1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003 Ferdinando Ametrano
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
/*
The implementation of the algorithm was inspired by
"Numerical Recipes in C", 2nd edition,
Press, Teukolsky, Vetterling, Flannery, chapter 6
*/
#include <ql/math/incompletegamma.hpp>
#include <ql/math/distributions/gammadistribution.hpp>
namespace QuantLib {
Real incompleteGammaFunction(Real a, Real x, Real accuracy,
Integer maxIteration) {
QL_REQUIRE(a>0.0, "non-positive a is not allowed");
QL_REQUIRE(x>=0.0, "negative x non allowed");
if (x < (a+1.0)) {
// Use the series representation
return incompleteGammaFunctionSeriesRepr(a, x,
accuracy, maxIteration);
} else {
// Use the continued fraction representation
return 1.0-incompleteGammaFunctionContinuedFractionRepr(a, x,
accuracy, maxIteration);
}
}
Real incompleteGammaFunctionSeriesRepr(Real a, Real x, Real accuracy,
Integer maxIteration) {
if (x==0.0) return 0.0;
Real gln = GammaFunction().logValue(a);
Real ap=a;
Real del=1.0/a;
Real sum=del;
for (Integer n=1; n<=maxIteration; n++) {
++ap;
del *= x/ap;
sum += del;
if (std::fabs(del) < std::fabs(sum)*accuracy) {
return sum*std::exp(-x+a*std::log(x)-gln);
}
}
QL_FAIL("accuracy not reached");
}
Real incompleteGammaFunctionContinuedFractionRepr(Real a, Real x,
Real accuracy,
Integer maxIteration) {
Integer i;
Real an, b, c, d, del, h;
Real gln = GammaFunction().logValue(a);
b=x+1.0-a;
c=1.0/QL_EPSILON;
d=1.0/b;
h=d;
for (i=1; i<=maxIteration; i++) {
an = -i*(i-a);
b += 2.0;
d=an*d+b;
if (std::fabs(d) < QL_EPSILON) d=QL_EPSILON;
c=b+an/c;
if (std::fabs(c) < QL_EPSILON) c=QL_EPSILON;
d=1.0/d;
del=d*c;
h *= del;
if (std::fabs(del-1.0) < accuracy) {
return std::exp(-x+a*std::log(x)-gln)*h;
}
}
QL_FAIL("accuracy not reached");
}
}
|
