class_docstr: Invariant metric on the positive lower triangular matrices.
class_docstr_tok: ["Invariant","metric","on","the","positive","lower","triangular","matrices","."]
docstr: Compute inner product at tangent space at identity.
  
  Parameters
  ----------
  tangent_vec_a : array-like, shape=[..., n, n]
      First tangent vector at identity.
  tangent_vec_b : array-like, shape=[..., n, n]
      Second tangent vector at identity.
  
  Returns
  -------
  inner_prod : array-like, shape=[...]
      Inner-product of the two tangent vectors.
docstr_tok: ["Compute","inner","product","at","tangent","space","at","identity",".","Parameters","--","--","--","--","--","tangent_vec_a",":","array-like",",","shape=","[","...",",","n",",","n","]","First","tangent","vector","at","identity",".","tangent_vec_b",":","array-like",",","shape=","[","...",",","n",",","n","]","Second","tangent","vector","at","identity",".","Returns","--","--","--","-","inner_prod",":","array-like",",","shape=","[","...","]","Inner-product","of","the","two","tangent","vectors","."]
code: def inner_product_at_identity(self, tangent_vec_a, tangent_vec_b):
      """Compute inner product at tangent space at identity.
  
      Parameters
      ----------
      tangent_vec_a : array-like, shape=[..., n, n]
          First tangent vector at identity.
      tangent_vec_b : array-like, shape=[..., n, n]
          Second tangent vector at identity.
  
      Returns
      -------
      inner_prod : array-like, shape=[...]
          Inner-product of the two tangent vectors.
      """
      if Matrices.is_diagonal(self.metric_mat_at_identity):
          return super().inner_product_at_identity(
              tangent_vec_a, tangent_vec_b
          )
  
      return gs.dot(
          gs.tril_to_vec(tangent_vec_a),
          gs.matvec(
              self.metric_mat_at_identity, gs.tril_to_vec(tangent_vec_b)
          ),
      )
  
imports: import geomstats.backend
  from geomstats.geometry.base import DiffeomorphicManifold, VectorSpaceOpenSet
  from geomstats.geometry.diffeo import Diffeo
  from geomstats.geometry.invariant_metric import _InvariantMetricMatrix
  from geomstats.geometry.lie_group import MatrixLieGroup
  from geomstats.geometry.lower_triangular_matrices import LowerTriangularMatrices
  from geomstats.geometry.matrices import Matrices
  from geomstats.geometry.open_hemisphere import OpenHemisphere, OpenHemispheresProduct
  from geomstats.geometry.pullback_metric import PullbackDiffeoMetric
  from geomstats.geometry.riemannian_metric import RiemannianMetric
label_desc: Use image node_id 1 for calling the InvariantPositiveLowerTriangularMatricesMetric obj's underlying member method code with example usage: obj.inner_product_at_identity(tangent_vec_a, tangent_vec_b) and returns: gs, super