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
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
    
vlmeval/vlm/ola/ola/model/speech_encoder/beats/kaldi.py