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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.
*/
#include <ql/math/interpolations/cubicinterpolation.hpp>
#include <ql/methods/finitedifferences/finitedifferencemodel.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/methods/finitedifferences/solvers/fdm1dimsolver.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmsnapshotcondition.hpp>
namespace QuantLib {
Fdm1DimSolver::Fdm1DimSolver(
const FdmSolverDesc& solverDesc,
const FdmSchemeDesc& schemeDesc,
const ext::shared_ptr<FdmLinearOpComposite>& op)
: solverDesc_(solverDesc),
schemeDesc_(schemeDesc),
op_(op),
thetaCondition_(ext::make_shared<FdmSnapshotCondition>(
0.99*std::min(1.0/365.0,
solverDesc.condition->stoppingTimes().empty()
? solverDesc.maturity
: solverDesc.condition->stoppingTimes().front()))),
conditions_(FdmStepConditionComposite::joinConditions(thetaCondition_,
solverDesc.condition)),
x_ (solverDesc.mesher->layout()->size()),
initialValues_(solverDesc.mesher->layout()->size()),
resultValues_ (solverDesc.mesher->layout()->size()) {
const ext::shared_ptr<FdmMesher> mesher = solverDesc.mesher;
const ext::shared_ptr<FdmLinearOpLayout> layout = mesher->layout();
const FdmLinearOpIterator endIter = layout->end();
for (FdmLinearOpIterator iter = layout->begin(); iter != endIter;
++iter) {
initialValues_[iter.index()]
= solverDesc_.calculator->avgInnerValue(iter,
solverDesc.maturity);
x_[iter.index()] = mesher->location(iter, 0);
}
}
void Fdm1DimSolver::performCalculations() const {
Array rhs(initialValues_.size());
std::copy(initialValues_.begin(), initialValues_.end(), rhs.begin());
FdmBackwardSolver(op_, solverDesc_.bcSet, conditions_, schemeDesc_)
.rollback(rhs, solverDesc_.maturity, 0.0,
solverDesc_.timeSteps, solverDesc_.dampingSteps);
std::copy(rhs.begin(), rhs.end(), resultValues_.begin());
interpolation_ = ext::make_shared<MonotonicCubicNaturalSpline>(x_.begin(), x_.end(),
resultValues_.begin());
}
Real Fdm1DimSolver::interpolateAt(Real x) const {
calculate();
return (*interpolation_)(x);
}
Real Fdm1DimSolver::thetaAt(Real x) const {
if (conditions_->stoppingTimes().front() == 0.0)
return Null<Real>();
calculate();
Array thetaValues(resultValues_.size());
const Array& rhs = thetaCondition_->getValues();
std::copy(rhs.begin(), rhs.end(), thetaValues.begin());
Real temp = MonotonicCubicNaturalSpline(
x_.begin(), x_.end(), thetaValues.begin())(x);
return ( temp - interpolateAt(x) ) / thetaCondition_->getTime();
}
Real Fdm1DimSolver::derivativeX(Real x) const {
calculate();
return interpolation_->derivative(x);
}
Real Fdm1DimSolver::derivativeXX(Real x) const {
calculate();
return interpolation_->secondDerivative(x);
}
}
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