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

/*

 Copyright (C) 2024 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.

*/

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

namespace QuantLib {

    HouseholderTransformation::HouseholderTransformation(Array v)

    : v_(std::move(v)) {}

    Array HouseholderTransformation::operator()(const Array& x) const {

        return x - (2.0*DotProduct(v_, x))*v_;

    }

    Matrix HouseholderTransformation::getMatrix() const {

        const Array y = v_ / Norm2(v_);

        const Size n = y.size();

        Matrix m(n, n);

        for (Size i=0; i < n; ++i)

            for (Size j=0; j < n; ++j)

                m[i][j] = ((i == j)? 1.0: 0.0) - 2*y[i]*y[j];

        return m;

    }

    HouseholderReflection::HouseholderReflection(Array e)

    : e_(std::move(e)) {}

    Array HouseholderReflection::reflectionVector(const Array& a) const {

        const Real na = Norm2(a);

        QL_REQUIRE(na > 0, "vector of length zero given");

        const Real aDotE = DotProduct(a, e_);

        const Array a1 = aDotE*e_;

        const Array a2 = a - a1;

        const Real eps = DotProduct(a2, a2) / (aDotE*aDotE);

        if (eps < QL_EPSILON*QL_EPSILON) {

            return Array(a.size(), 0.0);

        }

        else if (eps < 1e-4) {

            const Real eps2 = eps*eps;

            const Real eps3 = eps*eps2;

            const Real eps4 = eps2*eps2;

            const Array v =

                (a2 - a1*(eps/2.0 - eps2/8.0 + eps3/16.0 - 5/128.0*eps4))

                / (aDotE*std::sqrt(eps + eps2/4.0 - eps3/8.0 + 5/64.0*eps4));

            return v;

        }

        else {

            const Array c = a - na*e_;

            return c / Norm2(c);

        }

    }

    Array HouseholderReflection::operator()(const Array& a) const {

        const Array v = reflectionVector(a);

        return HouseholderTransformation(v)(a);

    }

}