1 | // |
---|
2 | // ******************************************************************** |
---|
3 | // * License and Disclaimer * |
---|
4 | // * * |
---|
5 | // * The Geant4 software is copyright of the Copyright Holders of * |
---|
6 | // * the Geant4 Collaboration. It is provided under the terms and * |
---|
7 | // * conditions of the Geant4 Software License, included in the file * |
---|
8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
---|
9 | // * include a list of copyright holders. * |
---|
10 | // * * |
---|
11 | // * Neither the authors of this software system, nor their employing * |
---|
12 | // * institutes,nor the agencies providing financial support for this * |
---|
13 | // * work make any representation or warranty, express or implied, * |
---|
14 | // * regarding this software system or assume any liability for its * |
---|
15 | // * use. Please see the license in the file LICENSE and URL above * |
---|
16 | // * for the full disclaimer and the limitation of liability. * |
---|
17 | // * * |
---|
18 | // * This code implementation is the result of the scientific and * |
---|
19 | // * technical work of the GEANT4 collaboration. * |
---|
20 | // * By using, copying, modifying or distributing the software (or * |
---|
21 | // * any work based on the software) you agree to acknowledge its * |
---|
22 | // * use in resulting scientific publications, and indicate your * |
---|
23 | // * acceptance of all terms of the Geant4 Software license. * |
---|
24 | // ******************************************************************** |
---|
25 | // |
---|
26 | // |
---|
27 | // $Id: G4GaussJacobiQ.cc,v 1.8 2007/11/13 17:35:06 gcosmo Exp $ |
---|
28 | // GEANT4 tag $Name: geant4-09-03 $ |
---|
29 | // |
---|
30 | #include "G4GaussJacobiQ.hh" |
---|
31 | |
---|
32 | |
---|
33 | // ------------------------------------------------------------- |
---|
34 | // |
---|
35 | // Constructor for Gauss-Jacobi integration method. |
---|
36 | // |
---|
37 | |
---|
38 | G4GaussJacobiQ::G4GaussJacobiQ( function pFunction, |
---|
39 | G4double alpha, |
---|
40 | G4double beta, |
---|
41 | G4int nJacobi ) |
---|
42 | : G4VGaussianQuadrature(pFunction) |
---|
43 | |
---|
44 | { |
---|
45 | const G4double tolerance = 1.0e-12 ; |
---|
46 | const G4double maxNumber = 12 ; |
---|
47 | G4int i=1, k=1 ; |
---|
48 | G4double root=0.; |
---|
49 | G4double alphaBeta=0.0, alphaReduced=0.0, betaReduced=0.0, |
---|
50 | root1=0.0, root2=0.0, root3=0.0 ; |
---|
51 | G4double a=0.0, b=0.0, c=0.0, |
---|
52 | newton1=0.0, newton2=0.0, newton3=0.0, newton0=0.0, |
---|
53 | temp=0.0, rootTemp=0.0 ; |
---|
54 | |
---|
55 | fNumber = nJacobi ; |
---|
56 | fAbscissa = new G4double[fNumber] ; |
---|
57 | fWeight = new G4double[fNumber] ; |
---|
58 | |
---|
59 | for (i=1;i<=nJacobi;i++) |
---|
60 | { |
---|
61 | if (i == 1) |
---|
62 | { |
---|
63 | alphaReduced = alpha/nJacobi ; |
---|
64 | betaReduced = beta/nJacobi ; |
---|
65 | root1 = (1.0+alpha)*(2.78002/(4.0+nJacobi*nJacobi)+ |
---|
66 | 0.767999*alphaReduced/nJacobi) ; |
---|
67 | root2 = 1.0+1.48*alphaReduced+0.96002*betaReduced |
---|
68 | + 0.451998*alphaReduced*alphaReduced |
---|
69 | + 0.83001*alphaReduced*betaReduced ; |
---|
70 | root = 1.0-root1/root2 ; |
---|
71 | } |
---|
72 | else if (i == 2) |
---|
73 | { |
---|
74 | root1=(4.1002+alpha)/((1.0+alpha)*(1.0+0.155998*alpha)) ; |
---|
75 | root2=1.0+0.06*(nJacobi-8.0)*(1.0+0.12*alpha)/nJacobi ; |
---|
76 | root3=1.0+0.012002*beta*(1.0+0.24997*std::fabs(alpha))/nJacobi ; |
---|
77 | root -= (1.0-root)*root1*root2*root3 ; |
---|
78 | } |
---|
79 | else if (i == 3) |
---|
80 | { |
---|
81 | root1=(1.67001+0.27998*alpha)/(1.0+0.37002*alpha) ; |
---|
82 | root2=1.0+0.22*(nJacobi-8.0)/nJacobi ; |
---|
83 | root3=1.0+8.0*beta/((6.28001+beta)*nJacobi*nJacobi) ; |
---|
84 | root -= (fAbscissa[0]-root)*root1*root2*root3 ; |
---|
85 | } |
---|
86 | else if (i == nJacobi-1) |
---|
87 | { |
---|
88 | root1=(1.0+0.235002*beta)/(0.766001+0.118998*beta) ; |
---|
89 | root2=1.0/(1.0+0.639002*(nJacobi-4.0)/(1.0+0.71001*(nJacobi-4.0))) ; |
---|
90 | root3=1.0/(1.0+20.0*alpha/((7.5+alpha)*nJacobi*nJacobi)) ; |
---|
91 | root += (root-fAbscissa[nJacobi-4])*root1*root2*root3 ; |
---|
92 | } |
---|
93 | else if (i == nJacobi) |
---|
94 | { |
---|
95 | root1 = (1.0+0.37002*beta)/(1.67001+0.27998*beta) ; |
---|
96 | root2 = 1.0/(1.0+0.22*(nJacobi-8.0)/nJacobi) ; |
---|
97 | root3 = 1.0/(1.0+8.0*alpha/((6.28002+alpha)*nJacobi*nJacobi)) ; |
---|
98 | root += (root-fAbscissa[nJacobi-3])*root1*root2*root3 ; |
---|
99 | } |
---|
100 | else |
---|
101 | { |
---|
102 | root = 3.0*fAbscissa[i-2]-3.0*fAbscissa[i-3]+fAbscissa[i-4] ; |
---|
103 | } |
---|
104 | alphaBeta = alpha + beta ; |
---|
105 | for (k=1;k<=maxNumber;k++) |
---|
106 | { |
---|
107 | temp = 2.0 + alphaBeta ; |
---|
108 | newton1 = (alpha-beta+temp*root)/2.0 ; |
---|
109 | newton2 = 1.0 ; |
---|
110 | for (G4int j=2;j<=nJacobi;j++) |
---|
111 | { |
---|
112 | newton3 = newton2 ; |
---|
113 | newton2 = newton1 ; |
---|
114 | temp = 2*j+alphaBeta ; |
---|
115 | a = 2*j*(j+alphaBeta)*(temp-2.0) ; |
---|
116 | b = (temp-1.0)*(alpha*alpha-beta*beta+temp*(temp-2.0)*root) ; |
---|
117 | c = 2.0*(j-1+alpha)*(j-1+beta)*temp ; |
---|
118 | newton1 = (b*newton2-c*newton3)/a ; |
---|
119 | } |
---|
120 | newton0 = (nJacobi*(alpha - beta - temp*root)*newton1 + |
---|
121 | 2.0*(nJacobi + alpha)*(nJacobi + beta)*newton2)/ |
---|
122 | (temp*(1.0 - root*root)) ; |
---|
123 | rootTemp = root ; |
---|
124 | root = rootTemp - newton1/newton0 ; |
---|
125 | if (std::fabs(root-rootTemp) <= tolerance) |
---|
126 | { |
---|
127 | break ; |
---|
128 | } |
---|
129 | } |
---|
130 | if (k > maxNumber) |
---|
131 | { |
---|
132 | G4Exception("G4GaussJacobiQ::G4GaussJacobiQ()", "OutOfRange", |
---|
133 | FatalException, "Too many iterations in constructor.") ; |
---|
134 | } |
---|
135 | fAbscissa[i-1] = root ; |
---|
136 | fWeight[i-1] = std::exp(GammaLogarithm((G4double)(alpha+nJacobi)) + |
---|
137 | GammaLogarithm((G4double)(beta+nJacobi)) - |
---|
138 | GammaLogarithm((G4double)(nJacobi+1.0)) - |
---|
139 | GammaLogarithm((G4double)(nJacobi + alphaBeta + 1.0))) |
---|
140 | *temp*std::pow(2.0,alphaBeta)/(newton0*newton2) ; |
---|
141 | } |
---|
142 | } |
---|
143 | |
---|
144 | |
---|
145 | // ---------------------------------------------------------- |
---|
146 | // |
---|
147 | // Gauss-Jacobi method for integration of |
---|
148 | // ((1-x)^alpha)*((1+x)^beta)*pFunction(x) |
---|
149 | // from minus unit to plus unit . |
---|
150 | |
---|
151 | |
---|
152 | G4double |
---|
153 | G4GaussJacobiQ::Integral() const |
---|
154 | { |
---|
155 | G4double integral = 0.0 ; |
---|
156 | for(G4int i=0;i<fNumber;i++) |
---|
157 | { |
---|
158 | integral += fWeight[i]*fFunction(fAbscissa[i]) ; |
---|
159 | } |
---|
160 | return integral ; |
---|
161 | } |
---|
162 | |
---|