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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2011 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 fdmg2op.cpp */
#include <ql/models/shortrate/twofactormodels/g2.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/fdmg2op.hpp>
#include <ql/methods/finitedifferences/operators/firstderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/secondordermixedderivativeop.hpp>
namespace QuantLib {
FdmG2Op::FdmG2Op(
const ext::shared_ptr<FdmMesher>& mesher,
const ext::shared_ptr<G2>& model,
Size direction1, Size direction2)
: direction1_(direction1),
direction2_(direction2),
x_(mesher->locations(direction1)),
y_(mesher->locations(direction2)),
dxMap_(FirstDerivativeOp(direction1, mesher).mult(-x_*model->a()).add(
SecondDerivativeOp(direction1, mesher)
.mult(0.5*model->sigma()*model->sigma()
*Array(mesher->layout()->size(), 1.0)))),
dyMap_(FirstDerivativeOp(direction2, mesher).mult(-y_*model->b()).add(
SecondDerivativeOp(direction2, mesher)
.mult(0.5*model->eta()*model->eta()
*Array(mesher->layout()->size(), 1.0)))),
corrMap_(SecondOrderMixedDerivativeOp(direction1, direction2, mesher)
.mult(Array(mesher->layout()->size(),
model->rho()*model->sigma()*model->eta()))),
mapX_(direction1, mesher),
mapY_(direction2, mesher),
model_(model) {
}
Size FdmG2Op::size() const { return 2U; }
void FdmG2Op::setTime(Time t1, Time t2) {
const ext::shared_ptr<TwoFactorModel::ShortRateDynamics> dynamics =
model_->dynamics();
const Real phi = 0.5*( dynamics->shortRate(t1, 0.0, 0.0)
+ dynamics->shortRate(t2, 0.0, 0.0));
const Array hr = -0.5*(x_ + y_ + phi);
mapX_.axpyb(Array(), dxMap_, dxMap_, hr);
mapY_.axpyb(Array(), dyMap_, dyMap_, hr);
}
Disposable<Array> FdmG2Op::apply(const Array& r) const {
return mapX_.apply(r) + mapY_.apply(r) + apply_mixed(r);
}
Disposable<Array> FdmG2Op::apply_mixed(const Array& r) const {
return corrMap_.apply(r);
}
Disposable<Array>
FdmG2Op::apply_direction(Size direction, const Array& r) const {
if (direction == direction1_) {
return mapX_.apply(r);
}
else if (direction == direction2_) {
return mapY_.apply(r);
}
else {
Array retVal(r.size(), 0.0);
return retVal;
}
}
Disposable<Array>
FdmG2Op::solve_splitting(Size direction, const Array& r, Real a) const {
if (direction == direction1_) {
return mapX_.solve_splitting(r, a, 1.0);
}
else if (direction == direction2_) {
return mapY_.solve_splitting(r, a, 1.0);
}
else {
Array retVal(r.size(), 0.0);
return retVal;
}
}
Disposable<Array>
FdmG2Op::preconditioner(const Array& r, Real dt) const {
return solve_splitting(direction1_, r, dt);
}
#if !defined(QL_NO_UBLAS_SUPPORT)
Disposable<std::vector<SparseMatrix> > FdmG2Op::toMatrixDecomp() const {
std::vector<SparseMatrix> retVal(3);
retVal[0] = mapX_.toMatrix();
retVal[1] = mapY_.toMatrix();
retVal[2] = corrMap_.toMatrix();
return retVal;
}
#endif
}
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