| Geant4 Cross Reference |
1 // 1 //
2 // ******************************************* 2 // ********************************************************************
3 // * License and Disclaimer 3 // * License and Disclaimer *
4 // * 4 // * *
5 // * The Geant4 software is copyright of th 5 // * The Geant4 software is copyright of the Copyright Holders of *
6 // * the Geant4 Collaboration. It is provided 6 // * the Geant4 Collaboration. It is provided under the terms and *
7 // * conditions of the Geant4 Software License 7 // * conditions of the Geant4 Software License, included in the file *
8 // * LICENSE and available at http://cern.ch/ 8 // * LICENSE and available at http://cern.ch/geant4/license . These *
9 // * include a list of copyright holders. 9 // * include a list of copyright holders. *
10 // * 10 // * *
11 // * Neither the authors of this software syst 11 // * Neither the authors of this software system, nor their employing *
12 // * institutes,nor the agencies providing fin 12 // * institutes,nor the agencies providing financial support for this *
13 // * work make any representation or warran 13 // * work make any representation or warranty, express or implied, *
14 // * regarding this software system or assum 14 // * regarding this software system or assume any liability for its *
15 // * use. Please see the license in the file 15 // * use. Please see the license in the file LICENSE and URL above *
16 // * for the full disclaimer and the limitatio 16 // * for the full disclaimer and the limitation of liability. *
17 // * 17 // * *
18 // * This code implementation is the result 18 // * This code implementation is the result of the scientific and *
19 // * technical work of the GEANT4 collaboratio 19 // * technical work of the GEANT4 collaboration. *
20 // * By using, copying, modifying or distri 20 // * By using, copying, modifying or distributing the software (or *
21 // * any work based on the software) you ag 21 // * any work based on the software) you agree to acknowledge its *
22 // * use in resulting scientific publicati 22 // * use in resulting scientific publications, and indicate your *
23 // * acceptance of all terms of the Geant4 Sof 23 // * acceptance of all terms of the Geant4 Software license. *
24 // ******************************************* 24 // ********************************************************************
25 // 25 //
26 // G4GaussLaguerreQ class implementation <<
27 // 26 //
28 // Author: V.Grichine, 13.05.1997 << 27 // $Id: G4GaussLaguerreQ.cc 67970 2013-03-13 10:10:06Z gcosmo $
29 // ------------------------------------------- << 28 //
30 <<
31 #include "G4GaussLaguerreQ.hh" 29 #include "G4GaussLaguerreQ.hh"
32 30
>> 31
>> 32
33 // ------------------------------------------- 33 // ------------------------------------------------------------
34 // 34 //
35 // Constructor for Gauss-Laguerre quadrature m 35 // Constructor for Gauss-Laguerre quadrature method: integral from zero to
36 // infinity of std::pow(x,alpha)*std::exp(-x)* 36 // infinity of std::pow(x,alpha)*std::exp(-x)*f(x).
37 // The value of nLaguerre sets the accuracy. 37 // The value of nLaguerre sets the accuracy.
38 // The constructor creates arrays fAbscissa[0, << 38 // The constructor creates arrays fAbscissa[0,..,nLaguerre-1] and
39 // fWeight[0,..,nLaguerre-1] . << 39 // fWeight[0,..,nLaguerre-1] .
40 // 40 //
41 41
42 G4GaussLaguerreQ::G4GaussLaguerreQ(function pF << 42 G4GaussLaguerreQ::G4GaussLaguerreQ( function pFunction,
43 G4int nLagu << 43 G4double alpha,
44 : G4VGaussianQuadrature(pFunction) << 44 G4int nLaguerre )
>> 45 : G4VGaussianQuadrature(pFunction)
45 { 46 {
46 const G4double tolerance = 1.0e-10; << 47 const G4double tolerance = 1.0e-10 ;
47 const G4int maxNumber = 12; << 48 const G4int maxNumber = 12 ;
48 G4int i = 1, k = 1; << 49 G4int i=1, k=1 ;
49 G4double newton0 = 0.0, newton1 = 0.0, temp1 << 50 G4double newton0=0.0, newton1=0.0,
50 temp = 0.0, cofi = 0.0; << 51 temp1=0.0, temp2=0.0, temp3=0.0, temp=0.0, cofi=0.0 ;
51 << 52
52 fNumber = nLaguerre; << 53 fNumber = nLaguerre ;
53 fAbscissa = new G4double[fNumber]; << 54 fAbscissa = new G4double[fNumber] ;
54 fWeight = new G4double[fNumber]; << 55 fWeight = new G4double[fNumber] ;
55 << 56
56 for(i = 1; i <= fNumber; ++i) // Loop over << 57 for(i=1;i<=fNumber;i++) // Loop over the desired roots
57 { << 58 {
58 if(i == 1) << 59 if(i == 1)
59 { << 60 {
60 newton0 = (1.0 + alpha) * (3.0 + 0.92 * << 61 newton0 = (1.0 + alpha)*(3.0 + 0.92*alpha)
61 (1.0 + 2.4 * fNumber + 1.8 * a << 62 / (1.0 + 2.4*fNumber + 1.8*alpha) ;
62 } << 63 }
63 else if(i == 2) << 64 else if(i == 2)
64 { << 65 {
65 newton0 += (15.0 + 6.25 * alpha) / (1.0 << 66 newton0 += (15.0 + 6.25*alpha)/(1.0 + 0.9*alpha + 2.5*fNumber) ;
66 } << 67 }
67 else << 68 else
68 { << 69 {
69 cofi = i - 2; << 70 cofi = i - 2 ;
70 newton0 += ((1.0 + 2.55 * cofi) / (1.9 * << 71 newton0 += ((1.0+2.55*cofi)/(1.9*cofi)
71 1.26 * cofi * alpha / (1.0 + << 72 + 1.26*cofi*alpha/(1.0+3.5*cofi))
72 (newton0 - fAbscissa[i - 3]) << 73 * (newton0 - fAbscissa[i-3])/(1.0 + 0.3*alpha) ;
73 } << 74 }
74 for(k = 1; k <= maxNumber; ++k) << 75 for(k=1;k<=maxNumber;k++)
75 { <<
76 temp1 = 1.0; <<
77 temp2 = 0.0; <<
78 for(G4int j = 1; j <= fNumber; ++j) <<
79 { 76 {
80 temp3 = temp2; << 77 temp1 = 1.0 ;
81 temp2 = temp1; << 78 temp2 = 0.0 ;
82 temp1 = << 79 for(G4int j=1;j<=fNumber;j++)
83 ((2 * j - 1 + alpha - newton0) * tem << 80 {
>> 81 temp3 = temp2 ;
>> 82 temp2 = temp1 ;
>> 83 temp1 = ((2*j - 1 + alpha - newton0)*temp2
>> 84 - (j - 1 + alpha)*temp3)/j ;
>> 85 }
>> 86 temp = (fNumber*temp1 - (fNumber +alpha)*temp2)/newton0 ;
>> 87 newton1 = newton0 ;
>> 88 newton0 = newton1 - temp1/temp ;
>> 89 if(std::fabs(newton0 - newton1) <= tolerance)
>> 90 {
>> 91 break ;
>> 92 }
84 } 93 }
85 temp = (fNumber * temp1 - (fNumber + << 94 if(k > maxNumber)
86 newton1 = newton0; <<
87 newton0 = newton1 - temp1 / temp; <<
88 if(std::fabs(newton0 - newton1) <= toler <<
89 { 95 {
90 break; << 96 G4Exception("G4GaussLaguerreQ::G4GaussLaguerreQ()",
>> 97 "OutOfRange", FatalException,
>> 98 "Too many iterations in Gauss-Laguerre constructor") ;
91 } 99 }
92 } << 100
93 if(k > maxNumber) << 101 fAbscissa[i-1] = newton0 ;
94 { << 102 fWeight[i-1] = -std::exp(GammaLogarithm(alpha + fNumber)
95 G4Exception("G4GaussLaguerreQ::G4GaussLa << 103 - GammaLogarithm((G4double)fNumber))/(temp*fNumber*temp2) ;
96 FatalException, << 104 }
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 } 105 }
106 106
107 // ------------------------------------------- 107 // -----------------------------------------------------------------
108 // 108 //
109 // Gauss-Laguerre method for integration of 109 // Gauss-Laguerre method for integration of
110 // std::pow(x,alpha)*std::exp(-x)*pFunction(x) 110 // std::pow(x,alpha)*std::exp(-x)*pFunction(x)
111 // from zero up to infinity. pFunction is eval 111 // from zero up to infinity. pFunction is evaluated in fNumber points
112 // for which fAbscissa[i] and fWeight[i] array 112 // for which fAbscissa[i] and fWeight[i] arrays were created in
113 // G4VGaussianQuadrature(double,int) construct 113 // G4VGaussianQuadrature(double,int) constructor
114 114
115 G4double G4GaussLaguerreQ::Integral() const << 115 G4double
>> 116 G4GaussLaguerreQ::Integral() const
116 { 117 {
117 G4double integral = 0.0; << 118 G4double integral = 0.0 ;
118 for(G4int i = 0; i < fNumber; ++i) << 119 for(G4int i=0;i<fNumber;i++)
119 { << 120 {
120 integral += fWeight[i] * fFunction(fAbscis << 121 integral += fWeight[i]*fFunction(fAbscissa[i]) ;
121 } << 122 }
122 return integral; << 123 return integral ;
123 } 124 }
124 125