code: def steppify(x, y):
  
      
  
      dx = 0.5 * (x[1:] + x[:-1])
      xx = numpy.zeros(2 * len(dx), dtype=float)
      yy = numpy.zeros(2 * len(y), dtype=float)
      xx[0::2], xx[1::2] = dx, dx
      yy[0::2], yy[1::2] = y, y
      xx = numpy.concatenate((
          [x[0] - (dx[0] - x[0])],
          xx,
          [x[-1] + (x[-1] - dx[-1])]
      ))
      return xx, yy
docs: Steppify a curve (x, y). This is useful for filling histograms manually.