How to use the pymap3d.ellipsoid.Ellipsoid function in pymap3d

Returns
    -------
    lat : float
           target geodetic latitude
    lon : float
           target geodetic longitude
    h : float
         target altitude above geodetic ellipsoid (meters)

    based on:
    You, Rey-Jer. (2000). Transformation of Cartesian to Geodetic Coordinates without Iterations.
    Journal of Surveying Engineering. doi: 10.1061/(ASCE)0733-9453
    """
    if ell is None:
        ell = Ellipsoid()

    r = sqrt(x ** 2 + y ** 2 + z ** 2)

    E = sqrt(ell.semimajor_axis ** 2 - ell.semiminor_axis ** 2)

    # eqn. 4a
    u = sqrt(0.5 * (r ** 2 - E ** 2) + 0.5 * sqrt((r ** 2 - E ** 2) ** 2 + 4 * E ** 2 * z ** 2))

    Q = hypot(x, y)

    huE = hypot(u, E)

    # eqn. 4b
    try:
        Beta = atan(huE / u * z / hypot(x, y))
    except ZeroDivisionError:

def rsphere_authalic(ell: Ellipsoid = None) -> float:
    """computes the radius of the sphere with equal surface area as the ellipsoid

    Parameters
    ----------
    ell : Ellipsoid, optional
          reference ellipsoid

    Returns
    -------
    radius: float
        radius of sphere
    """
    if ell is None:
        ell = Ellipsoid()

    e = ell.eccentricity

    if e > 0:
        f1 = ell.semimajor_axis ** 2 / 2
        f2 = (1 - e ** 2) / (2 * e)
        f3 = log((1 + e) / (1 - e))
        return sqrt(f1 * (1 + f2 * f3))
    else:
        return ell.semimajor_axis

Parameters
    ----------
    ell : Ellipsoid, optional
          reference ellipsoid
    method: str, optional
        "mean" or "norm"

    Returns
    -------
    radius: float
        radius of sphere
    """

    if ell is None:
        ell = Ellipsoid()

    if method == "mean":
        return (2 * ell.semimajor_axis + ell.semiminor_axis) / 3
    elif method == "norm":
        return (ell.semimajor_axis ** 2 * ell.semiminor_axis) ** (1 / 3)
    else:
        raise Exception("pymap3d.rsphere.rsphere_triaxial: method must be mean or norm")

def vdist_point(Lat1: float, Lon1: float, Lat2: float, Lon2: float, ell: Ellipsoid = None) -> typing.Tuple[float, float]:
    if ell is None:
        ell = Ellipsoid()
    # %% Input check:
    if (abs(Lat1) > 90) | (abs(Lat2) > 90):
        raise ValueError("Input latitudes must be in [-90, 90] degrees.")
    # %% Supply WGS84 earth ellipsoid axis lengths in meters:
    a = ell.semimajor_axis
    b = ell.semiminor_axis
    f = ell.flattening
    # %% convert inputs in degrees to radians:
    lat1 = radians(Lat1)
    lon1 = radians(Lon1)
    lat2 = radians(Lat2)
    lon2 = radians(Lon2)
    # %% correct for errors at exact poles by adjusting 0.6 millimeters:
    if abs(pi / 2 - abs(lat1)) < 1e-10:
        lat1 = sign(lat1) * (pi / 2 - 1e-10)

def rsphere_eqavol(ell: Ellipsoid = None) -> float:
    """computes the radius of the sphere with equal volume as the ellipsoid

    Parameters
    ----------
    ell : Ellipsoid, optional
          reference ellipsoid

    Returns
    -------
    radius: float
        radius of sphere
    """
    if ell is None:
        ell = Ellipsoid()

    f = ell.flattening

    return ell.semimajor_axis * (1 - f / 3 - f ** 2 / 9)

deg : bool, optional
        degrees input/output  (False: radians in/out)

    Results
    -------

    lats : list of float
        latitudes of points along track
    lons : list of float
        longitudes of points along track

    Based on code posted to the GMT mailing list in Dec 1999 by Jim Levens and by Jeff Whitaker 
    """

    if ell is None:
        ell = Ellipsoid()

    if npts < 2:
        raise ValueError("npts must be greater than 1")

    if npts == 2:
        return [lat1, lat2], [lon1, lon2]

    if deg:
        rlat1 = radians(lat1)
        rlon1 = radians(lon1)
        rlat2 = radians(lat2)
        rlon2 = radians(lon2)
    else:
        rlat1, rlon1, rlat2, rlon2 = lat1, lon1, lat2, lon2

    gcarclen = 2.0 * asin(sqrt((sin((rlat1 - rlat2) / 2)) ** 2 + cos(rlat1) * cos(rlat2) * (sin((rlon1 - rlon2) / 2)) ** 2))

Returns
    -------
    lat : float
           target geodetic latitude
    lon : float
           target geodetic longitude
    h : float
         target altitude above geodetic ellipsoid (meters)

    based on:
    You, Rey-Jer. (2000). Transformation of Cartesian to Geodetic Coordinates without Iterations.
    Journal of Surveying Engineering. doi: 10.1061/(ASCE)0733-9453
    """
    if ell is None:
        ell = Ellipsoid()

    r = sqrt(x**2 + y**2 + z**2)

    E = sqrt(ell.semimajor_axis**2 - ell.semiminor_axis**2)

    # eqn. 4a
    u = sqrt(0.5 * (r**2 - E**2) + 0.5 * sqrt((r**2 - E**2)**2 + 4 * E**2 * z**2))

    Q = hypot(x, y)

    huE = hypot(u, E)

    # eqn. 4b
    Beta = arctan(huE / u * z / hypot(x, y))

    # eqn. 13

def sanitize(lat: "ndarray", ell: Ellipsoid, deg: bool) -> typing.Tuple["ndarray", Ellipsoid]:
    if ell is None:
        ell = Ellipsoid()
    if asarray is not None:
        lat = asarray(lat)
    if deg:
        lat = radians(lat)

    if asarray is not None:
        if (abs(lat) > pi / 2).any():
            raise ValueError("-pi/2 <= latitude <= pi/2")
    else:
        if abs(lat) > pi / 2:
            raise ValueError("-pi/2 <= latitude <= pi/2")

    return lat, ell