class_docstr: Class for the Fisher information metric on Gamma distributions.
  
  References
  ----------
  .. [AD2008] Arwini, K. A., & Dodson, C. T. (2008).
      Information geometry (pp. 31-54). Springer Berlin Heidelberg.
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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=[..., 2]
      Base point.
  
  Returns
  -------
  mat : array-like, shape=[..., 2, 2]
      Inner-product matrix.
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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=[..., 2]
          Base point.
  
      Returns
      -------
      mat : array-like, shape=[..., 2, 2]
          Inner-product matrix.
      """
      kappa, gamma = base_point[..., 0], base_point[..., 1]
      mat_diag = gs.stack(
          [gs.polygamma(1, kappa) - 1 / kappa, kappa / gamma**2],
          axis=-1,
      )
      return from_vector_to_diagonal_matrix(mat_diag)
  
imports: from scipy.stats import gamma
  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, ScipyUnivariateRandomVariable
  from geomstats.numerics.bvp import ScipySolveBVP
  from geomstats.numerics.geodesic import ExpODESolver, LogODESolver
  from geomstats.numerics.ivp import ScipySolveIVP
  from geomstats.vectorization import check_is_batch
label_desc: Use image node_id 2 for calling the GammaMetric obj's underlying member method code with example usage: obj.metric_matrix(base_point) and returns: from_vector_to_diagonal_matrix