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25 // 7 //
26 // G4GaussLaguerreQ class implementation << 8 // $Id: G4GaussLaguerreQ.cc,v 1.2 1999/11/16 17:31:10 gcosmo Exp $
>> 9 // GEANT4 tag $Name: geant4-02-00 $
27 // 10 //
28 // Author: V.Grichine, 13.05.1997 <<
29 // ------------------------------------------- <<
30 <<
31 #include "G4GaussLaguerreQ.hh" 11 #include "G4GaussLaguerreQ.hh"
32 12
>> 13
>> 14
33 // ------------------------------------------- 15 // ------------------------------------------------------------
34 // 16 //
35 // Constructor for Gauss-Laguerre quadrature m 17 // Constructor for Gauss-Laguerre quadrature method: integral from zero to
36 // infinity of std::pow(x,alpha)*std::exp(-x)* << 18 // infinity of pow(x,alpha)*exp(-x)*f(x). The value of nLaguerre sets the accuracy.
37 // The value of nLaguerre sets the accuracy. << 19 // The constructor creates arrays fAbscissa[0,..,nLaguerre-1] and
38 // The constructor creates arrays fAbscissa[0, << 20 // fWeight[0,..,nLaguerre-1] .
39 // fWeight[0,..,nLaguerre-1] . <<
40 // 21 //
41 22
42 G4GaussLaguerreQ::G4GaussLaguerreQ(function pF << 23 G4GaussLaguerreQ::G4GaussLaguerreQ( function pFunction,
43 G4int nLagu << 24 G4double alpha,
44 : G4VGaussianQuadrature(pFunction) << 25 G4int nLaguerre )
>> 26 : G4VGaussianQuadrature(pFunction)
45 { 27 {
46 const G4double tolerance = 1.0e-10; << 28 const G4double tolerance = 1.0e-10 ;
47 const G4int maxNumber = 12; << 29 const G4int maxNumber = 12 ;
48 G4int i = 1, k = 1; << 30 G4int i, j, k ;
49 G4double newton0 = 0.0, newton1 = 0.0, temp1 << 31 G4double newton, newton1, temp1, temp2, temp3, temp, cofi ;
50 temp = 0.0, cofi = 0.0; << 32
51 << 33 fNumber = nLaguerre ;
52 fNumber = nLaguerre; << 34 fAbscissa = new G4double[fNumber] ;
53 fAbscissa = new G4double[fNumber]; << 35 fWeight = new G4double[fNumber] ;
54 fWeight = new G4double[fNumber]; << 36
55 << 37 for(i=1;i<=fNumber;i++) // Loop over the desired roots
56 for(i = 1; i <= fNumber; ++i) // Loop over << 38 {
57 { << 39 if(i == 1)
58 if(i == 1) << 40 {
59 { << 41 newton = (1.0 + alpha)*(3.0 + 0.92*alpha)/(1.0 + 2.4*fNumber + 1.8*alpha) ;
60 newton0 = (1.0 + alpha) * (3.0 + 0.92 * << 42 }
61 (1.0 + 2.4 * fNumber + 1.8 * a << 43 else if(i == 2)
62 } << 44 {
63 else if(i == 2) << 45 newton += (15.0 + 6.25*alpha)/(1.0 + 0.9*alpha + 2.5*fNumber) ;
64 { << 46 }
65 newton0 += (15.0 + 6.25 * alpha) / (1.0 << 47 else
66 } << 48 {
67 else << 49 cofi = i - 2 ;
68 { << 50 newton += ((1.0+2.55*cofi)/(1.9*cofi) + 1.26*cofi*alpha/(1.0+3.5*cofi))*
69 cofi = i - 2; << 51 (newton - fAbscissa[i-3])/(1.0 + 0.3*alpha) ;
70 newton0 += ((1.0 + 2.55 * cofi) / (1.9 * << 52 }
71 1.26 * cofi * alpha / (1.0 + << 53 for(k=1;k<=maxNumber;k++)
72 (newton0 - fAbscissa[i - 3]) <<
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 { 54 {
80 temp3 = temp2; << 55 temp1 = 1.0 ;
81 temp2 = temp1; << 56 temp2 = 0.0 ;
82 temp1 = << 57 for(j=1;j<=fNumber;j++)
83 ((2 * j - 1 + alpha - newton0) * tem << 58 {
>> 59 temp3 = temp2 ;
>> 60 temp2 = temp1 ;
>> 61 temp1 = ((2*j - 1 + alpha - newton)*temp2 - (j - 1 + alpha)*temp3)/j ;
>> 62 }
>> 63 temp = (fNumber*temp1 - (fNumber +alpha)*temp2)/newton ;
>> 64 newton1 = newton ;
>> 65 newton = newton1 - temp1/temp ;
>> 66 if(fabs(newton - newton1) <= tolerance)
>> 67 {
>> 68 break ;
>> 69 }
84 } 70 }
85 temp = (fNumber * temp1 - (fNumber + << 71 if(k > maxNumber)
86 newton1 = newton0; <<
87 newton0 = newton1 - temp1 / temp; <<
88 if(std::fabs(newton0 - newton1) <= toler <<
89 { 72 {
90 break; << 73 G4Exception("Too many iterations in Gauss-Laguerre constructor") ;
91 } 74 }
92 } << 75
93 if(k > maxNumber) << 76 fAbscissa[i-1] = newton ;
94 { << 77 fWeight[i-1] = -exp(GammaLogarithm(alpha + fNumber) -
95 G4Exception("G4GaussLaguerreQ::G4GaussLa << 78 GammaLogarithm((G4double)fNumber))/(temp*fNumber*temp2) ;
96 FatalException, << 79 }
97 "Too many iterations in Gaus <<
98 } <<
99 <<
100 fAbscissa[i - 1] = newton0; <<
101 fWeight[i - 1] = -std::exp(GammaLogarith <<
102 GammaLogarithm( <<
103 (temp * fNumber * temp2); <<
104 } <<
105 } 80 }
106 81
107 // ------------------------------------------- 82 // -----------------------------------------------------------------
108 // 83 //
109 // Gauss-Laguerre method for integration of << 84 // Gauss-Laguerre method for integration of pow(x,alpha)*exp(-x)*pFunction(x)
110 // std::pow(x,alpha)*std::exp(-x)*pFunction(x) << 85 // from zero up to infinity. pFunction is evaluated in fNumber points for which
111 // from zero up to infinity. pFunction is eval << 86 // fAbscissa[i] and fWeight[i] arrays were created in
112 // for which fAbscissa[i] and fWeight[i] array <<
113 // G4VGaussianQuadrature(double,int) construct 87 // G4VGaussianQuadrature(double,int) constructor
114 88
115 G4double G4GaussLaguerreQ::Integral() const << 89 G4double
>> 90 G4GaussLaguerreQ::Integral() const
116 { 91 {
117 G4double integral = 0.0; << 92 G4int i ;
118 for(G4int i = 0; i < fNumber; ++i) << 93 G4double integral = 0.0 ;
119 { << 94 for(i=0;i<fNumber;i++)
120 integral += fWeight[i] * fFunction(fAbscis << 95 {
121 } << 96 integral += fWeight[i]*fFunction(fAbscissa[i]) ;
122 return integral; << 97 }
>> 98 return integral ;
123 } 99 }
124 100