#include <G4GaussLegendreQ.hh>

Inheritance diagram for G4GaussLegendreQ:

Collaboration 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.

    : 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) ;
    }
 }

Here is the call graph for this function:

Member Function Documentation

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

Definition at line 154 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 ;
 }

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

Definition at line 99 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 ;
 }

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

Definition at line 122 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:

geant4.10.03.p01/source/global/HEPNumerics/include/G4GaussLegendreQ.hh
geant4.10.03.p01/source/global/HEPNumerics/src/G4GaussLegendreQ.cc

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation