code: def gevd(a, b=None):
      """This method computes the eigenvectors and the eigenvalues
      of complex Hermitian matrices. The method finds a solution to
      the problem AV = BVD where V are the eigenvectors and D are
      the eigenvalues.
  
      The eigenvectors returned by the method (vs) are stored in a tensor
      with the following format (*,C,C,2).
  
      The eigenvalues returned by the method (ds) are stored in a tensor
      with the following format (*,C,C,2).
  
      Arguments
      ---------
      a : tensor
          A first input matrix. It is equivalent to the matrix A in the
          equation in the description above. The tensor must have the
          following format: (*,2,C+P).
  
      b : tensor
          A second input matrix. It is equivalent tot the matrix B in the
          equation in the description above. The tensor must have the
          following format: (*,2,C+P).
          This argument is optional and its default value is None. If
          b == None, then b is replaced by the identity matrix in the
          computations.
  
      Example
      -------
  
      Suppose we would like to compute eigenvalues/eigenvectors on the
      following complex Hermitian matrix:
  
      A = [ 52        34 + 37j  16 + j28 ;
            34 - 37j  125       41 + j3  ;
            16 - 28j  41 - j3   62       ]
  
      >>> a = torch.FloatTensor([[52,34,16,125,41,62],[0,37,28,0,3,0]])
      >>> vs, ds = gevd(a)
  
      This corresponds to:
  
      D = [ 20.9513  0        0        ;
            0        43.9420  0        ;
            0        0        174.1067 ]
  
      V = [ 0.085976 - 0.85184j  -0.24620 + 0.12244j  -0.24868 - 0.35991j  ;
            -0.16006 + 0.20244j   0.37084 + 0.40173j  -0.79175 - 0.087312j ;
            -0.43990 + 0.082884j  -0.36724 - 0.70045j -0.41728 + 0 j       ]
  
      where
  
      A = VDV^-1
  
      """
  
      # Dimensions
      D = a.dim()
      P = a.shape[D - 1]
      C = int(round(((1 + 8 * P) ** 0.5 - 1) / 2))
  
      # Converting the input matrices to block matrices
      ash = f(a)
  
      if b is None:
          b = torch.zeros(a.shape, dtype=a.dtype, device=a.device)
          ids = torch.triu_indices(C, C)
          b[..., 0, ids[0] == ids[1]] = 1.0
  
      bsh = f(b)
  
      # Performing the Cholesky decomposition
      lsh = torch.linalg.cholesky(bsh)
      lsh_inv = torch.inverse(lsh)
      lsh_inv_T = torch.transpose(lsh_inv, D - 2, D - 1)
  
      # Computing the matrix C
      csh = torch.matmul(lsh_inv, torch.matmul(ash, lsh_inv_T))
  
      # Performing the eigenvalue decomposition
      es, ysh = torch.linalg.eigh(csh, UPLO="U")
  
      # Collecting the eigenvalues
      dsh = torch.zeros(
          a.shape[slice(0, D - 2)] + (2 * C, 2 * C),
          dtype=a.dtype,
          device=a.device,
      )
      dsh[..., range(0, 2 * C), range(0, 2 * C)] = es
  
      # Collecting the eigenvectors
      vsh = torch.matmul(lsh_inv_T, ysh)
  
      # Converting the block matrices to full complex matrices
      vs = ginv(vsh)
      ds = ginv(dsh)
  
      return vs, ds
  
file_path: speechbrain/speechbrain/processing/decomposition.py
imports: import torch
label_desc: Use image node_id 1 for calling a global function with example usage: gevd(a, b) and returns: vs,  ds