| Geant4 Cross Reference |
1 //
2 // ********************************************************************
3 // * License and Disclaimer *
4 // * *
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17 // * *
18 // * This code implementation is the result of the scientific and *
19 // * technical work of the GEANT4 collaboration. *
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24 // ********************************************************************
25 //
26 //
27 //
28 // ------------------------------------------------------------
29 // GEANT 4 class implementation
30 // ------------------------------------------------------------
31
32 #include <cmath>
33 #include <string.h>
34 #include "Gamma.hh"
35
36 MyGamma::MyGamma(){}
37
38 MyGamma::~MyGamma(){}
39
40 //____________________________________________________________________________
41 double MyGamma::Gamma(double z)
42 {
43 if (z <= 0)
44 return 0;
45
46 return std::tgamma(z);
47 }
48
49 //____________________________________________________________________________
50 double MyGamma::Gamma(double a, double x)
51 {
52 // Computation of the incomplete gamma function P(a,x)
53 //
54 // The algorithm is based on the formulas and code as denoted in
55 // Numerical Recipes 2nd ed. on p. 210-212 (W.H.Press et al.).
56 //
57 //--- Nve 14-nov-1998 UU-SAP Utrecht
58
59 if (a <= 0 || x <= 0) return 0;
60
61 if (x < (a + 1))
62 return GamSer(a, x);
63 else
64 return GamCf(a, x);
65 }
66
67 //____________________________________________________________________________
68 double MyGamma::GamCf(double a, double x)
69 {
70 // Computation of the incomplete gamma function P(a,x)
71 // via its continued fraction representation.
72 //
73 // The algorithm is based on the formulas and code as denoted in
74 // Numerical Recipes 2nd ed. on p. 210-212 (W.H.Press et al.).
75 //
76 //--- Nve 14-nov-1998 UU-SAP Utrecht
77
78 int itmax = 100; // Maximum number of iterations
79 double eps = 3.e-7; // Relative accuracy
80 double fpmin = 1.e-30; // Smallest double value allowed here
81
82 if (a <= 0 || x <= 0) return 0;
83
84 double gln = LnGamma(a);
85 double b = x + 1 - a;
86 double c = 1 / fpmin;
87 double d = 1 / b;
88 double h = d;
89 double an, del;
90 for (int i = 1; i <= itmax; i++) {
91 an = double(-i) * (double(i) - a);
92 b += 2;
93 d = an * d + b;
94 if (Abs(d) < fpmin) d = fpmin;
95 c = b + an / c;
96 if (Abs(c) < fpmin) c = fpmin;
97 d = 1 / d;
98 del = d * c;
99 h = h * del;
100 if (Abs(del - 1) < eps) break;
101 // if (i==itmax) cout << "*GamCf(a,x)* a too large or itmax too small" << endl;
102 }
103 double v = Exp(-x + a * Log(x) - gln) * h;
104 return (1 - v);
105 }
106
107 //____________________________________________________________________________
108 double MyGamma::GamSer(double a, double x)
109 {
110 // Computation of the incomplete gamma function P(a,x)
111 // via its series representation.
112 //
113 // The algorithm is based on the formulas and code as denoted in
114 // Numerical Recipes 2nd ed. on p. 210-212 (W.H.Press et al.).
115 //
116 //--- Nve 14-nov-1998 UU-SAP Utrecht
117
118 int itmax = 100; // Maximum number of iterations
119 double eps = 3.e-7; // Relative accuracy
120
121 if (a <= 0 || x <= 0) return 0;
122
123 double gln = LnGamma(a);
124 double ap = a;
125 double sum = 1 / a;
126 double del = sum;
127 for (int n = 1; n <= itmax; n++) {
128 ap += 1;
129 del = del * x / ap;
130 sum += del;
131 if (MyGamma::Abs(del) < Abs(sum * eps)) break;
132 // if (n==itmax) cout << "*GamSer(a,x)* a too large or itmax too small" << endl;
133 }
134 double v = sum * Exp(-x + a * Log(x) - gln);
135 return v;
136 }
137
138 double MyGamma::LnGamma(double z)
139 {
140 if (z <= 0)
141 return 0;
142
143 return std::lgamma(z);
144 }
145