G4GaussJacobiQ.cc

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// $Id: G4GaussJacobiQ.cc 67970 2013-03-13 10:10:06Z gcosmo $
//
#include "G4GaussJacobiQ.hh"


// -------------------------------------------------------------
//
// Constructor for Gauss-Jacobi integration method. 
//

G4GaussJacobiQ::G4GaussJacobiQ(       function pFunction,
                                      G4double alpha,
                                      G4double beta, 
                                      G4int nJacobi           ) 
   : G4VGaussianQuadrature(pFunction)

{
  const G4double tolerance = 1.0e-12 ;
  const G4double maxNumber = 12 ;
  G4int i=1, k=1 ;
  G4double root=0.;
  G4double alphaBeta=0.0, alphaReduced=0.0, betaReduced=0.0,
           root1=0.0, root2=0.0, root3=0.0 ;
  G4double a=0.0, b=0.0, c=0.0,
           newton1=0.0, newton2=0.0, newton3=0.0, newton0=0.0,
           temp=0.0, rootTemp=0.0 ;

  fNumber   = nJacobi ;
  fAbscissa = new G4double[fNumber] ;
  fWeight   = new G4double[fNumber] ;

  for (i=1;i<=nJacobi;i++)
  {
     if (i == 1)
     {
        alphaReduced = alpha/nJacobi ;
        betaReduced = beta/nJacobi ;
        root1 = (1.0+alpha)*(2.78002/(4.0+nJacobi*nJacobi)+
              0.767999*alphaReduced/nJacobi) ;
        root2 = 1.0+1.48*alphaReduced+0.96002*betaReduced
              + 0.451998*alphaReduced*alphaReduced
              + 0.83001*alphaReduced*betaReduced ;
        root  = 1.0-root1/root2 ;
     } 
     else if (i == 2)
     {
        root1=(4.1002+alpha)/((1.0+alpha)*(1.0+0.155998*alpha)) ;
        root2=1.0+0.06*(nJacobi-8.0)*(1.0+0.12*alpha)/nJacobi ;
        root3=1.0+0.012002*beta*(1.0+0.24997*std::fabs(alpha))/nJacobi ;
        root -= (1.0-root)*root1*root2*root3 ;
     } 
     else if (i == 3) 
     {
        root1=(1.67001+0.27998*alpha)/(1.0+0.37002*alpha) ;
        root2=1.0+0.22*(nJacobi-8.0)/nJacobi ;
        root3=1.0+8.0*beta/((6.28001+beta)*nJacobi*nJacobi) ;
        root -= (fAbscissa[0]-root)*root1*root2*root3 ;
     }
     else if (i == nJacobi-1)
     {
        root1=(1.0+0.235002*beta)/(0.766001+0.118998*beta) ;
        root2=1.0/(1.0+0.639002*(nJacobi-4.0)/(1.0+0.71001*(nJacobi-4.0))) ;
        root3=1.0/(1.0+20.0*alpha/((7.5+alpha)*nJacobi*nJacobi)) ;
        root += (root-fAbscissa[nJacobi-4])*root1*root2*root3 ;
     } 
     else if (i == nJacobi) 
     {
        root1 = (1.0+0.37002*beta)/(1.67001+0.27998*beta) ;
        root2 = 1.0/(1.0+0.22*(nJacobi-8.0)/nJacobi) ;
        root3 = 1.0/(1.0+8.0*alpha/((6.28002+alpha)*nJacobi*nJacobi)) ;
        root += (root-fAbscissa[nJacobi-3])*root1*root2*root3 ;
     } 
     else
     {
        root = 3.0*fAbscissa[i-2]-3.0*fAbscissa[i-3]+fAbscissa[i-4] ;
     }
     alphaBeta = alpha + beta ;
     for (k=1;k<=maxNumber;k++)
     {
        temp = 2.0 + alphaBeta ;
        newton1 = (alpha-beta+temp*root)/2.0 ;
        newton2 = 1.0 ;
        for (G4int j=2;j<=nJacobi;j++)
        {
           newton3 = newton2 ;
           newton2 = newton1 ;
           temp = 2*j+alphaBeta ;
           a = 2*j*(j+alphaBeta)*(temp-2.0) ;
           b = (temp-1.0)*(alpha*alpha-beta*beta+temp*(temp-2.0)*root) ;
           c = 2.0*(j-1+alpha)*(j-1+beta)*temp ;
           newton1 = (b*newton2-c*newton3)/a ;
        }
        newton0 = (nJacobi*(alpha - beta - temp*root)*newton1 +
               2.0*(nJacobi + alpha)*(nJacobi + beta)*newton2)/
              (temp*(1.0 - root*root)) ;
        rootTemp = root ;
        root = rootTemp - newton1/newton0 ;
        if (std::fabs(root-rootTemp) <= tolerance)
        {
           break ;
        }
     }
     if (k > maxNumber) 
     {
        G4Exception("G4GaussJacobiQ::G4GaussJacobiQ()", "OutOfRange",
                    FatalException, "Too many iterations in constructor.") ;
     }
     fAbscissa[i-1] = root ;
     fWeight[i-1] = std::exp(GammaLogarithm((G4double)(alpha+nJacobi)) + 
                        GammaLogarithm((G4double)(beta+nJacobi)) - 
                        GammaLogarithm((G4double)(nJacobi+1.0)) -
                        GammaLogarithm((G4double)(nJacobi + alphaBeta + 1.0)))
                        *temp*std::pow(2.0,alphaBeta)/(newton0*newton2) ;
  }
}


// ----------------------------------------------------------
//
// Gauss-Jacobi method for integration of
// ((1-x)^alpha)*((1+x)^beta)*pFunction(x)
// from minus unit to plus unit .


G4double 
G4GaussJacobiQ::Integral() const 
{
   G4double integral = 0.0 ;
   for(G4int i=0;i<fNumber;i++)
   {
      integral += fWeight[i]*fFunction(fAbscissa[i]) ;
   }
   return integral ;
}