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

/*

 Copyright (C) 2009 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

 <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 fdmblackscholesmultistrikemesher.cpp

    \brief 1-d mesher for the Black-Scholes process (in ln(S))

*/

#include <ql/processes/blackscholesprocess.hpp>

#include <ql/termstructures/yieldtermstructure.hpp>

#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>

#include <ql/math/distributions/normaldistribution.hpp>

#include <ql/methods/finitedifferences/meshers/uniform1dmesher.hpp>

#include <ql/methods/finitedifferences/meshers/concentrating1dmesher.hpp>

#include <ql/methods/finitedifferences/meshers/fdmblackscholesmultistrikemesher.hpp>

namespace QuantLib {

    FdmBlackScholesMultiStrikeMesher::FdmBlackScholesMultiStrikeMesher(

            Size size,

            const ext::shared_ptr<GeneralizedBlackScholesProcess>& process,

            Time maturity, const std::vector<Real>& strikes,

            Real eps, Real scaleFactor,

            const std::pair<Real, Real>& cPoint)

    : Fdm1dMesher(size) {

        const Real spot = process->x0();

        QL_REQUIRE(spot > 0.0, "negative or null underlying given");

        const DiscountFactor d =   process->dividendYield()->discount(maturity)

                                 / process->riskFreeRate()->discount(maturity);

        const Real minStrike= *std::min_element(strikes.begin(), strikes.end());

        const Real maxStrike= *std::max_element(strikes.begin(), strikes.end());

        const Real Fmin = spot*spot/maxStrike*d;

        const Real Fmax = spot*spot/minStrike*d;

        QL_REQUIRE(Fmin > 0.0, "negative forward given");

        // Set the grid boundaries

        const Real normInvEps = InverseCumulativeNormal()(1-eps);

        const Real sigmaSqrtTmin 

            = process->blackVolatility()->blackVol(maturity, minStrike)

                                                        *std::sqrt(maturity);

        const Real sigmaSqrtTmax 

            = process->blackVolatility()->blackVol(maturity, maxStrike)

                                                        *std::sqrt(maturity);

        const Real xMin

            = std::min(0.8*std::log(0.8*spot*spot/maxStrike),

                       std::log(Fmin) - sigmaSqrtTmin*normInvEps*scaleFactor

                                      - sigmaSqrtTmin*sigmaSqrtTmin/2.0);

        const Real xMax

            = std::max(1.2*std::log(0.8*spot*spot/minStrike),

                       std::log(Fmax) + sigmaSqrtTmax*normInvEps*scaleFactor

                                      - sigmaSqrtTmax*sigmaSqrtTmax/2.0);

        ext::shared_ptr<Fdm1dMesher> helper;

        if (   cPoint.first != Null<Real>() 

            && std::log(cPoint.first) >=xMin && std::log(cPoint.first) <=xMax) {

            helper = ext::shared_ptr<Fdm1dMesher>(

                new Concentrating1dMesher(xMin, xMax, size, 

                    std::pair<Real,Real>(std::log(cPoint.first),cPoint.second)));

        }

        else {

            helper = ext::shared_ptr<Fdm1dMesher>(

                                        new Uniform1dMesher(xMin, xMax, size));

        }

        locations_ = helper->locations();

        for (Size i=0; i < locations_.size(); ++i) {

            dplus_[i]  = helper->dplus(i);

            dminus_[i] = helper->dminus(i);

        }

    }            

}