/* ---------------------------------- */
/* save as x_xyz.h                   */
/* --------------------------------- */
double intx_dxdydz(
double (*P_f)(double x, double y, double z),
double z,
double y,
double (*Pux)(double y, double z),
double (*Pvx)(double y, double z),
   int nx
)
{
   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 * (*P_f)( ((*Pux)(y,z)) + i*(((*Pvx)(y,z))-((*Pux)(y,z)))/nx, y, z);
 }

  return( ((((*Pvx)(y,z)) -((*Pux)(y,z)))*M) / (3*nx) );
}
/* --------------------------------- */
double inty_dxdydz(
double (*P_f)(double x, double y, double z),
double z,

double (*Psy)(double x),
double (*Pty)(double x),
   int    ny,
   
double (*Pux)(double y, double z),
double (*Pvx)(double y, double z),
   int    nx
)
{
   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 *     intx_dxdydz((*P_f),
                                z,
                           (((*Psy)(z))+i*(((*Pty)(z))-((*Psy)(z)))/ny),
                           
                             (*Pux),
                             (*Pvx),
                               nx);
 }

 return( ((((*Pty)(z)) -((*Psy)(z)))*M) / (3*ny) );
}
/* --------------------------------- */
double sympson_dxdydz(
double (*P_f)(double x, double y, double z),

double az,
double bz,
   int nz,
   
double (*Psy)(double x),
double (*Pty)(double x),
   int    ny,
   
double (*Pux)(double y, double z),
double (*Pvx)(double y, double z),
   int    nx
)
{
   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 *       inty_dxdydz((*P_f),
                             (az+i*(bz-az)/nz),
                             
                             (*Psy),
                             (*Pty),
                                ny,
                               
                             (*Pux),
                             (*Pvx),
                                nx);
 }

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