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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2015 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 numericaldifferentiation.hpp
\brief numerical differentiation of arbitrary order
and on irregular grids
*/
#ifndef quantlib_numerical_differentiation_hpp
#define quantlib_numerical_differentiation_hpp
#include <ql/math/array.hpp>
#include <functional>
namespace QuantLib {
//! Numerical Differentiation on arbitrarily spaced grids
/*! References:
B. Fornberg, 1988. Generation of Finite Difference Formulas
on Arbitrarily Spaced Grids,
http://amath.colorado.edu/faculty/fornberg/Docs/MathComp_88_FD_formulas.pdf
*/
class NumericalDifferentiation {
public:
enum Scheme { Central, Backward, Forward };
NumericalDifferentiation(std::function<Real(Real)> f,
Size orderOfDerivative,
Array x_offsets);
NumericalDifferentiation(std::function<Real(Real)> f,
Size orderOfDerivative,
Real stepSize,
Size steps,
Scheme scheme);
Real operator()(Real x) const;
const Array& offsets() const;
const Array& weights() const;
private:
const Array offsets_, w_;
const std::function<Real(Real)> f_;
};
inline Real NumericalDifferentiation::operator()(Real x) const {
Real s = 0.0;
for (Size i=0; i < w_.size(); ++i) {
if (std::fabs(w_[i]) > QL_EPSILON*QL_EPSILON) {
s += w_[i] * f_(x+offsets_[i]);
}
}
return s;
}
inline const Array& NumericalDifferentiation::weights() const {
return w_;
}
inline const Array& NumericalDifferentiation::offsets() const {
return offsets_;
}
}
#endif
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