You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: vdWDF_uGenerate_Potential.m
    path of file: ./repos/M-SPARC/src/xc/vdW/vdWDF
    
    the code of the file until where you have to start completion: function [S, potential] = vdWDF_uGenerate_Potential(S, inptDrho, vdWDF_Dq0Drho, vdWDF_Dq0Dgradrho, ps, DpDq0s) 
% @file    vdWDF_uGenerate_Potential.m
% @brief   This file contains the functions for getting u in real space,
%          and generating vdW-DF potential
% @authors Boqin Zhang <bzhang376@gatech.edu>
%          Phanish Suryanarayana <phanish.suryanarayana@ce.gatech.edu>
% Reference:
% Dion, Max, Henrik Rydberg, Elsebeth Schröder, David C. Langreth, and Bengt I. Lundqvist. 
% "Van der Waals density functional for general geometries." 
% Physical review letters 92, no. 24 (2004): 246401.
% Román-Pérez, Guillermo, and José M. Soler. 
% "Efficient implementation of a van der Waals density functional: application to double-wall carbon nanotubes." 

    
function [S, potential] = vdWDF_uGenerate_Potential(S, inptDrho, vdWDF_Dq0Drho, vdWDF_Dq0Dgradrho, ps, DpDq0s) 
% @file    vdWDF_uGenerate_Potential.m
% @brief   This file contains the functions for getting u in real space,
%          and generating vdW-DF potential
% @authors Boqin Zhang <bzhang376@gatech.edu>
%          Phanish Suryanarayana <phanish.suryanarayana@ce.gatech.edu>
% Reference:
% Dion, Max, Henrik Rydberg, Elsebeth Schröder, David C. Langreth, and Bengt I. Lundqvist. 
% "Van der Waals density functional for general geometries." 
% Physical review letters 92, no. 24 (2004): 246401.
% Román-Pérez, Guillermo, and José M. Soler. 
% "Efficient implementation of a van der Waals density functional: application to double-wall carbon nanotubes." 
% Physical review letters 103, no. 9 (2009): 096102.
% Copyright (c) 2020 Material Physics & Mechanics Group, Georgia Tech.
% ==============================================================================================
	nnr = S.Nx*S.Ny*S.Nz;
	hPrefactor = zeros(nnr, 1);
    % ps and DpDq0s are computed in function vdWDF_splineInterpolation_energy
% 	[ps, DpDq0s] = spline_interpolation_more(S.vdWDF_qmesh, S.vdWDF_q0, S.vdWDF_D2yDx2);
	u = S.vdW_u; % attention: it is NOT wrong! u at here is thetas*Kernel(Phi)
    Drho = inptDrho;
	Dq0Drho = vdWDF_Dq0Drho;
	Dq0Dgradrho = vdWDF_Dq0Dgradrho;
	potential = zeros(nnr, 1);
    qnum = size(S.vdWDF_qmesh, 1);
	for q = 1:qnum
		potential = potential + u(:, q).*(ps(:, q) + DpDq0s(:, q).*Dq0Drho(:));
		hPrefactor = hPrefactor + u(:, q).*DpDq0s(:, q).*Dq0Dgradrho(:);
	end