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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003 Roman Gitlin
Copyright (C) 2003 StatPro Italia srl
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 trapezoidintegral.hpp
\brief integral of a one-dimensional function using the trapezoid formula
*/
#ifndef quantlib_trapezoid_integral_hpp
#define quantlib_trapezoid_integral_hpp
#include <ql/math/integrals/integral.hpp>
#include <ql/utilities/null.hpp>
#include <ql/errors.hpp>
namespace QuantLib {
//! Integral of a one-dimensional function
/*! Given a target accuracy \f$ \epsilon \f$, the integral of
a function \f$ f \f$ between \f$ a \f$ and \f$ b \f$ is
calculated by means of the trapezoid formula
\f[
\int_{a}^{b} f \mathrm{d}x =
\frac{1}{2} f(x_{0}) + f(x_{1}) + f(x_{2}) + \dots
+ f(x_{N-1}) + \frac{1}{2} f(x_{N})
\f]
where \f$ x_0 = a \f$, \f$ x_N = b \f$, and
\f$ x_i = a+i \Delta x \f$ with
\f$ \Delta x = (b-a)/N \f$. The number \f$ N \f$ of intervals
is repeatedly increased until the target accuracy is reached.
\test the correctness of the result is tested by checking it
against known good values.
*/
template <class IntegrationPolicy>
class TrapezoidIntegral : public Integrator {
public:
TrapezoidIntegral(Real accuracy,
Size maxIterations)
: Integrator(accuracy, maxIterations){}
protected:
Real integrate (const boost::function<Real (Real)>& f,
Real a,
Real b) const {
// start from the coarsest trapezoid...
Size N = 1;
Real I = (f(a)+f(b))*(b-a)/2.0, newI;
// ...and refine it
Size i = 1;
do {
newI = IntegrationPolicy::integrate(f,a,b,I,N);
N *= IntegrationPolicy::nbEvalutions();
// good enough? Also, don't run away immediately
if (std::fabs(I-newI) <= absoluteAccuracy() && i > 5)
// ok, exit
return newI;
// oh well. Another step.
I = newI;
i++;
} while (i < maxEvaluations());
QL_FAIL("max number of iterations reached");
}
};
// Integration policies
struct Default {
inline static Real integrate(const boost::function<Real (Real)>& f,
Real a,
Real b,
Real I,
Size N)
{
Real sum = 0.0;
Real dx = (b-a)/N;
Real x = a + dx/2.0;
for (Size i=0; i<N; x += dx, ++i)
sum += f(x);
return (I + dx*sum)/2.0;
}
inline static Size nbEvalutions(){ return 2;}
};
struct MidPoint {
inline static Real integrate(const boost::function<Real (Real)>& f,
Real a,
Real b,
Real I,
Size N)
{
Real sum = 0.0;
Real dx = (b-a)/N;
Real x = a + dx/6.0;
Real D = 2.0*dx/3.0;
for (Size i=0; i<N; x += dx, ++i)
sum += f(x) + f(x+D);
return (I + dx*sum)/3.0;
}
inline static Size nbEvalutions(){ return 3;}
};
}
#endif
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