code: def authalic2geodetic(
      authalic_lat, ell: Ellipsoid = None, deg: bool = True
  ):
      """
      converts from authalic latitude to geodetic latitude
  
      like Matlab map.geodesy.AuthalicLatitudeConverter.inverse()
  
      Parameters
      ----------
      authalic_lat : float
          latitude
      ell : Ellipsoid, optional
          reference ellipsoid (default WGS84)
      deg : bool, optional
          degrees input/output  (False: radians in/out)
  
      Returns
      -------
      geodetic_lat : float
          geodetic latiude
  
      Notes
      -----
      Equations from J. P. Snyder, "Map Projections - A Working Manual",
      US Geological Survey Professional Paper 1395, US Government Printing
      Office, Washington, DC, 1987, pp. 13-18.
      """
      authalic_lat, ell = sanitize(authalic_lat, ell, deg)
      e = ell.eccentricity
      f1 = e**2 / 3 + 31 * e**4 / 180 + 517 * e**6 / 5040
      f2 = 23 * e**4 / 360 + 251 * e**6 / 3780
      f3 = 761 * e**6 / 45360
  
      geodetic_lat = (
          authalic_lat
          + f1 * sin(2 * authalic_lat)
          + f2 * sin(4 * authalic_lat)
          + f3 * sin(6 * authalic_lat)
      )
  
      return degrees(geodetic_lat) if deg else geodetic_lat
  
imports: from __future__ import annotations
  import warnings
  from math import pi
  from .None import rcurve
  from .ellipsoid import Ellipsoid
  from .mathfun import asinh, atan, atanh, cos, degrees, exp, inf, radians, sign, sin, sqrt, tan
  from .utils import sanitize
label_desc: Use image node_id 11 for calling a global function with example usage: authalic2geodetic(authalic_lat, ell, deg) and returns: unknown