Mathc initiation/003d

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	x_sphabr.h

/* --------------------------------- */
/* save as x_sphabr.h                */
/* --------------------------------- */
double spheric_x_dadbdr(

double (*P_f)(double a, double b, double r),

double (*Pa0)(double b, double r),
double (*Pa1)(double b, double r),
   int   na,
   
double    b,
   
double    r
)
{
double a = 0;
   int i = 0;
double m = 0.;
double M = 0.;

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

  a = ((*Pa0)(b,r)) + i*(((*Pa1)(b,r))-((*Pa0)(b,r)))/na;
  
  M += m * (*P_f)(a,b,r) * r*r * sin(b);
 }

  return( ((((*Pa1)(b,r)) -((*Pa0)(b,r)))*M) / (3*na) );
}
/* --------------------------------- */
double spheric_b_dadbdr(
double (*P_f)(double a, double b, double r),
   
double (*Pa0)(double b, double r),
double (*Pa1)(double b, double r),
   int    na,

double (*Pb0)(double r),
double (*Pb1)(double r),
   int    nb,
   
double     r
)
{
   int i = 0;
double m = 0.;
double M = 0.;

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

  M += m * spheric_x_dadbdr(  (*P_f),
                           
                             (*Pa0),
                             (*Pa1),
                               na,
                               
                           (((*Pb0)(r))+i*(((*Pb1)(r))-((*Pb0)(r)))/nb),
                               
                              r);
 }

 return( ((((*Pb1)(r)) -((*Pb0)(r)))*M) / (3*nb) );
}
/* --------------------------------- */
double spheric_dadbdr(
double (*P_f)(double a, double b, double r),
   
double (*Pa0)(double b, double r),
double (*Pa1)(double b, double r),
   int    na,
   
double (*Pb0)(double r),
double (*Pb1)(double r),
   int    nb,

double    r0,
double    r1,
   int    nr
)
{
   int i = 0;
double m = 0.;
double M = 0.;

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

  M += m *  spheric_b_dadbdr((*P_f),
                               
                             (*Pa0),
                             (*Pa1),
                                na,
                             
                             (*Pb0),
                             (*Pb1),
                                nb,
                                
                             (r0+i*(r1-r0)/nr));
 }

  return( ((r1 -r0)*M) / (3*nr) );
}
/* --------------------------------- */
/* --------------------------------- */