129 lines
3.3 KiB
C++
129 lines
3.3 KiB
C++
// Copyright Nick Thompson, 2019
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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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#ifndef BOOST_MATH_INTERPOLATORS_WHITAKKER_SHANNON_DETAIL_HPP
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#define BOOST_MATH_INTERPOLATORS_WHITAKKER_SHANNON_DETAIL_HPP
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#include <cmath>
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#include <boost/math/tools/assert.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/math/special_functions/sin_pi.hpp>
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#include <boost/math/special_functions/cos_pi.hpp>
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namespace boost { namespace math { namespace interpolators { namespace detail {
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template<class RandomAccessContainer>
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class whittaker_shannon_detail {
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public:
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using Real = typename RandomAccessContainer::value_type;
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whittaker_shannon_detail(RandomAccessContainer&& y, Real const & t0, Real const & h) : m_y{std::move(y)}, m_t0{t0}, m_h{h}
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{
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for (size_t i = 1; i < m_y.size(); i += 2)
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{
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m_y[i] = -m_y[i];
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}
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}
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inline Real operator()(Real t) const {
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using boost::math::constants::pi;
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using std::isfinite;
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using std::floor;
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using std::ceil;
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Real y = 0;
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Real x = (t - m_t0)/m_h;
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Real z = x;
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auto it = m_y.begin();
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// For some reason, neither clang nor g++ will cache the address of m_y.end() in a register.
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// Hence make a copy of it:
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auto end = m_y.end();
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while(it != end)
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{
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y += *it++/z;
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z -= 1;
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}
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if (!isfinite(y))
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{
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BOOST_MATH_ASSERT_MSG(floor(x) == ceil(x), "Floor and ceiling should be equal.\n");
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auto i = static_cast<size_t>(floor(x));
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if (i & 1)
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{
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return -m_y[i];
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}
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return m_y[i];
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}
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return y*boost::math::sin_pi(x)/pi<Real>();
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}
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Real prime(Real t) const {
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using boost::math::constants::pi;
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using std::isfinite;
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using std::floor;
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using std::ceil;
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Real x = (t - m_t0)/m_h;
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if (ceil(x) == x) {
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Real s = 0;
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auto j = static_cast<long>(x);
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auto n = static_cast<long>(m_y.size());
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for (long i = 0; i < n; ++i)
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{
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if (j - i != 0)
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{
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s += m_y[i]/(j-i);
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}
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// else derivative of sinc at zero is zero.
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}
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if (j & 1) {
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s /= -m_h;
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} else {
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s /= m_h;
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}
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return s;
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}
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Real z = x;
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auto it = m_y.begin();
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Real cospix = boost::math::cos_pi(x);
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Real sinpix_div_pi = boost::math::sin_pi(x)/pi<Real>();
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Real s = 0;
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auto end = m_y.end();
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while(it != end)
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{
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s += (*it++)*(z*cospix - sinpix_div_pi)/(z*z);
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z -= 1;
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}
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return s/m_h;
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}
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Real operator[](size_t i) const {
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if (i & 1)
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{
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return -m_y[i];
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}
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return m_y[i];
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}
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RandomAccessContainer&& return_data() {
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for (size_t i = 1; i < m_y.size(); i += 2)
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{
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m_y[i] = -m_y[i];
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}
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return std::move(m_y);
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}
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private:
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RandomAccessContainer m_y;
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Real m_t0;
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Real m_h;
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};
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}}}}
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#endif
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