/* Implement Mixed Gradient (Lee et al. JCP 2016)*/

extern "C" void ScaLBL_D3Q19_MixedGradient(int *Map, double *Phi,
                                           double *Gradient, int start,
                                           int finish, int Np, int Nx, int Ny,
                                           int Nz) {
    static int D3Q19[18][3] = {{1, 0, 0},  {-1, 0, 0}, {0, 1, 0}, {0, -1, 0},
                               {0, 0, 1},  {0, 0, -1}, {1, 1, 0}, {-1, -1, 0},
                               {1, -1, 0}, {-1, 1, 0}, {1, 0, 1}, {-1, 0, -1},
                               {1, 0, -1}, {-1, 0, 1}, {0, 1, 1}, {0, -1, -1},
                               {0, 1, -1}, {0, -1, 1}};

    int i, j, k, n;
    int np, np2, nm;       // neighbors
    double v, vp, vp2, vm; // values at neighbors
    double grad;
    for (int idx = start; idx < finish; idx++) {
        n = Map[idx]; // layout in regular array
        //.......Back out the 3-D indices for node n..............
        k = n / (Nx * Ny);
        j = (n - Nx * Ny * k) / Nx;
        i = n - Nx * Ny * k - Nx * j;
        v = Phi[n];
        grad = 0.0;
        for (int q = 0; q < 6; q++) {
            int iqx = D3Q19[q][0];
            int iqy = D3Q19[q][1];
            int iqz = D3Q19[q][2];
            np = (k + iqz) * Nx * Ny + (j + iqy) * Nx + i + iqx;
            np2 = (k + 2 * iqz) * Nx * Ny + (j + 2 * iqy) * Nx + i + 2 * iqx;
            nm = (k - iqz) * Nx * Ny + (j - iqy) * Nx + i - iqx;
            vp = Phi[np];
            vp2 = Phi[np2];
            vm = Phi[nm];
            grad += 0.25 * (5.0 * vp - vp2 - 3.0 * v - vm);
        }
        for (int q = 6; q < 18; q++) {
            int iqx = D3Q19[q][0];
            int iqy = D3Q19[q][1];
            int iqz = D3Q19[q][2];
            np = (k + iqz) * Nx * Ny + (j + iqy) * Nx + i + iqx;
            np2 = (k + 2 * iqz) * Nx * Ny + (j + 2 * iqy) * Nx + i + 2 * iqx;
            nm = (k - iqz) * Nx * Ny + (j - iqy) * Nx + i - iqx;
            vp = Phi[np];
            vp2 = Phi[np2];
            vm = Phi[nm];
            grad += 0.125 * (5.0 * vp - vp2 - 3.0 * v - vm);
        }
        Gradient[n] = grad;
    }
}