class_docstr: Class for bi-invariant metrics on compact Lie groups.
  
  Compact Lie groups and direct products of compact Lie groups with vector
  spaces admit bi-invariant metrics [Gallier]_. Products Lie groups are not
  implemented. Other groups such as SE(3) admit bi-invariant pseudo-metrics.
  
  Parameters
  ----------
  space : LieGroup
      The group to equip with the bi-invariant metric
  
  References
  ----------
  .. [Gallier] Gallier, Jean, and Jocelyn Quaintance. Differential Geometry
      and Lie Groups: A Computational Perspective.
      Geonger International Publishing, 2020.
      https://doi.org/10.1007/978-3-030-46040-2.
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docstr: Compute Riemannian exponential of tangent vector from the identity.
  
  For a bi-invariant metric, this corresponds to the group exponential.
  
  Parameters
  ----------
  tangent_vec :
      Tangent vector at identity.
  base_point : array-like, shape=[..., {dim, [n, n]}]
      Point in the group.
      Optional, default : identity.
  
  Returns
  -------
  exp : array-like, shape=[..., {dim, [n, n]}]
      Point in the group.
  
  References
  ----------
  .. [Gallier] Gallier, Jean, and Jocelyn Quaintance. Differential
      Geometry and Lie Groups: A Computational Perspective.
      Geonger International Publishing, 2020.
      https://doi.org/10.1007/978-3-030-46040-2.
code: def exp(self, tangent_vec, base_point=None, **kwargs):
      """Compute Riemannian exponential of tangent vector from the identity.
  
      For a bi-invariant metric, this corresponds to the group exponential.
  
      Parameters
      ----------
      tangent_vec :
          Tangent vector at identity.
      base_point : array-like, shape=[..., {dim, [n, n]}]
          Point in the group.
          Optional, default : identity.
  
      Returns
      -------
      exp : array-like, shape=[..., {dim, [n, n]}]
          Point in the group.
  
      References
      ----------
      .. [Gallier] Gallier, Jean, and Jocelyn Quaintance. Differential
          Geometry and Lie Groups: A Computational Perspective.
          Geonger International Publishing, 2020.
          https://doi.org/10.1007/978-3-030-46040-2.
      """
      return self._space.exp(tangent_vec, base_point)
  
imports: import geomstats.backend
  from geomstats.geometry.matrices import Matrices
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.integrator import integrate
  from geomstats.numerics.geodesic import ExpODESolver, LogShootingSolver
  from geomstats.numerics.ivp import GSIVPIntegrator
  from geomstats.vectorization import repeat_out
label_desc: Use image node_id 3 for calling the BiInvariantMetric obj's underlying member method code with example usage: obj.exp(tangent_vec, base_point) and returns: self