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1/*2 * Copyright Nick Thompson, 20173 * Use, modification and distribution are subject to the4 * Boost Software License, Version 1.0. (See accompanying file5 * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)6 *7 * Given N samples (t_i, y_i) which are irregularly spaced, this routine constructs an8 * interpolant s which is constructed in O(N) time, occupies O(N) space, and can be evaluated in O(N) time.9 * The interpolation is stable, unless one point is incredibly close to another, and the next point is incredibly far.10 * The measure of this stability is the "local mesh ratio", which can be queried from the routine.11 * Pictorially, the following t_i spacing is bad (has a high local mesh ratio)12 * || | | | |13 * and this t_i spacing is good (has a low local mesh ratio)14 * | | | | | | | | | |15 *16 *17 * If f is C^{d+2}, then the interpolant is O(h^(d+1)) accurate, where d is the interpolation order.18 * A disadvantage of this interpolant is that it does not reproduce rational functions; for example, 1/(1+x^2) is not interpolated exactly.19 *20 * References:21 * Floater, Michael S., and Kai Hormann. "Barycentric rational interpolation with no poles and high rates of approximation."22* Numerische Mathematik 107.2 (2007): 315-331.23 * Press, William H., et al. "Numerical recipes third edition: the art of scientific computing." Cambridge University Press 32 (2007): 10013-2473.24 */25 26#ifndef BOOST_MATH_INTERPOLATORS_BARYCENTRIC_RATIONAL_HPP27#define BOOST_MATH_INTERPOLATORS_BARYCENTRIC_RATIONAL_HPP28 29#include <memory>30#include <boost/math/interpolators/detail/barycentric_rational_detail.hpp>31 32namespace boost{ namespace math{ namespace interpolators{33 34template<class Real>35class barycentric_rational36{37public:38 barycentric_rational(const Real* const x, const Real* const y, size_t n, size_t approximation_order = 3);39 40 barycentric_rational(std::vector<Real>&& x, std::vector<Real>&& y, size_t approximation_order = 3);41 42 template <class InputIterator1, class InputIterator2>43 barycentric_rational(InputIterator1 start_x, InputIterator1 end_x, InputIterator2 start_y, size_t approximation_order = 3, typename std::enable_if<!std::is_integral<InputIterator2>::value>::type* = nullptr);44 45 Real operator()(Real x) const;46 47 Real prime(Real x) const;48 49 std::vector<Real>&& return_x()50 {51 return m_imp->return_x();52 }53 54 std::vector<Real>&& return_y()55 {56 return m_imp->return_y();57 }58 59private:60 std::shared_ptr<detail::barycentric_rational_imp<Real>> m_imp;61};62 63template <class Real>64barycentric_rational<Real>::barycentric_rational(const Real* const x, const Real* const y, size_t n, size_t approximation_order):65 m_imp(std::make_shared<detail::barycentric_rational_imp<Real>>(x, x + n, y, approximation_order))66{67 return;68}69 70template <class Real>71barycentric_rational<Real>::barycentric_rational(std::vector<Real>&& x, std::vector<Real>&& y, size_t approximation_order):72 m_imp(std::make_shared<detail::barycentric_rational_imp<Real>>(std::move(x), std::move(y), approximation_order))73{74 return;75}76 77 78template <class Real>79template <class InputIterator1, class InputIterator2>80barycentric_rational<Real>::barycentric_rational(InputIterator1 start_x, InputIterator1 end_x, InputIterator2 start_y, size_t approximation_order, typename std::enable_if<!std::is_integral<InputIterator2>::value>::type*)81 : m_imp(std::make_shared<detail::barycentric_rational_imp<Real>>(start_x, end_x, start_y, approximation_order))82{83}84 85template<class Real>86Real barycentric_rational<Real>::operator()(Real x) const87{88 return m_imp->operator()(x);89}90 91template<class Real>92Real barycentric_rational<Real>::prime(Real x) const93{94 return m_imp->prime(x);95}96 97 98}}}99#endif100