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G4GaussLaguerreQ.cc
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28 #include "G4GaussLaguerreQ.hh"
29 
30 
31 
32 // ------------------------------------------------------------
33 //
34 // Constructor for Gauss-Laguerre quadrature method: integral from zero to
35 // infinity of std::pow(x,alpha)*std::exp(-x)*f(x).
36 // The value of nLaguerre sets the accuracy.
37 // The constructor creates arrays fAbscissa[0,..,nLaguerre-1] and
38 // fWeight[0,..,nLaguerre-1] .
39 //
40 
43  G4int nLaguerre )
44  : G4VGaussianQuadrature(pFunction)
45 {
46  const G4double tolerance = 1.0e-10 ;
47  const G4int maxNumber = 12 ;
48  G4int i=1, k=1 ;
49  G4double newton0=0.0, newton1=0.0,
50  temp1=0.0, temp2=0.0, temp3=0.0, temp=0.0, cofi=0.0 ;
51 
52  fNumber = nLaguerre ;
53  fAbscissa = new G4double[fNumber] ;
54  fWeight = new G4double[fNumber] ;
55 
56  for(i=1;i<=fNumber;i++) // Loop over the desired roots
57  {
58  if(i == 1)
59  {
60  newton0 = (1.0 + alpha)*(3.0 + 0.92*alpha)
61  / (1.0 + 2.4*fNumber + 1.8*alpha) ;
62  }
63  else if(i == 2)
64  {
65  newton0 += (15.0 + 6.25*alpha)/(1.0 + 0.9*alpha + 2.5*fNumber) ;
66  }
67  else
68  {
69  cofi = i - 2 ;
70  newton0 += ((1.0+2.55*cofi)/(1.9*cofi)
71  + 1.26*cofi*alpha/(1.0+3.5*cofi))
72  * (newton0 - fAbscissa[i-3])/(1.0 + 0.3*alpha) ;
73  }
74  for(k=1;k<=maxNumber;k++)
75  {
76  temp1 = 1.0 ;
77  temp2 = 0.0 ;
78  for(G4int j=1;j<=fNumber;j++)
79  {
80  temp3 = temp2 ;
81  temp2 = temp1 ;
82  temp1 = ((2*j - 1 + alpha - newton0)*temp2
83  - (j - 1 + alpha)*temp3)/j ;
84  }
85  temp = (fNumber*temp1 - (fNumber +alpha)*temp2)/newton0 ;
86  newton1 = newton0 ;
87  newton0 = newton1 - temp1/temp ;
88  if(std::fabs(newton0 - newton1) <= tolerance)
89  {
90  break ;
91  }
92  }
93  if(k > maxNumber)
94  {
95  G4Exception("G4GaussLaguerreQ::G4GaussLaguerreQ()",
96  "OutOfRange", FatalException,
97  "Too many iterations in Gauss-Laguerre constructor") ;
98  }
99 
100  fAbscissa[i-1] = newton0 ;
101  fWeight[i-1] = -std::exp(GammaLogarithm(alpha + fNumber)
102  - GammaLogarithm((G4double)fNumber))/(temp*fNumber*temp2) ;
103  }
104 }
105 
106 // -----------------------------------------------------------------
107 //
108 // Gauss-Laguerre method for integration of
109 // std::pow(x,alpha)*std::exp(-x)*pFunction(x)
110 // from zero up to infinity. pFunction is evaluated in fNumber points
111 // for which fAbscissa[i] and fWeight[i] arrays were created in
112 // G4VGaussianQuadrature(double,int) constructor
113 
114 G4double
116 {
117  G4double integral = 0.0 ;
118  for(G4int i=0;i<fNumber;i++)
119  {
120  integral += fWeight[i]*fFunction(fAbscissa[i]) ;
121  }
122  return integral ;
123 }