code: def convert_to_klein_coordinates(points):
      poincare_coords = points[:, 1:] / (1 + points[:, :1])
      poincare_radius = gs.linalg.norm(poincare_coords, axis=1)
      poincare_angle = gs.arctan2(
          poincare_coords[:, 1], poincare_coords[:, 0]
      )
  
      klein_radius = 2 * poincare_radius / (1 + poincare_radius**2)
      klein_angle = poincare_angle
  
      coords_0 = gs.expand_dims(
          klein_radius * gs.cos(klein_angle), axis=1
      )
      coords_1 = gs.expand_dims(
          klein_radius * gs.sin(klein_angle), axis=1
      )
      klein_coords = gs.concatenate([coords_0, coords_1], axis=1)
      return klein_coords
  
imports: import matplotlib.pyplot
  from mpl_toolkits.mplot3d import Axes3D
  import geomstats.backend
  from geomstats.geometry.hyperboloid import Hyperboloid
  from geomstats.geometry.poincare_half_space import PoincareHalfSpace
label_desc: Use image node_id 4 for calling the KleinDisk obj's underlying member method code with example usage: obj.convert_to_klein_coordinates(points) and returns: klein_coords