class_docstr: Class for invariant metrics on Lie groups represented by vectors.
  
  Parameters
  ----------
  space : LieGroup
      Group to equip with the invariant metric
  left : bool
      Whether to use a left or right invariant metric.
      Optional, default: True.
class_docstr_tok: ["Class","for","invariant","metrics","on","Lie","groups","represented","by","vectors",".","Parameters","--","--","--","--","--","space",":","LieGroup","Group","to","equip","with","the","invariant","metric","left",":","bool","Whether","to","use","a","left","or","right","invariant","metric",".","Optional",",","default",":","True","."]
docstr: Compute the exponential from identity with the left-invariant metric.
  
  Compute Riemannian exponential of a tangent vector at the identity
  associated to the left-invariant metric.
  
  If the method is called by a right-invariant metric, it uses the
  left-invariant metric associated to the same inner-product matrix
  at the identity.
  
  Parameters
  ----------
  tangent_vec : array-like, shape=[..., dim]
      Tangent vector at identity.
  
  Returns
  -------
  exp : array-like, shape=[..., dim]
      Point in the group.
code: def left_exp_from_identity(self, tangent_vec):
      """Compute the exponential from identity with the left-invariant metric.
  
      Compute Riemannian exponential of a tangent vector at the identity
      associated to the left-invariant metric.
  
      If the method is called by a right-invariant metric, it uses the
      left-invariant metric associated to the same inner-product matrix
      at the identity.
  
      Parameters
      ----------
      tangent_vec : array-like, shape=[..., dim]
          Tangent vector at identity.
  
      Returns
      -------
      exp : array-like, shape=[..., dim]
          Point in the group.
      """
      return self._space.regularize_tangent_vec_at_identity(
          tangent_vec=tangent_vec
      )
  
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 4 for calling the _InvariantMetricVector obj's underlying member method code with example usage: obj.left_exp_from_identity(tangent_vec) and returns: self