code: def vtln_warp_freq(
      vtln_low_cutoff: float,
      vtln_high_cutoff: float,
      low_freq: float,
      high_freq: float,
      vtln_warp_factor: float,
      freq: Tensor,
  ) -> Tensor:
      r"""This computes a VTLN warping function that is not the same as HTK's one,
      but has similar inputs (this function has the advantage of never producing
      empty bins).
  
      This function computes a warp function F(freq), defined between low_freq
      and high_freq inclusive, with the following properties:
          F(low_freq) == low_freq
          F(high_freq) == high_freq
      The function is continuous and piecewise linear with two inflection
          points.
      The lower inflection point (measured in terms of the unwarped
          frequency) is at frequency l, determined as described below.
      The higher inflection point is at a frequency h, determined as
          described below.
      If l <= f <= h, then F(f) = f/vtln_warp_factor.
      If the higher inflection point (measured in terms of the unwarped
          frequency) is at h, then max(h, F(h)) == vtln_high_cutoff.
          Since (by the last point) F(h) == h/vtln_warp_factor, then
          max(h, h/vtln_warp_factor) == vtln_high_cutoff, so
          h = vtln_high_cutoff / max(1, 1/vtln_warp_factor).
            = vtln_high_cutoff * min(1, vtln_warp_factor).
      If the lower inflection point (measured in terms of the unwarped
          frequency) is at l, then min(l, F(l)) == vtln_low_cutoff
          This implies that l = vtln_low_cutoff / min(1, 1/vtln_warp_factor)
                              = vtln_low_cutoff * max(1, vtln_warp_factor)
      Args:
          vtln_low_cutoff (float): Lower frequency cutoffs for VTLN
          vtln_high_cutoff (float): Upper frequency cutoffs for VTLN
          low_freq (float): Lower frequency cutoffs in mel computation
          high_freq (float): Upper frequency cutoffs in mel computation
          vtln_warp_factor (float): Vtln warp factor
          freq (Tensor): given frequency in Hz
  
      Returns:
          Tensor: Freq after vtln warp
      """
      assert (
          vtln_low_cutoff > low_freq
      ), "be sure to set the vtln_low option higher than low_freq"
      assert (
          vtln_high_cutoff < high_freq
      ), "be sure to set the vtln_high option lower than high_freq [or negative]"
      l = vtln_low_cutoff * max(1.0, vtln_warp_factor)
      h = vtln_high_cutoff * min(1.0, vtln_warp_factor)
      scale = 1.0 / vtln_warp_factor
      Fl = scale * l  # F(l)
      Fh = scale * h  # F(h)
      assert l > low_freq and h < high_freq
      # slope of left part of the 3-piece linear function
      scale_left = (Fl - low_freq) / (l - low_freq)
      # [slope of center part is just "scale"]
  
      # slope of right part of the 3-piece linear function
      scale_right = (high_freq - Fh) / (high_freq - h)
  
      res = torch.empty_like(freq)
  
      outside_low_high_freq = torch.lt(freq, low_freq) | torch.gt(
          freq, high_freq
      )  # freq < low_freq || freq > high_freq
      before_l = torch.lt(freq, l)  # freq < l
      before_h = torch.lt(freq, h)  # freq < h
      after_h = torch.ge(freq, h)  # freq >= h
  
      # order of operations matter here (since there is overlapping frequency regions)
      res[after_h] = high_freq + scale_right * (
          freq[after_h] - high_freq
      )
      res[before_h] = scale * freq[before_h]
      res[before_l] = low_freq + scale_left * (
          freq[before_l] - low_freq
      )
      res[outside_low_high_freq] = freq[outside_low_high_freq]
  
      return res
  
imports: import math
  from typing import Tuple
  import torch
  import torchaudio
  from torch import Tensor
label_desc: Use image node_id 14 for calling a global function with example usage: vtln_warp_freq(vtln_low_cutoff, vtln_high_cutoff, low_freq, high_freq, vtln_warp_factor, freq) and returns: res