File: PhiF.c

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/**********************************************************************
  PhiF.c:

    PhiF.c is a subroutine to calculate the value of a radial function  
    at R.

  Log of PhiF.c:

     7/Apr/2004  Released by T.Ozaki

***********************************************************************/

double PhiF(double R, double *phi0, double *MRV, int Grid_Num)
{
  int mp_min,mp_max,m,po;
  double h1,h2,h3,f1,f2,f3,f4;
  double g1,g2,x1,x2,y1,y2,f,df;
  double a,b,rm,y12,y22,result;

  mp_min = 0;
  mp_max = Grid_Num - 1;
  po = 0;

  if (MRV[Grid_Num-1]<R){
    result = 0.0;
    po = 1;
  }
  else if (R<MRV[0]){

    po = 1;
    m = 4;
    rm = MRV[m];

    h1 = MRV[m-1] - MRV[m-2];
    h2 = MRV[m]   - MRV[m-1];
    h3 = MRV[m+1] - MRV[m];

    f1 = phi0[m-2];
    f2 = phi0[m-1];
    f3 = phi0[m];
    f4 = phi0[m+1];

    g1 = ((f3-f2)*h1/h2 + (f2-f1)*h2/h1)/(h1+h2);
    g2 = ((f4-f3)*h2/h3 + (f3-f2)*h3/h2)/(h2+h3);

    x1 = rm - MRV[m-1];
    x2 = rm - MRV[m];
    y1 = x1/h2;
    y2 = x2/h2;
    y12 = y1*y1;
    y22 = y2*y2;

    f =  y22*(3.0*f2 + h2*g1 + (2.0*f2 + h2*g1)*y2)
       + y12*(3.0*f3 - h2*g2 - (2.0*f3 - h2*g2)*y1);

    df = 2.0*y2/h2*(3.0*f2 + h2*g1 + (2.0*f2 + h2*g1)*y2)
       + y22*(2.0*f2 + h2*g1)/h2
       + 2.0*y1/h2*(3.0*f3 - h2*g2 - (2.0*f3 - h2*g2)*y1)
       - y12*(2.0*f3 - h2*g2)/h2;

    a = 0.5*df/rm;
    b = f - a*rm*rm;      
    result = a*R*R + b;
  }

  else{
    do{
      m = (mp_min + mp_max)/2;
      if (MRV[m]<R)
        mp_min = m;
      else 
        mp_max = m;
    }
    while((mp_max-mp_min)!=1);
    m = mp_max;

    if (m<2)
      m = 2;
    else if (Grid_Num<=m)
      m = Grid_Num - 2;
  }
  
  /****************************************************
                 Spline like interpolation
  ****************************************************/

  if (po==0){

    h1 = MRV[m-1] - MRV[m-2];
    h2 = MRV[m]   - MRV[m-1];
    h3 = MRV[m+1] - MRV[m];

    f1 = phi0[m-2];
    f2 = phi0[m-1];
    f3 = phi0[m];
    f4 = phi0[m+1];

    /****************************************************
                   Treatment of edge points
    ****************************************************/

    if (m==1){
      h1 = -(h2+h3);
      f1 = f4;
    }
    if (m==(Grid_Num-1)){
      h3 = -(h1+h2);
      f4 = f1;
    }

    /****************************************************
                 Calculate the value at R
    ****************************************************/

    g1 = ((f3-f2)*h1/h2 + (f2-f1)*h2/h1)/(h1+h2);
    g2 = ((f4-f3)*h2/h3 + (f3-f2)*h3/h2)/(h2+h3);

    x1 = R - MRV[m-1];
    x2 = R - MRV[m];
    y1 = x1/h2;
    y2 = x2/h2;

    f =  y2*y2*(3.0*f2 + h2*g1 + (2.0*f2 + h2*g1)*y2)
       + y1*y1*(3.0*f3 - h2*g2 - (2.0*f3 - h2*g2)*y1);

    result = f;
  }

  return result;
}