class_docstr: Class for Lie groups.
  
  In this class, point_type ('vector' or 'matrix') will be used to describe
  the format of the points on the Lie group.
  If point_type is 'vector', the format of the inputs is
  [..., dimension], where dimension is the dimension of the Lie group.
  If point_type is 'matrix' the format of the inputs is
  [..., n, n] where n is the parameter of GL(n) e.g. the amount of rows
  and columns of the matrix.
  
  Parameters
  ----------
  dim : int
      Dimension of the Lie group.
  lie_algebra : MatrixLieAlgebra
      Lie algebra for matrix groups.
      Optional, default: None.
  
  Attributes
  ----------
  lie_algebra : MatrixLieAlgebra or None
      Tangent space at the identity.
docstr: Calculate the group exponential at base_point.
  
  Parameters
  ----------
  tangent_vec : array-like, shape=[..., {dim, [n, n]}]
      Tangent vector at base point.
  base_point : array-like, shape=[..., {dim, [n, n]}]
      Base point.
  
  Returns
  -------
  exp : array-like, shape=[..., {dim, [n, n]}]
      Group exponential.
docstr_tok: ["Calculate","the","group","exponential","at","base_point",".","Parameters","--","--","--","--","--","tangent_vec",":","array-like",",","shape=","[","...",",","{","dim",",","[","n",",","n","]","}","]","Tangent","vector","at","base","point",".","base_point",":","array-like",",","shape=","[","...",",","{","dim",",","[","n",",","n","]","}","]","Base","point",".","Returns","--","--","--","-","exp",":","array-like",",","shape=","[","...",",","{","dim",",","[","n",",","n","]","}","]","Group","exponential","."]
code: def exp_not_from_identity(self, tangent_vec, base_point):
      """Calculate the group exponential at base_point.
  
      Parameters
      ----------
      tangent_vec : array-like, shape=[..., {dim, [n, n]}]
          Tangent vector at base point.
      base_point : array-like, shape=[..., {dim, [n, n]}]
          Base point.
  
      Returns
      -------
      exp : array-like, shape=[..., {dim, [n, n]}]
          Group exponential.
      """
      if self.default_point_type == "vector":
          tangent_translation = self.tangent_translation_map(
              point=base_point, left=True, inverse=True
          )
  
          tangent_vec_at_id = tangent_translation(tangent_vec)
          exp_from_identity = self.exp_from_identity(
              tangent_vec=tangent_vec_at_id
          )
          exp = self.compose(base_point, exp_from_identity)
          exp = self.regularize(exp)
          return exp
  
      lie_vec = self.compose(self.inverse(base_point), tangent_vec)
      return self.compose(base_point, self.exp_from_identity(lie_vec))
  
imports: import abc
  import geomstats.backend
  from geomstats.geometry.invariant_metric import InvariantMetric
  from geomstats.geometry.manifold import Manifold
  from geomstats.geometry.matrices import Matrices
label_desc: Use image node_id 9 for calling the LieGroup obj's underlying member method code with example usage: obj.exp_not_from_identity(tangent_vec, base_point) and returns: self, exp