firstderivativeop.cpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2008 Andreas Gaida
 Copyright (C) 2008 Ralph Schreyer
 Copyright (C) 2008 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/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/firstderivativeop.hpp>
 
namespace QuantLib {
 
    FirstDerivativeOp::FirstDerivativeOp(
                                Size direction,
                                const ext::shared_ptr<FdmMesher>& mesher)
    : TripleBandLinearOp(direction, mesher) {
 
        for (const auto& iter : *mesher->layout()) {
            const Size i = iter.index();
            const Real hm = mesher->dminus(iter, direction_);
            const Real hp = mesher->dplus(iter, direction_);
 
            const Real zetam1 = hm*(hm+hp);
            const Real zeta0  = hm*hp;
            const Real zetap1 = hp*(hm+hp);
 
            if (iter.coordinates()[direction_] == 0) {
                //upwinding scheme
                lower_[i] = 0.0;
                diag_[i]  = -(upper_[i] = 1/hp);
            }
            else if (   iter.coordinates()[direction_]
                     == mesher->layout()->dim()[direction]-1) {
                 // downwinding scheme
                lower_[i] = -(diag_[i] = 1/hm);
                upper_[i] = 0.0;
            }
            else {
                lower_[i] = -hp/zetam1;
                diag_[i]  = (hp-hm)/zeta0;
                upper_[i] = hm/zetap1;
            }
        }
    }
}