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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 gradient_xyz(self, f, nit=3, tol=1e-3, guarantee_convergence=False):
 """ Return the cartesian components of the gradient of a scalar field on the surface of the sphere. The method consists of minimizing a quadratic functional Q(G) over gradient vectors, where Q is an approximation to the linearized curvature over the triangulation of a C-1 bivariate function F(x,y) which interpolates the nodal values and gradients. Parameters f : array of floats, shape (n,) field over which to evaluate the gradient nit: int (default: 3) number of iterations to reach a convergence tolerance, tol nit >= 1 tol: float (default: 1e-3) maximum change in gradient between iterations. convergence is reached when this condition is met. Returns ------- dfdx : array of floats, shape (n,) derivative of f in the x direction dfdy : array of floats, shape (n,) derivative of f in the y direction dfdz : array of floats, shape (n,) derivative of f in the z direction Notes ----- For SIGMA = 0, optimal efficiency was achieved in testing with tol = 0, and nit = 3 or 4. The restriction of F to an arc of the triangulation is taken to be the Hermite interpolatory tension spline defined by the data values and tangential gradient components at the endpoints of the arc, and Q is the sum over the triangulation arcs, excluding interior constraint arcs, of the linearized curvatures of F along the arcs -- the integrals over the arcs of D2F(T)**2, where D2F(T) is the second derivative of F with respect to distance T along the arc. """


        if f.size != self.npoints:
            raise ValueError('f should be the same size as mesh')

        # gradient = np.zeros((3,self.npoints), order='F', dtype=np.float32)
        sigma = 0
        iflgs = 0

        f = self._shuffle_field(f)

        ierr = 1
        while ierr == 1:
            grad, ierr = _ssrfpack.gradg(self._x, self._y, self._z, f, self.lst, self.lptr, self.lend,\
                                   iflgs, sigma, nit, tol)
            if not guarantee_convergence:
                break

        if ierr < 0:
            raise ValueError('ierr={} in gradg\n{}'.format(ierr, _ier_codes[ierr]))

        return self._deshuffle_field(grad[0], grad[1], grad[2])