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: Compute the group exponential at `base_point` of `tangent_vec`.
  
  Parameters
  ----------
  tangent_vec : array-like, shape=[..., {dim, [n, n]}]
      Tangent vector at base point.
  base_point : array-like, shape=[..., {dim, [n, n]}]
      Base point.
      Optional, default: self.identity
  
  Returns
  -------
  result : array-like, shape=[..., {dim, [n, n]}]
      Group exponential.
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code: def exp(self, tangent_vec, base_point=None):
      """Compute the group exponential at `base_point` of `tangent_vec`.
  
      Parameters
      ----------
      tangent_vec : array-like, shape=[..., {dim, [n, n]}]
          Tangent vector at base point.
      base_point : array-like, shape=[..., {dim, [n, n]}]
          Base point.
          Optional, default: self.identity
  
      Returns
      -------
      result : array-like, shape=[..., {dim, [n, n]}]
          Group exponential.
      """
      identity = self.identity
  
      if base_point is None:
          base_point = identity
      base_point = self.regularize(base_point)
  
      if gs.allclose(base_point, identity):
          return self.exp_from_identity(tangent_vec)
  
      return self.exp_not_from_identity(tangent_vec, base_point)
  
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 10 for calling the LieGroup obj's underlying member method code with example usage: obj.exp(tangent_vec, base_point) and returns: self, self