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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, nmax=None, grid='DH2', zeros=None):
 """ Expand the function on a grid using the first n Slepian coefficients. Usage ----- f = x.expand([nmax, grid, zeros]) Returns ------- f : SHGrid class instance Parameters nmax : int, optional, default = x.nmax The number of expansion coefficients to use when calculating the spherical harmonic coefficients. grid : str, optional, default = 'DH2' 'DH' or 'DH1' for an equisampled lat/lon grid with nlat=nlon, 'DH2' for an equidistant lat/lon grid with nlon=2*nlat, or 'GLQ' for a Gauss-Legendre quadrature grid. zeros : ndarray, optional, default = None The cos(colatitude) nodes used in the Gauss-Legendre Quadrature grids. """

        if type(grid) != str:
            raise ValueError('grid must be a string. ' +
                             'Input type was {:s}'
                             .format(str(type(grid))))

        if nmax is None:
            nmax = self.nmax

        if self.galpha.kind == 'cap':
            shcoeffs = _shtools.SlepianCoeffsToSH(self.falpha,
                                                  self.galpha.coeffs, nmax)
        else:
            shcoeffs = _shtools.SlepianCoeffsToSH(self.falpha,
                                                  self.galpha.tapers, nmax)

        if grid.upper() in ('DH', 'DH1'):
            gridout = _shtools.MakeGridDH(shcoeffs, sampling=1,
                                          norm=1, csphase=1)
            return SHGrid.from_array(gridout, grid='DH', copy=False)
        elif grid.upper() == 'DH2':
            gridout = _shtools.MakeGridDH(shcoeffs, sampling=2,
                                          norm=1, csphase=1)
            return SHGrid.from_array(gridout, grid='DH', copy=False)
        elif grid.upper() == 'GLQ':
            if zeros is None:
                zeros, weights = _shtools.SHGLQ(self.galpha.lmax)
            gridout = _shtools.MakeGridGLQ(shcoeffs, zeros,
                                           norm=1, csphase=1)
            return SHGrid.from_array(gridout, grid='GLQ', copy=False)
        else:
            raise ValueError(
                "grid must be 'DH', 'DH1', 'DH2', or 'GLQ'. " +
                "Input value was {:s}".format(repr(grid)))