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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2009 Andreas Gaida
Copyright (C) 2009 Ralph Schreyer
Copyright (C) 2009 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 fdmbackwardsolver.cpp
*/
#include <ql/mathconstants.hpp>
#include <ql/methods/finitedifferences/finitedifferencemodel.hpp>
#include <ql/methods/finitedifferences/solvers/fdmbackwardsolver.hpp>
#include <ql/methods/finitedifferences/schemes/douglasscheme.hpp>
#include <ql/methods/finitedifferences/schemes/craigsneydscheme.hpp>
#include <ql/methods/finitedifferences/schemes/cranknicolsonscheme.hpp>
#include <ql/methods/finitedifferences/schemes/hundsdorferscheme.hpp>
#include <ql/methods/finitedifferences/schemes/impliciteulerscheme.hpp>
#include <ql/methods/finitedifferences/schemes/expliciteulerscheme.hpp>
#include <ql/methods/finitedifferences/schemes/modifiedcraigsneydscheme.hpp>
#include <ql/methods/finitedifferences/schemes/methodoflinesscheme.hpp>
#include <ql/methods/finitedifferences/schemes/trbdf2scheme.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
namespace QuantLib {
FdmSchemeDesc::FdmSchemeDesc(FdmSchemeType aType, Real aTheta, Real aMu)
: type(aType), theta(aTheta), mu(aMu) { }
FdmSchemeDesc FdmSchemeDesc::Douglas() {
return FdmSchemeDesc(FdmSchemeDesc::DouglasType, 0.5, 0.0);
}
FdmSchemeDesc FdmSchemeDesc::CrankNicolson() {
return FdmSchemeDesc(FdmSchemeDesc::CrankNicolsonType, 0.5, 0.0);
}
FdmSchemeDesc FdmSchemeDesc::CraigSneyd() {
return FdmSchemeDesc(FdmSchemeDesc::CraigSneydType,0.5, 0.5);
}
FdmSchemeDesc FdmSchemeDesc::ModifiedCraigSneyd() {
return FdmSchemeDesc(FdmSchemeDesc::ModifiedCraigSneydType,
1.0/3.0, 1.0/3.0);
}
FdmSchemeDesc FdmSchemeDesc::Hundsdorfer() {
return FdmSchemeDesc(FdmSchemeDesc::HundsdorferType,
0.5+std::sqrt(3.0)/6, 0.5);
}
FdmSchemeDesc FdmSchemeDesc::ModifiedHundsdorfer() {
return FdmSchemeDesc(FdmSchemeDesc::HundsdorferType,
1.0-std::sqrt(2.0)/2, 0.5);
}
FdmSchemeDesc FdmSchemeDesc::ExplicitEuler() {
return FdmSchemeDesc(FdmSchemeDesc::ExplicitEulerType, 0.0, 0.0);
}
FdmSchemeDesc FdmSchemeDesc::ImplicitEuler() {
return FdmSchemeDesc(FdmSchemeDesc::ImplicitEulerType, 0.0, 0.0);
}
FdmSchemeDesc FdmSchemeDesc::MethodOfLines(Real eps, Real relInitStepSize) {
return FdmSchemeDesc(
FdmSchemeDesc::MethodOfLinesType, eps, relInitStepSize);
}
FdmSchemeDesc FdmSchemeDesc::TrBDF2() {
return FdmSchemeDesc(FdmSchemeDesc::TrBDF2Type, 2 - M_SQRT2, 1e-8);
}
FdmBackwardSolver::FdmBackwardSolver(
const ext::shared_ptr<FdmLinearOpComposite>& map,
const FdmBoundaryConditionSet& bcSet,
const ext::shared_ptr<FdmStepConditionComposite>& condition,
const FdmSchemeDesc& schemeDesc)
: map_(map), bcSet_(bcSet),
condition_((condition) != 0 ?
condition :
ext::make_shared<FdmStepConditionComposite>(
std::list<std::vector<Time> >(), FdmStepConditionComposite::Conditions())),
schemeDesc_(schemeDesc) {}
void FdmBackwardSolver::rollback(FdmBackwardSolver::array_type& rhs,
Time from, Time to,
Size steps, Size dampingSteps) {
const Time deltaT = from - to;
const Size allSteps = steps + dampingSteps;
const Time dampingTo = from - (deltaT*dampingSteps)/allSteps;
if ((dampingSteps != 0U) && schemeDesc_.type != FdmSchemeDesc::ImplicitEulerType) {
ImplicitEulerScheme implicitEvolver(map_, bcSet_);
FiniteDifferenceModel<ImplicitEulerScheme>
dampingModel(implicitEvolver, condition_->stoppingTimes());
dampingModel.rollback(rhs, from, dampingTo,
dampingSteps, *condition_);
}
switch (schemeDesc_.type) {
case FdmSchemeDesc::HundsdorferType:
{
HundsdorferScheme hsEvolver(schemeDesc_.theta, schemeDesc_.mu,
map_, bcSet_);
FiniteDifferenceModel<HundsdorferScheme>
hsModel(hsEvolver, condition_->stoppingTimes());
hsModel.rollback(rhs, dampingTo, to, steps, *condition_);
}
break;
case FdmSchemeDesc::DouglasType:
{
DouglasScheme dsEvolver(schemeDesc_.theta, map_, bcSet_);
FiniteDifferenceModel<DouglasScheme>
dsModel(dsEvolver, condition_->stoppingTimes());
dsModel.rollback(rhs, dampingTo, to, steps, *condition_);
}
break;
case FdmSchemeDesc::CrankNicolsonType:
{
CrankNicolsonScheme cnEvolver(schemeDesc_.theta, map_, bcSet_);
FiniteDifferenceModel<CrankNicolsonScheme>
cnModel(cnEvolver, condition_->stoppingTimes());
cnModel.rollback(rhs, dampingTo, to, steps, *condition_);
}
break;
case FdmSchemeDesc::CraigSneydType:
{
CraigSneydScheme csEvolver(schemeDesc_.theta, schemeDesc_.mu,
map_, bcSet_);
FiniteDifferenceModel<CraigSneydScheme>
csModel(csEvolver, condition_->stoppingTimes());
csModel.rollback(rhs, dampingTo, to, steps, *condition_);
}
break;
case FdmSchemeDesc::ModifiedCraigSneydType:
{
ModifiedCraigSneydScheme csEvolver(schemeDesc_.theta,
schemeDesc_.mu,
map_, bcSet_);
FiniteDifferenceModel<ModifiedCraigSneydScheme>
mcsModel(csEvolver, condition_->stoppingTimes());
mcsModel.rollback(rhs, dampingTo, to, steps, *condition_);
}
break;
case FdmSchemeDesc::ImplicitEulerType:
{
ImplicitEulerScheme implicitEvolver(map_, bcSet_);
FiniteDifferenceModel<ImplicitEulerScheme>
implicitModel(implicitEvolver, condition_->stoppingTimes());
implicitModel.rollback(rhs, from, to, allSteps, *condition_);
}
break;
case FdmSchemeDesc::ExplicitEulerType:
{
ExplicitEulerScheme explicitEvolver(map_, bcSet_);
FiniteDifferenceModel<ExplicitEulerScheme>
explicitModel(explicitEvolver, condition_->stoppingTimes());
explicitModel.rollback(rhs, dampingTo, to, steps, *condition_);
}
break;
case FdmSchemeDesc::MethodOfLinesType:
{
MethodOfLinesScheme methodOfLines(
schemeDesc_.theta, schemeDesc_.mu, map_, bcSet_);
FiniteDifferenceModel<MethodOfLinesScheme>
molModel(methodOfLines, condition_->stoppingTimes());
molModel.rollback(rhs, dampingTo, to, steps, *condition_);
}
break;
case FdmSchemeDesc::TrBDF2Type:
{
const FdmSchemeDesc trDesc
= FdmSchemeDesc::CraigSneyd();
const ext::shared_ptr<CraigSneydScheme> hsEvolver(
ext::make_shared<CraigSneydScheme>(
trDesc.theta, trDesc.mu, map_, bcSet_));
TrBDF2Scheme<CraigSneydScheme> trBDF2(
schemeDesc_.theta, map_, hsEvolver, bcSet_,schemeDesc_.mu);
FiniteDifferenceModel<TrBDF2Scheme<CraigSneydScheme> >
trBDF2Model(trBDF2, condition_->stoppingTimes());
trBDF2Model.rollback(rhs, dampingTo, to, steps, *condition_);
}
break;
default:
QL_FAIL("Unknown scheme type");
}
}
}
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