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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2014 Klaus Spanderen
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.
*/
/*! \file filonintegral.cpp
\brief Filon's formulae for sine and cosine Integrals
*/
#include <ql/errors.hpp>
#include <ql/utilities/null.hpp>
#include <ql/math/array.hpp>
#include <ql/math/functional.hpp>
#include <ql/math/integrals/filonintegral.hpp>
#include <cmath>
namespace QuantLib {
FilonIntegral::FilonIntegral(Type type, Real t, Size intervals)
: Integrator(Null<Real>(), intervals+1),
type_(type),
t_(t),
intervals_(intervals),
n_ (intervals/2){
QL_REQUIRE( !(intervals_ & 1), "number of intervals must be even");
}
Real FilonIntegral::integrate(const ext::function<Real (Real)>& f,
Real a, Real b) const {
const Real h = (b-a)/(2*n_);
Array x(2*n_+1, a, h);
const Real theta = t_*h;
const Real theta2 = theta*theta;
const Real theta3 = theta2*theta;
const Real alpha = 1/theta + std::sin(2*theta)/(2*theta2)
- 2*square<Real>()(std::sin(theta))/theta3;
const Real beta = 2*( (1+square<Real>()(std::cos(theta)))/theta2
- std::sin(2*theta)/theta3);
const Real gamma = 4*(std::sin(theta)/theta3 - std::cos(theta)/theta2);
Array v(x.size());
std::transform(x.begin(), x.end(), v.begin(), f);
ext::function<Real(Real)> f1, f2;
switch(type_) {
case Cosine:
f1 = static_cast<Real(*)(Real)>(std::sin);
f2 = static_cast<Real(*)(Real)>(std::cos);
break;
case Sine:
f1 = static_cast<Real(*)(Real)>(std::cos);
f2 = static_cast<Real(*)(Real)>(std::sin);
break;
default:
QL_FAIL("unknown integration type");
}
Real c_2n_1 = 0.0;
Real c_2n = v[0]*f2(t_*a)
- 0.5*(v[2*n_]*f2(t_*b) + v[0]*f2(t_*a));
for (Size i=1; i <= n_; ++i) {
c_2n += v[2*i] *f2(t_*x[2*i]);
c_2n_1 += v[2*i-1]*f2(t_*x[2*i-1]);
}
return h*(alpha*(v[2*n_]*f1(t_*x[2*n_]) - v[0]*f1(t_*x[0]))
*((type_ == Cosine) ? 1.0 : -1.0)
+ beta*c_2n + gamma*c_2n_1);
}
}
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