| 1 | /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ |
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| 2 | |
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| 3 | /* |
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| 4 | Copyright (C) 2003 Ferdinando Ametrano |
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| 5 | |
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| 6 | This file is part of QuantLib, a free-software/open-source library |
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| 7 | for financial quantitative analysts and developers - http://quantlib.org/ |
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| 8 | |
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| 9 | QuantLib is free software: you can redistribute it and/or modify it |
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| 10 | under the terms of the QuantLib license. You should have received a |
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| 11 | copy of the license along with this program; if not, please email |
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| 12 | <quantlib-dev@lists.sf.net>. The license is also available online at |
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| 13 | <http://quantlib.org/license.shtml>. |
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| 14 | |
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| 15 | This program is distributed in the hope that it will be useful, but WITHOUT |
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| 16 | ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
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| 17 | FOR A PARTICULAR PURPOSE. See the license for more details. |
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| 18 | */ |
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| 19 | |
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| 20 | #include <ql/math/beta.hpp> |
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| 21 | |
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| 22 | namespace QuantLib { |
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| 23 | |
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| 24 | /* |
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| 25 | The implementation of the algorithm was inspired by |
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| 26 | "Numerical Recipes in C", 2nd edition, |
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| 27 | Press, Teukolsky, Vetterling, Flannery, chapter 6 |
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| 28 | */ |
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| 29 | Real betaContinuedFraction(Real a, Real b, Real x, |
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| 30 | Real accuracy, Integer maxIteration) { |
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| 31 | |
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| 32 | Real aa, del; |
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| 33 | Real qab = a+b; |
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| 34 | Real qap = a+1.0; |
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| 35 | Real qam = a-1.0; |
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| 36 | Real c = 1.0; |
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| 37 | Real d = 1.0-qab*x/qap; |
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| 38 | if (std::fabs(x: d) < QL_EPSILON) |
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| 39 | d = QL_EPSILON; |
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| 40 | d = 1.0/d; |
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| 41 | Real result = d; |
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| 42 | |
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| 43 | Integer m, m2; |
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| 44 | for (m=1; m<=maxIteration; m++) { |
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| 45 | m2=2*m; |
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| 46 | aa=m*(b-m)*x/((qam+m2)*(a+m2)); |
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| 47 | d=1.0+aa*d; |
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| 48 | if (std::fabs(x: d) < QL_EPSILON) d=QL_EPSILON; |
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| 49 | c=1.0+aa/c; |
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| 50 | if (std::fabs(x: c) < QL_EPSILON) c=QL_EPSILON; |
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| 51 | d=1.0/d; |
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| 52 | result *= d*c; |
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| 53 | aa = -(a+m)*(qab+m)*x/((a+m2)*(qap+m2)); |
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| 54 | d=1.0+aa*d; |
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| 55 | if (std::fabs(x: d) < QL_EPSILON) d=QL_EPSILON; |
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| 56 | c=1.0+aa/c; |
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| 57 | if (std::fabs(x: c) < QL_EPSILON) c=QL_EPSILON; |
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| 58 | d=1.0/d; |
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| 59 | del=d*c; |
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| 60 | result *= del; |
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| 61 | if (std::fabs(x: del-1.0) < accuracy) |
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| 62 | return result; |
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| 63 | } |
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| 64 | QL_FAIL("a or b too big, or maxIteration too small in betacf" ); |
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| 65 | } |
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| 66 | |
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| 67 | Real incompleteBetaFunction(Real a, Real b, |
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| 68 | Real x, Real accuracy, |
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| 69 | Integer maxIteration) { |
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| 70 | |
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| 71 | QL_REQUIRE(a > 0.0, "a must be greater than zero" ); |
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| 72 | QL_REQUIRE(b > 0.0, "b must be greater than zero" ); |
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| 73 | |
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| 74 | |
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| 75 | if (x == 0.0) |
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| 76 | return 0.0; |
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| 77 | else if (x == 1.0) |
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| 78 | return 1.0; |
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| 79 | else |
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| 80 | QL_REQUIRE(x>0.0 && x<1.0, "x must be in [0,1]" ); |
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| 81 | |
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| 82 | Real result = std::exp(x: GammaFunction().logValue(x: a+b) - |
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| 83 | GammaFunction().logValue(x: a) - GammaFunction().logValue(x: b) + |
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| 84 | a*std::log(x: x) + b*std::log(x: 1.0-x)); |
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| 85 | |
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| 86 | if (x < (a+1.0)/(a+b+2.0)) |
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| 87 | return result * |
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| 88 | betaContinuedFraction(a, b, x, accuracy, maxIteration)/a; |
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| 89 | else |
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| 90 | return 1.0 - result * |
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| 91 | betaContinuedFraction(a: b, b: a, x: 1.0-x, accuracy, maxIteration)/b; |
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| 92 | } |
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| 93 | |
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| 94 | } |
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| 95 | |
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