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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2017 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 gmres.hpp
\brief generalized minimal residual method
*/
#ifndef quantlib_gmres_hpp
#define quantlib_gmres_hpp
#include <ql/math/array.hpp>
#include <functional>
#include <list>
namespace QuantLib {
/*! References:
Saad, Yousef. 1996, Iterative methods for sparse linear systems,
http://www-users.cs.umn.edu/~saad/books.html
Dongarra et al. 1994,
Templates for the Solution of Linear Systems: Building Blocks
for Iterative Methods, 2nd Edition, SIAM, Philadelphia
http://www.netlib.org/templates/templates.pdf
Christian Kanzow
Numerik linearer Gleichungssysteme (German)
Chapter 6: GMRES und verwandte Verfahren
http://bilder.buecher.de/zusatz/12/12950/12950560_lese_1.pdf
*/
struct GMRESResult {
std::list<Real> errors;
Array x;
};
class GMRES {
public:
typedef std::function<Array(const Array&)> MatrixMult;
GMRES(MatrixMult A, Size maxIter, Real relTol, MatrixMult preConditioner = MatrixMult());
GMRESResult solve(const Array& b, const Array& x0 = Array()) const;
GMRESResult solveWithRestart(
Size restart, const Array& b, const Array& x0 = Array()) const;
protected:
GMRESResult solveImpl(const Array& b, const Array& x0) const;
const MatrixMult A_, M_;
const Size maxIter_;
const Real relTol_;
};
}
#endif
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