code: def _tik_reg(
      mat: torch.Tensor, reg: float = 1e-7, eps: float = 1e-8
  ) -> torch.Tensor:
      """Perform Tikhonov regularization (only modifying real part).
  
      Args:
          mat (torch.Tensor): Input matrix with dimensions `(..., channel, channel)`.
          reg (float, optional): Regularization factor. (Default: 1e-8)
          eps (float, optional): Value to avoid the correlation matrix is all-zero. (Default: ``1e-8``)
  
      Returns:
          Tensor: Regularized matrix with dimensions `(..., channel, channel)`.
      """
      # Add eps
      C = mat.size(-1)
      eye = torch.eye(C, dtype=mat.dtype, device=mat.device)
      epsilon = _compute_mat_trace(mat).real[..., None, None] * reg
      # in case that correlation_matrix is all-zero
      epsilon = epsilon + eps
      mat = mat + epsilon * eye[..., :, :]
      return mat
  
imports: import math
  import tempfile
  import warnings
  from collections.abc import Sequence
  from typing import List, Optional, Tuple, Union
  import torch
  import torchaudio
  from torch import Tensor
  from torchaudio._internal.module_utils import deprecated
  from .filtering import highpass_biquad, treble_biquad
label_desc: Use image node_id 40 for calling a global function with example usage: _tik_reg(mat, reg, eps) and returns: mat