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