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25 // 22 //
26 // G4GaussHermiteQ class implementation <<
27 // 23 //
28 // Author: V.Grichine, 13.05.1997 V.Grichine << 24 // $Id: G4GaussHermiteQ.cc,v 1.4 2001/07/11 10:00:41 gunter Exp $
29 // ------------------------------------------- << 25 // GEANT4 tag $Name: geant4-05-02-patch-01 $
30 << 26 //
31 #include "G4GaussHermiteQ.hh" 27 #include "G4GaussHermiteQ.hh"
32 #include "G4PhysicalConstants.hh" <<
33 28
34 #include <limits> <<
35 29
36 // ------------------------------------------- 30 // ----------------------------------------------------------
37 // 31 //
38 // Constructor for Gauss-Hermite 32 // Constructor for Gauss-Hermite
39 33
40 G4GaussHermiteQ::G4GaussHermiteQ(function pFun << 34 G4GaussHermiteQ::G4GaussHermiteQ( function pFunction,
41 : G4VGaussianQuadrature(pFunction) << 35 G4int nHermite )
>> 36 : G4VGaussianQuadrature(pFunction)
42 { 37 {
43 const G4double tolerance = 1.0e-12; << 38 const G4double tolerance = 1.0e-12 ;
44 const G4int maxNumber = 12; << 39 const G4int maxNumber = 12 ;
45 << 40
46 G4int i = 1, j = 1, k = 1; << 41 G4int i, j, k ;
47 G4double newton0 = 0.; << 42 G4double newton=0.;
48 G4double newton1 = 0.0, temp1 = 0.0, temp2 = << 43 G4double newton1, temp1, temp2, temp3, temp ;
49 G4double piInMinusQ = std::pow(pi, -0.25); << 44 G4double piInMinusQ = pow(pi,-0.25) ; // 1.0/sqrt(sqrt(pi)) ??
50 << 45
51 fNumber = (nHermite + 1) / 2; << 46 fNumber = (nHermite +1)/2 ;
52 fAbscissa = new G4double[fNumber]; << 47 fAbscissa = new G4double[fNumber] ;
53 fWeight = new G4double[fNumber]; << 48 fWeight = new G4double[fNumber] ;
54 << 49
55 for(i = 1; i <= fNumber; ++i) << 50 for(i=1;i<=fNumber;i++)
56 { << 51 {
57 if(i == 1) << 52 if(i == 1)
58 { << 53 {
59 newton0 = << 54 newton = sqrt((G4double)(2*nHermite + 1)) -
60 std::sqrt((G4double)(2 * nHermite + 1) << 55 1.85575001*pow((G4double)(2*nHermite + 1),-0.16666999) ;
61 1.85575001 * std::pow((G4double)(2 * n << 56 }
62 } << 57 else if(i == 2)
63 else if(i == 2) << 58 {
64 { << 59 newton -= 1.14001*pow((G4double)nHermite,0.425999)/newton ;
65 newton0 -= 1.14001 * std::pow((G4double) << 60 }
66 } << 61 else if(i == 3)
67 else if(i == 3) << 62 {
68 { << 63 newton = 1.86002*newton - 0.86002*fAbscissa[0] ;
69 newton0 = 1.86002 * newton0 - 0.86002 * << 64 }
70 } << 65 else if(i == 4)
71 else if(i == 4) << 66 {
72 { << 67 newton = 1.91001*newton - 0.91001*fAbscissa[1] ;
73 newton0 = 1.91001 * newton0 - 0.91001 * << 68 }
74 } << 69 else
75 else << 70 {
76 { << 71 newton = 2.0*newton - fAbscissa[i - 3] ;
77 newton0 = 2.0 * newton0 - fAbscissa[i - << 72 }
78 } << 73 for(k=1;k<=maxNumber;k++)
79 for(k = 1; k <= maxNumber; ++k) << 74 {
80 { << 75 temp1 = piInMinusQ ;
81 temp1 = piInMinusQ; << 76 temp2 = 0.0 ;
82 temp2 = 0.0; << 77 for(j=1;j<=nHermite;j++)
83 for(j = 1; j <= nHermite; ++j) << 78 {
84 { << 79 temp3 = temp2 ;
85 temp3 = temp2; << 80 temp2 = temp1 ;
86 temp2 = temp1; << 81 temp1 = newton*sqrt(2.0/j)*temp2 - sqrt(((G4double)(j - 1))/j)*temp3 ;
87 temp1 = newton0 * std::sqrt(2.0 / j) * << 82 }
88 std::sqrt(((G4double)(j - 1)) << 83 temp = sqrt((G4double)2*nHermite)*temp2 ;
89 } << 84 newton1 = newton ;
90 temp = std::sqrt((G4double) 2 * nHerm << 85 newton = newton1 - temp1/temp ;
91 newton1 = newton0; << 86 if(fabs(newton - newton1) <= tolerance)
92 G4double ratio = std::numeric_limits<G4d << 87 {
93 if(temp > 0.0) << 88 break ;
94 { << 89 }
95 ratio = temp1 / temp; << 90 }
96 } << 91 if(k > maxNumber)
97 newton0 = newton1 - ratio; << 92 {
98 if(std::fabs(newton0 - newton1) <= toler << 93 G4Exception("Too many iterations in Gauss-Hermite constructor") ;
99 { << 94 }
100 break; << 95 fAbscissa[i-1] = newton ;
101 } << 96 fWeight[i-1] = 2.0/(temp*temp) ;
102 } << 97 }
103 if(k > maxNumber) <<
104 { <<
105 G4Exception("G4GaussHermiteQ::G4GaussHer <<
106 FatalException, <<
107 "Too many iterations in Gaus <<
108 } <<
109 fAbscissa[i - 1] = newton0; <<
110 fWeight[i - 1] = 2.0 / (temp * temp); <<
111 } <<
112 } 98 }
113 99
>> 100
114 // ------------------------------------------- 101 // ----------------------------------------------------------
115 // 102 //
116 // Gauss-Hermite method for integration of std << 103 // Gauss-Hermite method for integration of exp(-x*x)*nFunction(x) from minus infinity
117 // from minus infinity to plus infinity . << 104 // to plus infinity .
118 105
119 G4double G4GaussHermiteQ::Integral() const << 106 G4double
>> 107 G4GaussHermiteQ::Integral() const
120 { 108 {
121 G4double integral = 0.0; << 109 G4int i ;
122 for(G4int i = 0; i < fNumber; ++i) << 110 G4double integral = 0.0 ;
123 { << 111 for(i=0;i<fNumber;i++)
124 integral += << 112 {
125 fWeight[i] * (fFunction(fAbscissa[i]) + << 113 integral += fWeight[i]*(fFunction(fAbscissa[i]) + fFunction(-fAbscissa[i])) ;
126 } << 114 }
127 return integral; << 115 return integral ;
128 } 116 }
129 117