class_docstr: Class for invariant metrics on Lie groups.
  
  This class supports both left and right invariant metrics
  which exist on Lie groups.
  
  If `point_type == 'vector'`, points are parameterized by the Riemannian
  logarithm for the canonical left-invariant metric.
  
  Parameters
  ----------
  space : LieGroup
      Group to equip with the invariant metric
  metric_mat_at_identity : array-like, shape=[dim, dim]
      Matrix that defines the metric at identity.
      Optional, defaults to identity matrix if None.
  left : bool
      Whether to use a left or right invariant metric.
      Optional, default: True.
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docstr: Instantiate a special euclidean group.
  
  Select the object to instantiate depending on the point_type.
code: def __new__(cls, space, metric_mat_at_identity=None, left=True):
      """Instantiate a special euclidean group.
  
      Select the object to instantiate depending on the point_type.
      """
      if space.default_point_type == "vector":
          return _InvariantMetricVector(space, left=left)
      return _InvariantMetricMatrix(
          space,
          left=left,
          metric_mat_at_identity=metric_mat_at_identity,
      )
  
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 1 for calling the InvariantMetric obj's underlying member method code with example usage: obj.__new__(cls, space, metric_mat_at_identity, left) and returns: _InvariantMetricMatrix, _InvariantMetricVector