G4GaussLegendreQ Class Reference

#include <G4GaussLegendreQ.hh>

Inheritance diagram for G4GaussLegendreQ:

Public Member Functions
	G4GaussLegendreQ (function pFunction)
	G4GaussLegendreQ (function pFunction, G4int nLegendre)
	G4GaussLegendreQ (const G4GaussLegendreQ &)=delete
G4GaussLegendreQ &	operator= (const G4GaussLegendreQ &)=delete
G4double	Integral (G4double a, G4double b) const
G4double	QuickIntegral (G4double a, G4double b) const
G4double	AccurateIntegral (G4double a, G4double b) const
Public Member Functions inherited from G4VGaussianQuadrature
	G4VGaussianQuadrature (function pFunction)
virtual	~G4VGaussianQuadrature ()
	G4VGaussianQuadrature (const G4VGaussianQuadrature &)=delete
G4VGaussianQuadrature &	operator= (const G4VGaussianQuadrature &)=delete
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 = nullptr
G4double *	fWeight = nullptr
G4int	fNumber = 0

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.

  : G4VGaussianQuadrature(pFunction)
{}

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);
  }
}

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[] = {
    0.016276744849602969579, 0.048812985136049731112,
    0.081297495464425558994, 0.113695850110665920911,
    0.145973714654896941989, 0.178096882367618602759,  // 6
 
    0.210031310460567203603, 0.241743156163840012328,
    0.273198812591049141487, 0.304364944354496353024,
    0.335208522892625422616, 0.365696861472313635031,  // 12
 
    0.395797649828908603285, 0.425478988407300545365,
    0.454709422167743008636, 0.483457973920596359768,
    0.511694177154667673586, 0.539388108324357436227,  // 18
 
    0.566510418561397168404, 0.593032364777572080684,
    0.618925840125468570386, 0.644163403784967106798,
    0.668718310043916153953, 0.692564536642171561344,  // 24
 
    0.715676812348967626225, 0.738030643744400132851,
    0.759602341176647498703, 0.780369043867433217604,
    0.800308744139140817229, 0.819400310737931675539,  // 30
 
    0.837623511228187121494, 0.854959033434601455463,
    0.871388505909296502874, 0.886894517402420416057,
    0.901460635315852341319, 0.915071423120898074206,  // 36
 
    0.927712456722308690965, 0.939370339752755216932,
    0.950032717784437635756, 0.959688291448742539300,
    0.968326828463264212174, 0.975939174585136466453,  // 42
 
    0.982517263563014677447, 0.988054126329623799481,
    0.992543900323762624572, 0.995981842987209290650,
    0.998364375863181677724, 0.999689503883230766828  // 48
  };
 
  static const G4double weight[] = {
    0.032550614492363166242, 0.032516118713868835987,
    0.032447163714064269364, 0.032343822568575928429,
    0.032206204794030250669, 0.032034456231992663218,  // 6
 
    0.031828758894411006535, 0.031589330770727168558,
    0.031316425596862355813, 0.031010332586313837423,
    0.030671376123669149014, 0.030299915420827593794,  // 12
 
    0.029896344136328385984, 0.029461089958167905970,
    0.028994614150555236543, 0.028497411065085385646,
    0.027970007616848334440, 0.027412962726029242823,  // 18
 
    0.026826866725591762198, 0.026212340735672413913,
    0.025570036005349361499, 0.024900633222483610288,
    0.024204841792364691282, 0.023483399085926219842,  // 24
 
    0.022737069658329374001, 0.021966644438744349195,
    0.021172939892191298988, 0.020356797154333324595,
    0.019519081140145022410, 0.018660679627411467385,  // 30
 
    0.017782502316045260838, 0.016885479864245172450,
    0.015970562902562291381, 0.015038721026994938006,
    0.014090941772314860916, 0.013128229566961572637,  // 36
 
    0.012151604671088319635, 0.011162102099838498591,
    0.010160770535008415758, 0.009148671230783386633,
    0.008126876925698759217, 0.007096470791153865269,  // 42
 
    0.006058545504235961683, 0.005014202742927517693,
    0.003964554338444686674, 0.002910731817934946408,
    0.001853960788946921732, 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;
}

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;
}

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;
}

---

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

• G4GaussLegendreQ.hh
• G4GaussLegendreQ.cc