docs: def _fit_ellipsoid_partial(locations, cy):
      """identify only 5 ellipsoid parameters (y-center determined by e.g. Cz)"""
      a = np.vstack([locations[:, 0]**2,
                     locations[:, 1]**2 - 2 * locations[:, 1] * cy,
                     locations[:, 2]**2,
                     locations[:, 0]*2,
                     locations[:, 2]*2]).T
      x = sp.linalg.lstsq(a, np.ones(locations.shape[0]))[0]
      c = [-x[3] / x[0], cy, -x[4] / x[2]]
      gam = 1 + x[3]**2 / x[0] + x[4]**2 / x[2]
      r = np.sqrt([gam / x[0], gam / x[1], gam / x[2]])
      return c, r