ceph/src/boost/boost/math/interpolators/barycentric_rational.hpp

   1 /*
   2  *  Copyright Nick Thompson, 2017
   3  *  Use, modification and distribution are subject to the
   4  *  Boost Software License, Version 1.0. (See accompanying file
   5  *  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 an
   8  *  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." Numerische Mathematik 107.2 (2007): 315-331.
  22  *  Press, William H., et al. "Numerical recipes third edition: the art of scientific computing." Cambridge University Press 32 (2007): 10013-2473.
  23  */
  24
  25 #ifndef BOOST_MATH_INTERPOLATORS_BARYCENTRIC_RATIONAL_HPP
  26 #define BOOST_MATH_INTERPOLATORS_BARYCENTRIC_RATIONAL_HPP
  27
  28 #include <memory>
  29 #include <boost/math/interpolators/detail/barycentric_rational_detail.hpp>
  30
  31 namespace boost{ namespace math{
  32
  33 template<class Real>
  34 class barycentric_rational
  35 {
  36 public:
  37     barycentric_rational(const Real* const x, const Real* const y, size_t n, size_t approximation_order = 3);
  38
  39     template <class InputIterator1, class InputIterator2>
  40     barycentric_rational(InputIterator1 start_x, InputIterator1 end_x, InputIterator2 start_y, size_t approximation_order = 3, typename boost::disable_if_c<boost::is_integral<InputIterator2>::value>::type* = 0);
  41
  42     Real operator()(Real x) const;
  43
  44 private:
  45     std::shared_ptr<detail::barycentric_rational_imp<Real>> m_imp;
  46 };
  47
  48 template <class Real>
  49 barycentric_rational<Real>::barycentric_rational(const Real* const x, const Real* const y, size_t n, size_t approximation_order):
  50  m_imp(std::make_shared<detail::barycentric_rational_imp<Real>>(x, x + n, y, approximation_order))
  51 {
  52     return;
  53 }
  54
  55 template <class Real>
  56 template <class InputIterator1, class InputIterator2>
  57 barycentric_rational<Real>::barycentric_rational(InputIterator1 start_x, InputIterator1 end_x, InputIterator2 start_y, size_t approximation_order, typename boost::disable_if_c<boost::is_integral<InputIterator2>::value>::type*)
  58  : m_imp(std::make_shared<detail::barycentric_rational_imp<Real>>(start_x, end_x, start_y, approximation_order))
  59 {
  60 }
  61
  62 template<class Real>
  63 Real barycentric_rational<Real>::operator()(Real x) const
  64 {
  65     return m_imp->operator()(x);
  66 }
  67
  68
  69 }}
  70 #endif