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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
<https://www.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/bicubicsplineinterpolation.hpp>
#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/solvers/fdm3dimsolver.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmsnapshotcondition.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <utility>
namespace QuantLib {
Fdm3DimSolver::Fdm3DimSolver(const FdmSolverDesc& solverDesc,
const FdmSchemeDesc& schemeDesc,
ext::shared_ptr<FdmLinearOpComposite> op)
: solverDesc_(solverDesc), schemeDesc_(schemeDesc), op_(std::move(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)),
initialValues_(solverDesc.mesher->layout()->size()),
resultValues_(
solverDesc.mesher->layout()->dim()[2],
Matrix(solverDesc.mesher->layout()->dim()[1], solverDesc.mesher->layout()->dim()[0])),
interpolation_(solverDesc.mesher->layout()->dim()[2]) {
x_.reserve(solverDesc.mesher->layout()->dim()[0]);
y_.reserve(solverDesc.mesher->layout()->dim()[1]);
z_.reserve(solverDesc.mesher->layout()->dim()[2]);
for (const auto& iter : *solverDesc.mesher->layout()) {
initialValues_[iter.index()]
= solverDesc.calculator->avgInnerValue(iter,
solverDesc.maturity);
if ((iter.coordinates()[1] == 0U) && (iter.coordinates()[2] == 0U)) {
x_.push_back(solverDesc.mesher->location(iter, 0));
}
if ((iter.coordinates()[0] == 0U) && (iter.coordinates()[2] == 0U)) {
y_.push_back(solverDesc.mesher->location(iter, 1));
}
if ((iter.coordinates()[0] == 0U) && (iter.coordinates()[1] == 0U)) {
z_.push_back(solverDesc.mesher->location(iter, 2));
}
}
}
void Fdm3DimSolver::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);
for (Size i=0; i < z_.size(); ++i) {
std::copy(rhs.begin()+i *y_.size()*x_.size(),
rhs.begin()+(i+1)*y_.size()*x_.size(),
resultValues_[i].begin());
interpolation_[i] = ext::make_shared<BicubicSpline>(x_.begin(), x_.end(),
y_.begin(), y_.end(),
resultValues_[i]);
}
}
Real Fdm3DimSolver::interpolateAt(Real x, Real y, Rate z) const {
calculate();
Array zArray(z_.size());
for (Size i=0; i < z_.size(); ++i) {
zArray[i] = (*interpolation_[i])(x, y);
}
return MonotonicCubicNaturalSpline(z_.begin(), z_.end(),
zArray.begin())(z);
}
Real Fdm3DimSolver::thetaAt(Real x, Real y, Rate z) const {
if (conditions_->stoppingTimes().front() == 0.0)
return Null<Real>();
calculate();
const Array& rhs = thetaCondition_->getValues();
std::vector<Matrix> thetaValues(z_.size(), Matrix(y_.size(),x_.size()));
for (Size i=0; i < z_.size(); ++i) {
std::copy(rhs.begin()+i *y_.size()*x_.size(),
rhs.begin()+(i+1)*y_.size()*x_.size(),
thetaValues[i].begin());
}
Array zArray(z_.size());
for (Size i=0; i < z_.size(); ++i) {
zArray[i] = BicubicSpline(x_.begin(),x_.end(),
y_.begin(),y_.end(), thetaValues[i])(x,y);
}
return (MonotonicCubicNaturalSpline(z_.begin(), z_.end(),
zArray.begin())(z)
- interpolateAt(x, y, z)) / thetaCondition_->getTime();
}
}
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