docstr: Check metric determinant lower bound.
  
  References
  ----------
  .. [BP2019] Brigant, A.L. and Puechmorel, S. (2019)
  ‘The Fisher-Rao geometry of beta distributions applied to the study of
  canonical moments’. arXiv.
  Available at: https://doi.org/10.48550/arXiv.1904.08247.
docstr_tok: ["Check","metric","determinant","lower","bound",".","References","--","--","--","--","--","..","[","BP2019","]","Brigant",",","A.L",".","and","Puechmorel",",","S.","(","2019",")","\u2018","The","Fisher-Rao","geometry","of","beta","distributions","applied","to","the","study","of","canonical","moments","\u2019",".","arXiv",".","Available","at",":","https",":","\/\/doi.org\/10.48550\/arXiv.1904.08247","."]
code: def test_metric_det_lower_bound(self, n_points):
      """Check metric determinant lower bound.
  
      References
      ----------
      .. [BP2019] Brigant, A.L. and Puechmorel, S. (2019)
      ‘The Fisher-Rao geometry of beta distributions applied to the study of
      canonical moments’. arXiv.
      Available at: https://doi.org/10.48550/arXiv.1904.08247.
      """
      base_point = self.data_generator.random_point(n_points)
      res = self.space.metric.metric_det(base_point)
  
      alpha = base_point[..., 0]
      beta = base_point[..., 1]
  
      num = 1 + alpha + beta
      den = 2 * alpha * beta * gs.power((alpha + beta), 2)
      lower_bound = num / den
      self.assertTrue(gs.all(res > lower_bound))
  
file_path: geomstats/geomstats/test_cases/information_geometry/beta.py
imports: import pytest
  import geomstats.backend
  from geomstats.geometry.symmetric_matrices import SymmetricMatrices
  from geomstats.test_cases.information_geometry.dirichlet import DirichletDistributionsTestCase, DirichletMetricTestCase
label_desc: Use image node_id 3 for calling the BetaMetricTestCase obj's underlying member method code with example usage: obj.test_metric_det_lower_bound(n_points) without return types