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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def expand(self, a=None, f=None, lmax=None, lmax_calc=None, sampling=2):
 """ Create 2D cylindrical maps on a flattened and rotating ellipsoid of all three components of the magnetic field, the total magnetic intensity, and the magnetic potential, and return as a SHMagGrid class instance. Usage ----- mag = x.expand([a, f, lmax, lmax_calc, sampling]) Returns ------- mag : SHMagGrid class instance. Parameters a : optional, float, default = self.r0 The semi-major axis of the flattened ellipsoid on which the field is computed. f : optional, float, default = 0 The flattening of the reference ellipsoid: f=(a-b)/a. lmax : optional, integer, default = self.lmax The maximum spherical harmonic degree, which determines the number of samples of the output grids, n=2lmax+2, and the latitudinal sampling interval, 90/(lmax+1). lmax_calc : optional, integer, default = lmax The maximum spherical harmonic degree used in evaluating the functions. This must be less than or equal to lmax. sampling : optional, integer, default = 2 If 1 the output grids are equally sampled (n by n). If 2 (default), the grids are equally spaced in degrees (n by 2n). Description This method will create 2-dimensional cylindrical maps of the three components of the magnetic field, the total field, and the magnetic potential, and return these as an SHMagGrid class instance. Each map is stored as an SHGrid class instance using Driscoll and Healy grids that are either equally sampled (n by n) or equally spaced (n by 2n) in latitude and longitude. All grids use geocentric coordinates, and the units are either in nT (for the magnetic field), or nT m (for the potential), The magnetic potential is given by V = r0 Sum_{l=1}^lmax (r0/r)^{l+1} Sum_{m=-l}^l g_{lm} Y_{lm} and the magnetic field is B = - Grad V. The coefficients are referenced to a radius r0, and the function is computed on a flattened ellipsoid with semi-major axis a (i.e., the mean equatorial radius) and flattening f. """

        if a is None:
            a = self.r0
        if f is None:
            f = 0.
        if lmax is None:
            lmax = self.lmax
        if lmax_calc is None:
            lmax_calc = lmax

        if self.errors is not None:
            coeffs, errors = self.to_array(normalization='schmidt', csphase=1)
        else:
            coeffs = self.to_array(normalization='schmidt', csphase=1)

        rad, theta, phi, total, pot = _MakeMagGridDH(
            coeffs, self.r0, a=a, f=f, lmax=lmax,
            lmax_calc=lmax_calc, sampling=sampling)

        return _SHMagGrid(rad, theta, phi, total, pot, a, f, lmax, lmax_calc)