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segmentintegral.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*
 Copyright (C) 2000, 2001, 2002, 2003 RiskMap 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 segmentintegral.hpp
    \brief Integral of a one-dimensional function using segment algorithm
*/

#ifndef quantlib_segment_integral_h
#define quantlib_segment_integral_h

#include <ql/math/integrals/integral.hpp>
#include <ql/errors.hpp>

namespace QuantLib {

    //! Integral of a one-dimensional function
    /*! Given a number \f$ N \f$ of intervals, 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$.

        \test the correctness of the result is tested by checking it
              against known good values.
    */
00048     class SegmentIntegral : public Integrator {
      public:
        SegmentIntegral(Size intervals);
      protected:
        virtual Real integrate(const boost::function<Real (Real)>& f,
                               Real a,
                               Real b) const;
      private:
        Size intervals_;
    };


    // inline and template definitions

    inline Real
    SegmentIntegral::integrate(const boost::function<Real (Real)>& f,
                               Real a,
                               Real b) const {
        Real dx = (b-a)/intervals_;
        Real sum = 0.5*(f(a)+f(b));
        Real end = b - 0.5*dx;
        for (Real x = a+dx; x < end; x += dx)
            sum += f(x);
        return sum*dx;
    }

}

#endif

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