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/* -*- 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.
*/
#include <ql/math/beta.hpp>
namespace QuantLib {
/*
The implementation of the algorithm was inspired by
"Numerical Recipes in C", 2nd edition,
Press, Teukolsky, Vetterling, Flannery, chapter 6
*/
Real betaContinuedFraction(Real a, Real b, Real x,
Real accuracy, Integer maxIteration) {
Real aa, del;
Real qab = a+b;
Real qap = a+1.0;
Real qam = a-1.0;
Real c = 1.0;
Real d = 1.0-qab*x/qap;
if (std::fabs(d) < QL_EPSILON)
d = QL_EPSILON;
d = 1.0/d;
Real result = d;
Integer m, m2;
for (m=1; m<=maxIteration; m++) {
m2=2*m;
aa=m*(b-m)*x/((qam+m2)*(a+m2));
d=1.0+aa*d;
if (std::fabs(d) < QL_EPSILON) d=QL_EPSILON;
c=1.0+aa/c;
if (std::fabs(c) < QL_EPSILON) c=QL_EPSILON;
d=1.0/d;
result *= d*c;
aa = -(a+m)*(qab+m)*x/((a+m2)*(qap+m2));
d=1.0+aa*d;
if (std::fabs(d) < QL_EPSILON) d=QL_EPSILON;
c=1.0+aa/c;
if (std::fabs(c) < QL_EPSILON) c=QL_EPSILON;
d=1.0/d;
del=d*c;
result *= del;
if (std::fabs(del-1.0) < accuracy)
return result;
}
QL_FAIL("a or b too big, or maxIteration too small in betacf");
}
Real incompleteBetaFunction(Real a, Real b,
Real x, Real accuracy,
Integer maxIteration) {
QL_REQUIRE(a > 0.0, "a must be greater than zero");
QL_REQUIRE(b > 0.0, "b must be greater than zero");
if (x == 0.0)
return 0.0;
else if (x == 1.0)
return 1.0;
else
QL_REQUIRE(x>0.0 && x<1.0, "x must be in [0,1]");
Real result = std::exp(GammaFunction().logValue(a+b) -
GammaFunction().logValue(a) - GammaFunction().logValue(b) +
a*std::log(x) + b*std::log(1.0-x));
if (x < (a+1.0)/(a+b+2.0))
return result *
betaContinuedFraction(a, b, x, accuracy, maxIteration)/a;
else
return 1.0 - result *
betaContinuedFraction(b, a, 1.0-x, accuracy, maxIteration)/b;
}
}
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