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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
<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.
*/
#include <ql/math/integrals/discreteintegrals.hpp>
namespace QuantLib {
Real DiscreteTrapezoidIntegral::operator()(
const Array& x, const Array& f) const {
const Size n = f.size();
QL_REQUIRE(n == x.size(), "inconsistent size");
Real sum = 0.0;
for (Size i=0; i < n-1; ++i) {
sum += (x[i+1]-x[i])*(f[i]+f[i+1]);
}
return 0.5*sum;
}
Real DiscreteSimpsonIntegral::operator()(
const Array& x, const Array& f) const {
const Size n = f.size();
QL_REQUIRE(n == x.size(), "inconsistent size");
Real sum = 0.0;
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*dxj-dxjp1);
const Real dd = dxj+dxjp1;
const Real k = dd/(6*dxjp1*dxj);
const Real beta = dd*dd;
const Real gamma = dxj*(2*dxjp1-dxj);
sum += k*(alpha*f[j]+beta*f[j+1]+gamma*f[j+2]);
}
if ((n & 1) == 0U) {
sum += 0.5*(x[n-1]-x[n-2])*(f[n-1]+f[n-2]);
}
return sum;
}
Real DiscreteTrapezoidIntegrator::integrate(
const std::function<Real (Real)>& f, Real a, Real b) const {
const Size n=maxEvaluations()-1;
const Real d=(b-a)/n;
Real sum = f(a)*0.5;
for(Size i=0;i<n-1;++i) {
a += d;
sum += f(a);
}
sum += f(b)*0.5;
increaseNumberOfEvaluations(maxEvaluations());
return d * sum;
}
Real DiscreteSimpsonIntegrator::integrate(
const std::function<Real (Real)>& f, Real a, Real b) const {
const Size n=maxEvaluations()-1;
const Real d=(b-a)/n, d2=d*2;
Real sum = 0.0, x = a + d;
for(Size i=1;i<n;i+=2) {//to time 4
sum += f(x);
x += d2;
}
sum *= 2;
x = a+d2;
for(Size i=2;i<n-1;i+=2) {//to time 2
sum += f(x);
x += d2;
}
sum *= 2;
sum += f(a);
if((n&1) != 0U)
sum += 1.5*f(b)+2.5*f(b-d);
else
sum += f(b);
increaseNumberOfEvaluations(maxEvaluations());
return d/3 * sum;
}
}
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