code: def peak_widths(
      x, peaks, rel_height=0.5, prominence_data=None, wlen=None
  ):
      """
      Calculate the width of each peak in a signal.
  
      This function calculates the width of a peak in samples at a relative
      distance to the peak's height and prominence.
  
      Parameters
      ----------
      x : sequence
          A signal with peaks.
      peaks : sequence
          Indices of peaks in `x`.
      rel_height : float, optional
          Chooses the relative height at which the peak width is measured as a
          percentage of its prominence. 1.0 calculates the width of the peak at
          its lowest contour line while 0.5 evaluates at half the prominence
          height. Must be at least 0. See notes for further explanation.
      prominence_data : tuple, optional
          A tuple of three arrays matching the output of `peak_prominences` when
          called with the same arguments `x` and `peaks`. This data are
          calculated internally if not provided.
      wlen : int, optional
          A window length in samples passed to `peak_prominences` as an optional
          argument for internal calculation of `prominence_data`. This argument
          is ignored if `prominence_data` is given.
  
      Returns
      -------
      widths : ndarray
          The widths for each peak in samples.
      width_heights : ndarray
          The height of the contour lines at which the `widths` where evaluated.
      left_ips, right_ips : ndarray
          Interpolated positions of left and right intersection points of a
          horizontal line at the respective evaluation height.
  
      Raises
      ------
      ValueError
          If `prominence_data` is supplied but doesn't satisfy the condition
          ``0 <= left_base <= peak <= right_base < x.shape[0]`` for each peak,
          has the wrong dtype, is not C-contiguous or does not have the same
          shape.
  
      Warns
      -----
      PeakPropertyWarning
          Raised if any calculated width is 0. This may stem from the supplied
          `prominence_data` or if `rel_height` is set to 0.
  
      Warnings
      --------
      This function may return unexpected results for data containing NaNs. To
      avoid this, NaNs should either be removed or replaced.
  
      See Also
      --------
      find_peaks
          Find peaks inside a signal based on peak properties.
      peak_prominences
          Calculate the prominence of peaks.
  
      Notes
      -----
      The basic algorithm to calculate a peak's width is as follows:
  
      * Calculate the evaluation height :math:`h_{eval}` with the formula
        :math:`h_{eval} = h_{Peak} - P \\cdot R`, where :math:`h_{Peak}` is the
        height of the peak itself, :math:`P` is the peak's prominence and
        :math:`R` a positive ratio specified with the argument `rel_height`.
      * Draw a horizontal line at the evaluation height to both sides, starting
        at the peak's current vertical position until the lines either intersect
        a slope, the signal border or cross the vertical position of the peak's
        base (see `peak_prominences` for an definition). For the first case,
        intersection with the signal, the true intersection point is estimated
        with linear interpolation.
      * Calculate the width as the horizontal distance between the chosen
        endpoints on both sides. As a consequence of this the maximal possible
        width for each peak is the horizontal distance between its bases.
  
      As shown above to calculate a peak's width its prominence and bases must be
      known. You can supply these yourself with the argument `prominence_data`.
      Otherwise, they are internally calculated (see `peak_prominences`).
      """
      x = _arg_x_as_expected(x)
      peaks = _arg_peaks_as_expected(peaks)
      if prominence_data is None:
          # Calculate prominence if not supplied and use wlen if supplied.
          wlen = _arg_wlen_as_expected(wlen)
          prominence_data = _peak_prominences(
              x, peaks, wlen, check=True
          )
      return _peak_widths(
          x, peaks, rel_height, *prominence_data, check=True
      )
  
imports: import math
  import cupy
  from cupy._core._scalar import get_typename
  from cupy_backends.cuda.api import runtime
  from cupyx import jit
label_desc: Use image node_id 15 for calling a global function with example usage: peak_widths(x, peaks, rel_height, prominence_data, wlen) and returns: _peak_widths