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

/*

 Copyright (C) 2000, 2001, 2002, 2003 RiskMap srl

 Copyright (C) 2015 Peter Caspers

 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.

*/

/*! \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/math/comparison.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.

    */

    class SegmentIntegral : public Integrator {

      public:

        explicit SegmentIntegral(Size intervals);

      protected:

        Real integrate(const std::function<Real(Real)>& f, Real a, Real b) const override;

      private:

        Size intervals_;

    };

    // inline and template definitions

    inline Real

    SegmentIntegral::integrate(const std::function<Real (Real)>& f,

                               Real a,

                               Real b) const {

        if(close_enough(a,b))

            return 0.0;

        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