class_docstr: Class for Cholesky metric on Cholesky space.
  
  References
  ----------
  .. [TP2019] . "Riemannian Geometry of Symmetric
      Positive Definite Matrices Via Cholesky Decomposition"
      SIAM journal on Matrix Analysis and Applications , 2019.
      https://arxiv.org/abs/1908.09326
class_docstr_tok: ["Class","for","Cholesky","metric","on","Cholesky","space",".","References","--","--","--","--","--","..","[","TP2019","]",".","``","Riemannian","Geometry","of","Symmetric","Positive","Definite","Matrices","Via","Cholesky","Decomposition","''","SIAM","journal","on","Matrix","Analysis","and","Applications",",","2019.","https",":","\/\/arxiv.org\/abs\/1908.09326"]
docstr: Compute the Cholesky Metric squared distance.
  
  Compute the Riemannian squared distance between point_a and point_b.
  
  Parameters
  ----------
  point_a : array-like, shape=[..., n, n]
      Point.
  point_b : array-like, shape=[..., n, n]
      Point.
  
  Returns
  -------
  _ : array-like, shape=[...]
      Riemannian squared distance.
docstr_tok: ["Compute","the","Cholesky","Metric","squared","distance",".","Compute","the","Riemannian","squared","distance","between","point_a","and","point_b",".","Parameters","--","--","--","--","--","point_a",":","array-like",",","shape=","[","...",",","n",",","n","]","Point",".","point_b",":","array-like",",","shape=","[","...",",","n",",","n","]","Point",".","Returns","--","--","--","-","_",":","array-like",",","shape=","[","...","]","Riemannian","squared","distance","."]
code: def squared_dist(self, point_a, point_b, **kwargs):
      """Compute the Cholesky Metric squared distance.
  
      Compute the Riemannian squared distance between point_a and point_b.
  
      Parameters
      ----------
      point_a : array-like, shape=[..., n, n]
          Point.
      point_b : array-like, shape=[..., n, n]
          Point.
  
      Returns
      -------
      _ : array-like, shape=[...]
          Riemannian squared distance.
      """
      log_diag_a = gs.log(Matrices.diagonal(point_a))
      log_diag_b = gs.log(Matrices.diagonal(point_b))
      diag_diff = log_diag_a - log_diag_b
      squared_dist_diag = gs.sum((diag_diff) ** 2, axis=-1)
  
      sl_a = Matrices.to_strictly_lower_triangular(point_a)
      sl_b = Matrices.to_strictly_lower_triangular(point_b)
      sl_diff = sl_a - sl_b
      squared_dist_sl = Matrices.frobenius_product(sl_diff, sl_diff)
      return squared_dist_sl + squared_dist_diag
  
imports: import geomstats.backend
  from geomstats.geometry.base import DiffeomorphicManifold, VectorSpaceOpenSet
  from geomstats.geometry.diffeo import Diffeo
  from geomstats.geometry.invariant_metric import _InvariantMetricMatrix
  from geomstats.geometry.lie_group import MatrixLieGroup
  from geomstats.geometry.lower_triangular_matrices import LowerTriangularMatrices
  from geomstats.geometry.matrices import Matrices
  from geomstats.geometry.open_hemisphere import OpenHemisphere, OpenHemispheresProduct
  from geomstats.geometry.pullback_metric import PullbackDiffeoMetric
  from geomstats.geometry.riemannian_metric import RiemannianMetric
label_desc: Use image node_id 6 for calling the CholeskyMetric obj's underlying member method code with example usage: obj.squared_dist(point_a, point_b) and returns: unknown