G4GaussHermiteQ Class Reference

#include <G4GaussHermiteQ.hh>

Inheritance diagram for G4GaussHermiteQ:

Public Member Functions
	G4GaussHermiteQ (const G4GaussHermiteQ &)=delete
	G4GaussHermiteQ (function pFunction, G4int nHermite)
G4double	GetAbscissa (G4int index) const
G4int	GetNumber () const
G4double	GetWeight (G4int index) const
G4double	Integral () const
G4GaussHermiteQ &	operator= (const G4GaussHermiteQ &)=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 43 of file G4GaussHermiteQ.hh.

Constructor & Destructor Documentation

G4GaussHermiteQ() [1/2]

G4GaussHermiteQ::G4GaussHermiteQ	(	function	pFunction,
		G4int	nHermite
	)

Definition at line 38 of file G4GaussHermiteQ.cc.

  : G4VGaussianQuadrature(pFunction)
{
  const G4double tolerance = 1.0e-12;
  const G4int maxNumber    = 12;
 
  G4int i = 1, j = 1, k = 1;
  G4double newton0 = 0.;
  G4double newton1 = 0.0, temp1 = 0.0, temp2 = 0.0, temp3 = 0.0, temp = 0.0;
  G4double piInMinusQ = std::pow(pi, -0.25);  // 1.0/std::sqrt(std::sqrt(pi)) ??
 
  fNumber   = (nHermite + 1) / 2;
  fAbscissa = new G4double[fNumber];
  fWeight   = new G4double[fNumber];
 
  for(i = 1; i <= fNumber; ++i)
  {
    if(i == 1)
    {
      newton0 =
        std::sqrt((G4double)(2 * nHermite + 1)) -
        1.85575001 * std::pow((G4double)(2 * nHermite + 1), -0.16666999);
    }
    else if(i == 2)
    {
      newton0 -= 1.14001 * std::pow((G4double) nHermite, 0.425999) / newton0;
    }
    else if(i == 3)
    {
      newton0 = 1.86002 * newton0 - 0.86002 * fAbscissa[0];
    }
    else if(i == 4)
    {
      newton0 = 1.91001 * newton0 - 0.91001 * fAbscissa[1];
    }
    else
    {
      newton0 = 2.0 * newton0 - fAbscissa[i - 3];
    }
    for(k = 1; k <= maxNumber; ++k)
    {
      temp1 = piInMinusQ;
      temp2 = 0.0;
      for(j = 1; j <= nHermite; ++j)
      {
        temp3 = temp2;
        temp2 = temp1;
        temp1 = newton0 * std::sqrt(2.0 / j) * temp2 -
                std::sqrt(((G4double)(j - 1)) / j) * temp3;
      }
      temp    = std::sqrt((G4double) 2 * nHermite) * temp2;
      newton1 = newton0;
      newton0 = newton1 - temp1 / temp;
      if(std::fabs(newton0 - newton1) <= tolerance)
      {
        break;
      }
    }
    if(k > maxNumber)
    {
      G4Exception("G4GaussHermiteQ::G4GaussHermiteQ()", "OutOfRange",
                  FatalException,
                  "Too many iterations in Gauss-Hermite constructor.");
    }
    fAbscissa[i - 1] = newton0;
    fWeight[i - 1]   = 2.0 / (temp * temp);
  }
}

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

G4GaussHermiteQ() [2/2]

G4GaussHermiteQ::G4GaussHermiteQ ( const G4GaussHermiteQ &  )

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::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 G4GaussHermiteQ::Integral

(

)

const

Definition at line 112 of file G4GaussHermiteQ.cc.

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

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

operator=()

G4GaussHermiteQ & G4GaussHermiteQ::operator= ( const G4GaussHermiteQ &  )

delete

Field Documentation

fAbscissa

G4double* G4VGaussianQuadrature::fAbscissa = nullptr

protectedinherited

Definition at line 71 of file G4VGaussianQuadrature.hh.

Referenced by G4GaussChebyshevQ::G4GaussChebyshevQ(), G4GaussHermiteQ(), G4GaussJacobiQ::G4GaussJacobiQ(), G4GaussLaguerreQ::G4GaussLaguerreQ(), G4GaussLegendreQ::G4GaussLegendreQ(), G4VGaussianQuadrature::GetAbscissa(), Integral(), G4GaussJacobiQ::Integral(), G4GaussLaguerreQ::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(), Integral(), G4GaussJacobiQ::Integral(), G4GaussLaguerreQ::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(), G4GaussJacobiQ::G4GaussJacobiQ(), G4GaussLaguerreQ::G4GaussLaguerreQ(), G4GaussLegendreQ::G4GaussLegendreQ(), G4VGaussianQuadrature::GetNumber(), Integral(), G4GaussJacobiQ::Integral(), G4GaussLaguerreQ::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(), G4GaussJacobiQ::G4GaussJacobiQ(), G4GaussLaguerreQ::G4GaussLaguerreQ(), G4GaussLegendreQ::G4GaussLegendreQ(), G4VGaussianQuadrature::GetWeight(), Integral(), G4GaussJacobiQ::Integral(), G4GaussLaguerreQ::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/G4GaussHermiteQ.hh
• source/global/HEPNumerics/src/G4GaussHermiteQ.cc