G4GaussLaguerreQ Class Reference

#include <G4GaussLaguerreQ.hh>

Inheritance diagram for G4GaussLaguerreQ:

Public Member Functions
	G4GaussLaguerreQ (const G4GaussLaguerreQ &)=delete
	G4GaussLaguerreQ (function pFunction, G4double alpha, G4int nLaguerre)
G4double	GetAbscissa (G4int index) const
G4int	GetNumber () const
G4double	GetWeight (G4int index) const
G4double	Integral () const
G4GaussLaguerreQ &	operator= (const G4GaussLaguerreQ &)=delete

Protected Member Functions
G4double	GammaLogarithm (G4double xx)

Protected Attributes
G4double *	fAbscissa = nullptr
function	fFunction
G4int	fNumber = 0
G4double *	fWeight = nullptr

Detailed Description

Definition at line 44 of file G4GaussLaguerreQ.hh.

Constructor & Destructor Documentation

G4GaussLaguerreQ() [1/2]

G4GaussLaguerreQ::G4GaussLaguerreQ	(	function	pFunction,
		G4double	alpha,
		G4int	nLaguerre
	)

Definition at line 42 of file G4GaussLaguerreQ.cc.

  : G4VGaussianQuadrature(pFunction)
{
  const G4double tolerance = 1.0e-10;
  const G4int maxNumber    = 12;
  G4int i = 1, k = 1;
  G4double newton0 = 0.0, newton1 = 0.0, temp1 = 0.0, temp2 = 0.0, temp3 = 0.0,
           temp = 0.0, cofi = 0.0;
 
  fNumber   = nLaguerre;
  fAbscissa = new G4double[fNumber];
  fWeight   = new G4double[fNumber];
 
  for(i = 1; i <= fNumber; ++i)  // Loop over the desired roots
  {
    if(i == 1)
    {
      newton0 = (1.0 + alpha) * (3.0 + 0.92 * alpha) /
                (1.0 + 2.4 * fNumber + 1.8 * alpha);
    }
    else if(i == 2)
    {
      newton0 += (15.0 + 6.25 * alpha) / (1.0 + 0.9 * alpha + 2.5 * fNumber);
    }
    else
    {
      cofi = i - 2;
      newton0 += ((1.0 + 2.55 * cofi) / (1.9 * cofi) +
                  1.26 * cofi * alpha / (1.0 + 3.5 * cofi)) *
                 (newton0 - fAbscissa[i - 3]) / (1.0 + 0.3 * alpha);
    }
    for(k = 1; k <= maxNumber; ++k)
    {
      temp1 = 1.0;
      temp2 = 0.0;
      for(G4int j = 1; j <= fNumber; ++j)
      {
        temp3 = temp2;
        temp2 = temp1;
        temp1 =
          ((2 * j - 1 + alpha - newton0) * temp2 - (j - 1 + alpha) * temp3) / j;
      }
      temp    = (fNumber * temp1 - (fNumber + alpha) * temp2) / newton0;
      newton1 = newton0;
      newton0 = newton1 - temp1 / temp;
      if(std::fabs(newton0 - newton1) <= tolerance)
      {
        break;
      }
    }
    if(k > maxNumber)
    {
      G4Exception("G4GaussLaguerreQ::G4GaussLaguerreQ()", "OutOfRange",
                  FatalException,
                  "Too many iterations in Gauss-Laguerre constructor");
    }
 
    fAbscissa[i - 1] = newton0;
    fWeight[i - 1]   = -std::exp(GammaLogarithm(alpha + fNumber) -
                               GammaLogarithm((G4double) fNumber)) /
                     (temp * fNumber * temp2);
  }
}

References alpha, G4VGaussianQuadrature::fAbscissa, FatalException, G4VGaussianQuadrature::fNumber, G4VGaussianQuadrature::fWeight, G4Exception(), and G4VGaussianQuadrature::GammaLogarithm().

G4GaussLaguerreQ() [2/2]

G4GaussLaguerreQ::G4GaussLaguerreQ ( const G4GaussLaguerreQ &  )

delete

Member Function Documentation

GammaLogarithm()

G4double G4VGaussianQuadrature::GammaLogarithm ( G4double  xx )

protectedinherited

Definition at line 70 of file G4VGaussianQuadrature.cc.

{
  // Returns the value ln(Gamma(xx) for xx > 0.  Full accuracy is obtained for
  // xx > 1. For 0 < xx < 1. the reflection formula (6.1.4) can be used first.
  // (Adapted from Numerical Recipes in C)
 
  static const G4double cof[6] = { 76.18009172947146,     -86.50532032941677,
                                   24.01409824083091,     -1.231739572450155,
                                   0.1208650973866179e-2, -0.5395239384953e-5 };
  G4double x                   = xx - 1.0;
  G4double tmp                 = x + 5.5;
  tmp -= (x + 0.5) * std::log(tmp);
  G4double ser = 1.000000000190015;
 
  for(size_t j = 0; j <= 5; ++j)
  {
    x += 1.0;
    ser += cof[j] / x;
  }
  return -tmp + std::log(2.5066282746310005 * ser);
}

Referenced by G4GaussJacobiQ::G4GaussJacobiQ(), and G4GaussLaguerreQ().

GetAbscissa()

G4double G4VGaussianQuadrature::GetAbscissa ( G4int  index ) const

inherited

Definition at line 53 of file G4VGaussianQuadrature.cc.

{
  return fAbscissa[index];
}

References G4VGaussianQuadrature::fAbscissa.

GetNumber()

G4int G4VGaussianQuadrature::GetNumber ( ) const

inherited

Definition at line 63 of file G4VGaussianQuadrature.cc.

{ return fNumber; }

References G4VGaussianQuadrature::fNumber.

GetWeight()

G4double G4VGaussianQuadrature::GetWeight ( G4int  index ) const

inherited

Definition at line 58 of file G4VGaussianQuadrature.cc.

{
  return fWeight[index];
}

References G4VGaussianQuadrature::fWeight.

Integral()

G4double G4GaussLaguerreQ::Integral

(

)

const

Definition at line 115 of file G4GaussLaguerreQ.cc.

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

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

operator=()

G4GaussLaguerreQ & G4GaussLaguerreQ::operator= ( const G4GaussLaguerreQ &  )

delete

Field Documentation

fAbscissa

G4double* G4VGaussianQuadrature::fAbscissa = nullptr

protectedinherited

Definition at line 71 of file G4VGaussianQuadrature.hh.

Referenced by G4GaussChebyshevQ::G4GaussChebyshevQ(), G4GaussHermiteQ::G4GaussHermiteQ(), G4GaussJacobiQ::G4GaussJacobiQ(), G4GaussLaguerreQ(), G4GaussLegendreQ::G4GaussLegendreQ(), G4VGaussianQuadrature::GetAbscissa(), G4GaussHermiteQ::Integral(), G4GaussJacobiQ::Integral(), Integral(), G4GaussChebyshevQ::Integral(), G4GaussLegendreQ::Integral(), and G4VGaussianQuadrature::~G4VGaussianQuadrature().

fFunction

function G4VGaussianQuadrature::fFunction

protectedinherited

Definition at line 70 of file G4VGaussianQuadrature.hh.

Referenced by G4GaussLegendreQ::AccurateIntegral(), G4GaussHermiteQ::Integral(), G4GaussJacobiQ::Integral(), Integral(), G4GaussChebyshevQ::Integral(), G4GaussLegendreQ::Integral(), and G4GaussLegendreQ::QuickIntegral().

fNumber

G4int G4VGaussianQuadrature::fNumber = 0

protectedinherited

Definition at line 73 of file G4VGaussianQuadrature.hh.

Referenced by G4GaussChebyshevQ::G4GaussChebyshevQ(), G4GaussHermiteQ::G4GaussHermiteQ(), G4GaussJacobiQ::G4GaussJacobiQ(), G4GaussLaguerreQ(), G4GaussLegendreQ::G4GaussLegendreQ(), G4VGaussianQuadrature::GetNumber(), G4GaussHermiteQ::Integral(), G4GaussJacobiQ::Integral(), Integral(), G4GaussChebyshevQ::Integral(), and G4GaussLegendreQ::Integral().

fWeight

G4double* G4VGaussianQuadrature::fWeight = nullptr

protectedinherited

Definition at line 72 of file G4VGaussianQuadrature.hh.

Referenced by G4GaussChebyshevQ::G4GaussChebyshevQ(), G4GaussHermiteQ::G4GaussHermiteQ(), G4GaussJacobiQ::G4GaussJacobiQ(), G4GaussLaguerreQ(), G4GaussLegendreQ::G4GaussLegendreQ(), G4VGaussianQuadrature::GetWeight(), G4GaussHermiteQ::Integral(), G4GaussJacobiQ::Integral(), Integral(), G4GaussChebyshevQ::Integral(), G4GaussLegendreQ::Integral(), and G4VGaussianQuadrature::~G4VGaussianQuadrature().

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

• source/global/HEPNumerics/include/G4GaussLaguerreQ.hh
• source/global/HEPNumerics/src/G4GaussLaguerreQ.cc