fdm2dimsolver.cpp

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2010 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/bicubicsplineinterpolation.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/fdm2dimsolver.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 {
 
    Fdm2DimSolver::Fdm2DimSolver(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()[1], solverDesc.mesher->layout()->dim()[0]) {
 
        x_.reserve(solverDesc.mesher->layout()->dim()[0]);
        y_.reserve(solverDesc.mesher->layout()->dim()[1]);
 
        for (const auto& iter : *solverDesc.mesher->layout()) {
            initialValues_[iter.index()]
                 = solverDesc_.calculator->avgInnerValue(iter,
                                                         solverDesc.maturity);
 
            if (iter.coordinates()[1] == 0U) {
                x_.push_back(solverDesc.mesher->location(iter, 0));
            }
            if (iter.coordinates()[0] == 0U) {
                y_.push_back(solverDesc.mesher->location(iter, 1));
            }
        }
    }
 
 
    void Fdm2DimSolver::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<BicubicSpline>(x_.begin(), x_.end(),
                              y_.begin(), y_.end(),
                              resultValues_);
    }
 
    Real Fdm2DimSolver::interpolateAt(Real x, Real y) const {
        calculate();
        return (*interpolation_)(x, y);
    }
 
    Real Fdm2DimSolver::thetaAt(Real x, Real y) const {
        if (conditions_->stoppingTimes().front() == 0.0)
            return Null<Real>();
 
        calculate();
        Matrix thetaValues(resultValues_.rows(), resultValues_.columns());
 
        const Array& rhs = thetaCondition_->getValues();
        std::copy(rhs.begin(), rhs.end(), thetaValues.begin());
 
        return (BicubicSpline(x_.begin(), x_.end(), y_.begin(), y_.end(),
                              thetaValues)(x, y) - interpolateAt(x, y))
              / thetaCondition_->getTime();
    }
 
 
    Real Fdm2DimSolver::derivativeX(Real x, Real y) const {
        calculate();
        return interpolation_->derivativeX(x, y);
    }
 
    Real Fdm2DimSolver::derivativeY(Real x, Real y) const {
        calculate();
        return interpolation_->derivativeY(x, y);
    }
 
    Real Fdm2DimSolver::derivativeXX(Real x, Real y) const {
        calculate();
        return interpolation_->secondDerivativeX(x, y);
    }
 
    Real Fdm2DimSolver::derivativeYY(Real x, Real y) const {
        calculate();
        return interpolation_->secondDerivativeY(x, y);
    }
 
    Real Fdm2DimSolver::derivativeXY(Real x, Real y) const {
        calculate();
        return interpolation_->derivativeXY(x, y);
    }
 
}