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