docstr: Test optimized integrability tensor derivatives in pre-shape space.
  
  Optimized version for quotient-parallel vector fields should equal
  the general implementation.
code: def test_integrability_tensor_derivative_parallel_optimized(
      self, n_points, atol
  ):
      """Test optimized integrability tensor derivatives in pre-shape space.
  
      Optimized version for quotient-parallel vector fields should equal
      the general implementation.
      """
      base_point = self.data_generator.random_point(n_points)
      horizontal_vec_x = self._get_horizontal_vec(base_point)
      horizontal_vec_y = self._get_horizontal_vec(base_point)
      horizontal_vec_z = self._get_horizontal_vec(base_point)
  
      (
          nabla_x_a_y_z,
          a_y_z,
      ) = self.bundle.integrability_tensor_derivative_parallel(
          horizontal_vec_x,
          horizontal_vec_y,
          horizontal_vec_z,
          base_point,
      )
  
      a_x_y = self.bundle.integrability_tensor(
          horizontal_vec_x, horizontal_vec_y, base_point
      )
      a_x_z = self.bundle.integrability_tensor(
          horizontal_vec_x, horizontal_vec_z, base_point
      )
      (
          expected_nabla_x_a_y_z,
          expected_a_y_z,
      ) = self.bundle.integrability_tensor_derivative(
          horizontal_vec_x,
          horizontal_vec_y,
          a_x_y,
          horizontal_vec_z,
          a_x_z,
          base_point,
      )
  
      self.assertAllClose(
          nabla_x_a_y_z, expected_nabla_x_a_y_z, atol=atol
      )
      self.assertAllClose(a_y_z, expected_a_y_z, atol=atol)
  
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 19 for calling the PreShapeSpaceBundleTestCase obj's underlying member method code with example usage: obj.test_integrability_tensor_derivative_parallel_optimized(n_points, atol) without return types