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 exponential map.
  
  Compute the Riemannian exponential at point base_point
  of tangent vector tangent_vec wrt the Cholesky metric.
  This gives a lower triangular matrix with positive elements.
  
  Parameters
  ----------
  tangent_vec : array-like, shape=[..., n, n]
      Tangent vector at base point.
  base_point : array-like, shape=[..., n, n]
      Base point.
  
  Returns
  -------
  exp : array-like, shape=[..., n, n]
      Riemannian exponential.
docstr_tok: ["Compute","the","Cholesky","exponential","map",".","Compute","the","Riemannian","exponential","at","point","base_point","of","tangent","vector","tangent_vec","wrt","the","Cholesky","metric",".","This","gives","a","lower","triangular","matrix","with","positive","elements",".","Parameters","--","--","--","--","--","tangent_vec",":","array-like",",","shape=","[","...",",","n",",","n","]","Tangent","vector","at","base","point",".","base_point",":","array-like",",","shape=","[","...",",","n",",","n","]","Base","point",".","Returns","--","--","--","-","exp",":","array-like",",","shape=","[","...",",","n",",","n","]","Riemannian","exponential","."]
code: def exp(self, tangent_vec, base_point, **kwargs):
      """Compute the Cholesky exponential map.
  
      Compute the Riemannian exponential at point base_point
      of tangent vector tangent_vec wrt the Cholesky metric.
      This gives a lower triangular matrix with positive elements.
  
      Parameters
      ----------
      tangent_vec : array-like, shape=[..., n, n]
          Tangent vector at base point.
      base_point : array-like, shape=[..., n, n]
          Base point.
  
      Returns
      -------
      exp : array-like, shape=[..., n, n]
          Riemannian exponential.
      """
      sl_base_point = Matrices.to_strictly_lower_triangular(base_point)
      sl_tangent_vec = Matrices.to_strictly_lower_triangular(
          tangent_vec
      )
      diag_base_point = Matrices.diagonal(base_point)
      diag_tangent_vec = Matrices.diagonal(tangent_vec)
      diag_product_expm = gs.exp(
          gs.divide(diag_tangent_vec, diag_base_point)
      )
  
      sl_exp = sl_base_point + sl_tangent_vec
      diag_exp = gs.vec_to_diag(diag_base_point * diag_product_expm)
      return sl_exp + diag_exp
  
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 4 for calling the CholeskyMetric obj's underlying member method code with example usage: obj.exp(tangent_vec, base_point) and returns: unknown