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

/*

 Copyright (C) 2018 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 trbdf2scheme.hpp

    \brief trapezoidal BDF2 scheme

*/

#ifndef quantlib_tr_bdf2_scheme_hpp

#define quantlib_tr_bdf2_scheme_hpp

#include <ql/functional.hpp>

#include <ql/math/functional.hpp>

#include <ql/math/matrixutilities/bicgstab.hpp>

#include <ql/math/matrixutilities/gmres.hpp>

#include <ql/methods/finitedifferences/operators/fdmlinearopcomposite.hpp>

#include <ql/methods/finitedifferences/operatortraits.hpp>

#include <ql/methods/finitedifferences/schemes/boundaryconditionschemehelper.hpp>

#include <utility>

namespace QuantLib {

    template <class TrapezoidalScheme>

    class TrBDF2Scheme {

      public:

        enum SolverType { BiCGstab, GMRES };

        // typedefs

        typedef OperatorTraits<FdmLinearOp> traits;

        typedef traits::operator_type operator_type;

        typedef traits::array_type array_type;

        typedef traits::bc_set bc_set;

        typedef traits::condition_type condition_type;

        // constructors

        TrBDF2Scheme(Real alpha,

                     ext::shared_ptr<FdmLinearOpComposite> map,

                     const ext::shared_ptr<TrapezoidalScheme>& trapezoidalScheme,

                     const bc_set& bcSet = bc_set(),

                     Real relTol = 1e-8,

                     SolverType solverType = BiCGstab);

        void step(array_type& a, Time t);

        void setStep(Time dt);

        Size numberOfIterations() const;

      protected:

        Array apply(const Array& r) const;

        Time dt_;

        Real beta_;

        ext::shared_ptr<Size> iterations_;

        const Real alpha_;

        const ext::shared_ptr<FdmLinearOpComposite> map_;

        const ext::shared_ptr<TrapezoidalScheme>& trapezoidalScheme_;

        const BoundaryConditionSchemeHelper bcSet_;

        const Real relTol_;

        const SolverType solverType_;

    };

    template <class TrapezoidalScheme>

    inline TrBDF2Scheme<TrapezoidalScheme>::TrBDF2Scheme(

        Real alpha,

        ext::shared_ptr<FdmLinearOpComposite> map,

        const ext::shared_ptr<TrapezoidalScheme>& trapezoidalScheme,

        const bc_set& bcSet,

        Real relTol,

        SolverType solverType)

    : dt_(Null<Real>()), beta_(Null<Real>()), iterations_(ext::make_shared<Size>(0U)),

      alpha_(alpha), map_(std::move(map)), trapezoidalScheme_(trapezoidalScheme), bcSet_(bcSet),

      relTol_(relTol), solverType_(solverType) {}

    template <class TrapezoidalScheme>

    inline void TrBDF2Scheme<TrapezoidalScheme>::setStep(Time dt) {

        dt_=dt;

        beta_= (1.0-alpha_)/(2.0-alpha_)*dt_;

    }

    template <class TrapezoidalScheme>

    inline Size TrBDF2Scheme<TrapezoidalScheme>::numberOfIterations() const {

        return *iterations_;

    }

    template <class TrapezoidalScheme>

    inline Array TrBDF2Scheme<TrapezoidalScheme>::apply(const Array& r) const {

        return r - beta_*map_->apply(r);

    }

    template <class TrapezoidalScheme>

    inline void TrBDF2Scheme<TrapezoidalScheme>::step(array_type& fn, Time t) {

        QL_REQUIRE(t-dt_ > -1e-8, "a step towards negative time given");

        const Time intermediateTimeStep = dt_*alpha_;

        array_type fStar = fn;

        trapezoidalScheme_->setStep(intermediateTimeStep);

        trapezoidalScheme_->step(fStar, t);

        bcSet_.setTime(std::max(0.0, t-dt_));

        bcSet_.applyBeforeSolving(*map_, fn);

        const array_type f =

            (1/alpha_*fStar - squared(1-alpha_)/alpha_*fn)/(2-alpha_);

        if (map_->size() == 1) {

            fn = map_->solve_splitting(0, f, -beta_);

        }

        else {

            auto preconditioner = [&](const Array& _a){ return map_->preconditioner(_a, -beta_); };

            auto applyF = [&](const Array& _a){ return apply(_a); };

            if (solverType_ == BiCGstab) {

                const BiCGStabResult result =

                    QuantLib::BiCGstab(applyF, std::max(Size(10), fn.size()),

                        relTol_, preconditioner).solve(f, f);

                (*iterations_) += result.iterations;

                fn = result.x;

            } else if (solverType_ == GMRES) {

                const GMRESResult result =

                    QuantLib::GMRES(applyF, std::max(Size(10), fn.size() / 10U), relTol_,

                                    preconditioner)

                        .solve(f, f);

                (*iterations_) += result.errors.size();

                fn = result.x;

            }

            else

                QL_FAIL("unknown/illegal solver type");

        }

        bcSet_.applyAfterSolving(fn);

    }

}

#endif