/* ---------------------------------- */
/* save as x_fdydz                   */
/* ---------------------------------- */
double   fint_dyz(
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 (*P_k)(double y, double z),
double (*P_u)(double z),
double (*P_v)(double z),
   int ny,
   
double z,

double h
)
{
p2d   p;

   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.;}

        p.x = ((*P_u)(z)) + i*(((*P_v)(z))-((*P_u)(z)))/ny;
        p.y = z;        

  M += m * (
                              1*(*P_M)( (*P_k)(p.x,p.y),p.x,p.y)+ 
             -fxy_x((*P_k),h,p)*(*P_N)( (*P_k)(p.x,p.y),p.x,p.y)+ 
             -fxy_y((*P_k),h,p)*(*P_P)( (*P_k)(p.x,p.y),p.x,p.y)
            );
 }

  return( ((((*P_v)(z)) -((*P_u)(z)))*M) / (3*ny) );
}
/* ---------------------------------- */
double flux_dydz(
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 (*P_k)(double y, double z),
double (*P_u)(double z),
double (*P_v)(double z),
   int ny,
   
double az,
double bz,
   int nz,
   
double h
)
{
   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.;}

  M += m * fint_dyz( (*P_M),(*P_N),(*P_P),
                     (*P_k), (*P_u),(*P_v),
                      ny,
                     (az + i*(bz-az)/nz),
                      h);
 }

  return( ((bz -az)*M) / (3*nz) );
}
/* ---------------------------------- */
/* ---------------------------------- */