class_docstr: Class for the manifold of Dirichlet distributions.
  
  This is Dirichlet = :math:`(R_+^*)^dim`, the positive quadrant of the
  dim-dimensional Euclidean space.
  
  Attributes
  ----------
  dim : int
      Dimension of the manifold of Dirichlet distributions.
class_docstr_tok: ["Class","for","the","manifold","of","Dirichlet","distributions",".","This","is","Dirichlet","=",":","math",":","`","(","R_+^","*",")","^dim","`",",","the","positive","quadrant","of","the","dim-dimensional","Euclidean","space",".","Attributes","--","--","--","--","--","dim",":","int","Dimension","of","the","manifold","of","Dirichlet","distributions","."]
docstr: Metric to equip the space with if equip is True.
docstr_tok: ["Metric","to","equip","the","space","with","if","equip","is","True","."]
code: def default_metric():
      """Metric to equip the space with if equip is True."""
      return DirichletMetric
  
imports: import math
  import numpy
  from scipy.optimize import minimize
  from scipy.stats import dirichlet
  import geomstats.backend
  from geomstats.algebra_utils import from_vector_to_diagonal_matrix
  from geomstats.geometry.base import VectorSpaceOpenSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.information_geometry.base import InformationManifoldMixin, ScipyMultivariateRandomVariable
  from geomstats.numerics.bvp import ScipySolveBVP
  from geomstats.numerics.geodesic import ExpODESolver, LogODESolver
  from geomstats.numerics.ivp import ScipySolveIVP
  from geomstats.vectorization import repeat_out
label_desc: Use image node_id 2 for calling the DirichletDistributions obj's underlying member method code with example usage: obj.default_metric() and returns: DirichletMetric