code: def barlam(self, wavelengths=None):
          
          x = self._validate_wavelengths(wavelengths).value
          y = self(x).value
          num = np.trapz(y * np.log(x) / x, x=x)
          den = np.trapz(y / x, x=x)
  
          if num == 0 or den == 0:  # pragma: no cover
              bar_lam = 0.0
          else:
              bar_lam = np.exp(abs(num / den))
  
          return bar_lam * self._internal_wave_unit
docs: Calculate :ref:`mean log wavelength <synphot-formula-barlam>`.
  
          Parameters
          ----------
          wavelengths : array-like, `~astropy.units.quantity.Quantity`, or `None`
              Wavelength values for sampling.
              If not a Quantity, assumed to be in Angstrom.
              If `None`, `waveset` is used.
  
          Returns
          -------
          bar_lam : `~astropy.units.quantity.Quantity`
              Mean log wavelength.