/* ---------------------------------- */
/* save as x_gdxdy.h                   */
/* ---------------------------------- */
double gint_dx(
double (*P_M)(double x, double y),
double (*P_N)(double x, double y),
double (*P_u)(double y),
double (*P_v)(double y),
   int n,
double y,
double h
)
{
   int i = 0;
double m = 0.;
double M = 0.;

double tx = 0;
double ty = 0;

 for(i = 0; i <= n; i++)
 {
       if(i ==0 || i== n){m = 1.;}
  else if(fmod(i,2) == 0){m = 2.;}
  else                   {m = 4.;}
  
  tx = ( ((*P_u)(y)) + i*(((*P_v)(y))-((*P_u)(y)))/n );
  ty = y;  

  M += m * (fxy_x((*P_N),tx,ty,h) -
            fxy_y((*P_M),tx,ty,h) );
 }

  return( ((((*P_v)(y)) -((*P_u)(y)))*M) / (3*n) );
}
/* ---------------------------------- */
double green_dxdy(
double (*P_M)(double x, double y),
double (*P_N)(double x, double y),

double (*P_u)(double y),
double (*P_v)(double y),
   int n,
double ay,
double by,
   int ny,
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 * gint_dx((*P_M),(*P_N), (*P_u),(*P_v),n,(ay+i*(by-ay)/ny),h);
 }

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