class_docstr: Geodesic boundary value problem using an ODE solver.
  
  Parameters
  ----------
  n_nodes : Number of mesh nodes.
  integrator : ScipySolveBVP
      Instance of ScipySolveBVP.
  initialization : callable
      Function to provide initial solution. `f(space, point, base_point)`.
      Defaults to linear initialization.
class_docstr_tok: ["Geodesic","boundary","value","problem","using","an","ODE","solver",".","Parameters","--","--","--","--","--","n_nodes",":","Number","of","mesh","nodes",".","integrator",":","ScipySolveBVP","Instance","of","ScipySolveBVP",".","initialization",":","callable","Function","to","provide","initial","solution",".","`","f","(","space",",","point",",","base_point",")","`",".","Defaults","to","linear","initialization","."]
code: def _default_initialization(self, space, point, base_point):
      point_0, point_1 = base_point, point
  
      pos_init = gs.transpose(
          gs.linspace(point_0, point_1, self.n_nodes)
      )
  
      vel_init = self.n_nodes * (pos_init[:, 1:] - pos_init[:, :-1])
      vel_init = gs.hstack([vel_init, vel_init[:, [-2]]])
  
      return gs.vstack([pos_init, vel_init])
  
imports: import math
  from abc import ABC, abstractmethod
  import geomstats.backend
  from geomstats.numerics.bvp import ScipySolveBVP
  from geomstats.numerics.ivp import GSIVPIntegrator
  from geomstats.numerics.optimizers import ScipyMinimize
  from geomstats.vectorization import get_batch_shape
label_desc: Use image node_id 3 for calling the LogODESolver obj's underlying member method code with example usage: obj._default_initialization(space, point, base_point) and returns: gs