class_docstr: Class for affine connections.
  
  Parameters
  ----------
  space : Manifold object
      M in the tuple (M, g).
class_docstr_tok: ["Class","for","affine","connections",".","Parameters","--","--","--","--","--","space",":","Manifold","object","M","in","the","tuple","(","M",",","g",")","."]
docstr: Compute the covariant derivative of the directional curvature.
  
  For tangent vector fields at base_point :math:`P`:
  
  - :math:`X|_P = tangent\_vec\_a`,
  - :math:`Y|_P = tangent\_vec\_b`,
  
  the covariant derivative (in the direction `X`)
  :math:`(\nabla_X R_Y)(X) |_P = (\nabla_X R)(Y, X) Y |_P` of the
  directional curvature (in the direction `Y`)
  :math:`R_Y(X) = R(Y, X) Y`
  is a quadratic tensor in `X` and `Y` that
  plays an important role in the computation of the moments of the
  empirical Fréchet mean.
  
  References
  ----------
  .. [Pennec] Pennec, Xavier. Curvature effects on the empirical mean in
      Riemannian and affine Manifolds: a non-asymptotic high
      concentration expansion in the small-sample regime. Preprint. 2019.
      https://arxiv.org/abs/1906.07418
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code: def directional_curvature_derivative(
      self, tangent_vec_a, tangent_vec_b, base_point=None
  ):
      r"""Compute the covariant derivative of the directional curvature.
  
      For tangent vector fields at base_point :math:`P`:
  
      - :math:`X|_P = tangent\_vec\_a`,
      - :math:`Y|_P = tangent\_vec\_b`,
  
      the covariant derivative (in the direction `X`)
      :math:`(\nabla_X R_Y)(X) |_P = (\nabla_X R)(Y, X) Y |_P` of the
      directional curvature (in the direction `Y`)
      :math:`R_Y(X) = R(Y, X) Y`
      is a quadratic tensor in `X` and `Y` that
      plays an important role in the computation of the moments of the
      empirical Fréchet mean.
  
      References
      ----------
      .. [Pennec] Pennec, Xavier. Curvature effects on the empirical mean in
          Riemannian and affine Manifolds: a non-asymptotic high
          concentration expansion in the small-sample regime. Preprint. 2019.
          https://arxiv.org/abs/1906.07418
      """
      return self.curvature_derivative(
          tangent_vec_a,
          tangent_vec_b,
          tangent_vec_a,
          tangent_vec_b,
          base_point,
      )
  
imports: from abc import ABC
  import geomstats.backend
  import geomstats.errors
label_desc: Use image node_id 14 for calling the Connection obj's underlying member method code with example usage: obj.directional_curvature_derivative(tangent_vec_a, tangent_vec_b, base_point) and returns: self