class_docstr: Class that defines the canonical metric for Stiefel manifolds.
code: def _matrix_r_single(matrix_m):
      def _make_minor(i, matrix):
          return matrix[: i + 1, : i + 1]
  
      def _make_column_r(i, matrix, columns_list):
          if i == 0:
              return gs.array([1.0 / matrix[0, 0]])
  
          matrix_m_i = _make_minor(i, matrix_m)
          inv_matrix_m_i = gs.linalg.inv(matrix_m_i)
          b_i = _make_b(i, matrix_m, columns_list)
          column_r_i = gs.matvec(inv_matrix_m_i, b_i)
  
          if column_r_i[i] <= 0:
              raise ValueError("(r_i)_i <= 0")
          return column_r_i
  
      def _make_b(i, matrix, columns_list):
          return gs.array(
              [
                  -gs.dot(matrix[i, : j + 1], columns_list[j])
                  for j in range(i)
              ]
              + [1.0]
          )
  
      n = matrix_m.shape[-1]
  
      columns_list = []
      matrix_r = gs.zeros((n, n))
      for j in range(n):
          column_r_j = _make_column_r(j, matrix_m, columns_list)
          columns_list.append(column_r_j)
  
          matrix_r[: len(column_r_j), j] = column_r_j
  
      return matrix_r
  
imports: import warnings
  import geomstats.backend
  import geomstats.errors
  from geomstats import algebra_utils
  from geomstats.geometry.base import LevelSet
  from geomstats.geometry.hermitian_matrices import powermh
  from geomstats.geometry.matrices import Matrices
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.vectorization import repeat_out
label_desc: Use image node_id 6 for calling the StiefelCanonicalMetric obj's underlying member method code with example usage: obj._matrix_r_single(matrix_m) and returns: matrix_r, matrix, column_r_i, gs, gs