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

/*

 Copyright (C) 2013 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 expm.cpp

    \brief matrix exponential

*/

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

#include <ql/math/ode/adaptiverungekutta.hpp>

#include <algorithm>

#include <numeric>

#include <utility>

namespace QuantLib {

    namespace {

        class MatrixVectorProductFct {

          public:

            explicit MatrixVectorProductFct(Matrix m) : m_(std::move(m)) {}

            // implements x = M*y

            std::vector<Real> operator()(Real t, const std::vector<Real>& y) {

                std::vector<Real> result(m_.rows());

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

                    result[i] = std::inner_product(y.begin(), y.end(),

                                                   m_.row_begin(i), Real(0.0));

                }

                return result;

            }

          private:

            const Matrix m_;

        };

    }

    Matrix Expm(const Matrix& M, Real t, Real tol) {

        const Size n = M.rows();

        QL_REQUIRE(n == M.columns(), "Expm expects a square matrix");

        AdaptiveRungeKutta<> rk(tol);

        AdaptiveRungeKutta<>::OdeFct odeFct = MatrixVectorProductFct(M);

        Matrix result(n, n);

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

            std::vector<Real> x0(n, 0.0);

            x0[i] = 1.0;

            const std::vector<Real> r = rk(odeFct, x0, 0.0, t);

            std::copy(r.begin(), r.end(), result.column_begin(i));

        }

        return result;

    }

}