/* ---------------------------------- */
/* save as x_xzy.h                   */
/* --------------------------------- */
double intx_dxdzdy(
double (*P_f)(double x, double y, double z),
double y,
double z,

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                {m = 2.;}

  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) / (2*nx) );
}
/* --------------------------------- */
double intz_dxdzdy(
double (*P_f)(double x, double y, double z),
double y,

double (*Psz)(double x),
double (*Ptz)(double x),
   int    nz,
   
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                {m = 2.;}

M += m *      intx_dxdzdy((*P_f),
                                  y,
                           (((*Psz)(y))+i*(((*Ptz)(y))-((*Psz)(y)))/nz),
                             (*Pux),
                             (*Pvx),
                               nx);
 }

  return( ((((*Ptz)(y)) -((*Psz)(y)))*M) / (2*nz) );
}
/* --------------------------------- */
double trapezoid_dxdzdy(
double (*P_f)(double x, double y, double z),

double ay,
double by,
   int ny,
   
double (*Psz)(double x),
double (*Ptz)(double x),
   int    nz,
   
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                {m = 2.;}

M += m * intz_dxdzdy(        (*P_f),
                             (ay+i*(by-ay)/ny),
                             
                             (*Psz),
                             (*Ptz),
                                 nz,
                                 
                             (*Pux),
                             (*Pvx),
                               nx);
 }

  return( ((by -ay)*M) / (2*ny) );
}
/* --------------------------------- */