Mathc initiation/0030

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	x_jvwu.h

/* -------------------------------- */
/* save as x_jvwu.h                 */
/* -------------------------------- */
double Jv_vwu(
double (*P_f)(double x, double y, double z),

double (*P_X)(double u, double v, double w),
double (*P_Y)(double u, double v, double w),
double (*P_Z)(double u, double v, double w),

double (*Pv0)(double u, double w),
double (*Pv1)(double u, double w),
   int   nv,

double w,

double u
)
{
pt3d   p;

double v = 0;

   int i = 0;
double m = 0.;
double M = 0.;

 for(i = 0; i <= nv; i++)
 {
       if(i ==0 || i== nv){m = 1.;}
  else if(fmod(i,2) ==  0){m = 2.;}
  else                    {m = 4.;}
  
  v = ((*Pv0)(u,w)) + i*(((*Pv1)(u,w))-((*Pv0)(u,w)))/nv;
  
  p.x = u;
  p.y = v;   
  p.z = w;    
     
  M += m * (*P_f)( ((*P_X)(u,v,w)), 
                   ((*P_Y)(u,v,w)), 
                   ((*P_Z)(u,v,w)))
                          *
                   /* Jacobian */   
                      
                    fabs(
                    
              fxyz_x((*P_X),H,p) 
                       * 
   ( fxyz_y((*P_Y),H,p)*fxyz_z((*P_Z),H,p)
                       -
     fxyz_z((*P_Y),H,p)*fxyz_y((*P_Z),H,p) ) 
     
                       - 
                                       
              fxyz_y((*P_X),H,p) 
                       * 
   ( fxyz_x((*P_Y),H,p)*fxyz_z((*P_Z),H,p)
                       -
     fxyz_z((*P_Y),H,p)*fxyz_x((*P_Z),H,p) )
     
                       + 
                                       
              fxyz_z((*P_X),H,p) 
                       * 
   ( fxyz_x((*P_Y),H,p)*fxyz_y((*P_Z),H,p)
                       -
     fxyz_y((*P_Y),H,p)*fxyz_x((*P_Z),H,p) )
                        );
 }

  return( ((((*Pv1)(u,w)) -((*Pv0)(u,w)))*M) / (3*nv) );
}
/* --------------------------------- */
double Jw_vwu(
double (*P_f)(double x, double y, double z),

double (*P_X)(double u, double v, double w),
double (*P_Y)(double u, double v, double w),
double (*P_Z)(double u, double v, double w),
   
double (*Pv0)(double u, double w),
double (*Pv1)(double u, double w),
   int   nv,

double (*Pw0)(double u),
double (*Pw1)(double u),
   int   nw,

double u
)
{
   int i = 0;
double m = 0.;
double M = 0.;

 for(i = 0; i <= nw; i++)
 {
       if(i ==0 || i== nw){m = 1.;}
  else if(fmod(i,2) ==  0){m = 2.;}
  else                    {m = 4.;}
               
  M += m * Jv_vwu( (*P_f),
                    (*P_X),(*P_Y),(*P_Z),                           
                    (*Pv0),(*Pv1),nv,
                    (((*Pw0)(u))+i*(((*Pw1)(u))-((*Pw0)(u)))/nw),
                             u);
 }

 return( ((((*Pw1)(u)) -((*Pw0)(u)))*M) / (3*nw) );
}
/* --------------------------------- */
double J_vwu(
double (*P_f)(double x, double y, double z),

double (*P_X)(double u, double v, double w),
double (*P_Y)(double u, double v, double w),
double (*P_Z)(double u, double v, double w),
   
double (*Pv0)(double u, double w),
double (*Pv1)(double u, double w),
   int   nv,
   
double (*Pw0)(double u),
double (*Pw1)(double u),
   int   nw,

double u0,
double u1,
   int nu
)
{
   int i = 0;
double m = 0.;
double M = 0.;

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

  M += m * Jw_vwu( (*P_f),
                    (*P_X),(*P_Y),(*P_Z),                                
                    (*Pv0),(*Pv1),nv,
                    (*Pw0),(*Pw1),nw,
                    (u0+i*(u1-u0)/nu));
 }

  return( ((u1 -u0)*M) / (3*nu) );
}
/* --------------------------------- */
/* --------------------------------- */