docstr: Sectional curvature of Kendall shape space is larger than 1.
  
  The sectional curvature always increase by taking the quotient in a
  Riemannian submersion. Thus, it should larger in kendall shape space
  thane the sectional curvature of the pre-shape space which is 1 as it
  a hypersphere.
  The sectional curvature is computed here with the generic
  directional_curvature and sectional curvature methods.
code: def test_sectional_curvature_lower_bound(self, n_points, atol):
      """Sectional curvature of Kendall shape space is larger than 1.
  
      The sectional curvature always increase by taking the quotient in a
      Riemannian submersion. Thus, it should larger in kendall shape space
      thane the sectional curvature of the pre-shape space which is 1 as it
      a hypersphere.
      The sectional curvature is computed here with the generic
      directional_curvature and sectional curvature methods.
      """
      base_point = self.data_generator.random_point(n_points)
      hor_a = self.data_generator.random_horizontal_vec(base_point)
      hor_b = self.data_generator.random_horizontal_vec(base_point)
  
      tidal_force = self.space.metric.directional_curvature(
          hor_a, hor_b, base_point
      )
  
      numerator = self.space.metric.inner_product(
          tidal_force, hor_a, base_point
      )
      denominator = (
          self.space.metric.inner_product(hor_a, hor_a, base_point)
          * self.space.metric.inner_product(hor_b, hor_b, base_point)
          - self.space.metric.inner_product(hor_a, hor_b, base_point)
          ** 2
      )
  
      condition = ~gs.isclose(denominator, 0.0, atol=atol)
      kappa = numerator[condition] / denominator[condition]
      kappa_direct = self.space.metric.sectional_curvature(
          hor_a, hor_b, base_point
      )[condition]
      self.assertAllClose(kappa, kappa_direct)
  
      result = kappa > 1.0 - atol
      self.assertTrue(gs.all(result))
  
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 9 for calling the KendallShapeMetricTestCase obj's underlying member method code with example usage: obj.test_sectional_curvature_lower_bound(n_points, atol) without return types