91 lines
3.6 KiB
C++
91 lines
3.6 KiB
C++
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// Copyright Nick Thompson, 2017
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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// This implements the compactly supported cubic b spline algorithm described in
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// Kress, Rainer. "Numerical analysis, volume 181 of Graduate Texts in Mathematics." (1998).
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// Splines of compact support are faster to evaluate and are better conditioned than classical cubic splines.
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// Let f be the function we are trying to interpolate, and s be the interpolating spline.
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// The routine constructs the interpolant in O(N) time, and evaluating s at a point takes constant time.
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// The order of accuracy depends on the regularity of the f, however, assuming f is
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// four-times continuously differentiable, the error is of O(h^4).
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// In addition, we can differentiate the spline and obtain a good interpolant for f'.
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// The main restriction of this method is that the samples of f must be evenly spaced.
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// Look for barycentric rational interpolation for non-evenly sampled data.
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// Properties:
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// - s(x_j) = f(x_j)
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// - All cubic polynomials interpolated exactly
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#ifndef BOOST_MATH_INTERPOLATORS_CUBIC_B_SPLINE_HPP
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#define BOOST_MATH_INTERPOLATORS_CUBIC_B_SPLINE_HPP
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#include <boost/math/interpolators/detail/cubic_b_spline_detail.hpp>
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#include <boost/math/tools/header_deprecated.hpp>
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BOOST_MATH_HEADER_DEPRECATED("<boost/math/interpolators/cardinal_cubic_b_spline.hpp>");
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namespace boost{ namespace math{
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template <class Real>
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class cubic_b_spline
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{
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public:
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// If you don't know the value of the derivative at the endpoints, leave them as nans and the routine will estimate them.
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// f[0] = f(a), f[length -1] = b, step_size = (b - a)/(length -1).
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template <class BidiIterator>
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cubic_b_spline(const BidiIterator f, BidiIterator end_p, Real left_endpoint, Real step_size,
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Real left_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN(),
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Real right_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN());
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cubic_b_spline(const Real* const f, size_t length, Real left_endpoint, Real step_size,
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Real left_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN(),
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Real right_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN());
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cubic_b_spline() = default;
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Real operator()(Real x) const;
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Real prime(Real x) const;
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Real double_prime(Real x) const;
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private:
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std::shared_ptr<detail::cubic_b_spline_imp<Real>> m_imp;
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};
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template<class Real>
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cubic_b_spline<Real>::cubic_b_spline(const Real* const f, size_t length, Real left_endpoint, Real step_size,
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Real left_endpoint_derivative, Real right_endpoint_derivative) : m_imp(std::make_shared<detail::cubic_b_spline_imp<Real>>(f, f + length, left_endpoint, step_size, left_endpoint_derivative, right_endpoint_derivative))
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{
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}
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template <class Real>
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template <class BidiIterator>
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cubic_b_spline<Real>::cubic_b_spline(BidiIterator f, BidiIterator end_p, Real left_endpoint, Real step_size,
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Real left_endpoint_derivative, Real right_endpoint_derivative) : m_imp(std::make_shared<detail::cubic_b_spline_imp<Real>>(f, end_p, left_endpoint, step_size, left_endpoint_derivative, right_endpoint_derivative))
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{
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}
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template<class Real>
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Real cubic_b_spline<Real>::operator()(Real x) const
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{
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return m_imp->operator()(x);
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}
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template<class Real>
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Real cubic_b_spline<Real>::prime(Real x) const
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{
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return m_imp->prime(x);
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}
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template<class Real>
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Real cubic_b_spline<Real>::double_prime(Real x) const
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{
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return m_imp->double_prime(x);
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}
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}}
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#endif
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