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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2005 Joseph Wang
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 pde.hpp
\brief General class for one dimensional PDE's
*/
#ifndef quantlib_pde_hpp
#define quantlib_pde_hpp
#include <ql/math/array.hpp>
#include <ql/methods/finitedifferences/tridiagonaloperator.hpp>
#include <ql/math/transformedgrid.hpp>
namespace QuantLib {
class PdeSecondOrderParabolic {
public:
virtual ~PdeSecondOrderParabolic() = default;
virtual Real diffusion(Time t, Real x) const = 0;
virtual Real drift(Time t, Real x) const = 0;
virtual Real discount(Time t, Real x) const = 0;
virtual void
generateOperator(Time t, const TransformedGrid& tg, TridiagonalOperator& L) const {
for (Size i = 1; i < tg.size() - 1; i++) {
Real sigma = diffusion(t, tg.grid(i));
Real nu = drift(t, tg.grid(i));
Real r = discount(t, tg.grid(i));
Real sigma2 = sigma * sigma;
Real pd = -(sigma2 / tg.dxm(i) - nu) / tg.dx(i);
Real pu = -(sigma2 / tg.dxp(i) + nu) / tg.dx(i);
Real pm = sigma2 / (tg.dxm(i) * tg.dxp(i)) + r;
L.setMidRow(i, pd, pm, pu);
}
}
};
template <class PdeClass>
class PdeConstantCoeff : public PdeSecondOrderParabolic {
public:
PdeConstantCoeff(const typename PdeClass::argument_type &process,
Time t, Real x) {
PdeClass pde(process);
diffusion_ = pde.diffusion(t, x);
drift_ = pde.drift(t, x);
discount_ = pde.discount(t, x);
}
Real diffusion(Time, Real) const override { return diffusion_; }
Real drift(Time, Real) const override { return drift_; }
Real discount(Time, Real) const override { return discount_; }
private:
Real diffusion_;
Real drift_;
Real discount_;
};
template <class PdeClass>
class GenericTimeSetter:public TridiagonalOperator::TimeSetter {
public:
template <class T>
GenericTimeSetter(const Array &grid, T process) :
grid_(grid), pde_(process) {}
void setTime(Time t, TridiagonalOperator& L) const override {
pde_.generateOperator(t, grid_, L);
}
private:
typename PdeClass::grid_type grid_;
PdeClass pde_;
};
template <class PdeClass>
class PdeOperator:public TridiagonalOperator {
public:
template <class T>
PdeOperator(const Array& grid,
T process,
Time residualTime = 0.0) :
TridiagonalOperator(grid.size()) {
timeSetter_ =
ext::shared_ptr<GenericTimeSetter<PdeClass> >(
new GenericTimeSetter<PdeClass>(grid, process));
setTime(residualTime);
}
};
}
#endif
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