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

   1 // Copyright Nick Thompson, 2017
   2 // Use, modification and distribution are subject to the
   3 // Boost Software License, Version 1.0.
   4 // (See accompanying file LICENSE_1_0.txt
   5 // or copy at http://www.boost.org/LICENSE_1_0.txt)
   6
   7 // This implements the compactly supported cubic b spline algorithm described in
   8 // Kress, Rainer. "Numerical analysis, volume 181 of Graduate Texts in Mathematics." (1998).
   9 // Splines of compact support are faster to evaluate and are better conditioned than classical cubic splines.
  10
  11 // Let f be the function we are trying to interpolate, and s be the interpolating spline.
  12 // The routine constructs the interpolant in O(N) time, and evaluating s at a point takes constant time.
  13 // The order of accuracy depends on the regularity of the f, however, assuming f is
  14 // four-times continuously differentiable, the error is of O(h^4).
  15 // In addition, we can differentiate the spline and obtain a good interpolant for f'.
  16 // The main restriction of this method is that the samples of f must be evenly spaced.
  17 // Look for barycentric rational interpolation for non-evenly sampled data.
  18 // Properties:
  19 // - s(x_j) = f(x_j)
  20 // - All cubic polynomials interpolated exactly
  21
  22 #ifndef BOOST_MATH_INTERPOLATORS_CARDINAL_CUBIC_B_SPLINE_HPP
  23 #define BOOST_MATH_INTERPOLATORS_CARINDAL_CUBIC_B_SPLINE_HPP
  24
  25 #include <boost/math/interpolators/detail/cardinal_cubic_b_spline_detail.hpp>
  26
  27 namespace boost{ namespace math{ namespace interpolators {
  28
  29 template <class Real>
  30 class cardinal_cubic_b_spline
  31 {
  32 public:
  33     // If you don't know the value of the derivative at the endpoints, leave them as nans and the routine will estimate them.
  34     // f[0] = f(a), f[length -1] = b, step_size = (b - a)/(length -1).
  35     template <class BidiIterator>
  36     cardinal_cubic_b_spline(const BidiIterator f, BidiIterator end_p, Real left_endpoint, Real step_size,
  37                    Real left_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN(),
  38                    Real right_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN());
  39     cardinal_cubic_b_spline(const Real* const f, size_t length, Real left_endpoint, Real step_size,
  40        Real left_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN(),
  41        Real right_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN());
  42
  43     cardinal_cubic_b_spline() = default;
  44     Real operator()(Real x) const;
  45
  46     Real prime(Real x) const;
  47
  48     Real double_prime(Real x) const;
  49
  50 private:
  51     std::shared_ptr<detail::cardinal_cubic_b_spline_imp<Real>> m_imp;
  52 };
  53
  54 template<class Real>
  55 cardinal_cubic_b_spline<Real>::cardinal_cubic_b_spline(const Real* const f, size_t length, Real left_endpoint, Real step_size,
  56                                      Real left_endpoint_derivative, Real right_endpoint_derivative) : m_imp(std::make_shared<detail::cardinal_cubic_b_spline_imp<Real>>(f, f + length, left_endpoint, step_size, left_endpoint_derivative, right_endpoint_derivative))
  57 {
  58 }
  59
  60 template <class Real>
  61 template <class BidiIterator>
  62 cardinal_cubic_b_spline<Real>::cardinal_cubic_b_spline(BidiIterator f, BidiIterator end_p, Real left_endpoint, Real step_size,
  63    Real left_endpoint_derivative, Real right_endpoint_derivative) : m_imp(std::make_shared<detail::cardinal_cubic_b_spline_imp<Real>>(f, end_p, left_endpoint, step_size, left_endpoint_derivative, right_endpoint_derivative))
  64 {
  65 }
  66
  67 template<class Real>
  68 Real cardinal_cubic_b_spline<Real>::operator()(Real x) const
  69 {
  70     return m_imp->operator()(x);
  71 }
  72
  73 template<class Real>
  74 Real cardinal_cubic_b_spline<Real>::prime(Real x) const
  75 {
  76     return m_imp->prime(x);
  77 }
  78
  79 template<class Real>
  80 Real cardinal_cubic_b_spline<Real>::double_prime(Real x) const
  81 {
  82     return m_imp->double_prime(x);
  83 }
  84
  85
  86 }}}
  87 #endif