#include <G4GaussLegendreQ.hh>

Inheritance diagram for G4GaussLegendreQ:

Public Member Functions
G4double	AccurateIntegral (G4double a, G4double b) const

	G4GaussLegendreQ (const G4GaussLegendreQ &)=delete

	G4GaussLegendreQ (function pFunction)

	G4GaussLegendreQ (function pFunction, G4int nLegendre)

G4double	GetAbscissa (G4int index) const

G4int	GetNumber () const

G4double	GetWeight (G4int index) const

G4double	Integral (G4double a, G4double b) const

G4GaussLegendreQ &	operator= (const G4GaussLegendreQ &)=delete

G4double	QuickIntegral (G4double a, G4double b) const

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 G4GaussLegendreQ.hh.

Constructor & Destructor Documentation

◆ G4GaussLegendreQ() [1/3]

G4GaussLegendreQ::G4GaussLegendreQ ( function pFunction )

explicit

Definition at line 34 of file G4GaussLegendreQ.cc.

35 : G4VGaussianQuadrature(pFunction)

36{}

G4VGaussianQuadrature::G4VGaussianQuadrature

G4VGaussianQuadrature(function pFunction)

Definition: G4VGaussianQuadrature.cc:35

◆ G4GaussLegendreQ() [2/3]

G4GaussLegendreQ::G4GaussLegendreQ	(	function	pFunction,
		G4int	nLegendre
	)

Definition at line 47 of file G4GaussLegendreQ.cc.

  : G4VGaussianQuadrature(pFunction)
{
  const G4double tolerance = 1.6e-10;
  G4int k                  = nLegendre;
  fNumber                  = (nLegendre + 1) / 2;
  if(2 * fNumber != k)
  {
    G4Exception("G4GaussLegendreQ::G4GaussLegendreQ()", "InvalidCall",
                FatalException, "Invalid nLegendre argument !");
  }
  G4double newton0 = 0.0, newton1 = 0.0, temp1 = 0.0, temp2 = 0.0, temp3 = 0.0,
           temp = 0.0;
 
  fAbscissa = new G4double[fNumber];
  fWeight   = new G4double[fNumber];
 
  for(G4int i = 1; i <= fNumber; ++i)  // Loop over the desired roots
  {
    newton0 = std::cos(pi * (i - 0.25) / (k + 0.5));  // Initial root
    do                                                // approximation
    {                                                 // loop of Newton's method
      temp1 = 1.0;
      temp2 = 0.0;
      for(G4int j = 1; j <= k; ++j)
      {
        temp3 = temp2;
        temp2 = temp1;
        temp1 = ((2.0 * j - 1.0) * newton0 * temp2 - (j - 1.0) * temp3) / j;
      }
      temp    = k * (newton0 * temp1 - temp2) / (newton0 * newton0 - 1.0);
      newton1 = newton0;
      newton0 = newton1 - temp1 / temp;  // Newton's method
    } while(std::fabs(newton0 - newton1) > tolerance);
 
    fAbscissa[fNumber - i] = newton0;
    fWeight[fNumber - i]   = 2.0 / ((1.0 - newton0 * newton0) * temp * temp);
  }
}

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

◆ G4GaussLegendreQ() [3/3]

G4GaussLegendreQ::G4GaussLegendreQ ( const G4GaussLegendreQ & )

delete

Member Function Documentation

◆ AccurateIntegral()

G4double G4GaussLegendreQ::AccurateIntegral	(	G4double	a,
		G4double	b
	)		const

Definition at line 147 of file G4GaussLegendreQ.cc.

{
  // From Abramowitz M., Stegan I.A. 1964 , Handbook of Math... , p. 919
 
  static const G4double abscissa[] = {
016276744849602969579, 0.048812985136049731112,
081297495464425558994, 0.113695850110665920911,
145973714654896941989, 0.178096882367618602759,  // 6
 
210031310460567203603, 0.241743156163840012328,
273198812591049141487, 0.304364944354496353024,
335208522892625422616, 0.365696861472313635031,  // 12
 
395797649828908603285, 0.425478988407300545365,
454709422167743008636, 0.483457973920596359768,
511694177154667673586, 0.539388108324357436227,  // 18
 
566510418561397168404, 0.593032364777572080684,
618925840125468570386, 0.644163403784967106798,
668718310043916153953, 0.692564536642171561344,  // 24
 
715676812348967626225, 0.738030643744400132851,
759602341176647498703, 0.780369043867433217604,
800308744139140817229, 0.819400310737931675539,  // 30
 
837623511228187121494, 0.854959033434601455463,
871388505909296502874, 0.886894517402420416057,
901460635315852341319, 0.915071423120898074206,  // 36
 
927712456722308690965, 0.939370339752755216932,
950032717784437635756, 0.959688291448742539300,
968326828463264212174, 0.975939174585136466453,  // 42
 
982517263563014677447, 0.988054126329623799481,
992543900323762624572, 0.995981842987209290650,
998364375863181677724, 0.999689503883230766828  // 48
  };
 
  static const G4double weight[] = {
032550614492363166242, 0.032516118713868835987,
032447163714064269364, 0.032343822568575928429,
032206204794030250669, 0.032034456231992663218,  // 6
 
031828758894411006535, 0.031589330770727168558,
031316425596862355813, 0.031010332586313837423,
030671376123669149014, 0.030299915420827593794,  // 12
 
029896344136328385984, 0.029461089958167905970,
028994614150555236543, 0.028497411065085385646,
027970007616848334440, 0.027412962726029242823,  // 18
 
026826866725591762198, 0.026212340735672413913,
025570036005349361499, 0.024900633222483610288,
024204841792364691282, 0.023483399085926219842,  // 24
 
022737069658329374001, 0.021966644438744349195,
021172939892191298988, 0.020356797154333324595,
019519081140145022410, 0.018660679627411467385,  // 30
 
017782502316045260838, 0.016885479864245172450,
015970562902562291381, 0.015038721026994938006,
014090941772314860916, 0.013128229566961572637,  // 36
 
012151604671088319635, 0.011162102099838498591,
010160770535008415758, 0.009148671230783386633,
008126876925698759217, 0.007096470791153865269,  // 42
 
006058545504235961683, 0.005014202742927517693,
003964554338444686674, 0.002910731817934946408,
001853960788946921732, 0.000796792065552012429  // 48
  };
  G4double xMean = 0.5 * (a + b), xDiff = 0.5 * (b - a), integral = 0.0,
           dx = 0.0;
  for(G4int i = 0; i < 48; ++i)
  {
    dx = xDiff * abscissa[i];
    integral += weight[i] * (fFunction(xMean + dx) + fFunction(xMean - dx));
  }
  return integral *= xDiff;
}

References G4VGaussianQuadrature::fFunction.

◆ 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.

63{ 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 G4GaussLegendreQ::Integral	(	G4double	a,
		G4double	b
	)		const

Definition at line 96 of file G4GaussLegendreQ.cc.

{
  G4double xMean = 0.5 * (a + b), xDiff = 0.5 * (b - a), integral = 0.0,
           dx = 0.0;
  for(G4int i = 0; i < fNumber; ++i)
  {
    dx = xDiff * fAbscissa[i];
    integral += fWeight[i] * (fFunction(xMean + dx) + fFunction(xMean - dx));
  }
  return integral *= xDiff;
}

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

◆ operator=()

G4GaussLegendreQ & G4GaussLegendreQ::operator= ( const G4GaussLegendreQ & )

delete

◆ QuickIntegral()

G4double G4GaussLegendreQ::QuickIntegral	(	G4double	a,
		G4double	b
	)		const

Definition at line 117 of file G4GaussLegendreQ.cc.

{
  // From Abramowitz M., Stegan I.A. 1964 , Handbook of Math... , p. 916
 
  static const G4double abscissa[] = { 0.148874338981631, 0.433395394129247,
                                       0.679409568299024, 0.865063366688985,
                                       0.973906528517172 };
 
  static const G4double weight[] = { 0.295524224714753, 0.269266719309996,
                                     0.219086362515982, 0.149451349150581,
                                     0.066671344308688 };
  G4double xMean = 0.5 * (a + b), xDiff = 0.5 * (b - a), integral = 0.0,
           dx = 0.0;
  for(G4int i = 0; i < 5; ++i)
  {
    dx = xDiff * abscissa[i];
    integral += weight[i] * (fFunction(xMean + dx) + fFunction(xMean - dx));
  }
  return integral *= xDiff;
}

References G4VGaussianQuadrature::fFunction.

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

◆ fFunction

function G4VGaussianQuadrature::fFunction

protectedinherited

Definition at line 70 of file G4VGaussianQuadrature.hh.

Referenced by AccurateIntegral(), G4GaussHermiteQ::Integral(), G4GaussJacobiQ::Integral(), G4GaussLaguerreQ::Integral(), G4GaussChebyshevQ::Integral(), Integral(), and QuickIntegral().

◆ fNumber

G4int G4VGaussianQuadrature::fNumber = 0

protectedinherited

Definition at line 73 of file G4VGaussianQuadrature.hh.

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

◆ fWeight

G4double* G4VGaussianQuadrature::fWeight = nullptr

protectedinherited

Definition at line 72 of file G4VGaussianQuadrature.hh.

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

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

source/global/HEPNumerics/include/G4GaussLegendreQ.hh
source/global/HEPNumerics/src/G4GaussLegendreQ.cc

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ G4GaussLegendreQ() [1/3]

◆ G4GaussLegendreQ() [2/3]

◆ G4GaussLegendreQ() [3/3]

Member Function Documentation

◆ AccurateIntegral()

◆ GammaLogarithm()

◆ GetAbscissa()

◆ GetNumber()

◆ GetWeight()

◆ Integral()

◆ operator=()

◆ QuickIntegral()

Field Documentation

◆ fAbscissa

◆ fFunction

◆ fNumber

◆ fWeight