#include <stdio.h>

extern "C" void ScaLBL_D3Q19_AAeven_StokesMRT(
    double *dist, double *Velocity, double *ChargeDensity,
    double *ElectricField, double rlx_setA, double rlx_setB, double Gx,
    double Gy, double Gz, double rho0, double den_scale, double h,
    double time_conv, bool UseSlippingVelBC, int start, int finish, int Np) {
    double fq;
    // conserved momemnts
    double rho, jx, jy, jz;
    double ux, uy, uz;
    // non-conserved moments
    double m1, m2, m4, m6, m8, m9, m10, m11, m12, m13, m14, m15, m16, m17, m18;
    // body force due to electric field
    double rhoE; //charge density
    double Ex, Ey, Ez;
    // total body force
    double Fx, Fy, Fz;

    constexpr double mrt_V1 = 0.05263157894736842;
    constexpr double mrt_V2 = 0.012531328320802;
    constexpr double mrt_V3 = 0.04761904761904762;
    constexpr double mrt_V4 = 0.004594820384294068;
    constexpr double mrt_V5 = 0.01587301587301587;
    constexpr double mrt_V6 = 0.0555555555555555555555555;
    constexpr double mrt_V7 = 0.02777777777777778;
    constexpr double mrt_V8 = 0.08333333333333333;
    constexpr double mrt_V9 = 0.003341687552213868;
    constexpr double mrt_V10 = 0.003968253968253968;
    constexpr double mrt_V11 = 0.01388888888888889;
    constexpr double mrt_V12 = 0.04166666666666666;

    for (int n = start; n < finish; n++) {

        //Load data
        rhoE = ChargeDensity[n];
        Ex = ElectricField[n + 0 * Np];
        Ey = ElectricField[n + 1 * Np];
        Ez = ElectricField[n + 2 * Np];
        //compute total body force, including input body force (Gx,Gy,Gz)
        Fx = (UseSlippingVelBC==1) ? Gx : Gx + rhoE * Ex * (time_conv * time_conv) / (h * h * 1.0e-12) /
                      den_scale; //the extra factors at the end necessarily convert unit from phys to LB
        Fy = (UseSlippingVelBC==1) ? Gy : Gy + rhoE * Ey * (time_conv * time_conv) / (h * h * 1.0e-12) /
                      den_scale;
        Fz = (UseSlippingVelBC==1) ? Gz : Gz + rhoE * Ez * (time_conv * time_conv) / (h * h * 1.0e-12) /
                      den_scale;

        // q=0
        fq = dist[n];
        rho = fq;
        m1 = -30.0 * fq;
        m2 = 12.0 * fq;

        // q=1
        fq = dist[2 * Np + n];
        rho += fq;
        m1 -= 11.0 * fq;
        m2 -= 4.0 * fq;
        jx = fq;
        m4 = -4.0 * fq;
        m9 = 2.0 * fq;
        m10 = -4.0 * fq;

        // f2 = dist[10*Np+n];
        fq = dist[1 * Np + n];
        rho += fq;
        m1 -= 11.0 * (fq);
        m2 -= 4.0 * (fq);
        jx -= fq;
        m4 += 4.0 * (fq);
        m9 += 2.0 * (fq);
        m10 -= 4.0 * (fq);

        // q=3
        fq = dist[4 * Np + n];
        rho += fq;
        m1 -= 11.0 * fq;
        m2 -= 4.0 * fq;
        jy = fq;
        m6 = -4.0 * fq;
        m9 -= fq;
        m10 += 2.0 * fq;
        m11 = fq;
        m12 = -2.0 * fq;

        // q = 4
        fq = dist[3 * Np + n];
        rho += fq;
        m1 -= 11.0 * fq;
        m2 -= 4.0 * fq;
        jy -= fq;
        m6 += 4.0 * fq;
        m9 -= fq;
        m10 += 2.0 * fq;
        m11 += fq;
        m12 -= 2.0 * fq;

        // q=5
        fq = dist[6 * Np + n];
        rho += fq;
        m1 -= 11.0 * fq;
        m2 -= 4.0 * fq;
        jz = fq;
        m8 = -4.0 * fq;
        m9 -= fq;
        m10 += 2.0 * fq;
        m11 -= fq;
        m12 += 2.0 * fq;

        // q = 6
        fq = dist[5 * Np + n];
        rho += fq;
        m1 -= 11.0 * fq;
        m2 -= 4.0 * fq;
        jz -= fq;
        m8 += 4.0 * fq;
        m9 -= fq;
        m10 += 2.0 * fq;
        m11 -= fq;
        m12 += 2.0 * fq;

        // q=7
        fq = dist[8 * Np + n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx += fq;
        m4 += fq;
        jy += fq;
        m6 += fq;
        m9 += fq;
        m10 += fq;
        m11 += fq;
        m12 += fq;
        m13 = fq;
        m16 = fq;
        m17 = -fq;

        // q = 8
        fq = dist[7 * Np + n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx -= fq;
        m4 -= fq;
        jy -= fq;
        m6 -= fq;
        m9 += fq;
        m10 += fq;
        m11 += fq;
        m12 += fq;
        m13 += fq;
        m16 -= fq;
        m17 += fq;

        // q=9
        fq = dist[10 * Np + n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx += fq;
        m4 += fq;
        jy -= fq;
        m6 -= fq;
        m9 += fq;
        m10 += fq;
        m11 += fq;
        m12 += fq;
        m13 -= fq;
        m16 += fq;
        m17 += fq;

        // q = 10
        fq = dist[9 * Np + n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx -= fq;
        m4 -= fq;
        jy += fq;
        m6 += fq;
        m9 += fq;
        m10 += fq;
        m11 += fq;
        m12 += fq;
        m13 -= fq;
        m16 -= fq;
        m17 -= fq;

        // q=11
        fq = dist[12 * Np + n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx += fq;
        m4 += fq;
        jz += fq;
        m8 += fq;
        m9 += fq;
        m10 += fq;
        m11 -= fq;
        m12 -= fq;
        m15 = fq;
        m16 -= fq;
        m18 = fq;

        // q=12
        fq = dist[11 * Np + n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx -= fq;
        m4 -= fq;
        jz -= fq;
        m8 -= fq;
        m9 += fq;
        m10 += fq;
        m11 -= fq;
        m12 -= fq;
        m15 += fq;
        m16 += fq;
        m18 -= fq;

        // q=13
        fq = dist[14 * Np + n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx += fq;
        m4 += fq;
        jz -= fq;
        m8 -= fq;
        m9 += fq;
        m10 += fq;
        m11 -= fq;
        m12 -= fq;
        m15 -= fq;
        m16 -= fq;
        m18 -= fq;

        // q=14
        fq = dist[13 * Np + n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx -= fq;
        m4 -= fq;
        jz += fq;
        m8 += fq;
        m9 += fq;
        m10 += fq;
        m11 -= fq;
        m12 -= fq;
        m15 -= fq;
        m16 += fq;
        m18 += fq;

        // q=15
        fq = dist[16 * Np + n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jy += fq;
        m6 += fq;
        jz += fq;
        m8 += fq;
        m9 -= 2.0 * fq;
        m10 -= 2.0 * fq;
        m14 = fq;
        m17 += fq;
        m18 -= fq;

        // q=16
        fq = dist[15 * Np + n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jy -= fq;
        m6 -= fq;
        jz -= fq;
        m8 -= fq;
        m9 -= 2.0 * fq;
        m10 -= 2.0 * fq;
        m14 += fq;
        m17 -= fq;
        m18 += fq;

        // q=17
        fq = dist[18 * Np + n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jy += fq;
        m6 += fq;
        jz -= fq;
        m8 -= fq;
        m9 -= 2.0 * fq;
        m10 -= 2.0 * fq;
        m14 -= fq;
        m17 += fq;
        m18 += fq;

        // q=18
        fq = dist[17 * Np + n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jy -= fq;
        m6 -= fq;
        jz += fq;
        m8 += fq;
        m9 -= 2.0 * fq;
        m10 -= 2.0 * fq;
        m14 -= fq;
        m17 -= fq;
        m18 -= fq;

        // write the velocity
        ux = jx / rho0;
        uy = jy / rho0;
        uz = jz / rho0;
        Velocity[n] = ux;
        Velocity[Np + n] = uy;
        Velocity[2 * Np + n] = uz;

        //........................................................................
        //					READ THE DISTRIBUTIONS
        //		(read from opposite array due to previous swap operation)
        //........................................................................

        //..............incorporate external force................................................
        //..............carry out relaxation process...............................................
        m1 = m1 +
             rlx_setA *
                 ((19 * (jx * jx + jy * jy + jz * jz) / rho0 - 11 * rho) - m1);
        m2 = m2 +
             rlx_setA *
                 ((3 * rho - 5.5 * (jx * jx + jy * jy + jz * jz) / rho0) - m2);
        m4 = m4 + rlx_setB * ((-0.6666666666666666 * jx) - m4);
        m6 = m6 + rlx_setB * ((-0.6666666666666666 * jy) - m6);
        m8 = m8 + rlx_setB * ((-0.6666666666666666 * jz) - m8);
        m9 = m9 + rlx_setA * (((2 * jx * jx - jy * jy - jz * jz) / rho0) - m9);
        m10 =
            m10 +
            rlx_setA * (-0.5 * ((2 * jx * jx - jy * jy - jz * jz) / rho) - m10);
        m11 = m11 + rlx_setA * (((jy * jy - jz * jz) / rho0) - m11);
        m12 = m12 + rlx_setA * (-0.5 * ((jy * jy - jz * jz) / rho0) - m12);
        m13 = m13 + rlx_setA * ((jx * jy / rho0) - m13);
        m14 = m14 + rlx_setA * ((jy * jz / rho0) - m14);
        m15 = m15 + rlx_setA * ((jx * jz / rho0) - m15);
        m16 = m16 + rlx_setB * (-m16);
        m17 = m17 + rlx_setB * (-m17);
        m18 = m18 + rlx_setB * (-m18);
        //.......................................................................................................
        //.................inverse transformation......................................................

        // q=0
        fq = mrt_V1 * rho - mrt_V2 * m1 + mrt_V3 * m2;
        dist[n] = fq;

        // q = 1
        fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (jx - m4) +
             mrt_V6 * (m9 - m10) + 0.16666666 * Fx;
        dist[1 * Np + n] = fq;

        // q=2
        fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (m4 - jx) +
             mrt_V6 * (m9 - m10) - 0.16666666 * Fx;
        dist[2 * Np + n] = fq;

        // q = 3
        fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (jy - m6) +
             mrt_V7 * (m10 - m9) + mrt_V8 * (m11 - m12) + 0.16666666 * Fy;
        dist[3 * Np + n] = fq;

        // q = 4
        fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (m6 - jy) +
             mrt_V7 * (m10 - m9) + mrt_V8 * (m11 - m12) - 0.16666666 * Fy;
        dist[4 * Np + n] = fq;

        // q = 5
        fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (jz - m8) +
             mrt_V7 * (m10 - m9) + mrt_V8 * (m12 - m11) + 0.16666666 * Fz;
        dist[5 * Np + n] = fq;

        // q = 6
        fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (m8 - jz) +
             mrt_V7 * (m10 - m9) + mrt_V8 * (m12 - m11) - 0.16666666 * Fz;
        dist[6 * Np + n] = fq;

        // q = 7
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jx + jy) +
             0.025 * (m4 + m6) + mrt_V7 * m9 + mrt_V11 * m10 + mrt_V8 * m11 +
             mrt_V12 * m12 + 0.25 * m13 + 0.125 * (m16 - m17) +
             0.08333333333 * (Fx + Fy);
        dist[7 * Np + n] = fq;

        // q = 8
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 - 0.1 * (jx + jy) -
             0.025 * (m4 + m6) + mrt_V7 * m9 + mrt_V11 * m10 + mrt_V8 * m11 +
             mrt_V12 * m12 + 0.25 * m13 + 0.125 * (m17 - m16) -
             0.08333333333 * (Fx + Fy);
        dist[8 * Np + n] = fq;

        // q = 9
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jx - jy) +
             0.025 * (m4 - m6) + mrt_V7 * m9 + mrt_V11 * m10 + mrt_V8 * m11 +
             mrt_V12 * m12 - 0.25 * m13 + 0.125 * (m16 + m17) +
             0.08333333333 * (Fx - Fy);
        dist[9 * Np + n] = fq;

        // q = 10
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jy - jx) +
             0.025 * (m6 - m4) + mrt_V7 * m9 + mrt_V11 * m10 + mrt_V8 * m11 +
             mrt_V12 * m12 - 0.25 * m13 - 0.125 * (m16 + m17) -
             0.08333333333 * (Fx - Fy);
        dist[10 * Np + n] = fq;

        // q = 11
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jx + jz) +
             0.025 * (m4 + m8) + mrt_V7 * m9 + mrt_V11 * m10 - mrt_V8 * m11 -
             mrt_V12 * m12 + 0.25 * m15 + 0.125 * (m18 - m16) +
             0.08333333333 * (Fx + Fz);
        dist[11 * Np + n] = fq;

        // q = 12
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 - 0.1 * (jx + jz) -
             0.025 * (m4 + m8) + mrt_V7 * m9 + mrt_V11 * m10 - mrt_V8 * m11 -
             mrt_V12 * m12 + 0.25 * m15 + 0.125 * (m16 - m18) -
             0.08333333333 * (Fx + Fz);
        dist[12 * Np + n] = fq;

        // q = 13
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jx - jz) +
             0.025 * (m4 - m8) + mrt_V7 * m9 + mrt_V11 * m10 - mrt_V8 * m11 -
             mrt_V12 * m12 - 0.25 * m15 - 0.125 * (m16 + m18) +
             0.08333333333 * (Fx - Fz);
        dist[13 * Np + n] = fq;

        // q= 14
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jz - jx) +
             0.025 * (m8 - m4) + mrt_V7 * m9 + mrt_V11 * m10 - mrt_V8 * m11 -
             mrt_V12 * m12 - 0.25 * m15 + 0.125 * (m16 + m18) -
             0.08333333333 * (Fx - Fz);

        dist[14 * Np + n] = fq;

        // q = 15
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jy + jz) +
             0.025 * (m6 + m8) - mrt_V6 * m9 - mrt_V7 * m10 + 0.25 * m14 +
             0.125 * (m17 - m18) + 0.08333333333 * (Fy + Fz);
        dist[15 * Np + n] = fq;

        // q = 16
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 - 0.1 * (jy + jz) -
             0.025 * (m6 + m8) - mrt_V6 * m9 - mrt_V7 * m10 + 0.25 * m14 +
             0.125 * (m18 - m17) - 0.08333333333 * (Fy + Fz);
        dist[16 * Np + n] = fq;

        // q = 17
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jy - jz) +
             0.025 * (m6 - m8) - mrt_V6 * m9 - mrt_V7 * m10 - 0.25 * m14 +
             0.125 * (m17 + m18) + 0.08333333333 * (Fy - Fz);
        dist[17 * Np + n] = fq;

        // q = 18
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jz - jy) +
             0.025 * (m8 - m6) - mrt_V6 * m9 - mrt_V7 * m10 - 0.25 * m14 -
             0.125 * (m17 + m18) - 0.08333333333 * (Fy - Fz);
        dist[18 * Np + n] = fq;

        //........................................................................
    }
}

extern "C" void ScaLBL_D3Q19_AAodd_StokesMRT(
    int *neighborList, double *dist, double *Velocity, double *ChargeDensity,
    double *ElectricField, double rlx_setA, double rlx_setB, double Gx,
    double Gy, double Gz, double rho0, double den_scale, double h,
    double time_conv, bool UseSlippingVelBC, int start, int finish, int Np) {
    double fq;
    // conserved momemnts
    double rho, jx, jy, jz;
    double ux, uy, uz;
    // non-conserved moments
    double m1, m2, m4, m6, m8, m9, m10, m11, m12, m13, m14, m15, m16, m17, m18;
    int nread;
    // body force due to electric field
    double rhoE; //charge density
    double Ex, Ey, Ez;
    // total body force
    double Fx, Fy, Fz;

    constexpr double mrt_V1 = 0.05263157894736842;
    constexpr double mrt_V2 = 0.012531328320802;
    constexpr double mrt_V3 = 0.04761904761904762;
    constexpr double mrt_V4 = 0.004594820384294068;
    constexpr double mrt_V5 = 0.01587301587301587;
    constexpr double mrt_V6 = 0.0555555555555555555555555;
    constexpr double mrt_V7 = 0.02777777777777778;
    constexpr double mrt_V8 = 0.08333333333333333;
    constexpr double mrt_V9 = 0.003341687552213868;
    constexpr double mrt_V10 = 0.003968253968253968;
    constexpr double mrt_V11 = 0.01388888888888889;
    constexpr double mrt_V12 = 0.04166666666666666;

    for (int n = start; n < finish; n++) {

        //Load data
        rhoE = ChargeDensity[n];
        Ex = ElectricField[n + 0 * Np];
        Ey = ElectricField[n + 1 * Np];
        Ez = ElectricField[n + 2 * Np];

        //compute total body force, including input body force (Gx,Gy,Gz)
        //Fx = Gx + rhoE * Ex * (time_conv * time_conv) / (h * h * 1.0e-12) /
        //              den_scale; //the extra factors at the end necessarily convert unit from phys to LB
        //Fy = Gy + rhoE * Ey * (time_conv * time_conv) / (h * h * 1.0e-12) /
        //              den_scale;
        //Fz = Gz + rhoE * Ez * (time_conv * time_conv) / (h * h * 1.0e-12) /
        //              den_scale;
        //When Helmholtz-Smoluchowski slipping velocity BC is used, the bulk fluid is considered as electroneutral
        //and body force induced by external efectric field is reduced to slipping velocity BC. 
        Fx = (UseSlippingVelBC==1) ? Gx : Gx + rhoE * Ex * (time_conv * time_conv) / (h * h * 1.0e-12) /
                      den_scale; //the extra factors at the end necessarily convert unit from phys to LB
        Fy = (UseSlippingVelBC==1) ? Gy : Gy + rhoE * Ey * (time_conv * time_conv) / (h * h * 1.0e-12) /
                      den_scale;
        Fz = (UseSlippingVelBC==1) ? Gz : Gz + rhoE * Ez * (time_conv * time_conv) / (h * h * 1.0e-12) /
                      den_scale;

        // q=0
        fq = dist[n];
        rho = fq;
        m1 = -30.0 * fq;
        m2 = 12.0 * fq;

        // q=1
        nread = neighborList[n]; // neighbor 2 ( > 10Np => odd part of dist)
        fq = dist[nread];        // reading the f1 data into register fq
        //fp = dist[10*Np+n];
        rho += fq;
        m1 -= 11.0 * fq;
        m2 -= 4.0 * fq;
        jx = fq;
        m4 = -4.0 * fq;
        m9 = 2.0 * fq;
        m10 = -4.0 * fq;

        // f2 = dist[10*Np+n];
        nread =
            neighborList[n + Np]; // neighbor 1 ( < 10Np => even part of dist)
        fq = dist[nread];         // reading the f2 data into register fq
        //fq = dist[Np+n];
        rho += fq;
        m1 -= 11.0 * (fq);
        m2 -= 4.0 * (fq);
        jx -= fq;
        m4 += 4.0 * (fq);
        m9 += 2.0 * (fq);
        m10 -= 4.0 * (fq);

        // q=3
        nread = neighborList[n + 2 * Np]; // neighbor 4
        fq = dist[nread];
        //fq = dist[11*Np+n];
        rho += fq;
        m1 -= 11.0 * fq;
        m2 -= 4.0 * fq;
        jy = fq;
        m6 = -4.0 * fq;
        m9 -= fq;
        m10 += 2.0 * fq;
        m11 = fq;
        m12 = -2.0 * fq;

        // q = 4
        nread = neighborList[n + 3 * Np]; // neighbor 3
        fq = dist[nread];
        //fq = dist[2*Np+n];
        rho += fq;
        m1 -= 11.0 * fq;
        m2 -= 4.0 * fq;
        jy -= fq;
        m6 += 4.0 * fq;
        m9 -= fq;
        m10 += 2.0 * fq;
        m11 += fq;
        m12 -= 2.0 * fq;

        // q=5
        nread = neighborList[n + 4 * Np];
        fq = dist[nread];
        //fq = dist[12*Np+n];
        rho += fq;
        m1 -= 11.0 * fq;
        m2 -= 4.0 * fq;
        jz = fq;
        m8 = -4.0 * fq;
        m9 -= fq;
        m10 += 2.0 * fq;
        m11 -= fq;
        m12 += 2.0 * fq;

        // q = 6
        nread = neighborList[n + 5 * Np];
        fq = dist[nread];
        //fq = dist[3*Np+n];
        rho += fq;
        m1 -= 11.0 * fq;
        m2 -= 4.0 * fq;
        jz -= fq;
        m8 += 4.0 * fq;
        m9 -= fq;
        m10 += 2.0 * fq;
        m11 -= fq;
        m12 += 2.0 * fq;

        // q=7
        nread = neighborList[n + 6 * Np];
        fq = dist[nread];
        //fq = dist[13*Np+n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx += fq;
        m4 += fq;
        jy += fq;
        m6 += fq;
        m9 += fq;
        m10 += fq;
        m11 += fq;
        m12 += fq;
        m13 = fq;
        m16 = fq;
        m17 = -fq;

        // q = 8
        nread = neighborList[n + 7 * Np];
        fq = dist[nread];
        //fq = dist[4*Np+n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx -= fq;
        m4 -= fq;
        jy -= fq;
        m6 -= fq;
        m9 += fq;
        m10 += fq;
        m11 += fq;
        m12 += fq;
        m13 += fq;
        m16 -= fq;
        m17 += fq;

        // q=9
        nread = neighborList[n + 8 * Np];
        fq = dist[nread];
        //fq = dist[14*Np+n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx += fq;
        m4 += fq;
        jy -= fq;
        m6 -= fq;
        m9 += fq;
        m10 += fq;
        m11 += fq;
        m12 += fq;
        m13 -= fq;
        m16 += fq;
        m17 += fq;

        // q = 10
        nread = neighborList[n + 9 * Np];
        fq = dist[nread];
        //fq = dist[5*Np+n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx -= fq;
        m4 -= fq;
        jy += fq;
        m6 += fq;
        m9 += fq;
        m10 += fq;
        m11 += fq;
        m12 += fq;
        m13 -= fq;
        m16 -= fq;
        m17 -= fq;

        // q=11
        nread = neighborList[n + 10 * Np];
        fq = dist[nread];
        //fq = dist[15*Np+n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx += fq;
        m4 += fq;
        jz += fq;
        m8 += fq;
        m9 += fq;
        m10 += fq;
        m11 -= fq;
        m12 -= fq;
        m15 = fq;
        m16 -= fq;
        m18 = fq;

        // q=12
        nread = neighborList[n + 11 * Np];
        fq = dist[nread];
        //fq = dist[6*Np+n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx -= fq;
        m4 -= fq;
        jz -= fq;
        m8 -= fq;
        m9 += fq;
        m10 += fq;
        m11 -= fq;
        m12 -= fq;
        m15 += fq;
        m16 += fq;
        m18 -= fq;

        // q=13
        nread = neighborList[n + 12 * Np];
        fq = dist[nread];
        //fq = dist[16*Np+n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx += fq;
        m4 += fq;
        jz -= fq;
        m8 -= fq;
        m9 += fq;
        m10 += fq;
        m11 -= fq;
        m12 -= fq;
        m15 -= fq;
        m16 -= fq;
        m18 -= fq;

        // q=14
        nread = neighborList[n + 13 * Np];
        fq = dist[nread];
        //fq = dist[7*Np+n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jx -= fq;
        m4 -= fq;
        jz += fq;
        m8 += fq;
        m9 += fq;
        m10 += fq;
        m11 -= fq;
        m12 -= fq;
        m15 -= fq;
        m16 += fq;
        m18 += fq;

        // q=15
        nread = neighborList[n + 14 * Np];
        fq = dist[nread];
        //fq = dist[17*Np+n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jy += fq;
        m6 += fq;
        jz += fq;
        m8 += fq;
        m9 -= 2.0 * fq;
        m10 -= 2.0 * fq;
        m14 = fq;
        m17 += fq;
        m18 -= fq;

        // q=16
        nread = neighborList[n + 15 * Np];
        fq = dist[nread];
        //fq = dist[8*Np+n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jy -= fq;
        m6 -= fq;
        jz -= fq;
        m8 -= fq;
        m9 -= 2.0 * fq;
        m10 -= 2.0 * fq;
        m14 += fq;
        m17 -= fq;
        m18 += fq;

        // q=17
        //fq = dist[18*Np+n];
        nread = neighborList[n + 16 * Np];
        fq = dist[nread];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jy += fq;
        m6 += fq;
        jz -= fq;
        m8 -= fq;
        m9 -= 2.0 * fq;
        m10 -= 2.0 * fq;
        m14 -= fq;
        m17 += fq;
        m18 += fq;

        // q=18
        nread = neighborList[n + 17 * Np];
        fq = dist[nread];
        //fq = dist[9*Np+n];
        rho += fq;
        m1 += 8.0 * fq;
        m2 += fq;
        jy -= fq;
        m6 -= fq;
        jz += fq;
        m8 += fq;
        m9 -= 2.0 * fq;
        m10 -= 2.0 * fq;
        m14 -= fq;
        m17 -= fq;
        m18 -= fq;

        // write the velocity
        ux = jx / rho0;
        uy = jy / rho0;
        uz = jz / rho0;
        Velocity[n] = ux;
        Velocity[Np + n] = uy;
        Velocity[2 * Np + n] = uz;

        //..............incorporate external force................................................
        //..............carry out relaxation process...............................................
        m1 = m1 +
             rlx_setA *
                 ((19 * (jx * jx + jy * jy + jz * jz) / rho0 - 11 * rho) - m1);
        m2 = m2 +
             rlx_setA *
                 ((3 * rho - 5.5 * (jx * jx + jy * jy + jz * jz) / rho0) - m2);
        m4 = m4 + rlx_setB * ((-0.6666666666666666 * jx) - m4);
        m6 = m6 + rlx_setB * ((-0.6666666666666666 * jy) - m6);
        m8 = m8 + rlx_setB * ((-0.6666666666666666 * jz) - m8);
        m9 = m9 + rlx_setA * (((2 * jx * jx - jy * jy - jz * jz) / rho0) - m9);
        m10 =
            m10 +
            rlx_setA * (-0.5 * ((2 * jx * jx - jy * jy - jz * jz) / rho) - m10);
        m11 = m11 + rlx_setA * (((jy * jy - jz * jz) / rho0) - m11);
        m12 = m12 + rlx_setA * (-0.5 * ((jy * jy - jz * jz) / rho0) - m12);
        m13 = m13 + rlx_setA * ((jx * jy / rho0) - m13);
        m14 = m14 + rlx_setA * ((jy * jz / rho0) - m14);
        m15 = m15 + rlx_setA * ((jx * jz / rho0) - m15);
        m16 = m16 + rlx_setB * (-m16);
        m17 = m17 + rlx_setB * (-m17);
        m18 = m18 + rlx_setB * (-m18);
        //.......................................................................................................
        //.................inverse transformation......................................................

        // q=0
        fq = mrt_V1 * rho - mrt_V2 * m1 + mrt_V3 * m2;
        dist[n] = fq;

        // q = 1
        fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (jx - m4) +
             mrt_V6 * (m9 - m10) + 0.16666666 * Fx;
        nread = neighborList[n + Np];
        dist[nread] = fq;

        // q=2
        fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (m4 - jx) +
             mrt_V6 * (m9 - m10) - 0.16666666 * Fx;
        nread = neighborList[n];
        dist[nread] = fq;

        // q = 3
        fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (jy - m6) +
             mrt_V7 * (m10 - m9) + mrt_V8 * (m11 - m12) + 0.16666666 * Fy;
        nread = neighborList[n + 3 * Np];
        dist[nread] = fq;

        // q = 4
        fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (m6 - jy) +
             mrt_V7 * (m10 - m9) + mrt_V8 * (m11 - m12) - 0.16666666 * Fy;
        nread = neighborList[n + 2 * Np];
        dist[nread] = fq;

        // q = 5
        fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (jz - m8) +
             mrt_V7 * (m10 - m9) + mrt_V8 * (m12 - m11) + 0.16666666 * Fz;
        nread = neighborList[n + 5 * Np];
        dist[nread] = fq;

        // q = 6
        fq = mrt_V1 * rho - mrt_V4 * m1 - mrt_V5 * m2 + 0.1 * (m8 - jz) +
             mrt_V7 * (m10 - m9) + mrt_V8 * (m12 - m11) - 0.16666666 * Fz;
        nread = neighborList[n + 4 * Np];
        dist[nread] = fq;

        // q = 7
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jx + jy) +
             0.025 * (m4 + m6) + mrt_V7 * m9 + mrt_V11 * m10 + mrt_V8 * m11 +
             mrt_V12 * m12 + 0.25 * m13 + 0.125 * (m16 - m17) +
             0.08333333333 * (Fx + Fy);
        nread = neighborList[n + 7 * Np];
        dist[nread] = fq;

        // q = 8
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 - 0.1 * (jx + jy) -
             0.025 * (m4 + m6) + mrt_V7 * m9 + mrt_V11 * m10 + mrt_V8 * m11 +
             mrt_V12 * m12 + 0.25 * m13 + 0.125 * (m17 - m16) -
             0.08333333333 * (Fx + Fy);
        nread = neighborList[n + 6 * Np];
        dist[nread] = fq;

        // q = 9
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jx - jy) +
             0.025 * (m4 - m6) + mrt_V7 * m9 + mrt_V11 * m10 + mrt_V8 * m11 +
             mrt_V12 * m12 - 0.25 * m13 + 0.125 * (m16 + m17) +
             0.08333333333 * (Fx - Fy);
        nread = neighborList[n + 9 * Np];
        dist[nread] = fq;

        // q = 10
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jy - jx) +
             0.025 * (m6 - m4) + mrt_V7 * m9 + mrt_V11 * m10 + mrt_V8 * m11 +
             mrt_V12 * m12 - 0.25 * m13 - 0.125 * (m16 + m17) -
             0.08333333333 * (Fx - Fy);
        nread = neighborList[n + 8 * Np];
        dist[nread] = fq;

        // q = 11
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jx + jz) +
             0.025 * (m4 + m8) + mrt_V7 * m9 + mrt_V11 * m10 - mrt_V8 * m11 -
             mrt_V12 * m12 + 0.25 * m15 + 0.125 * (m18 - m16) +
             0.08333333333 * (Fx + Fz);
        nread = neighborList[n + 11 * Np];
        dist[nread] = fq;

        // q = 12
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 - 0.1 * (jx + jz) -
             0.025 * (m4 + m8) + mrt_V7 * m9 + mrt_V11 * m10 - mrt_V8 * m11 -
             mrt_V12 * m12 + 0.25 * m15 + 0.125 * (m16 - m18) -
             0.08333333333 * (Fx + Fz);
        nread = neighborList[n + 10 * Np];
        dist[nread] = fq;

        // q = 13
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jx - jz) +
             0.025 * (m4 - m8) + mrt_V7 * m9 + mrt_V11 * m10 - mrt_V8 * m11 -
             mrt_V12 * m12 - 0.25 * m15 - 0.125 * (m16 + m18) +
             0.08333333333 * (Fx - Fz);
        nread = neighborList[n + 13 * Np];
        dist[nread] = fq;

        // q= 14
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jz - jx) +
             0.025 * (m8 - m4) + mrt_V7 * m9 + mrt_V11 * m10 - mrt_V8 * m11 -
             mrt_V12 * m12 - 0.25 * m15 + 0.125 * (m16 + m18) -
             0.08333333333 * (Fx - Fz);
        nread = neighborList[n + 12 * Np];
        dist[nread] = fq;

        // q = 15
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jy + jz) +
             0.025 * (m6 + m8) - mrt_V6 * m9 - mrt_V7 * m10 + 0.25 * m14 +
             0.125 * (m17 - m18) + 0.08333333333 * (Fy + Fz);
        nread = neighborList[n + 15 * Np];
        dist[nread] = fq;

        // q = 16
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 - 0.1 * (jy + jz) -
             0.025 * (m6 + m8) - mrt_V6 * m9 - mrt_V7 * m10 + 0.25 * m14 +
             0.125 * (m18 - m17) - 0.08333333333 * (Fy + Fz);
        nread = neighborList[n + 14 * Np];
        dist[nread] = fq;

        // q = 17
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jy - jz) +
             0.025 * (m6 - m8) - mrt_V6 * m9 - mrt_V7 * m10 - 0.25 * m14 +
             0.125 * (m17 + m18) + 0.08333333333 * (Fy - Fz);
        nread = neighborList[n + 17 * Np];
        dist[nread] = fq;

        // q = 18
        fq = mrt_V1 * rho + mrt_V9 * m1 + mrt_V10 * m2 + 0.1 * (jz - jy) +
             0.025 * (m8 - m6) - mrt_V6 * m9 - mrt_V7 * m10 - 0.25 * m14 -
             0.125 * (m17 + m18) - 0.08333333333 * (Fy - Fz);
        nread = neighborList[n + 16 * Np];
        dist[nread] = fq;
    }
}

//extern "C" void ScaLBL_D3Q19_Momentum_Phys(double *dist, double *vel, double h, double time_conv, int Np)
//{
//    //h: resolution [um/lu]
//    //time_conv: time conversion factor [sec/lt]
//	int n;
//	// distributions
//	double f1,f2,f3,f4,f5,f6,f7,f8,f9;
//	double f10,f11,f12,f13,f14,f15,f16,f17,f18;
//	double vx,vy,vz;
//
//	for (n=0; n<Np; n++){
//		//........................................................................
//		// Registers to store the distributions
//		//........................................................................
//		f2 = dist[2*Np+n];
//		f4 = dist[4*Np+n];
//		f6 = dist[6*Np+n];
//		f8 = dist[8*Np+n];
//		f10 = dist[10*Np+n];
//		f12 = dist[12*Np+n];
//		f14 = dist[14*Np+n];
//		f16 = dist[16*Np+n];
//		f18 = dist[18*Np+n];
//		//........................................................................
//		f1 = dist[Np+n];
//		f3 = dist[3*Np+n];
//		f5 = dist[5*Np+n];
//		f7 = dist[7*Np+n];
//		f9 = dist[9*Np+n];
//		f11 = dist[11*Np+n];
//		f13 = dist[13*Np+n];
//		f15 = dist[15*Np+n];
//		f17 = dist[17*Np+n];
//		//.................Compute the velocity...................................
//		vx = f1-f2+f7-f8+f9-f10+f11-f12+f13-f14;
//		vy = f3-f4+f7-f8-f9+f10+f15-f16+f17-f18;
//		vz = f5-f6+f11-f12-f13+f14+f15-f16-f17+f18;
//		//..................Write the velocity.....................................
//		vel[0*Np+n] = vx*(h*1.0e-6)/time_conv;
//		vel[1*Np+n] = vy*(h*1.0e-6)/time_conv;
//		vel[2*Np+n] = vz*(h*1.0e-6)/time_conv;
//		//........................................................................
//	}
//}