QuantLib: a free/open-source library for quantitative finance
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beta.cpp
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1/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2
3/*
4 Copyright (C) 2003 Ferdinando Ametrano
5
6 This file is part of QuantLib, a free-software/open-source library
7 for financial quantitative analysts and developers - http://quantlib.org/
8
9 QuantLib is free software: you can redistribute it and/or modify it
10 under the terms of the QuantLib license. You should have received a
11 copy of the license along with this program; if not, please email
12 <quantlib-dev@lists.sf.net>. The license is also available online at
13 <http://quantlib.org/license.shtml>.
14
15 This program is distributed in the hope that it will be useful, but WITHOUT
16 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
17 FOR A PARTICULAR PURPOSE. See the license for more details.
18*/
19
20#include <ql/math/beta.hpp>
21
22namespace QuantLib {
23
24 /*
25 The implementation of the algorithm was inspired by
26 "Numerical Recipes in C", 2nd edition,
27 Press, Teukolsky, Vetterling, Flannery, chapter 6
28 */
30 Real accuracy, Integer maxIteration) {
31
32 Real aa, del;
33 Real qab = a+b;
34 Real qap = a+1.0;
35 Real qam = a-1.0;
36 Real c = 1.0;
37 Real d = 1.0-qab*x/qap;
38 if (std::fabs(d) < QL_EPSILON)
39 d = QL_EPSILON;
40 d = 1.0/d;
41 Real result = d;
42
43 Integer m, m2;
44 for (m=1; m<=maxIteration; m++) {
45 m2=2*m;
46 aa=m*(b-m)*x/((qam+m2)*(a+m2));
47 d=1.0+aa*d;
48 if (std::fabs(d) < QL_EPSILON) d=QL_EPSILON;
49 c=1.0+aa/c;
50 if (std::fabs(c) < QL_EPSILON) c=QL_EPSILON;
51 d=1.0/d;
52 result *= d*c;
53 aa = -(a+m)*(qab+m)*x/((a+m2)*(qap+m2));
54 d=1.0+aa*d;
55 if (std::fabs(d) < QL_EPSILON) d=QL_EPSILON;
56 c=1.0+aa/c;
57 if (std::fabs(c) < QL_EPSILON) c=QL_EPSILON;
58 d=1.0/d;
59 del=d*c;
60 result *= del;
61 if (std::fabs(del-1.0) < accuracy)
62 return result;
63 }
64 QL_FAIL("a or b too big, or maxIteration too small in betacf");
65 }
66
68 Real x, Real accuracy,
69 Integer maxIteration) {
70
71 QL_REQUIRE(a > 0.0, "a must be greater than zero");
72 QL_REQUIRE(b > 0.0, "b must be greater than zero");
73
74
75 if (x == 0.0)
76 return 0.0;
77 else if (x == 1.0)
78 return 1.0;
79 else
80 QL_REQUIRE(x>0.0 && x<1.0, "x must be in [0,1]");
81
82 Real result = std::exp(GammaFunction().logValue(a+b) -
83 GammaFunction().logValue(a) - GammaFunction().logValue(b) +
84 a*std::log(x) + b*std::log(1.0-x));
85
86 if (x < (a+1.0)/(a+b+2.0))
87 return result *
88 betaContinuedFraction(a, b, x, accuracy, maxIteration)/a;
89 else
90 return 1.0 - result *
91 betaContinuedFraction(b, a, 1.0-x, accuracy, maxIteration)/b;
92 }
93
94}
Beta and beta incomplete functions.
Gamma function class.
#define QL_REQUIRE(condition, message)
throw an error if the given pre-condition is not verified
Definition: errors.hpp:117
#define QL_FAIL(message)
throw an error (possibly with file and line information)
Definition: errors.hpp:92
Date d
ext::function< Real(Real)> b
#define QL_EPSILON
Definition: qldefines.hpp:178
QL_REAL Real
real number
Definition: types.hpp:50
QL_INTEGER Integer
integer number
Definition: types.hpp:35
Definition: any.hpp:35
Real betaContinuedFraction(Real a, Real b, Real x, Real accuracy, Integer maxIteration)
Definition: beta.cpp:29
Real incompleteBetaFunction(Real a, Real b, Real x, Real accuracy, Integer maxIteration)
Incomplete Beta function.
Definition: beta.cpp:67