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 logarithm map.
  
  Compute the Riemannian logarithm at point base_point,
  of point wrt the Cholesky metric.
  This gives a tangent vector at point base_point.
  
  Parameters
  ----------
  point : array-like, shape=[..., n, n]
      Point.
  base_point : array-like, shape=[..., n, n]
      Base point.
  
  Returns
  -------
  log : array-like, shape=[..., n, n]
      Riemannian logarithm.
docstr_tok: ["Compute","the","Cholesky","logarithm","map",".","Compute","the","Riemannian","logarithm","at","point","base_point",",","of","point","wrt","the","Cholesky","metric",".","This","gives","a","tangent","vector","at","point","base_point",".","Parameters","--","--","--","--","--","point",":","array-like",",","shape=","[","...",",","n",",","n","]","Point",".","base_point",":","array-like",",","shape=","[","...",",","n",",","n","]","Base","point",".","Returns","--","--","--","-","log",":","array-like",",","shape=","[","...",",","n",",","n","]","Riemannian","logarithm","."]
code: def log(self, point, base_point, **kwargs):
      """Compute the Cholesky logarithm map.
  
      Compute the Riemannian logarithm at point base_point,
      of point wrt the Cholesky metric.
      This gives a tangent vector at point base_point.
  
      Parameters
      ----------
      point : array-like, shape=[..., n, n]
          Point.
      base_point : array-like, shape=[..., n, n]
          Base point.
  
      Returns
      -------
      log : array-like, shape=[..., n, n]
          Riemannian logarithm.
      """
      sl_base_point = Matrices.to_strictly_lower_triangular(base_point)
      sl_point = Matrices.to_strictly_lower_triangular(point)
      diag_base_point = Matrices.diagonal(base_point)
      diag_point = Matrices.diagonal(point)
      diag_product_logm = gs.log(gs.divide(diag_point, diag_base_point))
  
      sl_log = sl_point - sl_base_point
      diag_log = gs.vec_to_diag(diag_base_point * diag_product_logm)
      return sl_log + diag_log
  
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 5 for calling the CholeskyMetric obj's underlying member method code with example usage: obj.log(point, base_point) and returns: unknown