code: def cydist_1d_sax(
      sax1,
      sax2,
      breakpoints_avg_middle_,
      breakpoints_slope_middle_,
      original_size,
  ):
      """Compute distance between 1d-SAX representations as defined in [1]_.
  
      Parameters
      ----------
      sax1 : array-like, shape=(sz, 2 * d), dtype=float64 (Linux and MacOS) or float32 (Windows)
          1d-SAX representation of a time series.
      sax2 : array-like, shape=(sz, 2 * d), dtype=float64 (Linux and MacOS) or float32 (Windows)
          1d-SAX representation of another time series.
      breakpoints_avg_middle_ : array-like, ndim=1, dtype=float64
      breakpoints_slope_middle_ : array-like, ndim=1, dtype=float64
      original_size : int64 (Linux and MacOS) or int32 (Windows)
          Length of the original time series.
  
      Returns
      -------
      dist_1d_sax : float64
          1d-SAX distance.
  
      Notes
      -----
      Unlike SAX distance, 1d-SAX distance does not lower bound Euclidean
      distance between original time series.
  
      References
      ----------
      .. [1] S. Malinowski, T. Guyet, R. Quiniou, R. Tavenard. 1d-SAX: a
         Novel Symbolic Representation for Time Series. IDA 2013.
      """
      sz, d_1d_sax = sax1.shape
      assert sz == sax2.shape[0] and d_1d_sax == sax2.shape[1]
      s = 0.0
      d = d_1d_sax // 2
      seg_sz = original_size // sz
  
      for t in prange(sz):
          t0 = t * seg_sz
          t_middle = float(t0) + 0.5 * seg_sz
          for di in range(d):
              avg1 = breakpoints_avg_middle_[sax1[t, di]]
              avg2 = breakpoints_avg_middle_[sax2[t, di]]
              slope1 = breakpoints_slope_middle_[sax1[t, di + d]]
              slope2 = breakpoints_slope_middle_[sax2[t, di + d]]
              for tt in range(t0, seg_sz * (t + 1)):
                  s += (
                      avg1
                      + slope1 * (tt - t_middle)
                      - (avg2 + slope2 * (tt - t_middle))
                  ) ** 2
      dist_1d_sax = np.sqrt(s)
      return dist_1d_sax
  
file_path: tslearn/tslearn/metrics/cysax.py
imports: import numpy
  from numba import njit, objmode, prange
  from sklearn.linear_model import LinearRegression
label_desc: Use image node_id 5 for calling a global function with example usage: cydist_1d_sax(sax1, sax2, breakpoints_avg_middle_, breakpoints_slope_middle_, original_size) and returns: dist_1d_sax