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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 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 gausslabottointegral.cpp
\brief integral of a one-dimensional function using the adaptive
Gauss-Lobatto integral
*/
#include <ql/math/integrals/gausslobattointegral.hpp>
namespace QuantLib {
const Real GaussLobattoIntegral::alpha_ = std::sqrt(2.0/3.0);
const Real GaussLobattoIntegral::beta_ = 1.0/std::sqrt(5.0);
const Real GaussLobattoIntegral::x1_ = 0.94288241569547971906;
const Real GaussLobattoIntegral::x2_ = 0.64185334234578130578;
const Real GaussLobattoIntegral::x3_ = 0.23638319966214988028;
GaussLobattoIntegral::GaussLobattoIntegral(Size maxIterations,
Real absAccuracy,
Real relAccuracy,
bool useConvergenceEstimate)
: Integrator(absAccuracy, maxIterations),
relAccuracy_(relAccuracy),
useConvergenceEstimate_(useConvergenceEstimate) {
}
Real GaussLobattoIntegral::integrate(
const boost::function<Real (Real)>& f,
Real a, Real b) const {
setNumberOfEvaluations(0);
const Real calcAbsTolerance = calculateAbsTolerance(f, a, b);
increaseNumberOfEvaluations(2);
return adaptivGaussLobattoStep(f, a, b, f(a), f(b), calcAbsTolerance);
}
Real GaussLobattoIntegral::calculateAbsTolerance(
const boost::function<Real (Real)>& f,
Real a, Real b) const {
Real relTol = std::max(relAccuracy_, QL_EPSILON);
const Real m = (a+b)/2;
const Real h = (b-a)/2;
const Real y1 = f(a);
const Real y3 = f(m-alpha_*h);
const Real y5 = f(m-beta_*h);
const Real y7 = f(m);
const Real y9 = f(m+beta_*h);
const Real y11= f(m+alpha_*h);
const Real y13= f(b);
Real acc=h*(0.0158271919734801831*(y1+y13)
+0.0942738402188500455*(f(m-x1_*h)+f(m+x1_*h))
+0.1550719873365853963*(y3+y11)
+0.1888215739601824544*(f(m-x2_*h)+ f(m+x2_*h))
+0.1997734052268585268*(y5+y9)
+0.2249264653333395270*(f(m-x3_*h)+f(m+x3_*h))
+0.2426110719014077338*y7);
increaseNumberOfEvaluations(13);
QL_REQUIRE(acc != 0.0, "can not calculate absolute accuracy from "
"relative accuracy");
Real r = 1.0;
if (useConvergenceEstimate_) {
const Real integral2 = (h/6)*(y1+y13+5*(y5+y9));
const Real integral1 = (h/1470)*(77*(y1+y13)+432*(y3+y11)+
625*(y5+y9)+672*y7);
if (std::fabs(integral2-acc) != 0.0)
r = std::fabs(integral1-acc)/std::fabs(integral2-acc);
if (r == 0.0 || r > 1.0)
r = 1.0;
}
if (relAccuracy_ != Null<Real>())
return std::min(absoluteAccuracy(), acc*relTol)/(r*QL_EPSILON);
else {
return absoluteAccuracy()/(r*QL_EPSILON);
}
}
Real GaussLobattoIntegral::adaptivGaussLobattoStep(
const boost::function<Real (Real)>& f,
Real a, Real b, Real fa, Real fb,
Real acc) const {
QL_REQUIRE(numberOfEvaluations() < maxEvaluations(),
"max number of iterations reached");
const Real h=(b-a)/2;
const Real m=(a+b)/2;
const Real mll=m-alpha_*h;
const Real ml =m-beta_*h;
const Real mr =m+beta_*h;
const Real mrr=m+alpha_*h;
const Real fmll= f(mll);
const Real fml = f(ml);
const Real fm = f(m);
const Real fmr = f(mr);
const Real fmrr= f(mrr);
increaseNumberOfEvaluations(5);
const Real integral2=(h/6)*(fa+fb+5*(fml+fmr));
const Real integral1=(h/1470)*(77*(fa+fb)
+432*(fmll+fmrr)+625*(fml+fmr)+672*fm);
// avoid 80 bit logic on x86 cpu
volatile Real dist = acc + (integral1-integral2);
if(dist==acc || mll<=a || b<=mrr) {
QL_REQUIRE(m>a && b>m,"Interval contains no more machine number");
return integral1;
}
else {
return adaptivGaussLobattoStep(f,a,mll,fa,fmll,acc)
+ adaptivGaussLobattoStep(f,mll,ml,fmll,fml,acc)
+ adaptivGaussLobattoStep(f,ml,m,fml,fm,acc)
+ adaptivGaussLobattoStep(f,m,mr,fm,fmr,acc)
+ adaptivGaussLobattoStep(f,mr,mrr,fmr,fmrr,acc)
+ adaptivGaussLobattoStep(f,mrr,b,fmrr,fb,acc);
}
}
}
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