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25 // 25 //
26 // G4GaussHermiteQ class implementation <<
27 // 26 //
28 // Author: V.Grichine, 13.05.1997 V.Grichine << 27 // $Id$
29 // ------------------------------------------- << 28 //
30 29
31 #include "G4GaussHermiteQ.hh" 30 #include "G4GaussHermiteQ.hh"
32 #include "G4PhysicalConstants.hh" 31 #include "G4PhysicalConstants.hh"
33 32
34 #include <limits> <<
35 <<
36 // ------------------------------------------- 33 // ----------------------------------------------------------
37 // 34 //
38 // Constructor for Gauss-Hermite 35 // Constructor for Gauss-Hermite
39 36
40 G4GaussHermiteQ::G4GaussHermiteQ(function pFun << 37 G4GaussHermiteQ::G4GaussHermiteQ ( function pFunction,
41 : G4VGaussianQuadrature(pFunction) << 38 G4int nHermite )
>> 39 : G4VGaussianQuadrature(pFunction)
42 { 40 {
43 const G4double tolerance = 1.0e-12; << 41 const G4double tolerance = 1.0e-12 ;
44 const G4int maxNumber = 12; << 42 const G4int maxNumber = 12 ;
45 << 43
46 G4int i = 1, j = 1, k = 1; << 44 G4int i=1, j=1, k=1 ;
47 G4double newton0 = 0.; << 45 G4double newton0=0.;
48 G4double newton1 = 0.0, temp1 = 0.0, temp2 = << 46 G4double newton1=0.0, temp1=0.0, temp2=0.0, temp3=0.0, temp=0.0 ;
49 G4double piInMinusQ = std::pow(pi, -0.25); << 47 G4double piInMinusQ = std::pow(pi,-0.25) ; // 1.0/std::sqrt(std::sqrt(pi)) ??
50 << 48
51 fNumber = (nHermite + 1) / 2; << 49 fNumber = (nHermite +1)/2 ;
52 fAbscissa = new G4double[fNumber]; << 50 fAbscissa = new G4double[fNumber] ;
53 fWeight = new G4double[fNumber]; << 51 fWeight = new G4double[fNumber] ;
54 << 52
55 for(i = 1; i <= fNumber; ++i) << 53 for(i=1;i<=fNumber;i++)
56 { << 54 {
57 if(i == 1) << 55 if(i == 1)
58 { << 56 {
59 newton0 = << 57 newton0 = std::sqrt((G4double)(2*nHermite + 1)) -
60 std::sqrt((G4double)(2 * nHermite + 1) << 58 1.85575001*std::pow((G4double)(2*nHermite + 1),-0.16666999) ;
61 1.85575001 * std::pow((G4double)(2 * n << 59 }
62 } << 60 else if(i == 2)
63 else if(i == 2) << 61 {
64 { << 62 newton0 -= 1.14001*std::pow((G4double)nHermite,0.425999)/newton0 ;
65 newton0 -= 1.14001 * std::pow((G4double) << 63 }
66 } << 64 else if(i == 3)
67 else if(i == 3) << 65 {
68 { << 66 newton0 = 1.86002*newton0 - 0.86002*fAbscissa[0] ;
69 newton0 = 1.86002 * newton0 - 0.86002 * << 67 }
70 } << 68 else if(i == 4)
71 else if(i == 4) << 69 {
72 { << 70 newton0 = 1.91001*newton0 - 0.91001*fAbscissa[1] ;
73 newton0 = 1.91001 * newton0 - 0.91001 * << 71 }
74 } << 72 else
75 else << 73 {
76 { << 74 newton0 = 2.0*newton0 - fAbscissa[i - 3] ;
77 newton0 = 2.0 * newton0 - fAbscissa[i - << 75 }
78 } << 76 for(k=1;k<=maxNumber;k++)
79 for(k = 1; k <= maxNumber; ++k) << 77 {
80 { << 78 temp1 = piInMinusQ ;
81 temp1 = piInMinusQ; << 79 temp2 = 0.0 ;
82 temp2 = 0.0; << 80 for(j=1;j<=nHermite;j++)
83 for(j = 1; j <= nHermite; ++j) << 81 {
84 { << 82 temp3 = temp2 ;
85 temp3 = temp2; << 83 temp2 = temp1 ;
86 temp2 = temp1; << 84 temp1 = newton0*std::sqrt(2.0/j)*temp2
87 temp1 = newton0 * std::sqrt(2.0 / j) * << 85 - std::sqrt(((G4double)(j - 1))/j)*temp3 ;
88 std::sqrt(((G4double)(j - 1)) << 86 }
89 } << 87 temp = std::sqrt((G4double)2*nHermite)*temp2 ;
90 temp = std::sqrt((G4double) 2 * nHerm << 88 newton1 = newton0 ;
91 newton1 = newton0; << 89 newton0 = newton1 - temp1/temp ;
92 G4double ratio = std::numeric_limits<G4d << 90 if(std::fabs(newton0 - newton1) <= tolerance)
93 if(temp > 0.0) << 91 {
94 { << 92 break ;
95 ratio = temp1 / temp; << 93 }
96 } << 94 }
97 newton0 = newton1 - ratio; << 95 if(k > maxNumber)
98 if(std::fabs(newton0 - newton1) <= toler << 96 {
99 { << 97 G4Exception("G4GaussHermiteQ::G4GaussHermiteQ()",
100 break; << 98 "OutOfRange", FatalException,
101 } << 99 "Too many iterations in Gauss-Hermite constructor.") ;
102 } << 100 }
103 if(k > maxNumber) << 101 fAbscissa[i-1] = newton0 ;
104 { << 102 fWeight[i-1] = 2.0/(temp*temp) ;
105 G4Exception("G4GaussHermiteQ::G4GaussHer << 103 }
106 FatalException, <<
107 "Too many iterations in Gaus <<
108 } <<
109 fAbscissa[i - 1] = newton0; <<
110 fWeight[i - 1] = 2.0 / (temp * temp); <<
111 } <<
112 } 104 }
113 105
>> 106
114 // ------------------------------------------- 107 // ----------------------------------------------------------
115 // 108 //
116 // Gauss-Hermite method for integration of std 109 // Gauss-Hermite method for integration of std::exp(-x*x)*nFunction(x)
117 // from minus infinity to plus infinity . << 110 // from minus infinity to plus infinity .
118 111
119 G4double G4GaussHermiteQ::Integral() const << 112 G4double G4GaussHermiteQ::Integral() const
120 { 113 {
121 G4double integral = 0.0; << 114 G4double integral = 0.0 ;
122 for(G4int i = 0; i < fNumber; ++i) << 115 for(G4int i=0;i<fNumber;i++)
123 { << 116 {
124 integral += << 117 integral += fWeight[i]*(fFunction(fAbscissa[i])
125 fWeight[i] * (fFunction(fAbscissa[i]) + << 118 + fFunction(-fAbscissa[i])) ;
126 } << 119 }
127 return integral; << 120 return integral ;
128 } 121 }
129 122