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