/* -*- 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

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

            // start from the coarsest trapezoid...

            Size N = 1;

            Real I = (f(a)+f(b))*(b-a)/2.0, newI;

            increaseNumberOfEvaluations(2);

            // ...and refine it

            Size i = 1;

            do {

                newI = IntegrationPolicy::integrate(f,a,b,I,N);

                increaseNumberOfEvaluations(N*(IntegrationPolicy::nbEvalutions()-1));

                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 {

        static Real integrate(const std::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;

        }

        static Size nbEvalutions(){ return 2;}

    };

    struct MidPoint {

        static Real integrate(const std::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;

        }

        static Size nbEvalutions(){ return 3;}

    };

}

#endif