docstr: Test integrability tensor identity.
  
  The integrability tensor is also alternating (:math:`A_X Y =
  - A_Y X`)  for horizontal vector fields :math:'X,Y',  and it is
  exchanging horizontal and vertical vector spaces.
code: def test_integrability_tensor_identity_2(self, n_points, atol):
      """Test integrability tensor identity.
  
      The integrability tensor is also alternating (:math:`A_X Y =
      - A_Y X`)  for horizontal vector fields :math:'X,Y',  and it is
      exchanging horizontal and vertical vector spaces.
      """
      base_point = self.data_generator.random_point(n_points)
      horizontal_a = self._get_horizontal_vec(base_point)
      tangent_vec_b, horizontal_b = self._get_horizontal_vec(
          base_point, return_tangent=True
      )
  
      result = self.bundle.integrability_tensor(
          horizontal_a, horizontal_b, base_point
      )
      expected = -self.bundle.integrability_tensor(
          horizontal_b, horizontal_a, base_point
      )
      self.assertAllClose(result, expected, atol=atol)
  
      is_vertical = self.bundle.is_vertical(
          result, base_point, atol=atol
      )
      expected = gs.ones(n_points, dtype=bool)
      self.assertAllEqual(is_vertical, expected)
  
      vertical_b = tangent_vec_b - horizontal_b
      result = self.bundle.integrability_tensor(
          horizontal_a, vertical_b, base_point
      )
      is_horizontal = self.bundle.is_horizontal(
          result, base_point, atol=atol
      )
      expected = gs.ones(n_points, dtype=bool)
      self.assertAllEqual(is_horizontal, expected)
  
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 10 for calling the PreShapeSpaceBundleTestCase obj's underlying member method code with example usage: obj.test_integrability_tensor_identity_2(n_points, atol) without return types