G4GaussLegendreQ Class Reference

#include <G4GaussLegendreQ.hh>

Inheritance diagram for G4GaussLegendreQ:

Public Member Functions
	G4GaussLegendreQ (function pFunction)
	G4GaussLegendreQ (function pFunction, G4int nLegendre)
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 ()
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 90 of file G4GaussLegendreQ.hh.

Constructor & Destructor Documentation

G4GaussLegendreQ::G4GaussLegendreQ ( function  pFunction )

explicit

Definition at line 33 of file G4GaussLegendreQ.cc.

   : G4VGaussianQuadrature(pFunction)
{
}

G4GaussLegendreQ::G4GaussLegendreQ	(	function	pFunction,
		G4int	nLegendre
	)

Definition at line 47 of file G4GaussLegendreQ.cc.

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

   : 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) ;
   }
}

Member Function Documentation

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

Definition at line 154 of file G4GaussLegendreQ.cc.

References test::b, and G4VGaussianQuadrature::fFunction.

{   
   // 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 ;
}

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

Definition at line 99 of file G4GaussLegendreQ.cc.

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

{
   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 ;
}

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

Definition at line 122 of file G4GaussLegendreQ.cc.

References test::b, and G4VGaussianQuadrature::fFunction.

{
   // 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