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

 /*

 Copyright (C) 2009 Frédéric Degraeve

 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.

*/

#include <ql/math/optimization/bfgs.hpp>

#include <ql/math/optimization/problem.hpp>

#include <ql/math/optimization/linesearch.hpp>

namespace QuantLib {

    Array BFGS::getUpdatedDirection(const Problem& P,

                                    Real,

                                    const Array& oldGradient) {

        if (inverseHessian_.rows() == 0)

        {

            // first time in this update, we create needed structures

            inverseHessian_ = Matrix(P.currentValue().size(),

                                     P.currentValue().size(), 0.);

            for (Size i = 0; i < P.currentValue().size(); ++i)

                inverseHessian_[i][i] = 1.;

        }

        Array diffGradient;

        Array diffGradientWithHessianApplied(P.currentValue().size(), 0.);

        diffGradient = lineSearch_->lastGradient() - oldGradient;

        for (Size i = 0; i < P.currentValue().size(); ++i)

            for (Size j = 0; j < P.currentValue().size(); ++j)

                diffGradientWithHessianApplied[i] += inverseHessian_[i][j] * diffGradient[j];

        Real fac, fae, fad;

        Real sumdg, sumxi;

        fac = fae = sumdg = sumxi = 0.;

        for (Size i = 0; i < P.currentValue().size(); ++i)

        {

            fac += diffGradient[i] * lineSearch_->searchDirection()[i];

            fae += diffGradient[i] * diffGradientWithHessianApplied[i];

            sumdg += std::pow(diffGradient[i], 2.);

            sumxi += std::pow(lineSearch_->searchDirection()[i], 2.);

        }

        if (fac > std::sqrt(1e-8 * sumdg * sumxi))  // skip update if fac not sufficiently positive

        {

            fac = 1.0 / fac;

            fad = 1.0 / fae;

            for (Size i = 0; i < P.currentValue().size(); ++i)

                diffGradient[i] = fac * lineSearch_->searchDirection()[i] - fad * diffGradientWithHessianApplied[i];

            for (Size i = 0; i < P.currentValue().size(); ++i)

                for (Size j = 0; j < P.currentValue().size(); ++j)

                {

                    inverseHessian_[i][j] += fac * lineSearch_->searchDirection()[i] * lineSearch_->searchDirection()[j];

                    inverseHessian_[i][j] -= fad * diffGradientWithHessianApplied[i] * diffGradientWithHessianApplied[j];

                    inverseHessian_[i][j] += fae * diffGradient[i] * diffGradient[j];

                }

        }

        //else

        //  throw "BFGS: FAC not sufficiently positive";

        Array direction(P.currentValue().size());

        for (Size i = 0; i < P.currentValue().size(); ++i)

        {

            direction[i] = 0.0;

            for (Size j = 0; j < P.currentValue().size(); ++j)

                direction[i] -= inverseHessian_[i][j] * lineSearch_->lastGradient()[j];

        }

        return direction;

    }

}