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/* -*- 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/experimental/math/expm.hpp>
#include <ql/experimental/math/adaptiverungekutta.hpp>
#include <numeric>
#include <algorithm>
namespace QuantLib {
namespace {
class MatrixVectorProductFct {
public:
MatrixVectorProductFct(const Matrix& m) : m_(m) {}
// implements x = M*y
Disposable<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), 0.0);
}
return result;
}
private:
const Matrix m_;
};
}
Disposable<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;
}
}
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