class_docstr: Class for the Fisher information metric on multinomial distributions.
  
  The Fisher information metric on the $n$-simplex of multinomial
  distributions parameters can be obtained as the pullback metric of the
  $n$-sphere using the componentwise square root.
  
  References
  ----------
  .. [K2003] R. E. Kass. The Geometry of Asymptotic Inference. Statistical
      Science, 4(3): 188 - 234, 1989.
docstr: Send tangent vector of the sphere to tangent space of simplex.
  
  This is the differential of the sphere_to_simplex map.
  
  Parameters
  ----------
  tangent_vec : array-like, shape=[..., dim + 1]
      Tangent vec to the sphere at base point.
  base_point : array-like, shape=[..., dim + 1]
      Point of the sphere.
  
  Returns
  -------
  tangent_vec_simplex : array-like, shape=[..., dim + 1]
      Tangent vec to the simplex at the image of
      base point by sphere_to_simplex.
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code: def tangent_sphere_to_simplex(tangent_vec, base_point):
      """Send tangent vector of the sphere to tangent space of simplex.
  
      This is the differential of the sphere_to_simplex map.
  
      Parameters
      ----------
      tangent_vec : array-like, shape=[..., dim + 1]
          Tangent vec to the sphere at base point.
      base_point : array-like, shape=[..., dim + 1]
          Point of the sphere.
  
      Returns
      -------
      tangent_vec_simplex : array-like, shape=[..., dim + 1]
          Tangent vec to the simplex at the image of
          base point by sphere_to_simplex.
      """
      return gs.einsum("...i,...i->...i", tangent_vec, 2 * base_point)
  
imports: from scipy.stats import dirichlet, multinomial
  import geomstats.backend
  from geomstats.algebra_utils import from_vector_to_diagonal_matrix
  from geomstats.geometry.base import LevelSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.hypersphere import Hypersphere
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.information_geometry.base import InformationManifoldMixin, ScipyMultivariateRandomVariable
  from geomstats.vectorization import repeat_out
label_desc: Use image node_id 6 for calling the MultinomialMetric obj's underlying member method code with example usage: obj.tangent_sphere_to_simplex(tangent_vec, base_point) and returns: gs