/* ---------------------------------- */
/* save as x_fluzxy.h                   */
/* --------------------------------- */
double flux_z_dzdxdy(
double (*P_M)(double x, double y, double z),
double (*P_N)(double x, double y, double z),
double (*P_P)(double x, double y, double z),
double y,
double x,
double (*P_u)(double x, double y),
double (*P_v)(double x, double y),
   int nz,
double h
)
{
pt3d n;
   int i = 0;
double m = 0.;
double M = 0.;

 for(i = 0; i <= nz; i++)
 {
       if(i ==0 || i== nz){m = 1.;}
  else if(fmod(i,2) == 0){m = 2.;}
  else                   {m = 4.;}

          n.x = x;
          n.y = y;
          n.z = ((*P_u)(x,y)) + i*(((*P_v)(x,y))-((*P_u)(x,y)))/nz;

  M += m *  (fxyz_x((*P_M),n,h) + fxyz_y((*P_N),n,h) + fxyz_z((*P_P),n,h)) ;
 }

  return( ((((*P_v)(x,y)) -((*P_u)(x,y)))*M) / (3*nz) );
}
/* --------------------------------- */
double flux_x_dzdxdy(
double (*P_M)(double x, double y, double z),
double (*P_N)(double x, double y, double z),
double (*P_P)(double x, double y, double z),
double y,
double (*P_s)(double y),
double (*P_t)(double y),
   int nx,
double (*P_u)(double x, double y),
double (*P_v)(double x, double y),
   int nz,
double h
)
{
   int i = 0;
double m = 0.;
double M = 0.;

 for(i = 0; i <= nx; i++)
 {
       if(i ==0 || i== nx){m = 1.;}
  else if(fmod(i,2) == 0){m = 2.;}
  else                   {m = 4.;}

  M += m * flux_z_dzdxdy(
                             (*P_M),
                             (*P_N),
                             (*P_P),
                                y,
                           (((*P_s)(y))+i*(((*P_t)(y))-((*P_s)(y)))/nx),
                             (*P_u),
                             (*P_v),
                               nz,
                               h
                               );
 }

 return( ((((*P_t)(y)) -((*P_s)(y)))*M) / (3*nx) );
}
/* --------------------------------- */
double flux_dzdxdy(
double (*P_M)(double x, double y, double z),
double (*P_N)(double x, double y, double z),
double (*P_P)(double x, double y, double z),
double ay,
double by,
   int ny,
double (*P_s)(double y),
double (*P_t)(double y),
   int nx,
double (*P_u)(double x, double y),
double (*P_v)(double x, double y),
   int nz,
double h
)
{
   int i = 0;
double m = 0.;
double M = 0.;

 for(i = 0; i <= ny; i++)
 {
       if(i ==0 || i== ny){m = 1.;}
  else if(fmod(i,2) == 0){m = 2.;}
  else                   {m = 4.;}

 M += m * flux_x_dzdxdy(
                             (*P_M),
                             (*P_N),
                             (*P_P),
                             (ay+i*(by-ay)/ny),
                             (*P_s),
                             (*P_t),
                               nx,
                             (*P_u),
                             (*P_v),
                               nz,
                               h);
 }

  return( ((by -ay)*M) / (3*ny) );
}
/* --------------------------------- */
/* --------------------------------- */