class_docstr: Class for the n-dimensional Poincare half-space.
  
  Class for the n-dimensional Poincaré half space model. For other
  representations of hyperbolic spaces see the `Hyperbolic` class.
  
  Parameters
  ----------
  dim : int
      Dimension of the hyperbolic space.
docstr: Metric to equip the space with if equip is True.
docstr_tok: ["Metric","to","equip","the","space","with","if","equip","is","True","."]
code: def default_metric():
      """Metric to equip the space with if equip is True."""
      return PoincareHalfSpaceMetric
  
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 2 for calling the PoincareHalfSpace obj's underlying member method code with example usage: obj.default_metric() and returns: PoincareHalfSpaceMetric