class_docstr: A diffeomorphism from UnitNormedRowsPLTDMatrices to OpenHemispheresProduct.
  
  A diffeomorphism between the space of lower triangular matrices with
  positive diagonal and unit normed rows and the product space of
  successively increasing factor-dimension open hemispheres.
  
  Given the way `OpenHemisphere` is implemented, i.e. the first component
  is positive, rows need to be flipped.
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docstr: Tangent diffeomorphism at base point.
  
  df_p is a linear map from T_pM to T_f(p)N.
  The diffeomorphism is linear, so its pushforward is itself
  
  Parameters
  ----------
  tangent_vec : array-like, shape=[..., n, n]
      Tangent vector at base point.
  base_point : array-like, shape=[..., n, n]
      Base point.
  image_point : array-like, shape=[..., space_dim]
      Image point.
  
  Returns
  -------
  image_tangent_vec : array-like, shape=[..., space_dim]
      Image tangent vector at image of the base point.
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code: def tangent_diffeomorphism(
      self, tangent_vec, base_point=None, image_point=None
  ):
      r"""Tangent diffeomorphism at base point.
  
      df_p is a linear map from T_pM to T_f(p)N.
      The diffeomorphism is linear, so its pushforward is itself
  
      Parameters
      ----------
      tangent_vec : array-like, shape=[..., n, n]
          Tangent vector at base point.
      base_point : array-like, shape=[..., n, n]
          Base point.
      image_point : array-like, shape=[..., space_dim]
          Image point.
  
      Returns
      -------
      image_tangent_vec : array-like, shape=[..., space_dim]
          Image tangent vector at image of the base point.
      """
      return self.diffeomorphism(tangent_vec)
  
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 5 for calling the UnitNormedRowsPLTDiffeo obj's underlying member method code with example usage: obj.tangent_diffeomorphism(tangent_vec, base_point, image_point) and returns: self