code: def forward(self, X: torch.Tensor) -> torch.Tensor:
      n, k = X.size(-2), X.size(-1)
      transposed = n < k
      if transposed:
          X = X.mT
          n, k = k, n
      # Here n > k and X is a tall matrix
      if (
          self.orthogonal_map == _OrthMaps.matrix_exp
          or self.orthogonal_map == _OrthMaps.cayley
      ):
          # We just need n x k - k(k-1)/2 parameters
          X = X.tril()
          if n != k:
              # Embed into a square matrix
              X = torch.cat(
                  [
                      X,
                      X.new_zeros(n, n - k).expand(
                          *X.shape[:-2], -1, -1
                      ),
                  ],
                  dim=-1,
              )
          A = X - X.mH
          # A is skew-symmetric (or skew-hermitian)
          if self.orthogonal_map == _OrthMaps.matrix_exp:
              Q = torch.matrix_exp(A)
          elif self.orthogonal_map == _OrthMaps.cayley:
              # Computes the Cayley retraction (I+A/2)(I-A/2)^{-1}
              Id = torch.eye(n, dtype=A.dtype, device=A.device)
              Q = torch.linalg.solve(
                  torch.add(Id, A, alpha=-0.5),
                  torch.add(Id, A, alpha=0.5),
              )
          # Q is now orthogonal (or unitary) of size (..., n, n)
          if n != k:
              Q = Q[..., :k]
          # Q is now the size of the X (albeit perhaps transposed)
      else:
          # X is real here, as we do not support householder with complex numbers
          A = X.tril(diagonal=-1)
          tau = 2.0 / (1.0 + (A * A).sum(dim=-2))
          Q = torch.linalg.householder_product(A, tau)
          # The diagonal of X is 1's and -1's
          # We do not want to differentiate through this or update the diagonal of X hence the casting
          Q = Q * X.diagonal(dim1=-2, dim2=-1).int().unsqueeze(-2)
  
      if hasattr(self, "base"):
          Q = self.base @ Q
      if transposed:
          Q = Q.mT
      return Q
  
imports: from enum import Enum, auto
  import torch
  from torch import Tensor
  from ..utils import parametrize
  from ..modules import Module
  from ..None import functional
  from typing import Optional
label_desc: Use image node_id 2 for calling the _Orthogonal obj's underlying member method code with example usage: obj.forward(X) and returns: Q