class_docstr: Class for the metric of the n-dimensional hyperbolic space.
  
  Class for the metric of the n-dimensional hyperbolic space
  as embedded in the Poincaré half space model.
code: def __init__(self, space):
      super().__init__(space=space)
      self._poincare_ball = PoincareBall(dim=space.dim)
  
imports: import math
  import geomstats.backend
  from geomstats.geometry._hyperbolic import _Hyperbolic
  from geomstats.geometry.base import VectorSpaceOpenSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.poincare_ball import PoincareBall
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.vectorization import repeat_out
label_desc: Use image node_id 1 to create a new PoincareHalfSpaceMetric object from inherited base classes: RiemannianMetric with example: obj = PoincareHalfSpaceMetric(space)