code: def generalized_eigenvalue_decomposition(
      a: torch.Tensor, b: torch.Tensor, eps=1e-6
  ):
      """Solves the generalized eigenvalue decomposition through Cholesky decomposition.
  
      ported from https://github.com/asteroid-team/asteroid/blob/master/asteroid/dsp/beamforming.py#L464
  
      a @ e_vec = e_val * b @ e_vec
      |
      |   Cholesky decomposition on `b`:
      |       b = L @ L^H, where `L` is a lower triangular matrix
      |
      |   Let C = L^-1 @ a @ L^-H, it is Hermitian.
      |
      => C @ y = lambda * y
      => e_vec = L^-H @ y
  
      Reference: https://www.netlib.org/lapack/lug/node54.html
  
      Args:
          a: A complex Hermitian or real symmetric matrix whose eigenvalues and
              eigenvectors will be computed. (..., C, C)
          b: A complex Hermitian or real symmetric definite positive matrix. (..., C, C)
      Returns:
          e_val: generalized eigenvalues (ascending order)
          e_vec: generalized eigenvectors
      """  # noqa: H405, E501
      try:
          cholesky = torch.linalg.cholesky(b)
      except RuntimeError:
          b = tik_reg(b, reg=eps, eps=eps)
          cholesky = torch.linalg.cholesky(b)
      inv_cholesky = cholesky.inverse()
      # Compute C matrix L⁻1 a L^-H
      cmat = inv_cholesky @ a @ inv_cholesky.conj().transpose(-1, -2)
      # Performing the eigenvalue decomposition
      e_val, e_vec = torch.linalg.eigh(cmat)
      # Collecting the eigenvectors
      e_vec = torch.matmul(inv_cholesky.conj().transpose(-1, -2), e_vec)
      return e_val, e_vec
  
imports: from typing import List, Union
  import torch
  from packaging.version import parse
  from torch_complex import functional
  from torch_complex.tensor import ComplexTensor
  from espnet2.enh.layers.complex_utils import cat, complex_norm, einsum, inverse, is_complex, is_torch_complex_tensor, matmul, reverse, solve, to_double
label_desc: Use image node_id 12 for calling a global function with example usage: generalized_eigenvalue_decomposition(a, b, eps) and returns: e_val,  e_vec