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25 // 22 //
26 // G4GaussJacobiQ class implementation <<
27 // 23 //
28 // Author: V.Grichine, 13.05.1997 << 24 // $Id: G4GaussJacobiQ.cc,v 1.4 2001/07/11 10:00:41 gunter Exp $
29 // ------------------------------------------- << 25 // GEANT4 tag $Name: geant4-04-01 $
30 << 26 //
31 #include "G4GaussJacobiQ.hh" 27 #include "G4GaussJacobiQ.hh"
32 28
>> 29
33 // ------------------------------------------- 30 // -------------------------------------------------------------
34 // 31 //
35 // Constructor for Gauss-Jacobi integration me << 32 // Constructor for Gauss-Jacobi integration method.
36 // 33 //
37 34
38 G4GaussJacobiQ::G4GaussJacobiQ(function pFunct << 35 G4GaussJacobiQ::G4GaussJacobiQ( function pFunction,
39 G4double beta, << 36 G4double alpha,
40 : G4VGaussianQuadrature(pFunction) << 37 G4double beta,
>> 38 G4int nJacobi )
>> 39 : G4VGaussianQuadrature(pFunction)
41 40
42 { 41 {
43 const G4double tolerance = 1.0e-12; << 42 const G4double tolerance = 1.0e-12 ;
44 const G4double maxNumber = 12; << 43 const G4double maxNumber = 12 ;
45 G4int i = 1, k = 1; << 44 G4int i, k, j ;
46 G4double root = 0.; << 45 G4double root=0.;
47 G4double alphaBeta = 0.0, alphaReduced = 0.0 << 46 G4double alphaBeta, alphaReduced, betaReduced, root1, root2, root3 ;
48 root2 = 0.0, root3 = 0.0; << 47 G4double a, b, c, newton1, newton2, newton3, newton, temp, rootTemp ;
49 G4double a = 0.0, b = 0.0, c = 0.0, newton1 << 48
50 newton3 = 0.0, newton0 = 0.0, temp << 49 fNumber = nJacobi ;
51 << 50 fAbscissa = new G4double[fNumber] ;
52 fNumber = nJacobi; << 51 fWeight = new G4double[fNumber] ;
53 fAbscissa = new G4double[fNumber]; <<
54 fWeight = new G4double[fNumber]; <<
55 52
56 for(i = 1; i <= nJacobi; ++i) << 53 for (i=1;i<=nJacobi;i++)
57 { 54 {
58 if(i == 1) << 55 if (i == 1)
59 { << 56 {
60 alphaReduced = alpha / nJacobi; << 57 alphaReduced = alpha/nJacobi ;
61 betaReduced = beta / nJacobi; << 58 betaReduced = beta/nJacobi ;
62 root1 = (1.0 + alpha) * (2.78002 << 59 root1 = (1.0+alpha)*(2.78002/(4.0+nJacobi*nJacobi)+
63 0.767999 * alph << 60 0.767999*alphaReduced/nJacobi) ;
64 root2 = 1.0 + 1.48 * alphaReduced << 61 root2 = 1.0+1.48*alphaReduced+0.96002*betaReduced +
65 0.451998 * alphaReduced * alphaR << 62 0.451998*alphaReduced*alphaReduced+0.83001*alphaReduced*betaReduced ;
66 0.83001 * alphaReduced * betaRed << 63 root = 1.0-root1/root2 ;
67 root = 1.0 - root1 / root2; << 64 }
68 } << 65 else if (i == 2)
69 else if(i == 2) << 66 {
70 { << 67 root1=(4.1002+alpha)/((1.0+alpha)*(1.0+0.155998*alpha)) ;
71 root1 = (4.1002 + alpha) / ((1.0 + alpha << 68 root2=1.0+0.06*(nJacobi-8.0)*(1.0+0.12*alpha)/nJacobi ;
72 root2 = 1.0 + 0.06 * (nJacobi - 8.0) * ( << 69 root3=1.0+0.012002*beta*(1.0+0.24997*fabs(alpha))/nJacobi ;
73 root3 = << 70 root -= (1.0-root)*root1*root2*root3 ;
74 1.0 + 0.012002 * beta * (1.0 + 0.24997 << 71 }
75 root -= (1.0 - root) * root1 * root2 * r << 72 else if (i == 3)
76 } << 73 {
77 else if(i == 3) << 74 root1=(1.67001+0.27998*alpha)/(1.0+0.37002*alpha) ;
78 { << 75 root2=1.0+0.22*(nJacobi-8.0)/nJacobi ;
79 root1 = (1.67001 + 0.27998 * alpha) / (1 << 76 root3=1.0+8.0*beta/((6.28001+beta)*nJacobi*nJacobi) ;
80 root2 = 1.0 + 0.22 * (nJacobi - 8.0) / n << 77 root -= (fAbscissa[0]-root)*root1*root2*root3 ;
81 root3 = 1.0 + 8.0 * beta / ((6.28001 + b << 78 }
82 root -= (fAbscissa[0] - root) * root1 * << 79 else if (i == nJacobi-1)
83 } << 80 {
84 else if(i == nJacobi - 1) << 81 root1=(1.0+0.235002*beta)/(0.766001+0.118998*beta) ;
85 { << 82 root2=1.0/(1.0+0.639002*(nJacobi-4.0)/(1.0+0.71001*(nJacobi-4.0))) ;
86 root1 = (1.0 + 0.235002 * beta) / (0.766 << 83 root3=1.0/(1.0+20.0*alpha/((7.5+alpha)*nJacobi*nJacobi)) ;
87 root2 = 1.0 / (1.0 + 0.639002 * (nJacobi << 84 root += (root-fAbscissa[nJacobi-4])*root1*root2*root3 ;
88 (1.0 + 0.71001 * << 85 }
89 root3 = 1.0 / (1.0 + 20.0 * alpha / ((7. << 86 else if (i == nJacobi)
90 root += (root - fAbscissa[nJacobi - 4]) << 87 {
91 } << 88 root1 = (1.0+0.37002*beta)/(1.67001+0.27998*beta) ;
92 else if(i == nJacobi) << 89 root2 = 1.0/(1.0+0.22*(nJacobi-8.0)/nJacobi) ;
93 { << 90 root3 = 1.0/(1.0+8.0*alpha/((6.28002+alpha)*nJacobi*nJacobi)) ;
94 root1 = (1.0 + 0.37002 * beta) / (1.6700 << 91 root += (root-fAbscissa[nJacobi-3])*root1*root2*root3 ;
95 root2 = 1.0 / (1.0 + 0.22 * (nJacobi - 8 << 92 }
96 root3 = << 93 else
97 1.0 / (1.0 + 8.0 * alpha / ((6.28002 + << 94 {
98 root += (root - fAbscissa[nJacobi - 3]) << 95 root = 3.0*fAbscissa[i-2]-3.0*fAbscissa[i-3]+fAbscissa[i-4] ;
99 } << 96 }
100 else << 97 alphaBeta = alpha + beta ;
101 { << 98 for (k=1;k<=maxNumber;k++)
102 root = 3.0 * fAbscissa[i - 2] - 3.0 * fA << 99 {
103 } << 100 temp = 2.0 + alphaBeta ;
104 alphaBeta = alpha + beta; << 101 newton1 = (alpha-beta+temp*root)/2.0 ;
105 for(k = 1; k <= maxNumber; ++k) << 102 newton2 = 1.0 ;
106 { << 103 for (j=2;j<=nJacobi;j++)
107 temp = 2.0 + alphaBeta; << 104 {
108 newton1 = (alpha - beta + temp * root) / << 105 newton3 = newton2 ;
109 newton2 = 1.0; << 106 newton2 = newton1 ;
110 for(G4int j = 2; j <= nJacobi; ++j) << 107 temp = 2*j+alphaBeta ;
111 { << 108 a = 2*j*(j+alphaBeta)*(temp-2.0) ;
112 newton3 = newton2; << 109 b = (temp-1.0)*(alpha*alpha-beta*beta+temp*(temp-2.0)*root) ;
113 newton2 = newton1; << 110 c = 2.0*(j-1+alpha)*(j-1+beta)*temp ;
114 temp = 2 * j + alphaBeta; << 111 newton1 = (b*newton2-c*newton3)/a ;
115 a = 2 * j * (j + alphaBeta) * (t << 112 }
116 b = (temp - 1.0) * << 113 newton = (nJacobi*(alpha - beta - temp*root)*newton1 +
117 (alpha * alpha - beta * beta + tem << 114 2.0*(nJacobi + alpha)*(nJacobi + beta)*newton2)/
118 c = 2.0 * (j - 1 + alpha) * (j - << 115 (temp*(1.0 - root*root)) ;
119 newton1 = (b * newton2 - c * newton3) << 116 rootTemp = root ;
120 } << 117 root = rootTemp - newton1/newton ;
121 newton0 = (nJacobi * (alpha - beta - tem << 118 if (fabs(root-rootTemp) <= tolerance)
122 2.0 * (nJacobi + alpha) * (nJ << 119 {
123 (temp * (1.0 - root * root)); << 120 break ;
124 rootTemp = root; << 121 }
125 root = rootTemp - newton1 / newton0; << 122 }
126 if(std::fabs(root - rootTemp) <= toleran << 123 if (k > maxNumber)
127 { << 124 {
128 break; << 125 G4Exception("Too many iterations in G4GaussJacobiQ::G4GaussJacobiQ") ;
129 } << 126 }
130 } << 127 fAbscissa[i-1] = root ;
131 if(k > maxNumber) << 128 fWeight[i-1] = exp(GammaLogarithm((G4double)(alpha+nJacobi)) +
132 { << 129 GammaLogarithm((G4double)(beta+nJacobi)) -
133 G4Exception("G4GaussJacobiQ::G4GaussJaco << 130 GammaLogarithm((G4double)(nJacobi+1.0)) -
134 FatalException, "Too many it << 131 GammaLogarithm((G4double)(nJacobi + alphaBeta + 1.0)))
135 } << 132 *temp*pow(2.0,alphaBeta)/(newton*newton2) ;
136 fAbscissa[i - 1] = root; <<
137 fWeight[i - 1] = <<
138 std::exp(GammaLogarithm((G4double)(alpha <<
139 GammaLogarithm((G4double)(beta <<
140 GammaLogarithm((G4double)(nJaco <<
141 GammaLogarithm((G4double)(nJaco <<
142 temp * std::pow(2.0, alphaBeta) / (newto <<
143 } 133 }
144 } 134 }
145 135
>> 136
146 // ------------------------------------------- 137 // ----------------------------------------------------------
147 // 138 //
148 // Gauss-Jacobi method for integration of << 139 // Gauss-Jacobi method for integration of ((1-x)^alpha)*((1+x)^beta)*pFunction(x)
149 // ((1-x)^alpha)*((1+x)^beta)*pFunction(x) <<
150 // from minus unit to plus unit . 140 // from minus unit to plus unit .
151 141
152 G4double G4GaussJacobiQ::Integral() const << 142
>> 143 G4double
>> 144 G4GaussJacobiQ::Integral() const
153 { 145 {
154 G4double integral = 0.0; << 146 G4int i ;
155 for(G4int i = 0; i < fNumber; ++i) << 147 G4double integral = 0.0 ;
156 { << 148 for(i=0;i<fNumber;i++)
157 integral += fWeight[i] * fFunction(fAbscis << 149 {
158 } << 150 integral += fWeight[i]*fFunction(fAbscissa[i]) ;
159 return integral; << 151 }
>> 152 return integral ;
160 } 153 }
>> 154
161 155