code: def batch_2x2_ellipse(m: Tensor) -> Tuple[Tensor, Tensor]:
      am = m[..., 0, 0]
      bm = m[..., 0, 1]
      cm = m[..., 1, 0]
      dm = m[..., 1, 1]
  
      a = am**2 + bm**2
      b = am * cm + bm * dm
      d = cm**2 + dm**2
  
      trh = (a + d) / 2
      # det = a * d - b * c
      sqrtdisc = torch.sqrt(((a - d) / 2) ** 2 + b**2)
  
      eigenvals = torch.stack(
          [trh + sqrtdisc, trh - sqrtdisc], dim=-1
      ).clamp(min=0)
      dens = eigenvals - a.unsqueeze(-1)
      dens[torch.abs(dens) < 1e-6] = 1e-6
      eigenvecs = torch.stack(
          [b.unsqueeze(-1) / dens, torch.ones_like(dens)], dim=-2
      )
      eigenvecs = eigenvecs / torch.norm(
          eigenvecs, dim=-2, keepdim=True
      )
  
      # err = eigenvecs @ torch.diag_embed(eigenvals) @ eigenvecs.transpose(-2, -1) - q
      return eigenvals, eigenvecs
  
file_path: kornia/kornia/feature/adalam/utils.py
imports: import math
  from typing import Tuple
  import torch
  from kornia.core import Tensor
label_desc: Use image node_id 9 for calling a global function with example usage: batch_2x2_ellipse(m) and returns: eigenvals,  eigenvecs