Higher order spatial operators for Finite Difference Methods #483
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| /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ | ||
| /* | ||
| Copyright (C) 2018 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 NthOrderDerivativeOp.cpp | ||
| \brief n-th order derivative linear operator | ||
| */ | ||
| #include <ql/qldefines.hpp> | ||
| #ifndef QL_NO_UBLAS_SUPPORT | ||
| #include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp> | ||
| #include <ql/methods/finitedifferences/operators/numericaldifferentiation.hpp> | ||
| #include <ql/methods/finitedifferences/operators/nthorderderivativeop.hpp> | ||
| #include <set> | ||
| namespace QuantLib { | ||
| NthOrderDerivativeOp::NthOrderDerivativeOp( | ||
| Size direction, Size order, Integer nPoints, | ||
| const ext::shared_ptr<FdmMesher>& mesher) | ||
| : m_(mesher->layout()->size(), mesher->layout()->size()) { | ||
| const Integer hPoints = nPoints/2; | ||
| const bool isEven = (nPoints == 2*hPoints); | ||
| const ext::shared_ptr<FdmLinearOpLayout> layout = mesher->layout(); | ||
| const FdmLinearOpIterator endIter = layout->end(); | ||
| Array xValues = mesher->locations(direction); | ||
| std::set<Real> tmp(xValues.begin(), xValues.end()); | ||
| xValues = Array(tmp.begin(), tmp.end()); //unique vector | ||
| const Integer nx(layout->dim()[direction]); | ||
| QL_REQUIRE(Integer(xValues.size()) == nx, | ||
| "inconsistent set of grid values in direction " << direction); | ||
| QL_REQUIRE(nPoints > 1 && Integer(nPoints) <= nx, | ||
| "inconsistent number of points"); | ||
| Array xOffsets(nPoints); | ||
| const boost::function<Real(Real)> emptyFct; | ||
| for (FdmLinearOpIterator iter = layout->begin(); iter!=endIter; ++iter) { | ||
| const Integer ix = Integer(iter.coordinates()[direction]); | ||
| const Integer offset = std::max(0, hPoints - ix) | ||
| - std::max(0, hPoints - (nx-((isEven)? 0 : 1) - ix)); | ||
| const Integer ilx = ix - hPoints + offset; | ||
| for (Integer j=0; j < nPoints; ++j) { | ||
| const Integer idx = ilx + j; | ||
| xOffsets[j] = xValues[idx] - xValues[ix]; | ||
| } | ||
| const Array weights = | ||
| NumericalDifferentiation(emptyFct, order, xOffsets).weights(); | ||
| const Size i = iter.index(); | ||
| for (Integer j=0; j < nPoints; ++j) { | ||
| const Size k = layout->neighbourhood(iter, direction, ilx - ix + j); | ||
| m_(i, k) = weights[j]; | ||
| } | ||
| } | ||
| } | ||
| Disposable<NthOrderDerivativeOp::array_type> | ||
| NthOrderDerivativeOp::apply(const array_type& r) const { | ||
| return prod(m_, r); | ||
| } | ||
| Disposable<SparseMatrix> NthOrderDerivativeOp::toMatrix() const { | ||
| SparseMatrix tmp(m_); | ||
| return tmp; | ||
| } | ||
| } | ||
| #endif |
| @@ -0,0 +1,50 @@ | ||
| /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ | ||
| /* | ||
| Copyright (C) 2018 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 nthorderderivativeop.hpp | ||
| \brief n-th order derivative linear operator | ||
| */ | ||
| #ifndef quantlib_nth_order_derivative_op_hpp | ||
| #define quantlib_nth_order_derivative_op_hpp | ||
| #include <ql/qldefines.hpp> | ||
| #ifndef QL_NO_UBLAS_SUPPORT | ||
| #include <ql/methods/finitedifferences/meshers/fdmmesher.hpp> | ||
| #include <ql/methods/finitedifferences/operators/fdmlinearop.hpp> | ||
| namespace QuantLib { | ||
| class NthOrderDerivativeOp : public FdmLinearOp { | ||
| public: | ||
| NthOrderDerivativeOp( | ||
| Size direction, Size order, Integer nPoints, | ||
| const ext::shared_ptr<FdmMesher>& mesher); | ||
| Disposable<array_type> apply(const array_type& r) const; | ||
| Disposable<SparseMatrix> toMatrix() const; | ||
| private: | ||
| SparseMatrix m_; | ||
| }; | ||
| } | ||
| #endif | ||
| #endif |
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