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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.
*/
#include <ql/math/integrals/discreteintegrals.hpp>
#include <boost/accumulators/accumulators.hpp>
#include <boost/accumulators/statistics/sum.hpp>
using namespace boost::accumulators;
namespace QuantLib {
Real DiscreteTrapezoidIntegral::operator()(
const Array& x, const Array& f) const {
const Size n = f.size();
QL_REQUIRE(n == x.size(), "inconsistent size");
accumulator_set<Real, features<tag::sum> > acc;
for (Size i=0; i < n-1; ++i) {
acc((x[i+1]-x[i])*(f[i]+f[i+1]));
}
return 0.5*sum(acc);
}
Real DiscreteSimpsonIntegral::operator()(
const Array& x, const Array& f) const {
const Size n = f.size();
QL_REQUIRE(n == x.size(), "inconsistent size");
accumulator_set<Real, features<tag::sum> > acc;
for (Size j=0; j < n-2; j+=2) {
const Real dxj = x[j+1]-x[j];
const Real dxjp1 = x[j+2]-x[j+1];
const Real alpha = -dxjp1*(2*x[j]-3*x[j+1]+x[j+2]);
const Real dd = x[j+2]-x[j];
const Real k = dd/(6*dxjp1*dxj);
const Real beta = dd*dd;
const Real gamma = dxj*(x[j]-3*x[j+1]+2*x[j+2]);
acc(k*alpha*f[j]+k*beta*f[j+1]+k*gamma*f[j+2]);
}
if ((n & 1) == 0U) {
acc(0.5*(x[n-1]-x[n-2])*(f[n-1]+f[n-2]));
}
return sum(acc);
}
Real DiscreteTrapezoidIntegrator::integrate(
const ext::function<Real (Real)>& f, Real a, Real b) const {
const Array x(maxEvaluations(), a, (b-a)/(maxEvaluations()-1));
Array fv(x.size());
std::transform(x.begin(), x.end(), fv.begin(), f);
increaseNumberOfEvaluations(maxEvaluations());
return DiscreteTrapezoidIntegral()(x, fv);
}
Real DiscreteSimpsonIntegrator::integrate(
const ext::function<Real (Real)>& f, Real a, Real b) const {
const Array x(maxEvaluations(), a, (b-a)/(maxEvaluations()-1));
Array fv(x.size());
std::transform(x.begin(), x.end(), fv.begin(), f);
increaseNumberOfEvaluations(maxEvaluations());
return DiscreteSimpsonIntegral()(x, fv);
}
}
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