class_docstr: Class for Riemannian and pseudo-Riemannian metrics.
  
  The associated Levi-Civita connection on the tangent bundle.
class_docstr_tok: ["Class","for","Riemannian","and","pseudo-Riemannian","metrics",".","The","associated","Levi-Civita","connection","on","the","tangent","bundle","."]
docstr: Compute derivative of the inner prod matrix at base point.
  
  Writing :math:`g_{ij}` the inner-product matrix at base point,
  this computes :math:`mat_{ijk} = \partial_k g_{ij}`, where the
  index k of the derivation is put last.
  
  Parameters
  ----------
  base_point : array-like, shape=[..., dim]
      Base point.
      Optional, default: None.
  
  Returns
  -------
  metric_derivative : array-like, shape=[..., dim, dim, dim]
      Derivative of the inner-product matrix, where the index
      k of the derivation is last: :math:`mat_{ijk} = \partial_k g_{ij}`.
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code: def inner_product_derivative_matrix(self, base_point=None):
      r"""Compute derivative of the inner prod matrix at base point.
  
      Writing :math:`g_{ij}` the inner-product matrix at base point,
      this computes :math:`mat_{ijk} = \partial_k g_{ij}`, where the
      index k of the derivation is put last.
  
      Parameters
      ----------
      base_point : array-like, shape=[..., dim]
          Base point.
          Optional, default: None.
  
      Returns
      -------
      metric_derivative : array-like, shape=[..., dim, dim, dim]
          Derivative of the inner-product matrix, where the index
          k of the derivation is last: :math:`mat_{ijk} = \partial_k g_{ij}`.
      """
      return gs.autodiff.jacobian_vec(self.metric_matrix)(base_point)
  
imports: from abc import ABC
  import joblib
  import geomstats.backend
  import geomstats.geometry
  from geomstats.geometry.connection import Connection
  from geomstats.vectorization import check_is_batch
label_desc: Use image node_id 6 for calling the RiemannianMetric obj's underlying member method code with example usage: obj.inner_product_derivative_matrix(base_point) and returns: gs