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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2015 Peter Caspers
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
<https://www.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 piecewiseintegral.hpp
\brief Integral of a piecewise well behaved function using
a custom integrator for the pieces. It can be forced
that the function is integrated only over intervals
strictly not containing the critical points
*/
#ifndef quantlib_piecewise_integral_hpp
#define quantlib_piecewise_integral_hpp
#include <ql/math/integrals/integral.hpp>
#include <ql/math/comparison.hpp>
#include <ql/shared_ptr.hpp>
#include <algorithm>
#include <vector>
namespace QuantLib {
class PiecewiseIntegral : public Integrator {
public:
PiecewiseIntegral(ext::shared_ptr<Integrator> integrator,
std::vector<Real> criticalPoints,
bool avoidCriticalPoints = true);
protected:
Real integrate(const std::function<Real(Real)>& f, Real a, Real b) const override;
private:
Real integrate_h(const std::function<Real(Real)> &f, Real a,
Real b) const;
const ext::shared_ptr<Integrator> integrator_;
std::vector<Real> criticalPoints_;
const Real eps_;
};
// inline
inline Real PiecewiseIntegral::integrate_h(const std::function<Real(Real)> &f,
Real a, Real b) const {
if (!close_enough(a, b))
return (*integrator_)(f, a, b);
else
return 0.0;
}
inline Real PiecewiseIntegral::integrate(const std::function<Real(Real)> &f,
Real a, Real b) const {
auto a0 = std::lower_bound(criticalPoints_.begin(), criticalPoints_.end(), a);
auto b0 = std::lower_bound(criticalPoints_.begin(), criticalPoints_.end(), b);
if (a0 == criticalPoints_.end()) {
Real tmp = 1.0;
if (!criticalPoints_.empty()) {
if (close_enough(a, criticalPoints_.back())) {
tmp = eps_;
}
}
return integrate_h(f, a * tmp, b);
}
Real res = 0.0;
if (!close_enough(a, *a0)) {
res += integrate_h(f, a, std::min(*a0 / eps_, b));
}
if (b0 == criticalPoints_.end()) {
--b0;
if (!close_enough(*b0, b)) {
res += integrate_h(f, (*b0) * eps_, b);
}
}
for (auto x = a0; x < b0; ++x) {
res += integrate_h(f, (*x) * eps_, std::min(*(x + 1) / eps_, b));
}
return res;
}
} // namespace QuantLib
#endif
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