code: def update(self, pointvol):
          
  
          # Initialize a K-D Tree to assist nearest neighbor searches.
          if self.use_kdtree:
              kdtree = spatial.KDTree(self.live_u)
          else:
              kdtree = None
  
          # Check if we should use the provided pool for updating.
          if self.use_pool_update:
              pool = self.pool
          else:
              pool = None
  
          # Update the N-spheres.
          self.radfriends.update(self.live_u, pointvol=pointvol,
                                 rstate=self.rstate, bootstrap=self.bootstrap,
                                 pool=pool, kdtree=kdtree)
          if self.enlarge != 1.:
              self.radfriends.scale_to_vol(self.radfriends.vol_ball *
                                           self.enlarge)
  
          return copy.deepcopy(self.radfriends)
docs: Update the N-sphere radii using the current set of live points.