#include <math.h>
#include <stdio.h>

extern "C" void ScaLBL_DFH_Init(double *Phi, double *Den, double *Aq, double *Bq, int start, int finish, int Np){
	int idx,n;
	double phi,nA,nB;

	for (idx=start; idx<finish; idx++){
		phi = Phi[idx];
		if (phi > 0.f){
			nA = 1.0; nB = 0.f;
		}
		else{
			nB = 1.0; nA = 0.f;
		}
		Den[idx] = nA;
		Den[Np+idx] = nB;

		Aq[idx]=0.3333333333333333*nA;
		Aq[Np+idx]=0.1111111111111111*nA;
		Aq[2*Np+idx]=0.1111111111111111*nA;
		Aq[3*Np+idx]=0.1111111111111111*nA;
		Aq[4*Np+idx]=0.1111111111111111*nA;
		Aq[5*Np+idx]=0.1111111111111111*nA;
		Aq[6*Np+idx]=0.1111111111111111*nA;

		Bq[idx]=0.3333333333333333*nB;
		Bq[Np+idx]=0.1111111111111111*nB;
		Bq[2*Np+idx]=0.1111111111111111*nB;
		Bq[3*Np+idx]=0.1111111111111111*nB;
		Bq[4*Np+idx]=0.1111111111111111*nB;
		Bq[5*Np+idx]=0.1111111111111111*nB;
		Bq[6*Np+idx]=0.1111111111111111*nB;
	}
}


// LBM based on density functional hydrodynamics
extern "C" void ScaLBL_D3Q19_AAeven_DFH(int *neighborList, double *dist, double *Aq, double *Bq, double *Den, double *Phi,
		double *SolidPotential, double rhoA, double rhoB, double tauA, double tauB, double alpha, double beta,
		double Fx, double Fy, double Fz, int start, int finish, int Np){

	int ijk,nn,n;
	double fq;
	// conserved momemnts
	double rho,jx,jy,jz;
	// non-conserved moments
	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
	double m3,m5,m7;
	double nA,nB; // number density
	double a1,b1,a2,b2,nAB,delta;
	double C,nx,ny,nz; //color gradient magnitude and direction
	double ux,uy,uz;
	double phi,tau,rho0,rlx_setA,rlx_setB;
	
	const double mrt_V1=0.05263157894736842;
	const double mrt_V2=0.012531328320802;
	const double mrt_V3=0.04761904761904762;
	const double mrt_V4=0.004594820384294068;
	const double mrt_V5=0.01587301587301587;
	const double mrt_V6=0.0555555555555555555555555;
	const double mrt_V7=0.02777777777777778;
	const double mrt_V8=0.08333333333333333;
	const double mrt_V9=0.003341687552213868;
	const double mrt_V10=0.003968253968253968;
	const double mrt_V11=0.01388888888888889;
	const double mrt_V12=0.04166666666666666;


	for (int n=start; n<finish; n++){
		
		// read the component number densities
		nA = Den[n];
		nB = Den[Np + n];

		// compute phase indicator field
		phi=(nA-nB)/(nA+nB);

		// local density
		rho0=rhoA + 0.5*(1.0-phi)*(rhoB-rhoA);
		// local relaxation time
		tau=tauA + 0.5*(1.0-phi)*(tauB-tauA);
		rlx_setA = 1.f/tau;
		rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);

		//					COMPUTE THE COLOR GRADIENT
		//........................................................................
		//.................Read Phase Indicator Values............................
		//........................................................................
		nn = neighborList[n+Np]%Np;
		m1 = Phi[nn];
		nn = neighborList[n]%Np;
		m2 = Phi[nn];
		nn = neighborList[n+3*Np]%Np;
		m3 = Phi[nn];
		nn = neighborList[n+2*Np]%Np;
		m4 = Phi[nn];		
		nn = neighborList[n+5*Np]%Np;
		m5 = Phi[nn];
		nn = neighborList[n+4*Np]%Np;
		m6 = Phi[nn];		
		nn = neighborList[n+7*Np]%Np;
		m7 = Phi[nn];
		nn = neighborList[n+6*Np]%Np;
		m8 = Phi[nn];		
		nn = neighborList[n+9*Np]%Np;
		m9 = Phi[nn];
		nn = neighborList[n+8*Np]%Np;
		m10 = Phi[nn];		
		nn = neighborList[n+11*Np]%Np;
		m11 = Phi[nn];
		nn = neighborList[n+10*Np]%Np;
		m12 = Phi[nn];		
		nn = neighborList[n+13*Np]%Np;
		m13 = Phi[nn];
		nn = neighborList[n+12*Np]%Np;
		m14 = Phi[nn];		
		nn = neighborList[n+15*Np]%Np;
		m15 = Phi[nn];
		nn = neighborList[n+14*Np]%Np;
		m16 = Phi[nn];		
		nn = neighborList[n+17*Np]%Np;
		m17 = Phi[nn];
		nn = neighborList[n+16*Np]%Np;
		m18 = Phi[nn];					
		
		//............Compute the wn fluid Gradient...................................
		nx = -(m1-m2+0.5*(m7-m8+m9-m10+m11-m12+m13-m14));
		ny = -(m3-m4+0.5*(m7-m8-m9+m10+m15-m16+m17-m18));
		nz = -(m5-m6+0.5*(m11-m12-m13+m14+m15-m16-m17+m18));
		
		// .... read the solid potential gradient.....................
		m1 = SolidPotential[n];
		m2 = SolidPotential[n+Np];
		m3 = SolidPotential[n+2*Np];
		nx += m1;
		ny += m2;
		nz += m3;

		//...........Normalize the Color Gradient.................................
		C = sqrt(nx*nx+ny*ny+nz*nz);
		if (C==0.0) C=1.0;
		nx = nx/C;
		ny = ny/C;
		nz = nz/C;		

		// 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;

		//........................................................................
		//..............carry out relaxation process..............................
		//..........Toelke, Fruediger et. al. 2006................................
		if (C == 0.0)	nx = ny = nz = 0.0;
		m1 = m1 + rlx_setA*((19*(jx*jx+jy*jy+jz*jz)/rho0 - 11*rho) -alpha*C - 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) + 0.5*alpha*C*(2*nx*nx-ny*ny-nz*nz) - m9);
		m10 = m10 + rlx_setA*( - m10);
		m11 = m11 + rlx_setA*(((jy*jy-jz*jz)/rho0) + 0.5*alpha*C*(ny*ny-nz*nz)- m11);
		m12 = m12 + rlx_setA*( - m12);
		m13 = m13 + rlx_setA*( (jx*jy/rho0) + 0.5*alpha*C*nx*ny - m13);
		m14 = m14 + rlx_setA*( (jy*jz/rho0) + 0.5*alpha*C*ny*nz - m14);
		m15 = m15 + rlx_setA*( (jx*jz/rho0) + 0.5*alpha*C*nx*nz - 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;

		//........................................................................

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

		// Instantiate mass transport distributions
		// Stationary value - distribution 0

		nAB = 1.0/(nA+nB);
		Aq[n] = 0.3333333333333333*nA;
		Bq[n] = 0.3333333333333333*nB;

		//...............................................
		// q = 0,2,4
		// Cq = {1,0,0}, {0,1,0}, {0,0,1}
		delta = beta*nA*nB*nAB*0.1111111111111111*nx;
		if (!(nA*nB*nAB>0)) delta=0;
		a1 = nA*(0.1111111111111111*(1+4.5*ux))+delta;
		b1 = nB*(0.1111111111111111*(1+4.5*ux))-delta;
		a2 = nA*(0.1111111111111111*(1-4.5*ux))-delta;
		b2 = nB*(0.1111111111111111*(1-4.5*ux))+delta;

		Aq[1*Np+n] = a1;
		Bq[1*Np+n] = b1;
		Aq[2*Np+n] = a2;
		Bq[2*Np+n] = b2;

		//...............................................
		// q = 2
		// Cq = {0,1,0}
		delta = beta*nA*nB*nAB*0.1111111111111111*ny;
		if (!(nA*nB*nAB>0)) delta=0;
		a1 = nA*(0.1111111111111111*(1+4.5*uy))+delta;
		b1 = nB*(0.1111111111111111*(1+4.5*uy))-delta;
		a2 = nA*(0.1111111111111111*(1-4.5*uy))-delta;
		b2 = nB*(0.1111111111111111*(1-4.5*uy))+delta;

		Aq[3*Np+n] = a1;
		Bq[3*Np+n] = b1;
		Aq[4*Np+n] = a2;
		Bq[4*Np+n] = b2;
		//...............................................
		// q = 4
		// Cq = {0,0,1}
		delta = beta*nA*nB*nAB*0.1111111111111111*nz;
		if (!(nA*nB*nAB>0)) delta=0;
		a1 = nA*(0.1111111111111111*(1+4.5*uz))+delta;
		b1 = nB*(0.1111111111111111*(1+4.5*uz))-delta;
		a2 = nA*(0.1111111111111111*(1-4.5*uz))-delta;
		b2 = nB*(0.1111111111111111*(1-4.5*uz))+delta;

		Aq[5*Np+n] = a1;
		Bq[5*Np+n] = b1;
		Aq[6*Np+n] = a2;
		Bq[6*Np+n] = b2;
		//...............................................

	}
	
}

//extern "C" void ScaLBL_D3Q19_AAodd_Color(int *neighborList, double *dist, double *Aq, double *Bq, double *Den, double *Velocity,
//		double *ColorGrad, double rhoA, double rhoB, double tauA, double tauB, double alpha, double beta,
//		double Fx, double Fy, double Fz, int start, int finish, int Np){
extern "C" void ScaLBL_D3Q19_AAodd_DFH(int *neighborList, double *dist, double *Aq, double *Bq, double *Den, 
		double *Phi, double *SolidPotential, double rhoA, double rhoB, double tauA, double tauB, double alpha, double beta,
		double Fx, double Fy, double Fz, int start, int finish, int Np){
	
	int n,nn,ijk,nread;
	int nr1,nr2,nr3,nr4,nr5,nr6;
	int nr7,nr8,nr9,nr10;
	int nr11,nr12,nr13,nr14;
	//int nr15,nr16,nr17,nr18;
	double fq;
	// conserved momemnts
	double rho,jx,jy,jz;
	// non-conserved moments
	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
	double m3,m5,m7;
	double nA,nB; // number density
	double a1,b1,a2,b2,nAB,delta;
	double C,nx,ny,nz; //color gradient magnitude and direction
	double ux,uy,uz;
	double phi,tau,rho0,rlx_setA,rlx_setB;

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

	for (int n=start; n<finish; n++){
		
		// read the component number densities
		nA = Den[n];
		nB = Den[Np + n];

		// compute phase indicator field
		phi=(nA-nB)/(nA+nB);

		// local density
		rho0=rhoA + 0.5*(1.0-phi)*(rhoB-rhoA);
		// local relaxation time
		tau=tauA + 0.5*(1.0-phi)*(tauB-tauA);
		rlx_setA = 1.f/tau;
		rlx_setB = 8.f*(2.f-rlx_setA)/(8.f-rlx_setA);
		
		//					COMPUTE THE COLOR GRADIENT
		//........................................................................
		//.................Read Phase Indicator Values............................
		//........................................................................
		nn = neighborList[n+Np]%Np;
		m1 = Phi[nn];
		nn = neighborList[n]%Np;
		m2 = Phi[nn];
		nn = neighborList[n+3*Np]%Np;
		m3 = Phi[nn];
		nn = neighborList[n+2*Np]%Np;
		m4 = Phi[nn];		
		nn = neighborList[n+5*Np]%Np;
		m5 = Phi[nn];
		nn = neighborList[n+4*Np]%Np;
		m6 = Phi[nn];		
		nn = neighborList[n+7*Np]%Np;
		m7 = Phi[nn];
		nn = neighborList[n+6*Np]%Np;
		m8 = Phi[nn];		
		nn = neighborList[n+9*Np]%Np;
		m9 = Phi[nn];
		nn = neighborList[n+8*Np]%Np;
		m10 = Phi[nn];		
		nn = neighborList[n+11*Np]%Np;
		m11 = Phi[nn];
		nn = neighborList[n+10*Np]%Np;
		m12 = Phi[nn];		
		nn = neighborList[n+13*Np]%Np;
		m13 = Phi[nn];
		nn = neighborList[n+12*Np]%Np;
		m14 = Phi[nn];		
		nn = neighborList[n+15*Np]%Np;
		m15 = Phi[nn];
		nn = neighborList[n+14*Np]%Np;
		m16 = Phi[nn];		
		nn = neighborList[n+17*Np]%Np;
		m17 = Phi[nn];
		nn = neighborList[n+16*Np]%Np;
		m18 = Phi[nn];					
		
		//............Compute the Color Gradient...................................
		nx = -(m1-m2+0.5*(m7-m8+m9-m10+m11-m12+m13-m14));
		ny = -(m3-m4+0.5*(m7-m8-m9+m10+m15-m16+m17-m18));
		nz = -(m5-m6+0.5*(m11-m12-m13+m14+m15-m16-m17+m18));
		// .... read the solid potential gradient.....................
		m1 = SolidPotential[n];
		m2 = SolidPotential[n+Np];
		m3 = SolidPotential[n+2*Np];
		nx += m1;
		ny += m2;
		nz += m3;
		
		//...........Normalize the Color Gradient.................................
		C = sqrt(nx*nx+ny*ny+nz*nz);
		if (C==0.0) C=1.0;
		nx = nx/C;
		ny = ny/C;
		nz = nz/C;		

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

		// q=1
		//nread = neighborList[n]; // neighbor 2 
		//fq = dist[nread]; // reading the f1 data into register fq		
		nr1 = neighborList[n]; 
		fq = dist[nr1]; // reading the f1 data into register fq
		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
		nr2 = neighborList[n+Np]; // neighbor 1 ( < 10Np => even part of dist)
		fq = dist[nr2];  // reading the f2 data into register fq
		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];
		nr3 = neighborList[n+2*Np]; // neighbor 4
		fq = dist[nr3];
		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];
		nr4 = neighborList[n+3*Np]; // neighbor 3
		fq = dist[nr4];
		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];
		nr5 = neighborList[n+4*Np];
		fq = dist[nr5];
		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];
		nr6 = neighborList[n+5*Np];
		fq = dist[nr6];
		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];
		nr7 = neighborList[n+6*Np];
		fq = dist[nr7];
		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];
		nr8 = neighborList[n+7*Np];
		fq = dist[nr8];
		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];
		nr9 = neighborList[n+8*Np];
		fq = dist[nr9];
		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];
		nr10 = neighborList[n+9*Np];
		fq = dist[nr10];
		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];
		nr11 = neighborList[n+10*Np];
		fq = dist[nr11];
		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];
		nr12 = neighborList[n+11*Np];
		fq = dist[nr12];
		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];
		nr13 = neighborList[n+12*Np];
		fq = dist[nr13];
		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];
		nr14 = neighborList[n+13*Np];
		fq = dist[nr14];
		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;
		
		//........................................................................
		//..............carry out relaxation process..............................
		//..........Toelke, Fruediger et. al. 2006................................
		if (C == 0.0)	nx = ny = nz = 0.0;
		m1 = m1 + rlx_setA*((19*(jx*jx+jy*jy+jz*jz)/rho0 - 11*rho) -alpha*C - 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) + 0.5*alpha*C*(2*nx*nx-ny*ny-nz*nz) - m9);
		m10 = m10 + rlx_setA*( - m10);
		m11 = m11 + rlx_setA*(((jy*jy-jz*jz)/rho0) + 0.5*alpha*C*(ny*ny-nz*nz)- m11);
		m12 = m12 + rlx_setA*( - m12);
		m13 = m13 + rlx_setA*( (jx*jy/rho0) + 0.5*alpha*C*nx*ny - m13);
		m14 = m14 + rlx_setA*( (jy*jz/rho0) + 0.5*alpha*C*ny*nz - m14);
		m15 = m15 + rlx_setA*( (jx*jz/rho0) + 0.5*alpha*C*nx*nz - 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[nr2] = 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[nr1] = 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[nr4] = 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[nr3] = 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[nr6] = 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[nr5] = 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[nr8] = 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[nr7] = 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[nr10] = 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[nr9] = 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[nr12] = 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[nr11]= 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[nr14] = 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[nr13] = 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;

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

		// Instantiate mass transport distributions
		// Stationary value - distribution 0
		nAB = 1.0/(nA+nB);
		Aq[n] = 0.3333333333333333*nA;
		Bq[n] = 0.3333333333333333*nB;

		//...............................................
		// q = 0,2,4
		// Cq = {1,0,0}, {0,1,0}, {0,0,1}
		delta = beta*nA*nB*nAB*0.1111111111111111*nx;
		if (!(nA*nB*nAB>0)) delta=0;
		a1 = nA*(0.1111111111111111*(1+4.5*ux))+delta;
		b1 = nB*(0.1111111111111111*(1+4.5*ux))-delta;
		a2 = nA*(0.1111111111111111*(1-4.5*ux))-delta;
		b2 = nB*(0.1111111111111111*(1-4.5*ux))+delta;

		// q = 1
		//nread = neighborList[n+Np];
		Aq[nr2] = a1;
		Bq[nr2] = b1;
		// q=2
		//nread = neighborList[n];
		Aq[nr1] = a2;
		Bq[nr1] = b2;

		//...............................................
		// Cq = {0,1,0}
		delta = beta*nA*nB*nAB*0.1111111111111111*ny;
		if (!(nA*nB*nAB>0)) delta=0;
		a1 = nA*(0.1111111111111111*(1+4.5*uy))+delta;
		b1 = nB*(0.1111111111111111*(1+4.5*uy))-delta;
		a2 = nA*(0.1111111111111111*(1-4.5*uy))-delta;
		b2 = nB*(0.1111111111111111*(1-4.5*uy))+delta;

		// q = 3
		//nread = neighborList[n+3*Np];
		Aq[nr4] = a1;
		Bq[nr4] = b1;
		// q = 4
		//nread = neighborList[n+2*Np];
		Aq[nr3] = a2;
		Bq[nr3] = b2;

		//...............................................
		// q = 4
		// Cq = {0,0,1}
		delta = beta*nA*nB*nAB*0.1111111111111111*nz;
		if (!(nA*nB*nAB>0)) delta=0;
		a1 = nA*(0.1111111111111111*(1+4.5*uz))+delta;
		b1 = nB*(0.1111111111111111*(1+4.5*uz))-delta;
		a2 = nA*(0.1111111111111111*(1-4.5*uz))-delta;
		b2 = nB*(0.1111111111111111*(1-4.5*uz))+delta;

		// q = 5
		//nread = neighborList[n+5*Np];
		Aq[nr6] = a1;
		Bq[nr6] = b1;
		// q = 6
		//nread = neighborList[n+4*Np];
		Aq[nr5] = a2;
		Bq[nr5] = b2;
		//...............................................
	}	
}

extern "C" void ScaLBL_D3Q7_AAodd_DFH(int *neighborList, double *Aq, double *Bq, 
			double *Den, double *Phi, int start, int finish, int Np){

	int idx,n,nread;
	double fq,nA,nB;

	for (int n=start; n<finish; n++){
		
		//..........Compute the number density for component A............
		// q=0
		fq = Aq[n];
		nA = fq;

		// q=1
		nread = neighborList[n]; 
		fq = Aq[nread];
		nA += fq;
		
		// q=2
		nread = neighborList[n+Np]; 
		fq = Aq[nread];  
		nA += fq;

		// q=3
		nread = neighborList[n+2*Np]; 
		fq = Aq[nread];
		nA += fq;

		// q = 4
		nread = neighborList[n+3*Np]; 
		fq = Aq[nread];
		nA += fq;

		// q=5
		nread = neighborList[n+4*Np];
		fq = Aq[nread];
		nA += fq;

		// q = 6
		nread = neighborList[n+5*Np];
		fq = Aq[nread];
		nA += fq;
		
		//..........Compute the number density for component B............
		// q=0
		fq = Bq[n];
		nB = fq;

		// q=1
		nread = neighborList[n];
		fq = Bq[nread]; 
		nB += fq;
		
		// q=2
		nread = neighborList[n+Np]; 
		fq = Bq[nread]; 
		nB += fq;

		// q=3
		nread = neighborList[n+2*Np];
		fq = Bq[nread];
		nB += fq;

		// q = 4
		nread = neighborList[n+3*Np]; 
		fq = Bq[nread];
		nB += fq;

		// q=5
		nread = neighborList[n+4*Np];
		fq = Bq[nread];
		nB += fq;

		// q = 6
		nread = neighborList[n+5*Np];
		fq = Bq[nread];
		nB += fq;
		
		// save the number densities
		Den[n] = nA;
		Den[Np+n] = nB;
		
		// save the phase indicator field
		//idx = Map[n];
		Phi[n] = (nA-nB)/(nA+nB); 
	}
}

extern "C" void ScaLBL_D3Q7_AAeven_DFH(double *Aq, double *Bq, double *Den, double *Phi, 
			int start, int finish, int Np){
	int idx,n,nread;
	double fq,nA,nB;
	for (int n=start; n<finish; n++){
		
		// compute number density for component A
		// q=0
		fq = Aq[n];
		nA = fq;
		
		// q=1
		fq = Aq[2*Np+n];
		nA += fq;

		// f2 = Aq[10*Np+n];
		fq = Aq[1*Np+n];
		nA += fq;

		// q=3
		fq = Aq[4*Np+n];
		nA += fq;

		// q = 4
		fq = Aq[3*Np+n];
		nA += fq;

		// q=5
		fq = Aq[6*Np+n];
		nA += fq;

		// q = 6
		fq = Aq[5*Np+n];
		nA += fq;

		// compute number density for component B
		// q=0
		fq = Bq[n];
		nB = fq;
		
		// q=1
		fq = Bq[2*Np+n];
		nB += fq;

		// f2 = Bq[10*Np+n];
		fq = Bq[1*Np+n];
		nB += fq;

		// q=3
		fq = Bq[4*Np+n];
		nB += fq;

		// q = 4
		fq = Bq[3*Np+n];
		nB += fq;

		// q=5
		fq = Bq[6*Np+n];
		nB += fq;

		// q = 6
		fq = Bq[5*Np+n];
		nB += fq;

		// save the number densities
		Den[n] = nA;
		Den[Np+n] = nB;
		
		// save the phase indicator field
		//idx = Map[n];
		Phi[n] = (nA-nB)/(nA+nB); 	
	}	
}

extern "C" void ScaLBL_D3Q19_Gradient_DFH(int *neighborList, double *Phi, double *ColorGrad, int start, int finish, int Np){
	
	int n,nn;
	// distributions
	double m1,m2,m4,m6,m8,m9,m10,m11,m12,m13,m14,m15,m16,m17,m18;
	double m3,m5,m7;
	double nx,ny,nz;

	// non-conserved moments
	// additional variables needed for computations

	for (n=start; n<finish; n++){
		nn = neighborList[n+Np]%Np;
		m1 = Phi[nn];
		nn = neighborList[n]%Np;
		m2 = Phi[nn];
		nn = neighborList[n+3*Np]%Np;
		m3 = Phi[nn];
		nn = neighborList[n+2*Np]%Np;
		m4 = Phi[nn];		
		nn = neighborList[n+5*Np]%Np;
		m5 = Phi[nn];
		nn = neighborList[n+4*Np]%Np;
		m6 = Phi[nn];		
		nn = neighborList[n+7*Np]%Np;
		m7 = Phi[nn];
		nn = neighborList[n+6*Np]%Np;
		m8 = Phi[nn];		
		nn = neighborList[n+9*Np]%Np;
		m9 = Phi[nn];
		nn = neighborList[n+8*Np]%Np;
		m10 = Phi[nn];		
		nn = neighborList[n+11*Np]%Np;
		m11 = Phi[nn];
		nn = neighborList[n+10*Np]%Np;
		m12 = Phi[nn];		
		nn = neighborList[n+13*Np]%Np;
		m13 = Phi[nn];
		nn = neighborList[n+12*Np]%Np;
		m14 = Phi[nn];		
		nn = neighborList[n+15*Np]%Np;
		m15 = Phi[nn];
		nn = neighborList[n+14*Np]%Np;
		m16 = Phi[nn];		
		nn = neighborList[n+17*Np]%Np;
		m17 = Phi[nn];
		nn = neighborList[n+16*Np]%Np;
		m18 = Phi[nn];					
		
		//............Compute the Color Gradient...................................
		//............Compute the wn fluid Gradient...................................
		nx = (m1-m2+0.5*(m7-m8+m9-m10+m11-m12+m13-m14));
		ny = (m3-m4+0.5*(m7-m8-m9+m10+m15-m16+m17-m18));
		nz = (m5-m6+0.5*(m11-m12-m13+m14+m15-m16-m17+m18));
		
		//...........Normalize the Color Gradient.................................
		//	C = sqrt(nx*nx+ny*ny+nz*nz);
		//	nx = nx/C;
		//	ny = ny/C;
		//	nz = nz/C;
		//...Store the Color Gradient....................
		ColorGrad[n] = nx;
		ColorGrad[Np+n] = ny;
		ColorGrad[2*Np+n] = nz;
		//...............................................
	}
}