G4GaussJacobiQ Class Reference

#include <G4GaussJacobiQ.hh>

Inheritance diagram for G4GaussJacobiQ:

Public Member Functions
	G4GaussJacobiQ (function pFunction, G4double alpha, G4double beta, G4int nJacobi)
G4double	Integral () const
Public Member Functions inherited from G4VGaussianQuadrature
	G4VGaussianQuadrature (function pFunction)
virtual	~G4VGaussianQuadrature ()
G4double	GetAbscissa (G4int index) const
G4double	GetWeight (G4int index) const
G4int	GetNumber () const

Additional Inherited Members
Protected Member Functions inherited from G4VGaussianQuadrature
G4double	GammaLogarithm (G4double xx)
Protected Attributes inherited from G4VGaussianQuadrature
function	fFunction
G4double *	fAbscissa
G4double *	fWeight
G4int	fNumber

Detailed Description

Definition at line 62 of file G4GaussJacobiQ.hh.

Constructor & Destructor Documentation

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

Definition at line 37 of file G4GaussJacobiQ.cc.

References test::a, test::b, test::c, G4VGaussianQuadrature::fAbscissa, FatalException, G4VGaussianQuadrature::fNumber, G4VGaussianQuadrature::fWeight, G4Exception(), and G4VGaussianQuadrature::GammaLogarithm().

   : 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) ;
  }
}

Member Function Documentation

G4double G4GaussJacobiQ::Integral

(

)

const

Definition at line 152 of file G4GaussJacobiQ.cc.

References G4VGaussianQuadrature::fAbscissa, G4VGaussianQuadrature::fFunction, G4VGaussianQuadrature::fNumber, and G4VGaussianQuadrature::fWeight.

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

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The documentation for this class was generated from the following files:

• G4GaussJacobiQ.hh
• G4GaussJacobiQ.cc