      self, n_reps, atol
  ):
      base_point = self.data_generator.random_point()
      horizontal_vec_x = self._get_horizontal_vec(base_point)
      horizontal_vec_y = self._get_horizontal_vec(base_point)
      (
          expected_nabla_x_a_y_v,
          expected_a_x_a_y_a_x_y,
          expected_nabla_x_v,
          expected_a_y_a_x_y,
          expected_vertical_vec_v,
      ) = self.bundle.iterated_integrability_tensor_derivative_parallel(
          horizontal_vec_x, horizontal_vec_y, base_point
      )
  
      vec_data = generate_vectorization_data(
          data=[
              dict(
                  horizontal_vec_x=horizontal_vec_x,
                  horizontal_vec_y=horizontal_vec_y,
                  base_point=base_point,
                  expected_nabla_x_a_y_v=expected_nabla_x_a_y_v,
                  expected_a_x_a_y_a_x_y=expected_a_x_a_y_a_x_y,
                  expected_nabla_x_v=expected_nabla_x_v,
                  expected_a_y_a_x_y=expected_a_y_a_x_y,
                  expected_vertical_vec_v=expected_vertical_vec_v,
                  atol=atol,
              )
          ],
          arg_names=["base_point"],
          expected_name=[
              "expected_nabla_x_a_y_v",
              "expected_a_x_a_y_a_x_y",
              "expected_nabla_x_v",
              "expected_a_y_a_x_y",
              "expected_vertical_vec_v",
          ],
          n_reps=n_reps,
      )
      self._test_vectorization(vec_data)
  
imports: import pytest
  import geomstats.backend
  from geomstats.geometry.matrices import Matrices
  from geomstats.test.random import KendalShapeRandomDataGenerator, get_random_times
  from geomstats.test.vectorization import generate_vectorization_data
  from geomstats.test_cases.geometry.base import LevelSetTestCase
  from geomstats.test_cases.geometry.fiber_bundle import FiberBundleTestCase
  from geomstats.test_cases.geometry.quotient_metric import QuotientMetricTestCase
  from geomstats.vectorization import get_batch_shape
label_desc: Use image node_id 21 for calling the PreShapeSpaceBundleTestCase obj's underlying member method code with example usage: obj.test_iterated_integrability_tensor_derivative_parallel_vec(n_reps, atol) without return types