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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
<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.
*/
/*! \file NthOrderDerivativeOp.cpp
\brief n-th order derivative linear operator
*/
#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);
Array xValues = mesher->locations(direction);
std::set<Real> tmp(xValues.begin(), xValues.end());
xValues = Array(tmp.begin(), tmp.end()); //unique vector
const Integer nx(mesher->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 std::function<Real(Real)> emptyFct;
for (const auto& iter : *mesher->layout()) {
const auto 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 = mesher->layout()->neighbourhood(iter, direction, ilx - ix + j);
m_(i, k) = weights[j];
}
}
}
NthOrderDerivativeOp::array_type NthOrderDerivativeOp::apply(const array_type& r) const {
return prod(m_, r);
}
SparseMatrix NthOrderDerivativeOp::toMatrix() const {
return m_;
}
}
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