class_docstr: Class for affine connections.
  
  Parameters
  ----------
  space : Manifold object
      M in the tuple (M, g).
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docstr: Compute the geodesic ODE associated with the connection.
  
  Parameters
  ----------
  state : array-like, shape=[..., dim]
      Tangent vector at the position.
  _time : array-like, shape=[..., dim]
      Point on the manifold, the position at which to compute the
      geodesic ODE.
  
  Returns
  -------
  geodesic_ode : array-like, shape=[..., dim]
      Value of the vector field to be integrated at position.
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code: def geodesic_equation(self, state, _time):
      """Compute the geodesic ODE associated with the connection.
  
      Parameters
      ----------
      state : array-like, shape=[..., dim]
          Tangent vector at the position.
      _time : array-like, shape=[..., dim]
          Point on the manifold, the position at which to compute the
          geodesic ODE.
  
      Returns
      -------
      geodesic_ode : array-like, shape=[..., dim]
          Value of the vector field to be integrated at position.
      """
      position, velocity = state
      gamma = self.christoffels(position)
      equation = gs.einsum("...kij,...i->...kj", gamma, velocity)
      equation = -gs.einsum("...kj,...j->...k", equation, velocity)
      return gs.stack([velocity, equation])
  
imports: from abc import ABC
  import geomstats.backend
  import geomstats.errors
label_desc: Use image node_id 3 for calling the Connection obj's underlying member method code with example usage: obj.geodesic_equation(state, _time) and returns: gs