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: Compute the inner-product matrix.
  
  Compute the inner-product matrix of the Fisher information metric
  at the tangent space at base point.
  
  Parameters
  ----------
  base_point : array-like, shape=[..., dim + 1]
      Base point.
  
  Returns
  -------
  mat : array-like, shape=[..., dim, dim]
      Inner-product matrix.
docstr_tok: ["Compute","the","inner-product","matrix",".","Compute","the","inner-product","matrix","of","the","Fisher","information","metric","at","the","tangent","space","at","base","point",".","Parameters","--","--","--","--","--","base_point",":","array-like",",","shape=","[","...",",","dim","+","1","]","Base","point",".","Returns","--","--","--","-","mat",":","array-like",",","shape=","[","...",",","dim",",","dim","]","Inner-product","matrix","."]
code: def metric_matrix(self, base_point):
      """Compute the inner-product matrix.
  
      Compute the inner-product matrix of the Fisher information metric
      at the tangent space at base point.
  
      Parameters
      ----------
      base_point : array-like, shape=[..., dim + 1]
          Base point.
  
      Returns
      -------
      mat : array-like, shape=[..., dim, dim]
          Inner-product matrix.
      """
      return self._space.n_draws * from_vector_to_diagonal_matrix(
          1 / 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 2 for calling the MultinomialMetric obj's underlying member method code with example usage: obj.metric_matrix(base_point) and returns: unknown